Title of Invention	THERMAL RESPONSE CORRECTION SYSTEM.
Abstract	A model of a thermal print head is provided the models the thermal response of thermal print head elements to the provision of energy to the print head elements over lime. The amount of energy to provide lo each of the print head elements during a print head cycle to produce a spot having the desired density is calculated based on: (1) the desired density to be produced by the print head element during the print head cycle, (2) the predicted temperature of the print head element at the beginning of the print head cycle, (3) the ambient printer temperature at the beginning of the print head cycle, and (4) the ambient relative humidity.

Title of Invention

THERMAL RESPONSE CORRECTION SYSTEM.

Abstract

A model of a thermal print head is provided the models the thermal response of thermal print head elements to the provision of energy to the print head elements over lime. The amount of energy to provide lo each of the print head elements during a print head cycle to produce a spot having the desired density is calculated based on: (1) the desired density to be produced by the print head element during the print head cycle, (2) the predicted temperature of the print head element at the beginning of the print head cycle, (3) the ambient printer temperature at the beginning of the print head cycle, and (4) the ambient relative humidity.

Full Text	WO 2005/105457 PCT/US2005/013324 Thermal Response Correction System BACKGROUND Field of the Invention [0001] The present invention relates to thermal printing and, more particularly, to techniques for improving thermal printer output by compensating for the effects of thermal history on thermal print heads. Related Art [0002] Thermal printers typically contain a linear array of heating elements (also referred to herein as "print head elements") that print on an output medium by, for example, transferring pigment or dye from a donor sheet to the output medium or by activating a color-forming chemistry in the output medium. The output medium is typically a porous receiver receptive to the transferred pigment, or a paper coated with the color-forming chemistry. Each of the print head elements, when-activated, forms color on the medium, passing underneath the print head element, creating a spot having a particular density. Regions with larger or denser spots are perceived as darker than regions with smaller or less dense spots. Digital images are rendered as two-dimensional arrays of very small and closely-spaced spots- WO 2005/105457 PCT/US2005/013324 E0003] A thermal print head element is activated by providing it with energy. Providing energy to the print head element increases the temperature of the print head element, causing either the transfer of pigment to the output medium or the formation of color in the receiver. The density of the output produced by the print head element in this manner is a function of the amount of energy provided to the print head element. The amount of energy provided to the print head element may be varied by, for example, varying the amount of power to the print head element within a particular time interval or by providing power to the print head element for a longer time interval. [0004] In conventional thermal printers, the time during which a digital image is printed is divided into fixed time intervals referred to herein as "print i head cycles." Typically, a single row of pixels (or portions thereof) in the digital image is printed during a single print head cycle. Each print head element is typically responsible for printing pixels {or sub-pixels) in a particular column of the digital image. During each print head cycle, an amount of energy is delivered to each print head element that is calculated to raise the temperature of the print head element to a level that will cause the print head element to produce output having the desired density. Varying amounts of energy may be provided to different print head elements i based on the varying desired densities to be produced by the print head elements. 2 - WO 2005/105457 PCT/US2005/013324 [0005] One problem with conventional thermal printers results from the fact that their print head elements retain heat after the conclusion of each print head cycle. This retention of heat can be problematic because, in some thermal printers, the amount of energy that is delivered to a particular print head element during a particular print head cycle is typically i calculated based on an assumption that the print head element's temperature at the beginning of the print head cycle is a known fixed temperature. Since, in reality, the temperature of the print head element at the beginning of a print head cycle depends on (among other things) the amount of energy delivered to the print head element during previous print head cycles, the actual temperature achieved by the print head element during a print head cycle may differ from the calibrated temperature, thereby resulting in a higher or lower output density than is desired. Further complications are similarly caused by the fact that the current temperature of a particular print head element is influenced not only by its own previous temperatures -referred to herein as its "thermal history" - but by the ambient, (room) temperature and the thermal histories of other print head elements in the print head. [0006] As may be inferred from the discussion above, in some conventional thermal printers, the average temperature of each particular thermal print head element tends to, gradually rise during the printing of a digital image due to retention of heat by the print head element and the over-provision of energy to the - 3 - WO 2005/105457 PCT/US2005/013324 print head element in light of such heat retention. This gradual temperature increase results in a corresponding gradual increase in density of the output produced by the print head element, which is perceived as increased darkness in the printed image. This phenomenon is referred to herein as "density drift." [0007] Furthermore, conventional thermal printers typically have difficulty accurately reproducing sharp density gradients between adjacent pixels both across the print head and in the direction of printing. For example, if a print head element is to print a white pixel following a black pixel, 'the ideally sharp edge between the two pixels will typically be blurred when printed. This problem results from the amount of time that is required to raise the temperature of the print head element to print the black pixel after printing the white pixel. More generally, this characteristic of conventional thermal printers results i in less than ideal sharpness when printing images having regions of high density gradient. [0008] The above-referenced U.S. Patent Application Serial No. 09/934,703, entitled "Thermal Response Correction System," discloses a model of a thermal print head that models the thermal response of thermal print head elements to the provision of energy to the print head elements over time. The thermal print head model generates predictions of the temperature of each of the thermal print head elements at the, beginning of each print head cycle based on,: (1) the current temperature of the thermal print head as measured by a _ 4 - WO 2005/105457 PCT/US2005/013324 temperature sensor, (2) the thermal history of the print head, and (3) the energy history of the print head. The amount of energy to provide to each of the print head elements during a print head cycle to produce a spot having the desired density is calculated based on: (1) the desired density to be produced by the print head element during the print head cycle, and (2) the predicted temperature of the print head element at the beginning of the print head cycle. [0009] Although such techniques take the temperature of the print head into account when performing thermal history control, the techniques discl'osed in the above-referenced patent application do not expressly take into account changes in ambient printer temperature over time when performing thermal history control. Similarly, any thermal effects of humidity are not expressly taken into account by the techniques disclosed in the above-referenced patent application. [0010] What is needed, therefore, are improved techniques for taking into account the ambient printing conditions, so as to render digital images more accurately. SUMMARY [0011] A model of a thermal print head is provided that models the thermal response of thermal print head elements to the provision of energy to the print head elements over time. The amount of energy to - 5 - WO 2005/105457 PCT/US2005/013324 provide to each of the print head elements during a print head cycle to produce a spot having the desired , density is calculated based on: (1) the desired density to be produced by the print head element during the print head cycle, (2) the predicted temperature of the print head element at the beginning of the print head cycle, (3) the ambient printer temperature at the beginning of the print head cycle, and (4) the ambient relative humidity. [0012] In one aspect of the present invention, a method is provided which includes steps of: (A) identifying a first print head temperature Ts of a print head in a printer; (B) identifying a current ambient temperature Tr in the printer; (C) identifying a modified print head temperature T's based on the first print head temperature Ts and the ambient printer temperature Tr; and (D) identifying an input energy to provide to a print head element in the print head based on the modified print head temperature Ts . The step (D) may include a step of identifying the input energy to provide to the print head element based on the modified print head temperature Ts and a current relative humidity. [0013] In another aspect of the present invention, a method is provided for use in conjunction with a thermal printer including a print head element. The method includes a step of: (A) computing an input energy to provide to the print head element based on a current temperature of the print head element, an - 6 - WO 2005/105457 PCT/US2005/013324 ambient printer temperature, and a plurality of one-dimensional functions of a desired output density to be printed by the print head element. [0014] In another aspect of the present invention, a method is provided for use in conjunction with a thermal printer having a print head including a plurality of print head elements. The method develops, for each of a plurality of print head cycles, a plurality of input energies to be provided to the plurality of print head elements during the print head cycle to produce a plurality of output densities. The method includes steps of: (A) using a multi-resolution heat propagation model to develop, for each of the plurality of print head cycles, a plurality of predicted temperatures of the plurality of print head elements at the beginning of the print head cycle; and (B) using an inverse media model to develop the plurality of input energies based on the plurality of predicted i temperatures, a plurality of densities to be output by the plurality of print head elements during the print head cycle, and at least one ambient printer temperature.. [0015] Other features and advantages of various aspects and embodiments of the present invention will become apparent from the following description and from the claims. - 7 - WO 2005/105457 PCT/US2005/013324 BRIEF DESCRIPTION OF THE DRAWINGS [0016] FIG. 1 is a data flow diagram of a system rat is used to print digital images according to one embodiment of the present invention; [0017] FIG. 2 is a data flow diagram of an inverse printer model used in one embodiment of the present invention; [0018] FIG. 3 is a data flow diagram of a thermal printer model used in one embodiment of the present invention; [0019] FIG. 4 is a data flow diagram of an inverse media density model used in one embodiment of the present invention; [0020] FIG. 5 is a schematic side view of a portion of a thermal printer including a thermal print head according to one embodiment of the present invention; [0021] FIG. 6 is a schematic diagram of a circuit that models heat diffusion through a receiver medium according to one embodiment of the present ¦invention; and [0022] FIGS. 7A-7F are flowcharts of methods for printing'digital' images using thermal history control according to various embodiments of the present invention. DETAILED DESCRIPTION 10023] A model of a thermal print head is provided that models ,the thermal response of thermal - 8 - WO 2005/105457 PCT/US2005/013324 print head elements to the provision of energy to the print head elements over time. The amount of energy to provide to each of the print head elements during1 a print head cycle to produce a spot having the desired density is calculated based on: (1) the desired density to be produced by the print head element during the print head cycle, (2) the predicted temperature of the print head element at the beginning of the print head cycle,{3) the ambient printer temperature at the beginning of the print head cycle, and (4) the ambient relative humidity. [0024] The above-referenced patent application i entitled "Thermal Response Correction System" disclosed a model of a thermal print head that models the thermal response of thermal print head elements to the provision of energy to the print head elements over time. The history of temperatures of print head elements of a thermal print head is referred to herein as the print head's "thermal history." The distribution of energies to the print, head elements over time is referred to herein as the print head's "energy history." [0025] In particular, the thermal print head model generates predictions of the temperature of each of the [thermal print head elements at the beginning of each print head cycle based on: (1) the current temperature of the thermal print head, (2) the thermal history of the print head, and (3) the energy history of the print head. In one embodiment of the disclosed thermal print head model, the thermal print head model generates a prediction of the temperature of a - 9 - WO 2005/105457 PCT/US2005/013324 particular thermal print head element at the beginning of a print head cycle based on: (1) the current temperature of the thermal print head, (2) the predicted temperatures of the print head element and one or more of-the other print head elements in the print head at the beginning of the previous print head cycle, and (3) the amount of energy provided to the print head element and one or more of the other print head elements in the print head during the previous print head cycle. [0026] In one embodiment disclosed in the above-referenced patent application,, the amount of energy to provide to each of the print head elements during a print head cycle to produce a spot having the desired density is calculated based on: (1) the desired density i to be produced by the print head element during the print head cycle, and (2) the predicted temperature of i the print head element at the beginning of the print head cycle. It should be appreciated that the amount of energy provided to a particular print head element using such a technique may be greater than or less than that provided by conventional thermal printers. For example, a lesser amount of energy may be provided to compensate for density-drift. A greater amount of energy may.be provided to produce a sharp density gradient. The disclosed model is flexible enough to either increase or decrease the input energies as appropriate to produce the desired output densities. [0027] Use of the thermal print head model decreases the sensitivity of the print engine to the ambient temperature and to previously printed image - 10 - WO 2005/105457 PCT/US2005/013324 content, which manifests itself in the thermal history of the print head elements. [0028] For example, referring to FIG. 1, a system for printing images is shown according to one embodiment of the present invention. The system includes an inverse printer model 102, which is used to compute the amount of input energy 106 to be provided to each print head element in a thermal printer 108 when printing a particular source image 100. As described in more detail below with respect to FIGS. 2 and 3, a thermal printer model 302 models the output (e.g., the printed image 110) produced by thermal printer 108 based on the input energy 106 that is provided to it. Note that the thermal printer model 302 includes both a print head temperature model and a model of the media response. The inverse printer model 102 is an inverse of the thermal printer model 302. More particularly, the inverse printer model 102 computes the input energy 106 for each print head cycle based on the source image 100 (which may, for example, be a two-dimensional grayscale or color digital image) and the current temperature 104 of the thermal printer's print head. The thermal printer 108 prints a printed image 110 of the source image 100 using the input energy 106. It should be appreciated that the input energy 106 may vary over time and for each of the print head elements. Similarly, the print head temperature 104 may vary over time. [0029] In general, the inverse printer model 102 models the distortions that are normally produced by the - 11 - WO 2005/105457 PCT/CS2005/013324 thermal printer 108 (such as those resulting from density drift, as described above and those resulting from the media response) and "pre-distorts" the source image 100 in an opposite direction to effectively cancel out the distortions that would otherwise be produced by the thermal printer 108, when printing the printed image 110. Provision of the input energy 106 to the thermal printer 108 therefore produces the desired densities in the printed image 110, which therefore does not suffer from the problems (such as density drift and degradation of sharpness) described above. In particular, the density distribution of the printed image 110 more closely matches the density distribution of the source image 100 than the density distributions typically produced by conventional thermal printers. [0030] As shown in FIG. 3, thermal printer model 302 is used to model the behavior of the thermal'printer 108 (FIG. 1) . As described in more detail with respect to FIG. 2, the thermal printer model 302 is used to develop the inverse printer model 102, which is used to develop input energy 106 to provide to the thermal printer 108 to produce the desired output densities in printed image ,110 by taking into account the thermal history, of the thermal printer 108. In addition, the thermal printer model 302 is used for calibration purposes, as described below. [0031] Before describing the thermal printer model 302 in more detail, certain notation