Method and apparatus for pixel synchronization

Abstract: An apparatus and a method are provided which can control the intensity level of an exposing device so that the desired pixel density is consistently disposed on the correct location on an image recording medium. Specifically, within a printing apparatus, even channel circuitry controls the intensity level of the exposing device during exposure of the even numbered pixels on the image recording medium and an odd channel circuitry controls the intensity level of the exposing device during the exposure of the odd numbered pixels on the image recording medium.

Description: FIELD OF THE INVENTION This invention relates generally to a printing apparatus and, more particularly, to an apparatus and a method for controlling the intensity level of an exposing device so that desired print densities provided by the printing apparatus are disposed on the image recording medium in approximately the correct locations. BACKGROUND OF THE INVENTION In a scanning printer which produces continuous tone images, an exposing device in the printer should travel across an image recording medium with as near a constant scanning velocity as possible in order to produce a high quality image on the image recording medium. Presently, circuitry which controls the positioning of the exposing device cannot meet this requirement to produce a sufficiently constant scanning velocity for the exposing device relative to the image recording medium. Accordingly, data circuitry which controls both the timing and the image management aspects of the printer compensates for this inability by using a variety of different approaches. One approach that has been used extensively is to employ a variable frequency oscillator as a high frequency pixel clock and a phase locked feedback loop interconnecting the high frequency clock to a position encoder. Critical to the success of this approach is the design of the feedback loop. If the loop responds too slowly, the position of pixels on the image recording medium will wander excessively with small changes in the scanning velocity of the exposing device. On the other hand, if the loop responds too fast, the phase locked feedback loop will tend to ring in response to sudden changes in the scanning velocity of the exposing device. Regardless of the tuning of the loop, this approach exacerbates errors in print density that arise when the scanning velocity changes. When the scanning velocity of the exposing device increases, the energy density of the exposure necessarily decreases which results in underexposure of the image recording medium. In addition, the variable frequency phase locked loop increases its frequency which shortens the exposing time for the exposing device. For constant exposing power, this means that less total energy is delivered to the image recording medium which, in turn, results in further underexposure of the image recording medium. To avoid the problems associated with the feedback loop system, another approach has been employed. This approach employs a spatial clock which produces a spatial clock pulsetrain wherein each spatial clock pulse defines the amount of time required for an exposing device to travel across a set distance on the image recording medium, a fixed timing clock which produces timing clock pulses at a rate substantially faster than the spatial clock, a counter which counts the timing clock pulses until a terminal value is reached and which has a phase that is periodically shifted to match that of the spatial clock. In this approach, the rising edge of the spatial clock triggers the counter to start counting to a terminal value. When the value of the count reaches a value associated with a desired print density of the pixel to be printed, the intensity level of the exposing device is switched from a first state which is the "on" state to a second state which is the "off" state. Then, when the counter reaches the terminal value, the intensity level of the exposing device is again switched from the second state back to the first state. This approach provides the proper duration of the intensity level of the exposing device at the proper state when the spatial clock is running at the normal rate. However, when the spatial clock is substantially faster than normal or substantially slower than normal, problems occur. This approach may keep the intensity level of the exposing device at a given state for too long a period when the spatial clock is substantially slower than normal. This occurs because the count reaches the terminal value before the next rising edge of the next spatial clock pulse and thereby switches the intensity level of the exposing device to the first state too soon. This approach may also prevent the printing apparatus from switching the intensity level of the exposing device to the first state when the spatial clock is substantially faster than normal. This occurs because the count never reaches the terminal value so that the intensity level of the exposing device can change from the second state to the first state. As a result, a need still exists in the art for improved data circuitry that can control the intensity level of the exposing device so that the desired pixel density can be consistently disposed on the image recording medium in a manner whereby the deleterious effects associated with a fast or a slow spatial clock are minimized. WO-A-91/15919 describes a scanner system including a light source and scanning components for moving a spot of light across a surface along a scan line of predetermined length. An electronic control system is included for controlling the light beam in order to produce a plurality of pixels on the surface along the scan line. It is configured to control the position and exposure of each of the pixels in order to compensate for pixel position distortion and pixel exposure distortion caused by variations in spot velocity. In accordance with one aspect of the present invention, we provide a process according to claim 1. In accordance with a second aspect of the present invention, we provide apparatus according to claim 7. Embodiments of the present invention solve the above-identified problem by providing within a printing apparatus an even channel circuitry which controls the intensity level of the exposing device during exposure of the even numbered pixels on the image recording medium and an odd channel circuitry which controls the intensity level of the exposing device during the exposure of the odd numbered pixels on the image recording medium. In one embodiment of the present invention, even channel circuitry and odd channel circuitry receive from the printing apparatus even and odd numbered spatial clock pulses, respectively, a desired print density for each even and odd numbered pixel to be printed, respectively, and timing clock pulses. A plurality of sequential timing clock pulses defines a pixel print cycle and each pixel print cycle defines the period that the exposing device will expose a single pixel on the image recording medium. The even channel circuitry, at the rising edge of the even numbered spatial clock pulses, counts the timing clock pulses until a terminal value is reached. When the count reaches a value associated with a desired print density of the present even numbered pixel to be printed, the even channel circuitry requests that the intensity level of the exposing device be changed from an initial first state to a second state. Thereafter, if the desired print density of the present even numbered pixel to be printed is less than a standard print density, the even channel circuitry adds or subtracts timing clock pulses to or from the present even numbered pixel print cycle so that the present even numbered pixel print cycle will terminate at the rising edge of the next odd numbered spatial clock pulse. At the rising edge of the next odd numbered spatial clock pulse, the even channel circuitry enables the odd channel circuitry to control the intensity level of the exposing device. Alternatively, if the desired print density of the present even numbered pixel to be printed is greater than the standard print density, the even channel circuitry adds or subtracts timing clock pulses to or from the next odd numbered pixel print cycle so that the next pixel odd numbered print cycle will start when the even count reaches the terminal value. When the count reaches the terminal value, the even channel circuitry enables the odd channel circuitry to control the intensity level of the exposing device. Thereafter, regardless of the desired print density of the present even numbered pixel to be printed, the even channel circuitry requests that the exposing device be set to the first state in anticipation of the even channel circuitry's regaining control over the intensity level of the exposing device. Similarly, the odd channel circuitry, at the rising edge of the odd numbered spatial clock pulses, counts the timing clock pulses until the terminal value is reached. When the count reaches a value associated with a desired print density of the present odd numbered pixel to be printed, the odd channel circuitry requests that the intensity level of the exposing device be changed from the first initial state to the second state. Thereafter, if the desired print density of the present odd numbered pixel to be printed is less than the standard print density, the odd channel circuitry adds or subtracts timing clock pulses to or from the present odd numbered pixel print cycle so that the present odd numbered pixel print cycle will terminate at the rising edge of the next spatial clock pulse. At the rising edge of the next even numbered spatial clock pulse, the odd channel circuitry enables the even channel circuitry to control the intensity level of the exposing device. Alternatively, if the desired print density of the present odd numbered pixel to be printed is greater than the standard print density, the odd channel circuitry adds or subtracts timing clock pulses to or from the next even numbered pixel print cycle so that the next even numbered pixel print cycle will start when the odd count reaches the terminal value. When the count reaches the terminal value, the odd channel circuitry enables the even channel circuitry to control the intensity level of the exposing device. Thereafter, regardless of the desired print density of the present odd numbered pixel to be printed, the odd channel circuitry requests that the exposing device be set to the first state in anticipation of the odd channel circuitry's regaining control over the intensity level of the exposing device. In a second embodiment of the present invention, even channel circuitry and odd channel circuitry receive from the printing apparatus even and odd numbered spatial clock pulses, respectively, a desired print density for each even and odd numbered pixel to be