Abstract:
Electric energy to be applied to each heating element of the thermal head is controlled by taking into account the energy applied to the heating element one scan period before as well as the effect of heat accumulated in heating elements surrounding the heating element, and then the energy thus controlled is recorrected taking into consideration the temperature change in a thermal head base plate or the change in printing time between lines.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to the field of thermal heads to be used in thermal printing, and in particular, to a heat accumulation compensation method and improvement of related apparatus wherein compensation for the heat accumulation is performed taking into account the effects of heat accumulation in adjacent heating elements on a heating element currently heating printing medium. 
     2. Description of the Prior Art 
     In a conventional thermal head to be used for the thermal printing, an array of a multiplicity of heating elements are normally arranged in the main scan direction of the thermal printing medium such as a thermal printing paper and an ink donor sheet so as to corresponds to the number of picture elements in one scan line, and colors are caused to develop in the thermal printing medium which is, in slidingly contact with the heating parts of the heating elements, causing relevant heating elements to heat the medium corresponding to the picture image information. 
     In printing with such thermal head, effects of heat accumulation on each heating element varies according to the manner in which the image information is applied. That is, for example, when a heating element has been heated continuously in previous lines, the printing of data in the next line starts while this particular heating element does not become cool completely. On the other hand, when a heating element has not been heated for a long time, the printing of data of the next line starts with the heating element being completely cool. As a result the print density (shade level) varies in the above two cases lowering the quality of the printed picture image. Such phenomenon is particularly remarkable when a high speed printing is performed in which the printing time is less than 10 msec per line. 
     In order to cope with such problem, the prior art controls the width of a pulse (hereinafter called heating pulse) or voltage to be applied to heating elements currently performing printing to energize these elements. For example, when a heating element has been energized in the previous line, the width of a heating pulse is shortened when printing the current line. 
     However, in such prior art heat accumulation compensation system, a heating element is subject to heat accumulation compensation independently from other heating elements and the effect of the heat accumulation for heating elements adjacent to the heating element are not taken into account, making the prior art heat accumulation compensation unsatisfactory. Particularly, in the thermal printing of the transferring type which uses ink donor sheets as a printing medium, effect from heat accumulation in the adjacent heating elements is increased due to thermal diffusion on the ink donor surface, and favorable printing could not be effected. 
     SUMMARY OF THE INVENTION 
     Accordingly, an object of the present invention is to provide a heat accumulation compensation methods and devices for thermal heads capable of obtaining a good printing quality free of the shade level variation by controlling energy to be applied to each heating element while taking into account the effect of the heat accumulation in heating elements adjacent on each heating element. 
     According to the present invention, the energy to be applied to a heating element is controlled by taking into account the energy applied to the heating element one scan period before as well as the effect of heat accumulated in heating elements surrounding the heating element, and then the energy thus controlled is recorrected taking into consideration the temperature change in a thermal head base plate or the change in printing time between lines. 
     According to the first aspect of the present invention, there are provided a first step for calculating the heat accumulation state of each heating element and its adjacent elements based on the present and past image information of these heating elements, a second step for correcting the energy applied to said each heating element in printing the immediately preceding line based on the heat accumulation state calculated in the first step, and a third step for controlling the energy to be applied to each heating element in printing the present line based on information representing the corrected energy as well as the temperature of the base plate of a thermal head. 
     According to the second aspect of the present invention, there are provided a first step for calculating the heat accumulation state of each heating element by assigning predetermined weight values to the present and past image information of each heating element and heating elements adjacent thereto according to the information representing temperature of the thermal head base plate and the extend of effect of the heat accumulation on the heating element and then totalizing the weighted picture information, and a second step for controlling the energy to be applied to each heating element in printing the present line based on the heat accumulation state calculated in the first step and the information representing the energy applied to each heating element in printing the immediately preceding line. 
     In the first and second aspects, the information representing temperature of the thermal head base plate is typically calculated based on the resistance value of a thermistor normally provided in the thermal head. 
     Further, according to the third aspect of the present invention, there are provided a first step for calculating the heat accumulation state of a heating element based on the present and past image information of each heating element and heating element adjacent thereto, a second step for correcting the energy to be applied to the heating element in printing the immediately preceding line based on the interval time information representing the time required from the start of printing the immediately preceding line to the start of printing the present line, and a third step for controlling the energy to be applied to each heating element in printing the present line based on the heat accumulation state calculated in the first step. 
     Further, according to the fourth aspect of the present invention, there are provided a first step for calculating heat accumulation state of each heating element by assigning predetermined weight values to the present and past images information of each heating element and heating elements adjacent thereto according to the interval time information representing the time required from the start of printing the preceding line to the start of printing the present line and the extent of effect that the heat accumulation has on the heating element and by totalizing these weighted image information, and a second step for controlling the energy to be applied to each heating element in printing the present line based on the heat accumulation state of each heating element calculated in the first step and the information representing the energy applied to each heating element in printing the immediately preceding line. 
     In the aforementioned first through fourth aspects, the control of the energy applied to the heating elements is typically performed by correcting the pulse width of the heating pulse or voltage to be applied to each heating element of the thermal head. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
     FIG. 1 illustrates the arrangement of picture element on an original to be printed; 
     FIG. 2 is a graph for the calculation of heat history information Xi; 
     FIG. 3 is a graph showing the relationship between the heat history information Xi and the corrected pulse width T&#39;i with the heating pulse width Ti-1 of the immediately preceding line as a parameter; 
     FIG. 4 is a graph showing the relationship between base plate temperature t and thermistor resistance value R; 
     FIG. 5 is a graph showing the relationships shown in FIG. 3 through FIG. 5 collectively; 
     FIG. 7 is a block diagram showing a typical configuration of the apparatus embodying the first aspect of the present invention; 
     FIG. 8 is a block diagram showing a typical configuration of the Xi operator. 
     FIG. 9 is a circuit diagram showing circuitry of a thermal head; 
     FIG. 10 is a time chart illustrating the operation of the circuitry in FIG. 9; 
     FIG. 11 is a block diagram showing a typical configuration of an apparatus embodying the second aspect of the present invention; 
     FIG. 12 is a graph showing the relationship between the heat history information Xi and the corrected pulse width Ti with the heating pulse width Ti-1 of the immediately preceding line and the false pulse width Ti-1&#39; as parameters; 
     FIG. 13 is a graph showing the relationship between the printing pulse width Ti-1 of the immediately preceding line and the false pulse width Fi-1 with the interval time Ii as a parameter; 
     FIG. 14 is a graph showing the relationship of FIG. 13 by another aspect; 
     FIG. 15 is a block diagram showing a typical configuration of an apparatus embodying the third aspect of the present invention; 
     FIG. 16 is a graph for calculating the heat accumulation state information Zi; 
     FIG. 17 is a graph showing the relationship between the heat accumulation state information Zi and the corrected pulse width T&#39;i with the heating pulse width Ti-1 of the immediately preceding line as a parameter; 
     FIG. 18 is a block diagram showing a typical configuration of an apparatus embodying the fourth aspect of the present invention; and 
     FIG. 19 is a block diagram showing a configuration of a Zi operator in the apparatus of FIG. 18. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring to FIG. 1 through FIG. 10, the first embodiment of the present invention will be described. 
     In this first embodiment, the pulse width Ti to be applied to each heating element of the thermal head is determined based on the following formula. 
     
