This application claims the benefit of U.S. Provisional Application No. 61/076,789, filed Jun. 30, 2008, and incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     This description relates to ink jetting. 
     BACKGROUND 
     Ink jetting can be done using an ink jetting printhead that includes jetting assemblies. Ink is introduced into the ink jetting printhead and when activated, the jetting assemblies jet ink and form images on a substrate. 
     SUMMARY 
     In one aspect, for use in ink jetting, a method includes reducing an anticipated variation in a characteristic of ink drops being jetted from an ink jet assembly, the reducing comprising causing a voltage that is applied on a jetting assembly to respond to the anticipated variation. 
     In another aspect, for use in ink jet printing, a method comprising determining a quantitative relationship between a jetting frequency of a jetting assembly and a characteristic of ink drops jetted from the jetting assembly; and providing the determined quantitative relationship for use in varying the characteristic of the ink drop. 
     In another aspect, an ink jet printing system includes a jetting assembly and a unit for determining an anticipated variation in a characteristic of ink drops jetted from the jetting assembly and applying a voltage to the jetting assembly based on the anticipated variation. 
     Implementations may include one or more of the following features. The characteristic of ink drops comprises the mass of the ink drops. The characteristic of ink drops comprises the speed of the ink drops. The characteristic of ink drops is anticipated based on a frequency of jetting of the ink drops. The frequency is determined based on transport speed of a substrate on which the ink drops are jetted. The characteristic of the ink drops jetted at the frequency is determined using a pre-determined quantitative relationship between the frequency and the characteristic. The anticipated variation of the characteristic is determined by comparing the characteristic to a standard. The voltage applied on the jetting assembly is in the form of pulses. Causing the voltage to respond to the variation comprises varying an amplitude of the pulses. Causing the voltage to respond to the variation comprises varying a width of the pulses. The pulses have a form that comprises at least square, triangle, and trapezoidal. The voltage is generated based on the anticipated variation. The generated voltage is amplified and applied to the jetting assembly. The voltage applied on the jetting assembly ranges between about 70 V to about 150 V. The ink drops have a size of about 1 pico-liter to about 80 pico-liter. The ink drops have a speed of about 1 m/s to about 12 m/s. The frequency ranges from about 1 KHz to about 25 KHz. 
     Implementations may also include one or more of the following features. The quantitative relationship is non-linear. The characteristic of the ink drops is varied by varying a voltage applied to the jetting assembly. 
     Implementations may also include one or more of the following features. The ink jet printing system also includes an encoder to determine a transport speed of a substrate on which the ink drops are jetted and a microprocessor to calculate a frequency of the jetting assembly based on the transport speed. The unit comprises a controller for receiving the frequency. The controller is connected to a microprocessor for determining the anticipated variation in the characteristic and the voltage to reduce the anticipated variation. The microprocessor determines a pulse magnitude of the voltage. The microprocessor determines a pulse width of the voltage. The microprocessor includes a medium that stores a pre-determined relationship between the frequency and the characteristic of the ink drops. The unit comprises a pulse generator for generating the voltage. The jetting assembly comprises 100 to 2000 jets. The ink jet printing system also includes an amplifier to amply the voltage applied on the jetting assembly. The ink jet printing system also includes additional jetting assemblies, each having a pre-determined relationship between a jetting frequency of the corresponding jetting assembly and characteristics of ink drops jetted from the jetting assembly. 
     All mentioned publications, patent applications, patents, and other references are incorporated by reference in their entirety. 
     Other features and advantages of the invention will be apparent from the following detailed description, and from the claims. 
    
    
     
       DESCRIPTION 
         FIG. 1A  is an exploded perspective view of an ink jet printhead. 
         FIG. 1B  is an exploded perspective view of a jetting assembly. 
         FIG. 1C  is an exploded perspective view of a portion of a jetting assembly. 
         FIG. 2  is a block diagram of an ink jet printer. 
         FIGS. 3A and 3B  are graphs of ink drop mass versus jetting frequency and ink drop velocity versus jetting frequency. 
         FIG. 3C  is a look-up table. 
     
    
    
     Referring to  FIG. 1A , ink jetting can be done using an ink jetting printhead  2  that includes at least one jetting assembly  4  assembled into a collar element  10 . The collar element  10  is attached to a manifold plate  12  which is attached to a plate  14  having orifices  16 . When in use, the printhead  2  and a substrate  18  move relative to each other along a process direction y perpendicular to a length  6  of the jetting assembly (see also  FIG. 1B ) and during the relative motion, ink is loaded into the jetting assembly  4  through the collar element  10  and jetted through orifices  16  to form images  8  on a substrate  18 . 
