Abstract:
Imaging apparatus and method for providing images of uniform print density. The apparatus includes a print head having a plurality of nozzles containing ink. Each nozzle has an image forming characteristic, such as print density, associated therewith. A heater associated with each nozzle is in heat transfer communication with the ink for heating the ink, so that, as the ink is heated, its surface tension relaxes. As surface tension relaxes, static back-pressure acting on the ink ejects the ink from the nozzle. A voltage supply unit is provided for supplying a voltage pulse to each of the heaters for activating the heaters and a controller interconnects the heaters and the voltage supply unit for controlling the voltage pulse. Controlling the voltage pulse causes the image forming characteristic for each nozzle to be altered to the extent that the image forming characteristics for all the heaters will become uniform. In this regard, the controller includes a memory unit capable of informing the controller of the voltage pulse duration to be applied to each heater for obtaining uniform image forming characteristics. Alternatively, the memory unit may inform the controller of the pulse amplitude to be applied to each heater for obtaining uniform image forming characteristics. Therefore, either the voltage pulse amplitude or the voltage pulse duration applied to each heater is controlled such that the image forming characteristics (e.g., print densities) of all nozzles are uniform.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Reference is made to commonly assigned, copending U.S. patent application Ser. No. 08/783,256 filed Jan. 14, 1997 and commonly assigned, copending U.S. patent application Ser. No. 08/826,357 filed Mar. 26, 1997 both in the name of Xin Wen. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to imaging apparatus and methods and, more particularly, to an imaging apparatus and method for providing images of uniform print density, so that printing non-uniformities, such as banding, are avoided. 
     BACKGROUND OF THE INVENTION 
     In a typical ink jet printer using a multi-nozzle head, digital signals as to each of four colors (i.e., red, green, blue and black) regarding an image are processed in a manner so that the multi-nozzle head forms a printed color image on a recorder medium, such as paper or transparencies. 
     Indeed, ink jet printing has become recognized as a prominent contender in the digitally controlled, electronic printing arena because, e.g., of its non-impact, low-noise characteristics, its use of plain paper and its avoidance of toner transfers and fixing. Ink jet printing mechanisms can be categorized as either continuous ink jet or drop-on-demand ink jet. U.S. Pat. No. 3,946,398, which issued to Kyser et al. in 1970, discloses a drop-on-demand ink jet printer which applies a high voltage to a piezoelectric crystal, causing the crystal to bend, applying pressure on an ink reservoir and jetting drops on demand. Other types of piezoelectric drop-on-demand printers utilize piezoelectric crystals in push mode, shear mode, and squeeze mode. Piezoelectric drop-on-demand printers have achieved commercial success at image resolutions up to 720 dpi for home and office printers. However, piezoelectric printing mechanisms usually require complex high voltage drive circuitry and bulky piezoelectric crystal arrays, which are disadvantageous in regard to manufacturability and performance. 
     Great Britain Pat No. 2,007,162, which issued to Endo et al. in 1979, discloses an electrothermal drop-on-demand ink jet printer which applies a power pulse to an electrothermal heater which is in thermal contact with water based ink in a nozzle. A small quantity of ink rapidly evaporates, forming a bubble which cause drops of ink to be ejected from small apertures along the edge of the heater substrate. This technology is known as Bubblejet™ (trademark of Canon K.K. of Japan). 
     U.S. Pat. No. 4,490,728, which issued to Vaught et al. in 1982, discloses an electrothermal drop ejection system which also operates by bubble formation to eject drops in a direction normal to the plane of the heater substrate. As used herein, the term “thermal ink jet” is used to refer to both this system and system commonly known as Bubblejet™. 
     Thermal ink jet printing typically requires a heater energy of approximately 20 μJ over a period of approximately 2 μsec to heat the ink to a temperature between 280° C. and 400° C. to cause rapid, homogeneous formation of a bubble. The rapid bubble formation provides the momentum for drop ejection. The collapse of the bubble causes a tremendous pressure pulse on the thin film heater materials due to the implosion of the bubble. The high temperatures needed necessitates the use of special inks, complicates the driver electronics, and precipitates deterioration of heater elements. The 10 Watt active power consumption of each heater is one of many factors preventing the manufacture of low cost high speed pagewidth printheads. 
     U.S. Pat. No. 4,275,290, which issued to Cielo et al., discloses a liquid ink printing system in which ink is supplied to a reservoir at a predetermined pressure and retained in orifices by surface tension until the surface tension is reduced by heat from an electrically energized resistive heater, which causes ink to issue from the orifice and to thereby contact a paper receiver. This system requires that the ink be designed so as to exhibit a change, preferably large, in surface tension with temperature. The paper receiver must also be in close proximity to the orifice in order to separate the drop from the orifice. 
     U.S. Pat. No. 4,166,277, which also issued to Cielo et al., discloses a related liquid ink printing system in which ink is supplied to a reservoir at a predetermined pressure and retained in orifices by surface tension. The surface tension is overcome by the electrostatic force produced by a voltage applied to one or more electrodes which lie in an array above the ink orifices, causing ink to be ejected from selected orifices and to contact a paper receiver. The extent of ejection is claimed to be very small in the above Cielo patents, as opposed to an “ink jet”, contact with the paper being the primary means of printing an ink drop. This system is disadvantageous, in that a plurality of high voltages must be controlled and communicated to the electrode array. Also, the electric fields between neighboring electrodes interfere with one another. Further, the fields required are larger than desired to prevent arcing, and the variable characteristics of the paper receiver such as thickness or dampness can cause the applied field to vary. 
     In U.S. Pat. No. 4,751,531, which issued to Saito, a heater is located below the meniscus of ink contained between two opposing walls. The heater causes, in conjunction with an electrostatic field applied by an electrode located near the heater, the ejection of an ink drop. There are a plurality of heater/electrode pairs, but there is no orifice array. The force on the ink causing drop ejection is produced by the electric field, but this force is alone insufficient to cause drop ejection. That is, the heat from the heater is also required to reduce either the viscous drag and/or the surface tension of the ink in the vicinity of the heater before the electric field force is sufficient to cause drop ejection. The use of an electrostatic force alone requires high voltages. This system is thus disadvantageous in that a plurality of high voltages must be controlled and communicated to the electrode array. Also the lack of an orifice array reduces the density and controllability of ejected drops. 
     Each of the above-described ink jet printing systems has advantages and disadvantages. However, there remains a widely recognized need for an improved ink jet printing approach, providing advantages for example, as to cost, speed, quality, reliability, power usage, simplicity of construction and operation, durability and consumables. 
     Commonly assigned U.S. patent application Ser. No. 08/750,438 entitled A LIQUID INK PRINTING APPARATUS AND SYSTEM filed in the name of Kia Silverbrook on Dec. 3, 1996, discloses a liquid printing system that affords significant improvements toward overcoming the prior art problems associated with drop size and placement accuracy, attainable printing speeds, power usage, durability, thermal stresses, other printer performance characteristics, manufacturability, and characteristics of useful inks. Silverbrook provides a drop-on-demand printing mechanism wherein the means of selecting drops to be printed produces a difference in position between selected drops and drops which are not selected, but which is insufficient to cause the ink drops to overcome the ink surface tension and separate from the body of ink, and wherein an additional means is provided to cause separation of said selected drops from said body of ink. Several drop separation techniques are disclosed by Silverbrook, the following table entitled “Drop separation means” shows some of the possible methods for separating selected drops from the body of ink, and ensuring that the selected drops form dots on the printing medium. The drop separation means discriminates between selected drops and un-selected drops to ensure that un-selected drops do not form dots on the printing medium. 
     