printed, respectively, and timing clock pulses. The even channel circuitry, at the rising edge of the even numbered spatial clock pulses, counts the timing clock pulses until a terminal value is reached. When the count reaches a value associated with a desired print density of a present even numbered pixel to be printed, the even channel circuitry requests that the exposing device be changed from the first initial state to the second state. Thereafter, the even channel circuitry passes control over the intensity level of the exposing device to an odd channel circuitry as follows. If the desired print density of the present even numbered pixel to be printed is less than a standard print density, the even channel circuitry passes control over the intensity level of the exposing device to the odd channel circuitry at the rising edge of the next odd numbered spatial clock pulse. Alternatively, if the desired print density of the present even numbered pixel to be printed is greater than the standard print density, the even channel circuitry passes control over the intensity level of the exposing device to the odd channel circuitry when the count reaches the terminal value. Thereafter, regardless of the desired print density of the present even numbered pixel to be printed, the even channel circuitry requests that the exposing device be set to the first state in anticipation of the even channel circuitry's regaining control over the intensity level of the exposing device. Similarly, the odd channel circuitry, at the rising edge of the odd numbered spatial clock pulses, counts the timing clock pulses until the terminal value is reached. When the count reaches a value associated with a desired print density of a present odd numbered pixel to be printed, the odd channel circuitry requests that the intensity level of the exposing device be changed from the first initial state to the second state. Thereafter, the odd channel circuitry passes control over the intensity level of the exposing device to the even channel circuitry as follows. If the desired print density of the present odd numbered pixel to be printed is less than the standard print density, the odd channel circuitry passes control over the intensity level of the exposing device to the even channel circuitry at the rising edge of the next even numbered spatial clock pulse. Alternatively, if the desired print density of the present odd numbered pixel to be printed is greater than the standard print density, the odd channel circuitry passes control over the intensity level of the exposing device to the even channel circuitry when the count reaches the terminal value. Thereafter, regardless of the standard print density of the present odd numbered pixel to be printed, the odd channel circuitry requests that the exposing device be set to the first state in anticipation of the odd channel circuitry's regaining control over the intensity level of the exposing device. More specifically, in each embodiment discussed above, the even channel circuitry comprises an even counter circuitry, an even comparator circuitry, an even termination selector circuitry, and an even request circuitry. The even counter circuitry, upon receipt of an even rising edge signal from a spatial clock rising edge detector circuitry, to be discussed fully below, starts counting the timing signals generated by the printing apparatus until the terminal value is reached. During this period, the even counter circuitry continually generates an even count signal for each timing clock pulse that is counted and then generates an even overflow signal when the even count signal exceeds the terminal value. An even comparator circuitry receives the continually generated even count signal from the even counter circuitry and the desired print density of the present even pixel to be printed from the printing apparatus. The even comparator circuitry then generates an even comparator signal when the value of the even count signal reaches the value associated with the desired print density of the present even numbered pixel to be printed. An even termination selector circuitry receives the odd rising edge signal from the spatial clock rising edge detector circuitry, the standard print density associated with the present even numbered pixel to be printed from the printing apparatus, and the even overflow signal from the even counter circuitry. The even termination selector circuitry then generates an even termination signal upon either (i) receipt of the even overflow signal if the desired print density associated with the present even pixel to be printed is greater than the standard print density value or (ii) receipt of the odd rising edge signal if the desired print density associated with the present even pixel to printed is less than the standard print density value. Finally, an even request circuitry generates an even request signal upon the receipt of the even termination signal from the even termination selector circuitry and disables the even request signal upon receipt of the even comparator signal from the even comparator circuitry. Similarly, in each embodiment discussed above, the odd channel circuitry comprises an odd counter circuitry, an odd comparator circuitry, an odd termination selector circuitry, and an odd request circuitry. The odd counter circuitry, upon receipt of an odd rising edge signal from a spatial clock rising edge detector circuitry, starts counting the timing signals generated by the printing apparatus until the terminal value is reached. During this period, the odd counter circuitry continually generates an odd count signal for each timing clock pulse that is counted and then generates an odd overflow signal when the odd count signal exceeds the terminal value. An odd comparator circuitry receives the continually generated odd count signal from the odd counter circuitry and the desired print density of the present odd pixel to be printed from the printing apparatus. The odd comparator circuitry then generates an odd comparator signal when the value of the odd count signal reaches the value associated with the desired print density of the present odd numbered pixel to be printed. An odd termination selector circuitry receives the even rising edge signal from the spatial clock rising edge detector circuitry, the standard print density associated with the present odd numbered pixel to be printed from the printing apparatus, and the odd overflow signal from the odd counter circuitry. The odd termination selector circuitry then generates an odd termination signal upon either (i) receipt of the odd overflow signal if the desired print density associated with the present odd pixel to be printed is greater than the standard print density value or (ii) receipt of the even rising edge signal if the desired print density associated with the present odd pixel to printed is less than the standard print density value. Finally, an odd request circuitry generates an odd request signal upon the receipt of the odd termination signal from the odd termination selector circuitry and disables the odd request signal upon the receipt of the odd comparator signal from the odd comparator circuitry. In each embodiment discussed above, the even channel circuitry and the odd channel circuitry jointly share a spatial clock rising edge detector circuitry and selection circuitry. The spatial clock rising edge detector circuitry receives the spatial clock pulses and the timing clock pulses from the printing apparatus and provides the odd rising edge signal at the rising edge of each odd spatial clock pulse and the even rising edge signal at the rising edge of each even spatial clock pulse. Similarly, the selection circuitry receives both termination signals and both channel request signals from, respectively, both termination selector circuitry and both request circuitry. The selection circuitry then passes control of the intensity level of the exposing device (i) to the even request signal upon receipt of the odd termination signal or (ii) to the odd request signal upon receipt of the even termination signal. The novel even and odd channel circuitry discussed above also share several common novel characteristics. First, the ratio of the frequency of the timing clock to the nominal frequency of the spatial clock defines the terminal count. Second, the standard print density is substantially at the minimum of the derivative of the perceived lightness with respect to the exposure of the image recording medium or, alternatively, is in the range between 0.4 to 0.6 of the maximum value for the desired print density. Finally, the first and second state of the even and the odd request signals are related to two different intensity setting levels on the exposing device, preferably, on and off. DESCRIPTION OF THE DRAWINGS The novel features that are considered characteristic of the invention are set forth with particularity in the appended claims. The invention itself, however, both as to its organization and its method of operation together with other objects and advantages thereof will be best understood from the following description of the illustrated embodiment when read in connection with the accompanying drawings wherein: Figure 1 is an electrical block diagram of the preferred pixel synchronizer circuitry of the present invention; Figure 1A is an electrical diagram of one embodiment of the termination selector circuitry found in Figure 1; Figure 1B is an electrical diagram of one embodiment of the data selector circuitry found in Figure 1; Figure 2 depicts several waveform diagrams useful in explaining the steady state operation of the pixel synchronizer circuitry of Figure 1 when the spatial clock is at a normal frequency; Figure 3 depicts several waveform diagrams useful in explaining the steady state operation of the pixel synchronizer circuitry of Figure 1 when the spatial clock is at a low frequency; and Figure 4 depicts several waveform diagrams useful in explaining the steady state operation of the pixel synchronizer circuitry of Figure 1 when the spatial clock is at a high frequency. DESCRIPTION OF THE PREFERRED EMBODIMENTS Figure 1 shows data circuitry 2 which resides within an image processing apparatus (not shown) and which controls the intensity level (on-off) of an exposing device (not shown) so that the correct pixel density is consistently exposed at approximately the correct location on an image recording medium (not shown). The data circuitry 2 comprises even channel circuitry 4 which controls the intensity level of the exposing device (not shown) during exposure of the even numbered pixels on the image recording medium (not shown) and odd channel circuitry 6 which controls the intensity level of the exposing device (not shown) during the exposure of the odd numbered pixels on the image recording medium (not shown). The data circuitry 2 receives from the printing apparatus (not shown) a