Abstract:
A method of producing, on a physical medium, a gradient tonal representation of an image and a printhead for producing the same. An input image is divided into first and second regions. First, continuously variable intensity level, continuous tone and second, discretely variable intensity level, half-tone portions of the representation which respectively correspond to the first and second regions of the image are then printed by depositing selected quantities of ink on the first and second portions of the physical medium such that each pixel thereof has an ink intensity level corresponding to the image intensity level for the corresponding one of the pixels of the first region of the image. The ink is deposited on the second portion of the physical medium by depositing a spot of ink having a first diameter on selected ones of the pixels of the second portion, depositing a spot of ink having a second diameter on others of the pixels of the second portion and depositing no ink on still others of the pixels of the second portion such that the second portion of the representation has the desired ink intensity level. The color of the ink ejected may be black, in which case, the gradient tonal representation produced thereby shall be a gray scale representation, or other color such as yellow, cyan or magenta.

Description:
This application is a continuation, of application Ser. No. 08/259,862, filed Jun. 15, 1994, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention generally relates to printhead apparatus and, more particularly, to a method and apparatus for producing gradient tonal representations, for example, gray scale or other gradient single color representations, of images by combining continuous and halftone printing techniques. 
     2. Description of Related Art 
     Printers provide a means of outputting a permanent record in human readable form. Typically, a printing technique may be categorized as either impact printing or non-impact printing. In impact printing, an image is formed by striking an inked ribbon placed near the surface of the paper. Impact printing techniques may be further characterized as either formed-character printing or matrix printing. In formed-character printing, the element which strikes the ribbon to produce the image consists of a raised mirror image of the desired character. In matrix printing, the character is formed as a series of closely spaced dots which are produced by striking a provided wire or wires against the ribbon. Here, characters are formed as a series of closely spaced dots produced by striking the provided wire or wires against the ribbon. By selectively striking the provided wires, any character representable by a matrix of dots can be produced. 
     Non-impact printing techniques is often preferred over impact printing in view of its tendency to provide higher printing speeds as well as its better suitability for printing graphics and halftone images. Non-impact printing techniques include matrix, electrostatic and electrophotographic type printing techniques. In matrix type printing, wires are selectively heated by electrical pulses and the heat thereby generated causes a mark to appear on a sheet of paper, usually specially treated paper. In electrostatic type printing, an electric arc between the printing element and the conductive paper removes an opaque coating on the paper to expose a sublayer of a contrasting color. Finally, in electrophotographic printing, a photoconductive material is selectively charged utilizing a light source such as a laser. A powder toner is attracted to the charged regions and, when placed in contact with a sheet of paper, transfers to the paper&#39;s surface. The toner is then subjected to heat which fuses it to the paper. 
     Another form of non-impact printing is generally classified as ink jet printing. Ink jet printing devices use the ejection of tiny droplets of ink to produce an image. The devices produce highly reproducible and controllable droplets of ink, such that an ejected droplet may be precisely directed to a location specified by digitally stored image data for deposition thereat. Most ink jet printing devices commercially available may be generally classified as either a “continuous jet” type ink jet printing device where droplets are continuously ejected from the printhead and either directed to or away from a substrate, for example, a sheet of paper, depending on the desired image to be produced or as a “drop-on-demand” type ink jet printing device where droplets are ejected from the printhead in response to a specific command related to the image to be produced and all such ejected droplets are directed to the substrate for deposition. 
     Many drop-on-demand type ink jet printheads utilize electromechanically induced pressure waves to produce the desired droplets of ink. In one representative configuration thereof, a drop-on-demand type ink jet printhead has a horizontally spaced parallel array of internal ink-carrying channels. These internal channels are covered at their front ends by a plate member through which a spaced series of small ink discharge orifices are formed. Each channel opens outwardly through a different one of the spaced orifices. Within such a printhead, a volumetric change in fluid contained in the internal channels is induced by the application of a voltage pulse to a piezoelectric material which is directly or indirectly coupled to the fluid. This volumetric change causes pressure/velocity transients to occur in the fluid and these are directed so as to force a small, fixed quantity of ink, in droplet form, outwardly through the discharge orifice at a fixed velocity. The droplet strikes the paper at a specified location related to the image being produced and forms an ink “spot” having a diameter directly related to the volume of the ejected droplet. 