     Referring to  FIG. 1B , the ink jetting assembly  4  has a body  20  that includes one or more ink passages  24  and an ink fill passage  26 . A cavity plate and a stiffener plate (not shown) are attached on the opposite surfaces of the body  20  to form an array of wells  22  (not all shown) on each surface. Each well  22  can be elongated and the body  20  can include ceramic, sintered carbon, or silicon. Each ink passage  24  receives ink from an ink reservoir (not shown) and delivers ink to the ink fill passage  26 . When the opposite surfaces are covered by polymer films  32  and  32 ′, elongated pumping chambers are formed by the wells  22 , each including an ink inlet  28  to receive ink from the ink fill passage  26  and an ink outlet end  30  to direct ink back into the body  20  through an ink jetting passage (not shown) and be jetted at one of a row of openings (not shown) at the bottom of the body  20 . In some embodiments, the orifice plate  14  ( FIG. 1A ) is attached directly to the bottom of the body  20 . Each orifice  16  on the orifice plate  14  corresponds to one opening and ink is jetted through the orifices  16  onto the substrate  18  ( FIG. 1A ). In some embodiments, when two or more jetting assemblies  4  are assembled in the printhead  2  as shown in  FIG. 1A , the manifold plate  12  is arranged between bottoms of the bodies  20  and the orifice plate  12  and manifolds multiple rows of openings, each at the bottom of one body  20 , into a single row of openings from which ink passes. 
     Generally, each pumping chamber, together with its corresponding ink jetting passage, the opening and the orifice can be referred to as a jet of the jetting assembly. Information about the jetting assembly  4  is also provided in U.S. Ser. No. 12/125,648, filed May 22, 2008, which is incorporated here by reference. 
     The jetting assembly  4  also includes electronic components  29  to trigger the pumping chambers formed from the wells  22  to jet ink. For example, the electronic components include two sets of electrodes  33  and  33 ′ on the polymer films  32  and  32 ′, which are connected by leads (not shown) to respective flexible circuits  31 ,  31 ′ and integrated circuits  34  and  34 ′, to which the information about the image to be printed is loaded. Piezoelectric elements  36  and  36 ′ are attached to the outer side of each of the polymer films  32  and  32 ′, respectively and each includes a set of electrodes  35  and  35 ′ that contacts the polymer films  32  and  32 ′. 
     The integrated circuits  34  and  34 ′ each includes a set of switches, each switch corresponding to one of the pumping chambers in the body  20 . Based on the loaded image data, in one jetting event, the switches corresponding to the pumping chambers that are required to jet ink are set to be on and the switches corresponding to the rest of the pumping chambers are set to be off. The integrated circuits  34  and  34 ′ then forward voltage pulses to the electrodes  35  that address those pumping chambers corresponding to switches in the “on” state to activate the portion of piezoelectric elements  34  and  34 ′ over these chambers. 
     Referring to  FIG. 1C , the electrodes  35  on the piezoelectric element  36  register with electrical contacts  33 , allowing the electrodes to be individually addressed by the integrated circuit  34  as explained above. Each of the electrodes  35  is placed and sized to correspond to a pumping chamber in the body  20 . In particular, each electrode  35  has an elongated region  56 , having a length and width slightly narrower than the dimensions of each pumping chamber such that gap  58  exists between the perimeter of the electrodes  35  and the sides and end of each pumping chamber. Each electrode region  56  is centered on a pumping chamber and is the drive electrode that covers a jetting region of the piezoelectric element  36 . A second electrode  52  on the piezoelectric element  34  generally corresponds to the area of the body  20  outside the pumping chambers. The electrode  52  is the common (ground) electrode and can be comb-shaped (as shown) or can be individually addressable electrode strips. The electrical contacts  33  and the electrodes  35  overlap sufficiently for good electrical contact and easy alignment of the electrical contacts  33  and the piezoelectric element  36 . Information about the ink jet module  2  is also provided in U.S. Pat. No. 6,755,511, which is incorporated here by reference. 