       
         
               
             
               
               
               
             
           
               
                   
               
               
                    Drop separation means 
               
             
          
           
               
                    Means 
                 Advantage 
                 Limitation 
               
               
                   
               
               
                    1. Electrostatic 
                 Can print on rough 
                 Requires high voltage power 
               
               
                 attraction 
                 surfaces, simple 
                 supply 
               
               
                   
                 implementation 
               
               
                 2. AC electric field 
                 Higher field strength is 
                 Requires high voltage AC 
               
               
                   
                 possible than electrostatic, 
                 power supply synchronized. 
               
               
                   
                 operating margins can be 
                 to drop ejection phase. 
               
               
                   
                 increased, ink pressure 
                 Multiple drop phase 
               
               
                   
                 reduced, and dust 
                 operation is difficuit 
               
               
                   
                 accumulation is reduced 
               
               
                 3. Proximity 
                 Very small spot sizes can 
                 Requires print maximum to be 
               
               
                 (printhead in close 
                 be achieved. Very low 
                 very close to printhead 
               
               
                 proximity to, but not 
                 power dissipation. High 
                 surface, not suitable for 
               
               
                 touching, recording 
                 drop position accuracy 
                 rough print media, usually 
               
               
                 medium) 
                   
                 requires transfer roller or 
               
               
                 4. Transfer Proximity 
                 Very small spot sizes can 
                 Not compact due to size of 
               
               
                 (print-head is in close 
                 be achieved, very low 
                 transfer roller or transfer 
               
               
                 proximity to a 
                 power dissipation, high 
                 belt. 
               
               
                 transfer roller or belt 
                 accuracy, can print on 
               
               
                   
                 rough paper 
               
               
                 5. Proximity with 
                 Useful for hot melt inks 
                 Requires print medium to be 
               
               
                 oscillating ink 
                 using viscosity reduction 
                 very close to printhead 
               
               
                 pressure 
                 drop selection method, 
                 surface, not suitable for 
               
               
                   
                 reduces possibility of 
                 rough print media. Requires 
               
               
                   
                 nozzle clogging, can use 
                 ink pressure oscillation 
               
               
                   
                 pigments instead of dyes 
                 apparatus 
               
               
                 6. Magnetic 
                 Can print on rough. 
                 Requires uniform high 
               
               
                 attraction 
                 surfaces. Low power if 
                 magnetic field strength, 
               
               
                   
                 permanent magnets are 
                 requires magnetic ink 
               
               
                   
                 used 
               
               
                   
               
             
          
         
       
     
