Patent Publication Number: US-2019168507-A1

Title: Controlling waveforms to reduce cross-talk between inkjet nozzles

Description:
FIELD OF THE INVENTION 
     This invention pertains to the field of inkjet printing and more particularly to a method of controlling drop-formation waveforms to an array of nozzles to reduce printing artifacts. 
     BACKGROUND OF THE INVENTION 
     Continuous inkjet printing is a printing technology that is well suited for high speed printing applications, having high throughput and low cost per page. Recent advances in continuous inkjet printing technology have included thermally induced drop formation, which is capable of selectively altering the drop breakoff phase relative to a charging electrode waveform or selectively altering the velocity of a pair of drops (one of which is charged and the other uncharged) to cause them to merge, and electrostatic deflection of charged drops to separate the charged non-printing drops from the charged printing drops, as disclosed in U.S. Pat. No. 7,938,516 (Piatt et al.), U.S. Pat. No. 8,382,259 (Panchawagh et al.), U.S. Pat. No. 8,465,129 (Panchawagh et al.), U.S. Pat. No. 8,469,496 (Panchawagh et al.), U.S. Pat. No. 8,585,189 (Marcus et al.), U.S. Pat. No. 8,651,632 (Marcus et al.), U.S. Pat. No. 8,651,633 (Marcus et al.), and U.S. Pat. No. 8,657,419 (Panchawagh et al.), all commonly assigned. These advances have enabled the print resolution to be significantly improved while maintaining the throughput of the printer. 
     It has been found that under certain printing conditions, print artifacts can be produced. There is a need for a more effective means to prevent the formation of such print artifacts. 
     SUMMARY OF THE INVENTION 
     The present invention represents a method of printing, including: providing a liquid chamber having a plurality of nozzles disposed along a nozzle array direction, the plurality of nozzles including a first group of nozzles and a second group of nozzles, the nozzles of the first group being interleaved with the nozzles of the second group; 
     providing liquid under pressure in the liquid chamber, the pressure being sufficient to eject liquid jets through the plurality of nozzles; 
     providing a drop formation device associated with each of the plurality of nozzles; 
     providing a first set of drop-formation waveforms and a second set of drop-formation waveforms, wherein the first set of drop-formation waveforms and the second set of drop-formation waveforms each include:
         one or more printing-drop drop-formation waveforms having a waveform period, which, when supplied to a drop formation device associated with a particular nozzle, modulate the liquid jet ejected from the particular nozzle to selectively cause portions of the liquid jet to break off into a pair of drops traveling along a path, the pair of drops including a small printing drop and a small non-printing drop; and   one or more non-printing-drop drop-formation waveforms, which, when supplied to a drop formation device associated with a particular nozzle, modulate the liquid jet ejected from the particular nozzle to selectively cause a portion of the liquid jet to break off into a large non-printing drop traveling along the path, the large non-printing drop being larger than the small printing drop and the small non-printing drop, the non-printing-drop drop-formation waveforms having the same waveform period as the printing-drop drop-formation waveforms;       

     wherein each of the drop-formation waveforms provides an associated waveform energy when supplied to the corresponding drop formation device, and wherein the waveform energies associated with the drop-formation waveforms in the second set of drop-formation waveforms is larger than the waveform energies associated with the corresponding drop-formation waveforms in the first set of drop-formation waveforms; 
     providing input image data; 
     controlling the drop formation devices associated with each of the plurality of nozzles in response to the provided input image data, wherein the first group of nozzles are controlled with a sequence of drop-formation waveforms selected from the first set of drop-formation waveforms and the second group of nozzles are controlled with a sequence of drop-formation waveforms selected from the second set of drop-formation waveforms; 
     providing a timing delay device to time-shift the drop-formation waveforms used to control the drop formation devices associated with the second group of nozzles by a specified second-group time shift relative to the drop-formation waveforms used to control the drop formation devices associated with the first group of nozzles, wherein the second-group time shift is a fraction of the waveform period; 
     providing a charging device including:
         a common charging electrode positioned in proximity to the liquid jets ejected through both the first and second groups of nozzles; and   a charging-electrode waveform source providing a varying electrical potential between the charging electrode and the liquid jets according to a predefined periodic charging-electrode waveform, the charging-electrode waveform including a first portion providing a first electrical potential and a second portion providing a second electrical potential, wherein the charging-electrode waveform has the same waveform period as the drop-formation waveforms;       

     synchronizing the drop formation devices, the timing delay device, and the charging device, wherein the waveform energies associated with the drop-formation waveforms in the first and second sets of drop-formation waveforms and the second-group time shift are selected such that the small printing drops break off from the liquid jets during the first portion of the charging-electrode waveform to provide a first printing-drop charge state, and the small non-printing drops and the large non-printing drops break off from the liquid jets during the second portion of the charging-electrode waveform to provide a second non-printing-drop charge state; 
     providing a deflection device which causes the printing drops having the first printing-drop charge state to travel along a different path from the non-printing drops having the second non-printing-drop charge state; and 
     intercepting the non-printing drops using an ink catcher while allowing the printing drops to travel along a path toward a receiver. 
     This invention has the advantage that the shifting the phase of the drop formation waveforms applied to interleaved sets of drop-formation devices reduces cross-talk artifacts, and appropriately modifying the waveform energies for the sets of drop-formation devices synchronizes the drop break-off times enabling electrostatic drop deflection using a common charging electrode. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a simplified block schematic diagram of an exemplary continuous inkjet system; 
         FIG. 2  illustrates a liquid jet being ejected from a drop generator and its subsequent break off into drops with a regular period; 
         FIG. 3  shows a cross-sectional view of an exemplary inkjet printhead of a continuous liquid ejection system in accordance with the present invention; 
         FIG. 4  shows an exemplary timing diagram illustrating drop-formation pulses and a charging-electrode waveform; 
         FIG. 5  illustrates a liquid jet being ejected from a drop generator and its subsequent break off into drops; 
         FIG. 6  is a representation of a portion of the print media including a spatially periodic printed pattern and induced print defects; 
         FIG. 7  is a simplified block schematic diagram of four adjacent nozzles arranged into two groups and associated drop formation devices according to an exemplary embodiment; 
         FIG. 8  shows a timing diagram illustrating drop formation pulses applied to two groups of drop formation transducers, where the drop formation pulses applied to the second group are time delayed and have a higher amplitude than the drop formation pulses applied to the first group; 
         FIG. 9  shows a timing diagram illustrating drop formation pulses applied to two groups of drop formation transducers, where the drop formation pulses applied to the second group are time delayed and have a larger pulse width than the drop formation pulses applied to the first group; 
         FIG. 10  is a simplified block schematic diagram of four adjacent nozzles arranged into two groups and associated drop formation transducers, where the drop formation transducers associated with the second group have a lower resistance than the drop formation transducers associated with the first group to provide higher waveform energies; 
         FIG. 11  shows a timing diagram illustrating drop formation pulses applied to two groups of drop formation transducers, where the drop-formation waveforms include secondary pulses in addition to the primary drop-formation pulses; 
         FIG. 12  shows a timing diagram illustrating drop formation pulses applied to two groups of drop formation transducers, where the drop-formation waveforms associated with the second group have more drop formation pulses than the drop-formation waveforms associated with the first group; 
         FIG. 13  shows a timing diagram illustrating drop formation pulses applied to two groups of drop formation transducers, where the drop-formation waveforms associated with the second group have inverted drop formation pulses; 
         FIG. 14  shows a timing diagram of a sequence of drop-formation waveforms, illustrating flexibility in defining the start and end points of each waveform; 
         FIG. 15  shows a timing diagram illustrating drop formation pulses applied to two groups of drop formation transducers, where the time delay for the second group is introduced by shifting the drop-formation pulses within the boundaries of the drop-formation waveforms; 
         FIG. 16  is a simplified block schematic diagram of four adjacent nozzles arranged into three groups and associated drop formation devices according to another exemplary embodiment; 
         FIG. 17  shows a timing diagram illustrating drop formation pulses applied to three groups of drop formation transducers, where the drop formation pulses applied to the second group are time delayed relative and have a higher waveform energy relative to the drop formation pulses applied to the first group, and the drop formation pulses applied to the third group are time delayed and have a higher waveform energy relative to the drop formation pulses applied to the second group; and 
         FIGS. 18A-18B  are photographs comparing drops being formed with drop-formation waveforms in accordance with the present invention to those being formed with a prior art method. 
     