         Ti=f (Xi, Ti-1, Ki)                                        (1) 
    
     where Xi is heat history information, Ti-1 is information representing the pulse width applied to the heating element in the preceding line, and Ki is information representing temperature of the base plate of a thermal head. The heating pulse width Ti of a pulse to be applied to the heating element in the present line is determined as a function of these information Xi, Ti-1, and Ki. During a period when printing is not performed, it is not the pulse widths Ti-1 and Ti but the voltage to be applied to the heating element which is brought to 0. 
     First, the heat history information Xi will be explained. 
     FIG. 1 shows the arrangement of picture elements on an original to be printed. A line I is a scan line currently being printed, a line II is a line printed immediately before, and a line III is a line printed immediately before the line II was printed. 
     The heat accumulation state of a picture element D is determined based on whether picture elements D1 through D6 are black or white. Weight values as shown in Table are assigned to these picture elements D1 through D6 according to the extent of heat accumulation effect which causes effect on the picture element D. 
     
                       TABLE 1______________________________________Picture element          Weight value______________________________________D1             70D2             70D3             100D4             17D5             17D6             40______________________________________ 
    
     Table 2 shows an example of sum Yi of the weight values considering the fact whether or not a picture element is black or white. In Table 2, &#34;1&#34; signifies that the picture element is black and &#34;0&#34; signifies that the element is white. 
     
