Abstract:
A method of printing a two-dimensional bit-mapped image having a number of pixels per row for printing is disclosed. The method and apparatus use either a plurality of overlapping printheads ( 300 ) or a printhead or plurality of printheads indexed through overlapping positions. The or each printhead has a row of ejection channels ( 301 ), each of which has associated ejection electrodes to which a voltage is applied to cause particulate concentrations to be formed from within a body of printing fluid. In order to cause volumes of charged particulate concentrations of one of a number of predetermined volume sizes to be ejected as printed droplets from selected ejection channels of the overlapping printheads, voltage pulses (V E ) of respective predetermined amplitude and duration, as determined by respective image pixel bit values, are applied to the electrodes of the selected ejection channels. For each row of the image, the values of the voltage pulses to be applied to the overlapping printheads to form pixels printed by overlapped ejection channels are adjusted in dependence on the position of the pixel within an overlapped region of the printheads and in dependence on the predetermined volume size of the pixel.

Description:
BACKGROUND 
       [0001]    The present invention relates to electrostatic inkjet print technologies and, more particularly, to printheads and printers of the type such as described in WO 93/11866 and related patent specifications. 
         [0002]    Electrostatic printers of this type eject charged solid particles dispersed in a chemically inert, insulating carrier fluid by using an applied electric field to first concentrate and then eject the solid particles. Concentration occurs because the applied electric field causes electrophoresis and the charged particles move in the electric field towards the substrate until they encounter the surface of the ink. Ejection occurs when the applied electric field creates an electrophoretic force that is large enough to overcome the surface tension. The electric field is generated by creating a potential difference between the ejection location and the substrate; this is achieved by applying voltages to electrodes at and/or surrounding the ejection location. One particular advantage of this type of print technology over that of conventional drop-on-demand (DOD) printers is the ability to print using greyscale, something which is not possible with conventional DOD printers. 
         [0003]    The location from which ejection occurs is determined by the printhead geometry and the position and shape of the electrodes that create the electric field. Typically, a printhead consists of one or more protrusions from the body of the printhead and these protrusions (also known as ejection upstands) have electrodes on their surface. The polarity of the bias applied to the electrodes is the same as the polarity of the charged particle so that the direction of the electrophoretic force is towards the substrate. Further, the overall geometry of the printhead structure and the position of the electrodes are designed such that concentration and then ejection occurs at a highly localised region around the tip of the protrusions. 
         [0004]    To operate reliably, the ink must flow past the ejection location continuously in order to replenish the particles that have been ejected. To enable this flow the ink must be of a low viscosity, typically a few centipoise. The material that is ejected is more viscous because of the concentration of particles; as a result, the technology can be used to print onto non-absorbing substrates because the material will not spread significantly upon impact. 
         [0005]    Various printhead designs have been described in the prior art, such as those in WO 93/11866, WO 97/27058, WO 97/27056, WO 98/32609, WO 01/30576 and WO 03/101741, all of which relate to the so-called Tonejet® method described in WO 93/11866. 
         [0006]      FIG. 1  is a drawing of the tip region of an electrostatic printhead  1  of the type described in this prior art, showing several ejection upstands  2  each with a tip  21 . Between each two ejection upstands is a wall  3 , also called a cheek, which defines the boundary of each ejection cell  5 . In each cell, ink flows in the two pathways  4 , one on each side of the ejection upstand  2  and in use the ink meniscus is pinned between the top of the cheeks and the top of the ejection upstand. In this geometry the positive direction of the z-axis is defined as pointing from the substrate towards the printhead, the x-axis points along the line of the tips of the ejection upstands and the y-axis is perpendicular to these. 
         [0007]      FIG. 2  is a schematic diagram in the x-z plane of a single ejection cell  5  in the same printhead  1 , looking along the y-axis taking a slice through the middle of the tips of the upstands  2 . This figure shows the cheeks  3 , the ejection upstand  2 , which defines the position of the ejection location  6 , the ink pathways  4 , the location of the ejection electrodes  7  and the position of the ink meniscus  8 . The solid arrow  9  shows the ejection direction and also points towards the substrate. Each upstand  2  and its associated electrodes and ink pathways effectively forms an ejection channel. Typically, the pitch between the ejection channels is 168 μm (this provides a print density of 150 dpi). In the example shown in  FIG. 2  the ink usually flows into the page, away from the reader. 
         [0008]      FIG. 3  is a schematic diagram of the same printhead  1  in the y-z plane showing a side-on view of an ejection upstand along the x-axis. This figure shows the ejection upstand  2 , the location of the electrode  7  on the upstand and a component known as an intermediate electrode ( 10 ). The intermediate electrode  10  is a structure that has electrodes  101 , on its inner face (and sometimes over its entire surface), that in use are biased to a different potential from that of the ejection electrodes  7  on the ejection upstands  2 . The intermediate electrode  10  may be patterned so that each ejection upstand  2  has an electrode facing it that can be individually addressed, or it can be uniformly metallised such that the whole surface of the intermediate electrode  10  is held at a constant bias. The intermediate electrode  10  acts as an electrostatic shield by screening the ejection channel from external electric fields and allows the electric field at the ejection location  6  to be carefully controlled. 