     Silverbrook discloses a liquid printing system that affords significant improvements toward overcoming the prior art problems associated with drop size and placement accuracy, attainable printing speeds, power usage, durability, thermal stresses, other printer performance characteristics, manufacturability, and characteristics of useful inks. Silverbrook discloses a single microscopic nozzle tip having pressurized ink extending from the nozzle, which is formed from silicon dioxide layers with a heater and a nozzle tip. The nozzle tip is passivated with silicon nitride. The “Silverbrook” technique provides for low power consumption, high speed, and page-wide printing. In such ink jet printheads, the energy barrier for ejecting an ink droplet is reduced by reducing the surface tension of the ink solution. The ink solution in an ink reservoir is under a static pressure so that an ink meniscus is bulged outward at a nozzle outlet. For each selected nozzle, a voltage pulse is applied to a ring-shaped resistor. The heating of the resistor by the electric pulse reduces the surface tension of the ink solution in the vicinity of the rim of the nozzle. The heated ink solution is pushed outward by the static pressure. The interplay between the surface tension reduction by heating and the static pressure begins to dominate, and finally ejects the ink droplet to a receiver media. The separation of the droplet from the nozzle can be assisted by a static electric field applied that attracts the ink droplet toward the receiving media. 
     In other words, such an ink jet printer as described immediately hereinabove includes a multiplicity of nozzles having orifices opening toward the recorder medium. An ink droplet in each nozzle is under a predetermined static back-pressure in order to propel the ink droplet onto the recorder medium. However, before the ink droplet is propelled toward the recorder medium, it is initially restrained or held in the orifice by surface tension even though the ink droplet is under static back-pressure. This results in an ink meniscus bulging outwardly at the nozzle orifice without leaving the orifice. This is so because, by design, the back-pressure is initially insufficient to overcome the ink droplet&#39;s surface tension. Therefore, in order to print on the recorder medium, the surface tension of the ink droplet is decreased, so that the ink droplet is released from the nozzle orifice and propelled onto the recorder medium by the previously mentioned back-pressure. To decrease surface tension, a voltage pulse is applied to an electrical resistance heater that is located inside the nozzle and that is therefore in heat transfer communication with the ink droplet. Heating of the resistance heater by the voltage pulse heats the ink droplet, thereby reducing the surface tension of the ink droplet. Of course, the static back-pressure acting on the ink droplet coacts with the simultaneous decrease in surface tension to eject the ink droplet from the orifice and propel it onto the recorder medium. 
     However, ink jet printers may produce non-uniform print density with respect to the image deposited on the recorder medium. Such non-uniform print density may be visible as so-called “banding”. “Banding” is evinced, for example, by repeated variations in the print density caused by delineations in individual dot rows comprising the output image. Thus, “banding” can appear as light or dark streaks or lines within a printed area. “Banding” is influenced by factors such as ink drop volume variations, print head carriage motion anomalies, electrical resistance variation of the heaters, and/or the presence of damaged nozzles. 
     One important factor producing “banding” is variability in the nozzle orifice diameter caused by variations in the manufacturing process used to make the nozzles constituting the print head. Even small variations between nozzles of a print head may lead to visible “banding”. More specifically, when the ink droplet is pushed outwardly during ejection from the nozzle, the moving ink droplet must overcome flow resistance caused by the nozzle&#39;s flow channel and also flow resistance caused by the nozzle&#39;s orifice. Therefore, the ejection speed of the droplet is strongly dependent on the flow resistance or drag force exerted by the nozzle&#39;s flow channel and the nozzle&#39;s orifice. Nozzle diameter affects flow resistance or drag force and therefore affects the amount of ink ejected from the nozzles. Moreover, nozzle diameter also affects the meniscus shape of the ink at the nozzle&#39;s orifice, which in turn affects droplet volume and ejection rate. In addition, heater electrical resistance can vary among nozzles due to slight variations in the composition of the material comprising the electric resistance heaters disposed in the nozzles. Variations in electrical resistance among nozzles causes variations in the amount and ejection speed of the ink thereby leading to variations in print density. All the afore mentioned factors negatively affect print density and invite “banding”. Therefore, a problem in the art is non-uniform print density due to the presence of physical variations among the print nozzles, such as variations in nozzle diameter and electrical resistance. 
     Techniques specifically addressing the problem of non-uniform print density are known. One such technique is disclosed in U.S. Pat. No. 5,038,208 titled “Image Forming Apparatus With A Function For Correcting Recording Density Unevenness” issued Aug. 6, 1991 in the name of Hiroyuki Ichikawa This patent discloses memory means for storing data corresponding to image forming characteristics (i.e., print density) of each nozzle of multi-nozzle print heads, and a corrector means for correcting the image forming signals based on the data stored in the memory means. However, this patent does not appear to disclose an efficient and cost effective solution to the problem of non-uniform print density or “banding”. For example, the Ichikawa patent discloses that image processing is required for correcting density non-uniformities for each input image file. That is, image processing is required for each and every input image for which output density correction is desired. Correcting density non-uniformities for each input image file is undesirable because it is time consuming. Also, this patent discloses that modulation in the output code value is made at a relatively limited number of discrete levels for halftoned images at a typical printing resolution (i.e., 600 dots per inch). However, printing at discrete levels may not eliminate visual printing defects, such as “banding”. 
     Therefore, what has long been needed is a suitable imaging apparatus and method for providing images of uniform print density, so that printing non-uniformities, such banding, are avoided. 
     DISCLOSURE OF THE INVENTION 
     The invention in its broad form resides in an imaging apparatus, comprising a plurality of nozzles, each of the nozzles having an image forming characteristic associated therewith, each of the nozzles adapted to receive a voltage pulse capable of altering the image forming characteristic and a controller connected to the nozzles for controlling the voltage pulse received by the nozzles, so that the altered image forming characteristics for all of said nozzles are uniform. 
     An object of the present invention is to provide a suitable imaging apparatus and method for providing images of uniform print density produced by print nozzles, so that printing non-uniformities, such as banding, are avoided, even when the print nozzles have different physical attributes resulting in different printing characteristics. 
     A feature of the present invention is the provision of a controller connected to the heater elements for controlling the heater elements disposed in the nozzles, so that the nozzles print with uniform print density. 
     Another feature of the present invention is the provision of a memory unit connected to the controller for storing print density as a function of voltage pulse amplitude for each nozzle, the memory unit capable of informing the controller of the pulse amplitude required for obtaining a desired print density. 
     Still another feature of the present invention is the provision of a memory unit connected to the controller for storing the print density as a function of voltage pulse duration for each nozzle, the memory unit capable of informing the controller of the pulse duration required for obtaining a desired print density. 
     An advantage of the present invention is that images of uniform print density are provided even in the presence of variations in such factors as electrical resistance of the heater and/or diameter of the nozzle orifice. 
     Another advantage of the present invention is that images of uniform print density are produced in a more time efficient manner compared to prior art techniques. 
     A further advantage of the present invention is that use thereof eliminates visual printing defects, such as “banding”. 
     These and other objects, features and advantages of the present invention will become apparent to those skilled in the art upon a reading of the following detailed description when taken in conjunction with the drawings wherein there is shown and described illustrative embodiments of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the detailed description of the preferred embodiments of the invention presented hereinbelow, reference is made to the accompanying drawings, in which: 
     FIG. 1 is a view in partial vertical section, with parts removed for clarity, of the imaging apparatus showing an ink-jet print head printing an image onto a recorder medium, this view also showing a controller connected to the print head for controlling image forming characteristics associated with the print head; 
     FIG. 2 is a view in horizontal section of a portion of the print head, this view also showing a plurality of nozzles and associated cavities filled with ink, each of the nozzles having an electric resistance heater in heat transfer communication therewith; 
     FIG. 3 is a detail view in horizontal section of one of the nozzles; 
     FIG. 4 is a view in vertical section of the nozzle showing the ink being restrained by surface tension from emerging from the nozzle; 