spatial clock pulsetrain, a timing clock pulsetrain, and a signal associated with a desired print density. The spatial clock pulsetrain is divided into individual spatial clock pulses and each spatial clock pulse is the actual time that the exposing device (not shown) spends travelling across a known set distance of the image recording medium (not shown). In the embodiment shown in Figure 1, as the exposing device (not shown) travels across each pixel on the image recording medium (not shown), a spatial clock pulse will be generated. The diameter of one pixel on the image recording medium (not shown) is approximately 18 microns. Similarly, the timing clock pulsetrain is divided into individual timing clock pulses and a plurality of sequential timing clock pulses defines the period that the exposing device (not shown) spends exposing a single pixel on the image recording medium (not shown). Accordingly, the timing clock pulsetrain has a frequency that is substantially greater than that of the spatial clock pulsetrain and, in the embodiment shown in Figure 1, the timing clock pulsetrain has a 32 megaHertz frequency. The signal associated with the desired print density is part of the image data associated with each pixel that is to be printed. Specifically, the desired print density is the print density that the printing apparatus wants to expose onto a given pixel location on the image recording medium; however, the desired print density may not be the actual print density that is ultimately exposed onto the image recording medium. The desired print density may also be thought of as the energy that is to be delivered to a given pixel location on the image recording medium (not shown). Alternatively, the desired pixel density is also indicative of where physically within the pixel the exposing beam from the exposing device (not shown) will be turned on or turned off. DISCUSSION OF FIGURE 1 Referring once again to Figure 1, a spatial clock rising edge detector 8 receives the spatial clock pulsetrain and the timing clock pulsetrain and produces therefrom an odd edge signal for each rising edge of an odd numbered spatial clock pulse and an even edge signal for each rising edge of an even numbered spatial clock pulse. An even channel counter 10 in the even channel circuitry 4 receives the even edge signal from the spatial clock rising edge detector 8 and timing clock pulses from the printing apparatus (not shown). Similarly, an odd channel counter 12 in the odd channel circuitry 6 receives the odd edge signal from the spatial clock rising edge detector 8 and the timing clock pulses from the printing apparatus (not shown). Upon receipt of the respective edge signal, each counter 10, 12 starts counting the timing clock pulses and starts generating a count signal which is incrementally increased for each timing clock pulse that is counted. In this embodiment, the count signal incrementally increases from 0 to 1023. Ideally, in this embodiment, the exposing device (not shown) should travel across one pixel in the time it takes the counter 10, 12 to incrementally increase the count signal from 0 to 1024. Alternatively, this means that one spatial clock pulse should equal exactly 1024 sequential timing clock pulses. If one spatial clock pulse does equal 1023 sequential timing clock pulses, then the spatial clock is said to be running at a normal frequency. That is, the exposing device (not shown) is travelling across the image recording medium (not shown) at the correct constant velocity which is 0.6 meters per second in this embodiment. The correct constant velocity for a given exposing device and a given image recording medium is dependant on the pixel size, the exposure rate of the image recording medium, and the power delivered to the image recording medium by the exposing device. If a spatial clock pulse equals less than 1024 sequential timing clock pulses, the spatial clock pulse associated with the pixel is said to be running at a high frequency which means that the exposing device (not shown) is travelling too fast across the pixel. Alternatively, if a spatial clock pulse equals more than 1024 sequential timing clock pulses, the spatial clock pulse associated with the pixel is said to be running at a low frequency which means that the exposing device (not shown) is travelling too slowly across pixel. Each counter 10, 12 also generates an overflow signal when the count signal exceeds the capacity of the counter 10, 12. In this embodiment, this occurs when the count signal exceeds a value of 1023. The count signal produced by the even channel counter 10 along with the desired print density provided by the printing apparatus is provided to an even channel comparator 14 in the even channel circuitry 4. Similarly, the count signal produced by the odd channel counter 12 along with the desired print density provided by the printing apparatus is provided to an odd channel comparator 16 in the odd channel circuitry 6. Each comparator 14, 16 is 10 bits wide and produces therefrom a comparator signal which is indicative of the duration of the exposure or non exposure of a specific pixel on the image recording medium. The comparator signal is produced when the value of the count signal represents the value of the desired print density; the desired print density being approximately a logarithmic function of the exposure or, alternatively, a logarithmic function of the count signal generated by the counters 10, 12. The odd edge signal generated by the spatial clock rising edge detector 8, the overflow signal generated by the even channel counter 10, and the most significant bit from the desired print density are provided to an even channel termination selector circuitry 18 in the even channel circuitry 4. Similarly, the even edge signal generated by the spatial clock rising edge detector 8, the overflow signal generated by the odd channel counter 12, and the most significant bit from the desired print density are provided to an odd channel termination selector circuitry 20 in the odd channel circuitry 6. The termination selector circuitry 18, 20 produces therefrom a termination signal. Specifically, referring to Figure 1A, one embodiment for the termination selector 18, 20 is shown. In this embodiment, the termination selector 18, 20 acts as a switching element that is controlled by the most significant bit of the desired print density. That is, when the most significant bit of the desired print density is equal to one, the termination signal is equal to the overflow signal while, if the most significant bit of the desired print density is equal to zero, the termination signal is equal to the edge signal. A quantity known as the standard print density is particularly relevant to this invention. The standard print density is ideally at the minimum of dS/dE where S is the perceived lightness of the image captured on the image recording medium and E is the exposure of the image recording medium. The perceived lightness is a subjective psycho visual scale defined as an attribute of visual sensation whereby an illuminated area appears to exhibit more or less light in proportion to that exhibited by a reference area. Alternatively, the standard print density can also be represented as the value of C at the minimum of dS/dC where C is the count signal generated by the counters 10, 12. In this embodiment, the ideal standard print density is approximated by one half of full exposure of a pixel and is represented in Figure 1 by the most significant bit of the desired print density which is sent to the termination selector circuitry 18, 20. The comparator signal generated by the even channel comparator 14 along with the termination signal generated by the even channel termination selector circuitry 18 are provided to an even request flip-flop 22 in the even channel circuitry 4. Similarly, the comparator signal generated by the odd channel comparator 16 along with the termination signal generated by the odd channel termination selector circuitry 20 are provided to an odd request flip-flop 24 in the odd channel circuitry 6. The request flip-flops 22, 24 generate therefrom, respectively, an even request signal and an odd request signal. Specifically, the assertion of the termination signal causes the request flip-flop 22, 24 to generate the channel request signal and the assertion of the comparator signal disables the channel request signal. Selection circuitry 26 which is jointly shared by both the even channel circuitry 4 and the odd channel circuitry 6, then receives both termination signals and both channel request signals from, respectively, both termination selector circuitry 18, 20 and both request flip-flops 22, 24. The selection circuitry 26 is comprised of a control flip-flop 28 and a data selector 30. The control flip-flop 28 receives the termination signals from both termination selector circuitry 18, 20 and produces therefrom a control signal which controls the enabling of the data selector 30. Specifically, the assertion of either termination signal causes the control flip-flop 28 to switch the state of the control signal to the opposite channel. From the control signal and both channel request signals, the data selector 30 produces an exposure signal. Specifically, referring to Figure 1B, one embodiment for the data selector 30 is shown. In this embodiment, the data selector 30 acts as a switching element that is controlled by the control signal. That is, when the control signal is equal to one which is the odd level, the exposure signal is equal to the odd request signal while, if the control signal is equal to zero which is the even level, the exposure signal is equal to the even request signal. The exposure signal generated by the data selector 30 is indicative of the intensity with which the exposing device (not shown) should irradiate the present pixel on the image recording device (not shown). The exposing device (not shown) in this embodiment is a laser diode, however, the exposing device (not shown) can be selected from the group comprising a light emitting diode, an shuttered arc lamp, a shuttered Xenon lamp, a shuttered gas laser, a solid state laser, and a semiconductor laser. Moreover, the image recording medium (not shown) in this embodiment is a carbon based thermal medium and other examples for the image recording medium include dye based thermal medium and photo-chemical based medium. DISCUSSION OF FIGURE 2 Figure 2 discloses several waveform diagrams useful in explaining the steady state operation of the data circuitry of Figure 1 when the spatial clock is at a normal frequency. That is, the normal frequency being when one spatial clock pulse exactly equals 1024 sequential timing clock pulses so that the exposing device (not shown) travels across the image recording medium (not shown) at the correct velocity. The spatial clock pulsetrain in Figure 2 is segmented into four spatial