    
    
     It is to be understood that the attached drawings are for purposes of illustrating the concepts of the invention and may not be to scale. Identical reference numerals have been used, where possible, to designate identical features that are common to the figures. 
     DETAILED DESCRIPTION OF THE INVENTION 
     The present description will be directed in particular to elements forming part of, or cooperating more directly with, apparatus in accordance with the present invention. It is to be understood that elements not specifically shown or described may take various forms well known to those skilled in the art. References to “a particular embodiment” and the like refer to features that are present in at least one embodiment of the invention. Separate references to “an embodiment” or “particular embodiments” or the like do not necessarily refer to the same embodiment or embodiments; however, such embodiments are not mutually exclusive, unless so indicated or as are readily apparent to one of skill in the art. The use of singular or plural in referring to the “method” or “methods” and the like is not limiting. It should be noted that, unless otherwise explicitly noted or required by context, the word “or” is used in this disclosure in a non-exclusive sense. 
     The example embodiments of the present invention are illustrated schematically and not to scale for the sake of clarity. One of the ordinary skills in the art will be able to readily determine the specific size and interconnections of the elements of the example embodiments of the present invention. 
     As described herein, exemplary embodiments of the present invention provide a printhead or printhead components typically used in inkjet printing systems. However, many other applications are emerging which use printheads to emit liquids (other than inks) that need to be finely metered and deposited with high spatial precision. As such, as described herein, the terms “liquid” and “ink” refer to any material that can be ejected by the printhead or printhead components described below. 
     Referring to  FIG. 1 , a continuous printing system  20  includes an image source  22  such as a scanner or computer which provides raster image data, outline image data in the form of a page description language, or other forms of digital image data. This image data is converted to half-toned bitmap image data by an image processing unit (image processor)  24  which also stores the image data in memory. A plurality of drop-forming transducer control circuits  26  reads data from the image memory and apply time-varying electrical pulses to a drop-forming transducers  28  that are associated with one or more nozzles of a printhead  30 . These pulses are applied at an appropriate time, and to the appropriate nozzles, so that drops formed from a continuous inkjet stream will form spots on a print medium  32  in the appropriate position designated by the data in the image memory. 
     Print medium  32  is moved relative to the printhead  30  by a print medium transport system  34 , which is electronically controlled by a media transport controller  36  in response to signals from a speed measurement device  35 . The media transport controller  36  is in turn is controlled by a micro-controller  38 . The print medium transport system  34  shown in  FIG. 1  is a schematic only, and many different mechanical configurations are possible. For example, a transfer roller could be used in the print medium transport system  34  to facilitate transfer of the ink drops to the print medium  32 . Such transfer roller technology is well known in the art. In the case of page width printheads, it is most convenient to move the print medium  32  along a media path past a stationary printhead. However, in the case of scanning print systems, it is often most convenient to move the printhead along one axis (the sub-scanning direction) and the print medium  32  along an orthogonal axis (the main scanning direction) in a relative raster motion. 
     Ink is contained in an ink reservoir  40  under pressure. In the non-printing state, continuous inkjet drop streams are unable to reach print medium  32  due to an ink catcher  72  that blocks the stream of drops, and which may allow a portion of the ink to be recycled by an ink recycling unit  44 . The ink recycling unit  44  reconditions the ink and feeds it back to the ink reservoir  40 . Such ink recycling units are well known in the art. The ink pressure suitable for optimal operation will depend on a number of factors, including geometry and thermal properties of the nozzles and thermal properties of the ink. A constant ink pressure can be achieved by applying pressure to the ink reservoir  40  under the control of an ink pressure regulator  46 . Alternatively, the ink reservoir  40  can be left unpressurized, or even under a reduced pressure (vacuum), and a pump can be employed to deliver ink from the ink reservoir  40  under pressure to the printhead  30 . In such an embodiment, the ink pressure regulator  46  can include an ink pump control system. The ink is distributed to the printhead  30  through an ink channel  47 . The ink preferably flows through slots or holes etched through a silicon substrate of printhead  30  to its front surface, where a plurality of nozzles and drop-forming transducers, for example, heaters, are situated. When printhead  30  is fabricated from silicon, the drop-forming transducer control circuits  26  can be integrated with the printhead  30 . The printhead  30  also includes a deflection mechanism  70  which is described in more detail below with reference to  FIGS. 2 and 3 . 
     Referring to  FIG. 2 , a schematic view of continuous liquid printhead  30  is shown. A jetting module  48  of printhead  30  includes an array of nozzles  50  formed in a nozzle plate  49 . In  FIG. 2 , nozzle plate  49  is affixed to the jetting module  48 . Alternatively, the nozzle plate  49  can be integrally formed with the jetting module  48 . Liquid, for example, ink, is supplied to the nozzles  50  via ink channel  47  at a pressure sufficient to form continuous liquid streams  52  (sometimes referred to as filaments) from each nozzle  50 . In  FIG. 2 , the array of nozzles  50  extends into and out of the figure. 
     Jetting module  48  is operable to cause liquid drops  54  to break off from the liquid stream  52  in response to image data. To accomplish this, jetting module  48  includes a drop stimulation or drop-forming transducer  28 , which, when selectively activated, perturbs the liquid stream  52 , to induce portions of each filament to break off and coalesce to form the drops  54 . Examples of drop-forming transducer  28  include thermal devices such as heaters for heating the ink, MEMS piezoelectric, electrostrictive or thermal actuators such as are disclosed in commonly-assigned U.S. Pat. No. 8,087,740 (Piatt et al.), electrohydrodynamic devices such as disclosed in U.S. Pat. No. 3,949,410 (Bassous et al.), or optical devices such as those disclosed in U.S. Pat. No. 3,878,519 (Eaton). Depending on the type of transducer used, the transducer can be located in or adjacent to the liquid chamber that supplies the liquid to the nozzles  50  to act on the liquid in the liquid chamber, can be located in or immediately around the nozzles  50  to act on the liquid as it passes through the nozzle, or can be located adjacent to the liquid stream  52  to act on the liquid stream  50  after it has passed through the nozzle  50 . 
     In  FIG. 2 , the drop-forming transducer  28  is a heater  51 , for example, an asymmetric heater or a ring heater (either segmented or not segmented), located in the nozzle plate  49  on one or both sides of the nozzle  50 . This type of drop formation is known and has been described in, for example, U.S. Pat. No. 6,457,807 (Hawkins et al.); U.S. Pat. No. 6,491,362 (Jeanmaire); U.S. Pat. No. 6,505,921 (Chwalek et al.); U.S. Pat. No. 6,554,410 (Jeanmaire et al.); U.S. Pat. No. 6,575,566 (Jeanmaire et al.); U.S. Pat. No. 6,588,888 (Jeanmaire et al.); U.S. Pat. No. 6,793,328 (Jeanmaire); U.S. Pat. No. 6,827,429 (Jeanmaire et al.); and U.S. Pat. No. 6,851,796 (Jeanmaire et al.), each of which is incorporated herein by reference. 
     Typically, one drop-forming transducer  28  is associated with each nozzle  50  of the nozzle array. However, in some configurations, a drop-forming transducer  28  can be associated with groups of nozzles  50  in the nozzle array. 
     Referring to  FIG. 2  the printing system has associated with it, a printhead  30  that is operable to produce, from an array of nozzles  50 , an array of liquid streams  52 , also called liquid jets. A drop-forming device is associated with each liquid stream  52 . The drop-formation device includes a drop-forming transducer  28  and a drop-formation waveform source  55  that supplies a drop-formation waveform sequence  60  to the drop-forming transducer  28 . The drop-formation waveform source  55  is a portion of the mechanism control circuits  26 . In some embodiments in which the nozzle plate is fabricated of silicon, the drop-formation waveform source  55  is formed at least partially on the nozzle plate  49 . The drop-formation waveform source  55  supplies a drop-formation waveform sequence  60 , which typically includes a sequence of pulses having a fundamental frequency f o  and a fundamental period of T o =1/f o , to the drop-formation transducer  28 , which produces a modulation in the diameter of the liquid stream; the modulation having a wavelength λ along the liquid stream. The jet-diameter modulation moves with the flowing liquid down the liquid stream and it grows in amplitude, causing the larger diameter portions of the liquid stream to further increase in diameter and the smaller diameter portions of the liquid stream to decrease further in diameter. The modulation amplitude grows until, at a distance BL from the nozzle plate  49 , the small diameter portions of the liquid stream shrink to a diameter of zero, causing the end portion of the liquid stream  52  to break off into drops  54 . Through the action of the drop-formation device, a sequence of drops  54  is produced. In accordance with the drop-formation waveform sequence  60 , the drops  54  are formed at the fundamental frequency f o  with a fundamental period of T o =1/f o . In  FIG. 2 , liquid stream  52  breaks off into drops with a regular period at breakoff location  59 , which is a distance, called the break off length, BL from the nozzle  50 . The distance between a pair of successive drops  54  is essentially equal to the wavelength λ of the perturbation on the liquid stream  52 . The stream of drops  54  formed from the liquid stream  52  follow an initial trajectory  57 . 
     The time from when a drop-formation waveform pulse is applied to the drop-formation transducer until the jet-diameter modulation produced by the waveform pulse causes a portion of the liquid stream to break off as a drop is called the break-off time BOT. The break-off time BOT of the droplet for a particular printhead can be altered by changing at least one of the amplitude, duty cycle, or number of the stimulation pulses to the respective resistive elements surrounding a respective resistive nozzle orifice, all of which alter the initial modulation amplitude on the liquid stream. In this way, small variations of either pulse duty cycle or amplitude allow the droplet break-off times to be modulated in a predictable fashion within ±one-tenth the droplet generation period. 