                       TABLE 2______________________________________ Picture   Exampleelement (a)   (b)       (c)   (d)           (e)______________________________________D1      0     0         1     1       . . .                                      1D2      0     0         0     1       . . .                                      1D3      0     1         1     1       . . .                                      1D4      0     0         1     0       . . .                                      1D5      0     1         0     0       . . .                                      1D6      0     0         0     0       . . .                                      1Yi      0     117       187   240     . . .                                      314Xi      0     3         5     6       . . .                                      7______________________________________ 
    
     Referring to Table 2, in column, for example, (c), when the picture elements D1, D3 and D4, are black and other elements are white Yi is 187. This Yi is converted to an eight level heat history information Xi from &#34;0&#34; to &#34;7&#34; based on the relation shown in the graph of FIG. 2. In FIG. 2, Yi is plotted in abscissa and Xi in ordinate. At the bottom of Table 2, values of Xi are shown. For example, in the case of (c), Yi is 187 and Xi is 5. FIG. 3 shows the heating pulse width Ti-1 of the preceding line which is corrected based on the heat history information Xi. The upper limit value 1.2 of the corrected pulse width T&#39;i(msec) of FIG. 3 is a pulse width to be applied to a heating element which can perform a good printing when previous picture elements are white in succession. For example, when the heat history information Xi is 3 and Ti-1 is 0.6 msec, the corrected pulse width T&#39;i becomes 0.5 msec, while when Xi is 4 and Ti-1 is 1.0 msec, T&#39;i becomes 0.8 msec. 
     Now, the information Ki representing the base plate temperature of thermal head will be explained. 
     The thermal head base plate temperature t is continuously detected by a thermistor mounted on the base plate. FIG. 4 shows the relationship between resistance value R of the thermistor and the base plate temperature t. As seen in this drawing, the thermistor resistance value R and the base plate temperature t are approximately in a proportional relationship. The base plate temperature t can be known by detecting the thermistor resistance value R. The information Ki corresponds to the thermistor resistance value R. FIG. 5 shows the relation when the corrected pulse width T&#39;i is further corrected in accordance with the thermistor resistance vlaue R, in which ΔT&#39;i represents a value to be added to or reduced from the corrected pulse width T&#39;i. In FIG. 4 and FIG. 5, when the base plate temperature t is, for example, 34° C., the thermistor resistance value R is 20 KΩ, and ΔT&#39;i at this time is 0 msec. On the other hand, when the base plate temperature t is 18° C., the thermistor resistance value R becomes 40 KΩ, and ΔT&#39;i at this time is +0.2 msec. 
     Although the thermistor is typically mounted on the rear side of the base plate, it may be designed such that a single thermistor is provided on a single thermal head base plate or a plurality of thermistors are provided at various points of a single thermal head base plate, the resistance values of those thermistors being averaged and the thermal head base plate temperature t being obtained based on the average value. Further, when a fine control is required, it may be designed such that the thermal head base plate is divided to a plurality of areas with a single thermistor being provided in each area, and for the heating elements in each area the heat accumulation compensation is performed based on the resistance value of the thermistor in the corresponding area. 
     FIG. 6 is a graph in which the relationships shown in FIG. 3 through FIG. 5 are combined. According to the relation in FIG. 6, when the heat history information Xi is 4 and the pulse width Ti-1 of the preceding line is 0.8 msec, T&#39;i becomes 0.6 msec, and further when the thermistor resistance value R at this time is 40 kΩ, the heating pulse width Ti of the present time for this heating element becomes 0.8 msec. Still further, when the heat history information Xi is 6 and the pulse width Ti-1 of the preceding line is 1.2 msec, T&#39;i becomes 0.8 msec, and if the thermistor resistance value R at this time is 10 kΩ, the pulse width Ti of the present time becomes 0.6 msec. 
     FIG. 7 shows a typical configuration of a heat accumulation compensation circuit 10 designed based on the heat accumulation compensation method of the first embodiment given above. 