         [0009]    The solid arrow  11  shows the ejection direction and again points in the direction of the substrate. In  FIG. 3  the ink usually flows from left to right. 
         [0010]    In operation, it is usual to hold the substrate at ground (0 V), and apply a voltage, V IE , between the intermediate electrode  10  and the substrate. A further potential difference of V B  is applied between the intermediate electrode  10  and the electrodes  7  on the ejection upstand  2  and the cheeks  3 , such that the potential of these electrodes is V IE +V B . The magnitude of V B  is chosen such that an electric field is generated at the ejection location  6  that concentrates the particles, but does not eject the particles. Ejection spontaneously occurs at applied biases of V B  above a certain threshold voltage, V S , corresponding to the electric field strength at which the electrophoretic force on the particles exactly balances the surface tension of the ink. It is therefore always the case that V B  is selected to be less than V S . Upon application of V B , the ink meniscus moves forwards to cover more of the ejection upstand  2 . To eject the concentrated particles, a further voltage pulse of amplitude V P  is applied to the ejection upstand  2 , such that the potential difference between the ejection upstand  2  and the intermediate electrode  10  is V B +V P . Ejection will continue for the duration of the voltage pulse. Typical values for these biases are V IE =500 volts, V B =1000 V and V P =300 volts. 
         [0011]    The voltages actually applied in use may be derived from the bit values of the individual pixels of a bit-mapped image to be printed. The bit-mapped image is created or processed using conventional design graphics software such as Adobe Photoshop and saved to memory from where the data can be output by a number of methods (parallel port, USB port, purpose-made data transfer hardware) to the printhead drive electronics, where the voltage pulses which are applied to the ejection electrodes of the printhead are generated. 
         [0012]    One of the advantages of electrostatic printers of this type is that greyscale printing can be achieved by modulating either the duration or the amplitude of the voltage pulse. The voltage pulses may be generated such that the amplitude of individual pulses are derived from the bitmap data, or such that the pulse duration is derived from the bitmap data, or using a combination of both techniques. 
         [0013]    Printheads comprising any number of ejectors can be constructed by fabricating numerous cells  5  of the type shown in  FIGS. 1 to 3  side-by-side along the x-axis, but in order to prevent gaps in the printed image resulting from spacing between the individual printheads, it may be necessary to ‘overlap’ the edges of adjacent printheads, by staggering the position of the printheads in the y-axis direction. A controlling computer converts image data (bit-mapped pixel values) stored in its memory into voltage waveforms (commonly digital square pulses) that are supplied to each ejector individually. By moving the printheads relative to the substrate in a controllable manner, large area images can be printed onto the substrate in multiple ‘swathes’. It is also known to use multiple passes of one or more printheads to build up images wider than the printhead and to ‘scan’ or index a single printhead across the substrate in multiple passes. 
         [0014]    However, stitch lines frequently result from the use of overlapped printheads or from overlapping on multiple passes and therefore it is known to use interleaving techniques (printing alternate single or groups of pixels from adjacent printheads or from different passes of the same or a different printhead) to distribute and hide the edge effects of the print swathes resulting from the overlapping ends of the printheads. It is generally recognised that a stitching strategy is necessary to obtain good print quality across a join between printed swathes. The known techniques rely on the use of a binary interleaving strategy i.e. a given pixel is printed by one printhead or the other. For example, alternate pixels along the x-axis are printed from adjacent overlapping printheads. Alternatively, a gradual blend from one swathe to the next can be used, by gradually decreasing the numbers of adjacent pixels printed from one printhead while increasing the numbers of adjacent pixels printed from the other printhead. This latter technique can be expanded by dithering the print in the y-axis direction. Another known technique is the use of a saw tooth or sinusoidal ‘stitch’ to disrupt any visible stitch line. 
         [0015]    These techniques all represent different ways in which printing can be alternated between the nozzles of two overlapping printheads and the success of them depends on the droplet placement accuracy and registration of the two printheads, and is particularly sensitive to factors like substrate wander between lines of printheads. This can be mitigated by the dispersion and deliberate movement of the stitch to break up visible lines and disperse the errors over the width of the overlapping regions of the adjacent printed swathes. 
       SUMMARY OF THE INVENTION 
       [0016]    According to the present invention there is provided a method of printing a two-dimensional bit-mapped image having a number of pixels per row for printing using a plurality of overlapping printheads or a printhead or printheads indexed through overlapping positions, the or each printhead having a row of ejection channels, each ejection channel having associated ejection electrodes to which a voltage is applied in use sufficient to cause particulate concentrations to be formed from within a body of printing fluid, and wherein, in order to cause volumes of charged particulate concentrations of one of a number of predetermined volume sizes to be ejected as printed droplets from selected ejection channels of the overlapping printheads, voltage pulses of respective predetermined amplitude and duration, as determined by respective image pixel bit values, are applied to the electrodes of the selected ejection channels, characterised in that
       for each row of the image, the values of the voltage pulses to be applied to the overlapping printheads to form pixels printed by overlapped ejection channels are adjusted in dependence on the position of the pixel within an overlapped region of the printheads and in dependence on the predetermined volume size of the pixel.       
 