     Also, shown in  FIG. 2 , is a charging device  61  comprising charging electrode  62  and charging-electrode waveform source  63 . The charging electrode  62  associated with the liquid jet is positioned adjacent to the break off point  59  of the liquid stream  52 . If a voltage is applied to the charging electrode  62 , electric fields are produced between the charging electrode and the electrically grounded liquid jet, and the capacitive coupling between the two produces a net charge on the end of the electrically conductive liquid stream  52 . (The liquid stream  52  is grounded by means of contact with the liquid chamber of the grounded drop generator.) If the end portion of the liquid jet breaks off to form a drop while there is a net charge on the end of the liquid stream  52 , the charge of that end portion of the liquid stream  52  is trapped on the newly formed drop  54 . 
     The voltage on the charging electrode  62  is controlled by the charging-electrode waveform source  63 , which provides a charging-electrode waveform  64  operating at a charging-electrode waveform  64  period  80  (shown in  FIG. 4 ). The charging-electrode waveform source  63  provides a varying electrical potential between the charging electrode  62  and the liquid stream  52 . The charging-electrode waveform source  63  generates a charging-electrode waveform  64 , which includes a first voltage state and a second voltage state; the first voltage state being distinct from the second voltage state. An example of a charging-electrode waveform is shown in part B of  FIG. 4 . The two voltages are selected such that the drops  54  breaking off during the first voltage state acquire a first charge state and the drops  54  breaking off during the second voltage state acquire a second charge state. The charging-electrode waveform  64  supplied to the charging electrode  62  is independent of, or not responsive to, the image data to be printed. The charging device  61  is synchronized with the drop-formation device using a conventional synchronization device  27 , which is a portion of the control circuits  26 , (see  FIG. 1 ) so that a fixed phase relationship is maintained between the charging-electrode waveform  64  produced by the charging-electrode waveform source  63  and the clock of the drop-formation waveform source  55 . As a result, the phase of the break off of drops  54  from the liquid stream  52 , produced by the drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3 ,  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4  (see  FIG. 4 ), is phase locked to the charging-electrode waveform  64 . As indicated in  FIG. 4 , there can be a phase shift  109  (or equivalently a time shift) between the charging-electrode waveform  64  and the drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3 ,  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4 . 
     With reference now to  FIG. 3 , printhead  30  includes a drop-forming transducer  28  which creates a liquid stream  52  that breaks up into ink drops  54 . Selection of drops  54  as printing drops  66  or non-printing drops  68  will depend upon the phase of the droplet break off relative to the charging electrode voltage pulses that are applied to the to the charging electrode  62  that is part of the deflection mechanism  70 , as will be described below. The charging electrode  62  is variably biased by a charging-electrode waveform source  63 . The charging-electrode waveform source  63  provides a charging-electrode waveform  64 , in the form of a sequence of charging pulses. The charging-electrode waveform  64  is periodic, having a charging-electrode waveform period  80  ( FIG. 4 ). 
     An embodiment of a charging-electrode waveform  64  is shown in part B of  FIG. 4 . The charging-electrode waveform  64  comprises a first voltage state  82  and a second voltage state  84 . Drops breaking off during the first voltage state  82  are charged to a first charge state and drops breaking off during the second voltage state  84  are charged to a second charge state. The second voltage state  84  is typically at a high level, biased sufficiently to charge the drops  54  as they break off. The first voltage state  82  is typically at a low level relative to the printhead  30  such that the first charge state is relatively uncharged when compared to the second charge state. An exemplary range of values of the electrical potential difference between the first voltage state  82  and a second voltage state  84  is 50 to 300 volts and more preferably 90 to 150 volts. 
     Returning to a discussion of  FIG. 3 , when a relatively high-level voltage or electrical potential is applied to the charging electrode  62  and a drop  54  breaks off from the liquid stream  52  in front of the charging electrode  62 , the drop  54  acquires a charge and is deflected by deflection mechanism  70  towards the ink catcher  72  as non-printing drop  68 . The non-printing drops  68  that strike the catcher face  74  form an ink film  76  on the face of the ink catcher  72 . The ink film  76  flows down the catcher face  74  and enters liquid channel  78  (also called an ink channel), through which it flows to the ink recycling unit  44 . The liquid channel  78  is typically formed between the body of the ink catcher  72  and a lower plate  79 . 
     Deflection occurs when drops  54  break off from the liquid stream  52  while the potential of the charging electrode  62  is provided with an appropriate voltage. The drops  54  will then acquire an induced electrical charge that remains upon the droplet surface. The charge on an individual drop  54  has a polarity opposite that of the charging electrode  62  and a magnitude that is dependent upon the magnitude of the voltage and the coupling capacitance between the charging electrode  62  and the drop  54  at the instant the drop  54  separates from the liquid jet. This coupling capacitance is dependent in part on the spacing between the charging electrode  62  and the drop  54  as it is breaking off. It can also be dependent on the vertical position of the breakoff point  59  relative to the center of the charge electrode  62 . After the charged drops  54  have broken away from the liquid stream  52 , they continue to pass through the electric fields produced by the charge plate. These electric fields provide a force on the charged drops deflecting them toward the charging electrode  62 . The charging electrode  62 , even though it cycled between the first and the second voltage states, thus acts as a deflection electrode to help deflect charged drops away from the initial trajectory  57  and toward the ink catcher  72 . After passing the charging electrode  62 , the drops  54  will travel in close proximity to the catcher face  74  which is typically constructed of a conductor or dielectric. The charges on the surface of the non-printing drops  68  will induce either a surface charge density charge (for a catcher face  74  constructed of a conductor) or a polarization density charge (for a catcher face  74  constructed of a dielectric). The induced charges on the catcher face  74  produce an attractive force on the charged non-printing drops  68 . The attractive force on the non-printing drops  68  is identical to that which would be produced by a fictitious charge (opposite in polarity and equal in magnitude) located inside the ink catcher  72  at a distance from the surface equal to the distance between the ink catcher  72  and the non-printing drops  68 . The fictitious charge is called an image charge. The attractive force exerted on the charged non-printing drops  68  by the catcher face  74  causes the charged non-printing drops  68  to deflect away from their initial trajectory  57  and accelerate along a non-print trajectory  86  toward the catcher face  74  at a rate proportional to the square of the droplet charge and inversely proportional to the droplet mass. In this embodiment, the ink catcher  72 , due to the induced charge distribution, comprises a portion of the deflection mechanism  70 . In other embodiments, the deflection mechanism  70  can include one or more additional electrodes to generate an electric field through which the charged droplets pass so as to deflect the charged droplets. For example, an optional single biased deflection electrode  71  in front of the upper grounded portion of the catcher can be used. In some embodiments, the charging electrode  62  can include a second portion on the second side of the jet array, denoted by the dashed line charging electrode  62 ′, which is supplied with the same charging-electrode waveform  64  as the first portion of the charging electrode  62 . 
     In the alternative, when the drop-formation waveform sequence  60  supplied to the drop-forming transducer  28  causes a drop  54  to break off from the liquid stream  52  when the electrical potential of the charging electrode  62  is at the first voltage state  82  ( FIG. 4 ) (i.e., at a relatively low potential or at a zero potential), the drop  54  does not acquire a charge. Such uncharged drops are unaffected during their flight by electric fields that deflect the charged drops. The uncharged drops therefore become printing drops  66 , which travel in a generally undeflected path along the trajectory  57  and impact the print medium  32  to form print dots  88  on the print medium  32 , as the recoding medium is moved past the printhead  30  at a speed V m . The charging electrode  62 , deflection electrode  71  and ink catcher  72  serve as a drop selection system  69  for the printhead  30 . 
       FIG. 4  illustrates how selected drops can be printed by the control of the drop-formation waveforms  60  supplied to the drop-forming transducer  28 . Section A of  FIG. 4  shows a drop-formation waveform sequence  60  that includes three large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3 , and four small-drop drop-formation waveforms  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4 . The small-drop drop-formation waveforms  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4  each have a period  96  and include a pulse  98 , and each of the large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3  have a longer period  100  and include a longer pulse  102 . In this example, the period  96  of the small-drop drop-formation waveforms  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4  is the fundamental period T o , and the period  100  of the large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3  is twice the fundamental period, 2T o . The small-drop drop-formation waveforms  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4  each cause individual drops to break off from the liquid stream. The large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3 , due to their longer period, each cause a larger drop  54  to be formed from the liquid stream  52 . The larger drops  54  formed by the large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3  each have a volume that is approximately equal to twice the volume of the drops  54  formed by the small-drop drop-formation waveforms  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4 . 
