Patent Publication Number: US-6669324-B1

Title: Method and apparatus for optimizing a relationship between fire energy and drop velocity in an imaging device

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method and apparatus for optimizing a relationship between fire energy and drop velocity in an imaging device, and, more particularly, in one embodiment, to a method and apparatus for adjusting pre-fire and fire pulses used to jet ink from a printhead in an imaging device. 
     2. Description of the Related Art 
     An ink jet printer typically includes a printhead, which is carried by a carrier. The printhead is fluidly coupled to an ink supply. Such a printhead includes a plurality of nozzles having corresponding ink ejection actuators, such as heater elements. 
     Ink is jetted from the nozzles onto a print medium at selected ink dot locations within an image area. The carrier moves the printhead across the print medium in a scan direction while the ink dots are jetted onto selected pixel locations within a given raster line. Between passes of the printhead, the print medium is advanced a predetermined distance and the printhead is again moved across the print medium. 
     Ink jet printers may utilize a single printhead, or multiple printheads. For example, some ink jet printing systems utilize a monochrome ink cartridge including a monochrome, e.g. black, printhead, and a color ink cartridge including a color printhead having cyan, magenta and yellow nozzle groups. In another type of ink jet printing system, each printhead is connected to a respective remote ink supply. 
     The manufacture of printheads involves certain manufacturing tolerances resulting in manufacturing variations (e.g., variations in sheet resistance of the material used in heater elements; mask alignment variations, which lead to variations in the width and length of heater elements; the rise and fall times of transistors that drive the heater elements; the thickness of the layer between the heater element and the ink, which influences heat transfer to the ink; the ink chemistry; and the voltage level of the power source), which in turn result in printheads that require differing amounts of energy to attain a drop velocity deemed suitable (e.g., high enough) for attaining a desired print quality. Thus, typically, from printhead to printhead, the amount of energy required to attain a suitable drop velocity varies. 
     Because of these manufacturing variations, an energy level for driving such printheads will be selected so that most printheads will attain a certain minimum drop velocity (e.g., 400-600 inches per second). This energy level is a statistical average value meant to encompass the largest range of printhead variations possible. Because the same predetermined amount of energy is used for each printhead, the energy is not optimized for a particular printhead. 
     One problem with this manner of ink delivery is that variations in the printheads lead to inefficiencies in printhead operation. The result is drop velocity variations and difficulty in maintaining nominal head temperatures. Another problem is that driving ink jet heaters at an energy level required to jet ink at an acceptable drop velocity means overdriving some printheads. By overdriving printheads, the overdriven nozzles can fail prematurely due to electromigration of the heater element. 
     What is needed in the art is a method and apparatus that reduces variations in drop velocities among a type of printhead, and/or provides for fire energy adjustment for the printhead. 
     SUMMARY OF THE INVENTION 
     The present invention provides, in one embodiment, an apparatus and method for measuring ink drop velocities and adjusting the energy used to eject ink. 
     The invention, in one form thereof, is directed to a method of adjusting fire energy supplied to an actuator of a printhead of an ink jet printer. The method includes printing a test pattern on a print media by selectively supplying energy distribution signals to a plurality of actuators of the printhead, the energy distribution signals having distinct energy profiles; scanning the test pattern to obtain offset values, each of the offset values representative of a distance between at least two corresponding portions of the test patterns; calculating drop velocities from the offset values; and selecting from the energy distribution signals an energy distribution signal that corresponds with an optimal one of the drop velocities. 
     The invention, in another form thereof, is directed to an ink jet printer. The ink jet printer includes a controller, a sensor and a printhead having actuators that are capable of jetting ink with a drop velocity when an energy distribution signal having a fire energy is supplied. The controller is capable of communicating with the printhead and the sensor. The controller employs a method including printing a test pattern on a print media by selectively supplying energy distribution signals to a plurality of the actuators of the printhead, the energy distribution signals having distinct energy profiles; scanning the test pattern with the sensor to obtain offset values, each of the offset values representative of a distance between at least two corresponding portions of the test pattern; calculating drop velocities from the offset values; and selecting from the energy distribution signals an energy distribution signal that corresponds with an optimal one of the drop velocities. 