     FIG. 5 is a view in vertical section of the nozzle showing an ink droplet emerging from the nozzle as the surface tension begins to relax; 
     FIG. 6 is a view in vertical section of the nozzle showing the ink droplet emerging further from the nozzle as the surface tension further relaxes; 
     FIG. 7 is a view in vertical section of the nozzle showing the ink droplet having emerged from the nozzle and propelled toward the recorder medium by back-pressure; 
     FIG. 8 is a graph illustrating print density as a function of pulse voltage amplitude; 
     FIG. 9 is a graph illustrating print density as a function of pulse width or duration; 
     FIG. 10 shows a test image printed on recorder medium for a density uniformity calibration of the print head nozzles; 
     FIG. 11 shows a density patch belonging to the test image, this density patch having a marginal area of insufficient print density; 
     FIG. 12 is a graph illustrating a voltage pulse with a predetermined constant amplitude and a predetermined duration, the voltage pulse being provided to the electric resistance heater in the nozzle for heating the ink in order to relax the surface tension of the ink; 
     FIG. 13 is a graph illustrating electrical resistance as a function of nozzle number; 
     FIG. 14 provides a look-up table showing print density as a function of voltage pulse amplitude supplied to each nozzle; 
     FIG. 15 provides a look-up table showing print density as a function of voltage pulse duration supplied to each nozzle; 
     FIG. 16 is a graph illustrating print density as a function of number of scanned pixels of the test image; 
     FIG. 17 is a flow-chart illustrating certain steps belonging to the method of the invention; and 
     FIG. 18 is a graph illustrating a voltage pulse with a constant voltage amplitude portion and a logrithmically varying amplitude portion: 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 1, there is shown an imaging apparatus, generally referred to as  10 , having a uniform image forming characteristic for producing an output image lacking printing defects such as “banding”. In the preferred embodiment of the invention, the image forming characteristic is print density. Imaging apparatus  10  comprises a printer, generally referred to as  20 , electrically connected to an input source  30  for reasons disclosed hereinbelow. Input source  30  may provide raster image data from a scanner or computer, outline image data in the form of a page description language, or other form of digital image data. The output signal generated by input source  30  is received by a controller  40 , for reasons disclosed in detail hereinbelow. 
     Referring to FIGS. 1 and 2, controller  40  processes the output signal generated by input source  30  and generates a controller output signal that is received by a print head  45  capable of printing on a recorder medium  50 . In some printers recorder medium  50  may be fed past print head  45  at a predetermined feed rate by a plurality of rollers  60  (only some of which are shown). That is, recorder medium  50  may fed, by rollers  60 , from an input supply tray  70  containing a supply of recorder medium  50 . Each line of image information from input source  30  is printed on recorder medium  50  as that line of image information is communicated from input source  30  to controller  40 . Controller  40  in turn communicates that line of image information to print head  45  as recorder medium  50  is fed past print head  45 . When a completely printed image is formed on recorder medium  50 , recorder medium  50  exits the interior of printer  20  to be deposited in an output tray  80  for retrieval by an operator of imaging apparatus  10 . Although the terminology referring to “print head  45 ” is used in the singular, it is appreciated by the person of ordinary skill in the art that the terminology “print head  45 ” is intended to also include its plural form because there may be, for example, four print heads  110 , each one of the print heads  110  being respectively dedicated to printing one of four colors (i.e., red, green, blue and black). 
     Turning now to FIGS. 1,  2 ,  3 , and  4 , print head  45 , which belongs to printer  20 , is there shown in operative condition for printing an image on recorder medium  50 . Print head  45  comprises a plurality of ink fluid cavities  90  for holding print fluid, such as a body of ink  100 . Each cavity  90  is in communication with a print fluid reservoir  110  for supplying ink  100  into cavity  90 . Moreover, associated with each cavity  90  is a nozzle  120  for allowing ink  100  to exit cavity  90 . In this regard, each nozzle  120  includes a flow channel  130  and a generally circular orifice portion  140  in communication with flow channel  130 . Orifice portion  140 , which is disposed proximate recorder medium  50 , opens toward recorder medium  50  for depositing ink  100  onto recorder medium  50 . Moreover, lining orifice portion  140  and flow channel  130  is a generally annular electrothermal actuator (i.e., an electrical resistance heater element)  150  for heating ink  100 , heater  150  having a predetermined electrical resistance. Thus, each heater  150  is in heat transfer communication with ink  100 . A voltage supply unit  160  is electrically connected to print head  45  for supplying a voltage pulse to each heater  150 . Each nozzle  120  has an image forming characteristic (e.g., print density) associated therewith. As described more fully hereinbelow, the voltage pulse is capable of altering the image forming characteristic to define an altered image forming characteristic. Controller  40  controls the voltage pulse so that the altered image forming characteristics for all nozzles  120  are uniform. 
     As best seen in FIGS. 5 and 6, an ink bulge, meniscus or droplet  170  outwardly emerges from orifice region  140  as resistance heater  150  increases temperature in order to heat ink  100 . This heating of ink  100  results in a localized decrease in surface tension of droplet  170 . As the surface tension of droplet  170  decreases, it assumes a substantially cylindrical form due to a surface tension gradient from the tip of orifice region  140  to the center of droplet  170 , and due to viscous drag or flow resistance along the surface of flow channel  130  and orifice region  140 . 
     FIG. 7 shows droplet  170  separated from ink body  100  and ejected from orifice region  140  as it is propelled outwardly toward recorder medium  50  to establish an ink mark upon recorder medium  50 . In this regard, it is appreciated by the person of ordinary skill in the art that gravity does not significantly affect the trajectory of droplet  170  because gravity is not significant on this scale. Droplet  170  will eventually be intercepted by recorder medium  50  to “soak into” and be absorbed by recorder medium  50 . Moreover, each resistance heater  150  may be selectively energized many times by voltage supply unit  160  to deposit a multiplicity of ink marks upon recorder medium  50  in a predetermined pattern according to the image file residing in input source  30 . Of course, the image printed onto recorder medium  50  should possess a uniform print density to avoid “banding”. 
     However, it is known that “banding” is a recurring problem in the printing arts. Often “banding” (i.e., print density non-uniformity) results from variability in the print head fabrication process. For example, banding can be caused by variability in the diameter of orifice region  140  due to variations in the manufacturing process used to make nozzle  120  or by variability in electrical resistance among resistance heaters  150  due to slight variations in the chemical composition comprising heaters  150 . Even small variations in diameter and electrical resistance can lead to visible “banding”. Therefore, a long-standing problem experienced in the art is banding, which is caused by the presence of physical variations among individual print nozzles  120 . 
     To solve this problem, the present invention controls the voltage pulse amplitude or, alternatively, the voltage pulse duration supplied to each heater  150  to compensate for physical anomalies (e.g., variations in the diameter of orifice region  140 , and/or variations in electrical resistance of heaters  150 ) associated with individual nozzles  120 . Controlling the voltage pulse in this manner obtains uniform print density on recorder medium  150 . This result is attainable because controlling the voltage pulse amplitude and/or voltage pulse duration supplied to each nozzle  120  controls the surface tension of ink droplet  170 , which in turn controls the rate and the volume of ink released from each nozzle  120 . Controlling the release of ink from each nozzle  120  controls the print density provided by each nozzle  120 . As described more fully hereinbelow, nozzles  120  are calibrated, such that each nozzle  120  will selectively receive a predetermined pulse voltage amplitude or pulse voltage duration as print head  45  is operated in order that print densities for all nozzles  120  are substantially the same (i.e., uniform), even though physical attributes among nozzles  120  may vary. However, to fully appreciate the present invention, it is instructive first to briefly discuss the relationship between print density, voltage pulse amplitude, voltage pulse duration, and heater resistance. 
     Therefore, according to the present invention, the volume of ink  100  ejected by print head  45  is a function of the amplitude and duration of the voltage pulse supplied to print head  45 . Larger droplets  170  with larger volumes of ink will cause higher density images on recorder medium  50 . Conversely, smaller droplets  170  with smaller volumes of ink will cause lower density images on recorder medium  50 . Thus, print density is a function of the amplitude and the duration of the electric pulse received by print head  45  because the volume of ink released is a function of the amplitude and duration of the voltage pulse. In other words, the dependence of print density of print head  45 , as a whole, on voltage amplitude and voltage duration can be expressed by the following functional relationship: 
     