     As previously mentioned, the charge induced on a drop  54  depends on the voltage state of the charging electrode at the instant of drop breakoff. The B section of  FIG. 4  shows the charging-electrode waveform  64  and the times, denoted by the diamonds, at which the drops  54  break off from the liquid stream  52 . The large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3  cause large drops  104 - 1 ,  104 - 2 ,  104 - 3  to break off from the liquid stream  52  while the charging-electrode waveform  64  is in the second voltage state  84 . Due to the high voltage applied to the charging electrode  62  in the second voltage state  84 , the large drops  104 - 1 ,  104 - 2 ,  104 - 3  are charged to a level that causes them to be deflected as non-printing drops  68  such that they strike the catcher face  74  of the ink catcher  72  in  FIG. 3 . The small-drop drop-formation waveforms  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4  cause small drops  106 - 1 ,  106 - 2 ,  106 - 3 ,  106 - 4  to form. Arrows  99  denote the link between the waveforms and the drops that they cause to form. As previously mentioned, there is a break-off time interval BOT between the application of a waveform to the drop-formation transducer and the break off of the resulting drop  54 . The breaks in the arrows  99  and the BOT arrow are present to indicate that the break-off time BOT is typically many times longer than the drop-formation waveform period  100 . Small drops  106 - 1  and  106 - 3  break off during the first voltage state  82 , and therefore will be relatively uncharged. Therefore, they are not deflected into the ink catcher  72 , but rather pass by the ink catcher  72  as printing drops  66  and strike the print medium  32  (see  FIG. 3 ). Small drops  106 - 2  and  106 - 4  break off during the second voltage state  84  and are deflected to strike the catcher face  74  as non-printing drops  68 . The drop-formation waveform sequence  60  is determined by the print data, while the charging-electrode waveform  64  is not controlled by the pixel data to be printed. This type of drop deflection is known and has been described in, for example, U.S. Pat. No. 8,585,189 (Marcus et al.); U.S. Pat. No. 8,651,632 (Marcus); U.S. Pat. No. 8,651,633 (Marcus et al.); U.S. Pat. No. 8,696,094 (Marcus et al.); and U.S. Pat. No. 8,888,256 (Marcus et al.), each of which is incorporated herein by reference. 
     As illustrated in part (A) of  FIG. 5 , the large drops  65  created by the large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3  ( FIG. 4 ) may be formed as a single drop that remains a single drop. Under other conditions as illustrated in part (B) of  FIG. 5 , the large drops  65  can form as two drops  65   a  and  65   b  that break off from the liquid stream  52  at almost the same time that subsequently merge to form the large drop  65 . Alternatively, as indicated in part (C) of  FIG. 5 , the large drop can form as a large drop  65  that breaks off from the liquid stream that breaks apart into two drops  65   a,    65   b  and then merges back to a single large drop  65 . The distance below the breakoff point  59  at which the drops  65   a  and  65   b  coalesce to form the large drop  65  is called the coalescence distance CD. It is generally desirable to keep the coalescence distance CD small. The large drop formation process of part (A) of  FIG. 5  is denoted in  FIG. 4  by the large diamond for large drop  104 - 1 . The large drop formation process of part (B) of  FIG. 5  is denoted in  FIG. 4  by two closely spaced diamonds for large drop  104 - 2 , and the large drop formation process of part (C) of  FIG. 5  is denoted in  FIG. 4  by the double diamond for large drop  104 - 3 . 
     For each nozzle in the nozzle array, a drop-formation waveform sequence  60  including a sequence of large-drop drop-formation waveforms  92  (e.g.,  92 - 1 ,  92 - 2 ,  92 - 3  of  FIG. 4 ) and small-drop drop-formation waveforms  94  (e.g.,  94 - 1 ,  94 - 2 ,  94 - 3 ,  94 - 4  of  FIG. 4 ) is created by the by the drop-formation waveform source  55  in response to the image data to be printed. When the image data for a particular nozzle requires a print drop is to be formed, a pair of small-drop drop-formation waveforms  94  is added to the waveform sequence  60  for that nozzle, and conversely when no print drop is to be created, a large-drop drop-formation waveform  92 , which can also be referred to as a non-printing drop-formation waveform, is added to the waveform sequence  60  for that nozzle. As the small-drop drop-formation waveforms  94  are always added to the drop-formation waveform sequence  60  in pairs whenever a print drop is required, the pair of small-drop drop-formation waveforms  94  (e.g.,  94 - 1 ,  94 - 2 ) is herein considered to be a printing-drop drop-formation waveform  97  (e.g.,  97 - 1 ). The printing-drop drop-formation waveform  97  can also be referred to as a drop-pair drop-formation waveform or more simply as a printing drop-formation waveform. The printing-drop drop-formation waveform  97  has the same period  96  as the non-printing drop-formation waveform  92 . In  FIG. 4 , the small-drop drop-formation waveforms  94 - 1 ,  94 - 2  together form the printing-drop drop-formation waveform  97 - 1 , and the small-drop drop-formation waveforms  94 - 3 ,  94 - 4  together form the printing-drop drop-formation waveform  97 - 2 . 
     While the example of  FIG. 4  shows each of the non-printing large-drop drop-formation-waveforms  92 - 1 ,  92 - 2 ,  92 - 3  as being identical with each other and each of the printing-drop drop-formation waveforms  97 - 1 ,  97 - 2  as being identical with each other, this is not a requirement. In some embodiments, there may be multiple variations of non-printing large-drop drop-formation waveforms  92  and multiple variations of printing-drop drop-formation waveforms  97 . In this case, selection of a particular one of the waveforms may depend not only on the printing/non-printing status of a corresponding pixel but also on printing/non-printing status for one or both of preceding and trailing drops as well, as is disclosed in U.S. Pat. No. 8,469,495 (Gerstenberger et al.). 
     Referring to  FIG. 6 , although the above-described printing system has been found to generally work well, certain print situations have been found to produce print defects, commonly referred to as print artifacts. When images including certain periodic patterns  110  of spaced-apart, broad character strokes  120  are printed, diffuse regions  124  of scattered ink spots have been found in the spaces  122  between the character strokes  120 . The presence of these diffuse regions  124  of undesirable ink spots depends on the spatial period  125  of the pattern of the character strokes  120  and on the print speed; the print defect is more pronounced at high print speeds. Without being bound by the understanding of the physics involved, this form of print defect seems to be an outcome of a resonance excited by the spatially periodic application of drop-formation waveforms, which are required to print the periodic pattern  110 . 
     It has been discovered that the formation of these diffuse regions  124  of scattered ink spots can be suppressed by segmenting the array of nozzles  50  into first and second groups of interleaved nozzles  50 , and introducing a phase shift and a drop-formation waveform energy difference between the drop-formation waveforms supplied to the drop-formation devices associated with these two groups of nozzles  50 . In order to accomplish this, the plurality of nozzles  50  are arranged or grouped into a first group G 1  and a second group G 2  in which the nozzles  50  of the first group G 1  and the second group G 2  are interleaved such that nozzles  50  of the first group G 1  are positioned between adjacent nozzles  50  in the second group G 2  and nozzles  50  of the second group G 2  are positioned between adjacent nozzles  50  in the first group G 1 , as shown in  FIG. 7 . 
     Each of the nozzles  50  in the first group G 1  has an associated drop-formation device (which includes a drop-forming transducer  28  such as a heater  51 ), which for brevity will be referred to as a first-group drop-formation device. Each of the nozzles  50  in the second group G 2  has an associated drop-formation device, which for brevity will be referred to as a second-group drop-formation device. 
     A timing delay device  134  supplies a first group trigger pulse  130  to control the starting time of the drop-formation waveforms  60  provided to the first-group drop-formation devices and a second group trigger pulse  132  to control the starting time of the drop-formation waveforms  60 ′ supplied to the second-group drop-formation devices. In a preferred embodiment, the timing delay device  134  shifts the timing of the drop-formation waveforms  60 ,  60 ′ supplied to one or both of the first-group drop-formation devices and the second-group drop-formation devices so that the waveform pulses in the drop-formation waveforms  60  supplied to the first-group drop-formation devices precedes the waveform pulses in corresponding drop-formation waveforms  60 ′ supplied to the second-group drop-formation devices by a defined second-group time shift  108 . (The second group time shift  108  can equivalently be referred to as a “second group phase shift” since it shifts the phase of the drop formation waveforms  60 ′ relative to the phase of the drop formation waveforms  60 ). 
     In addition, the waveform energy of the drop-formation waveforms  60 ′ supplied to the second-group drop-formation devices are increased relative to the waveform energy of the drop-formation waveforms  60  supplied to the first-group drop-formation devices. In this way, the break-off times BOT′ of the drops from the second-group nozzles  50  are controlled so that they are less than the break-off times BOT of the drops from the first-group nozzles  50 . 
     The waveform energies and the timing delay are selected such that the printing small drops  106 - 1 ,  106 - 3 ,  106 - 1 ′,  106 - 3 ′ break off from the liquid jets during the first voltage state  82  of the charging-electrode waveform  64  to provide the first printing-drop charge state, and the non-printing small drops  106 - 2 ,  106 - 4 ,  106 - 2 ′,  106 - 4 ′ and the non-printing large drops  104 - 1 ,  104 - 2 ,  104 - 3 ,  104 - 1 ′,  104 - 2 ′,  104 - 3 ′ break off from the liquid jets during the second voltage state  84  of the charging-electrode waveform  64  to provide the second non-printing-drop charge state. 