clock pulses and each spatial clock pulse has a desired print density and an actual print density associated therewith. The desired print density is the print density that the printing apparatus should expose onto the image recording medium (not shown) while the actual print density is the print density that is actually exposed onto the image recording medium (not shown). Also, Figures 2, 3, and 4 assume steady state conditions with an even pixel printing cycle of 1024 density at the normal frequency that ends just as each figure begins. Thus, the two request signals and the exposure signal are in the "high" or "1" state, the control signal is about to switch from the "Even" to the "Odd", independently of anything in the Figures, and all the remaining signal are assumed at the "low" or "0" state at the beginning of the first odd spatial clock pulse. Referring now to Figure 2, the first odd spatial clock pulse has associated therewith a desired pixel density of 7 and a pulsewidth that is equal to 1024 timing clock pulses. The rising edge of the first odd spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an odd edge signal to the 10 bit counter 12 (Figure 1) in the odd channel circuitry 6. This allows the odd counter 12 (Figure 1) to start counting the individual timing clock pulses and to produce an incrementally increasing odd count signal as shown in Figure 2. Although the odd and even count signals are shown in Figures 2, 3, and 4 as a ramp function, it should be understood that the odd and the even count signals are, in fact, 10 bits wide and upcount from 0 to 1023 for the first through the 1024 th timing clock pulse, respectively. The ordinal numbers of the timing clock pulse is always greater than the cardinal numbers contained in the counters. With only 10 bits of resolution, it is impossible to express all the integral states between no exposure (0 counts) and full exposure (1024 counts) inclusive - one state must be excluded. This embodiment excludes the case of zero exposure and includes the case of exposing for all 1024 counts of the cycle. Thus, the exposure equals the ordinal number of timing clock pulse which causes the comparator to generate the comparator signal and not the cardinal number presented to the comparator. Accordingly, to request 7 units of exposure, the comparator should be set to 6. When the odd count signal reaches a count of six, the odd count signal matches the desired print density for the first odd spatial clock pulse. Since this embodiment is synchronous the odd comparator 16 (Figure 1) will assert the odd comparator signal for one timing clock pulse during the eighth timing clock pulse. The odd comparator signal causes the odd request flip-flop 24 (Figure 1) to switch the state of the odd request signal from a "high" state to a "low" state at the ninth timing clock pulse as shown in Figure 2. Since the control signal is set to the "odd channel", the exposure signal produced by the data selector 30 (Figure 1) is controlled by the odd request signal. Accordingly, the exposure signal changes from the "high" state which is associated with the exposing device (not shown) irradiating the image recording medium (not shown) at full power to the "low" state which is associated with the exposing device (not shown) being shut off. The odd counter 12 (Figure 1) continues counting the timing clock pulses and continues producing incrementally increasing odd count signals until the 1024 th timing clock pulse is counted. This causes the odd counter 12 (Figure 1) to assert the odd overflow signal as shown in Figure 2. The odd termination selector 20 (Figure 1) receives the odd overflow signal from the odd counter 12 (Figure 1) but this has no effect on the odd termination selector 20 (Figure 1) because the most significant bit of the desired print density is "0". The rising edge of the first even spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an even edge signal which is sent to the 10 bit counter 10 (Figure 1) in the even channel circuitry 4 and to the odd termination selector 20 (Figure 1). Since the desired print density from the first odd spatial clock pulse is still provided to the odd channel circuitry 6 (Figure 1), the most significant bit of the desired print density provided to the odd termination selector 20 (Figure 1) is still a "0". The combination of the most significant bit of the desired print density being "0" and the assertion of the even edge signal will cause the termination selector 20 (Figure 1A) to assert the odd termination signal on the first timing clock pulse of the first even spatial clock pulse as shown in Figure 2. The assertion of the odd termination signal causes the odd request flip-flop 24 (Figure 1) to change the state of the odd request from the "low" state to the "high" state and also causes the control flip-flop 28 (Figure 1) in the selection circuitry 26 (Figure 1) to change the control signal from the "odd channel" to the "even channel". Since as shown in Figure 2 the even request signal is in the "high" state, the exposure signal will change from the "low" state to the "high" state and, correspondingly, the exposing device (not shown) will begin irradiating the image recording medium (not shown) with full intensity. This completes the pixel print cycle associated with the first odd spatial clock pulse and, as shown in Figure 2, this pixel print cycle has been labelled "Pixel #1". A pixel print cycle is defined as the period that the exposing device exposes a single pixel on the image recording medium and for purposes of this embodiment it is defined as the period required for the control signal to make the transition from the "even" state to the "odd" state or from the "odd" state to the "even" state. Applying this definition here, Pixel #1 has a period or width associated therewith that is equal to 1024 timing clock pulses and, accordingly, Pixel #1 has a "normal" width. That is, Pixel #1 has been disposed onto the image recording medium (not shown) without being either compressed or stretched. Also, Pixel #1 has been disposed onto the image recording medium (not shown) with an actual print density of 7 which corresponds exactly with the desired print density. The even edge signal provided to the even counter 10 (Figure 1) in the even channel circuitry 4 causes the even counter 10 (Figure 1) to start counting the timing clock pulses and to start generating incrementally increasing even count signals as shown in Figure 2. When the even count signal reaches a count of 512, which equals the value associated with the desired print density of the first even spatial clock pulse, the even comparator 14 (Figure 1) on the 515 th timing clock pulse will assert the even comparator signal for one timing clock pulse as shown in Figure 2. The even comparator signal causes the even request flip-flop 22 (Figure 1) to switch the state of the even request signal from the "high" state to the "low" state at the 515 th timing clock pulse as shown in Figure 2. Since the exposure signal follows the even request signal, the state of the exposure signal is set to the "low" state. The even counter 10 (Figure 1) continues counting the timing clock pulses and continues producing an incrementally increasing even count signal until the 1024 rd timing clock pulse is counted. This causes the even counter 10 (Figure 1) to assert the even overflow signal as shown in Figure 2. The even termination selector 18 receives the even overflow signal which causes it to assert the even termination signal on the first timing clock pulse of the second odd spatial clock pulse as shown in Figure 2. The assertion of the even termination signal causes the even request flip-flop 22 to change the state of the even request to the "high" state and also causes the control flip-flop 28 (Figure 1) to change the control signal from the "even channel" to the "odd channel". Since the odd request signal was left in the "high" state at the end of the first odd spatial clock pulse, the exposure signal will change from the "low" state to the "high" state and the odd request signal will control the exposure signal. This completes the pixel print cycle associated with the first even spatial clock pulse and this pixel print cycle has been labeled "Pixel #2". Pixel #2 has a "normal" width associated therewith and has an actual print density of 513 which corresponds exactly with the desired print density for the first even spatial clock pulse. The third spatial clock pulse is sent to the spatial clock rising edge detector 8 (Figure 1) which causes it to generate an odd edge signal to the odd counter 12 (Figure 1). The odd counter 12 (Figure 1) starts counting the individual timing clock pulses and starts producing the incrementally increasing odd count signal as shown in Figure 2. When the odd count reaches a count of 1023, the odd count signal equals the desired print density of the second odd spatial clock pulse and so the odd comparator 16 (Figure 1) on the first timing clock pulse of the second even spatial clock pulse will assert the odd comparator signal for one timing clock pulse. The odd count reaching the count of 1023 also causes the odd counter 12 (Figure 1) to assert the odd overflow signal. The odd termination selector 20 (Figure 1) receives the odd overflow signal and produces therefrom an odd termination signal on the first timing clock pulse of the second even spatial clock pulse. The odd comparator signal causes the odd request flip-flop 24 (Figure 1) to change the state of the odd request signal to the "low" state but soon thereafter the odd termination signal causes the odd request flip-flop 24 (Figure 1) to change, yet again, the state of the odd request signal to the "high" state. Accordingly, in Figure 2, the odd request signal never appears to have changed states. The odd termination signal also causes the control flip-flop 28 to change the state of the control signal from the "odd channel" to the "even channel". Since the even request signal was left in the "high" state at the end of the first even spatial clock pulse, the exposure signal will remain at the "high" state and the even request signal will now control the exposure signal. This completes the pixel print cycle associated with the second odd spatial clock pulse and this pixel print cycle has been labeled "Pixel #3". Pixel #3 has a "normal" width associated therewith and has an actual print density of 1024 which corresponds exactly with the desired print density for the second odd spatial clock pulse. The rising edge of the fourth spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an even edge signal to the even counter 10 (Figure 1). This allows the even counter 10 (Figure 1) to start counting the individual timing clock pulses and to start producing an incrementally increasing even count signal as shown in Figure 2. When the even count signal reaches a count of three, the even count signal equals