       
           D=ƒ ( V   p , T)  Equation (1) 
       
     
     where, 
     D=print density of print head  45 ; 
     V p =voltage pulse amplitude supplied to print head  45 ; and 
     T=voltage pulse duration supplied to print head  45 . 
     Equation (1) provides print density for print head  45 , taken as a whole, and is illustrated graphically for print head  45  in FIGS. 8 and 9. In FIG. 8, print density D is shown as a function of voltage pulse amplitude V p  while holding the voltage pulse duration T constant. In FIG. 9, print density D is shown as a function of voltage pulse duration T while holding the voltage pulse amplitude V p  constant. The precise functional dependence of print density D upon voltage pulse amplitude V p  and voltage pulse duration T as illustrated by FIGS. 8 and 9, respectively, is obtainable by measuring print density D of a uniform test image printed by the relatively large number of nozzles  120  of print head  45 , as described more fully hereinbelow. 
     Therefore, referring to FIG. 10, there is shown a representative test image  180  used for calibrating nozzles  120 , so that nozzles  120  will print with uniform print density regardless of physical anomalies among individual nozzles  120 . Test image  180  includes a plurality of “density patches”  190  having print densities D varying from a minimum print density D 1  (i.e., near white or light halftone) to a maximum print density D W . The print densities D for each of the density patches  190  is preferably measured by use of a densitometer (not shown) which scans a generally circular print area (e.g., approximately 0.20 square centimeters) of each density patch  190 . Preferably, the densitometer is used to scan many different areas of each density patch  190 . These multiple densitometer readings are averaged to provide an averaged density value for each density patch  190 . A separate test image  180  is produced at each of a plurality of voltage pulse amplitudes while keeping the voltage pulse duration constant. Also, a separate test image  180  is produced at each of a plurality of voltage pulse durations while keeping the voltage pulse amplitude constant. This process results in a multiplicity of print density measurements because measurement of print density using the densitometer is repeated for each density patch  190  of each test image  180 . Moreover, the foregoing process is repeated for each of the print heads  110  (e.g., for each of the print heads corresponding to each of the colors red, green, blue and black). 
     Referring to FIG. 11, more valid densitometer readings are obtained when the densitometer avoids a marginal region  200  of density patch  190 . This is so because the print density in marginal region  200  may not be representative of the print density of density patch  190  as a whole. This assumes, of course, that printing is begun in marginal region  200  of density patch  260  and moves vertically downwardly. Such non-representative printing in marginal region  200  may be due, for example, to the halftoning algorithm used to generate test image  180 . 
     With this densitometer data, the precise function shown in Equation (1) for print head  45  is obtained by mathematical means well known in the art, such as by means of statistical curve-fitting procedures. A precise function, which provides print density D as a function of V p , is plotted in FIG. 8. A precise function, which provides print density D as a function of T, is plotted in FIG.  9 . However, it should be appreciated that FIGS. 8 and 9 show print density D of print head  45  taken as a whole and does not provide print density of individual nozzles  120 . In other words, Equation (1), from which FIGS. 8 and 9 are plotted, provides a functional relationship defining print density for print head  45 , as whole. However, as stated hereinabove, print density among nozzles  120  may vary due, for example, to variations in nozzle orifice diameter and/or electrical resistance of heaters  150 . It is therefore desirable to calibrate nozzles  120 , so that all nozzles  120  of print head  45  print with uniform print density, even though physical attributes among nozzles  120  may vary. 
     Therefore, according to the present invention, either of two techniques may be used to provide uniform print density of individual nozzles  120  in view of the unique physical attributes associated with each nozzle  120 . These two techniques are defined herein as the “Resistance Calibration Technique” and the “Density Calibration Technique” and are described in detail hereinbelow. 
     Resistance Calibration Technique 
     The Resistance Calibration Technique may be used to determine the print density D of each nozzle  120  in view of the inherent electrical resistance of each resistance heater element  150  associated with each nozzle  120 . Electrical resistance among heater elements  150  may vary due to slight variations in the chemical composition of individual heater elements  150 . However, print density D of each nozzle  120  can be controlled by controlling the electric heating pulse applied to each heater element  150  (i.e., to each nozzle  120 ), even though the electrical resistance among heater elements  150  may vary. As previously mentioned, print density D of print head  45  as a whole is provided by Equation (1); however, it is desirable to determine the print density D for each nozzle  120  within print head  45 . In this regard, print density D for each nozzle  120  is provided by an approximation to Equation (1) as follows: 
     