     An embodiment of this is illustrated in  FIG. 8 . The upper portion of  FIG. 8  shows a portion of a drop-formation waveform sequence  60  which is supplied to a first-group drop-formation device. The drop-formation waveform sequence  60  is formed in response to the image data for a first-group nozzle  50 . In this example, the drop-formation waveform sequence  60  includes large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3  and printing-drop drop-formation waveforms  97 - 1 ,  97 - 2 . The lower portion of  FIG. 8  shows a portion of a drop-formation waveform sequence  60 ′ which is supplied to a second-group drop-formation device. The drop-formation waveform sequence  60 ′ is formed in response to the image data for a second-group nozzle  50 . In this example, the drop-formation waveform sequence  60 ′ includes large-drop drop-formation waveforms  92 - 1 ′,  92 - 2 ′,  92 - 3 ′ and printing-drop drop-formation waveforms  97 - 1 ′,  97 - 2 ′. 
     For brevity, the first drop-formation waveform sequence  60  can be referred to as first-set waveforms, and the second drop-formation waveform sequence  60 ′ can be referred to as second-set waveforms. The first-set and the second-set waveforms each include one or more printing-drop-formation waveforms  97  (e.g.,  97 - 1 ,  97 - 2 ,  97 - 1 ′,  97 - 2 ′), which, when supplied to a drop-formation device associated with a particular nozzle, modulate the liquid jet ejected from the particular nozzle to selectively cause portions of the liquid jet to break off into a pair of drops traveling along a path. The first-set and the second-set waveforms also each include non-printing large-drop drop-formation waveforms  92  (e.g.,  92 - 1 ,  92 - 2 ,  92 - 3 ,  92 - 1 ′,  92 - 2 ′,  92 - 3 ′), which, when supplied to a drop-formation device associated with a particular nozzle, modulate the liquid jet ejected from the particular nozzle to selectively cause a portion of the liquid jet to break off into a large non-printing drop traveling along the path. Each of these printing and non-printing drop-formation waveforms have the same waveform period. 
     The central portion of  FIG. 8  shows a portion of the charging electrode waveform  64 , along with the times at which the drops  54  ( FIG. 3 ) break off from the liquid stream  52  ( FIG. 3 ) in response to the illustrated portions of the drop-formation waveforms  60  and  60 ′. The times at which the drops  54  break off from the liquid streams  52  from the first-group nozzles are denoted by filled diamonds, and the times at which the drops  54  break off from the liquid streams  52  from the second-group nozzles are denoted by open diamonds. For clarity, the first drop-formation waveform sequence  60  and the second drop-formation waveform sequence  60 ′ are shown with the same pattern of printing and non-printing drops. However, in practice, the first and second sequences can differ in response to their corresponding image data. It can be seen that the second drop-formation waveform sequence  60 ′ has been delayed by a second-group time shift  108  relative to the first drop-formation waveform sequence  60 . 
     The first-set and second-set waveforms from which the first drop-formation waveform sequence  60  and the second drop-formation waveform sequence  60 ′ are formed differ in their amplitude. The amplitude  140 ′ of the second-set waveforms is larger than the amplitude  140  of the first-set waveforms. As each of the drop-formation waveforms has an associated waveform energy that it supplies to its corresponding drop-formation device, the larger waveform amplitudes  140 ′ of the second-set waveforms supply the second-group drop-formation transducers  28  ( FIG. 3 ) with larger waveform energies than is supplied to the first-group drop-formation transducers  28  by the corresponding drop-formation waveforms from the first-set waveforms. 
     More particularly the energy levels of the Fourier components of the printing-drop drop-formation waveforms  97  (e.g.,  97 - 1 ′,  97 - 2 ′) used to from the small printing drops and the energy levels of the Fourier components of the large-drop drop-formation waveforms  92  (e.g.,  92 - 1 ′,  92 - 2 ′,  92 - 3 ′) used to form the large non-printing drops are larger for the second-set waveforms than for the corresponding drop-formation waveforms in the first-set waveforms. For brevity, the term waveform energy of a printing-drop drop-formation waveform  97  (e.g.,  97 - 1 ′) shall refer to the energy level of the Fourier components of the drop-formation waveform at the frequency appropriate for the modulating the liquid stream to form a pair of small drops  106  (e.g.,  106 - 1 ′,  106 - 2 ′), and the waveform energy of a non-printing large-drop drop-formation waveform  92  (e.g.,  92 - 1 ′) shall refer to the energy level of the Fourier components of the drop-formation waveform at the frequency appropriate for the modulating the liquid stream to form a non-printing larger drop  104  (e.g.,  104 - 1 ′). 
     As a result of the larger waveform energies associated with of the second-set waveforms, the second-group drop-formation devices modulate the diameters of the liquid streams emitted from the second group nozzles at higher initial modulation amplitudes than the initial modulation amplitudes created on liquid streams  52  emitted from the first group nozzles  50  by the first-group drop-formation devices. As higher initial modulation amplitudes created on the liquid streams  52  from second group nozzles  50  reduce the time required for the modulation amplitude to grow sufficiently to cause drops  54  to break off from the liquid streams  52 , the break-off times BOT′ for drops from the second group G 2  of nozzles  50  will be less than the break-off times BOT for drops from the first group G 1  of nozzles  50 . 
     Consider now the times at which large drops  104 - 3 ,  104 - 3 ′ break off from the liquid streams  52  from the first group and second group nozzles  50 , respectively. If the same waveform energies were supplied to both groups of drop-formation devices, the second-group time shift  108  between the first and second drop-formation waveform sequences  60 ,  60 ′ would cause the time of break off for the drops from the second group of nozzles to be delayed by the same time delay as the first group as indicated by the position of the large drop  104 - 3 ″. However, if large drop  104 - 3 ″ from the second group nozzle were to break off at this time, then it would break off during the first voltage state  82  instead of breaking off as it should have during the second voltage state  84  like the large drop  104 - 3  from the first nozzle group. This would cause the large drop  104 - 3 ″ to have a first charge state instead of the desired second charge state and would cause the large drop  104 - 3 ″ to be printed instead of being deflected to the catcher as intended. But the difference in the break-off times BOT and BOT′ produced by the waveform energy difference between the first-set and second-set waveforms advances the time of break off for the large drop back to the position of the large drop  104 - 3 ′. Consequently, the large drop  104 - 3 ′ breaks off during the second voltage state  84 , causing the large drop  104 - 3 ′ to be charged to the second charge state as intended. 
     The increased waveform energies associated with the second-set large-drop drop-formation waveform  92 - 3 ′ relative to the waveform energy associated with first-set large-drop drop-formation waveform  92 - 3  at least partially compensates for the second-group time shift  108 . In a similar manner, the increased waveform energies associated with the each of the second-set printing and non-printing drop-formation waveforms  97 ′,  92 ′, relative to the waveform energies associated with the corresponding first-set printing and non-printing drop-formation waveforms  97 ,  92 , at least partially compensate for the second-group time shift  108  between the waveforms. This enables each of the drops from the nozzles  50  in the second group G 2  to break off during the intended voltage state of the charging electrode waveform  64 , while still having a time shift between the first set and the second-set waveforms that suppresses the formation of diffuse regions  124  of scattered ink spots discussed relative to  FIG. 5 . For acceptable suppression of the diffuse regions  124  of scattered ink spots, it has been found that the drop-formation waveform sequence  60 ′ supplied to the drop-formation devices associated with the second group G 2  of nozzles  50  should be delayed by a second-group time shift  108  in the range of ¼ to ¾ of the waveform period  100  relative to the drop-formation waveform sequence  60  used to control the drop-formation devices associated with the first group G 1  of nozzles  50 . In a preferred embodiment, the second-group time shift  108  should be approximately ½ of the waveform period  100 . 
     In the exemplary configuration of  FIG. 8 , the second-set drop-formation waveform sequence  60 ′ was delayed by a second-group time shift  108  relative to the first-set drop-formation waveform sequence  60  and the waveform energies associated with the second-set drop-formation waveform sequence  60 ′ was increased relative to the waveform energies associated with the first-set drop-formation waveform sequence  60  by increasing the voltage amplitude of the second-set drop-formation waveform sequence  60 ′ relative to the voltage amplitude of the first-set drop-formation waveform sequence  60 . Within the bounds of the invention, alternate means can be used for supplying second-set drop-formation waveform sequence  60 ′ with higher associated waveform energies than the waveform energies of the first-set drop-formation waveform sequence  60 . 
       FIG. 9  illustrates an alternate configuration where the waveform energies are adjusted by changing the pulse widths/duty cycles rather than the waveform amplitudes. In this example, the amplitude  140 ′ of the second-set drop-formation waveform sequence  60 ′ is the same as the amplitude  140  of the first-set drop-formation waveform sequence  60 , but the drop-formation waveforms differ in the duty cycle or pulse width of the waveform pulses. The drop-formation waveforms in the first set drop-formation waveform sequence  60  and the second-set drop-formation waveform sequence  60 ′ are similar to each other, such that each waveform pulse in the drop-formation waveforms in the second-set drop-formation waveform sequence  60 ′ corresponds to a waveform pulse in the corresponding drop-formation waveforms in the first-set drop-formation waveform sequence  60 . That is, for each pulse in a first-set drop-formation waveform there is exactly one pulse in the corresponding second-set drop-formation waveform, and the phase at which the pulses are placed within the drop-formation waveforms are similar (i.e., to within 45°) for the first-set and second-set drop-formation waveforms. The drop-formation pulses also have a similar shape. In this case, the drop-formation pulses have a square-wave shape, although this is not a requirement. In other configurations, the drop-formation pulses can have other shapes such as triangular pulse shapes or trapezoidal pulse shapes. 