     Referring to FIG. 7, the heat accumulation compensation circuit 10 comprises a first line buffer 20, a second line buffer 21 and a third line buffer 22 each having memory areas corresponding to the total number of heating elements of the thermal head. The first line buffer 20 stores picture information corresponding to the scan line to be printed at the present time, the second line buffer 21 stores picture information corresponding to the scan line printed at the time immediately before, and the third line buffer 22 stores picture information corresponding to the scan line printed at the time before the last. An Xi operator 30 sequentially calculates the heat history information Xi of each heating element of the line to be printed at present based on the picture information stored in the line buffers 20, 21 and 22, and outputs the results of calculation to a Ti operator 60 sequentially. As shown in FIG. 8, the Xi operator 30 includes a weight assigning circuit 31 and a Yi/Xi converter 32. The weight assigning circuit 31 assigns the weight value shown in Table 1 to each picture information (refer to FIG. 1) to be fed 6 bits by 6 bits for a one-dot heating element, sums up these 6 bits, and outputs the result Yi of the summation to the Yi/Xi converter 32. The Yi/Xi converter 32 converts Yi fed sequentially into the heat history information Xi of 8 levels from &#34;0&#34; to &#34;7&#34; based typically on the relation shown in the graph of FIG. 2, and outputs the heat history information Xi to the Ti operator 60 sequentially. These weight assigning circuit 31 and the Yi/Xi converter 32 may be comprised of memory means, arithmetic circuit, etc. 
     A Ki operator 40 is connected to a thermistor (not shown) mounted on the base plate of the thermal head, and the information representing the thermistor resistance value R corresponding to the base plate temperature t in that particular instant is fed constantly from the thermistor. The Ki operator 40 converts this information to a multilevel signal of several levels, typically stepping at every 10 kΩ as shown in FIG. 5, and outputs the signal to the Ti operator 60. A memory 50 is for storing the information representing the heating pulse width of each dot calculated by the Ti operator 60, and the memory content of the memory 50 is updated as the scan line to be printed advances. Accordingly, Ti-1 outputted from the memory 50 and fed back to the Ti operator 60 becomes the information showing the heating pulse width of the previous scan line for the Ti operator 60. 
     The Ti operator 60 calculates the heating pulse width Ti to be applied to each heating element based on the information Xi, Ki, and Ti-1 from, say, the relation shown in FIG. 6, and feeds Ti to the memory 50 and a picture signal operator 70. 
     To the picture signal operator 70 the heating pulse width information Ti is fed from the Ti operator 60, and the picture information of the current scan line is fed from the first line buffer 20. Prior to the printing of a line, the picture signal operator 70 first outputs the picture information obtained from the first line buffer as an output Vi without changing its form. In this case, the shortest heating pulse width to be applied to each heating element of the thermal head is set at 0.5 msec, and the longest heating pulse width at 1.2 msec. Then, the picture signal operator 70 picks up picture elements in which the heating pulse width is 0.6 msec or more based on the heating pulse width information Ti which are fed sequentially from the Ti operator 60. Then, the picture signal operator 70 outputs picture elements whose heating pulse width is 0.6 msec or more as logical value &#34;1&#34;. A series of operation mentioned above are repeated until the picking up of picture elements in which the heating pulse width is 1.2 msec is completed. 
     FIG. 9 shows a typical configuration of the thermal head. 
     In FIG. 9, the thermal head comprises rectifying diodes ml to mn which are connected to heating elements Rl to Rn respectively, and power is supplied from a terminal C through these diodes ml to mn to heat individual heating elements. Other sides of the heating elements Rl to Rn are connected to output terminals of NAND gates Gl to Gn respectively. These NAND gates Gl to Gn are typically of the open collector type, and operate so as to direct a printing current to be applied from the terminal C to the heating elements only when the AND condition is satisfied at the NAND gates Gl to Gn. 
     The configuration of the heat accumulation compensation circuit 10 is shown in FIG. 7. Picture information Vi in the aforementioned sequence are outputted to a shift register 90. The shift register 90 is of the serial input parallel output type, and shifts the picture information Vi fed serially to a position in which the resistor is to be heated based on a transfer clock. After the completion of the specified shift by the shift register 90, the picture information is stored in a buffer 91 temporarily. During the shift operation by the shift register 90, the buffer 91 holds the picture information of the preceding time, and feeds it to the gates Gl to Gn, thereby preventing the heating resistor from releasing heat while the heating pulse is being applied. A heating pulse width applying circuit 80 controls the width of the heating pulse to be applied to the gates Gl to Gn, width will be described later. 
     Typical operation of the device shown in FIG. 9 will now be described with reference to the time chart shown in FIG. 10. FIG. 10 shows pulses to be output from the heating pulse applying circuit 80. 