     Due to their ability to produce a spot at any location on a sheet of paper, ink jet and other non-impact printers have long been contemplated as being particularly well suited to the production of continuous and halftone images. However, the ability of ink jet printers to produce continuous and half tone images has been quite limited due to the fact that most ink jet printheads can only produce droplets having both a fixed volume and a fixed velocity. As a result, ink spots produced by such droplets striking a sheet of paper are of a fixed size, typically in the range of 120 μm to 150 μm, and the same intensity. Additionally, all ink jet printheads use a fixed resolution, typically 300-400 dpi (or “dots per inch”) or lower, to place droplets on a sheet of paper. In contrast, a typical high quality halftone image produced using offset printing techniques uses variable sized spots at resolutions of up to 240 dots per inch. 
     Due to the aforementioned limitations, ink jet printheads have heretofore utilized spot density, as opposed to spot size, when attempting to produce a gray scale image. To do so, the ink jet printhead creates various shades of gray by varying the density of the fixed size ink spots. Darker shades are created by increasing spot density and lighter shades are created by reducing spot density. Producing a gray scale image in this manner, however, reduces the spacial resolution of the printer, thereby limiting its ability to produce finely detailed images. Furthermore, the more levels added to the gray scale, the greater the resultant degradation of the printer&#39;s spacial resolution. A second proposed solution has been to direct multiple droplets at a single location on the sheet of paper to form variably sized spots. While such a method can produce the variably sized spots necessary to produce a gray scale image, such a technique tends to reduce the operating speed of the printer to an unacceptably low level. Furthermore, this technique may also produce elongated or elliptical dot patterns. 
     It can be readily seen from the foregoing that it would be desirable to provide a method and associated printing apparatus capable of producing a gray scale or other gradient tonal representation of an image. It is, therefore, an object of the present invention to provide such an improved drop-on-demand type ink jet printhead. 
     SUMMARY OF THE INVENTION 
     In one embodiment, the present invention is of a method of producing, on a physical medium, a gradient tonal representation of an image in which the image is divided into first and second regions. First, continuously variable intensity level and second, discretely variable intensity level portions of the representation which correspond to the first and second regions of the image are then printed. The steps of printing the first and second portions of said representation may further include the steps of printing continuous and halftone representations of the first and second regions of the image, respectively. The image is comprised of a plurality of pixels and, in one aspect thereof, the image may be divided into the first and second regions by determining an intensity level for each pixel of the image and assigning each of the pixels to either the first or second region based upon its intensity level. Each pixel may be assigned to the first region if its intensity level is within a range for which a continuously variable level representation may be printed and to the second level if its intensity level is within a range for which a discretely variable intensity level representation may be printed. 
     In further aspects thereof, the continuously variable intensity level portion of the representation may be produced by depositing a selected quantity of ink on the first portion of the physical medium such that each pixel thereof has an ink intensity level corresponding to the image intensity level for the corresponding one of the pixels of the first region of the image and the discretely variable intensity level portion of the representation may be produced by depositing ink on the second portion of the physical medium such that the second portion has an ink intensity level corresponding to the determined image intensity level for the corresponding portion of the second region of the image. The ink may deposited on the second portion of the physical medium by depositing a spot of ink having a first diameter on selected ones of the pixels of the second portion and a spot of ink having a second diameter on others of the pixels of the second portion such that the second portion of the representation has the desired ink intensity level. The color of the ejected ink may be black, in which case, the gradient tonal representation produced thereby shall be a gray scale representation, or other color such as yellow, cyan or magenta. 
     In another embodiment, the present invention is of a method of producing, on a physical medium, a gradient tonal representation of an image. An image intensity level is determined for each pixel of the image and each corresponding pixel of the representation is assigned to a first portion thereof if the image intensity level is within a first range and to a second portion thereof if the image intensity level is within a second range. From a continuously variable range of quantities, a quantity of ink to be deposited on each pixel of the representation is selected and a continuous tone portion of the representation generated by depositing the selected quantities of ink on each of the pixels of the first portion of the representation. Certain ones (or all) of the pixels of the second portion of the representation are then selected to have ink deposited thereon. From a discretely variable range of quantities, a quantity of ink to be deposited on each selected pixel of the second portion of the representation is selected and a half-tone portion of the representation generated by depositing the selected quantity of ink on each of the selected pixels of the second portion of the representation. In one aspect thereof, the selected quantity is deposited on each selected pixel by depositing a spot of ink having a first diameter on certain ones, a spot of ink having a second diameter on others and/or no ink spot on still others of the selected pixels of the second portion of the representation. The color of the ejected ink may be black, in which case, the gradient tonal representation produced thereby shall be a gray scale representation, or other color such as yellow, cyan or magenta. 