     In the example of  FIG. 9 , the first-set and the second-set drop-formation waveforms differ in that the drop-formation pulses of each of the second-set drop-formation waveforms have increased duty cycles (or pulse widths) relative to corresponding drop-formation pulses of the first-set drop-formation waveforms. In the upper section of  FIG. 9 , the printing-drop drop-formation waveforms  97 - 1 ,  97 - 2  for the first-set drop-formation waveform sequence  60  each include two drop-formation pulses  98  with a pulse width  150 , and the non-printing drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3  each include a drop-formation pulse  102  with a pulse width  152 . Similarly, in the lower section of  FIG. 9 , the printing-drop drop-formation waveforms  97 - 1 ′,  97 - 2 ′ for the second-set drop-formation waveform sequence  60 ′ each include two drop-formation pulses  98 ′ with a pulse width  150 ′, and the non-printing drop-formation waveforms  92 - 1 ′,  92 - 2 ′,  92 - 3 ′ each include a drop-formation pulse  102 ′ with a pulse width  152 ′. In this exemplary configuration, the pulse widths  150 ′ of the second-set printing-drop drop-formation waveform pulses  98 ′ are larger than the pulse widths  150  of the corresponding first-set printing-drop drop-formation waveform pulses  98 . Similarly, the pulse widths  152 ′ of the second-set non-printing drop-formation waveform pulses  102 ′ are larger than the pulse widths  150  of the corresponding first-set non-printing drop-formation waveform pulses  102 . 
     In the exemplary configuration of  FIG. 9 , the rising edges of the pulses within the first-set drop-formation waveforms occur at the same phase from the onset of the waveform as the rising edges of the pulses within the second-set drop-formation waveforms. In other embodiments, it may be the falling edges or the midpoints of the corresponding drop-formation pulses of the first set and second-set waveforms that coincide to within 45° of each other from the onset of the waveforms. 
     Another exemplary embodiment is illustrated in  FIG. 10 . In this case, the difference in the waveform energies between the first group G 1  and second group G 2  of nozzles  50  are provided by a difference in the construction between the first-group drop-formation devices and the second-group drop-formation devices, such that the second-group drop-formation devices produce a greater modulation amplitude of the liquid streams than the first-group drop-formation devices when both the first and the second-group drop-formation devices are supplied with the same drop-formation waveforms. 
     In the exemplary embodiment of  FIG. 10 , the drop-formation devices are heaters  51  formed in the nozzle plate  49  ( FIG. 3 ) around each nozzle  50 . The geometry of the heaters  51  associated with the two groups of nozzles  50  differ (in this case, the outer diameter  144 ′ of the heaters  51  in the second group G 2  is greater than the outer diameter  144  of the heaters  51  in the first group) so that the heaters  51  associated with the second group G 2  of nozzles  50  have a lower resistance than the heaters  51  associated with the first group G 1  of nozzles  50 . As a result, the heaters  51  associated with the second group G 2  of nozzles  50  produce more heat than the heaters  51  associated with the second group G 2  of nozzles  50  when both are supplied with the same drop-formation waveforms. 
     In an alternative embodiment, the physical geometries of the two group of heaters  51  can be identical, but the heaters  51  associated with the second group G 2  of nozzles  50  can have a lower resistance than the heaters  51  associated with the first group G 1  of nozzles  50  due to the use of different heater materials having different resistivities. Alternatively, the coupling factor between the heaters  51  and the ink can be altered to modify the waveform energy imparted to the liquid stream  52 , for example by providing different amounts of thermal insulation between the heaters  51  and the nozzles  50 . 
     In a similar manner, differences in the construction of other types of drop-formation transducers  28  (e.g., piezoelectric devices, MEMS actuators, electrohydrodynamic devices, optical devices, or electrostrictive devices) could enable the drop-formation waveforms supplied to the drop-formation transducers  28  associated with the second group G 2  of nozzles  50  to supply more associated waveform energy to the drop-formation transducers  28  than the waveform energy supplied to the drop-formation transducers  28  associated with the first group G 1  of nozzles  50  by a similar drop-formation waveform, such that the initial modulation amplitude of the liquid streams is larger for the second group G 2  of nozzles  50  than for the first group G 1 . 
     In the preceding embodiments, each of the drop-formation waveforms included a single drop-formation pulse for each drop that was to be formed by the drop-formation waveform. The printing-drop drop-formation waveform  97  therefore included two drop-formation pulses to create the printing drop and the non-printing drop of the drop pair, and the non-printing large-drop drop-formation waveform  92  had a single drop-formation pulse to create the single non-printing large drop. In the alternate embodiment of  FIG. 11 , the drop-formation waveforms include not only primary pulses  154  (i.e., the drop-formation pulses primarily responsible for initiating the formation of a drop), but they also include one or more secondary pulses  156  as well. These additional secondary pulses  156 , which can also be referred to as secondary drop-formation pulses, typically have smaller duty cycles than the primary pulses  154 . 
     As discussed in commonly-assigned U.S. Pat. No. 7,828,420 to Fagerquist et al., entitled “Continuous ink jet printer with modified actuator activation waveform,” which is incorporated herein by reference, if the time separation between a secondary pulse  156  and a primary pulse  154  is less than the Rayleigh cut-off period, such that spacing between perturbations is less than n times the diameter of the liquid stream, then the secondary pulse  156  will not induce the break off of an additional drop from the liquid stream  52 . (The secondary pulses  156  are typically separated in time from the primary pulses  154  by greater than the thermal response time of the heater so that they create a heat pulse on the liquid stream that is distinct from the heat pulse of the primary pulse  154 .) 
     As described in U.S. Pat. No. 7,828,420 (Fagerquist et al.), U.S. Pat. No. 8,714,676 (Grace et al.), and U.S. Pat. No. 8,684,483 (Grace et al.), all commonly assigned, the inclusion of one or more secondary pulses in a large-drop drop-formation waveform  92  can aid in stabilizing the formation of the non-printing large drops  65  to correspond to the drop formation condition of part (A) of  FIG. 5 , or in accelerating the coalescence of the large drop  65  from two or more smaller drops  65   a  and  65   b  to reduce the coalescence distance CD of parts (B) and (C) of  FIG. 5 . Similarly, the inclusion of one or more secondary pulse in the printing-drop drop-formation waveforms  97  can reduce the formation of undesirable satellite drops or speed up the merging of satellites drops with the printing drop and the non-printing drop of the drop pair. The inclusion of secondary pulses can also be used to alter the velocity of the drops formed by the primary drop-formation pulses as discussed in U.S. Patent Application Publication 2011/0242169 (Link et al.), U.S. Pat. No. 8,469,496 (Panchawagh et al.), and U.S. Pat. No. 8,657,419 (Panchawagh et al.), all commonly assigned. 
     In the embodiment of  FIG. 11 , the larger waveform energy associated with the second-set drop-formation waveform sequence  60 ′ when compared to the first-set drop-formation waveform sequence  60  is provided by the primary pulses  154 ′ in the second-set drop-formation waveform sequence  60 ′ having larger pulse widths than the corresponding primary pulses  154  in the first-set drop-formation waveform sequence  60 , while the pulse widths of secondary pulses  156 ′ in the second-set drop-formation waveform sequence  60 ′ are equal to the pulse widths of the corresponding secondary pulses  156  in the first-set drop-formation waveform sequence  60 . In some embodiments, the second-set drop-formation waveforms can have different numbers of secondary pulses  156  than the corresponding drop-formation waveform from the first-set drop-formation waveforms. 
     In certain embodiments, the first-set and the second-set waveforms can each include a plurality of printing-drop drop-formation waveform  97  to accommodate different printing drop/non-printing drop sequence options. As was discussed in commonly-assigned U.S. Pat. No. 8,469,495 (Gerstenberger et al.), the selection of an appropriate drop-formation waveform from the set predefined set of drop-formation waveforms can depend not only on the printing/non-printing state of the image data for the current drop-formation waveform, but also on the printing/non-printing state of the image data for the previous drop-formation waveform and/or the following drop-formation waveform. For example, certain printing-drop drop-formation waveforms  97  are used when the preceding drop-formation waveform is a non-printing large-drop drop-formation waveform  92 , while other printing-drop drop-formation waveforms  97  are used when the preceding drop-formation waveform is a printing-drop drop-formation waveform  97 . Similarly, certain printing-drop drop-formation waveforms  97  are used when the following drop-formation waveform is a non-printing large-drop drop-formation waveform  92 , while other printing-drop drop-formation waveforms  97  are used when the following drop-formation waveform is a printing-drop drop-formation waveform  97 . The plurality of printing-drop drop-formation waveforms can vary in the duty cycles and onset times of the primary pulses  154  or the secondary pulses  156 . The different printing-drop drop-formation waveforms  97  can also vary in the number of secondary pulses  156 . 
     Similarly, the first-set and the second-set drop-formation waveforms can each include more than one non-printing large-drop drop-formation waveform  92  to accommodate different printing/non-printing sequences. The plurality of non-printing large-drop drop-formation waveforms  92  can vary in the duty cycles and onset times of the primary pulses  154  or of the secondary pulses  156 . The different non-printing large-drop drop-formation waveforms  92  can also vary in the number of secondary pulses  156 . 
     In some embodiments, the first and second sets of drop-formation waveforms each include eight drop-formation waveforms (labeled A-H), and the selection of the drop-formation waveform for the kth time interval in the waveform sequence depends not only on the printing/non-printing state of time interval k but also on the printing/non-printing states of preceding and following time intervals k−1 and k+1, respectively, as indicated by the table below. 
     