         [0018]    This technique provides an alternative strategy to those known in the art, which creates each printed pixel in the overlap region of printheads from a contribution from both printheads in the overlap region, i.e. an ejection from one printhead plus an ejection from the overlapping printhead, which together give a pixel of the required size and/or density. The relative contributions from the two printheads change to create a progressive fade-out from the one printhead with an overlapping fade-in to the other printhead across the overlap region. This is less sensitive to dot placement errors and substrate wander, because such errors are less inclined to produce white space between dots. 
         [0019]    This fading technique involves reducing the pulse lengths (or else the amplitude) of the ejection voltage pulses to vary the volume of the droplets providing the pixels printed in the overlap region so that one printhead fades out as the other fades in, the sum of the print from the two heads producing the required optical density uniformly across the overlap. 
         [0020]    The technique is not usable by other greyscale inkjet technologies, whose ejection is limited to a fixed set of droplet sizes as it requires a high level of variable droplet size control. The Tonejet® method as referred to above, by contrast, has the feature that the ejection volume is continuously, addressably, variable through the mechanism of pulse length control. In the Tonejet® method, for a given pixel level, a continuous-tone pulse value can be assigned to produce the desired dot size. Such calibrations are not possible for a conventional drop-on-demand (DOD) printhead whose drop volumes are quantised by chamber volume, nozzle size, etc. 
         [0021]    Similar issues arise and the same solution can be used whether the printheads carry out printing in a single pass, printing the required pixels from multiple (interleaved) printheads closely spaced one behind another, or if the pixels are printed from multiple passes of the same or different printheads. The printhead(s) may be indexed multiple times. 
         [0022]    In order to provide the required ‘fade’, a fading function for each printhead or swathe of print is used to define the profile of the fade across the overlap region. It is usual to restrict droplet volumes in printheads of the Tonejet® type to a number of predetermined sizes to simplify computations. In the method of the invention it is advantageous to provide a different fading function for different droplet volumes. This arises from the fact that the additive print density of pixels printed by two droplets follows a function which is non-linear with droplet volume. 
         [0023]    The invention also includes apparatus for printing a two-dimensional bit-mapped image having a number of pixels per row, said apparatus having a plurality of overlapping printheads or a printhead or printheads indexed through overlapping positions, the or each printhead having a row of ejection channels, each ejection channel having associated ejection electrodes to which a voltage is applied in use sufficient to cause particulate concentrations to be formed from within a body of printing fluid, and wherein, in order to cause volumes of charged particulate concentrations of one of a number of predetermined volume sizes to be ejected as printed droplets from selected ejection channels of the overlapping printheads, voltage pulses of respective predetermined amplitude and duration, as determined by respective image pixel bit values, are applied to the electrodes of the selected ejection channels, characterised in that
       for each row of the image, the values of the voltage pulses to be applied to the overlapping printheads to form pixels printed by overlapped ejection channels are adjusted in dependence on the position of the pixel within an overlapped region of the printheads and in dependence on the predetermined volume size of the pixel.       
 
