Patent Publication Number: US-10791245-B2

Title: System for identification and control of z-axis printhead position in a three-dimensional object printer

Description:
PRIORITY CLAIM 
     This application is a divisional application and claims priority to pending U.S. patent application Ser. No. 14/603,710, which is entitled “System And Method For Identification And Control Of Z-Axis Printhead Position In A Three-Dimensional Object Printer,” which was filed on Jan. 23, 2015, and which issued as U.S. Pat. No. 10,291,815 on May 14, 2019. 
    
    
     TECHNICAL FIELD 
     This disclosure is directed to three-dimensional object printing systems and, more particularly, to systems and methods of identification and control of the relative position of printheads with a support member or upper layer of a printed object along a z-axis. 
     BACKGROUND 
     Three-dimensional printing, also known as additive manufacturing, is a process of making a three-dimensional solid object from a digital model of virtually any shape. Many three-dimensional printing technologies use an additive process in which successive layers of the part are built on top of previously deposited layers. Some of these technologies use inkjet printing, where one or more printheads eject successive layers of material. Three-dimensional printing is distinguishable from traditional object-forming techniques, which mostly rely on the removal of material from a work piece by a subtractive process, such as cutting or drilling. 
     During production of three-dimensional printed objects with an inkjet printer, the printer adjusts the relative position of one or more printheads within a comparatively narrow range distances from a surface of a substrate that receives the build material. In some instances the substrate is a support member in the three-dimensional object printer, while in other instances the substrate is an upper layer of an object that is formed in the three-dimensional object printer. The printer adjusts the relative distance between the printheads and the support member that holds the object to enable the printheads to print additional layers of material on an upper layer of the object as the printer forms the object from a series of layers of a build material. The printer controls the position of the printheads to ensure that the printheads are close enough to a surface of the substrate for precise and accurate placement of drops of the build material. The printer also controls the position of the printheads to maintain sufficient separation between the printhead and the substrate, which prevents the printed object from contacting the printhead which would result in clogging of the nozzles preventing the future firing or causing misfiring of the jets in addition to damage of the object being built. 
     During operation of a three-dimensional object printer, at least one of the support member or the printheads moves along the z-axis during the object printing process to accommodate the printed object that extends from the support member toward the printheads. Accurate measurements of the distance between the support member or upper layer of the object and the printheads enable the printheads to operate with improved precision and reliability. Consequently, improved systems and methods for identifying and controlling the separation between printheads and support members or objects in a three-dimensional object printer would be beneficial. 
     SUMMARY 
     In one embodiment, a method of operating a three-dimensional object printer to identify a z-axis distance between a printhead and a substrate has been developed. The method includes operating a plurality of ejectors in a first printhead to form a first predetermined test pattern having a first plurality of marks arranged in a cross-process direction on a surface of a substrate, generating with an image sensor image data of the first predetermined test pattern on the substrate, identifying with a controller a dispersion of cross-process direction distances between marks in the first plurality of marks of the first predetermined test pattern with reference to the generated image data, identifying with the controller a first z-axis distance between the first printhead and the substrate with reference to the identified dispersion, the z-axis being perpendicular to the surface of the substrate, and operating with the controller at least one actuator to move at least one of the first printhead and the substrate along the z-axis in response to the identified first z-axis distance being outside of a predetermined z-axis distance range. 