     To print each line  38  of the two-dimensional image  8  on the substrate  18  ( FIG. 1A ), appropriate voltage pulses sent from the integrated circuits  34  and  34 ′ cause the piezoelectric elements  36  and  36 ′ to change their shapes and apply pressures to selected pumping chambers from which ink drops are to be jetted. Successive lines are printed as the substrate moves along the y direction. Thus, for a given number of lines per inch along the process direction y to be printed on the substrate  18 , the frequency at which voltage pulses must be provided for a given pumping chamber is related to the transport speed of the substrate  18  along the process direction y. The resolution of a printed image along the y direction and the direction perpendicular to the y direction can be expressed by the number of dots per inch (dpi). In some embodiments, the jetting assembly  4  or the ink jet module  2  can print an image having a resolution of greater than 100 dpi, greater than 200 dpi, greater than 400 dpi, greater than 500 dpi, greater than 800 dpi, greater than 1000 dpi, or even larger along each direction. 
     The mass and velocity of the jetted ink drops vary with the frequency of jetting and therefore with the transport speed of the substrate. 
     In  FIG. 2 , the voltage pulses are provided to the piezoelectric elements of an ink jet printhead  40  having the same features as the ink jet printhead  4  of  FIG. 1A  from a pulse unit  46  to jet ink drops  42  out of orifices  44  onto a substrate  48 . The pulse unit  46  also measures the current transport speed of the substrate  48  along the process direction y from signals received from an encoder  50  that is coupled to sense motion of the transport  52  on which the substrate  48  is carried along. 
     The encoder  50  can be a shaft angle encoder in communication with the transport  52  and can provide a stream of signals from which a transport speed of the substrate  48  can be determined. The transport speed of the substrate  48  is associated with a jetting frequency at which voltage pulses are delivered to the ink jet printhead  40  and ink is jetted from the pumping chambers. In some embodiments, the jetting frequency of the ink jet printhead  40  can be computationally determined using a microprocessor based on the transport speed. For example, the encoder  50  is located on a transport belt (not shown) that transports the substrate  18  and produces a stream of pulses related to the speed of the belt. For example, the higher the transport speed the higher number of pulses/sec and therefore the higher the frequency of change. A microprocessor (not shown) can be used to measure the time period between the rising edges of the stream of pulses and then determine the operational jetting frequency of the ink jet printhead  40  using the following formula Frequency (Hertz)=1/Period (sec). 
     Alternatively, a frequency to voltage converter can be used to generate an analog voltage, for example, between 1 to 10 volts, based on the transport speed. A digital representation of the transport speed and the jetting frequency are converted from the voltage by an analog to digital converter in communication with the frequency to voltage converter. For example, the frequency to voltage converter uses the repetitive pulses from the encoder  50  to charge a circuit to produce an analog voltage representative of the speed of the transport of the substrate  18 . 
     The jetting assemblies performs ink jetting differently in response to different jetting frequencies, which vary accordingly with the variation in the transport speed of the substrate  18 , and/or the variation in properties of the jetting assemblies, the properties of the ink used, for example, viscosity, and/or the operational temperature of the ink jetting. For example, the ink drops  42  out of the orifices  44  jetted at different jetting frequencies can have different characteristics, for example, mass or speed. To achieve high quality printing, it is desirable to have the jetting assemblies&#39; performance uniform at different jetting frequencies. 
     To produce ink drops with uniform characteristics, it is therefore desirable to understand the relationship between the transport speeds of the substrate  48  or jetting frequency of the ink jet printhead  40  and the characteristic of the ink drops  42  and reduce the variations in the characteristic of the ink drops  42 . The jetting frequency of the ink jet printhead  40  is the frequency at which the printhead  40  places an ink drop at every pixel. The individual jets in the printhead  40  can be operating at an operating frequency different from the jetting frequency of the printhead  40 . 
     Referring to  FIGS. 3A and 3B , the mass and velocity of ink drops vary irregularly from one jetting frequency to another frequency. For example, when the jetting frequency of the jetting assembly  12  is 14.5 KHz, the ink drops have a lower drop mass and a lower velocity, which could result in light printing or misaligned printing. Also, when the jetting frequency is increased to 25.5 KHz, the ink drop has a mass and a velocity about 100% higher than those of the ink drops jetted at the jetting frequency 14.5 KHz. Depending on the printing requirement and other related conditions, the ink drops can have a size of about 1 pico-liter to about 100 pico-liters, for example, 1 pico-liter to 80 pico-liters and a speed of about 1 m/s to about 20 m/s, for example, 1 m/s to 12 m/s. 