     In printing a single scan line, picture information Vi, in other words picture information for current scan line, which is logical value &#34;1&#34; for every heating resistor to perform printing at this time (hereinafter referred to as the first picture information) and logical value &#34;0&#34; for other heating resistor is first fed from the heat accumulation compensation circuit to the shift register 90 sequentially. The shift register 90 shifts the first picture information up to a predetermined bit position, and then transfers it to the buffer 91. The buffer 91 feeds the first picture information to the gates Gl to Gn in parallel. In conjunction with the above feeding, a heating pulse of the shortest pulse width of 0.5 msec is fed from the heating pulse applying circuit 80 to each gate (refer to FIG. 10(a)). As a result, every heating resistor corresponding to the first picture information Vi is energized for a period of 0.5 msec. 
     As, the first picture information is transferred from the shift register 90 to the buffer 91, second picture information is fed to the shift register sequentially. The second picture information eventually picks up the picture elements corresponding to the heating elements to be applied the heating pulse whose width is 0.6 msec or more from the first picture information. The second picture information represents logical level &#34;1&#34; only for the picture elements thus extracted. Similar to the first picture information, this second picture information is transferred to the buffer 91, and thence fed to the gates G l  to G n . In synchronizm with the feeding above, a pulse having the heating pulse width of 0.1 msec is fed to each gate from the heating pulse applying circuit 80 (refer to FIG. 10(b)). As a result, the heating elements corresponding to the second picture information are eventually energized for a period of 0.6 msec (0.5+0.1). In this connection, operations of the heat accumulation compensation circuit 10, the shift register 90, the buffer 91, and the heating pulse applying circuit 80 are synchronized, and, it is so designed that before the beginning of heat release of the heating elements, the heating pulse is applied. 
     Then, in the same manner as mentioned above, third picture information outputted from the heat accumulation compensation circuit 10 enters each gate through the shift register 90 and the buffer 91. The third picture information eventually extracts picture elements corresponding to the heating elements to which the heating pulse whose pulse width is 0.7 msec or more is applied from the second picture information. This third picture information represents logical level &#34;1&#34; only for the information thus extracted. When the third picture information is fed to each of the gates Gl to Gn, a 0.1 msec additional pulse is output from the heating pulse applying circuit 80 (refer to FIG. 10(c)). Accordingly, it eventually results that the heating resistor corresponding to the third picture information is energized for a period of 0.7 msec together with the previous energizing. 
     By the subsequent applications of 0.1 msec additional pulses in the similar fashion, energizing of the heating elements for a period of up to 1.2 msec is performed. 
     Although in this embodiment, as shown in FIGS. 5 and 6, the resistance value of the thermistor is graduated in 10 kΩ threshold values and the pulse width of the heating pulse is adapted to change according to that gradient, it is obvious that the selection of the threshold value for the gradient is optional, and a suitable value may be employed according to the various conditions. 
     Referring now to FIG. 11, the second embodiment of the present invention will be described. FIG. 11 shows a typical configuration of the heat accumulation compensation circuit 10. 
     In FIG. 11, similar reference numerals and characters are used for similar component elements as shown in FIG. 7, and the description thereof is omitted. 
     A heat accumulation state operator 35 assigns a specified weight value to each picture information which is fed 6 bits by 6 bits from the first, second, and thrid line buffers 20, 21 and 22 corresponding to the extent of effect of heat accumulation on the heating element and also corresponding to the information Ki representing the thermal head base plate temperature to be fed from a Ki operator 40, sums up these 6 bits, converts the resultant sum to a 8-level (typically from &#34;0&#34; to &#34;7&#34;) multilevel information, and enters the resultant information to a Ti operator 60. The Ti operator 60 determines the heating pulse width for each heating element ready to print based on the multilevel information and the information Ti-1 representing the heating pulse width of the preceding line to be fed from a memory 50. 
     That is, while in the first embodiment, a weight value is assigned to each picture information to be fed 6 bits by 6 bits corresponding only to the extent of the effect of heat accumulation on the heating element, the values are summed up, and the sum is corrected according to the thermal head base plate temperature, in the second embodiment, a weight value corresponding to both the thermal head base plate temperature and the extent of the effect of heat accumulation on the heating element is assigned to each picture information to be fed 6 bits by 6 bits, and these weight values are summed up. Except the difference described above, the output to be obtained from a device 10 of the second embodiment is the same as that to be obtained from the device of the first embodiment shown in FIG. 7. 
     The third embodiment of the present invention will now be described. 
     In the third embodiment, the pulse width Ti to be applied to each heating element of the thermal head is determined by the following formula. 
     