     In another embodiment, a method of operating a three-dimensional object printer to generate a profile corresponding to dispersions in printed test patterns and a z-axis distance between a printhead and substrate has been developed. The method includes operating a plurality of ejectors in a first printhead to form a first predetermined test pattern having a first plurality of marks arranged in a cross-process direction on a surface of a substrate at a first z-axis distance between the first printhead and the substrate, the z-axis being perpendicular to the surface of the substrate, generating with an image sensor first image data of the first predetermined test pattern on the substrate, identifying with a controller a first dispersion of cross-process direction distances between marks in the first plurality of marks of the first predetermined test pattern with reference to the first generated image data, operating an actuator to move at least one of the first printhead and the substrate along the z-axis by a predetermined offset distance to separate the first printhead and the substrate by a second z-axis distance, operating the plurality of ejectors in the first printhead to form a second predetermined test pattern having a second plurality of marks arranged in the cross-process direction on the surface of the substrate at the second z-axis distance between the first printhead and the substrate, generating with the image sensor second image data of the second predetermined test pattern on the substrate, identifying with the controller a second dispersion of cross-process direction distances between marks in the second plurality of marks of the second predetermined test pattern with reference to the second generated image data, generating with the controller a profile for the first printhead with reference to the first dispersion, the second dispersion, and the predetermined offset distance, the profile including a relationship between a plurality of dispersions of cross-process direction distances between marks in printed test patterns and corresponding z-axis distances between the first printhead and the substrate, and storing the profile in a memory for use in identification of the z-axis distance between the first printhead and the substrate during a printing operation. 
     In another embodiment, a three-dimensional object printer that is configured to identify a z-axis distance between a printhead and a substrate has been developed. The printer includes a first printhead having a plurality of ejectors, a support member having a surface configured to receive material ejected from the plurality of ejectors in the first printhead, at least one actuator operatively connected to the first printhead or the support member, an image sensor configured to generate image data of the surface of the support member, and a controller operatively connected to the first printhead, the at least one actuator, and the image sensor. The controller is configured to operate the plurality of ejectors in the first printhead to form a first predetermined test pattern having a first plurality of marks arranged in a cross-process direction on the surface of the support member, generate image data of the first predetermined test pattern with the image sensor, identify a dispersion of cross-process direction distances between marks in the first plurality of marks of the first predetermined test pattern with reference to the image data, identify a first z-axis distance between the first printhead and the surface of the support member with reference to the identified dispersion, the z-axis being perpendicular to the surface of the support member, and operate the at least one actuator to move at least one of the first printhead and the support member along the z-axis in response to the identified first z-axis distance being outside of a predetermined z-axis distance range. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing aspects and other features of an apparatus or printer that identifies z-direction distances between one or more printheads and a substrate during operation are explained in the following description, taken in connection with the accompanying drawings. 
         FIG. 1A  is a diagram of a three-dimensional object printer. 
         FIG. 1B  is a diagram of the three-dimensional object printer of  FIG. 1A  during an object printing operation. 
         FIG. 2  is a diagram depicting an illustrative distribution of drops that are ejected from a printhead onto a substrate at different z-axis distances between the printhead and substrate. 
         FIG. 3  is a block diagram of a process for generating a profile for a printhead in a three-dimensional object printer that includes a relationship between z-axis distances of the printhead from a substrate and dispersions in the cross-process direction positions of drops ejected from the printhead at the different z-axis distances. 
         FIG. 4  is a block diagram of a process for identifying a z-axis distance between a printhead and a substrate in a three-dimensional object printer. 
         FIG. 5A  is a block diagram of a process for identifying tilt of a substrate in a three-dimensional object printer. 
         FIG. 5B  is a block diagram of another process for identifying tilt of a substrate in a three-dimensional object printer. 
         FIG. 6  is an illustrative example of a predetermined test pattern that includes printed marks formed in a cross-process direction. 
         FIG. 7  is a graph depicting a relationship between dispersions in the cross-process direction positions of drops ejected from a printhead on a surface of a substrate and different z-axis distances between the printhead and the substrate. 
     