     In yet another embodiment, the present invention is of a printhead for producing a gradient tonal representation of an image on a physical medium. The printhead includes means for forming, for a first portion of the image having an image intensity within a first image intensity range, a continuous tone representation of the first portion of the image on the physical medium and means for forming, for a second portion of the image having an image intensity within a second image intensity range, a half-tone representation of the second portion of the image on the physical medium. In one aspect thereof, the means for forming a continuous tone representation of the first portion of the image further includes means for producing, at selected locations for the continuous tone representation, a spot of ink having a volume selectable from a first continuously variable range of values and, in another aspect thereof, the means for forming a half-tone representation of the second portion of the image further comprises means for producing, at selected locations for the half-tone representation, a spot of ink having a volume selectable between first and second discrete values outside the continuously variable range of values. In a further aspect thereof, the means for forming a continuous tone representation of the first portion of the image may further include means for generating a spot of ink having a size selectable from a second continuously variable range of values in which the first discrete value forms an upper boundary for the first continuously variable range of values and the second discrete value forms a lower boundary for the second continuously variable range of values. 
     In still yet another embodiment, the present invention is of a drop-on-demand ink jet printhead for producing a gradient tonal representation of an image on a physical medium. The ink jet printhead includes means for forming, for a first portion of the image having an image intensity within a first image intensity range, a continuous tone representation of the first portion of the image on the physical medium and means for forming, for a second portion of the image having an image intensity within a second image intensity range, a half-tone representation of the second portion of the image on the physical medium. In one aspect thereof, the means for forming a continuous tone representation of the first portion of the image further includes means for generating a droplet of ink having a volume selectable from a first continuously variable range of values and, in another aspect thereof, the means for forming a half-tone representation of the second portion of the image further comprises means for generating a droplet of ink having a volume selectable between first and second discrete values outside the continuously variable range of values. In a further aspect thereof, the means for forming a continuous tone representation of the first portion of the image may further include means for generating a droplet of ink having a volume selectable from a second continuously variable range of values in which the first discrete value forms an upper boundary for the first continuously variable range of values and the second discrete value forms a lower boundary for the second continuously variable range of values. The color of the ink ejected may be black, in which case, the gradient tonal representation produced thereby shall be a gray scale representation, or other color such as yellow, cyan or magenta. 
     In another embodiment thereof, the present invention is of a drop-on-demand ink jet printhead for producing a gradient tonal representation of an image on a physical medium which includes a main body portion having an ink-carrying channel extending therethrough. Further provided are means for ejecting, from the ink-carrying channel, droplets of ink capable of forming a continuous tone representation of a first portion of the image on the physical medium. The droplets have a volume which may be selected from a first continuously variable range. The ink jet printhead is further provided with means for ejecting, from the ink-carrying channel, droplets of ink capable of forming a half-tone representation of a second portion of the image on the physical medium. These droplets have a volume selectable between first and second discrete values outside the first continuously variable range of values. In one aspect thereof, the means for ejecting droplets of ink having a volume which may be selected from the first continuously variable range may be comprised of a piezoelectric actuator acoustically coupled to the ink-carrying channel and means for applying a first selected voltage to the piezoelectric actuator for a first selected period of time to cause a deflection of the piezoelectric actuator. The deflection of the piezoelectric actuator generates a pressure wave in the channel which causes the ejection of a droplet of ink having the volume within the first continuously variable range. In a further aspect thereof, the means for ejecting droplets of ink having a volume which may be selected from the first discrete value or the second discrete value further comprises means for applying a second selected voltage to the piezoelectric actuator for a second selected period of time to cause a deflection of the piezoelectric actuator. The deflection of the piezoelectric actuator generates a pressure wave in the channel which causes the ejection of a droplet of ink having the volume at the first discrete value or the second discrete value. The color of the ink ejected thereby may be black, in which case, the gradient tonal representation produced thereby shall be a gray scale representation, or other color such as yellow, cyan or magenta. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 is a perspective view of a specially designed, drop-on-demand ink jet printhead which is constructed in accordance with the teachings of the present invention and configured for the generation of gray scale or other gradient tonal representations of images; 
     FIG. 2 is an enlarged scale, partial cross-sectional view through the ink jet printhead taken along line  2 — 2 . of FIG.  1  and illustrating a plurality of piezoelectrically actuated ink-carrying channels suitable for ejecting droplets of ink therefrom; 
     FIG. 3 is a schematic illustration of a voltage waveform suitable for application to the piezoelectrically actuated ink-carrying channels of FIG. 3 to cause the ejection of droplets of ink therefrom; 
     FIG. 4A is a graphical illustration of the relationship between reflectance of a spot produced by a droplet of ink ejected by the ink jet printhead of FIGS.  1 - 2  and pulse length of the voltage waveform of FIG. 3 used to eject the droplet of ink; 
     FIG. 4B is a graphical relationship between intensity of an image and intensity of a representation of the image produced by the ink jet printhead of FIGS.  1 - 2 ; 
     FIG. 5 is a flowchart of a method for producing gradient tonal representations by combining continuous and halftone printing techniques in accordance with the teachings of the present invention; 
     FIG. 6A is an enlarged view of a four pixel area of a half-tone representation produced using a dither matrix technique and uniformly sized spots; and 
     FIG. 6B is an enlarged view of a four pixel area of a half-tone portion of a gradient tonal representation produced using non-uniformly sized spots in accordance with the teachings of the present invention. 
    
    
     DETAILED DESCRIPTION 
     Referring now to the drawing where like reference numerals designate the same or similar elements throughout the several views, in FIG. 1, a drop-on-demand ink jet printhead  2  may now be seen. The ink jet printhead  2  has a body  14  having upper and lower rectangular portions  16  and  18 , with an intermediate rectangular body portion  20  secured between the upper and lower portions  16  and  18  in the indicated aligned relationship therewith. A front end section of the body  14  is defined by an orifice plate member  22  having a spaced series of small ink discharge orifices  24  extending rearwardly therethrough. As shown, the orifices  24  are arranged in horizontally sloped rows of three orifices each. 
     The printhead body portions  16 , 20  are shorter than the body portion  18 , thereby leaving a top rear surface portion  26  of the lower printhead body portion  18  exposed. For purposes later described, a spaced series of electrical actuation leads  28  are suitably formed on the exposed surface  26  and extend between the underside of the intermediate body portion  20  and a controller portion  30  of the drive system  7  mounted on the surface  26  near the rear end of the body portion  18 . 
     Referring now to FIG. 2, a plurality of vertical grooves of predetermined width and depth are formed in the printhead body portions  18  and  20  to define within the printhead body  14  a spaced, parallel series of internal ink receiving channels  32  that longitudinally extend rearwardly from the orifice plate  22  and open at their front ends outwardly through the orifices  24 . The channels  32  are laterally bounded along their lengths by opposed pairs of a series of internal actuation sidewall sections  34  of the printhead body. 
     Sidewall sections  34  have upper parts  34   a  defined by horizontally separated vertical sections of the body portion  20 , and lower parts  34   b  defined by horizontally separated sections of the body portion  18 . The underside of the body portion  16 , the top and bottom sides of the actuation sidewall section parts  34   a , and the top sides of the actuation sidewall section parts  34   b  are respectively coated with electrically conductive metal layers  36 ,  38 , 40  and  42 . 
     Body portions  16  and  20  are secured to one another by a layer of electrically conductive adhesive material  44  positioned between the metal layers  36  and  38 , and the upper and lower actuator parts  34   a  and  34   b  are intersecured by layers of electrically conductive material  46  positioned between the metal layers  40  and  42 . The metal layer  36  on the underside of the upper printhead body portion  16  is connected to ground  48 . Accordingly, the top sides of the upper actuator parts  34   a  are electrically coupled to one another and to ground  48  via the metal layers  38 , the conductive adhesive layer  44  and the metal layer  36 . 