         Ti=f (Xi, Ii, Ti-1)                                        (2) 
    
     where Xi is heat history information, Ii is an interval time information indicating the period between scan lines, and Ti-1 is a heating pulse width information of the previous scan line which concerns each heating element. The heating pulse width Ti in the present line of the heating element is determined as a function which takes these three information as parameters. In this case, for the heating element not subject to printing the heating pulse width Ti-1 and Ti are not zero but the applied voltage is zero. 
     The heat history information Xi is the same as that shown in the first embodiment. The weight value shown in Table 1 is assigned to each picture element D1 to D6 (refer to FIG. 1), the weight values are summed up, and then the resultant sum is converted to a multilevel information from &#34;0&#34; to &#34;7&#34; based on the relation shown in the graph of FIG. 2. In this manner, the heat history information Xi can be calculated. 
     When the heating pulse width of the heating element in the present print line is set based on the heat history information Xi and the heating pulse width Ti-1 of the preceding line, the result becomes as shown in FIG. 12. For example, when the heat hisory information Xi is 5 and Ti-1 is 0.6 msec, Ti becomes 0.6 msec, while when Xi is 2 and Ti-1 is 0.6 msec, Ti becomes 0.8 msec. 
     On the other hand, even when a heating pulse of the same pulse width is applied when the heat history information Xi and the heating pulse width of the preceding line are equal, it is possible that the print density (shade level) differs. This fact owes much to the difference in an interval time Ii. The interval time Ii is a period from the start of the printing of a certain scan line to the start of the next scan line. In FIG. 1, II is the interval time from the start of the printing of the line III to the start of the printing of the line II, and I2 is the interval time from the start of the printing of the line II to the start of the printing of the line I. For example, when the case when T2 of FIG. 1 is 5 msec is compared with the case when T2 is 10 msec, the effect of remaining heat of a black data in the line II differs. Accordingly, even when the heat history information Xi and Ti-1 are equal, if T2 differs, print density (shade level) variation would result even when a pulse of the same pulse width is applied to those lines. 
     In order to solve such problem, particularly in the third embodiment, the heating pulse width Ti-1 of the preceding scan line is changed artificially (falsely) based on the interval time ti, and subsequent processing is performed taking the false pulse width Fi-1 thus changed as the heating pulse width Ti-1 of the previous scan line. The relationship between Ti-1  and Fi-1 is shown in FIG. 13. As evident from FIG. 13, the longer the interval time Ii, the lower the temperature of the heating element becomes due to heat release. Accordingly, the false pulse width Fi-1 is lengthened proportionally. More detailed relationship between the interval time Ii and the false pulse width Fi-1 in the case of Ti-1=1.0 msec is shown in FIG. 14. 
     According to FIG. 14, if the interval time Ii is 5 msec when the pulse width Ti-1 of the previous scan line was 1.0 msec, Fi-1 becomes 1.0 msec. Further, if the heat history information in this case is 5, the pulse width Ti of the present line becomes 0.9 msec. However, if, in the same condition as above, the interval time Ii is set at 20 msec, Fi-1 becomes 1.2 msec, and Ii 1.0 msec. 
     By changing the heating pulse width Ti-1 of the preceding scan line by means of such approximation, it becomes possible that, even when the interval time Ii becomes different, optimum heating pulse width Ti to be applied to each heating element can always be calculated. 
     FIG. 15 shows a typical configuration of the heat accumulation compensation circuit 10 composed based on the heat accumulation compensation method which is in line with the third embodiment. 
     In FIG. 15, first, second and third line buffers 20, 21 and 22, an Xi operator 30, a pulse width memory 50 and picture signal operator 70 are totally identical with those shown in FIG. 7 and FIG. 11. 
     An interval time operator 80 outputs interval time information Ii representing each interval time to a false pulse width operator 81 from time to time. The false pulse width operator 81 calculates the false pulse width Fi-1 from the relations shown in FIGS. 13 and 14 based on the information representing the heating pulse width of the preceding scan line to be fed from the pulse width memory 50 and the interval time information Ii and feeds Fi-1 to a Ti operator 61. The Ti operator 61 calculates the heating pulse width Ti to be applied to each heating element from the relation shown in FIG. 12 based on the heat history information Xi calculated by the Xi operator 30 and the false pulse width information Fi-1 and feeds Ti to the memory 40 and a picture signal operator 70. The picture signal operator 70 extracts picture information as described previously, and sequentially outputs the extracted picture information. This picture information Vi is fed to the thermal head driving circuit shown in FIG. 9. By a series of operations similar to aforementioned operations, the heating elements R1 through Rn are heated. 
     The fourth embodiment of the present invention will now be described. 
     In this embodiment, the pulse width Ti to be applied to each heating element of the thermal head is determined based on the following equation. 
     