     The invention, in yet another form thereof, is directed to an imaging device including a carrier, a printhead carrier by the carrier, a sensor carried by the carrier, and a controller communicatively coupled with the printhead and the sensor. The controller is configured to print an image on a sheet of print media. The image includes a test pattern. The controller employs an energy distribution signal adjustment method to determine an energy profile for the printhead. 
     The aforementioned energy distribution signal adjustment method includes printing the test pattern using distinct energy profiles; scanning the test pattern with the sensor to obtain offset values, wherein a respective one of the offset values is representative of a distance between corresponding portions of the test pattern; and calculating drop velocities corresponding to the distinct energy profiles based on the offset values; Based on the drop velocities, an optimal energy profile is determined. The optimal energy profile is determined by using the drop velocities to determine when an incremental change in energy corresponds with a disproportionate change in drop velocity. 
     The invention, in yet another form thereof, is directed to a method of optimizing an energy distribution signal for use by a printhead including a plurality of heater elements. The method includes printing a test pattern using energy profiles; scanning the test pattern to obtain offset values, wherein a respective one of the offset values is representative of a distance between corresponding portions of the test pattern; and calculating drop velocities corresponding to the energy profiles, wherein the optimal energy profile is determined by using the drop velocities to determine when an incremental change in energy corresponds with a disproportionate change in drop velocity. An energy distribution signal corresponding to the optimal energy profile is selected. 
     The invention, in still a further form thereof, is directed to a method of optimizing a relationship between fire energy and drop velocity. In such a method, a test pattern is printed by selectively supplying energy distribution signals to a plurality of actuators of a printhead. The energy distribution signals have distinct energy profiles. The test pattern is scanned to obtain drop velocity information corresponding to the energy distribution signals. Based on the drop velocity information, an energy profile is determined that optimizes the relationship between fire energy and drop velocity. 
     An advantage of certain embodiments of the present invention is that the fire energy used in an ink jet printer printhead is optimized thereby increasing the life of the printhead. 
     Another advantage of certain embodiments of the present invention is that the printhead heats less; thus, throughput levels of the printer can increase since the time required to cool a printhead is reduced or eliminated. 
     Still yet another advantage of certain embodiments of the present invention results from allowing thin film printheads to run open loop without any temperature sensor resistor being required. 
     A further advantage of certain embodiments of the present invention is that variations that occur in the manufacture of the printhead can be compensated. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above-mentioned and other features and advantages of this invention, and the manner of attaining them, will become more apparent and the invention will be better understood by reference to the following description of an embodiment of the invention taken in conjunction with the accompanying drawings, wherein: 
     FIG. 1 is diagrammatic representation of an imaging system employing an embodiment of the method of the present invention; 
     FIG. 2 is a diagrammatic representation of circuitry for supplying energy pulses to the heater elements of the printheads of FIG.  1 . 
     FIG. 3 depicts pulse widths associated with fire energy of the ink jet printer of FIG. 1; 
     FIGS. 4A,  4 B and  4 C represent a flowchart of a method employed by the ink jet printer of the imaging system of FIG. 1; and 
     FIG. 5 depicts a test pattern printed on a print media by the ink jet printer of the imaging system of FIG.  1 . 
     Corresponding reference characters indicate corresponding parts throughout the several views. The exemplification set out herein illustrates one embodiment of the invention, in one form, and such exemplification is not to be construed as limiting the scope of the invention in any manner. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to the drawings and more particularly to FIG. 1, there is shown an imaging system  10  embodying the present invention. Imaging system  10  includes a computer  12  and an imaging device in the form of an ink jet printer  14 . Computer  12  is communicatively coupled to ink jet printer  14  by way of a communications link  16 . Communications link  16  may be, for example, an electrical, an optical or a network connection. 
     Computer  12  is typical of that known in the art, and includes a display, an input device such as a keyboard, a processor and associated memory. Resident in the memory of computer  12  is printer driver software. The printer driver software places print data and print commands in a format that can be recognized by ink jet printer  14 . 