     The quantitative relationship between the jetting frequency of the printhead  40  and the mass of the ink drops and the quantitative relationship between the jetting frequency and the velocity at which the ink drops are jetted are both nonlinear and have a similar trend. To make the ink drop mass and velocity more uniform at all frequencies, the voltage pulses to be applied on the jetting assemblies can be adjusted based on these known quantitative relationships. For example, at a jetting frequency 14.5 KHz, a higher voltage pulse can be delivered to the ink jet printhead  40  to cause the piezoelectric element to generate higher pressures over the pumping chambers to compensate the anticipated low drop mass and drop velocity implied by the known relationships. By contrast, at a jetting frequency of 25.5 KHz, a lower voltage can be delivered to cause the piezoelectric element to provide proper pressures on the pumping chambers to reduce the anticipated high drop mass and drop velocity. 
     In some embodiments, ink jet printheads of the same type demonstrate similar trends in these quantitative relations, for example, when using the same type of ink. This allows use of these quantitative relationships in producing uniform ink drops with uniform velocities for high quality images on ink jet printers that include the same type of ink jet printheads in a systematic way. In practice, the quantitative relationships like the ones shown in  FIGS. 3A and 3B  are predetermined, for example established empirically, for one type of ink jet printhead and ink, and a standard for the desired mass and velocity of ink drops is chosen. 
     Based on the chosen standard and the determined quantitative relationships, at each jetting frequency, an anticipated variation of the ink drop mass and velocity with respect to the standard is calculated. To reduce the anticipated variation and make the ink drop characteristics conform uniformly to the standard, a compensating voltage additional to the original voltage pulse associated with that jetting frequency is calculated and added to the original voltage pulse to provide a compensated voltage pulse. In some embodiments, the compensating voltage has a negative magnitude and is deducted from the original voltage pulse to decrease the ink drop mass and velocity. In some embodiments, the compensating voltage has a positive magnitude and is added to the original voltage to increase the ink drop mass and velocity. 
     In some implementations, for each type of ink that is used, tests on the characteristics of the ink drops jetted from the printheads are conducted using various compensated voltage pulse parameters, e.g., amplitude, rise/fall time, and width, where a camera is used to visually see how the ink drops are jetted and formed. The parameters describing the compensated voltage pulses are empirically modified or chosen to provide the desired drop formation with consistent print quality across the jetting frequency range. 
     The jetting frequency obtained from the transport speed of the substrate  48  as described above is associated with all pumping chambers of the ink jet printhead  40  and can be different, for example, larger, than the operating frequency of an individual jet because at each moment, only a portion of the jets are jetting ink based on the requirement of the image to be printed. Therefore, the variations in the characteristics of ink drops from different individual jets at one jetting frequency of the ink jetting printhead  40  are different. For example, at the determined printhead jetting frequency 14.5 KHz, some of the jets are not jetting ink, some are jetting at a frequency of 7.25 KHz if they are printing every other pixel, or some others are jetting at a lower frequency if they are printing fewer than every other pixel. According to the quantitative relationships of  FIGS. 3A and 3B , the mass and velocity of the ink drops jetted from these different jets at these different operating frequencies are different and needs different adjustments to the voltage pulses applied to the corresponding pumping chambers to make the ink drops uniform. 
     In some embodiments, the compensating voltage is applied to all jets that are printing at the moment when the printhead  40  has the corresponding jetting frequency. Even though only some of the jets are operating at the jetting frequency of the printhead  40 , uniform application of the compensating voltage improves the image quality. 
     In some embodiments, to reduce the overall variations in ink drop characteristics that are jetted from different individual jets, the compensating voltage corresponding to the jetting frequency of the ink jet printhead  40  is further adjusted, for example, the magnitude of the voltage to be 90%, 80%, 70%, 60%, or 50% of the calculated or determined value. 
     Referring to  FIG. 3C , a look-up table  80  recording the calculated or adjusted compensated voltage pulse associated with each jetting frequency of the printhead  40  is generated. In some embodiments, the look-up table  80  records information of the voltage pulses that includes, for example, magnitude, rise time, fall time, and/or width. In the example shown in the figure, the standard pulse voltage is chosen to have a magnitude of about 80 volts, a width of about 10 μseconds, a rise time of about 2 μseconds, and a fall time of about 2 μseconds. Using the determined quantitative relationship between the ink drop characteristics and the jetting frequencies of  FIGS. 3A and 3B  and the standard, at jetting frequency 9 KHz, where a low ink drop mass and velocity are anticipated, a 10 volt compensating voltage is estimated and the compensated voltage has a magnitude of about 90 volts and an prolonged pulse width of about 11 μseconds. When the jetting frequency is 24 KHz, where a high ink drop mass and velocity are anticipated, a −15 volt compensating voltage is estimated and the compensated voltage has a magnitude of about 65 volts and a shortened pulse width of about 8 μseconds. 
     In some embodiments, multiple printheads may be used to print an image and each printhead may have an associated look-up table. 