will be introduced. The source image 100 (FIG. 1) may-be viewed as a two-dimensional density distribution ds having r - 12 - WO 2005/105457 PC T/US2005/013324 rows and c columns. In one embodiment of the present invention, the thermal printer 108 prints one row of the source [image 100 during each print head cycle. As used herein, the variable n will be used to refer to discrete time intervals (such as particular print head cycles). Therefore, the print head temperature 104 at the beginning of time interval n is referred to herein as Ts(n) . Similarly, ds(n) refers to the density distribution of the row of the source image 100 being printed during time interval n. [0032] Similarly, it should be appreciated- that the input energy 106 may be viewed as a two-dimensional energy distribution E. Using the notation just described, E{n) refers to the one-dimensional energy distribution to be applied to the thermal printer's linear array of print head elements during time interval n. The predicted temperature- of a print head element is referred to herein as Th (referred to as Ta in the above-referenced patent application). The predicted temperatures for the linear array of print head elements at the beginning of time interval n is referred to herein as Th{n) . [0033] As shown in FIG. 3, the thermal printer model 302 takes as inputs during each time interval n: (1) the temperature Ts(n) 104 of the thermal print head at the beginning of time interval n, , and (2) the input energy E(n) 106 to be provided to the thermal print head elements during time interval n. The thermal printer model 302 produces as an output a predicted printed image 306, one row at a time (dp(n)). The thermal - 13 - WO 2005/105457 PCT/US2005/013324 printer model 302 includes a head temperature model 202 (as described in more detail below, with respect to FIG. 2) and a media density model 304. The media density model 304 takes as inputs the predicted temperatures Th{n) 204 produced by the head temperature model 202 and the input energy E(n) 106, and produces as an output the predicted printed image 306. [0034] Referring to FIG. 2, one embodiment of i the inverse printer model 102 is shown. The inverse printer model 102 receives as inputs for each time interval n: (1) the print head temperature 104 Ts(n) at the beginning of time interval n, and (2) the densities ds{n) of the row of the source image 100 to be printed during time interval n. The inverse printer model.102 produces the input energy E(n) 106 as an output. [0035] Inverse printer model 102.includes head temperature model 202 and an inverse media density model 206. [In general, the head temperature model 202 predicts the temperatures of the print head elements over time/while the printed image 110 is being printed. More specifically, the head temperature model 202 outputs a prediction of the temperatures Th{n) 204 of the print head elements at the beginning of a particular time interval n based on: (1) the current temperature of the print head Ts(n) 104, and (2) the input energy E(n -1} that was provided to the print head elements during time interval n - 1. [0036] In general, the inverse media density model 206 computes the amount of energy E(n) 106 to provide to each of the print head elements during time - 14 - WO 2005/105457 PCT/US2005/013324 interval n based on: (1) the predicted temperatures Th(n) 204 of each of the print head elements at the beginning of time interval n, and (2) the desired densities ds(n) 100 to be output by the print head elements during time interval n. The input energy E{n) 106 is prbvided to the head temperature model 202 for use during the next time interval n + 1. It should be appreciated that the inverse media density model 206, unlike the techniques typically used by conventional thermal printers, takes both the current (predicted) temperatures Th(n) 204 of the print head elements and the temperature-dependent i media response into account when computing the energy E(n) 106, thereby achieving an improved compensation for the effects of thermal history and other printer-induced imperfections. [0037] Although not shown explicitly in FIG. 2, the head temperature model 202 may internally store at least some of the predicted temperatures Th(n) 204, and it should therefore be appreciated that previous predicted temperatures (such as Tb{n - 1)) may also be considered to be inputs to the head temperature model 202 for use in computing Th(n) 204. [0038] As described in the above-referenced patent application, the inverse media density model 206 receives as inputs during each time interval n: (1) the source image densities ds{n) 100, and (2) Th{n) 204, the predicted temperatures of the thermal print head elements at the beginning of time interval n. The inverse media density model 206 produces as an output the input energy E{n) 106. 15 WO 2005/105457, , PGT/US2005/013324 In other words, the transfer function defined by i the inverse media density model 206 is a two-dimensional function E-F{dsTh). In one embodiment, the function E = F(d,Th) described above is represented using Equation E = G(d) + S(d)Tk Equation 1 [0039] This equation may be interpreted as the first two terms of a Taylor series expansion in Th for the exact energy that would provide the desired density. Such a representation may be advantageous for a variety of reasons. For example, a direct software and/or hardware (implementation of E = F(d,Th) as a two-dimensional function may require a large amount of storage or a significant number of computations to compute the energy E. In contrast, the one dimensional functions G{d) and S{d) may be stored as look-up tables using a relatively small amount of memory, and the inverse media density model 206 may compute the results i of Equation 1 using a relatively small number of computations. [-0040]- One embodiment of the head temperature model 202 (FIGS. 2-3) is now described in more detail. Referring to FIG. 5, a schematic side view is shown of a portion 530 of the thermal printer 108 including a thermal print head 500. The print head 500 includes several layers, including a heat sink 502a, ceramic 502b, and glaze 502c. Underneath the glaze 502c is a - 16 - WO 2005/105457 PCT/US2005/013324 linear array of print head elements 520a-i. It should be appreciated that although only nine heating elements 520a~i are shown in FIG. 5 for ease of illustration, a typical thermal print head will have hundreds of very small and closely-spaced print head elements per inch. The print head elements 520a-i produce output on a receiver medium 522. [0041] As described above, energy may be provided to the print head elements 520a-i to heat them, thereby; causing them to transfer pigment to an output medium. Heat generated by the .print head elements 520a-i diffuses upward through the layers 502a-c. [0042] It may be difficult or unduly burdensome to directly measure the temperatures of the individual print head elements 520a-i over time (e.g., while a digital image is being printed). Therefore, in one embodiment of the present invention, rather than directly measuring the temperatures of the print h model 202 may predict the temperatures of the print head elements 520a-i by modeling the thermal history of the print head elements 520a-i using knowledge of: (1) the temperature of the print head 500, and (2) the energy that has been previously provided to the print head elements 520a-i. The temperature of the print head 500 may be measured using a temperature sensor 512 (such as a thermistor) that measures the temperature Ts(n) at some point on the heat sink 512. - 17 - WO 2005/105457 PCT/US2005/013324 [0043] The head temperature model 202 may model the thermal history, of the print head elements 520a-i in any of a variety of ways. For example, in one . embodiment of the present invention, the head temperature model 202 uses the temperature Ts{n) measured by temperature sensor.512, in conjunction with a model of heat diffusion from the print head elements 520a-i to the temperature sensor 512 through the layers of the print head 500, to predict the current temperatures of the print head elements 520a-i. It should be appreciated, however, that the head temperature model 202 may use techniques other than modeling heat diffusion through the print head 500 to predict the temperatures of the print head elements 520a-i. Examples of techniques that may be used to implement the head temperature model 202 are disclosed in more detail in the above-referenced patent application entitled "Thermal Response Correction System." [0044] As mentioned above, the techniques disclosed in the above-referenced patent application entitled "Thermal Response Correction System" do not explicitly account for changes in ambient printer temperature or humidity. Rather, the method was calibrated with data collected at a particular ambient printer temperature and humidity. The parameters of the thermal printer model 302 and inverse media model 206 were then estimated to minimize the mean square error between the model predictions and the data. This yields an accurate model for describing thermal history effects at a reference set of ambient conditions. - 18 - WO 2005/105457 PCT/US2005/013324 [0045] Examples of techniques will now be disclosed for modifying the above-described techniques to explicitly account for changes in ambient conditions. In particular, techniques will be disclosed for: (1) modeling the effects of ambient temperature fluctuations explicitly to enable the correction of thermal effects at a wide range of ambient temperatures; and (2) correcting for thermal effects of humidity variations. [0046] Recall that the 2-D function E = F(d,Tb) may be iapproximated by a linear combination of the 1-D functions G(d) and S(d), as shown in Equation 1. The arguments Th and d denote the absolute temperature of the print head element at the beginning of the print cycle (line time) and the desired print density, respectively. The required energy E should depend on the temperature of the receiver medium, and not the head temperature as shown in Equation 1. However, the form of Equation 1 remains the same even if we use the media temperature, as long as the temperature of the medium under the print head is a linear function of the head element temperature. Rewriting Equation 1in terms of media temperature that is linearly related to the head element temperature Th results in Equation. 2. E = G(d) + S'(d)Tm Equation 2 [0047] In Equation 2, Tm denotes the absolute temperature of the media, and the functions G'(.) and S'(•) are. related to the. G(.) and S(.) functions, respectively, - 19 - WO 2005/105457 PCT/US2005/013324 in Equation 1. The functions G'(.) and S'(.) may be estimated using, for example, techniques disclosed in the above-referenced patent application for estimating the functions G(.) and S(.) . [0048] In various embodiments of the present invention, the media temperature Tm is estimated by modeling the heat diffusion occurring within the print head and receiver medium. In one embodiment of the present invention, such temperature estimation is performed by translating the heat diffusion problem into an equivalent electrical circuit problem. [0049] Referring to FIG. 6, ah example of such an electrical circuit 600 is shown according to one embodiment of the present invention. The thermal resistance, heat capacity, heat flow, and temperature in the media translate to electrical resistance, capacitance, current, and voltage, respectively, in the elements of the circuit 600. Such a mapping facilitates the computation of as well as the graphical representation of the heat diffusion problem. [0050] An RC circuit network 602 in the circuit 600 (FIG.6) models the print head 500 (FIG. 5). In particular, RC circuits 604a-c model the layers 502a-c, respectively, of the print head 500. The voltage at node 606 models the predicted print head element temperature Th. Note, however, that there need not be a one-to-one mapping between circuits 604a-c and layers 502a-c. Rather, a single layer in the print head 500 may be modeled by multiple circuits, and a single circuit may model multiple layers in the print head - 20 - WO 2005/105457 PCT/US2005/013324 500.The receiver medium 522 is modeled by a plurality of RC circuit networks 608a-f. The circuit network 608c coupled directly to node 606 models the portion of the medium 522 directly below the print head element. Adjacent ones of the circuit networks 608a-f model adjacent portions of the receiver medium 522 in the direction covered by the print head 500 in successive print cycles. [0051] The circuit 600 illustrated in FIG. 6 approximates the continuous motion of the print head 500 over the receiving medium 522 as discrete steps taken by the head 500 during a line time (print cycle) in the direction indicated by arrow 612. Referring again to FIG. 5, note that the printer 530 may include a second temperature sensor 532 for sensing the ambient printer temperature Tr inside of the printer 530. When the head 500 move's over a fresh region of the medium 522 at the start of a line, the initial temperature of the new region Tm is very close to the ambient temperature Tr measured by the temperature sensor 532. Although circuit networks 608a-f include cross-network resistors (such as resistor 610) to model lateral heat diffusion within the medium 522, such resistors are not taken into consideration in the present analysis because it is assumed that within the short print cycle there is little heat diffusion occurring in the printing direction within the medium 522. Such resistors could be taken into account however, if it were desired to consider the effects of this heat diffusion within the medium 522. - 21 - WO 2005/105457 PCT/US2005/013324 [0052] As heat starts to flow from the head 500 to the medium 522, the media temperature Tm begins to rise. The rate of heat flow will be proportional to the temperature gradient between, the head 500 and the media 522. The final media temperature Tm will depend on the line time At and the time constant of the media 522 given by RmCm. For short line times, the media temperature Tm can be approximated 'by Equation 3: 'Tm"Tr +Am(Th,-Tr) Equation 3 [0053] Am in Equation 3 is given by Equation 4: Equation 4 [0054] Plugging Equation 3 into Equation 2, we obtain Equation 5: E = G’(d) + S’ (d)Tr (1-Am + S'(d)AmTh Equation 5 [0055] ' Comparing Equation 1 and Equation 5, we obtain Equation 6 and Equation 7: G(d,Tr)=G’(d)+S’(d)(1-Am)Tr Equation 6 S(d)=S’(d)Am Equation 7 - 22 - WO 2005/105457 PCT/US2005/013324 [0056] Note that in Equation 6 the implicit dependence of the original G(•) function on Tr has been made explicit. [0057] For example, referring to FIG. 4, one embodiment of the inverse media density model 206 (FIG. 2) is now described in more detail. The inverse media density' model 206 receives as inputs during each time interval m (1) the source image densities ds(n) 100, (2) Th(n) 204, the predicted temperatures of the thermal print head elements at the beginning of time interval n; and Tr{n), the ambient printer temperature at the beginning of time interval n. The inverse media density model 206 produces as an output the input energy E(n) 106- In other words, the transfer function defined by the inverse media density model 206 shown in FIG. 4 is a three-dimensional function E — F{d,Th,Tr). [0058] It may be seen from FIG. 4 that the inverse media density model 206 illustrated in FIG. 4 implements Equation 5. For example, the model 206 includes a function G'(.) 424 and a function S"(•) 416. A first multiplier 430 multiplies S'(-) 416, Tr(n) 426, and (l-Am) to produce the second term in Equation 5. A second-multiplier 432 multiplies S'(.) 416, Am-Am 426, and Th{n) 204 to produce the third term in Equation 5. An adder 434 adds G(•) to the outputs of the first and second multipliers 430 and 432 to produce the input energy,E{n) 106. [0059] Referring, to FIG. 7A, a flowchart is shown of a method 700 that is performed by the inverse - 23 - WO 2005/105457 PCT/US2005/013324 printer model 102 in one embodiment of the present invention to produce the input energy 106 to provide tc the thermal printer 108 to produce the printed image ; 110. The method 700 enters a loop over each pixel P in the source image 100 (step 702). The method 700 identifies the temperature Th of the print head element that is to print pixel P (step 704) . The temperature Th may, for example, be predicted using the techniques disclosed in the above-referenced patent application or using techniques disclosed herein. [0060] The method 700 identifies the ambient printer temperature Tr (step 706). The ambient printer temperature Tr may, for example, be identified by measurement using the temperature sensor 532. [0061] The method 700 identifies the temperature TM of the region of the print medium 522 in which pixel P is to ibe printed (step 708) . The temperature Tm may, for example, be estimated using Equation 3. [0062] The method 700 identifies the density ds of pixel P (step 710). The method 700 identifies the input energy E required to print pixel P based on the identified print head element temperature Thr ambient printer temperature Tr, media region temperature Tmr and density ds (step 712) . The energy E may, for example, be identified using Equation 5. The method 700 provides energy E to the appropriate print head element, thereby causing pixel P to be printed (step 714). The method 700 repeats steps 704-714 for the remaining pixels P in the source image 100 (step 716), thereby printing the remainder of the source image 100. - 24 - WO 2005/105457 PCT/US2005/013324 [0063] Note, that step 708 (identification of the media temperature Tm) need not be performed as a separate step in the method 700. For example, if Tm is estimated i using Equation 3, then identification of Tm is performed implicitly in step 712 based on Th and Tr. [0064] The method 700 illustrated in FIG. 7A, may be implemented in a variety of ways. For example, referring to FIG. 7B, a flowchart is shown of a method 720 that is used in one embodiment of the present invention to implement the method 700 of FIG. 7A. The method 720 includes the same steps 702-706 as the method 700 illustrated in FIG. 7B. The method 720, however, identifies the media temperature Tm for each pixel P by computing the value of Tm using Equation 3 (step 722) . The method 720 identifies the density ds of pixel P (step 710) and computes the required energy E by substituting the computed value of Tm into Equation 2. One advantage of the method 720 illustrated in FIG. 7B is that, by computing media temperature Tm for each pixel P, changes in the ambient printer temperature Tr may be taken into account'on a line-by-line basis. [0065] Taking changes in the ambient printer temperature Tr into account on a