       
           D≈ƒ ( E )=ƒ(( V   p ) 2   T/R )  Equation (2) 
       
     
     where, 
     E=average heat energy applied to each heater element  150  (i.e., each nozzle  120 ); and 
     R=electrical resistance inherent in each heater element  150  (i.e., each nozzle  120 ). 
     Referring to FIGS. 12 and 13, a square wave voltage pulse  210  of constant voltage amplitude V pi  is sequentially applied to each heater  150  associated with each nozzle  120 . That is, constant voltage pulse  210  is sequentially applied to each heater  150  from the first heater  150  to the last heater  150  in print head  45 . The last heater  150  is represented as heater number “N” in FIG.  13 . As square wave voltage pulse  210  is input to each heater  150 , the output voltage is measured at each heater  150  and a resistance R i  is calculated for each heater  150 . Using these calculated values of heater electrical resistances R i , the average resistance R for all heaters  150  in print head  45  is then calculated as follows: 
     
       
           {overscore (R)} =(Σ R   i )/ N   Equation (3) 
       
     
     where, 
     {overscore (R)}=calculated average electrical resistance of all heaters  150  (i.e., all nozzles  120 ); 
     R i =calculated electrical resistance of the “i th ” heater  150  (i.e., the “i th ” nozzle  120 ); 
     N=total number of heaters  150  (i.e., nozzles  120 ); and 
     i=1 to N. 
     In this manner, the average electrical resistance R is calculated. Next, the corrected voltage pulse amplitude V pi  or the corrected voltage pulse duration T i  to be applied to each nozzle  110  is calculated. In this regard, Equation (2) can be rewritten as follows: 
     
       
         ( V   pi ) 2   /R   i =( V   p ) 2   {overscore (R)}=E/T   Equation (4) 
       
     
     which, in turn, can be rewritten as 
     
       
           V   pi =( ER   i   /T ) ½   =V   p ( R   i   /{overscore (R)} ) ½   Equation (5) 
       
     
     where, 
     V pi =voltage pulse amplitude to be applied to the “i th ” nozzle to obtain the desired heating energy E for each heating voltage pulse. 
     In other words, V pi  is the voltage pulse amplitude to be applied to the “i th ” nozzle  120  in order for the print density of the “i th ” nozzle  120  to be equal to the print density D of print head  45 . Thus, voltage amplitude V pi  for each nozzle  120  is selected such that print density of each nozzle  120  matches the desired print density for print head  45  as a whole. In this manner, nozzles  120  will print with uniform print density because each nozzle  120  will print with the print density D of print head  45 . 
     Alternatively, the voltage pulse duration of the square wave voltage pulse  210  may be used to calibrate each heater  150  in order to provide uniform print density. In this regard, the voltage pulse duration T i  applied to each heater  150  (i.e., each nozzle  110 ) is calculated by first rearranging Equation (4) as follows: 
     
       
           T   i   /R   i   =T/{overscore (R)}=E /( V   p ) 2   Equation (6) 
       
     
     where, 
     T i =voltage pulse duration to be applied to the “i th ” nozzle to obtain the desired heating energy E for each heating voltage pulse. 
     Equation (6) can be rewritten as follows: 
     
       
           T   i   =R   i   E/V   p ) 2   =TR   i   /{overscore (R)}.   Equation (7) 
       