         [0025]    The plurality of overlapping printheads may be fixed in position relative to one another in use. 
         [0026]    The plurality of overlapping printheads may comprise a first printhead printing on a first pass over the print substrate and the same or another printhead printing on a later pass over the print substrate and overlapping in position with the position of the first printhead. The first printhead can be indexed between passes over the substrate by a distance equal to the width of the row of channels of the printhead less the desired overlap. 
         [0027]    The printhead may be one of a number of identical printheads disposed in a module parallel to one another and offset by a proportion of the distance between adjacent ejection channels whereby the printed image has a resolution greater than the distance between adjacent ejection channels. A plurality of said modules can be overlapped one with another to enable a print width greater than the width of an individual module. Alternatively, the module can be indexed between passes over the substrate by a distance equal to the width of the row of channels of a printhead less the desired overlap. 
         [0028]    In the case of a single printhead, the printhead may be indexed by a proportion of the distance between adjacent ejection channels whereby the printed image has a resolution greater than the distance between adjacent ejection channels. 
         [0029]    Preferably, the values of the voltage pulses to be applied to the overlapping printheads may be determined from a predetermined fading function dependent on the level of the predetermined volume sizes of the pixels to be printed in the overlapped region of the printheads. 
         [0030]    The pixel bit values may be adjusted in dependence on the position of the pixel within an overlapped region of the printheads and in dependence on the predetermined volume size of the pixel, prior to conversion of the pixel values into voltage pulses of respective predetermined amplitude and duration to cause printing. 
         [0031]    Alternatively, the pixel bit values of the image may be provided to printhead drive electronics which converts the values into voltage pulses, and the voltage pulse values are therein determined in dependence on the position of the pixel within an overlapped region of the printheads and in dependence on the predetermined volume size of the pixel, prior to being applied to the ejection electrodes of the printhead. 
         [0032]    In a particular method, fading functions of the following form can be used to define the profile of the fade across the overlap region of two printheads/swathes of print A and B: 
         [0000]        f   A ( x )= f   min +(1− f   min )(1− x ) α 
 
         [0000]        f   B ( x )= f   min +(1− f   min )· x   α 
 
         [0033]    Where
       f A  is the fading function of printhead/swathe A   f B  is the fading function of printhead/swathe B, which is the mirror-image of f A      f min  is the minimum value for the fading function, producing the minimum printable level   x is the normalised position across the overlap region, 0≦x≦1   α is the power of the fading function.       
 
         [0039]    In colour printers the printheads of each colour may be provided with different fading functions. The overlap position between printheads of the different colours may also be different. 
         [0040]    The fading function may additionally be adjusted, either randomly or according to a suitable waveform function, so as to move the centre point of the fade around within the area of overlap to ‘dither’, effectively, the stitching between the print swathes to still further reduce the observable artifacts. 
         [0041]    The fading functions may be applied at one of a number of stages in the processing of the image for printing, for example:
       In the Raster Image Processing software on the controlling computer, resulting in a modified version of each swathe of the bitmap image that may then be converted into print pulses by the printhead drive electronics in the normal way;   In the printhead drive electronics, which in this case may be programmed to generate modified pulse amplitudes or durations in response to incoming pulse data according to the position of the ejector in the overlap region.       
 