       
         
           
               
               
               
            
               
                   
                   
               
               
                   
                 Printing State 
                 Drop-Formation 
               
            
           
           
               
               
               
               
               
            
               
                   
                 k 
                 k − 1 
                 k + 1 
                 Waveform 
               
               
                   
                   
               
               
                   
                 Printing 
                 Printing 
                 Printing 
                 A 
               
               
                   
                 Printing 
                 Printing 
                 Non-printing 
                 B 
               
               
                   
                 Printing 
                 Non-printing 
                 Printing 
                 C 
               
               
                   
                 Printing 
                 Non-printing 
                 Non-printing 
                 D 
               
               
                   
                 Non-printing 
                 Printing 
                 Printing 
                 E 
               
               
                   
                 Non-printing 
                 Printing 
                 Non-printing 
                 F 
               
               
                   
                 Non-printing 
                 Non-printing 
                 Printing 
                 G 
               
               
                   
                 Non-printing 
                 Non-printing 
                 Non-printing 
                 H 
               
               
                   
                   
               
            
           
         
       
     
     When consecutive heater pulses are supplied to the drop-formation heater  51  having a time separation between the pulses that is less than the thermal response time of the drop-formation heater  51 , these heater pulses act on the liquid stream  52  as if a single heater pulse were applied to the drop-formation heater  51 , as noted in commonly-assigned U.S. Pat. No. 8,087,740.  FIG. 12  shows an embodiment in which the increased waveform energy of the drop-formation waveforms in the second drop-formation waveform sequence  60 ′ is provided by the adding additional pulses to the drop-formation waveforms, wherein the additional pulses are separated in time from the primary drop-formation pulses by less than the thermal response time of the drop-formation heater  51 . For example, in the printing-drop drop-formation waveform  97 - 2 ′, an additional pulse  158  follows immediately after the primary drop-formation pulse  98 ′ to effectively add more waveform energy to that drop-formation pulse. Similarly, in large-drop drop-formation waveform  92 - 3 ′, an additional pulse  160  follows immediately after the primary drop-formation pulse  102 ′ to effectively add more waveform energy to that drop-formation pulse. 
     Another embodiment is shown in  FIG. 13 . In this embodiment, the first-set waveforms in the drop-formation waveform sequence  60  are similar to those in  FIG. 9 . These first-set waveforms are normally held at a low value (e.g., zero volts), with pulses that rise to some higher potential to produce heat pulses that induce the formation of drops. The second-set waveforms in the drop-formation waveform sequence  60 ′ differ in that the waveform potential is normally held at a non-zero voltage, with pulses that fall downward to a lower potential (e.g., to zero volts). Such downward pulses produce a temporary reduction in the energy provided to the drop-formation device or heater  51 . These temporary reductions in the energy provided to the drop-formation device can be considered to be “cooling pulses” rather than heating pulses. Such cooling pulses act on the liquid stream in a manner similar to that of heating pulses to induce the formation of drops. As with the normal drop-formation waveforms, such inverted drop-formation waveforms have an associated waveform energy. With the inverted drop-formation waveforms, the waveform energy of the printing drop-formation waveform shall refer to the energy level of the Fourier components of the drop-formation waveform at the frequency appropriate for the modulating the liquid stream to form the pair of small drops and the waveform energy of a non-printing drop-formation waveform shall refer to the energy level of the Fourier components of the drop-formation waveform at the frequency appropriate for the modulating the liquid stream to form the larger non-printing drop. In this embodiment, the increased waveform energy of the second-set waveforms is provided by the cooling pulses having a larger pulse width  152 ′ than the pulse width  152  of the heating pulses of the first-set waveforms. In the illustrated configuration, the second-set waveforms include an inverted waveform pulse which reduces an energy provided by the drop-formation device. In other embodiments, the first-set waveforms can include inverted waveform pulses which reduce the energy provided by the drop-formation device. In still other embodiments, both the first-set and the second-set waveforms include inverted waveform pulses. 
     As the drop break off phase can vary depending not only on the waveform energy of the drop-formation waveforms, but also dependent on nozzle size, ink pressure and ink properties, some printhead embodiments also include a drop break-off phase detector (not shown) for determining the phase at which drops break off from the first group G 1  of nozzles  50  and from the second group G 2  of nozzles  50 . A variety of drop break-off phase detectors are known in the art, such as are disclosed in U.S. Pat. Nos. 3,761,941, 4,616,234, 7,249,828 and 3,836,912, each of which is incorporated herein by reference. Using such a drop break-off phase detector, the drop break-off phase difference between the drops from the first group G 1  of nozzles  50  and the drops from the second group G 2  of nozzles  50  can be determined. As discussed above, this phase difference is produced by both the second-group time shift  108  ( FIG. 8 ) between the first-set waveforms and the second-set waveforms and the waveform energy difference between the first-set waveforms and the second-set waveforms. To maximize the latitude for setting the phase of the charging-electrode waveform relative to the drop-formation waveforms, it is desirable that the drop break-off time difference or phase difference between the drops from the first group G 1  of nozzles  50  and the drops from the second group G 2  of nozzles  50  be kept small. The drop break-off time difference can be adjusted by adjusting either the second-group time shift  108  applied by group timing delay device  134  ( FIG. 7 ) or the waveform energy of the drop-formation waveforms. As it is typically simpler to adjust the second-group time shift  108  than it is to adjust the waveform energy, in some embodiments the time shift  108  is adjusted responsive to the measured drop break-off time difference to minimize the drop break-off time difference. 
       FIG. 14  shows a portion of a sequence of drop-formation waveforms, the portion including three non-printing large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3  and two printing-drop drop-formation waveforms  97 - 1 ,  97 - 2 . As indicated by the different three boundary sets  162 ,  164 ,  166  of brackets and waveform break marks, the boundaries between the drop-formation waveforms can be shifted within a range while still retaining the required drop-formation pulses within the printing-drop drop-formation waveforms  97 - 1 ,  97 - 2  for the creation of a printing drop and a non-printing drop, and retaining the required drop-formation pulse for the creation of a large non-printing drop in the large-drop drop-formation waveforms  92 - 1 ,  92 - 2 ,  92 - 3 . 
     In the embodiment of  FIG. 15 , the placement of the waveform boundaries of the second set waveforms in the drop-formation waveform sequence  60 ′ has been shifted relative to the drop formation pulses within the waveforms. (While the trailing edge boundaries of the large-drop drop-formation waveform  92 - 1 ,  92 - 2 ,  92 - 3  are aligned with the falling edge of the drop formation pulses  102  and the trailing edge boundaries of the printing-drop drop-formation waveform  97 - 1 ,  97 - 2  are aligned with the falling edge of one of the drop formation pulses  98  in the first-set waveforms in the drop-formation waveform sequence  60 , the boundaries have been shifted from those locations in the second-set of waveforms in the drop-formation waveform sequence  60 ′. As a result of the shifts in the waveform boundaries it is still possible to have a second group time shift  108  even though the waveform boundaries of the first set and the second-set waveforms are aligned. The group timing delay device  134  therefore does not need to delay the second group trigger pulses relative to the first group trigger pulses to effectively delay the phase of the second-set waveforms relative to the first-set waveforms. Rather, the “time shift” is embodied in the set of drop-formation waveforms in order to provide the phase control means. 
     In the embodiment of  FIG. 16 , the plurality of nozzles  50  are arranged or grouped into three nozzle groups. The nozzle groups include a third group G 3  of nozzles  50  in addition to the first group G 1  and the second group G 2 . The nozzles  50  of the third group G 3  are interleaved with nozzles of the first group G 1  and the second group G 2 . Between any two first group nozzles there is a second group nozzle and a third group nozzle. Similarly, between any two second group nozzles there is a first group nozzle and a third group nozzle, and between any two third group nozzles there is a first group nozzle and a second group nozzle. Each of the nozzles  20  has an associated drop-formation device (e.g., a heater  51 ). For brevity, the drop-formation device associated with a nozzle of the third group G 3  will be referred to as a third-group drop-formation device. The drop-formation waveforms supplied to the third group drop-formation devices are referred to as third group waveforms. 
     A timing delay device  134  supplies a first group trigger pulse  130  to control the starting time of the first-group waveforms in the drop-formation waveform sequence  60 , a second group trigger pulse  132  to control the starting time of the second-set waveforms in the drop-formation waveform sequence  60 ′, and a third group trigger pulse  136  to control the starting time of the third-group waveforms in the drop-formation waveform sequence  60 ″. The timing delay device  134  is a particular example of a phase control means which controls the relative phase of the waveforms supplied to the first and second groups of nozzles. 
     In an exemplary embodiment, the timing delay device  134  shifts the timing of the different groups so that the pulses in the first-group waveforms precede corresponding pulses in the second-group waveforms by a time shift  108  and precede the corresponding pulses in the third-group waveforms by a time shift  108 ′ which is larger than time shift  108 , as indicated in  FIG. 17 . The second-group waveforms in the drop-formation waveform sequence  60 ′ therefore precede the third-group waveforms in the drop-formation waveform sequence  60 ″. 
     In addition, the pulse widths  150 ″,  152 ″ for the third-group waveforms are increased relative to the pulse widths  150 ′,  152 ′ of the second-group waveforms so that the waveform energies of the third-group waveforms in the drop-formation waveform sequence  60 ″ are increased relative to the waveform energies of the of the second-group waveforms  60 ′. This causes the break-off times BOT″ of the drops from the third group G 3  of nozzles  50  to be less than the break-off times BOT′ of the drops from the second group G 2  of nozzles  50 , which in turn is less than the break-off times BOT of the drops from the first group G 1  of nozzles  50 . As with the previous embodiments, the waveform energies of the second-group waveforms are increased relative to the waveform energies of the of the first-group waveforms so that the break-off times BOT′ of the drops from the second group G 2  of nozzles  50  are less than the break-off times BOT of the drops from the first group G 1  of nozzles  50 . 
     The printing drops are relatively uncharged when compared to the charge of either the small or the large non-printing drops. But even a small amount of charge on the printing drops can cause the printing drops to undergo some drop deflection, altering the position at which they impact the print medium. To ensure the highest quality print, it is desirable to ensure that the printing drops have a consistent drop charge. As the charge on the printing drops is influenced by the charge on the preceding drops, some embodiments require each pair of drops formed by a printing-drop drop-formation waveform  97  to be preceded by a large non-printing drop. As the trajectory of the printing drops can be influenced by the drop-to-drop electrostatic and aerodynamic interactions, some embodiments require each pair of drops formed by a printing-drop drop-formation waveform  97  to be followed by a large non-printing drop. 
     While each of the preceding embodiments have involved drop-formation waveforms made up of a set of one or more waveform pulses, the drop-formation waveforms are not limited to such sets of waveform pulses. Other waveforms such as sinusoidal, triangular, chirp waveforms, or portions or combinations thereof may also be used. 
     The preceding embodiments have described the timing delay device  134  as producing a first group trigger pulse  130  and a second group trigger pulse  132  for controlling the timing of the first-set waveforms relative to the second-set waveforms. In alternate embodiments, the timing delay device  134  can use other timing control configurations that do not involve using separate trigger pulses for controlling the timing of the different groups of drop-formation devices. For example, the second-set waveforms could be delayed by a predefined number of clock pulses relative to first-set waveforms. Furthermore, in certain embodiments, the different drop-formation waveforms in each sequence of waveforms are concatenated together with no breaks between waveforms. In such embodiments, there is no need for a trigger pulse to initiate each waveform. In such embodiments, the group timing delay device can refer to software implementation for delaying the second-set waveforms relative to the first-set waveforms. 
       FIG. 18A  is a photograph of ink drops being formed in accordance with the present invention. The ink drops being formed in this example are non-printing large drops  65 . (The pair of drops has not yet merged into a single large drop  65  at this point in time.) Ink streams  52  are formed through an array of nozzles  50 . The odd-numbered nozzles form a first group of nozzles G 1 , and the even-numbered nozzles  50  form a second group of nozzles G 2 . The second-group waveforms used to control the second group of nozzles G 2  are time-shifted (by one half of the waveform period) and have a higher waveform energy relative to the first-group waveforms used to control the first group of nozzles G 1 . It can be seen that at the instant of time where the photograph was captured, drops are breaking off at breakoff locations  59  for both the first and second groups of nozzles. As a result, the resulting large drops  65  will all have the same charge state. In contrast,  FIG. 18B  shows the results obtained without the method of the present invention. In this case, the phase of the second-group waveforms has been shifted by 180 degrees, but the same waveform energy is used. It can be seen that the drops are breaking off at the breakoff location  59  for the first group of nozzles G 1 , but the drops being formed by the second group of nozzles G 2  are not close to break-off. As a result, the charge state of the resulting large drops will not be the same. 
     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 
     