the desired print density for the second even spatial clock pulse and so the even comparator 14 (Figure 1) on the fifth timing clock pulse will assert the even comparator signal for one timing clock pulse. The even comparator signal causes the even request flip-flop 22 (Figure 1) to switch the state of the even request signal to the "low" state at the sixth timing clock pulse as shown in Figure 2. Since the control signal is set to the "even channel", the exposure signal changes from the "high" state to the "low" state. The even counter 12 (Figure 1) continues counting the timing clock pulses and continues producing an incrementally increasing even signal count signal until the 1024 th timing clock pulse is counted. The counting of the 1024 th timing clock pulse causes the even counter 10 (Figure 1) to assert the even overflow signal as shown in Figure 2. The even termination selector 18 (Figure 1) receives the even overflow signal but this has no effect on the even termination selector 18 (Figure 1) because the most significant bit of the desired print density is "0". The rising edge of the third odd spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an odd edge signal to the even termination selector 18 and the odd counter 12. The combination of the most significant bit of the second even spatial clock pulse being "0" and the assertion of the odd edge signal causes the termination selector 20 (Figure 1A) to assert the even termination signal on the first timing clock pulse of the third odd spatial clock pulse as shown in Figure 2. The assertion of the even termination signal causes the even request flip-flop 22 (Figure 1) to change the state of the even request from the "low" state to the "high" state and also causes the control flip-flop 28 to change the exposure signal from the "even channel" to the "odd channel". Since the odd request signal was left in the "high" state at the end of the second odd spatial clock pulse, the exposure signal will change to the "high" state and the odd request signal will now control the exposure signal. This completes the pixel print cycle associated with the second even spatial clock pulse and this pixel print cycle has been labeled "Pixel #4". Pixel #4 has a "normal" width associated therewith and has an actual print density of 4 which corresponds exactly with the desired print density for the second even spatial clock pulse. DISCUSSION OF FIGURE 3 Figure 3 discloses several waveform diagrams useful in explaining the steady state operation of the data circuitry of Figure 1 when the spatial clock is at a low frequency, that is, one spatial clock pulse is greater than 1024 sequential timing clock pulses so that the exposing device (not shown) travels too slowly across the image recording medium (not shown). Figure 3 has also been segmented into four spatial clock pulses and each spatial clock pulse has a desired print density and an actual print density associated therewith. The desired print density associated with each spatial clock pulse in Figure 3 is the same as the desired print density associated with each spatial clock pulse in Figure 2. Also, the initial conditions for Figure 3 are the same as in Figure 2. Referring now to Figure 3, the rising edge of the first odd spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an odd edge signal to the odd counter 12 (Figure 1) which allows the odd counter 12 (Figure 1) to start counting the individual timing clock pulses and to produce an incrementally increasing odd count signal as shown in Figure 3. When the odd count signal reaches a count of six, the odd count signal equals the desired print density for the first odd spatial clock pulse and so the odd comparator (Figure 1) on the eighth timing clock pulse will assert the odd comparator signal for one timing clock pulse. The odd request flip-flop 24 (Figure 1) switches the state of the odd request signal from the "high" state to the "low" state at the ninth timing clock pulse as shown in Figure 3. Since the control signal is set to the "odd channel", the exposure signal produced by the data selector 30 (Figure 1) is controlled by the odd request signal. Accordingly, the exposure signal changes from the "high" state to the "low" state. The odd counter 12 (Figure 1) continues counting the timing clock pulses and continues producing incrementally increasing odd count signals until the 1024 th timing clock pulse is counted. This causes the odd counter 12 (Figure 1) to assert the odd overflow signal as shown in Figure 3. The odd termination selector 20 (Figure 1) receives the odd overflow signal from the odd counter 12 (Figure 1) but this has no effect on the odd termination selector 20 (Figure 1). Timing clock pulses 1024 through 1028 in the first odd spatial clock pulse then occur but they are not counted by the odd channel circuitry 6. The rising edge of the first even spatial clock pulse occurs after the 1029 th timing clock pulse which causes the spatial clock rising edge detector 8 (Figure 1) to generate an even edge signal which is sent to the even counter 10 (Figure 1) and to the odd termination selector 20 (Figure 1). Since the desired print density from the first odd spatial clock pulse is still provided to the odd channel circuitry 6 (Figure 1), the most significant bit of the desired print density provided to the odd termination selector 20 (Figure 1) is still a "0". The combination of the most significant bit of the first odd spatial clock pulse being "0" and the assertion of the even edge signal will cause the termination selector 20 (Figure 1A) to assert the odd termination signal on the first timing clock pulse of the first even spatial clock pulse as shown in Figure 3. The assertion of the odd termination signal causes the odd request flip-flop 24 (Figure 1) to change the state of the odd request from the "low" state to the "high" state and also causes the control flip-flop 28 (Figure 1) to change the control signal from the "odd channel" to the "even channel". Since, as shown in Figure 3, the even request signal is in the "high" state, the exposure signal will change from the "low" state to the "high" state. This completes the pixel print cycle associated with the first odd spatial clock pulse and, as shown in Figure 3, this pixel print cycle has been labelled "Pixel #1". Pixel #1 has a width associated therewith that is equal to 1029 timing clock pulses which is greater than the 1024 timing clock pulses associated with a "normal" pixel width. Accordingly, Pixel #1 has a "stretched" width. Also, Pixel #1 has been disposed onto the image recording medium (not shown) with an actual print density of 7 which corresponds exactly with the desired print density. The even edge signal provided to the even counter 10 (Figure 1) causes the even counter 10 (Figure 1) to start counting the timing clock pulses and start generating incrementally increasing even count signals as shown in Figure 3. When the even count signal reaches a count of 512, which equals the value associated with the desired print density of the first even spatial clock pulse, the even comparator 14 (Figure 1) on the 514 th timing clock pulse will assert the even comparator signal for one timing clock pulse as shown in Figure 3. The even comparator signal causes the even request flip-flop 22 (Figure 1) to switch the state of the even request signal from the "high" state to the "low" state at the 515 th timing clock pulse as shown in Figure 3. Since the exposure signal follows the even request signal, the state of the exposure signal is set to the "low" state. The even counter 10 (Figure 1) continues counting the timing clock pulses and continues producing an incrementally increasing even count signal until the 1024 th timing clock pulse is counted. This causes the even counter 10 (Figure 1) to assert the even overflow signal as shown in Figure 3. The even termination selector 18 receives the even overflow signal which causes it to assert the even termination signal on the 1025 th timing clock pulse of the first even spatial clock pulse as shown in Figure 3. The assertion of the even termination signal causes the even request flip-flop 22 to change the state of the even request to a "high" state and also causes the control flip-flop 28 (Figure 1) to change the control signal from the "even channel" to the "odd channel". Since the odd request signal was left in the "high" state at the end of the first odd spatial clock pulse, the exposure signal will change from the "low" state to the "high" state and the exposing device (not shown) will expose the image recording medium (not shown) at full intensity between the 1026 th and the 1029 th timing clock pulses in the first even spatial clock pulse. This completes the pixel print cycle associated with the first even spatial clock pulse and this pixel print cycle has been labeled "Pixel #2". Pixel #2 has a "normal" width of 1024 timing clock pulses and has an actual print density of 513 which corresponds exactly with the desired print density for the first even spatial clock pulse. The third spatial clock pulse is sent to the spatial clock rising edge detector 8 (Figure 1) which causes it to generate an odd edge signal to the odd counter 12 (Figure 1). The odd counter 12 (Figure 1) starts counting the individual timing clock pulses and starts producing the incrementally increasing odd count signal as shown in Figure 3. When the odd count reaches a count of 1023, the odd count signal equals the desired print density of the second odd spatial clock pulse and so the odd comparator 16 (Figure 1) on the 1025 th timing clock pulse of the second odd spatial clock pulse will assert the odd comparator signal for one timing clock pulse. When the odd count reaches the count of 1023, this also causes the odd counter 12 (Figure 1) to assert the odd overflow signal. The odd termination selector 20 (Figure 1) receives the odd overflow signal and produces therefrom an odd termination signal on the 1025 th clock pulse of the second odd spatial clock pulse. The odd overflow signal causes the odd request flip-flop 24 (Figure 1) to change the state of the odd request signal to the "low" state but immediately thereafter the odd termination signal causes the odd request flip-flop 24 (Figure 1) to change, yet again, the state of the odd request signal to the "high" state. Accordingly, in Figure 3, the odd request signal never appears to have changed states. The odd termination signal also causes the control flip-flop 28 to change the state of the control signal from the "odd channel" to the "even channel". Since the even request signal was left in the "high" state at the end of the first even spatial clock pulse, the exposure signal will remain at the "high" state through the 1025 th timing clock pulse in the second odd spatial clock pulse. This completes the pixel print cycle associated with the second odd spatial clock pulse and this pixel print