     Ink jet printer  14  includes a carrier system  18 , a feed roll unit  20 , a frame  22 , a media source  24  holding a sheet of print media  26 , a sensor  28  and a controller  30 . Carrier system  18  includes a printhead carrier  32 , a black printhead  34 , a color printhead  36 , guide rods  38 , a carrier transport belt  42 , a carrier motor  44 , a driven pulley  46  and a carrier motor shaft  48 . Carrier system  18  and printheads  34  and  36  may be configured for unidirectional printing or bi-directional printing. 
     Printhead carrier  32  is guided by the pair of guide rods  38 . Guide rods  38 , also known as carrier support  38 , are connected to frame  22 . Axes  38   a , associated with guide rods  38 , define a bi-directional printing/scanning path of printhead carrier  32 . Printhead carrier  32  is slidingly connected to carrier support  38 . Printhead carrier  32  is also connected to a carrier transport belt  42  that is driven by carrier motor  44  by way of driven pulley  46 . 
     Controller  30  includes, for example, a processor and associated memory for executing process steps to control the operation of ink jet printer  14 . At a directive of controller  30 , printhead carrier  32  is transported in a reciprocating manner, along guide rods  38 . Carrier motor  44  can be, for example, a direct current drive or a stepper motor. 
     The reciprocation of printhead carrier  32  transports ink jet printheads  34  and  36  across the sheet of print media  26  along a bi-directional path  38   a . This reciprocation occurs in a direction that is parallel with bi-directional printing/scanning path  38   a  and is also commonly referred to as the main scan, or horizontal, direction. At the direction of controller  30 , the sheet of print media  26  is fed by feed roll unit  20 , including feed roller  40 , in an indexed manner under ink jet printheads  34  and  36 . 
     Additionally referring to FIG. 2, printheads  34  and  36  each have a plurality of individually selectable nozzles  52 , represented by dots, for effecting the controllable ejection of ink toward the sheet of print media  26 . Associated with each nozzle is an actuator, such as heater element  54 , represented by a square. Controller  30  is connected to a printhead driver  56  via communication link  60 . Printhead driver  56  is connected to heater elements  54  of printheads  34 ,  36  via a printhead cable  58 . Thus, controller  30  is controllably coupled to printheads  34  and  36  to thereby control the fire energy supplied to each heater element  54 . 
     Also attached to printhead carrier  32  is sensor  28 . Sensor  28  may be for example an optical sensor that includes a light emitter and a light detector. Light emitted by sensor  28  is reflected off of the sheet of print media  26  and is received by the light detector of sensor  28 . Thus, sensor  28  can provide information to controller  30  relating to the location and quality of the printing effected by printheads  34  and  36 . In an exemplary embodiment, sensor  28  can be used to align printheads  34  and  36 . 
     Feed roll unit  20  advances the sheet of print media  26  through ink jet printer  14  via rotation of feed roller  40 . Feed roll unit  20  is controllably linked to controller  30 . Media source  24  is connected to frame  22  and is configured and arranged to supply individual sheets of print media  26  to feed roll unit  20 , which in turn transports the sheets of print media  26  during a printing operation. 
     Controller  30  is linked to carrier motor  44  by way of a communications link  50 . Controller  30  controls the speed direction and acceleration of carrier transport belt  42 , which thereby controls the direction speed and acceleration of printhead carrier  32 . Controller  30  is communicatively linked with black printhead  34  and color printhead  36  by way of communications link  60 . Controller  30  selectively actuates one or more of heater elements  54  of printheads  34  and/or  36  by way of communications link  60  to effect the printing of an image on the sheet of print media  26 . 
     Controller  30  is connected with feed roll unit  20  by way of communications link  62  thereby passing commands for controlling the feeding of the sheet of print media  26  through ink jet printer  14 . Controller  30  is also communicatively coupled to sensor  28  by way of communications link  64 . Information from sensor  28  is passed by way of communications link  64  to controller  30 . 