         [0044]    The fading functions may be applied to the pixel value data in the form of a mathematical function in software, or in the form of a look-up table stored in the memory of the controlling computer, the data feed electronics or the pulse generation electronics. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0045]    Examples of methods and apparatus according to the present invention will now be described with reference to the accompanying drawings, in which: 
           [0046]      FIG. 1  is a CAD drawing showing detail of the ejection channels and ink feed pathways for an electrostatic printer; 
           [0047]      FIG. 2  is a schematic diagram in the x-z plane of the ejection channel in an electrostatic printhead of the type shown in  FIG. 1 ; 
           [0048]      FIG. 3  is a schematic diagram in the y-z plane of the ejection channel in an electrostatic printhead of the type shown in  FIG. 1 ; 
           [0049]      FIG. 4  illustrates a plan view of part of an example of a multi-printhead printer; 
           [0050]      FIG. 5  illustrates a plan view of a number of printhead modules mounted together; 
           [0051]      FIG. 6  illustrates an example of another multi-printhead printer arranged in four modules; 
           [0052]      FIG. 7  is a block diagram of some of the printer components of the example of  FIGS. 4 and 5 ; 
           [0053]      FIG. 8  is a flowchart showing the process of preparing print data for individual printheads of the exemplified printer; 
           [0054]      FIG. 9  is a flowchart showing (for simplicity) the process of applying respective fading functions to print data for a pair of printheads of the exemplified printer; 
           [0055]      FIG. 10  shows sets of pulse length curves corresponding to the last iteration of the calculated parameters; 
           [0056]      FIG. 11  shows a set of fading functions plotted to show the voltage pulse length multiplier against position across the overlap between a pair of adjacent printheads; 
           [0057]      FIG. 12  is a block diagram illustrating how the amplitude of an ejection pulse can be adjusted and a related waveform diagram showing resulting illustrative adjusted amplitudes of a pulse; 
           [0058]      FIG. 13  is a block diagram illustrating how the duration of an ejection pulse can be adjusted and a related waveform diagram showing resulting illustrative adjusted durations of a pulse; and 
           [0059]      FIG. 14  is a representation of a typical look-up table representing voltage pulse values adjusted in accordance with the corresponding fading function. 
       
    
    