cycle has been labeled "Pixel #3". Pixel #3 has a "stretched" width associated therewith and has an actual print density of 1029 which is larger than the desired print density for the second odd spatial clock pulse. This occurs because Pixel #3 also includes the 1026 th through the 1029 th timing clock pulses of the first even spatial clock pulse. Since a pixel print cycle is defined as the period required for the control signal to make the transition from the "Even" state to the "Odd" state or from the "Odd" state to the "Even" state, Pixel #2 must end at and Pixel #3 must start on the 1026 th timing clock pulse of the first even spatial clock pulse. Pixel #3 also includes the 1026 th through the 1029 th timing clock pulses of the first even spatial clock for a far more important reason. The preferred image recording medium for use with this embodiment of this invention is a carbon based medium which is normally transparent but which turns to darker shades of the grey scale as it is irradiated with increased light intensity. Since this carbon based thermal medium is intended to be used as a transparency, the human visual system can much more easily identify "pin hole" transparent regions in a dark field rather than a grey scale shift to a darker shade in an already dark field. Although the 1026 th through the 1029 th timing clock pulses in the first spatial clock pulse do produce an artifact, this type of artifact is much less distinguishable to the human visual system than the alternative pin hole artifact. It should be obvious to one skilled in the art that many different types of image recording mediums can be used in conjunction with this invention and that minor modifications to the circuitry discussed in Figure 1 might also be necessary in order for the circuitry in Figure 1 to be optimized for use with a specific image recording medium. These modifications to the circuitry shown in Figure 1, however, are obvious to one of ordinary skill in the art. These modifications are also specific to a specific image recording medium, are much to numerous to discuss individually, and accordingly will not be discussed here. The rising edge of the fourth spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an even edge signal to the even counter 10 (Figure 1). This allows the even counter 10 (Figure 1) to start counting the individual timing clock pulses and to start producing an incrementally increasing even count signal as shown in Figure 3. When the even count signal reaches a count of three, the even count signal equals the desired print density for the second even spatial clock pulse and so the even comparator 14 (Figure 1) on the fifth timing clock pulse will assert the even comparator signal for one timing clock pulse. The even comparator signal causes the even request flip-flop 22 (Figure 1) to switch the state of the even request signal to the "low" state at the sixth timing clock pulse as shown in Figure 3. Since the control signal is set to the "even channel", the exposure signal changes from the "high" state to the "low" state. The even counter 12 (Figure 1) continues counting the timing clock pulses and continues producing an incrementally increasing even signal count signal until the 1024 th timing clock pulse is counted. The counting of the 1024 th timing clock pulse causes the even counter 10 (Figure 1) to assert the even overflow signal as shown in Figure 3. The even termination selector 18 (Figure 1) receives the even overflow signal but this has no effect on the even termination selector 18 (Figure 1) because the most significant bit of the desired print density is "0". Timing clock pulses 1024 through 1028 in the second even spatial clock pulse then occur but they are not counted by the even channel circuitry 4. The rising edge of the third odd spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an odd edge signal to the even termination selector 18 and the odd counter 12. The combination of the most significant bit of the second even spatial clock pulse being "0" and the assertion of the odd edge signal causes the termination selector 18 (Figure 1A) to assert the even termination signal on the first timing clock pulse of the third odd spatial clock pulse as shown in Figure 3. The assertion of the even termination signal causes the even request flip-flop 22 (Figure 1) to change the state of the even request from the "low" state to the "high" state and also causes the control flip-flop 28 to change the exposure signal from the "even channel" to the "odd channel". Since the odd request signal was left in the "high" state at the end of the second odd spatial clock pulse, the exposure signal will switch to the "high" state and the odd request signal will now control the exposure signal. This completes the pixel print cycle associated with the second even spatial clock pulse and this pixel print cycle has been labeled "Pixel #4". Pixel #4 has a "stretched" width associated therewith and has an actual print density of 9. The actual print density associated with Pixel #4 differs from the desired print density associated with the second even spatial clock pulse because all of the accumulated errors produced by the data circuitry 2 (Figure 1) are disposed into Pixel #4. The accumulated errors are all the errors associated with the data circuitry 2 (Figure 1) sequentially exposing individual adjacent pixel locations on the image recording medium (not shown) with an exposing device (not shown) that is travelling too slow or too fast across the image recording medium (not shown). The reason why the accumulated errors are disposed into Pixel #4 is quite simple, the human visual system has a hard time perceiving the accumulated error when it is disposed in Pixel #4. The human visual system is hard pressed to distinguish any minor grey scale errors in the color of adjacent pixels when the colors associated with the adjacent pixels are at or near the opposite ends of the grey scale. In Figure 3 using the preferred carbon based thermal medium as the image recording medium (not shown), the desired pixel density associated with Pixel #3 represents a very dark grey color while the desired pixel density associated with Pixel #4 represents a very light grey color. The transition between the dark grey color of Pixel #3 to the light grey color of Pixel #4 produces a distinct visible edge. The human visual system is hard pressed to distinguish any minor grey scale errors in the colors of the adjacent pixels, namely, Pixel #3 and Pixel #4, which make up the distinct visible edge. Accordingly, the data circuitry 2 in Figure 1 disposes all the accumulated errors due to the data circuitry operating under a slow or a fast spatial clock frequency into the later of the two adjacent pixels that produce the distinct visible edge, namely, into Pixel #4. It should also be obvious to one skilled in the art that the data circuitry 2 in Figure 1 could also be modified such that the accumulated errors due to the data circuitry 2 operating under high or a low spatial clock frequency could be disposed in the former of the two adjacent pixels that produce the distinct visible edge, namely, into Pixel #3 by merely redefining the pixel boundaries. DISCUSSION OF FIGURE 4 Figure 4 discloses several waveform diagrams useful in explaining the steady state operation of the data circuitry of Figure 1 when the spatial clock is at a high frequency, that is, one spatial clock pulse is less than 1024 sequential timing clock pulses so that the exposing device (not shown) travels too fast across the image recording medium (not shown). Like Figures 2 and 3, Figure 4 has been segmented into four spatial clock pulses and each spatial clock pulse has a desired print density and an actual print density associated therewith. The desired print density associated with each spatial clock pulse in Figure 4 is the same as the desired print density associated with each spatial clock pulse in Figures 2 and 3. Also, the initial conditions for Figure 4 are the same as in Figures 2 and 3. Referring now to Figure 4, the rising edge of the first odd spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an odd edge signal to the odd counter 12 (Figure 1) which allows the odd counter 12 (Figure 1) to start counting the individual timing clock pulses and to produce an incrementally increasing odd count signal as shown in Figure 4. When the odd count signal reaches a count of six, the odd count signal equals the desired print density for the first odd spatial clock pulse and so the odd comparator (Figure 1) on the eighth timing clock pulse will assert the odd comparators signal for one timing clock pulse. The odd request flip-flop 24 (Figure 1) switches the state of the odd request signal from the "high" state to the "low" state at the ninth timing clock pulse as shown in Figure 4. Since the control signal is set to the "odd channel", the exposure signal produced by the data selector 30 (Figure 1) is controlled by the odd request signal. Accordingly, the exposure signal changes from the "high" state to the "low" state. The odd counter 12 (Figure 1) continues counting the timing clock pulses and continues producing incrementally increasing odd count signal until the 1024 th timing clock pulse after the rising edge of the first odd spatial clock pulse or, alternatively, until the 3 rd timing clock pulse in the first even spatial clock pulse. The rising edge of the first even spatial clock pulse occurs after the 1021 st timing clock pulse which causes the spatial clock rising edge detector 8 (Figure 1) to generate an even edge signal which is sent to the even counter 10 (Figure 1) and to the odd termination selector 20 (Figure 1). Since the desired print density from the first odd spatial clock pulse is still provided to the odd channel circuitry 6 (Figure 1), the most significant bit of the desired print density provided to the odd termination selector 20 (Figure 1) is still a "0". The combination of the most significant bit of the first odd spatial clock pulse being "0" and the assertion of the even edge signal will cause the termination selector 20 (Figure 1A) to assert the odd termination signal on the first timing clock pulse of the first even spatial clock pulse as shown in Figure 4. The assertion of the odd termination signal causes the odd request flip-flop 24 (Figure 1) to change the state of the odd request from the "low" state to the "high" state and also causes the control flip-flop 28 (Figure 1) to change the control signal from the "odd channel" to the "even channel". Since the even request signal is in the "high" state, the exposure signal will change from the "low" state to the "high" state. The odd count continues counting sequential timing clock pulses until 1024 timing clock pulses after the rising edge of the first odd spatial clock pulse which corresponds with the 3 rd timing clock pulse in the first even spatial clock pulse. The 