line-by-line basis, however, may not provide a significant benefit, since the ambient printer, temperature Tr will typically have a long time constant. Referring to FIG. 7C, a flowchart is shown of another method 730 that is used in one embodiment of the present invention to implement the method 700 of FIG. 7A with increased computational efficiency by eliminating the ability to take ambient - 25 - WO 2005/105457 PCT/US2005/013324 printer temperature changes into account 'during a print job. [0066] The method 730 precomputes the functions G(.) and S(.) using Equation 6 and Equation 7 prior to calculating the individual pixel energies (step 732). If the ambient printer temperature Tr is not expected to change appreciably during printing, the use of a single value of Tr in the precompirtation performed in step 732 will not have an appreciable effect on the output produced in the remainder of the method 730. [0067] The method 730 enters a loop over each pixel P in the source image 100 (step 702) and identifies the temperature Th of the corresponding print head element (step 704). The method 730 identifies the density ds of pixel P (step 710) . The method 730 may omit steps 706 and 708 (FIG. 7A), because the effect produced by such steps is achieved by the precomputation performed in step 732. [0068] Having precomputed the functions G(.) and S(•) ; the method 730 identifies the input energy E using Equation 1, which only requires the density ds and the print head temperature Th as inputs (step 734), thereby implemen ting step 712 of the method 700 shown in FIG. 7A. It may be appreciated that Equation 1, which requires only two table lookups, a single addition, and a single multiplication, may be computed more efficiently than the combination of Equation 2 and Equation 3 used in the method 720 of FIG. 7B. - 26 - WO 2005/105457 PCT/US2005/013324 [0069] The method 730 provides the energy E to the print head element (step 714) and repeats steps 704, 710, 734, and 714 for the remaining pixels P {step 716). [0070] Referring to FIG. 7D, a flowchart is shown of a method 740 that is used in another embodiment of the present invention to implement the method 700 illustrated' in FIG. 7A. The method 740 retains the ability to take ambient temperature into account, but with greater computational efficiency than the method 720 illustrated in FIG. ,7B. Let Trc be the ambient temperature at which the inverse media density model 206 is calibrated. Let ft -(l-Am)/Am . Using Equation 5, Equation 6, and Equation 7, we obtain Equation 8: s = G'(d)+s'(d)(1-Am)Trc + s'(d)(1-Am)(Tr -Trc)+S'(d)AmTh = G(d,Trc) + S(d)(Th+ftDTr) Equation 8 [0071] In Equation 8, DTr=Tr-Trc. In other words. Equation 8 allows ambient temperature changes to be taken into account when computing the input energy E by using a correction, term DThr added to the print head i element temperature Th[ based on the difference between the current ambient printer temperature Tr and the calibration temperature Trc. The correction term DTh is given by Equation 9. Wh=f, DTr Equation 9 WO 2005/105457 PCT/US2005/013324 [0072] Referring to FIG. 7D, in one embodiment of the present invention lookup tables are precomputed for the functions G(;,Trc) and S(.) (step 742). The method 740 enters a loop over each pixel P in the source image 100 (step 702), identifies the temperature Th of the print head element (step 704), identifies the ambient printer temperature Tr (step 706), and identifies the density ds of the pixel P (step 710). Equation 9 is used to compute the value of the correction term DTh for pixel ,P (step 744). The method 740 uses Equation 8 to compute the input energy E by adding the computed correction term DTh to the absolute temperature Th and by using the lookup tables to obtain values for G(d,Trc) and S(d) (step 74 6). The method 740 provides the input energy E to the print head element (step 714) and repeats steps 704, 710, 744, 746, ,and 714 for the remaining pixels in the source image 100 (step 716). [0073] The addition of the correction term DTh to the print head element temperature Th in step 746 may, however, be eliminated by recognizing that the computation of the absolute temperatures Th by the thermal history control algorithm includes adding the relative temperatures of all the layers of the print head 500 to the thermistor reading obtained (by temperature sensor 512) at the coarsest layer, as described in more detail in the above-referenced patent application entitled "Thermal Response Correction System." Consequently, ,if the correction term DTh is - 28 - WO 2005/105457 PCT/US2005/013324 added to the thermistor reading Ts, the correction term AT}, is effectively propagated to every pixel by the thermal history coitrol algorithm computation of the absolute print head elenent temperature Th. Recall that Ts denotes the temperatire recorded by the thermistor 512. Then, a modified thermistor temperature T's is given by Equation 10: T;=Ts+f, DTr Equation 10 [0074] The modified thermistor temperature T's may then be used to compute the predicted print head element temperatures Th using the techniques disclosed in the above-referenced patent application, and thereby eliminating the need to add the correction term DTh for each pixel in the computation of the input energy E. [0075] More specifically, referring to FIG. 7E, a flowchart is shown of a method 750 that is used in' one embodiment of the present invention to perform the same function as the method 740 shown in FIG. 7D, but without the addition performed in step 746. The method 750 precomputes lookup tables for the functions G(-,Trc) .and S(.) (step 742), as described above with respect to FIG. 7D. The method 750 enters a loop over each block B of pixels in the source image 100 (step 751). A block of pixels may, for example, be a subset of the source image 100 or the entire source image 100. - 29 - WO 2005/105457 PCT/US2005/013324 [0076] The method 750 identifies the ambient printer temperature Tr (step 706). The method 750 computes the modified print head temperature T's based on the current ambient printer temperature Tr and the calibration ambient printer temperature Txc using Equation 10 (step 752). [0077] The method 750 enters a loop over each pixel P in the block B (step 702), as described above with respect to FIG. 7A. The method 750 identifies the temperature Th of the print head element that is to print pixel P (step 704), identifies the ambient printer temperature Tr (step 706), and identifies the density ds of pixel P (step 710). Step 708 (FIG. 7A) need not be performed because the media temperature Tm was taken into account implicitly in step 752. [0078] The method 750 computes the input energy E using Equation 11 (step 754). Note that Equation 11 results from removing the correction term DTh from Equation 10 because DTh was taken into account in the1 computation of the modified print head temperature T's in step 752., E = G(d,Trc) + S(d)Th Equation 11 [0079] The method 750 provides the input energy E to the print head element (step 714) and repeats steps 704, 710, 754, and 714 for the remaining pixels in the source image 100 (step 7,16). The method 750 repeats the - 30 - WO 2005/105457 i PCT/US2005/013324 steps described above for the remaining blocks in the source image 100 (step 755). [0080] One advantage of the method 750 illustrated in FIG. 7E is that it has negligible overhead in terms of run-time computation, since calculating Equation 11 requires only two table lookups, one addition, and one multiplication, which is no more computationally intensive than Equation 1. Furthermore, the method 750 has the ability to take into account changes in the ambient printer temperature Tr during a long print job, if required. Such changes are reflected in the print head element temperatures Th identified in step 704. [0081] Changes in humidity may affect the densities in the printed image 110 produced by the thermal printer 108 (FIG. 1) . The effects of humidity variation on the printed density, however, may be difficult to represent if humidity alters the media model 206 in such a complex manner that it cannot be accommodated by the structure imposed in Equation 2. As may be seen from the discussion above, the media model 206 may easily be used to account for any variations in the ambient printer-temperature Tr In -one - embodiment-of the present invention, the effect of humidity is taken into account by translating it into an equivalent . temperature variation. - 31 - WO 2005/105457 PCT/US2005/013324 [0082] Using the techniques described in U.S. Patent'No. 6,537,410, entitled "Thermal Transfer Recording System," printing may be achieved by melting the thermal solvent in the donor layer that in turn dissolves the dye. The dissolved dye is then drawn into the receiver by capillary action. Ideally, the thermal solvent melts at a fixed temperature. The presence of impurities in the media, however, may influence the melting temperature. We hypothesize that the moisture in the, air is absorbed by the donor layer and lowers the melting point of the thermal solvent. The amount of moisture absorbed by the donor layer is driven by the ambient relative humidity. Therefore, in one embodiment of the present invention a temperature correction is applied that is proportional to the change in relative humidity. ['0083] Let ARH denote the difference between the current relative humidity and the relative humidity for which the media model 206 was calibrated. Equation 10, which calculates the modified print head temperature measurement TS, may be modified to take into account the humidity effect as shown in Equation 12. Equation 12 [0084] In Equation 12, fh(.) denotes the proportionality constant that converts the relative humidity change ARH into an equivalent temperature change. We have experimentally observed that humidity - 32 - WO 2005/105457 PCT/US2005/013324 has a larger effect at higher ambient temperatures. The dependence of fh(•) on Tr is meant to reproduce this change in sensitivity to humidity with temperature. [0085] Note that Equation 12 shows a particular form of the correction term that is added to the print head temperature Ts . In general, this correction term may be written as a two-dimensional function f(Tr, DRH), where the functional dependence of the correction term on Tr and DRH takes a different form than that shown in Equation 12. The value of this function at a particular ambient printer temperature and relative humidity may be found experimentally by determining the modified print head temperature that results in a printed image most similar to the image printed under the reference ambient conditions. Experimental procedures can also be used to determine the values of ft and fh(.). [0086] Referring to FIG. 7F, a flowchart is shown of a method 760 that is used in one embodiment of the present invention to perform the same function as the method 750 shown in FIG. 7E, except that the method 760 shown in FIG. 7F additionally takes changes in relative. humidity into account. The method 7 60 precomputes lookup tables for the functions G(,Trc) and S(.) (step 742), as described above with respect to FIG. 7D. The method 760 enters a loop over each block B of i pixels in the source image 100 (step 751). The method 760 identifies the ambient printer temperature Tr (step 706) . - 33 - WO 2005/105457 PCT/US2005/013324 [0087] The method 7 60 computes the modified print head temperature Ts based on the current ambient printer temperature Tr, the calibration ambient printer temperature Trcr and the change in relative humidity DRH using Equation 12 (step 762). The remainder of the method 760 performs steps 702, 704, 710, 754, 714, 716, and 755 in the same manner as described above with respect to FIG. 7E, except that the input energy E calculated in step 754 in FIG. 7F effectively takes the effects of humidity into account because the modified . print head temperature TS' produced in step 762 reflects the effects of humidity, and because the modified print head temperature Ts in turn influences the print' head element temperatures Th identified in step 704 for the reasons described above. [0088] An alternative hypothesis is that the glass transition temperature Tg of the dye layer changes as a function of relative humidity. The rate at which the dye is drawn into the receiver is a function of the viscosity, which in turn1 is a function of Tg . Based on these premises, one may develop a formula for calculating—the-equiva-len-t—change in- temperature-that—is again proportional to relative humidity, and in which the proportionality constant has a quadratic dependence on the ambient temperature. Note that the form of the humidity correction term to the thermistor temperature given in Equation 12 accommodates this hypothesis as well. - 34 - WO 2005/105457 PCT/US2005/013324 [0089] The techniques disclosed herein have a variety of advantages. As described above, ambient temperature changes that occur after the thermal history control algorithm has been calibrated can cause the printer to produce suboptimal output if such changes are not taken into account. By taking ambient temperature change's into account explicitly when computing the input energies to provide to a printer to print an image, the technigues disclosed herein compensate for such temperature changes, thereby improving the quality of the printed output. [0090] Similarly, as described above, changes in humidity that occur after the thermal history control algorithm has been calibrated can cause the printer to i produce suboptimal output if such changes are not taken into account. By taking humidity changes into account explicitly when computing the input energies to provide to a printer to print an image, the techniques disclosed herein compensate for such temperature changes, thereby improving the quality of the printed output. [0091] Furthermore, the techniques disclosed herein ;have the advantages disclosed in the above-referenced patent application entitled "Thermal History Control." For example, the techniques disclosed herein reduce or eliminate the problem of "density drift" by taking ithe current ambient temperature of the print head and the thermal and energy histories of the print head into account when computing the energy to be provided to the print head elements, thereby raising the temperatures of the print head elements only-to the - 35 - WO 2005/105457 PCT/US2005/013324 temperatures necessary to produce the desired densities. A further advantage of various embodiments of the present invention is that they may either increase or decrease the input energy provided to the print head elements, as may be necessary or desirable to produce the desired densities. [0092] Another advantage of various embodiments of the present invention is that they compute the energies to be provided to the print head elements in a computationally efficient manner. For example, as described above, in one embodiment of the present i invention, the input energy is computed using two one-dimensional functions (G(d) and S(d)), thereby enabling the input energy to be computed more efficiently than with the single four-dimensional function F(d,Th,Tr, DRH). [0093] It is to be understood that although the i i invention has been described above in terms of particular embodiments, the foregoing embodiments are provided as illustrative,only, and do not limit ox define the scope of the invention. Various other embodiments, including but not limited to the following, are also within the scope of the claims.. For example, elements and components described herein may be further divided into additional components -or joined together to form fewer components for performing the same functions. [0094] Although some embodiments may be described herein with respect to thermal transfer printers, it should be appreciated that this is not a limitation of the present invention. Rather, the techniques described above may be applied to printers - 36 - WO 2005/105457 PCTAJS2005/013324 other than thermal transfer printers (e.g. direct thermal printers). Furthermore, various features of thermal printers described above are described merely for purposes of example and do not constitute limitations of the present invention. [0095] It should be appreciated that the results of the various equations shown and described above may be generated in any of a variety of ways. For example, such equations (such as' Equation 1) may be implemented in software and their results calculated on the fly. Alternatively, lookup tables may be pre-generated which store inputs to such equations and their corresponding outputs. Approximations to the equations may also be used to, for example, provide increased computational efficiency. Furthermore, any combination of these or other techniques may be used to implement the equations described above. Therefore, it should be appreciated that use of terms such as "computing" and "calculating" the results of equations in the description above does not merely refer to on-the-fly calculation but rather refers to any techniques which may be used to produce the same results. [0096] The techniques described above may be implemented, for example, in hardware, software, firmware,,or any combination thereof. The techniques described above may be implemented in one or more computer programs executing on a programmable computer including a processor, a storage medium readable by the processor (including, for example, volatile and nonvolatile memory and/or storage elements), at least one - 37 - PCT/US2005/013324 WO 2005/105457 input device, and at least one output device. Program cote may be applied to input entered using the input device to perform the functions described and to generate output. The output may be provided to one ox flvore output devices. [0097] Each computer program within the scope of the claims below may be implemented in any programming language, such as assembly language, machine language, a high-level procedural programming language, or an object-oriented programming language. The programming language may, for example, be a compiled or interpreted programming language. [0098] Each such, computer program may be implemented in a computer program product tangibly embodied in a machine-readable storage device for execution by a computer processor. Method steps of the invention may be performed by a computer processor executing a program tangibly embodied on a computer-readable medium to perform functions of the invention by operating on input and generating output. Suitable processors include, by way of example, both general and special purpose microprocessors. Generally, the processor receives instructions and data from a readonly mmory and/or" a random access'memory, "storage" devices suitable for tangibly embodying computer program instructions include, for example, all forms of non-volatile memory, such as semiconductor memory devices, including EPROM, EEPROM, and flash memory devices, magnetic disks such as internal hard disks and removabZe disks; magneto-optical disks; and CD-ROMs. Any of the - 38 WO 2005/105457 PCT/US2005/013324 foregoing may be supplemented by, or incorporated in, specially-designed ASICs (application-specific integrated circuits) or FPGAs (Field-Programmable Gate Arrays). A computer can generally also receive programs and data from a storage medium such as an internal disk (not shown) or a removable disk. These elements will also be found in a conventional desktop or workstation computer as well as other computers suitable for executing computer programs implementing the methods described herein, which may be used in conjunction with any digital print engine or marking engine, display monitor, or other raster output device capable of producing color or gray scale pixels on paper, film, display screen, or other output medium. - 39 - WO 2005/105457 PCT/US2005/013324 What is claimed is: 1. A method comprising steps of: (A) identifying a first print head temperature Ts of a print head in a printer; (B) identifying a current ambient temperature Tr in the printer; (C) identifying a modified print head temperature T's based on the first print head temperature Ts and at least one property selected from the group consisting of the ambient printer temperature Tr and a current relative humidity; and (D) identifying an input energy to provide to a print head element in the print head based on the modified print head temperature Ts . 