     The fluidic properties of the ink in printheads  34  and  36  play a role in print quality and throughput. The maximum frequency at which printheads  34  and  36  can eject an ink drop from each of nozzles  52  is primarily determined by how quickly an ink chamber (not shown) can refill. The refill time is related to the force of nucleation. 
     By over-driving some heater elements  54  and ejecting too much ink, the ink chamber cannot refill quickly enough to print at a given frequency. This means that either the printhead will not eject a drop of ink or that it will eject a drop of the incorrect mass, both of which decrease print quality. By minimizing the nucleation force, thereby minimizing refill time, print quality improves. Minimizing the refill time also increases the frequency at which printheads  34  or  36  can operate, allowing printhead carrier  32  to travel at an increased velocity, thereby, advantageously, raising throughput. 
     “Fire energy” refers to the total amount of energy (in joules, for example) supplied by an energy distribution signal to an actuator, such as heater element  54 , to jet a drop of ink. Fire energy can be adjusted, for example, by adjusting a duration of a pre-fire and/or a fire pulse of an energy distribution signal supplied to heater element  54 . A pulse of brief duration supplies less total energy to a heater element than a lengthier pulse duration. A printhead according to one embodiment of the present invention strives to optimize a relationship between drop velocity and fire energy by using a pulse duration(s) that attains a suitable drop velocity with a minimal amount of energy. 
     The mechanisms behind the velocity/energy response relate to the dynamics of bubble formation and expansion. As a bubble forms in printhead  34  or  36 , the bubble wall expands outward extremely quickly. The bubble itself is filled with a thermally insulating water vapor. This vapor separates and isolates the bubble wall from the heater element  54  nearly instantaneously. 
     Because of this condition, additional energy supplied to the heater after the onset of nucleation has little or no effect on expansion of the bubble wall. It is the rate of expansion of the bubble wall that provides the pressure pulse that ejects ink from the respective nozzle of printhead  34  or  36 . The magnitude of the pressure pulse determines the ink drop velocity. Energy supplied to heater element  54  after nucleation is merely dissipated as heat and serves to degrade the performance of printhead  34  or  36 . 
     By varying the duration of a fire pulse and/or a pre-fire pulse, for example, and measuring the corresponding drop velocity attained, a point where adding additional energy provides only marginal (or no) changes in drop velocity can be determined. Once this point is determined, an optimal duration (e.g., a duration closest to this point) can be selected for use with the printhead in future printing, thereby optimizing the relationship between fire energy and drop velocity. 
     Referring to FIG. 3, there is shown an exemplary energy profile for an energy distribution signal including a pre-fire pulse  66 , a delay  68 , a fire pulse  70 , and a recharge time  72  that is supplied to heater element  54  to eject ink from a respective nozzle. The time interval of pre-fire pulse  66  has a duration t 1 . In a similar manner the durations of delay  68 , fire pulse  70  and recharge time  72  are, respectively, t 2 , t 3  and t 4 . The amplitude of pulses  66  and  70  are each typically fixed but are not necessarily equal. 
     The fire energy consists of the total energy of pre-fire pulse  66  and fire pulse  70 . Pre-fire duration t 1 , delay duration t 2 , fire pulse duration t 3 , and recharge duration t 4  can be varied and adjusted to optimize the drop velocity (e.g., maximize it), and to minimize the amount of energy expended through pulses  66  and  70 . In one embodiment, pulse durations t 1  and t 3  can be varied to minimize energy consumption. For example, pre-fire duration t 1 , delay duration t 2  and fire pulse duration t 3  can be incrementally varied using, for example, predetermined values to optimize a relationship between drop velocity and fire energy. 
     Referring to FIGS. 4A,  4 B and  4 C there is shown a block diagram representing a method according to one embodiment of the present invention used to determine an optimal energy distribution signal having an energy profile including pre-fire duration t 1 , delay duration t 2  and pulse fire duration t 3 . The method of FIGS. 4A-4C is depicted by a plurality of processing steps, hereinafter referred to as process  100 , which may be executed by controller  30 . Alternatively, process  100  can be executed by computer  12  as it interacts with ink jet printer  14 . 