3 rd timing clock pulse in the first even spatial clock pulse causes the odd counter 12 (Figure 1) to assert the odd overflow signal which is associated with the first odd spatial clock pulse as shown in Figure 4. The odd termination selector 20 (Figure 1) receives the odd overflow signal associated with the first odd spatial clock pulse but this has no effect on the odd termination selector 20 (Figure 1). This completes the pixel print cycle associated with the first odd spatial clock pulse and, as shown in Figure 4, this pixel print cycle has been labelled "Pixel #1". Pixel #1 has a width associated therewith that is equal to 1021 timing clock pulses which is less than the 1024 timing clock pulses associated with a "normal" pixel width. Accordingly, Pixel #1 has a "compressed" width. Also, Pixel #1 has been disposed onto the image recording medium (not shown) with an actual print density of 7 which corresponds exactly with the desired print density. The even edge signal provided to the even counter 10 (Figure 1) in the even channel circuitry 4 causes the even counter 10 (Figure 1) to start counting the timing clock pulses and to start generating incrementally increasing even count signals as shown in Figure 4. When the even count signal reaches a count of 512, which equals the value associated with the desired print density of the first even spatial clock pulse, the even comparator 14 (Figure 1) on the 514 th timing clock pulse will assert the even comparator signal for one timing clock pulse as shown in Figure 4. The even comparator signal causes the even request flip-flop 22 (Figure 1) to switch the state of the even request signal from the "high" state to the "low" state at the 515 th timing clock pulse as shown in Figure 4. Since the exposure signal follows the even request signal, the state of the exposure signal is set to the "low" state. The even counter 10 (Figure 1) continues counting the timing clock pulses and continues producing an incrementally increasing even count signal until the 3 rd timing clock pulse in the second odd spatial clock pulse. The 3 rd timing clock pulse causes the even counter 10 (Figure 1) to assert the even overflow signal as shown in Figure 4. The even termination selector 18 receives the even overflow signal which causes it to assert the even termination signal on the fourth timing clock pulse of the second odd spatial clock pulse as shown in Figure 4. The assertion of the even termination signal causes the even request flip-flop 22 to change the state of the even request to a "high" state and also causes the control flip-flop 28 (Figure 1) to change the control signal from the "even channel" to the "odd channel". Since the odd request signal was left in the "high" state at the end of the first odd spatial clock pulse, the exposure signal will change from the "low" state to the "high" state and the odd request signal will control the exposure signal on the fifth timing clock pulse in the second odd spatial clock pulse. This completes the pixel print cycle associated with the first even spatial clock pulse and this pixel print cycle has been labeled "Pixel #2". Pixel #2 has a "normal" width associated therewith and has an actual print density of 513 which corresponds exactly with the desired print density for the first even spatial clock pulse. The third spatial clock pulse is sent to the spatial clock rising edge detector 8 (Figure 1) which causes it to generate an odd edge signal to the odd counter 12 (Figure 1). The odd counter 12 (Figure 1) starts counting the individual timing clock pulses and starts producing the incrementally increasing odd count signal as shown in Figure 4. When the odd count reaches a count of 1023 which is the 3 rd timing clock pulse in the second even spatial clock pulse, the odd count signal equals the desired print density of the second odd spatial clock pulse and so the odd comparator 16 (Figure 1) on the fourth timing clock pulse of the second even spatial clock pulse will assert the odd comparator signal for one timing clock pulse. When the odd count reaches the count of 1023, this also causes the odd counter 12 (Figure 1) to assert the odd overflow signal. The odd termination selector 20 (Figure 1) receives the odd overflow signal and produces therefrom an odd termination signal on the fourth timing clock pulse of the second even spatial clock pulse. The odd comparator signal causes the odd request flip-flop 24 (Figure 1) to change the state of the odd request signal to the "low" state but immediately thereafter the odd termination signal causes the odd request flip-flop 24 (Figure 1) to change, yet again, the state of the odd request signal to the "high" state. Accordingly, in Figure 4, the odd request signal never appears to have changed states. The odd termination signal also causes the control flip-flop 28 to change the state of the control signal from the "odd channel" to the "even channel". Since the even request signal was left in the "high" state at the end of the first even spatial clock pulse, the exposure signal will remain at the "high" state and the even request signal will now control the exposure signal. This completes the pixel print cycle associated with the second odd spatial clock pulse and this pixel print cycle has been labeled "Pixel #3". Pixel #3 has a "compressed" width associated therewith and has an actual print density of 1021 which corresponds with the desired print density for the second odd spatial clock pulse as closely as possible given the speed of the exposing device. The rising edge of the fourth spatial clock cycle causes the spatial clock rising edge detector 8 (Figure 1) to generate an even edge signal to the even counter 10 (Figure 1). This allows the even counter 10 (Figure 1) to start counting the individual timing clock pulses and to start producing an incrementally increasing even count signal as shown in Figure 4. When the even count signal reaches a count of three, the even count signal equals the desired print density for the second even spatial clock pulse and so the even comparator 14 (Figure 1) on the fifth timing clock pulse will assert the even comparator signal for one timing clock pulse. The even comparator signal causes the even request flip-flop 22 (Figure 1) to switch the state of the even request signal to the "low" state at the sixth timing clock pulse as shown in Figure 4. Since the control signal is set to the "even channel", the exposure signal changes from the "high" state to the "low" state. The even counter 12 (Figure 1) continues counting the timing clock pulses and continues producing an incrementally increasing even signal count signal until the 1024 th timing clock pulse after the rising edge of the second even spatial clock pulse which corresponds to the 3 rd timing clock pulse in the third odd spatial clock pulse. The counting of the 1024 th timing clock pulse causes the even counter 10 (Figure 1) to assert the even overflow signal as shown in Figure 4. The even termination selector 18 (Figure 1) receives the even overflow signal but this has no effect on the even termination selector 18 (Figure 1) because the most significant bit of the desired print density is "0". The rising edge of the third odd spatial clock pulse causes the spatial clock rising edge detector 8 (Figure 1) to generate an odd edge signal to the even termination selector 18 and the odd counter 12. The combination of the most significant bit of the second even spatial clock pulse being "0" and the assertion of the odd edge signal causes the termination selector 18 (Figure 1A) to assert the even termination signal on the first timing clock pulse of the third odd spatial clock pulse as shown in Figure 4. The assertion of the even termination signal causes the even request flip-flop 22 (Figure 1) to change the state of the even request from the "low" state to the "high" state and also causes the control flip-flop 28 to change the exposure signal from the "even channel" to the "odd channel". Since the odd request signal was left in the "high" state at the end of the second odd spatial clock pulse, the exposure signal will change to the "high" state and the odd request signal will now control the exposure signal. This completes the pixel print cycle associated with the second even spatial clock pulse and this pixel print cycle has been labeled "Pixel #4". Pixel #4 has a "compressed" width associated therewith and has an actual print density of 1. The actual print density associated with Pixel #4 differs from the desired print density associated with the second even spatial clock pulse because all of the accumulated errors produced by the data circuitry 2 (Figure 1) are disposed into Pixel #4. The accumulated errors are all the errors associated with the data circuitry 2 (Figure 1) sequentially exposing individual adjacent pixel locations on the image recording medium (not shown) with an exposing device (not shown) that is travelling to slow or to fast across the image recording medium (not shown). The reason why the accumulated errors are disposed into Pixel #4 is quite simple, the human visual system has a hard time perceiving the accumulated error when it is disposed in Pixel #4. The human visual system is hard pressed to distinguish any minor grey scale errors in the color of adjacent pixels when the colors associated with the adjacent pixels are at or near the opposite ends of the grey scale. In Figure 4 using the preferred carbon based thermal medium as the image recording medium (not shown), the desired pixel density associated with Pixel #3 represents a very dark grey color while the desired pixel density associated with Pixel #4 represents a very light grey color. The transition between the dark grey color of Pixel #3 to the light grey color of Pixel #4 produces a distinct visible edge. The human visual system is hard pressed to distinguish any minor grey scale errors in the colors of the adjacent pixels, namely, Pixel #3 and Pixel #4, which make up the distinct visible edge. Accordingly, the data circuitry 2 in Figure 1 disposes all the accumulated errors due to the data circuitry operating under a high or a low spatial clock frequency into the later of the two adjacent pixels that produce the distinct visible edge, namely, into Pixel #4. It should also be obvious to one skilled in the art that the data circuitry 2 in Figure 1 could also be modified such that the accumulated errors due to the data circuitry 2 operating under high or a low spatial clock frequency could be disposed in the former of the two adjacent pixels that produce the distinct visible edge, namely, into Pixel #3 by merely redefining the pixel boundaries. Other embodiments of the invention including additions, subtractions, deletions, and other modifications of the preferred disclosed embodiments of the invention will be obvious to those skilled in the art and are within the scope of the following claims.