2. The method of claim 1, wherein the step (C) comprises steps of: (C) (1) identifying a temperature Trc at which the method was- calibrated; and (C)(2) identifying the modified print head temperature Ts based on at least- one value selected from the group consisting of: {a) the difference between the current ambient printer temperature Tr -and the calibration ambient printer - 40 - WO 2005/105457 PCT/US2005/013324 temperature Trc, and (b) the difference between the current relative humidity and a relative humidity at which the method was calibrated. 3. The method of claim 2, wherein the step (C)(2) comprises a step of identifying Ts using a formula selected from the group consisting of: • wherein Am is a constant, wherein DTr is a difference between the current ambient printer temperature Tr and an ambient printer temperature at which the method was calibrated, wherein DRH comprises a difference between the current relative humidity and a relative humidity at which the method was calibrated, and wherein fb{)comprises a proportionality constant that converts the relative humidity difference DRH into an equivalent temperature difference. 4. A device comprising: first identification means for identifying a first print head temperature- Ts of a print head in a printer; second identification means for identifying a current ambient temperature Tr in the printer; - 41 - WO 2005/105457 PCT/US2005/013324 third identification means for identifying a modified print head temperature Ts based on the first print head temperature Ts and at least one property selected from the group consisting ,of the ambient printer temperature Tr and a current relative humidity; and fourth identification means for identifying an input energy to provide to a print head element in the print head based on the modified print head temperature Tr. 5. The device of claim 4, wherein the third identification means comprises: fifth identification means for identifying a temperature Tec at which the method was. calibrated; and sixth identification means for identifying the modified print head temperature Ts based on at least one value selected from the group consisting of: (a) the difference between the current ambient printer temperature Tr and the calibration,ambient printer temperature Trc, and (b) the difference between the current relative humidity and a relative humidity at which the method was calibrated. 6. The device of claim 5, wherein the sixth identification means comprises means for identifying Ts' using a formula selected from the group consisting of: - 42 - WO 2005/105457 PCT/US2005/013324 wherein Am is a constant, wherein DTr is a difference between the current ambient printer temperature Tr and an ambient printer temperature at which the method was calibrated, wherein DRH comprises a. difference between the current relative humidity and a relative humidity at which the method was calibrated, and wherein fh()comprises a proportionality constant that converts the relative humidity difference DRH into an equivalent temperature difference. 7. In a thermal printer including a print head element, a method comprising a step of: (A) computing an input energy to provide to the print head element based on a current temperature of the print head element, a plurality of one-dimensional functions of a desired output density to be printed by the print head element, and at least one property selected from the group consisting of an ambient printer, temperature and a current humidity. 8. The method of claim 7, wherein the print head element is one of a plurality of print head elements in a print head, wherein Ts is a current temperature of the print head, wherein DTr is a difference between the - 43 - WO 2005/105457 PCT/US2005/013324 ambient printer temperature and an ambient temperature at which the method was calibrated, wherein the method further pomprises a step of: computing a modified current print head temperature T's is computed according to a formula selected from the group consisting of: wherein Am is a constant, wherein DRH comprises a difference between the current humidity and a humidity at which the method was calibrated, wherein fh() converts the relative humidity difference DRM into an equivalent temperature difference, and wherein the step (A) comprises a step of identifying the current temperature of the print head based on the modified current print head temperature Ts . 9. The method of claim 8, further comprising a step of: (C) performing step (A) for each pixel in a subset of pixels in a source image. 10. The method of claim 9, wherein the subset comprises the entire source image. - 44 - WO 2005/105457 PCT/US2005/013324 11,. The method of claim 9, further comprising a step of: (D) repeating step (B) for each of a plurality of subsets of the source image. 12,. Tne method of claim 7, wherein the step (A) comprises a step of computing an input energy to provide to the print head element based on a temperature of an output medium, the current temperature of the print head element, the ambient printer temperature, and the plurality of one-dimensional functions. 13. The method of claim 12, wherein Tr is the ambient printer temperature, Th is the current temperature of the. print head element, and wherein the step (A) comprises steps of: (A)(1) calculating the output medium temperature Tm as Tnr-Tx+Am(Th-Tr) , wherein Am is a constant; and (A) (2) computing the input energy E as E=G' (d)+S' (d)Tm, wherein G' (d) and S' (d)' comprise two of the plurality of one-dimensional functions. 14. The method of claim 7, wherein G' (d) and S' (d) comprise two of the plurality of one-dimensional functions, and wherein the method further comprises steps of: (B) prior to the step (A), precomputing values for functions G(d,Tr) and S(d) using the - 45 - WO 2005/105457 PCT/US2005/013324 formulas G(d,Tr) = G'(d) + S'(d)(1-Am)Tr and S(d) = S'(d)Amr wherein d represents density, wherein Tr represents the ambient printer temperature, and wherein Am is a constant; (C) for each of a plurality of pixels P in a source image, performing step (A) using the precomputed functions G(d, Tr) and S(d). 15. The method of claim 14, wherein the step (C) comprises performing, for each of the plurality of pixels P in the source image, a step of computing the input energy E as E=G{d, Tz)+S(d) Th, wherein Th comprises the temperature of the print head element. 16. The method of claim 7, wherein the print head element1 is one of a plurality of print he'ad elements in a print head, wherein Trc is an ambient printer temperature at which the method was calibrated, wherein DTr is a difference between Trc and the current ambient printer temperature, wherein a modified print head element temperature Th is computed according to a formula selected from the group consisting of:' 46 - WO 2005/105457 PCT/US2005/013324 wherein Am is a constant, wherein DRH comprises a difference between the current humidity and a humidity at which the method was calibrated, wherein fh() converts the relative humidity difference DRH into an equivalent temperature difference, and wherein the step (A) comprises a step of computing the input energy based on the modified print head element temperature T'h . 17. The method of claim 7, further comprising a step of: (B) providing the input energy'to the print head element. 18. The method of claim 7, wherein the current temperature of the print head element comprises a predicted current temperature of the print head element. 19. The method of claim 18, wherein the predicted temperature is predicted based on an ambient print head temperature and an energy previously provided to the print head element. 20. The method of claim 7, wherein, the, thermal, printer includes a plurality of print head elements, and wherein the predicted temperature is predicted based on a print head temperature, an energy previously provided to the print head element, and an energy previously provided to at least one other print head element in the plurality of print head elements. - 47 - WO 2005/105457 PCT/US2005/013324 21. A printer comprising; a print head element; and: first computation means for computing an input energy to provide to the print head element based on a current temperature of the print head element, a plurality of one-dimensional functions of a desired output density to be printed by the print head element, and at least one property selected from the group consisting of an ambient printer temperature and a current humidity. 22. The device of claim 21, wherein the print head element is one of a plurality of print head elements in a print head, wherein Ts is a current temperature of the print head, wherein DTr is a difference between the ambient printer temperature and an ambient temperature at which the method was calibrated, wherein the device further comprises: second computation means for computing a modified current print head temperature Ts' is computed according to a formula selected from the group consisting of: wherein Am is a constant, wherein DRH comprises a difference between the current humidity and a humidity - 48 - WO 2005/305457 PCT/US2005/013324 at which the method was calibrated, wherein fh() converts the relative humidity difference DRH into an equivalent temperature difference, and wherein the first computation means comprises means for identifying the current temperature of the print head based on the modified current print head temperature Ts . 23. The device of claim 22, further comprising: means for applying the first computation means to each pixel in a subset of pixels in a source image. 24. The device of claim 23, wherein the subset comprises the entire source image. 25. The device of claim 23, further comprising: means for applying the second computation means to each of a plurality of subsets of the source image. 26. The device of claim 21, wherein the first computation means comprises means for computing an input energy to provide to the print head element based on a temperature of an output medium, the current temperature of__the__print head element, the ambient printer temperature, and the plurality of one-dimensional functions. 27. The device of claim 26, wherein Tr is the ambient printer temperature, Th, is the current - 49 - WO 2005/105457 PCT/US2005/013324 temperature of the print head element, and wherein the first computation means comprises: means for calculating the output medium temperature Tm as Tm=Tr+Am{Th-Tr), wherein Am is a constant; and means for computing the input energy E as E=G' (d)+Sr (d) Tm' wherein G' (d) and S' (d) comprise two of the plurality of one-dimensional functions., 28. The device of claim 21, wherein G' (d) and S' (d) comprise two of the plurality of one-dimensional functions, and wherein the device further comprises:; means for precomputing, prior to the step (A), values for functions G(d,Tx) and S{d) using the formulas G(d,Tr) = G'(d) + S'(d)(1-Am)Tr and S(d) = S' (d)Am, wherein d represents density, wherein Tr represents the ambient printer temperature, and wherein Am is a constant; means, for each of a plurality of pixels P in a source;image, for applying the first computation means using the precomputed functions G(d,Tr) and S{d) . 29. The device of claim 28, wherein the means for precomputing comprises means for performing, for. each of the plurality of pixels ,P in the source image, a step of computing the input energy E as E=G(dr Tr) +S(d) Th' wherein Th comprises the temperature of the print head element. 30. The device of claim 21, wherein the print head element is one of a plurality of print head elements in a print head, wherein Trc is an ambient printer temperature at which the method was calibrated, wherein - 50 - WO 2005/105457 PCT/US2005/013324 DTr is a difference between Trc and the current ambient printer temperature, wherein a modified print head element temperature Th is computed according to a formula selected from the group consisting of: wherein Am is a constant, wherein DRH comprises a difference between the current humidity and a humidity at which the method was calibrated, wherein fh() converts the relative humidity difference DRH into an equivalent temperature difference, and wherein the first computation means comprises means for computing the input energy based on the modified print head element temperature Th 31. The device of claim 21, further comprising:- means for providing the input energy to the print head element. 32. The device of claim 21, wherein the current temperature of the print,head element comprises a predicted current temperature of the print head element. 33. The device of claim 32, wherein the predicted temperature is predicted based on an ambient print head - 51 - WO 2005/105457 PCT/US2005/013324 temperature and an energy previously provided to the print head element. 340. The device of claim 31, wherein the thermal printer includes a plurality of print head elements, and wherein the predicted temperature is predicted based on a print head temperature, an energy previously provided to the' print head element, and an energy previously provided to at least one other print head element in the plurality of print head elements. 35". In a thermal printer having a print head including a plurality of print head elements, a method for developing, for each of a plurality of print head cycles, a plurality of input energies to be provided to the plurality of print head elements during the print head cycle to produce a plurality of output densities, the method comprising steps of: (A) using a multi-resolution heat propagation model to develop, for each of the plurality of print head cycles, a plurality of predicted temperatures of the plurality of print head elements at the beginning of the print head cycle; and - 52 - WO 2005/105457 PCT/US2005/013324 (B) using an inverse media model to develop the plurality of input energies based on the plurality of predicted temperatures, a plurality of densities to be output by the plurality of print head elements during the print head cycle, and at least one property selected from the group consisting of at least one ambient printer temperature and at least one humidity. 36. The method of claim 35, wherein the step (A) comprises a step of developing the plurality of predicted temperatures based on a print head temperature and a plurality of input energies provided to the plurality of print head elements during at least one previous print head cycle. 37. The method of claim 35, wherein the step (A) comprises a step of developing the plurality of predicted temperatures based on a plurality of previous predicted temperatures for the plurality of print head elements. 38. The method of claim 35, wherein the step (A) comprises a step of developing, for each of the plurality of print head elements, a predicted temperature based on a predicted temperature of at least one of the other print head elements at the beginning of at least one previous print head cycle. - 53 - WO 2005/105457 PCT/US2005/013324 39. The method of claim 35, wherein the steps (A) and (B) are performed during a single print head cycle of the thermal printer. 40. A thermal printer comprising: a, print head including a plurality of print head elements; means for developing, for each of a plurality of print head cycles, a plurality of input energies to be provided to the plurality of print head elements during the print head cycle to produce a plurality of output densities, the means for developing comprising: temperature prediction means for using a multi-resolution heat propagation model to develop, for each of the plurality of print head cycles, a plurality of predicted temperatures of the plurality of print head elements at the beginning of the print head cycle.; and energy development means for using an inverse media model to develop the plurality of input energies based on the (plurality of predicted temperatures, a plurality of densities to be output by the plurality of print head elements during the print head cycle, and at least one property selected from the group consisting of at least one ambient printer temperature and at least one humidity. 41. The device of claim 40, wherein the temperature prediction means comprises means for developing the plurality of predicted temperatures based on a print head temperature and a plurality of input energies - 54 - WO 2005/105457 PCT/US2005/013324 provided to the plurality of print head elements during at least one previous print head cycle. 42. The device of claim 40, wherein the temperature prediction means comprises means for developing the plurality of predicted temperatures based on a plurality of previous predicted temperatures for the plurality of print head elements. 43. The device of claim 40, wherein the temperature prediction means comprises means for developing, for each of the plurality of print head elements, a predicted temperature based on a predicted temperature of at least one of the other print head elements at the beginning of at least one previous print head cycle. 44. The device of claim 40, wherein the temperature prediction means and the energy prediction means are applied during a single print head cycle of the thermal printer. - 55 -