     DETAILED DESCRIPTION 
       [0060]    The examples illustrated with reference to  FIGS. 4 to 11  can utilise printheads and a printing process as generally described with reference to  FIGS. 1 to 3 ,  12  and  13 . 
         [0061]      FIG. 4  illustrates a printing bar or module  300  utilising four printheads  300 A-D, each having multiple print locations (ejection channels or channels)  301  at a spacing providing 150 channels per inch (60 channels per centimetre) (150 dpi printing) to provide an appropriate swathe of the printed image in use, and with an overlap between each printhead and its adjacent printhead(s) such that a number of ejection channels  301  (in this case 10) are overlapped between printhead pairs  300 A/ 300 B,  300 B/ 300 C &amp;  300 C/ 300 D in the direction of print substrate movement (arrow  302 ) in order to stitch each swathe of print with it neighbour(s). 
         [0062]      FIG. 5  illustrates a further example of a printer having modules  300  also utilising four printheads  300 A-D of the same construction and channel spacing (150 dpi) as those of  FIG. 4 , but the printheads being disposed substantially in alignment one behind the other in the intended direction of substrate movement and offset across the direction of print substrate motion only by the distance necessary to enable the required higher definition printing, in this case 600 dpi (an offset of approximately 42 μm). In this case, adjacent pixels of the printed image are printed from adjacent printheads to achieve the required print density and the plural modules  300 , disposed one behind the other but offset to provide the desired print swathes, produce the desired overall print width in a similar manner to the example of  FIG. 4  and hence with a similar overlap of the respective printheads of each module in order to stitch the swathes of print together. The multiple modules  300  together provide a printer of a width sufficient to allow 600 dpi printing in a single pass relative to the substrate. 
         [0063]    In a variation (not shown) a single one of the modules as per  FIG. 5  is indexed in multiple passes over the substrate across the print motion direction to provide the required number of print swathes to form the overall width of print required. In this case, the overlap of adjacent indexed positions is provided as per the overlap between modules in  FIG. 5 , to enable stitching of one swathe to another. 
         [0064]      FIG. 6  illustrates a still further example having modules  300 - 1 ,  300 - 2 ,  300 - 3 ,  300 - 4  also arranged to provide for 600 dpi printing from printheads having a 150 dpi spacing, in this case each of the modules being substantially the same as that of  FIG. 4 , but each successive module being displaced or offset transversely to the print substrate direction of motion by approximately 42 μm. In this case stitching may be effected between adjacent printheads  300 A,  300 B etc. in each module as per  FIG. 4 , or between the swathes of print printed by each set of four interleaved printheads that are substantially in alignment with each other in the substrate movement direction  302 . 
         [0065]    A further example of printhead (not shown) may utilise a single printhead indexed by substantially a quarter of the printhead width between passes to (a) provide (say) 600 dpi printing from a 150 dpi printhead, and (b) an overall print width much greater than the printhead width (the number of indexing motions and hence passes being determined by the desired overall print width. In this case, swathes of 150 dpi print from each pass are interleaved to create 600 dpi print. The overlap between 150 dpi swathes occurs between the first, fifth, ninth, etc. passes/indexations and stitching of the swathes correspondingly occurs between opposite ends of the (single) printhead on the first, fifth, ninth, etc. passes/indexations; similarly, overlap and stitching of 150 dpi swathes occurs between the second, sixth, tenth, etc. passes, between the third, seventh, eleventh, etc. passes and between the fourth, eighth, twelfth, etc. passes. 
         [0066]    In all examples, a substrate position synchronisation signal (originating from, for example, a shaft encoder  216  (see  FIG. 7 ) or substrate position servo controller) is used to ensure that droplets are printed at appropriate times depending on the offsets of printheads along the direction of print substrate motion. Such a process is well understood in the art and does not form a part of the present invention. The use of shaft encoders overcomes potential problems otherwise arising from variations in substrate speed relative to the printhead(s) and from offsets of the printhead(s) in the direction of print substrate motion either in printers with multiple offset printheads or in printers with multiple passes of a single printhead or printhead module (having itself multiple printheads). 
         [0067]    Before describing an example of the method according to the invention, it may be useful to describe the two methods generally usable to control the volume of droplets printed (or ejected) using the Tonejet® method. 
         [0068]      FIG. 12  shows the block diagram of a circuit  30  that can be used to control the amplitude of the ejection voltage pulses V E  for each ejector (upstand  2  and tip  21 ) of the printhead, whereby the value P n  of the bitmap pixel to be printed (an 8-bit number, i.e having values between 0 and 255) is converted to a low-voltage amplitude by a digital-to-analogue converter  31 , whose output is gated by a fixed-duration pulse V G  that defines the duration of the high-voltage pulse V P  to be applied to the ejector of the printhead. This low-voltage pulse is then amplified by a high-voltage linear amplifier  32  to yield the high-voltage pulse V P , typically of amplitude 100 to 400V, dependent on the bit-value of the pixel, which in turn is superimposed on the bias voltages V B  and V IE  to provide the ejection pulse V E =V IE +V B +V P . 