     Each of the channels  32  is filled with ink received from a suitable ink supply reservoir  27  (see FIG. 1) connected to the channels via an ink delivery conduit  29  connected to an ink supply manifold (not shown) disposed within the printhead body  14  and coupled to rear end portions of the internal channels  32 . In a manner subsequently described, each horizontally opposed pair of the sidewall actuators  34  is piezoelectrically deflectable into and out of their associated channel  32 , under the control of the drive system  7 , to force ink (in droplet form) outwardly through the orifice  24  associated with the actuated channel. 
     Referring next to FIG. 3, the voltage waveform to be applied to a horizontally opposed pair of sidewall actuators  34  to force the ejection of a droplet of ink out of their associated channel  32  will now be described in greater detail. The voltage waveform  51 , also referred to as an “echo pulse” waveform, includes primary and echo portions  51   a ,  51   b  which generate a pressure wave in an ink-carrying channel of the ink jet printhead  2  to cause the ejection of a droplet of ink, the volume of which may be readily modulated, in a manner more fully described below. In turn, when striking a sheet of paper, the modulatable volume droplets of ink produce modulatable size spots capable of producing a gradient tonal representation, such as a gray scale, in a manner to be more fully described below. 
     From a rest state  53 , during which a rest state voltage is applied across a piezoelectric actuator  34  and the actuator remains in a undeflected rest position, the voltage waveform  53  begins a first rapid rise  55  at time T 1  to a first or peak voltage to be applied across the piezoelectric actuator  34 . The first rapid rise  55  in the voltage waveform  53  causes the piezoelectric actuator  34  to move to a first, outwardly deflected position, thereby producing an expansive pressure wave that begins to propagate both forwardly and rearwardly through an ink-carrying channel  32  partially defined thereby. 
     Once reaching the peak value, the voltage waveform  53  enters a primary dwell state  57  which extends from time T 1  to time T 2 . During the primary dwell state  57 , the voltage is held constant at the first value to hold the piezoelectric actuator  34  in the deflected position. While the voltage waveform  51  is held in the dwell state  57 , the rearwardly propagating negative pressure wave will have deflected off the back wall of the printhead  2  and propagated forwardly within the channel  32  to its origination point. When the forwardly propagating reflected pressure wave reaches its origination point at time T 2 , the voltage waveform  51  begins a rapid fall  59  during which the voltage drops below the rest voltage (thereby ending the primary portion  51   a  and beginning the echo portion  51   b  of the voltage waveform  51 ) to a second, lower value. During the fall  59 , the voltage applied across the piezoelectric actuator  34  drops to the second value, thereby causing the piezoelectric actuator  34  to move, from the first, outwardly deflected position, past the rest position, and into a second, inwardly deflected position which compresses the channel  32 . By compressing the channel  32 , the piezoelectric actuator  34  imparts a positive pressure wave into the channel which reinforces the forwardly propagating, reflected pressure wave. 
     Once reaching the second, lower value, the voltage waveform  51  enters an echo dwell state  61  which extends from time T 2  to time T 3 . During this state, the voltage is held constant at the second value to hold the piezoelectric actuator  34  in the second, channel compressing, deflected position. While the voltage waveform  51  is held in the echo dwell state  61 , the forwardly propagating reinforced pressure wave will propagate towards the orifice  24 . At time T 3 , the voltage waveform  51  will begin a second rapid rise  63  which will return the voltage waveform  51  to the rest state  53 , thereby ending the echo portion  51   b  of the voltage waveform  51 . The piezoelectric actuator  34  will move from the second, channel compressing, deflected position to the rest position, thereby imparting a negative pressure wave into the channel  32 . This negative pressure wave acts as an active pull-up which prematurely terminates the droplet formation process by the forwardly propagating reinforced pressure pulse. Having returned to the rest state, the voltage waveform  51  remains at this state to allow the pressure pulse within the channel  34  to dissipate over time. In an exemplary embodiment of the invention, the rest, first and second voltages may be 0, +20 and −20 volts, respectively, and the dwell and echo dwell times may both be 10 μsec. It is specifically contemplated, however, that numerous other values other than those specifically disclosed herein may be used for the rest, first and second voltages. It is further contemplated that durations for the dwell and echo dwell times other than those specifically disclosed herein may also be used. 