Full Text

WO 2005/105457 PCT/US2005/013324
Thermal Response Correction System
BACKGROUND
Field of the Invention
[0001] The present invention relates to thermal printing and, more particularly, to techniques for improving thermal printer output by compensating for the effects of thermal history on thermal print heads.
Related Art
[0002] Thermal printers typically contain a linear array of heating elements (also referred to herein as "print head elements") that print on an output medium by, for example, transferring pigment or dye from a donor sheet to the output medium or by activating a color-forming chemistry in the output medium. The output medium is typically a porous receiver receptive to the transferred pigment, or a paper coated with the color-forming chemistry. Each of the print head elements, when-activated, forms color on the medium, passing underneath the print head element, creating a spot having a particular density. Regions with larger or denser spots are perceived as darker than regions with smaller or less dense spots. Digital images are rendered as two-dimensional arrays of very small and closely-spaced spots-

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E0003] A thermal print head element is activated by providing it with energy. Providing energy to the print head element increases the temperature of the print head element, causing either the transfer of pigment to the output medium or the formation of color in the receiver. The density of the output produced by the print head element in this manner is a function of the amount of energy provided to the print head element. The amount of energy provided to the print head element may be varied by, for example, varying the amount of power to the print head element within a particular time interval or by providing power to the print head element for a longer time interval.
[0004] In conventional thermal printers, the time during which a digital image is printed is divided
into fixed time intervals referred to herein as "print
i
head cycles." Typically, a single row of pixels (or portions thereof) in the digital image is printed during a single print head cycle. Each print head element is typically responsible for printing pixels {or sub-pixels) in a particular column of the digital image. During each print head cycle, an amount of energy is delivered to each print head element that is calculated to raise the temperature of the print head element to a level that will cause the print head element to produce output having the desired density. Varying amounts of
energy may be provided to different print head elements
i
based on the varying desired densities to be produced by the print head elements.
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[0005] One problem with conventional thermal printers results from the fact that their print head elements retain heat after the conclusion of each print head cycle. This retention of heat can be problematic because, in some thermal printers, the amount of energy that is delivered to a particular print head element
during a particular print head cycle is typically
i calculated based on an assumption that the print head
element's temperature at the beginning of the print head cycle is a known fixed temperature. Since, in reality, the temperature of the print head element at the beginning of a print head cycle depends on (among other things) the amount of energy delivered to the print head element during previous print head cycles, the actual temperature achieved by the print head element during a print head cycle may differ from the calibrated temperature, thereby resulting in a higher or lower output density than is desired. Further complications are similarly caused by the fact that the current temperature of a particular print head element is influenced not only by its own previous temperatures -referred to herein as its "thermal history" - but by the ambient, (room) temperature and the thermal histories of other print head elements in the print head.
[0006] As may be inferred from the discussion above, in some conventional thermal printers, the average temperature of each particular thermal print head element tends to, gradually rise during the printing of a digital image due to retention of heat by the print head element and the over-provision of energy to the
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print head element in light of such heat retention. This gradual temperature increase results in a corresponding gradual increase in density of the output produced by the print head element, which is perceived as increased darkness in the printed image. This phenomenon is referred to herein as "density drift."
[0007] Furthermore, conventional thermal printers typically have difficulty accurately reproducing sharp density gradients between adjacent pixels both across the print head and in the direction of printing. For example, if a print head element is to print a white pixel following a black pixel, 'the ideally sharp edge between the two pixels will typically be blurred when printed. This problem results from the amount of time that is required to raise the temperature of the print head element to print the black pixel after printing the white pixel. More generally, this
characteristic of conventional thermal printers results
i in less than ideal sharpness when printing images having
regions of high density gradient.
[0008] The above-referenced U.S. Patent Application Serial No. 09/934,703, entitled "Thermal Response Correction System," discloses a model of a thermal print head that models the thermal response of thermal print head elements to the provision of energy to the print head elements over time. The thermal print head model generates predictions of the temperature of each of the thermal print head elements at the, beginning of each print head cycle based on,: (1) the current temperature of the thermal print head as measured by a
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temperature sensor, (2) the thermal history of the print head, and (3) the energy history of the print head. The amount of energy to provide to each of the print head elements during a print head cycle to produce a spot having the desired density is calculated based on: (1) the desired density to be produced by the print head element during the print head cycle, and (2) the predicted temperature of the print head element at the beginning of the print head cycle.
[0009] Although such techniques take the temperature of the print head into account when performing thermal history control, the techniques discl'osed in the above-referenced patent application do not expressly take into account changes in ambient printer temperature over time when performing thermal history control. Similarly, any thermal effects of humidity are not expressly taken into account by the techniques disclosed in the above-referenced patent application.
[0010] What is needed, therefore, are improved techniques for taking into account the ambient printing conditions, so as to render digital images more accurately.
SUMMARY
[0011] A model of a thermal print head is provided that models the thermal response of thermal print head elements to the provision of energy to the print head elements over time. The amount of energy to
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provide to each of the print head elements during a print head cycle to produce a spot having the desired , density is calculated based on: (1) the desired density to be produced by the print head element during the print head cycle, (2) the predicted temperature of the print head element at the beginning of the print head cycle, (3) the ambient printer temperature at the beginning of the print head cycle, and (4) the ambient relative humidity.
[0012] In one aspect of the present invention, a method is provided which includes steps of: (A) identifying a first print head temperature Ts of a print head in a printer; (B) identifying a current ambient temperature Tr in the printer; (C) identifying a modified
print head temperature T's based on the first print head
temperature Ts and the ambient printer temperature Tr; and (D) identifying an input energy to provide to a print head element in the print head based on the modified print head temperature Ts . The step (D) may include a step of identifying the input energy to provide to the print head element based on the modified print head temperature Ts and a current relative humidity.
[0013] In another aspect of the present invention, a method is provided for use in conjunction with a thermal printer including a print head element. The method includes a step of: (A) computing an input energy to provide to the print head element based on a current temperature of the print head element, an
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ambient printer temperature, and a plurality of one-dimensional functions of a desired output density to be printed by the print head element.
[0014] In another aspect of the present invention, a method is provided for use in conjunction with a thermal printer having a print head including a plurality of print head elements. The method develops, for each of a plurality of print head cycles, a plurality of input energies to be provided to the plurality of print head elements during the print head cycle to produce a plurality of output densities. The method includes steps of: (A) using a multi-resolution heat propagation model to develop, for each of the plurality of print head cycles, a plurality of predicted temperatures of the plurality of print head elements at the beginning of the print head cycle; and (B) using an inverse media model to develop the plurality of input
energies based on the plurality of predicted
i
temperatures, a plurality of densities to be output by the plurality of print head elements during the print head cycle, and at least one ambient printer temperature..
[0015] Other features and advantages of various aspects and embodiments of the present invention will become apparent from the following description and from the claims.
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BRIEF DESCRIPTION OF THE DRAWINGS
[0016] FIG. 1 is a data flow diagram of a system rat is used to print digital images according to one embodiment of the present invention;
[0017] FIG. 2 is a data flow diagram of an inverse printer model used in one embodiment of the present invention;
[0018] FIG. 3 is a data flow diagram of a thermal printer model used in one embodiment of the present invention;
[0019] FIG. 4 is a data flow diagram of an inverse media density model used in one embodiment of the present invention;
[0020] FIG. 5 is a schematic side view of a portion of a thermal printer including a thermal print head according to one embodiment of the present invention;
[0021] FIG. 6 is a schematic diagram of a circuit that models heat diffusion through a receiver medium according to one embodiment of the present ¦invention; and
[0022] FIGS. 7A-7F are flowcharts of methods for printing'digital' images using thermal history control according to various embodiments of the present invention.
DETAILED DESCRIPTION
10023] A model of a thermal print head is provided that models ,the thermal response of thermal
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print head elements to the provision of energy to the print head elements over time. The amount of energy to provide to each of the print head elements during1 a print head cycle to produce a spot having the desired density is calculated based on: (1) the desired density to be produced by the print head element during the print head cycle, (2) the predicted temperature of the
print head element at the beginning of the print head
cycle,{3) the ambient printer temperature at the
beginning of the print head cycle, and (4) the ambient relative humidity.
[0024] The above-referenced patent application
i
entitled "Thermal Response Correction System" disclosed a model of a thermal print head that models the thermal response of thermal print head elements to the provision of energy to the print head elements over time. The history of temperatures of print head elements of a thermal print head is referred to herein as the print head's "thermal history." The distribution of energies to the print, head elements over time is referred to herein as the print head's "energy history."
[0025] In particular, the thermal print head model generates predictions of the temperature of each of the [thermal print head elements at the beginning of each print head cycle based on: (1) the current temperature of the thermal print head, (2) the thermal history of the print head, and (3) the energy history of the print head. In one embodiment of the disclosed thermal print head model, the thermal print head model generates a prediction of the temperature of a
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particular thermal print head element at the beginning of a print head cycle based on: (1) the current temperature of the thermal print head, (2) the predicted temperatures of the print head element and one or more of-the other print head elements in the print head at the beginning of the previous print head cycle, and (3) the amount of energy provided to the print head element and one or more of the other print head elements in the print head during the previous print head cycle.
[0026] In one embodiment disclosed in the above-referenced patent application,, the amount of energy to provide to each of the print head elements during a print head cycle to produce a spot having the desired
density is calculated based on: (1) the desired density
i
to be produced by the print head element during the
print head cycle, and (2) the predicted temperature of
i the print head element at the beginning of the print
head cycle. It should be appreciated that the amount of energy provided to a particular print head element using such a technique may be greater than or less than that provided by conventional thermal printers. For example, a lesser amount of energy may be provided to compensate for density-drift. A greater amount of energy may.be provided to produce a sharp density gradient. The disclosed model is flexible enough to either increase or decrease the input energies as appropriate to produce the desired output densities.
[0027] Use of the thermal print head model decreases the sensitivity of the print engine to the ambient temperature and to previously printed image
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content, which manifests itself in the thermal history of the print head elements.
[0028] For example, referring to FIG. 1, a system for printing images is shown according to one embodiment of the present invention. The system includes an inverse printer model 102, which is used to compute the amount of input energy 106 to be provided to each print head element in a thermal printer 108 when printing a particular source image 100. As described in
more detail below with respect to FIGS. 2 and 3, a

thermal printer model 302 models the output (e.g., the printed image 110) produced by thermal printer 108 based on the input energy 106 that is provided to it. Note that the thermal printer model 302 includes both a print head temperature model and a model of the media response. The inverse printer model 102 is an inverse of the thermal printer model 302. More particularly, the inverse printer model 102 computes the input energy 106 for each print head cycle based on the source image 100 (which may, for example, be a two-dimensional grayscale or color digital image) and the current temperature 104 of the thermal printer's print head. The thermal printer 108 prints a printed image 110 of the source image 100 using the input energy 106. It should be appreciated that the input energy 106 may vary over time and for each of the print head elements. Similarly, the print head temperature 104 may vary over time.
[0029] In general, the inverse printer model 102 models the distortions that are normally produced by the
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thermal printer 108 (such as those resulting from density drift, as described above and those resulting from the media response) and "pre-distorts" the source image 100 in an opposite direction to effectively cancel out the distortions that would otherwise be produced by the thermal printer 108, when printing the printed image 110. Provision of the input energy 106 to the thermal printer 108 therefore produces the desired densities in the printed image 110, which therefore does not suffer from the problems (such as density drift and degradation of sharpness) described above. In particular, the density distribution of the printed image 110 more closely matches the density distribution of the source image 100 than the density distributions typically produced by conventional thermal printers.
[0030] As shown in FIG. 3, thermal printer model 302 is used to model the behavior of the thermal'printer 108 (FIG. 1) . As described in more detail with respect to FIG. 2, the thermal printer model 302 is used to develop the inverse printer model 102, which is used to develop input energy 106 to provide to the thermal printer 108 to produce the desired output densities in printed image ,110 by taking into account the thermal history, of the thermal printer 108. In addition, the thermal printer model 302 is used for calibration purposes, as described below.
[0031] Before describing the thermal printer model 302 in more detail, certain notation will be
introduced. The source image 100 (FIG. 1) may-be viewed
as a two-dimensional density distribution ds having r
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rows and c columns. In one embodiment of the present
invention, the thermal printer 108 prints one row of the
source [image 100 during each print head cycle. As used herein, the variable n will be used to refer to discrete time intervals (such as particular print head cycles). Therefore, the print head temperature 104 at the beginning of time interval n is referred to herein as Ts(n) . Similarly, ds(n) refers to the density distribution of the row of the source image 100 being
printed during time interval n.