     
     Thus, Equation (5) provides the voltage pulse amplitude V pi  or alternatively Equation (7) provides the voltage pulse duration T i  to be applied to each nozzle  110  in order to calibrate each heater  150  (i.e., each nozzle  120 ) so that all nozzles  120  provide uniform print density even though electrical resistances among heaters  150  may vary. However, it should be recalled that calibration of each heater  150  (i.e., each nozzle  120 ) using the Resistance Calibration Technique compensates for variabilities only in electrical resistance among individual heaters  150  (i.e., among individual nozzles  120 ). 
     Referring to FIGS. 1,  2 ,  3 ,  14  and  15 , once the pulse voltage amplitudes V pi  and/or the pulse voltage durations T i  are obtained by the steps recited hereinabove, these values of V pi  and T i  and the print density D of print head  45  are stored electronically in a memory unit, such as a Read-Only-Memory (ROM) semiconductor computer chip  220  connected to controller  40 . As best seen in FIGS. 14 and 15, the values of D, V pi , and T i  stored in chip  220  are represented herein as first and second look-up tables, generally referred to as  230  and  240 , respectively. The values of D, V pi , and T i  stored in chip  220  are used as parameters for each nozzle  120  during normal operation of apparatus  10 , as described in more detail hereinbelow. More specifically, during normal operation of apparatus  10 , the desired print density D is selected, such as by means of input source  30 , and is then communicated to controller  40 . Once controller  40  accepts density value D to be printed by print head  45 , controller  40  is informed by first lookup table  230  in chip  220  as to the correct voltage amplitude V pi  to apply to each nozzle  120  in order to obtain uniform print density D from each nozzle  120 . In this case, only first look-up table  230  is stored in chip  220 . This is so because pulse voltage duration T is held at a constant value by controller  40  and, therefore, there is no need to store second look-up table  240  in chip  220 . 
     Alternatively, once controller  40  accepts a density value D to be printed by print head  45 , controller  40  is informed by second lookup table  240  stored in chip  220  as to the correct voltage pulse duration T i  to apply to each nozzle  120  in order to obtain uniform print density D from each nozzle  120 . In this case only second look-up table  240  is stored in chip  220 . This is so because the pulse voltage amplitude V p  is held at a constant value by controller  40  and, therefore, there is no need to store first look-up table  230  in chip  220 . 
     Although the Resistance Calibration Technique only calibrates heaters  150  to compensate for variabilities in electrical resistance, an advantage of using the Resistance Calibration Technique is its simplicity. That is, each heater  150  (i.e., nozzle  120 ) belonging to print head  45  is calibrated merely by supplying the square wave voltage pulse  210  illustrated by FIG.  12  and measuring the resulting electrical resistance R i  of each heater  150 , as illustrated by FIG.  13 . In this manner, each nozzle  120  can be conveniently calibrated during manufacture of print head  45 . In addition, each nozzle  120  can be recalibrated, if necessary, “in the field” at a customer site to accommodate print head  45  to the specific environmental conditions (e.g., humidity, dust, temperature, etc.) present at the customer&#39;s site. Such environmental conditions may have altered the original calibration of print head  45  performed during manufacture of print head  45 . 
     However, print density depends on other physical characteristics of nozzles  120  in addition to electrical resistance. Therefore, if desired, nozzles  120  may be calibrated to compensate for physical characteristics in addition to electrical resistance. To achieve this result, the present invention provides a technique, defined herein as the Density Calibration Technique, which compensates for variability in substantially all physical characteristics in addition to electrical resistance. 
     Density Calibration Technique 
     The Density Calibration Technique calibrates nozzles  120  to compensate for substantially all variabilities among nozzles  120 , including variabilities caused by different amounts of electrical resistance, in order to obtain uniform print density. This technique is described in detail hereinbelow. 
     Returning to FIGS. 10,  11 ,  12 ,  13  and  16 , print head  45  to be calibrated is used to print the previously mentioned test image  180  in the manner described hereinabove. This produces print density patches D 1  to D W . The previously mentioned densitometer is then used to measure the resulting print densities in two directions (i.e., vertically and horizontally), preferably at a resolution of at least 300 dpi. The density values are integrated vertically down each density patch in order to obtain the one-dimensional density profile of FIG.  16 . Thus, FIG. 16 characterizes print density non-uniformity due to physical variabilities among nozzles  120 . It is understood that print density measurements are not taken in marginal region  200  for the reasons provided hereinabove. These print density values may be fit, by means well known in the art, to an analytical function so that the print density value for each nozzle  120  is conveniently obtained by reference merely to the analytical function. 
     After the print densities are obtained, the required voltage pulse amplitude and voltage pulse duration are calculated, as described in detailed hereinbelow. In this regard, print density D i  at the “i th ” nozzle  120  for a specific density patch  220  is provided by modifying Equation (1) as follows: 
     
       
           D   i =ƒ i ( V   pi   , T )  Equation (8) 
       
     
     where, 
     D i =print density for “i th ” nozzle  120 ; 
     V pi =the corrected pulse voltage amplitude for “i th ” nozzle  120 ; 
     T=pulse voltage duration for “i th ” nozzle  120 ; and 
     i=1 to total number of nozzles “N”. 
     It is appreciated that Equation (1) and Equation (8) differ to the extent that Equation (8) provides print density D i  considering differences in physical characteristics among nozzles  120  and Equation (1) provides a print density D for print head  45  as a whole irrespective of differences among nozzles  120 . In this regard, print head  45  will print with the ideal print density D only if each nozzle  120  prints with this same print density D. However, each nozzle  120  will not necessarily print with the same print density D due to variabilities found, for example, in the diameter of nozzle orifice portion  140  and/or the electrical resistance in heaters  150 . Therefore, it remains to determine the print density D i  for each “i th ” nozzle  120 . In this regard, the ideal print density D is obtained by supplying the corrected pulse voltage amplitude V pi , at a constant pulse voltage duration T, to each nozzle  120 , or alternatively, by supplying the corrected voltage pulse duration T i , at constant pulse amplitude V p , to each nozzle  120 . 
     Thus, for a constant voltage pulse duration T, the print density D i  which is produced by the “i th ” nozzle  120  is obtained by first noting the following equation: 
     
       
           D   i =ƒ i (V pi , T).  Equation (9) 
       
     
     Subtracting Equation (9) from Equation (1) leads to the following mathematical expression: 
     
       
           D−D   i =ƒ( V   p   , T )−ƒ i ( V   pi   , T ).  Equation (10) 
       
     
     However, it is understood that the differences among nozzles  120  are assumed to be small so that the derivatives of ƒ i  and ƒ are the same to a first order approximation, as follows: 
     
       
           D−D   i =ƒ( V   p   , T )−ƒ i ( V   pi   , T )≈(∂ƒ/∂ V   p ) ( V   pi   −V   p )  Eqn. (11) 
       
     
     where, 
     ∂ƒ i   /∂V   p =partial derivative of the function “ƒi” with respect to voltage amplitude V p . 
     When solved for V pi , Equation (11) becomes: 
     
       
           V   pi   =V   p +( D−D   i )/(∂ƒ( V   pi   , T )/∂ V   pi ).  Equation (12) 
       