Claims: A process for modulating an exposing device in a printing apparatus so as to expose a continuous tone image onto an image recording medium wherein the printing apparatus is of the type that includes a spatial clock which produces spatial clock pulses, each spatial clock pulse defining the amount of time required for the exposing device to travel across a pixel on the image recording medium, and a timing clock which produces timing clock pulses at a rate substantially faster than the rate at which the spatial clock produces spatial clock pulses, a plurality of sequential timing clock pulses defining a pixel print cycle, the printing apparatus also providing a desired print density for each pixel to be printed, the process comprising the steps of: A) commencing to count the timing clock pulses at the rising edge of a first spatial clock pulse, i) continuing to count the timing clock pulses of the first spatial clock pulse until a terminal value is reached, ii) setting a first channel request signal to a first state at the commencement of the count of the timing clock pulses of the first spatial clock pulse and thereafter setting the first channel request signal to a second state when the count of the timing clock pulses of the first spatial clock pulse represents a desired print density of a pixel to be printed onto the image recording medium, iii) adding or subtracting timing clock pulses to or from the present pixel print cycle so that the present pixel print cycle will terminate at the rising edge of the next succeeding spatial clock pulse and, at the rising edge of the next succeeding spatial clock pulse, setting the first channel request signal to the first state and enabling a second channel to control the intensity level of the exposing device when the desired print density of the pixel to be printed is less than a standard print density, or iv) adding or subtracting timing clock pulses to or from the next pixel print cycle so that the next pixel print cycle will start when the counting of the timing clock pulses of the first spatial clock pulse reaches the terminal value and, when the counting of the timing clock pulses of the first spatial clock pulse reaches the terminal value, setting the first channel request signal to the first state and enabling the second channel to control the intensity level of the exposing device when the desired print density of the pixel to be printed is more than the standard print density; B) commencing to count the timing clock pulses at the rising edge of the next succeeding spatial clock pulse independently of the count of the first spatial clock pulse, i) continuing to count the timing clock pulses of the next succeeding spatial clock pulse until the terminal value is reached, ii) setting the second channel request signal to the second state when the count of the timing clock pulses of the next succeeding spatial clock pulse represents a desired print density for the next succeeding pixel to be printed onto the image recording medium, iii) adding or subtracting timing clock pulses to or from the present pixel print cycle so that the present pixel print cycle will terminate at the rising edge of the next succeeding spatial clock pulse and, at the rising edge of the next succeeding spatial clock pulse, setting the second channel request signal to the first state and enabling a first channel to control the intensity level of the exposing device when the desired print density of the pixel to be printed is less than the standard print density, or iv) adding or subtracting timing clock pulses to or from the next pixel print cycle so that the next pixel print cycle will start when the counting of the timing clock pulses reaches the terminal value and, when the counting of the timing clock pulses of the next succeeding spatial clock pulse reaches the terminal value, setting the second channel request signal to the first state and enabling the first channel to control the intensity level of the exposing device when the desired print density of the pixel to be printed is more than the standard print density; and C) repeating the aforementioned steps until the scan line of the image is completely exposed. The process of claim 1 wherein the first state and the second state of the first channel and the second channel request signals are related to two different intensity setting levels on the exposing device. The process of any preceding claim, wherein the ratio of the frequency of the timing clock to the nominal frequency of the spatial clock defines the terminal value. The process of any preceding claim, wherein the standard print density is substantially at the minimum of the derivative of the perceived lightness with respect to the exposure of the image recording medium. The process of any of claims 1 to 3, wherein a standard print density value is in the range between 0.4 to 0.6 of a maximum value for the desired print density. The process of any preceding claim, wherein the exposing device is selected from the group comprising a light emitting diode, a shuttered arc lamp, a shuttered Xenon lamp, a shuttered gas laser, a solid state laser, and a semiconductor laser. An apparatus (2) for modulating the intensity of an exposing device in a printing apparatus so as to expose a continuous tone image onto an image recording medium, the printing apparatus including a spatial clock which produces spatial clock pulses, each spatial clock pulse defining the amount of time required for the exposing device to travel across a pixel on the image recording medium, and a timing clock which produces timing clock pulses at a rate substantially faster than the rate at which the spatial clock produces spatial clock pulses, the printing apparatus also providing a desired print density for each pixel to be printed, the apparatus comprising: A) odd channel circuitry means (6) for counting, in odd counter circuitry (12), the timing clock pulses commencing at the rising edge of each odd numbered spatial clock pulse and continuing until the terminal value is reached ; and B) even channel circuitry means (4) for counting, in even counter circuitry (10), the timing clock pulses commencing at the rising edge of each even numbered spatial clock pulse and continuing until the terminal value is reached, wherein, when the count by the odd counter circuitry (12) reaches a value associated with a desired print density of the present odd numbered pixel to be printed, as determined by odd comparator circuitry (16), odd request circuitry (24) requests that the intensity level of the exposing device be changed from a first initial state to a second state and, thereafter, if the desired print density of the present odd numbered pixel to be printed is less than a standard print density, selection circuitry (26) passes control over the intensity level of the exposing device to the even channel circuitry means (4) at the rising edge of the next even numbered spatial clock pulse or, if the desired print density of the present odd numbered pixel to be printed is greater than the standard print density, the selection circuitry (26) passes control over the intensity level of the exposing device to the even channel circuitry means (4) when the count of the odd counter circuitry (12) reaches the terminal value as determined by odd comparator circuitry (16) and, thereafter, regardless of the standard print density of the present pixel to be printed, the odd request circuitry (24) requests that the exposing device be set to the first state in anticipation of the odd channel circuitry means (6) regaining control over the intensity level of the exposing device during the subsequent odd numbered spatial clock pulses, and, when the count by even counter circuitry (10) reaches a value associated with a desired print density of the present even numbered pixel to be printed as determined by even comparator circuitry (14), even request circuitry (22) requests that the intensity level of the exposing device be changed from the first initial state to a second state and, thereafter, if the desired print density of the present even numbered pixel to be printed is less than the standard print density, selection circuitry (26) passes control over the intensity level of the exposing device to the odd channel circuitry means (6) at the rising edge of the next odd numbered spatial clock pulse or, if the desired print density of the present even numbered pixel to be printed is greater than the standard print density, the selection circuitry (26) passes control over the intensity level of the exposing device to the odd channel circuitry means (6) when the count of the even counter circuitry (10) reaches the terminal value as determined by odd comparator circuitry (16), and, thereafter, regardless of the standard print density of the present even numbered pixel to be printed, the even channel circuitry means (4) requests that the exposing device be set to the first state in anticipation of the even channel circuitry means (4) regaining control over the intensity level of the exposing device during the subsequent even numbered spatial clock pulses. The apparatus of claim 7, wherein the first state and the second state of the exposing device are different intensity levels of the exposing device. The apparatus of claims 7 or 8, further comprising a spatial clock rising edge detector circuitry (8) which receives the spatial clock pulses and the timing clock pulses from the printing apparatus and provides an odd rising edge signal at the rising edge of each odd spatial clock pulse and an even rising edge signal at the rising edge of each even spatial clock pulse. The apparatus of any of claims 7 to 9, wherein the even channel circuitry means (4) comprises: a) the even counter circuitry (10) for counting the timing clock pulses, upon receipt of the even rising edge signal from the spatial clock rising edge detector circuitry (8), to the terminal value and for generating an even count signal for each timing clock pulse that is counted and an even overflow signal when the even count signal exceeds the terminal value; b) the even comparator circuitry (14) for receiving the even count signal from the even counter circuitry (10) and the desired print density of the present even pixel to be printed from the printing apparatus and for generating an even comparator signal when the value of the even count signal represents the value of the desired point density of the present even pixel to be printed; c) the even termination selector circuitry (18) for receiving the odd rising edge signal from the spatial clock rising edge detector circuitry (8), the standard print density associated with the present even pixel to be printed from the printing apparatus, and the even overflow signal from the even counter circuitry (10) and for either (i) generating an even termination signal upon the receipt of the even overflow signal if the desired print density associated with the present even pixel to be printed is greater than the standard print density value or (ii) generating the even termination signal upon receipt of the odd rising edge signal if the desired print density associated with the present even pixel to be printed is less than the standard print density value; and d) the even request circuitry (22) for generating an even request signal upon the receipt of the even termination signal from the even termination selector circuitry (18) and for the disabling of the even request signal upon the receipt of the even comparator signal from the even comparator circuitry (14). The apparatus of any of claims 7 to 10, wherein the odd channel circuitry means (6) comprises: a) the odd counter circuitry (12) for counting the timing clock pulses, upon receipt of the odd rising edge signal from the spatial clock rising edge detector circuitry (8), to the terminal value and for generating an odd count signal for each timing clock pulse that is counted and an odd overflow signal when the odd count signal exceeds the terminal value; b) the odd comparator circuitry (16) for receiving the odd count signal from the odd counter circuitry (12) and the desired print density of the present odd pixel to be printed from the printing apparatus and for generating an odd comparator signal when the value of the odd count signal represents the value of the desired print density of the present odd pixel to be printed; c) the odd termination selector circuitry (20) for receiving the even rising edge signal from the spatial clock rising edge detector circuitry (8), the standard print density associated with the present odd pixel to be printed from the printing apparatus, and the odd overflow signal from the odd counter circuitry (12) and for either (i) generating an odd termination signal upon the receipt of the odd overflow signal if the desired print density associated with the present odd pixel to be printed is greater than the standard print density value or (ii) generating the odd termination signal upon receipt of the even rising edge signal if the desired print density associated with the present odd pixel to be printed is less than the standard print density value; and d) the odd request circuitry (24) for generating an odd request signal upon the receipt of the odd termination signal from the odd termination selector circuitry (20) and for the disabling of the odd request signal upon receipt of the odd comparator signal from the odd comparator circuitry (16). The apparatus of any of claims 7 to 11, wherein the odd channel circuitry means (6) and the even channel circuitry means (4) further comprise selection circuitry (26) which is jointly shared by both the odd channel circuitry means (6) and the even channel circuitry means (4), the selection circuitry (26) receives both termination signals and both channel request signals from, respectively, both termination selector circuitry (20, 18) and both request circuitry (24, 22) and therefrom passes control of the intensity level of the exposing device (i) to the even request signal upon receipt of the odd termination signal or (ii) to the odd request signal upon receipt of the even termination signal. The apparatus of any of the claims 7 to 12, wherein the ratio of the frequency of the timing clock to the nominal frequency of the spatial clock defines the terminal value. The apparatus of any of claims 7 to 13, wherein the standard print density is substantially at the minimum of the derivative of the perceived lightness with respect to the exposure of the image recording medium. The apparatus of any of claims 7 to 13, wherein the standard print density value is in the range between 0.4 to 0.6 of the maximum value for the desired print density. The apparatus of any of claims 7 to 15, wherein the exposing device is selected from the group comprising a light emitting diode, a shuttered arc lamp, a shuttered Xenon lamp, a shuttered gas laser, a solid state laser, and a semiconductor laser.

Inventors: SULLIVAN PAUL F, SULLIVAN, PAUL F.
Applicants: POLAROID CORP, POLAROID CORPORATION
Application year: 1993
Main classification: H04N1
IPC codes: B41J2, H04N1