     Using the drive system  7 , a selected one or more of the ink receiving channels  32  may be actuated to drive a quantity of ink therein, in droplet form, outwardly through the associated ink discharge orifice(s)  24 . To illustrate the operation of the drive system  7 , the actuation of a representative channel  32   a  will now be described in conjunction with FIGS.  1 - 3 . Prior to the actuation of the channel  32   a , its horizontally opposed left and right sidewall actuators  34   L  and  34   R  are (at time T O  in FIG. 3) in initial, laterally undeflected (or “rest”) positions indicated by solid lines in FIG.  2 . To initiate the channel actuation cycle, the drive system  7  is operated to impose upon the left sidewall actuator  34   L  a constant positive DC voltage pulse (i.e. the primary portion  51   a ) during the time interval T 1 -T 2  shown in FIG.  3 . Simultaneously therewith, the drive system  7  is further operated to impose upon the right sidewall actuator  34   R  an equal constant negative DC voltage pulse during the time interval T 1 -T 2 . These opposite polarity DC voltage pulses transmitted to the sidewall actuators  34   L  and  34   R  outwardly deflect them away from the channel  32   a  being actuated and into the outwardly adjacent channels  32   b  and  32   c  as indicated by the dotted lines  72  in FIG. 2, thereby imparting respective compressive pressure pulses to the channels  32   b  and  32   c  and expansive pressure pulses to the channel  32   a.    
     Next, at time T 2 , the positive voltage pulse transmitted to sidewall actuator  34   L  and the corresponding negative voltage pulse on the sidewall actuator  34   R  are terminated, and the drive system  7  is operated to simultaneously impose a constant negative DC voltage pulse (i.e. the echo portion  51   b ) on the left sidewall actuator  34   L , while imposing an equal constant positive DC voltage pulse on actuator  34   R , during the time interval T 2 -T 3 . These opposite polarity constant DC voltage pulses inwardly deflect the sidewall actuators  34   L  and  34   R  past their initial undeflected positions and into the channel  32   a  as indicated by the dotted lines  76  in FIG. 2, thereby simultaneously imparting respective compressive pressure pulses into the channel  32   a . Such inward deflection of the actuators  34   L  and  34   R  reduces the volume of channel  32   a , thereby elevating the pressure of ink therein to an extent sufficient to force a quantity of the ink, in droplet form, outwardly through the orifice  24  associated with the actuated channel  32   a.    
     The size of ink spots formed on a sheet of paper when struck by a droplet of ink ejected in the manner described above will vary depending on the volume of ink contained in the droplet ejected by the selected channel  32   a . More specifically, by applying the voltage waveform  51  having a primary portion  51   a  having a selected positive peak value and extending for a first selected time period and an echo portion  51   b  having a selected negative peak portion and extending for a second selected time period to the sidewall actuators  34   L  and  34   R  defining the channel  32   a  to be actuated, a droplet of ink will be ejected which contains a volume of ink which, when striking the sheet of paper, will form a spot having the selected spot size. Such spot size modulation may be achieved by selecting positive and negative peak values and varying the dwell and echo dwell times during which the selected peak values are applied to the sidewall actuators  34   L  and  34   R . 
     Referring next to FIG. 4A, the relationship between spot size and pulse width for the primary and echo portions  51   a ,  51   b  of the voltage waveform  51  may now be seen. In FIG. 4A, pulse width is plotted against reflectance. Reflectance is a measure of the relative intensity of the representation produced by the ink jet printhead  2  wherein a reflectance of 0.0 is considered “full ink color” and a reflectance of 1.0 is considered “white”. As, for an representation formed by depositing a single ink spot in each one of a plurality of pixel elements, reflectance is directly proportional to the size of the ink spot deposited within the pixel element of a representation, reflectance is directly related to spot size. 