     Referring back to  FIG. 2 , the look up table is stored in the memory of a microprocessor  66  in a pulse control unit  62  of the pulse unit  46 . In some embodiments, the microprocessor  66  has a communication interface  69 . In some embodiments, the pulse control unit  62  uses programmed parameters of the desired voltage pulse waveform, for example, amplitude, pulse width, and rise and fall time, to create the desired shape and size of the pulse voltage waveform. In use, the pulse controller  62  receives signals representative of the transport speed of the substrate  48  generated by the encoder  50  and encodes the signals to a jetting frequency associated with the transport speed so that the pulse voltages are generated at the right time at appropriate dots/inch resolution. 
     The information of the jetting frequency is used by the microprocessor  66 , to find the information of the voltage pulse corresponding to that jetting frequency in the stored look-up table. 
     A voltage pulse to be applied on the piezoelectric element of the printhead  40  is generated in the pulse generation unit  64  of the pulse unit  46 , based on the information sent from the pulse control unit  62 . The pulse generation unit  64  includes a pulse generator  70  and a pulse shaper  72 . The pulse generator  70  includes a digital to analog (D/A) converter that generates a voltage pulse based on the information received from the pulse control unit  62 . In some embodiments, the D/A converter generates a voltage pulse that has a magnitude, for example, of about 5 volts, 10 volts, or 15 volts, and/or up to, for example, about 30 volts, a rise time, for example, of about 1 μseconds, or 2 μseconds, and/or up to, for example, about 4 μseconds, or about 5 μseconds, a fall time, for example, of 1 μseconds, or 2 μseconds, and/or up to, for example, about 4 seconds, or about 5 μseconds, and a width, for example, of about 2 μseconds, 4 seconds, 5 μseconds, and/or up to, for example, about 15 μseconds, 20 μseconds, or about 25 μseconds. 
     Generally, the voltage pulses generated from the D/A converter have low magnitudes and need to be amplified proportionally before applying to the ink jet printhead  40 , which will be discussed later. The pulses generated from the pulse generator  70  are filtered by a pulse shaper filter at the pulse shaper  72  to provide a desired waveform. 
     Examples of pulse shaper filter include, for example, trivial boxcar filter, sinc shaped filter, raised-cosine filter, and Gaussian filter. Examples of waveforms of the voltage pulses include, for example, sine waves, sawtooth waves, square waves, triangle waves, trapezoidal waves and their combinations. 
     The voltage pulse from the pulse shaper  72  is delivered to an amplifier  76 . A high voltage supply  78  is connected to the amplifier  76  to provide a high voltage. The amplified voltage pulse can have a magnitude, for example, of at least about 30 V, 60 V, 65 V, or 70 V, and/or up to, for example, about 160 V, 155 V, or 150 V. The amplified voltage pulse is applied to the ink jet printhead  40  to cause ink to be jetted with desired drop mass and velocity onto the substrate  48 . 
     The system response time of pulse unit  46  to changes in transport speed is in the order of milliseconds. This allows the ink pulse unit  46  to respond to the anticipated variation in the ink drop characteristics associated with a jetting frequency of the ink jet printer  40  and effectively reduce the anticipated variation to produce high quality images. 
     Other embodiments are in the following claims. 
     For example, printheads other than that described in  FIG. 1A  can be used, for example, printheads that are made of silicon and described in U.S. Pat. No. 5,265,315 and print heads described in U.S. Ser. No. 12/125,648, filed May 22, 2008, both of which are incorporated here by reference. For example, the jetting assembly  4  can include the body  20  having wells machined on surfaces of the body  20 . Pumping chambers can be formed without the use of the cavity plate and by sealing the machined wells in the body  20  using polymer films. The pumping chambers can be activated by piezoelectric elements attached to an outer surface of the polymer films that is opposite to an inner surface that contacts the body  20 . In some implementations, the piezoelectric elements can directly seal the wells to form pumping chambers without the polymer films between the wells and the piezoelectric elements. Activation of the pumping chambers can be done using elements, e.g., electrodes and integrate circuits, similar to those discussed with regard to  FIGS. 1A-1C . Features of the ink droplets and images, for example, sizes of the ink droplets and resolution of the images, printed by such jetting assemblies are similar to those printed by the jetting assemblies of  FIGS. 1A-1C .
Among other things, for use in ink jetting, a method includes reducing an anticipated variation in a characteristic of ink drops being jetted from an ink jet assembly, the reducing comprising causing a voltage that is applied on a jetting assembly to respond to the anticipated variation.