     
     Therefore, Equation (12) provides the voltage pulse amplitude V pi  which should be applied to nozzle “i” to obtain a required print density D, which is the print density for print head  45  as a whole. Print density D is selected by the operator of apparatus  10 , such as by means of input source  30 . 
     Moreover, using an analogous derivation, the voltage pulse duration T i  which can be applied to nozzle “i” to obtain print density D is found as follows: 
       T   i   =T+ ( D−D   i )/(∂ƒ( V   p   , T )/ ∂ T ).  Equation (13) 
     As disclosed more fully hereinbelow, the first and second look-up tables  230 / 240  described hereinabove for the Resistance Calibration Technique are also constructed for the Density Calibration Technique. 
     Therefore, referring to FIGS. 1,  2 ,  3 ,  14  and  15 , once the pulse voltage amplitudes V pi  and/or the pulse voltage durations T i  are obtained by the steps recited hereinabove for the Density Calibration Technique, these values of V pi  and T i  and the corresponding print densities D i  are stored electronically in chip  220 , which is connected to controller  40 . The values of D i , V pi , and T i  stored in chip  220  are used as parameters for each nozzle  120  during normal operation of nozzles  120 . That is, the desired print density D is selected, such as by means of input source  30 , and is then communicated to controller  40 . Once controller  40  accepts a density value D to be printed by print head  45 , controller  40  is informed by first lookup table  230  in chip  220  as to the correct voltage amplitude V pi  to apply to each nozzle  120  in order to obtain uniform print density D among nozzles  120 . In this case only first look-up table  230 , which contains the V pi  values as a function of density D i , is stored in chip  220 . Also, pulse voltage duration T is held at a constant value by controller  40  and therefore, in this case, there is no need to store second look-up table  240  in chip  220 . 
     Alternatively, once controller  40  accepts a density value D to be printed by print head  45 , controller  40  is informed by second lookup table  240  stored in chip  220  as to the correct voltage pulse duration T i  to apply to each nozzle  120  in order to obtain uniform print density among nozzles  120 . In this case only second look-up table  240 , which contains the T i  values as a function of density D i , is stored in chip  220 . Also, the pulse voltage amplitude V p  is held at a constant value by controller  40  and therefore, in this case, there is no need to store first look-up table  230  in chip  220 . 
     Moreover, efficacy of both the Resistance Calibration Technique and Density Calibration Technique are enhanced when print line times are compatible with the calibration technique selected. “Print line time” is defined herein to mean the time spent on marking each row of ink pixels on recorder medium  180 . That is, when voltage pulse amplitude V pi  is varied, the voltage pulse duration T is held constant among all nozzles  120  in print head  45  and the printing line time is set equal to or greater than the constant voltage pulse duration T. Alternatively, when voltage pulse duration T i  is varied, the voltage pulse amplitude V p  is held constant among all nozzles  120  in print head  45  and the printing line time is set equal to or greater than the maximum pulse duration allowable for nozzles  120  in the entire print head  45 . 
     FIG. 17 presents a flow chart  250  summarizing selected steps in the method of the invention. More specifically, flow chart  250  illustrates steps for arriving at Equations (5), (7), (12) and (13). The steps of the Density Calibration technique described hereinabove calibrates nozzles  120  in such a manner that effectively all physical variations among nozzles  120  will be compensated for, in order to obtain uniform print density from nozzles  120 . 
     Returning briefly to FIG. 12, the square wave form of voltage pulse  210  is preferably used in those cases where control of print head  45  is provided digitally. That is, square wave voltage pulse  210  is preferable in those cases where the digital signal supplied to print head  45  is either “1” (e.g., for “on”) or “0” (e.g., for “off”). 
     However, one constraint or limitation on the amount of heat energy “E” supplied to ink droplet  170  is that the temperature of ink droplet  170  is preferably kept below its boiling temperature, so that nozzles  120  will not be blocked by coalescence of bubbles. As described more fully hereinbelow, a different pulse wave form is substituted for the square wave form of FIG. 12 in order to mitigate formation of voids or bubbles. 
     Therefore, referring to FIG. 18, in order to mitigate formation of bubbles, an analog wave form  260  may be used. Analog wave form  260  has a low voltage preheat region to warm-up ink droplet  170 , a peak voltage, and then a logrithmically decreasing voltage region. Analog wave form  260  will allow ink droplet  170  to be released from nozzle  120  without excessive heating, so that significant void formation is precluded. It is understood that analog wave form  260  may be substituted for the square wave form  210 , if desired. 
     It is appreciated from the teachings herein, that an advantage of the present invention is that images of uniform print density are provided even in the presence of variations in such factors as electrical resistance of the heaters and/or diameter of the nozzle orifice. This is so because each nozzle  120  is calibrated by means of either the Resistance Calibration Technique or by means of the Density Calibration Technique to compensate for such variability among nozzles  120 . 
     Another advantage of the present invention is that use thereof saves time because correcting print density non-uniformities for each input image file is not required. That is, image processing is not required for each and every input image for which output density correction is desired. This is so because print head  45  is preferably calibrated once, such as at manufacture, rather than each time an image file is acquired by input source  30 . 
     A further advantage of the present invention is that it eliminates visual printing defects, such as “banding”. Of course, this is so because the print nozzles print with uniform density. 
     While the invention has been described with particular reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements of the preferred embodiment without departing from the invention. In addition, many modifications may be made to adapt a particular situation and material to a teaching of the present invention without departing from the essential teachings of the invention. For example, the invention is described with reference to a scanner or computer being used to provide the input image. However, any suitable input imaging device may be used to provide the input image. As another example, the invention is described with reference to an ink-jet printer. However, the invention may be used, with obvious modifications, in a so-called “thermal dye” printer. As a further example, the image forming characteristic is print density in the preferred embodiment of the invention. However, any applicable image forming characteristic may be selected, such as ink droplet volume. 
     Therefore, what is provided is an imaging apparatus and method for providing images of uniform print density, so that printing non-uniformities, such as banding, are avoided. 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention. 
     Parts List 
       10  . . . imaging apparatus 
       20  . . . printer 
       30  . . . input device 
       40  . . . controller 
       45  . . . print head 
       50  . . . recorder medium 
       60  . . . rollers 
       70  . . . input supply tray 
       80  . . . output tray 
       90  . . . ink fluid cavities 
       100  . . . body of ink 
       110  . . . ink fluid reservoir 
       120  . . . nozzle 
       130  . . . flow channel 
       140  . . . orifice portion 
       150  . . . heater 
       160  . . . voltage supply unit 
       170  . . . droplet 
       180  . . . test image 
       190  . . . density patches 
       200  . . . marginal region 
       210  . . . square wave voltage pulse 
       220  . . . memory unit/chip 
       230  . . . first look-up table 
       240  . . . second look-up table 
       250  . . . flow chart 
       260  . . . analog wave form