     In the example illustrated herein, the channel  32   a  of the ink jet printhead  2  was fired by applying equal duration primary and echo pulses to the sidewall actuators  34   L  and  34   R  As may be seen in FIG. 4A, by varying the duration of the primary and echo portions of the echo pulse applied to the sidewall actuators  34   L  and  34   R  between approximately 6.2 and approximately 9.8 μs, the reflectance (or intensity) and, therefore, the size of the ink spot produced thereby, is varied such that the reflectance thereof will range between 0.37 (point C) to 0.29 (point B). This range of spot sizes is herein defined as a first “continuously variable” range for the reason that, by varying the pulse duration between these values, the size of the ink spot produced thereby may be varied such that the reflectance thereof will range between 0.29 and 0.37. This ability to continuously vary spot size between 0.29 and 0.37 is particularly useful in producing a continuous tone representation of an image. To produce a continuous tone representation of an image, or a portion thereof, in which the image intensity is varied between 0.29 and 0.37, the pulse width applied to the sidewall actuators  34   L  and  34   R  are modulated between 6.2 and 9.8 μsec so that the droplets of ink are ejected from the channels  32  have sufficient volume such that an ink spot having the desired size/intensity is deposited on each pixel element of the representation. 
     As may be further seen in FIG. 4A, a second continuously variable range of spot size/intensity may be achieved by “double spotting”, applying, preferably in sequence, a pair of echo pulses to a channel while the physical medium remains in a stationary position relative to the ink jet printhead  2  such that a pair of ink droplets strike the target pixel. By modulating the pulse between about 6.2 μsec and about 11 μsec while maintaining the physical medium in a stationary position relative to the ink jet printhead so that two droplets of ink strike the same pixel, the size of the ink spot produced thereby, is varied such that the resultant reflectance will range between 0.06 (point A) to 0.00. This range of spot sizes is herein defined as a second “continuously variable” range for the reason that, by varying the pulse duration between these values, any spot size between 0.06 and 0.00 may be produced. As before, this ability to continuously vary spot size between 0.06 and 0.00 improves the aforementioned ability to produce a continuous tone representation of an image, or a portion thereof, in that the range of image intensity for which the ink jet printhead  2  may be used to produce a continuous tone representation of an image is expanded. 
     As herein described, the ink jet printhead  2  is capable of producing a continuous tone representation of an image if the desired intensity of the representation is between 0.00 and 0.06 or between 0.29 and 0.37. However, outside of these ranges are gap ranges which includes numerous image intensity levels for which the ink jet printhead  2  cannot produce a continuous tone representation. More specifically, the ink jet printhead cannot produce a continuous tone representation of an image, or portion thereof, having an image intensity level “I” within the range 0.06&lt;I&lt;0.28 or the range 0.37&lt;I&lt;1.00. For an image, or portion thereof, having an intensity level within these gap ranges, the ink jet printhead  2  is configured to produce a half-tone representation in accordance with the method described below. 
     Specifically, to produce a representation having an image intensity between 0.06 and 0.29, a first group of droplets having a volume such that the spots produced thereby will have intensity of 0.06 are directed to a first set of selected locations within that portion of the representation to have an image intensity level between 0.06 and 0.29 and a second group of droplets having a volume such that the spots produced thereby will have an intensity of 0.29 are directed to a second set of selected locations within that portion of the representation such that the resultant representation has the desired image intensity level or levels. The production of a representation having one or more intensity levels between lower and upper bounds (in the example illustrated herein 0.06 and 0.29, respectively) by depositing spots of either the first or second size at various locations is herein defined as the formation of a representation of an image using a “discretely variable intensity level”. Similarly, to produce a representation, or a portion thereof, having an image intensity level between 0.37 and 1.00, a group of droplets having a volume such that the spots produced thereby will have an intensity of 0.37 are directed to selected locations within that portion of the representation such that the resultant representation, or portion thereof, will again have the desired image intensity. 
     Referring next to FIG. 4B, the relationship between input and output intensity levels for the ink jet printhead  2  will now be described in greater detail. As before, a “full color” image has an intensity of 0.00 while a “white” image has an intensity of 1.00. A printer divides this range into a series of levels, for example, 256 levels. Then, when producing a representation of a 256 level image input thereto, the printer ejects droplets of ink at selected locations of a physical medium so that the resultant representation has one or more intensity levels which corresponds to the intensity levels of the input image. 
     By varying the pulse parameter in combination with the selective use of single or double spotting, the ink jet printhead  2 , in response to the receipt of a 256 level input image, can produce a continuous tone representation of the input image having a first continuously variable range  80  which extends between image intensity levels 0 and 14 and a second continuously variable range  82  which extends between image intensity levels 73 and 94. For a first discretely variable range  84  which extends between image intensity levels 14 and 73, an output image is produced by depositing spots of sizes 0.06 and 0.29 at selected pixels of the representation. Finally, for a second discretely variable range  86  which extends between image intensity levels 94 and 255, an output representation is produced by depositing spots have size 0.37 at selected pixels of the representation. 