         [0069]      FIG. 13  shows the block diagram of an alternative circuit  40  that can be used to control the duration of the ejection voltage pulses V E  for each ejector of the printhead, whereby the value P n  of the bitmap pixel to be printed is loaded into a counter  41  by a transition of a “print sync” signal PS at the start of the pixel to be printed, setting the counter output high; successive cycles (of period T) of the clock input to the counter cause the count to decrement until the count reaches zero, causing the counter output to be reset low. The counter output is therefore a logic-level pulse V PT  whose duration is proportional to the pixel value (the product of the pixel value P n  and the clock period T); this pulse is then amplified by a high voltage switching circuit  42 , which switches between a voltage (V IE + B ) when low to (V IE +V B +V P ) when high, thus generating the duration-controlled ejection pulse V E =V IE +V B +V P . 
         [0070]    The value of P n  of the bitmap pixel to be printed corresponds to a duty cycle (of the ejection pulse) between 0% and 100%. Typically, when printing at a resolution of 600 dpi and with relative motion between the print substrate and the printhead being at a speed of 1 ms −1 , this equates to a pulse length of between 0 and 42 μm on a 42 μm pulse repetition period. 
         [0071]    Of these alternative techniques, in practice it is simpler to modulate the duration of the pulse, but either technique may be appropriate in given circumstances and both may be used together. 
         [0072]    In operation, in one example according to the invention, as shown in  FIGS. 4 ,  7  and  8 , a colour image  200 , for example created by using (say) any one of a number of well-known image creation software packages such as Adobe Illustrator, is uploaded into a memory  201  of a computer  202 . The initial image  200  is then rasterised within the computer  202  using image processing software  203  (see  FIGS. 7 and 8 ) and a corresponding colour bitmap image  204  is then created and saved in memory  205 . A colour profile  206  is then applied to the bitmap image to enable a calibration for tonal response of the print process to be achieved, and each pixel is then ‘screened’ or filtered  207  so that each colour component of the pixel is filtered into one of a number (n) of different ‘levels’ and the data, representing in this case the CMYK n-level image  208 , is then stored in RAM  209  and the individual primary colour components separated  210  into respective data sets  212   c ,  212   m ,  212   y  and  212   k.    
         [0073]    Given the known number of strips or swathes of print which are required to be laid down, greyscale data for each primary colour is then stripped  213  into data sets—in this case two data sets  302 A,  302 B for one pair of overlapped print swathes or printheads  300 A/ 300 B to represent pixel values for each column of the individual printhead widths (number of pixels across the print substrate provided by a single printhead). These data sets provide bitmaps which correspond to the ejection channels  301  of the individual printheads  300 A,  300 B used to print the final image. 
         [0074]      FIG. 9  illustrates the process of ‘stitching’ the swathes of print of a single colour separation to be generated by adjacent printheads  300 A and  300 B and specifically illustrates the application of appropriate respective fading functions to the pixel values. The desired fading functions are stored in corresponding look-up tables  214  held within memory  215 . Each level of pixel value for each colour will usually have a separate fading function held in the look-up tables  214 . The individual fading functions are then applied  303 A/ 303 B to each pixel within the bitmap datasets for the individual heads  300 A,  300 B in accordance with its colour and level to generate pulse length values (or pulse amplitude values or both) to create respective printhead pulse datasets  304 A,  304 B. 
         [0075]    The pulse data  304 A,  304 B is then transferred in step  305 A/ 305 B, according to the relative position of the print substrate and the printheads (as determined by the shaft encoder  216 ), to the driver cards (pulse generator electronics)  306 A,  306 B in which the data is utilised to determine the length of the drive pulses applied to the individual printhead ejection channels  301  as required and in which voltage pulses of predetermined duration and/or amplitude are generated according to the pulse data for each pixel. The data is transferred in time-dependency on the substrate position and offset of the ejection channels  301  of one printhead  300 A from those of the adjacent overlapping printhead  300 B. 
         [0076]    A process of generating and applying the fading functions will now be described in an example which uses four passes of two 150 channel per inch printheads overlapped to print a cylindrical substrate with the two overlapped heads spanning the width of the substrate, and the substrate being spun four times to achieve full coverage at 600 dpi. The fading technique described is directly applicable to the overlapped portions of multiple or single printheads making one or more passes over the substrate. 
         [0077]    An overlap of 10 printhead channels (40 pixels) is used in the specific example described. However, the width of the overlap region will affect the visibility of the join: generally, the larger the overlap, the more the errors can be dispersed and the less visible the join. This has to be balanced with the desire for the smallest overlap to maximise the print width. 
         [0078]    In order to prepare the required fading functions a series of test images were prepared using single printheads and printed with a selection of fading functions to experimentally determine the most effective. The image used was a benchmark test image that contains a full range of print levels. The image was screened using a standard 4-level error diffusion method, rendering the image in dot sizes of 0%, 50%, 75% and 100% of the maximum dot size that gives the required maximum optical density of print. Initial function parameters were estimated and then iterated twice until the print quality looked acceptable. The parameters were then determined to be as follows: 
         [0000]    
       