     Process  100  can be utilized to optimize, for example, pre-fire duration t 1 , delay duration t 2  and pulse fire duration t 3  for printheads  34  and/or  36 , and durations t 1 , t 2  and t 3  may differ as between printhead  34  and printhead  36 . Process  100  may be initiated each time one of printhead  34  or  36  is changed. Also, process  100  may be periodically initiated to re-optimize a relationship between drop velocity and fire energy for printheads  34  and/or  36 . Process  100  will be described hereinafter with respect to printhead  36 . 
     At step  102 , ink jet printer  14  is initialized and printhead gap G relating to the printhead of interest is determined. Printhead gap G represents the distance from, for example, the sheet of print media  26  to the surface of color printhead  36 . As described later herein, gap G can be used to help determine drop velocity. 
     Printhead gap G may be fixed. Alternatively, gap G may be adjustable, and selected by an operator. In one embodiment of the present invention, a gap G can be predetermined for a particular combination of printer and printhead. 
     At step  104 , controller  30  turns off dynamic and static adjustments relative to printhead  36 , thereby allowing a test pattern to be printed on the sheet of print media  26  without any of the static or dynamic compensations, which are stored by controller  30 . Alternatively, controller  30  can account for the adjustments and compensate therefor. At step  106 , controller  30  issues a command to feed roll unit  20  causing it to feed a sheet of print media  26  into ink jet printer  14 . 
     At step  108 , controller  30  initializes a variable X to an initial value, where X might represent a type of adjustment that is being incremented (e.g., a black pre-fire pulse, a black fire pulse, a color pre-fire pulse or a color fire pulse). Typically, a pre-fire pulse will be adjusted prior to adjusting a corresponding fire pulse. Step  110 , similar to step  108 , initializes a variable Y, where Y might represent a specific increment (e.g., in energy). For example, Y might represent pulse duration increments of about 50-75 ns. Each increment of Y can relate to a particular portion of a test pattern to be printed on a sheet of print media for a particular adjustment type X. Variable X and Y are used as control variables to control looping of process  100 . 
     At step  112 , controller  30  prints at least part of a test pattern using an energy distribution signal having an energy profile corresponding to a respective combination of variables X and Y. The energy distribution signal could be predetermined or might be generated as part of an algorithm. As each of the various combinations of X and Y variables are indexed (as further described below), a different energy distribution signal with a distinct energy profile is used to print at least a portion of a test pattern. 
     According to one embodiment of the present invention, only energy distribution signals that will eject ink regardless of manufacturing variability of the printhead are used (e.g., for the sake of error checking data that will be acquired). Moreover, according to an exemplary embodiment of the invention, the printhead is ran at less that its maximum frequency (e.g., a constant frequency) when printing the test pattern. 
     With reference to FIG. 5, there is shown an exemplary test pattern comprising a set of test subpatterns  74  and  76 , each including several blocks  78 . Each of blocks  78  may, for example, be a 2 mm by 4 mm rectangle. According to one embodiment of the present invention, each of blocks  78  is printed using all of the heaters that can be actuated with the signal being optimized. 
     First test subpattern  74  can be printed by printhead  36  in one direction as carrier  32  transports printhead  36  in a horizontal direction. Second test subpattern  76  can be printed in another direction by printhead  36  as carrier  32  transports printhead  36  in a horizontal direction opposite to the direction in which first test subpattern  74  was printed. Alternatively, test subpatterns  74  and  76  may be interleaved or in some other form, such as moiré patterns. 
     In one embodiment of the present invention, a respective set of test subpatterns  74  and  76  is printed using an energy distribution signal having an energy profile corresponding to a respective combination of variables X and Y. In another embodiment, a respective set of corresponding blocks  78  in a set of test subpatterns  74  and  76  is printed using an energy distribution signal having an energy profile corresponding to a respective combination of variables X and Y. One advantage of such an embodiment could include reducing the test pattern down to only one set of test subpatterns  74  and  76 . 