     Referring next to FIG. 5, the method of producing a gradient tonal representation will now be described in greater detail. Commencing at step  88 , an image is input to a printing system, for example, an ink jet printer having the spot size modulation capability described above. The input image is comprised of a plurality of picture elements (or “pixels”), each having an intensity level between 0 and 255. Proceeding to step  90 , each pixel is classified depending on its image intensity level I. For the embodiment of the invention described herein, the pixels would be subdivided into first, second and third groups, depending on the image intensity level for that group. Specifically, pixels having image intensities between 0 and 14 and between 73 and 94 would be placed in the first group, pixels having image intensities greater than 14 but less than 73 would be placed in the second group and pixels having image intensities greater than 94 would be placed into the third group. 
     Proceeding to step  92 , those pixels having image intensities between 0 and 14 or 73 or 94 would be selected for continuous tone printing in a first portion of the representation comprised of selected pixels of the representation corresponding to the pixels of the image having the aforementioned image intensity levels. At step  94 , those pixels having an image intensity level greater than 14 but less than 73 are arranged into a second image area. Proceeding to step  96 , and based upon the image intensity, the desired resolution of the representation to be produced and the printing technique utilized to produce the representation, a half-tone representation comprised of spots having intensity levels 0.06 and 0.28 would be configured. 
     Similarly, at step  98 , those pixels having an image intensity level greater than 0.37 would be arranged into a third image area and, at step  100 , a half-tone representation comprised of spots having intensity level 0.37 is configured based upon the image intensity, the desired resolution of the representation to be produced and the printing technique utilized to produce the representation. Finally, at step  102 , the first, second and third portions of the representation are combined and the desired representation of the image printed by the ink jet printhead  2 . 
     Referring next to FIGS.  6 A-B, one of the print techniques suitable for use in conjunction with the methods described herein will now be described in greater detail. In FIG. 6A, a four pixel region  104  of a half-tone representation printed using a dither matrix technique may be seen. In this technique, ink spots are deposited on selected pixels of the region  104  while no ink is deposited on the remaining pixels (designated in FIG. 6A as “W” areas. By selectively depositing ink spots within the region  104 , the resultant representation will have a desired image intensity level. Since spots may be produced in a single size, there are only  5  intensity levels available for the region  104 . These are WWWW, WWWS, WWSS (illustrated in FIG.  6 A), WSSS and SSSS. Of course, should the region  104  be enlarged, for example, to 16 pixels, additional intensity levels would be available. To do so, however, would significant degrade the resolution of the region  104 . 
     In FIG. 6B, on the other hand, a four pixel region  106  of a representation produced using the discretely variable printing technique disclosed herein wherein ink spots having either a first or a second size may be directed to selected pixels within the region  106 . As the size of the ink spot deposited onto a selected pixel may be discretely varied between first and second sizes, a significantly greater number of image intensity levels are possible. Specifically, for the four pixel region  106  illustrated in FIG. 6B,  15  intensity levels are available. These are WWWW, WWWs, WWWS, WWss, WWSS, WWsS, Wsss, WssS, WsSS, WSSS, ssss, sssS, ssSS, sSSS and SSSS. Thus, for a given printing technique and resolution level, a significantly greater number of intensity levels are possible by application of the present invention. 
     Thus, there has been described and illustrated herein, a method for producing a representation of an image on a physical medium and an associated piezoelectrically actuated ink jet printhead which produces a representation of an image by combining the generation of a first portion of the representation using a continuously variable printing technique and a second portion of the representation using a discretely variable printing technique. In this manner, an improved representation may be achieved by utilization of the printing techniques combining continuously and discretely variable printing described herein. It should be clearly understood, however, that while a single printing technique (dither matrix) and a single type of printer (drop-on-demand ink jet printer) have been disclosed, the techniques described herein are equally applicable to a wide array of both printing techniques and printers. Accordingly, the foregoing detailed description is to be clearly understood as being given by way of illustration and example only, the spirit and scope of the present invention being limited solely by the appended claims.