[0032] Similarly, it should be appreciated- that the input energy 106 may be viewed as a two-dimensional energy distribution E. Using the notation just described, E{n) refers to the one-dimensional energy distribution to be applied to the thermal printer's linear array of print head elements during time interval n. The predicted temperature- of a print head element is referred to herein as Th (referred to as Ta in the above-referenced patent application). The predicted temperatures for the linear array of print head elements at the beginning of time interval n is referred to herein as Th{n) .
[0033] As shown in FIG. 3, the thermal printer model 302 takes as inputs during each time interval n: (1) the temperature Ts(n) 104 of the thermal print head at the beginning of time interval n, , and (2) the input energy E(n) 106 to be provided to the thermal print head elements during time interval n. The thermal printer model 302 produces as an output a predicted printed image 306, one row at a time (dp(n)). The thermal
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printer model 302 includes a head temperature model 202 (as described in more detail below, with respect to FIG. 2) and a media density model 304. The media density model 304 takes as inputs the predicted temperatures Th{n) 204 produced by the head temperature model 202 and the input energy E(n) 106, and produces as an output the predicted printed image 306.
[0034] Referring to FIG. 2, one embodiment of i the inverse printer model 102 is shown. The inverse
printer model 102 receives as inputs for each time interval n: (1) the print head temperature 104 Ts(n) at the beginning of time interval n, and (2) the densities ds{n) of the row of the source image 100 to be printed during time interval n. The inverse printer model.102 produces the input energy E(n) 106 as an output.
[0035] Inverse printer model 102.includes head temperature model 202 and an inverse media density model 206. [In general, the head temperature model 202 predicts the temperatures of the print head elements over time/while the printed image 110 is being printed. More specifically, the head temperature model 202 outputs a prediction of the temperatures Th{n) 204 of the print head elements at the beginning of a particular time interval n based on: (1) the current temperature of the print head Ts(n) 104, and (2) the input energy E(n -1} that was provided to the print head elements during time interval n - 1.
[0036] In general, the inverse media density model 206 computes the amount of energy E(n) 106 to provide to each of the print head elements during time
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interval n based on: (1) the predicted temperatures Th(n) 204 of each of the print head elements at the beginning of time interval n, and (2) the desired densities ds(n) 100 to be output by the print head elements during time interval n. The input energy E{n) 106 is prbvided to the head temperature model 202 for use during the next time interval n + 1. It should be appreciated that the inverse media density model 206, unlike the techniques typically used by conventional thermal printers, takes both the current (predicted) temperatures Th(n) 204 of
the print head elements and the temperature-dependent
i
media response into account when computing the energy E(n) 106, thereby achieving an improved compensation for the effects of thermal history and other printer-induced imperfections.
[0037] Although not shown explicitly in FIG. 2, the head temperature model 202 may internally store at least some of the predicted temperatures Th(n) 204, and it should therefore be appreciated that previous predicted temperatures (such as Tb{n - 1)) may also be considered to be inputs to the head temperature model 202 for use in computing Th(n) 204.
[0038] As described in the above-referenced patent application, the inverse media density model 206 receives as inputs during each time interval n: (1) the source image densities ds{n) 100, and (2) Th{n) 204, the predicted temperatures of the thermal print head elements at the beginning of time interval n. The inverse media density model 206 produces as an output the input energy E{n) 106.
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In other words, the transfer function defined by
i the inverse media density model 206 is a two-dimensional
function E-F{dsTh). In one embodiment, the function E = F(d,Th) described above is represented using Equation
E = G(d) + S(d)Tk Equation 1
[0039] This equation may be interpreted as the first two terms of a Taylor series expansion in Th for the exact energy that would provide the desired density. Such a representation may be advantageous for a variety of reasons. For example, a direct software and/or hardware (implementation of E = F(d,Th) as a two-dimensional function may require a large amount of storage or a significant number of computations to compute the energy E. In contrast, the one dimensional functions G{d) and S{d) may be stored as look-up tables using a relatively small amount of memory, and the
inverse media density model 206 may compute the results
i of Equation 1 using a relatively small number of
computations.
[-0040]- One embodiment of the head temperature model 202 (FIGS. 2-3) is now described in more detail. Referring to FIG. 5, a schematic side view is shown of a portion 530 of the thermal printer 108 including a thermal print head 500. The print head 500 includes several layers, including a heat sink 502a, ceramic 502b, and glaze 502c. Underneath the glaze 502c is a
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linear array of print head elements 520a-i. It should be appreciated that although only nine heating elements 520a~i are shown in FIG. 5 for ease of illustration, a typical thermal print head will have hundreds of very small and closely-spaced print head elements per inch. The print head elements 520a-i produce output on a receiver medium 522.
[0041] As described above, energy may be provided to the print head elements 520a-i to heat them, thereby; causing them to transfer pigment to an output medium. Heat generated by the .print head elements 520a-i diffuses upward through the layers 502a-c.
[0042] It may be difficult or unduly burdensome to directly measure the temperatures of the individual print head elements 520a-i over time (e.g., while a digital image is being printed). Therefore, in one embodiment of the present invention, rather than directly measuring the temperatures of the print h model 202 may predict the temperatures of the print head
elements 520a-i by modeling the thermal history of the print head elements 520a-i using knowledge of: (1) the temperature of the print head 500, and (2) the energy that has been previously provided to the print head elements 520a-i. The temperature of the print head 500 may be measured using a temperature sensor 512 (such as a thermistor) that measures the temperature Ts(n) at some point on the heat sink 512.
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[0043] The head temperature model 202 may model the thermal history, of the print head elements 520a-i in any of a variety of ways. For example, in one . embodiment of the present invention, the head temperature model 202 uses the temperature Ts{n) measured by temperature sensor.512, in conjunction with a model of heat diffusion from the print head elements 520a-i to the temperature sensor 512 through the layers of the print head 500, to predict the current temperatures of the print head elements 520a-i. It should be appreciated, however, that the head temperature model 202 may use techniques other than modeling heat diffusion through the print head 500 to predict the temperatures of the print head elements 520a-i. Examples of techniques that may be used to implement the head temperature model 202 are disclosed in more detail
in the above-referenced patent application entitled
"Thermal Response Correction System."
[0044] As mentioned above, the techniques disclosed in the above-referenced patent application entitled "Thermal Response Correction System" do not explicitly account for changes in ambient printer temperature or humidity. Rather, the method was calibrated with data collected at a particular ambient printer temperature and humidity. The parameters of the thermal printer model 302 and inverse media model 206 were then estimated to minimize the mean square error between the model predictions and the data. This yields an accurate model for describing thermal history effects at a reference set of ambient conditions.
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[0045] Examples of techniques will now be disclosed for modifying the above-described techniques to explicitly account for changes in ambient conditions. In particular, techniques will be disclosed for: (1) modeling the effects of ambient temperature fluctuations explicitly to enable the correction of thermal effects at a wide range of ambient temperatures; and (2) correcting for thermal effects of humidity variations.
[0046] Recall that the 2-D function E = F(d,Tb)
may be iapproximated by a linear combination of the 1-D functions G(d) and S(d), as shown in Equation 1. The arguments Th and d denote the absolute temperature of the print head element at the beginning of the print cycle (line time) and the desired print density, respectively. The required energy E should depend on the temperature of the receiver medium, and not the head temperature as shown in Equation 1. However, the form of Equation 1 remains the same even if we use the media temperature, as long as the temperature of the medium under the print head is a linear function of the head element temperature. Rewriting Equation 1in terms of media temperature that is linearly related to the head element temperature Th results in Equation. 2.
E = G(d) + S'(d)Tm
Equation 2
[0047] In Equation 2, Tm denotes the absolute temperature of the media, and the functions G'(.) and S'(•) are. related to the. G(.) and S(.) functions, respectively,
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in Equation 1. The functions G'(.) and S'(.) may be estimated using, for example, techniques disclosed in the above-referenced patent application for estimating
the functions G(.) and S(.) .
[0048] In various embodiments of the present
invention, the media temperature Tm is estimated by modeling the heat diffusion occurring within the print head and receiver medium. In one embodiment of the present invention, such temperature estimation is performed by translating the heat diffusion problem into an equivalent electrical circuit problem.
[0049] Referring to FIG. 6, ah example of such an electrical circuit 600 is shown according to one embodiment of the present invention. The thermal resistance, heat capacity, heat flow, and temperature in the media translate to electrical resistance, capacitance, current, and voltage, respectively, in the elements of the circuit 600. Such a mapping facilitates the computation of as well as the graphical representation of the heat diffusion problem.
[0050] An RC circuit network 602 in the circuit 600 (FIG.6) models the print head 500 (FIG. 5). In particular, RC circuits 604a-c model the layers 502a-c, respectively, of the print head 500. The voltage at node 606 models the predicted print head element temperature Th. Note, however, that there need not be a one-to-one mapping between circuits 604a-c and layers 502a-c. Rather, a single layer in the print head 500 may be modeled by multiple circuits, and a single circuit may model multiple layers in the print head
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500.The receiver medium 522 is modeled by a plurality of RC circuit networks 608a-f. The circuit network 608c coupled directly to node 606 models the portion of the medium 522 directly below the print head element. Adjacent ones of the circuit networks 608a-f model adjacent portions of the receiver medium 522 in the direction covered by the print head 500 in successive print cycles.
[0051] The circuit 600 illustrated in FIG. 6 approximates the continuous motion of the print head 500 over the receiving medium 522 as discrete steps taken by the head 500 during a line time (print cycle) in the direction indicated by arrow 612. Referring again to FIG. 5, note that the printer 530 may include a second temperature sensor 532 for sensing the ambient printer temperature Tr inside of the printer 530. When the head 500 move's over a fresh region of the medium 522 at the start of a line, the initial temperature of the new region Tm is very close to the ambient temperature Tr
measured by the temperature sensor 532. Although
circuit networks 608a-f include cross-network resistors
(such as resistor 610) to model lateral heat diffusion within the medium 522, such resistors are not taken into consideration in the present analysis because it is assumed that within the short print cycle there is little heat diffusion occurring in the printing direction within the medium 522. Such resistors could be taken into account however, if it were desired to consider the effects of this heat diffusion within the medium 522.
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[0052] As heat starts to flow from the head 500 to the medium 522, the media temperature Tm begins to
rise. The rate of heat flow will be proportional to the
temperature gradient between, the head 500 and the media
522. The final media temperature Tm will depend on the
line time At and the time constant of the media 522
given by RmCm. For short line times, the media temperature Tm can be approximated 'by Equation 3:
'Tm"Tr +Am(Th,-Tr)
Equation 3
[0053] Am in Equation 3 is given by Equation 4:

Equation 4
[0054] Plugging Equation 3 into Equation 2, we
obtain Equation 5:
E = G’(d) + S’ (d)Tr (1-Am + S'(d)AmTh
Equation 5
[0055] ' Comparing Equation 1 and Equation 5, we obtain Equation 6 and Equation 7:
G(d,Tr)=G’(d)+S’(d)(1-Am)Tr
Equation 6
S(d)=S’(d)Am
Equation 7
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[0056] Note that in Equation 6 the implicit dependence of the original G(•) function on Tr has been
made explicit.
[0057] For example, referring to FIG. 4, one embodiment of the inverse media density model 206 (FIG. 2) is now described in more detail. The inverse media density' model 206 receives as inputs during each time interval m (1) the source image densities ds(n) 100, (2)
Th(n) 204, the predicted temperatures of the thermal
print head elements at the beginning of time interval n; and Tr{n), the ambient printer temperature at the beginning of time interval n. The inverse media density model 206 produces as an output the input energy E(n) 106- In other words, the transfer function defined by the inverse media density model 206 shown in FIG. 4 is a three-dimensional function E — F{d,Th,Tr).
[0058] It may be seen from FIG. 4 that the inverse media density model 206 illustrated in FIG. 4 implements Equation 5. For example, the model 206 includes a function G'(.) 424 and a function S"(•) 416. A first multiplier 430 multiplies S'(-) 416, Tr(n) 426, and (l-Am) to produce the second term in Equation 5. A second-multiplier 432 multiplies S'(.) 416, Am-Am 426, and Th{n) 204 to produce the third term in Equation 5. An adder 434 adds G(•) to the outputs of the first and second multipliers 430 and 432 to produce the input energy,E{n) 106.
[0059] Referring, to FIG. 7A, a flowchart is shown of a method 700 that is performed by the inverse
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printer model 102 in one embodiment of the present invention to produce the input energy 106 to provide tc the thermal printer 108 to produce the printed image ; 110. The method 700 enters a loop over each pixel P in the source image 100 (step 702). The method 700 identifies the temperature Th of the print head element that is to print pixel P (step 704) . The temperature Th may, for example, be predicted using the techniques disclosed in the above-referenced patent application or using techniques disclosed herein.
[0060] The method 700 identifies the ambient printer temperature Tr (step 706). The ambient printer temperature Tr may, for example, be identified by measurement using the temperature sensor 532.
[0061] The method 700 identifies the temperature TM of the region of the print medium 522 in which pixel P is to ibe printed (step 708) . The temperature Tm may, for example, be estimated using Equation 3.
[0062] The method 700 identifies the density ds
of pixel P (step 710). The method 700 identifies the
input energy E required to print pixel P based on the identified print head element temperature Thr ambient printer temperature Tr, media region temperature Tmr and
density ds (step 712) . The energy E may, for example, be identified using Equation 5. The method 700 provides energy E to the appropriate print head element, thereby causing pixel P to be printed (step 714). The method 700 repeats steps 704-714 for the remaining pixels P in the source image 100 (step 716), thereby printing the remainder of the source image 100.
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WO 2005/105457 PCT/US2005/013324
[0063] Note, that step 708 (identification of the media temperature Tm) need not be performed as a separate
step in the method 700. For example, if Tm is estimated
i using Equation 3, then identification of Tm is performed
implicitly in step 712 based on Th and Tr.
[0064] The method 700 illustrated in FIG. 7A, may be implemented in a variety of ways. For example, referring to FIG. 7B, a flowchart is shown of a method
720 that is used in one embodiment of the present
invention to implement the method 700 of FIG. 7A. The method 720 includes the same steps 702-706 as the method 700 illustrated in FIG. 7B. The method 720, however, identifies the media temperature Tm for each pixel P by computing the value of Tm using Equation 3 (step 722) . The method 720 identifies the density ds of pixel P (step 710) and computes the required energy E by substituting the computed value of Tm into Equation 2. One advantage of the method 720 illustrated in FIG. 7B is that, by computing media temperature Tm for each pixel P, changes in the ambient printer temperature Tr may be taken into account'on a line-by-line basis.
[0065] Taking changes in the ambient printer temperature Tr into account on a line-by-line basis, however, may not provide a significant benefit, since the ambient printer, temperature Tr will typically have a long time constant. Referring to FIG. 7C, a flowchart is shown of another method 730 that is used in one embodiment of the present invention to implement the method 700 of FIG. 7A with increased computational efficiency by eliminating the ability to take ambient
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printer temperature changes into account 'during a print job.
[0066] The method 730 precomputes the functions G(.) and S(.) using Equation 6 and Equation 7 prior to calculating the individual pixel energies (step 732). If the ambient printer temperature Tr is not expected to change appreciably during printing, the use of a single value of Tr in the precompirtation performed in step 732 will not have an appreciable effect on the output produced in the remainder of the method 730.
[0067] The method 730 enters a loop over each pixel P in the source image 100 (step 702) and identifies the temperature Th of the corresponding print head element (step 704). The method 730 identifies the density ds of pixel P (step 710) . The method 730 may omit steps 706 and 708 (FIG. 7A), because the effect produced by such steps is achieved by the precomputation performed in step 732.
[0068] Having precomputed the functions G(.) and S(•) ; the method 730 identifies the input energy E using Equation 1, which only requires the density ds and the

print

head temperature Th as inputs (step 734), thereby

implemen ting step 712 of the method 700 shown in FIG. 7A. It may be appreciated that Equation 1, which requires only two table lookups, a single addition, and a single multiplication, may be computed more efficiently than the combination of Equation 2 and Equation 3 used in the method 720 of FIG. 7B.
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[0069] The method 730 provides the energy E to the print head element (step 714) and repeats steps 704, 710, 734, and 714 for the remaining pixels P {step 716).
[0070] Referring to FIG. 7D, a flowchart is shown of a method 740 that is used in another embodiment of the present invention to implement the method 700 illustrated' in FIG. 7A. The method 740 retains the ability to take ambient temperature into account, but with greater computational efficiency than the method 720 illustrated in FIG. ,7B. Let Trc be the ambient temperature at which the inverse media density model 206 is calibrated. Let ft -(l-Am)/Am . Using Equation 5, Equation 6, and Equation 7, we obtain Equation 8:
s = G'(d)+s'(d)(1-Am)Trc + s'(d)(1-Am)(Tr -Trc)+S'(d)AmTh
= G(d,Trc) + S(d)(Th+ftDTr)
Equation 8
[0071] In Equation 8, DTr=Tr-Trc. In other
words. Equation 8 allows ambient temperature changes to
be taken into account when computing the input energy E

by using a correction, term DThr added to the print head
i element temperature Th[ based on the difference between
the current ambient printer temperature Tr and the calibration temperature Trc. The correction term DTh is given by Equation 9.
Wh=f, DTr Equation 9