     At step  114 , controller  30  directs the movement of printhead carrier  32  and reads information supplied by sensor  28 . The test subpatterns  74  and  76  printed on the sheet of print media  26  are scanned by sensor  28 , and the information gathered is sent to controller  30 . Although process  100  indicates that a set or portion of test subpatterns are scanned before a next set or portion of test subpatterns is printed, alternative embodiments of the present invention could print all or a group of such sets before scanning the same. 
     When test subpatterns  74  and  76  are printed, each in a different direction, an offset distance D between corresponding blocks  78  of test subpattern  74  and test subpattern  76  can be observed. Offset distance D is a measure of the shift between test subpattern  74  and test subpattern  76 , which are printed in opposite directions. Offset distances D can be determined by sensor  28  detecting an attribute of blocks  78  such as the edges of corresponding blocks  78 . Whereas several blocks  78  are printed, several offset distances D (also referred to herein as offset values) can be sent to controller  30  for each set of test subpatterns  74  and  76  printed. 
     At step  116 , controller  30  determines if the number of blocks  78  detected by sensor  28  is equal to the number of blocks  78  printed by ink jet printer  14 . If the number of blocks  78  detected is not equal to the number of blocks  78  printed, process  100  continues to step  130 . If the number of blocks  78  detected is equal to the number of blocks  78  printed, then process  100  continues to step  118 . The purpose of this test is to determine if the pattern blocks have all been printed, otherwise it is assumed that the print velocities were insufficient or caused such degradation of performance that the pulse durations (e.g., t 1  and t 3 ) are not appropriate for use with printhead  36 . 
     At step  118 , controller  30  calculates a value for the offset associated with the particular durations t 1 , t 2  and t 3  that correspond to a particular combination of X and Y. At step  120 , controller  30  stores the offset value for the combination of X and Y (e.g., in the controller memory). 
     At step  122 , controller  30  calculates drop velocity for the particular X, Y values of this implementation of the loop. Drop velocity can be represented as a function of gap G, the velocity CV of printhead carrier  32  and the offset (X,Y). An exemplary equation for calculating drop velocity DV follows: 
       DV ( X,Y )=( G *2 CV )/(Offset( X,Y )) 
     At step  124 , controller  30  determines if the drop velocity associated with a particular combination of X and Y is between a lower limit and an upper limit. The lower limit being, for example, 200 inches per second and the upper limit being, for example, 700 inches per second. If the drop velocity is between the lower and upper limits, then process  100  continues to step  128 , otherwise process  100  continues to step  126 . 
     At step  126 , controller  30  sets a drop velocity variable for the combination of X and Y index variables equal to the value of one. The setting of drop velocity (X,Y) equal to one is for use by controller  30 , to mark the fact that drop velocity (X,Y) was outside of the prescribed limits. Following step  126 , process  100  continues to step  128 . 
     If, at step  116 , the number of blocks  78  detected is not equal to the number of blocks  78  printed, at step  130 , the drop velocity variable for that combination of X and Y is set to a value of zero. The setting of drop velocity (X,Y) to zero is for use by controller  30  to mark the fact that at least some of the pattern blocks  78  were not printed. Following the step  130 , process  100  continues to step  128 . 
     At step  128 , controller  30  stores drop velocity (X,Y) in controller memory. Alternatively, controller  30  can store drop velocity information (e.g., drop velocity (X,Y) and/or offset (X,Y)) in a memory contained in computer  12 . Process  100  then continues to step  132 . 
     At step  132 , controller  30  determines if index variable Y is equal to the last increment for a particular adjustment type X. If index variable Y is not equal to the last increment then process  100  continues to step  134 . If index variable Y is equal to the last increment then process control continues to step  136 . 
     At step  134 , controller  30  sets index variable Y equal to a succeeding value for Y. Process  100  then returns to step  112 . 
     At step  136 , it has already been determined, at step  132 , that Y is equal to the last increment in the index sequence. At step  136 , it is determined whether index variable X is equal to the last adjustment type. If index variable X is equal to the last adjustment type, then process  100  continues to step  140 . If index variable X is not equal to the last adjustment type, then, at step  138 , index variable X is set to the succeeding value for index variable X, and process  100  returns to step  110 . 