         
           20  printing system 
           22  image source 
           24  image processing unit 
           26  control circuits 
           27  synchronization device 
           28  drop-forming transducer 
           30  printhead 
           32  print medium 
           34  print medium transport system 
           35  speed measurement device 
           36  media transport controller 
           38  micro-controller 
           40  ink reservoir 
           44  ink recycling unit 
           46  ink pressure regulator 
           47  ink channel 
           48  jetting module 
           49  nozzle plate 
           50  nozzle 
           51  heater 
           52  liquid stream 
           54  drop 
           55  drop-formation waveform source 
           57  trajectory 
           59  breakoff location 
           60  drop-formation waveform sequence 
           60 ′ drop-formation waveform sequence 
           60 ″ drop-formation waveform sequence 
           61  charging device 
           62  charging electrode 
           62 ′ charging electrode 
           63  charging-electrode waveform source 
           64  charging-electrode waveform 
           65  large drop 
           65   a  drop 
           65   b  drop 
           66  printing drop 
           68  non-printing drop 
           69  drop selection system 
           70  deflection mechanism 
           71  deflection electrode 
           72  ink catcher 
           74  catcher face 
           76  ink film 
           78  liquid channel 
           79  lower plate 
           80  charging-electrode waveform period 
           82  first voltage state 
           84  second voltage state 
           86  non-print trajectory 
           88  print dot 
           92  large-drop drop-formation waveform 
           92 - 1  large-drop drop-formation waveform 
           92 - 1 ′ large-drop drop-formation waveform 
           92 - 2  large-drop drop-formation waveform 
           92 - 2 ′ large-drop drop-formation waveform 
           92 - 3  large-drop drop-formation waveform 
           92 - 3 ′ large-drop drop-formation waveform 
           94  small-drop drop-formation waveform 
           94 - 1  small-drop drop-formation waveform 
           94 - 2  small-drop drop-formation waveform 
           94 - 3  small-drop drop-formation waveform 
           94 - 4  small-drop drop-formation waveform 
           96  period 
           97  printing-drop drop-formation waveform 
           97 - 1  printing-drop drop-formation waveform 
           97 - 1 ′ printing-drop drop-formation waveform 
           97 - 2  printing-drop drop-formation waveform 
           97 - 2 ′ printing-drop drop-formation waveform 
           98  pulse 
           98 ′ pulse 
           99  arrows 
           100  period 
           102  pulse 
           102 ′ pulse 
           104  large drop 
           104 - 1  large drop 
           104 - 1 ′ large drop 
           104 - 2  large drop 
           104 - 2 ′ large drop 
           104 - 3  large drop 
           104 - 3 ′ large drop 
           104 - 3 ″ large drop 
           106 - 1  small drop 
           106 - 1 ′ small drop 
           106 - 2  small drop 
           106 - 2 ′ small drop 
           106 - 3  small drop 
           106 - 3 ′ small drop 
           106 - 4  small drop 
           106 - 4 ′ small drop 
           108  time shift 
           108 ′ time shift 
           109  phase shift 
           110  periodic pattern 
           120  stroke 
           122  space 
           124  diffuse region 
           125  spatial period 
           130  first group trigger pulse 
           132  second group trigger pulse 
           134  timing delay device 
           136  third group trigger pulse 
           140  amplitude 
           140 ′ amplitude 
           144  outer diameter 
           144 ′ outer diameter 
           150  pulse width 
           150 ′ pulse width 
           150 ″ pulse width 
           152  pulse width 
           152 ′ pulse width 
           152 ″ pulse width 
           154  primary pulse 
           156  secondary pulse 
           158  additional pulse 
           160  additional pulse 
           162  boundary set 
           164  boundary set 
           166  boundary set