WO 2005/105457 PCT/US2005/013324
[0072] Referring to FIG. 7D, in one embodiment of the present invention lookup tables are precomputed for the functions G(;,Trc) and S(.) (step 742). The method
740 enters a loop over each pixel P in the source image 100 (step 702), identifies the temperature Th of the print head element (step 704), identifies the ambient printer temperature Tr (step 706), and identifies the density ds of the pixel P (step 710). Equation 9 is used to compute the value of the correction term DTh for
pixel ,P (step 744). The method 740 uses Equation 8 to compute the input energy E by adding the computed correction term DTh to the absolute temperature Th and by
using the lookup tables to obtain values for G(d,Trc) and S(d) (step 74 6). The method 740 provides the input energy E to the print head element (step 714) and repeats steps 704, 710, 744, 746, ,and 714 for the remaining pixels in the source image 100 (step 716).
[0073] The addition of the correction term DTh
to the print head element temperature Th in step 746 may, however, be eliminated by recognizing that the computation of the absolute temperatures Th by the thermal history control algorithm includes adding the relative temperatures of all the layers of the print head 500 to the thermistor reading obtained (by temperature sensor 512) at the coarsest layer, as described in more detail in the above-referenced patent application entitled "Thermal Response Correction System." Consequently, ,if the correction term DTh is
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added to the thermistor reading Ts, the correction term AT}, is effectively propagated to every pixel by the
thermal history coitrol algorithm computation of the absolute print head elenent temperature Th. Recall that Ts denotes the temperatire recorded by the thermistor
512. Then, a modified thermistor temperature T's is given by Equation 10:
T;=Ts+f, DTr
Equation 10
[0074] The modified thermistor temperature T's
may then be used to compute the predicted print head element temperatures Th using the techniques disclosed in the above-referenced patent application, and thereby eliminating the need to add the correction term DTh for
each pixel in the computation of the input energy E.
[0075] More specifically, referring to FIG. 7E, a flowchart is shown of a method 750 that is used in' one embodiment of the present invention to perform the same function as the method 740 shown in FIG. 7D, but without the addition performed in step 746. The method 750 precomputes lookup tables for the functions G(-,Trc) .and S(.) (step 742), as described above with respect to FIG. 7D. The method 750 enters a loop over each block B of pixels in the source image 100 (step 751). A block of pixels may, for example, be a subset of the source image 100 or the entire source image 100.
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[0076] The method 750 identifies the ambient printer temperature Tr (step 706). The method 750 computes the modified print head temperature T's based on
the current ambient printer temperature Tr and the calibration ambient printer temperature Txc using Equation 10 (step 752).
[0077] The method 750 enters a loop over each pixel P in the block B (step 702), as described above with respect to FIG. 7A. The method 750 identifies the temperature Th of the print head element that is to print pixel P (step 704), identifies the ambient printer temperature Tr (step 706), and identifies the density ds of pixel P (step 710). Step 708 (FIG. 7A) need not be performed because the media temperature Tm was taken into account implicitly in step 752.
[0078] The method 750 computes the input energy E using Equation 11 (step 754). Note that Equation 11 results from removing the correction term DTh from
Equation 10 because DTh was taken into account in the1 computation of the modified print head temperature T's in step 752.,
E = G(d,Trc) + S(d)Th
Equation 11
[0079] The method 750 provides the input energy E to the print head element (step 714) and repeats steps
704, 710, 754, and 714 for the remaining pixels in the
source image 100 (step 7,16). The method 750 repeats the
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steps described above for the remaining blocks in the source image 100 (step 755).
[0080] One advantage of the method 750
illustrated in FIG. 7E is that it has negligible
overhead in terms of run-time computation, since
calculating Equation 11 requires only two table lookups, one addition, and one multiplication, which is no more computationally intensive than Equation 1. Furthermore, the method 750 has the ability to take into account changes in the ambient printer temperature Tr during a long print job, if required. Such changes are reflected
in the print head element temperatures Th identified in
step 704.
[0081] Changes in humidity may affect the densities in the printed image 110 produced by the thermal printer 108 (FIG. 1) . The effects of humidity variation on the printed density, however, may be difficult to represent if humidity alters the media model 206 in such a complex manner that it cannot be accommodated by the structure imposed in Equation 2. As may be seen from the discussion above, the media model 206 may easily be used to account for any variations in the ambient printer-temperature Tr In -one - embodiment-of the present invention, the effect of humidity is taken into account by translating it into an equivalent . temperature variation.
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[0082] Using the techniques described in U.S. Patent'No. 6,537,410, entitled "Thermal Transfer Recording System," printing may be achieved by melting the thermal solvent in the donor layer that in turn dissolves the dye. The dissolved dye is then drawn into the receiver by capillary action. Ideally, the thermal solvent melts at a fixed temperature. The presence of impurities in the media, however, may influence the melting temperature. We hypothesize that the moisture in the, air is absorbed by the donor layer and lowers the melting point of the thermal solvent. The amount of moisture absorbed by the donor layer is driven by the ambient relative humidity. Therefore, in one embodiment of the present invention a temperature correction is applied that is proportional to the change in relative humidity.
['0083] Let ARH denote the difference between the current relative humidity and the relative humidity for which the media model 206 was calibrated. Equation 10, which calculates the modified print head temperature measurement TS, may be modified to take into account the humidity effect as shown in Equation 12.

Equation 12

[0084] In Equation 12, fh(.) denotes the
proportionality constant that converts the relative humidity change ARH into an equivalent temperature change. We have experimentally observed that humidity
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has a larger effect at higher ambient temperatures. The dependence of fh(•) on Tr is meant to reproduce this change in sensitivity to humidity with temperature.
[0085] Note that Equation 12 shows a particular form of the correction term that is added to the print
head temperature Ts . In general, this correction term

may be written as a two-dimensional function f(Tr, DRH), where the functional dependence of the correction term on Tr and DRH takes a different form than that shown in Equation 12. The value of this function at a particular ambient printer temperature and relative humidity may be found experimentally by determining the modified print head temperature that results in a printed image most similar to the image printed under the reference ambient
conditions. Experimental procedures can also be used to
determine the values of ft and fh(.).
[0086] Referring to FIG. 7F, a flowchart is shown of a method 760 that is used in one embodiment of the present invention to perform the same function as the method 750 shown in FIG. 7E, except that the method 760 shown in FIG. 7F additionally takes changes in relative. humidity into account. The method 7 60
precomputes lookup tables for the functions G(,Trc) and S(.) (step 742), as described above with respect to FIG.
7D. The method 760 enters a loop over each block B of
i
pixels in the source image 100 (step 751). The method 760 identifies the ambient printer temperature Tr (step 706) .
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[0087] The method 7 60 computes the modified print head temperature Ts based on the current ambient printer temperature Tr, the calibration ambient printer temperature Trcr and the change in relative humidity DRH using Equation 12 (step 762). The remainder of the method 760 performs steps 702, 704, 710, 754, 714, 716, and 755 in the same manner as described above with respect to FIG. 7E, except that the input energy E calculated in step 754 in FIG. 7F effectively takes the effects of humidity into account because the modified .
print head temperature TS' produced in step 762 reflects the effects of humidity, and because the modified print
head temperature Ts in turn influences the print' head
element temperatures Th identified in step 704 for the
reasons described above.
[0088] An alternative hypothesis is that the
glass transition temperature Tg of the dye layer changes
as a function of relative humidity. The rate at which the dye is drawn into the receiver is a function of the viscosity, which in turn1 is a function of Tg . Based on
these premises, one may develop a formula for calculating—the-equiva-len-t—change in- temperature-that—is again proportional to relative humidity, and in which the proportionality constant has a quadratic dependence on the ambient temperature. Note that the form of the humidity correction term to the thermistor temperature given in Equation 12 accommodates this hypothesis as well.
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[0089] The techniques disclosed herein have a variety of advantages. As described above, ambient temperature changes that occur after the thermal history control algorithm has been calibrated can cause the printer to produce suboptimal output if such changes are not taken into account. By taking ambient temperature change's into account explicitly when computing the input energies to provide to a printer to print an image, the technigues disclosed herein compensate for such
temperature changes, thereby improving the quality of

the printed output.
[0090] Similarly, as described above, changes in humidity that occur after the thermal history control
algorithm has been calibrated can cause the printer to
i
produce suboptimal output if such changes are not taken into account. By taking humidity changes into account explicitly when computing the input energies to provide to a printer to print an image, the techniques disclosed herein compensate for such temperature changes, thereby improving the quality of the printed output.
[0091] Furthermore, the techniques disclosed herein ;have the advantages disclosed in the above-referenced patent application entitled "Thermal History Control." For example, the techniques disclosed herein reduce or eliminate the problem of "density drift" by taking ithe current ambient temperature of the print head and the thermal and energy histories of the print head into account when computing the energy to be provided to the print head elements, thereby raising the temperatures of the print head elements only-to the
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WO 2005/105457 PCT/US2005/013324
temperatures necessary to produce the desired densities.
A further advantage of various embodiments of the
present invention is that they may either increase or
decrease the input energy provided to the print head elements, as may be necessary or desirable to produce the desired densities.
[0092] Another advantage of various embodiments of the present invention is that they compute the energies to be provided to the print head elements in a computationally efficient manner. For example, as
described above, in one embodiment of the present
i
invention, the input energy is computed using two one-dimensional functions (G(d) and S(d)), thereby enabling the input energy to be computed more efficiently than with the single four-dimensional function F(d,Th,Tr, DRH).
[0093] It is to be understood that although the
i i
invention has been described above in terms of
particular embodiments, the foregoing embodiments are
provided as illustrative,only, and do not limit ox

define the scope of the invention. Various other embodiments, including but not limited to the following, are also within the scope of the claims.. For example, elements and components described herein may be further
divided into additional components -or joined together to
form fewer components for performing the same functions.
[0094] Although some embodiments may be described herein with respect to thermal transfer printers, it should be appreciated that this is not a limitation of the present invention. Rather, the techniques described above may be applied to printers
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WO 2005/105457 PCTAJS2005/013324
other than thermal transfer printers (e.g. direct
thermal printers). Furthermore, various features of
thermal printers described above are described merely for purposes of example and do not constitute limitations of the present invention.
[0095] It should be appreciated that the results of the various equations shown and described above may be generated in any of a variety of ways. For example, such equations (such as' Equation 1) may be implemented in software and their results calculated on the fly. Alternatively, lookup tables may be pre-generated which store inputs to such equations and their corresponding outputs. Approximations to the equations may also be used to, for example, provide increased computational efficiency. Furthermore, any combination of these or other techniques may be used to implement the equations described above. Therefore, it should be appreciated that use of terms such as "computing" and "calculating" the results of equations in the description above does
not merely refer to on-the-fly calculation but rather
refers to any techniques which may be used to produce
the same results.
[0096] The techniques described above may be
implemented, for example, in hardware, software, firmware,,or any combination thereof. The techniques described above may be implemented in one or more computer programs executing on a programmable computer including a processor, a storage medium readable by the processor (including, for example, volatile and nonvolatile memory and/or storage elements), at least one
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PCT/US2005/013324 WO 2005/105457
input device, and at least one output device. Program cote may be applied to input entered using the input device to perform the functions described and to generate output. The output may be provided to one ox
flvore output devices.
[0097] Each computer program within the scope of the claims below may be implemented in any programming language, such as assembly language, machine language, a high-level procedural programming language, or an object-oriented programming language. The programming language may, for example, be a compiled or interpreted programming language.
[0098] Each such, computer program may be implemented in a computer program product tangibly embodied in a machine-readable storage device for execution by a computer processor. Method steps of the invention may be performed by a computer processor executing a program tangibly embodied on a computer-readable medium to perform functions of the invention by operating on input and generating output. Suitable processors include, by way of example, both general and special purpose microprocessors. Generally, the processor receives instructions and data from a readonly mmory and/or" a random access'memory, "storage" devices suitable for tangibly embodying computer program instructions include, for example, all forms of non-volatile memory, such as semiconductor memory devices, including EPROM, EEPROM, and flash memory devices, magnetic disks such as internal hard disks and removabZe disks; magneto-optical disks; and CD-ROMs. Any of the
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WO 2005/105457 PCT/US2005/013324
foregoing may be supplemented by, or incorporated in, specially-designed ASICs (application-specific integrated circuits) or FPGAs (Field-Programmable Gate Arrays). A computer can generally also receive programs and data from a storage medium such as an internal disk (not shown) or a removable disk. These elements will also be found in a conventional desktop or workstation computer as well as other computers suitable for executing computer programs implementing the methods described herein, which may be used in conjunction with any digital print engine or marking engine, display monitor, or other raster output device capable of producing color or gray scale pixels on paper, film, display screen, or other output medium.
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What is claimed is:
1. A method comprising steps of:
(A) identifying a first print head temperature
Ts of a print head in a printer;
(B) identifying a current ambient temperature
Tr in the printer;
(C) identifying a modified print head
temperature T's based on the first print
head temperature Ts and at least one property selected from the group consisting of the ambient printer temperature Tr and a current relative humidity; and
(D) identifying an input energy to provide to
a print head element in the print head
based on the modified print head
temperature Ts .
2. The method of claim 1, wherein the step (C)
comprises steps of:
(C) (1) identifying a temperature Trc at which the
method was- calibrated; and (C)(2) identifying the modified print head
temperature Ts based on at least- one
value selected from the group consisting of: {a) the difference between the current ambient printer temperature Tr -and the calibration ambient printer
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temperature Trc, and (b) the difference between the current relative humidity and a relative humidity at which the method was calibrated.
3. The method of claim 2, wherein the step (C)(2)
comprises a step of identifying Ts using a formula
selected from the group consisting of:

• wherein Am is a constant, wherein DTr is a difference between the current ambient printer temperature Tr and an ambient printer temperature at which the method was calibrated, wherein DRH comprises a difference between the current relative humidity and a relative humidity at which the method was calibrated, and wherein fb{)comprises a proportionality constant that converts the relative humidity difference DRH into an equivalent temperature difference.
4. A device comprising:
first identification means for identifying a first print head temperature- Ts of a print head in a printer;
second identification means for identifying a current ambient temperature Tr in the printer;
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third identification means for identifying a modified print head temperature Ts based on the first print head temperature Ts and at least one property selected from the group consisting ,of the ambient printer temperature Tr and a current relative humidity; and
fourth identification means for identifying an input energy to provide to a print head element in the print head based on the modified print head temperature
Tr.
5. The device of claim 4, wherein the third
identification means comprises:
fifth identification means for identifying a temperature Tec at which the method was. calibrated; and sixth identification means for identifying the
modified print head temperature Ts based on at least one
value selected from the group consisting of: (a) the difference between the current ambient printer temperature Tr and the calibration,ambient printer temperature Trc, and (b) the difference between the current relative humidity and a relative humidity at which the method was calibrated.
6. The device of claim 5, wherein the sixth
identification means comprises means for identifying Ts'
using a formula selected from the group consisting of:

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WO 2005/105457 PCT/US2005/013324

wherein Am is a constant, wherein DTr is a difference between the current ambient printer temperature Tr and an ambient printer temperature at which the method was calibrated, wherein DRH comprises a. difference between the current relative humidity and a relative humidity at which the method was calibrated, and wherein fh()comprises a proportionality constant that converts the relative humidity difference DRH into an equivalent temperature difference.
7. In a thermal printer including a print head element, a method comprising a step of:
(A) computing an input energy to provide to
the print head element based on a current temperature of the print head element, a plurality of one-dimensional functions of a desired output density to be printed by the print head element, and at least one property selected from the group consisting of an ambient printer, temperature and a current humidity.
8. The method of claim 7, wherein the print head element is one of a plurality of print head elements in a print head, wherein Ts is a current temperature of the print head, wherein DTr is a difference between the
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ambient printer temperature and an ambient temperature at which the method was calibrated, wherein the method further pomprises a step of:
computing a modified current print head temperature
T's is computed according to a formula selected from the group consisting of:

wherein Am is a constant, wherein DRH comprises a difference between the current humidity and a humidity at which the method was calibrated, wherein fh() converts the relative humidity difference DRM into an equivalent temperature difference, and wherein the step (A) comprises a step of identifying the current temperature of the print head based on the modified current print head temperature Ts .
9. The method of claim 8, further comprising a step
of:
(C) performing step (A) for each pixel in a subset of pixels in a source image.
10. The method of claim 9, wherein the subset
comprises the entire source image.
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11,. The method of claim 9, further comprising a step of:
(D) repeating step (B) for each of a plurality of subsets of the source image.
12,. Tne method of claim 7, wherein the step (A) comprises a step of computing an input energy to provide to the print head element based on a temperature of an output medium, the current temperature of the print head element, the ambient printer temperature, and the
plurality of one-dimensional functions.

13. The method of claim 12, wherein Tr is the
ambient printer temperature, Th is the current
temperature of the. print head element, and wherein the
step (A) comprises steps of:
(A)(1) calculating the output medium temperature Tm as Tnr-Tx+Am(Th-Tr) , wherein Am is a constant; and
(A) (2) computing the input energy E as
E=G' (d)+S' (d)Tm, wherein G' (d) and S' (d)' comprise two of the plurality of one-dimensional functions.

14. The method of claim 7, wherein G' (d) and S' (d)
comprise two of the plurality of one-dimensional functions, and wherein the method further comprises steps of:
(B) prior to the step (A), precomputing values
for functions G(d,Tr) and S(d) using the
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formulas G(d,Tr) = G'(d) + S'(d)(1-Am)Tr and
S(d) = S'(d)Amr wherein d represents density, wherein Tr represents the ambient printer temperature, and wherein Am is a constant; (C) for each of a plurality of pixels P in a source image, performing step (A) using the precomputed functions G(d, Tr) and S(d).
15. The method of claim 14, wherein the step (C)
comprises performing, for each of the plurality of pixels P in the source image, a step of computing the input energy E as E=G{d, Tz)+S(d) Th, wherein Th comprises the temperature of the print head element.
16. The method of claim 7, wherein the print head
element1 is one of a plurality of print he'ad elements in
a print head, wherein Trc is an ambient printer
temperature at which the method was calibrated, wherein
DTr is a difference between Trc and the current ambient
printer temperature, wherein a modified print head
element temperature Th is computed according to a formula selected from the group consisting of:'

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wherein Am is a constant, wherein DRH comprises a difference between the current humidity and a humidity at which the method was calibrated, wherein fh() converts the relative humidity difference DRH into an equivalent temperature difference, and wherein the step (A) comprises a step of computing the input energy based on
the modified print head element temperature T'h .
17. The method of claim 7, further comprising a
step of:
(B) providing the input energy'to the print head element.
18. The method of claim 7, wherein the current
temperature of the print head element comprises a
predicted current temperature of the print head element.
19. The method of claim 18, wherein the predicted
temperature is predicted based on an ambient print head
temperature and an energy previously provided to the
print head element.
20. The method of claim 7, wherein, the, thermal,
printer includes a plurality of print head elements, and
wherein the predicted temperature is predicted based on
a print head temperature, an energy previously provided
to the print head element, and an energy previously
provided to at least one other print head element in the
plurality of print head elements.
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21. A printer comprising;
a print head element; and:
first computation means for computing an input energy to provide to the print head element based on a current temperature of the print head element, a plurality of one-dimensional functions of a desired output density to be printed by the print head element, and at least one property selected from the group consisting of an ambient printer temperature and a current humidity.
22. The device of claim 21, wherein the print head
element is one of a plurality of print head elements in
a print head, wherein Ts is a current temperature of the
print head, wherein DTr is a difference between the
ambient printer temperature and an ambient temperature
at which the method was calibrated, wherein the device
further comprises:
second computation means for computing a modified
current print head temperature Ts' is computed according to a formula selected from the group consisting of:

wherein Am is a constant, wherein DRH comprises a difference between the current humidity and a humidity
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at which the method was calibrated, wherein fh() converts the relative humidity difference DRH into an equivalent temperature difference, and wherein the first computation means comprises means for identifying the current temperature of the print head based on the
modified current print head temperature Ts .
23. The device of claim 22, further comprising:
means for applying the first computation means to
each pixel in a subset of pixels in a source image.
24. The device of claim 23, wherein the subset
comprises the entire source image.
25. The device of claim 23, further comprising: means for applying the second computation means to each of a plurality of subsets of the source image.
26. The device of claim 21, wherein the first
computation means comprises means for computing an input
energy to provide to the print head element based on a
temperature of an output medium, the current temperature
of__the__print head element, the ambient printer
temperature, and the plurality of one-dimensional
functions.
27. The device of claim 26, wherein Tr is the
ambient printer temperature, Th, is the current
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temperature of the print head element, and wherein the first computation means comprises:
means for calculating the output medium temperature Tm as Tm=Tr+Am{Th-Tr), wherein Am is a constant; and
means for computing the input energy E as E=G' (d)+Sr (d) Tm' wherein G' (d) and S' (d) comprise two of the plurality of one-dimensional functions.,
28. The device of claim 21, wherein G' (d) and S' (d)
comprise two of the plurality of one-dimensional
functions, and wherein the device further comprises:;
means for precomputing, prior to the step (A), values for functions G(d,Tx) and S{d) using the formulas G(d,Tr) = G'(d) + S'(d)(1-Am)Tr and S(d) = S' (d)Am, wherein d
represents density, wherein Tr represents the ambient printer temperature, and wherein Am is a constant;
means, for each of a plurality of pixels P in a source;image, for applying the first computation means using the precomputed functions G(d,Tr) and S{d) .
29. The device of claim 28, wherein the means for
precomputing comprises means for performing, for. each of
the plurality of pixels ,P in the source image, a step of
computing the input energy E as E=G(dr Tr) +S(d) Th' wherein
Th comprises the temperature of the print head element.
30. The device of claim 21, wherein the print head
element is one of a plurality of print head elements in
a print head, wherein Trc is an ambient printer
temperature at which the method was calibrated, wherein
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WO 2005/105457 PCT/US2005/013324
DTr is a difference between Trc and the current ambient printer temperature, wherein a modified print head
element temperature Th is computed according to a formula selected from the group consisting of:

wherein Am is a constant, wherein DRH comprises a difference between the current humidity and a humidity at which the method was calibrated, wherein fh() converts the relative humidity difference DRH into an equivalent temperature difference, and wherein the first computation means comprises means for computing the input energy based on the modified print head element
temperature Th
31. The device of claim 21, further comprising:-
means for providing the input energy to the print
head element.
32. The device of claim 21, wherein the current
temperature of the print,head element comprises a
predicted current temperature of the print head element.
33. The device of claim 32, wherein the predicted
temperature is predicted based on an ambient print head
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WO 2005/105457 PCT/US2005/013324
temperature and an energy previously provided to the print head element.
340. The device of claim 31, wherein the thermal printer includes a plurality of print head elements, and wherein the predicted temperature is predicted based on a print head temperature, an energy previously provided to the' print head element, and an energy previously provided to at least one other print head element in the plurality of print head elements.
35". In a thermal printer having a print head including a plurality of print head elements, a method
for developing, for each of a plurality of print head cycles, a plurality of input energies to be provided to the plurality of print head elements during the print head cycle to produce a plurality of output densities, the method comprising steps of:
(A) using a multi-resolution heat propagation model to develop, for each of the plurality of print head cycles, a plurality of predicted temperatures of the plurality of print head elements at the beginning of the print head cycle; and
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WO 2005/105457 PCT/US2005/013324
(B) using an inverse media model to develop the plurality of input energies based on the plurality of predicted temperatures, a plurality of densities to be output by the plurality of print head elements during the print head cycle, and at least one property selected from the group consisting of at least one ambient printer temperature and at least one humidity.
36. The method of claim 35, wherein the step (A)
comprises a step of developing the plurality of
predicted temperatures based on a print head temperature
and a plurality of input energies provided to the
plurality of print head elements during at least one
previous print head cycle.
37. The method of claim 35, wherein the step (A)
comprises a step of developing the plurality of
predicted temperatures based on a plurality of previous
predicted temperatures for the plurality of print head elements.
38. The method of claim 35, wherein the step (A)
comprises a step of developing, for each of the plurality of print head elements, a predicted temperature based on a predicted temperature of at least one of the other print head elements at the beginning of at least one previous print head cycle.
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WO 2005/105457 PCT/US2005/013324
39. The method of claim 35, wherein the steps (A)
and (B) are performed during a single print head cycle
of the thermal printer.
40. A thermal printer comprising:
a, print head including a plurality of print head elements;
means for developing, for each of a plurality of print head cycles, a plurality of input energies to be provided to the plurality of print head elements during the print head cycle to produce a plurality of output densities, the means for developing comprising:
temperature prediction means for using a multi-resolution heat propagation model to develop, for each of the plurality of print head cycles, a plurality of predicted temperatures of the plurality of print head elements at the beginning of the print head cycle.; and
energy development means for using an inverse media model to develop the plurality of input energies based on the (plurality of predicted temperatures, a plurality of densities to be output by the plurality of print head elements during the print head cycle, and at least one property selected from the group consisting of at least one ambient printer temperature and at least one humidity.
41. The device of claim 40, wherein the temperature
prediction means comprises means for developing the
plurality of predicted temperatures based on a print
head temperature and a plurality of input energies
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WO 2005/105457 PCT/US2005/013324
provided to the plurality of print head elements during at least one previous print head cycle.
42. The device of claim 40, wherein the temperature
prediction means comprises means for developing the
plurality of predicted temperatures based on a plurality
of previous predicted temperatures for the plurality of
print head elements.
43. The device of claim 40, wherein the temperature
prediction means comprises means for developing, for
each of the plurality of print head elements, a
predicted temperature based on a predicted temperature
of at least one of the other print head elements at the
beginning of at least one previous print head cycle.
44. The device of claim 40, wherein the temperature
prediction means and the energy prediction means are
applied during a single print head cycle of the thermal
printer.
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Documents:

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Patent Number

270590

Indian Patent Application Number

2987/KOLNP/2006

PG Journal Number

02/2016

Publication Date

08-Jan-2016

Grant Date

31-Dec-2015

Date of Filing

16-Oct-2006

Name of Patentee

POLAROID CORPORATION

Applicant Address

1265 MAIN STREET ,WALTHAM, MA 02451, U.S.A.

Inventors:

#	Inventor's Name	Inventor's Address
1	BUSCH BRIAN D	582 PEAKHAM ROAD, SUDBURY,MA 01776, U.S.A.
2	VETTERLING WILLIAM T	35 TURNING MILL ROAD, LEXINGTON, MA 02420 ,U.S.A.
3	SAQUIB SUHAIL S	33 TROWBRIDGE LANE, SHIREWSBURY, MA 01545, U.S.A.

PCT International Classification Number

B41J2/05; B41J2/07

PCT International Application Number

PCT/US2005/013324

PCT International Filing date

2005-04-18

PCT Conventions:

#	PCT Application Number	Date of Convention	Priority Country
1	10/831,925	2004-04-26	U.S.A.