         
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Dot size level: 
               
             
          
           
               
                   
                 50% 
                 75% 
                 100% 
               
             
          
           
               
                 Iteration 
                 f min   
                 P min   
                 α 
                 f min   
                 P min   
                 α 
                 f min   
                 P min   
                 α 
               
               
                   
               
             
          
           
               
                 1 
                 0.24 
                 0.12 
                 0.80 
                 0.27 
                 0.20 
                 0.65 
                 0.17 
                 0.17 
                 0.6 
               
               
                 2 
                 0.30 
                 0.15 
                 0.85 
                 0.2 
                 0.15 
                 0.68 
                 0.17 
                 0.17 
                 0.6 
               
               
                 3 
                 0.30 
                 0.15 
                 0.85 
                 0.2 
                 0.15 
                 0.75 
                 0.17 
                 0.17 
                 0.6 
               
               
                   
               
             
          
         
       
     
         [0079]    For information, the pulse length curves corresponding to the last iteration of the parameters are shown plotted in  FIG. 10 . 
         [0080]    As mentioned above, in this example, for each droplet volume size level, fading functions of the following form are used to define the profile of the fade across the overlap region of two printheads/swathes  300 A,  300 B of print A and B: 
         [0000]        f   A ( x )= f   min +(1− f   min )(1− x ) α 
 
         [0000]        f   B ( x )= f   min +(1− f   min )· x   α 
 
         [0081]    Where
       f A  is the fading function of printhead/swathe A   f B  is the fading function of printhead/swathe B, which is the mirror-image of f A      f min  is the minimum value for the fading function, producing the minimum printable level   x is the normalised position across the overlap region, 0≦x≦1   α is the power of the fading function.       
 
         [0087]    Examples of the fading functions are shown plotted in  FIG. 11 . The function produces a linear fade for α=1, a convex curve for α&lt;1 and a concave curve for α&gt;1.  FIG. 11  shows fading functions for α=1, 0.5 and 2. Here f min  is set to 0.2. 
         [0088]    The fading functions are applied to the image data by multiplying with the image pixel values. This is applied to the image data after screening, i.e. after the pixel values have otherwise been calculated, and may be applied in Raster Image Processing on a controlling computer or in the printhead drive electronics. As the fading function is dependent on the grey level/droplet volume size, the function to apply for a given pixel is chosen according the screened value of that pixel. For example, a 50% level pixel will be multiplied by the fading function for the 50% level, etc. A family of fading functions therefore exists that contains as many curves as there are non-zero droplet sizes in the screened image (e.g. 3 to a 4-level image; 7 for an 8-level image). 
         [0089]    The pixel values that result from multiplying an image pixel of level P L  by the fading function for that level are derived from the following: 
         [0090]    Taking the generic fading function for one side (B): 
         [0000]        f ( x )= f   min +(1− f   min )· x   α 
 
         [0091]    For each pixel level L in the screened image there is a fading function f L (x): 
         [0000]        f   L ( x )= f   min     L   +(1− f   min     L   )· x   α     L    
 
         [0092]    A pixel of level L in position x across the image is faded by multiplying its value P L  by the fading function for its level: 
         [0000]        P ( x )= P   L   ·f   L ( x ) 
         [0000]        P ( x )= P   L   {f   min     L   +(1− f   min     L   )· x   α     L}   
 
         [0000]        P ( x )= P   min     L   +( P   L   −P   min     L   )· x   α     L    
 
         [0093]    where
       P min     L   =P L ·f min     L            
 
         [0095]    P minL  is a minimum desired pixel value, which is approximately the same whatever the original value P L  of a pixel. 
         [0096]    Hence, the pixel values that result from multiplying an image pixel of level P L  by the fading function for that level are: 
         [0000]        P   A ( x )= P   min     L   +( P   L   −P   min     L   )(1− x ) α     L    
 
         [0000]        P   B ( x )= P   min     L   +( P   L   −P   min     L   )· x   α     L    
 
         [0097]    Where
       P A  is the modified value of the pixel of head/swathe A   P B  is the modified value of the pixel of head/swathe B   P minL  is the minimum desired value for the pixel.