         Ti=f(Zi, Ti-1)                                             (3) 
    
     where 
     
         Zi-g(Xi, Ii)                                               (4) 
    
     In the above equations (3) and (4), Zi is information representing the heat accumulation state of each heating element, and Ti-1 is the information representing the heating pulse width of the preceding scan line. Zi is calculated based on the heat history information Xi and the interval time information Ii representing the period between scan lines. Accordingly, the heating pulse width Ti in the present scan line of the heating element is determined as a function which takes Zi and Ti-1 as parameters. When no printing is performed, the heating pulse width Ti-1 and Ti are not taken as zero but the voltage applied to the heating element is taken as zero. 
     The heat history information Xi is identical with that shown in the first embodiment and that shown in the third embodiment. A predetermined weight value shown in Table 1 is assigned to each picture element D1 to D6 (refer to FIG. 1), these weight values are summed up, and the resultant value is converted to a multilevel information from &#34;0&#34; to &#34;7&#34; based on the relation shown in the graph of FIG. 2. In this manner, heat history information Xi is calculated. 
     On the other hand, even when the heat history information Xi and the heating pulse width Ti-1 are equal, it is possible that the print density (shade level) varies even if a heating pulse of the same pulse width is applied in the present scan line, if the interval time Ii varies. 
     Based on this fact, in the fourth embodiment, the weight values to be assigned to the picture elements D1 to D6 (refer to Table 1) are changed according to the change in the interval time Ii. 
     Tables 3 and 4 show the relationship between the weight values of the picture element D1 through D6 and the interval times Ii and I2 (refer to FIG. 1). 
     
                       TABLE 3______________________________________           Interval timePicture         (msec)element   τ2           5˜10 10˜20                            Over 20______________________________________D1              70D2              70D3              100        50    20D4              17          8     4D5              17          8     4______________________________________ 
    
     
                       TABLE 4______________________________________(msec) Interval timePicture τ.sub.1       5˜10     10˜20 Overele-                      over       10˜                                     Over 20ment  τ.sub.2       5˜10               10˜20                     20   5˜10                                20   20   Over 5______________________________________D6          40      20    0    10    0    0    0______________________________________ 
    
     According to Tables 3 and 4, the weight value of, for example, the picture element D3 is &#34;100&#34; when the interval time I2 from the line II to the line I is 7 msec, and &#34;20&#34; when I2 exceeds 20 msec. Further, when the weight value of the picture element D6 is &#34;20&#34; when the interval time I1 from the line III to the line II is 7 msec and I2 is 15 msec, and &#34;0&#34; when I1 is 15 msec and I2 is 15 msec. 
     Table 5 shows the sum Yi of the weight values (Tables 3 and 4) of the picture elements D1 to D6 considering the fact whether the color of the picture element is black or white, as an example. In Table 5, black is represented by &#34;1&#34;, and white is denoted by &#34;0&#34;. Further, in this case, I1 is 7 msec, and I2 is 15 msec. 
     
                       TABLE 5______________________________________ Picture   Exampleelement (a)    (b)      (c)  (d)           (e)______________________________________D1      0      0        0    1      . . .  1D2      0      0        0    0      . . .  1D3      0      1        1    0      . . .  1D4      0      0        0    1      . . .  1D5      0      0        0    0      . . .  1D6      1      0        1    1      . . .  1Yi      20     50       70   98     . . .  226Zi      0      1        1    2      . . .  5______________________________________ τ 1 = 7 msec τ 2 = 15 msec 
    
     According to Table 5, as shown in, for example, (c), when the picture elements D3 and D6 are black, Yi is 70. Then, Yi is converted to a 8-level (from &#34;0&#34; to &#34;7&#34;) heat accumulation state information Zi. In FIG. 16, Yi is plotted in abscissa, and Zi is ordinate. At the bottom of Table 5, values of Zi are shown. In the case of (c), Yi and Zi are 70 and 1, respectively. 
     In Table 6, an example when I1 and I2 are set at 5 msec is shown. In this example, the color of each picture element is the same as in the case of Table 5. 
     
                       TABLE 6______________________________________ Picture  Exampleelement  (a)    (b)       (c)   (d)          (e)______________________________________D1     0      0         0     1       . . .                                      1D2     0      0         0     0       . . .                                      1D3     0      1         1     0       . . .                                      1D4     0      0         0     1       . . .                                      1D5     0      0         0     0       . . .                                      1D6     1      0         1     1       . . .                                      1Yi     40     100       140   127     . . .                                      314Zi     1      2         3     3       . . .                                      7______________________________________ τ1 = 5 msec τ2 = 5 msec 
    