     At step  140 , controller  30  determines an energy distribution signal having optimized pre-fire pulse durations t 1 , delay durations t 2  and fire pulse durations t 3 , based upon drop velocity (X,Y) information stored in memory. Drop velocities increase with an increase in fire energy to a certain point, and thereafter additional energy supplied has a marginal or no effect on drop velocity. A marginal effect is indicated when, for example, an increase in the duration of fire pulse  70 , for example, does not result in a drop velocity increase substantially proportional to the increase observed between drop velocities (X,Y) reflecting preceding adjacent durations t 3 . 
     For example, an optimal relationship might be determined by analyzing for the knee of a curve representing drop velocity versus fire energy (or duration). In another embodiment, as offset can be presumed to be the only variable in the aforementioned exemplary equation for determining drop velocity (e.g., gap G and carrier velocity CV can be presumed constant), offset values can be directly used, instead of their corresponding drop velocities, to determine an optimal relationship. As used herein, a “knee” of a curve can be defined as a point or area on a curve where the curvature of the curve is a maximum (or, alternatively, where the radius of curvature is a minimum). In one embodiment of the present invention, all of the measured offsets, or drop velocities determined therefrom, are considered in the determination 
     Optimized pre-fire pulse duration t 1 , delay duration t 2  and/or fire pulse duration t 3  may be selected from those values used to print a particular set or portion of test subpatterns  74  and  76 , in step  112 , or optimized durations t 1 , t 2  and/or t 3  may be calculated based on the drop velocity (X,Y) information stored in memory. For example, if drop velocity (A,B), where A is a particular value for X and B is a particular value for Y, is less than a desired value, and drop velocity (A,D), where D is a particular value for Y and is a successor value of B, is higher than the desired value, then a duration t 3  may be used for fire pulse  70  which lies between the duration of the fire pulse associated with fire pulse duration (A,B) and fire pulse duration (A,D). 
     According to an exemplary embodiment, process  100  is used only to determine an optimal fire duration t 3 . According to such an embodiment, pre-fire duration t 1  may then be determined using an algorithm that has as an input the duration of the fire pulse. For example, the pre-fire duration t 1  may be determined as a predetermined ratio of fire duration t 3 , such as 3 or 4:1 (e.g., if a fire duration of 800 ns is selected, a pre-fire duration of 200 ns might be used. 
     If not otherwise indexed through use of the variable X, process  100  may be repeated for printhead  34 . If at least one of printheads  34  or  36  are replaced, then process  100  can be reinitiated for the replaced or both printheads. Process  100  can also be initiated at timed intervals, after a certain number of characters are printed or manually by an operator, for example. 
     Thus, a controller can determine optimized values for durations t 1 , t 2  and/or t 3  based upon the measured information for a particular printhead. The selection of pre-fire pulse duration t 1 , delay duration t 2  and fire pulse duration t 3  could be made by the controller to thereby optimize a relationship between drop velocity and the fire energy associated with the printhead. This can reduce the amount of energy supplied to actuators in a particular printhead from that which would need to be supplied by a printer without the present invention. Once optimized values for pre-fire pulse duration t 1 , delay duration t 2  and/or fire pulse duration t 3  have been selected, an ink jet printer can continue with its normal printing operations using these optimized pulse durations to selectively actuate individual ones of actuators of the printhead. 
     While this invention has been described with respect to one embodiment, the present invention can be further modified within the spirit and scope of this disclosure. This application is therefore intended to cover any variations, uses, or adaptations of the invention using its general principles. For example, although an exemplary embodiment was described herein with reference to an energy distribution signal having a profile that included a pre-fire and a fire pulse, the present invention is believed to be equally applicable to other energy distribution signals, such as those having a profile that includes only a single pulse. Further, this application is intended to cover such departures from the present disclosure as come within known or customary practice in the art to which this invention pertains and which fall within the limits of the appended claims.