     According to Table 6, in the case of, for example, (c), Yi and Zi are 140 and 3, respectively. As evident from the comparison of Table 5 with Table 6, the heat accumulation state information Zi changes according to the difference in the interval times I1 and I2. 
     When the heating pulse width Ti applied to the heating element to print at the current time is determined based on the heat accumulation state information Zi and the heating pulse width Ti-1 of the preseding line, the result beocmes as shown in FIG. 17. For example, when the heat accumulation state information Zi is 2 and Ti-1 is 0.6 msec, Ti becomes 0.8 msec, and when Zi is 5 and Ti-1 is 0.6 msec, Ti becomes 0.6 msec. 
     FIG. 18 shows a typical configuration of the heat accumulation compensation circuit structured based on the heat accumulation compensation method in line with the fourth embodiment. 
     In FIG. 18, each of a first line buffer 20, a second line buffer 21 and a third line buffer 22 has memory areas corresponding to the total number of the heating elements of the thermal head. The first line buffer 20 stores the picture information corresponding to the scan line being printed at the current time, the second line buffer 21 stores the picture information corresponding to the scan line printed at the time immediately before, and the third line buffer 22 stores the picture information corresponding to the scan line printed at the time before last, similar to those described previously. A Zi operator 36 calculates the heat accumulation state information Zi of each heating element sequentially based on the picture information stored in the line buffers 20 through 22, and outputs the result thereof to a Ti operator 60. As shown in FIG. 19, the Zi operator 36 comprises an Ii operator 37, a weight assigning circuit 38, and a Yi/Zi converter 39. The Ii operator 37 is comprised of a ROM for storing weight vlaues, for example, as shown in Tables 3 and 4, and outputs the weight values corresponding to the calculated interval time to the weight assigning circuit 38. The weight assigning circuit 38 assigns the weight value to be fed from the Ii operator 37 to the picture information (refer to FIG. 1) to be fed 6 bits by 6 bits for a one-dot heating element, sums up these 6 bits, and outputs the result thereof to the Yi/Zi converter sequentially. The Yi/Zi converter 39 converts sequentially received Yi to the heat accumulation state information Zi of 8 levels from &#34; 0&#34; to &#34;7&#34; based, for example, on the relation in FIG. 16, and outputs Zi to the Ti operator 62 sequentially. The weight assigning circuit 38 and the Yi/Zi converter 39 may be comprised of such components as memory means and an arithmetic circuit. 
     A memory 50 is for storing the information representing the heating pulse width applied to each heating element calculated by the Ti operator 62, and the memory content of the memory 50 is updated as the scan line advances. Accordingly, Ti-1 outputted from the memory 50 and fed back to the Ti operator 60 becomes the information representing the heating pulse width of the previous scan line for the Ti operator 62. 
     The Ti operator 62 calculates the heating pulse width Ti to be applied to each heating element based on the information Zi and Ti-1 from, for example, the relation shown in FIG. 17, and feeds Ti to the memory 50 and a picture signal operator 70. 
     The picture signal operator 70 extracts the picture information similar to that described previously, and outputs sequentially extracted picture information. The picture information Vi is fed to the shift register 90 of the thermal head driver circuit shown in FIG. 9, and subsequently operation similar to that described previously is performed, thereby heating the heating elements R1, . . . Rn of the thermal head. 
     Although the picture elements to be reference for determining the heat history information Xi which are shown in FIG. 1 can give sufficiently satisfactory result, the picture elements are not limited to those shown in FIG. 1. The number of reference picture elements may be lessened accoridng to the requirement in terms of speed and cost, or may be increased if higher precision is required. 
     Further, though, in the embodiment of the present invention, the heat history information Xi or the heat accumulation state information is divided to 8 levels from &#34;0&#34; to &#34;7&#34;, the number of levels is, of course, optional, and the heat accumulation compensation of higher precision may be made by increasing the number of levels to, say, 16 or 32. 
     Further, while in the embodiment of the present invention the picture element density (shade level) variation is prevented by the variable control of the heating pulse width (duration of energizing) of the pulse to be applied to each heating element of the thermal head, the similar effect may be obtained alternatively by changing the duty of a high frequency pulse applying the high frequency pulse to each heating element. Alternatively, the applied voltage may be subjected to variable control. In conjucntion with the above alternative, the heating pulse width Ti-1 of the immediately preceding line of each heating element to be referenced at the time of heat accumulation compensation allows its alternatives, and the impressed voltage or the duty of the immediately preceding line of each heating element may be referenced. 
     In addition, there is a system wherein heating elements of the thermal head are divided to a plurality of blocks and driven separately typically for saving power, and in this case providing the aforementioned heat accumulation compensation circuit in each block is a sole modification.