    
    
     DETAILED DESCRIPTION 
     For a general understanding of the environment for the device disclosed herein as well as the details for the device, reference is made to the drawings. In the drawings, like reference numerals designate like elements. 
     As used herein, the term “build material” refers to a material that is ejected in the form of liquid drops from a plurality of ejectors in one or more printheads to form layers of material in an object that is formed in a three-dimensional object printer. Examples of build materials include, but are not limited to, thermoplastics, UV curable polymers, and binders that can be liquefied for ejection as liquid drops from ejectors in one or more printheads and subsequently hardened into a solid material that forms an object through an additive three-dimensional object printing process. In some three-dimensional object printer embodiments, multiple forms of build material are used to produce an object. In some embodiments, different build materials with varying physical or chemical characteristics form a single object. In other embodiments, the printer is configured to eject drops of a single type of build material that incorporates different colors through dyes or other colorants that are included in the build material. The three-dimensional object printer controls the ejection of drops of build materials with different colors to form objects with varying colors and optionally with printed text, graphics, or other single and multi-color patterns on the surface of the object. 
     As used herein, the term “support material” refers to another material that is ejected from printheads during a three-dimensional object printing process to stabilize the object that is formed from the build materials. For example, as the three-dimensional object printer applies layers of the build material to form the object, at least one printhead in the printer also ejects layers of the support material that engage portions of the object. The support material holds one or more sections of the build material in place before the object constructed with the build material is a complete object and supported because it is a single object. A simple example of the use of support material includes construction of a cane using the three-dimensional object printer. The arched part of the cane is at the top of the object, and the support material provides support for the downward pointing part of the handle prior to completion of the top of the arch in the cane. The support material also prevents newly formed features from breaking before sufficient build material is present to hold the object together, and prevents portions of the build material that have not fully solidified from flowing out of position before the hardening process is completed. Examples of support material include, but are not limited to, waxy materials that provide support to the object during the printing process and that can be easily removed from the object after the printing process is completed. 
     As used herein, the term “process direction” refers to a direction of movement of a support member past one or more printheads during a three-dimensional object formation process. The support member holds the three-dimensional object and accompanying support material and building material during the print process. In some embodiments, the support member is a planar member such as a metal plate, while in other embodiments the support member is a rotating cylindrical member or a member with another shape that supports the formation of an object during the three-dimensional object printing process. In some embodiments, the printheads remain stationary while the support member and object moves past the printhead. In other embodiments, the printheads move while the support member remains stationary. In still other embodiments, both the printheads and the support member move. 
     As used herein, the term “cross-process direction” refers to a direction that is perpendicular to the process direction and in the plane of the support member. The ejectors in two or more printheads are registered in the cross-process direction to enable an array of printheads to form printed patterns of build material and support material over a two-dimensional planar region. During a three-dimensional object printing process, successive layers of build material and support material that are formed from the registered printheads form a three-dimensional object. 
     As used herein, the term “z-axis” refers to an axis that is perpendicular to the process direction, the cross-process direction, and to the plane of the support member in a three-dimensional object printer. At the beginning of the three-dimensional object printing process, a separation along the z-axis refers to a distance of separation between the support member and the printheads that form the layers of build material and support material. As the ejectors in the printheads form each layer of build material and support material, the printer adjusts the z-axis separation between the printheads and the uppermost layer to maintain a substantially constant distance between the printheads and the uppermost layer of the object during the printing operation. In many three-dimensional object printer embodiments, the z-axis separation between the printheads and the uppermost layer of printed material is maintained within comparatively narrow tolerances to enable consistent placement and control of the ejected drops of build material and support material. In some embodiments, the support member moves away from the printheads during the printing operation to maintain the z-axis separation, while in other embodiments the printheads move away from the partially printed object and support member to maintain the z-axis separation. 
     As used herein, the term “dispersion” refers to any statistical measurement corresponding to a difference between the relative cross-process direction locations of printed marks in a printed test pattern from a printhead in the printer compared to the cross-process direction locations of the printed marks in predetermined test pattern. As used herein, the term “mark” refers to a printed pattern of one or more drops that are formed by a single ejector in a printhead and arranged the process direction axis. A test pattern is formed from an arrangement of marks using multiple ejectors in the printhead. Non-limiting examples of dispersion statistics for marks that are printed in the test pattern include the standard deviation, variance, mean absolute deviation, range, interquartile range, and the like. For example, a predetermined test pattern includes multiple rows of printed marks that are formed with uniform cross-process direction distances between adjacent marks in each row. A printhead with ejectors that eject drops of the material in parallel with the z-axis forms the predetermined test pattern with no dispersion or minimal dispersion. However, the practical embodiments of printheads in the printer include at least some ejectors that eject drops of material at an angle that produces differences between the cross-process direction distances between the printed marks in the test pattern. As described in more detail below, the printer identifies the z-axis distance between different printheads and a substrate in the printer with reference to an identified level of dispersion in the cross-process direction locations of printed marks in test patterns. 
       FIG. 1A  and  FIG. 1B  depict a three-dimensional object printer  100  that is configured to identify the z-axis distance between one or more printheads and a substrate in the printer  100 . The printer  100  includes a support member  102 , a first printhead array including printheads  104 A- 104 C, a second printhead array including printheads  108 A- 108 C, printhead array actuators  120 A and  120 B, support member actuator  124 , an image sensor  116 , a controller  128 , and a memory  132 . In one configuration, the printhead arrays  104 A- 104 C and  108 A- 108 C emit two different types of build material to form three-dimensional printed objects with two different types of build material. In another configuration, one printhead array emits a build material and the other printhead array emits a support material to form three-dimensional printed objects. Alternative printer embodiments include a different number of printhead arrays or a different number of printheads in each printhead array. 
     In the printer  100 , the support member  102  is a planar member, such as a metal plate, that moves in a process direction P. The printhead arrays  104 A- 104 C and  108 A- 108 C and image sensor  116  form a print zone  110 . The support member  102  carries any previously formed layers of the support material and build material through the print zone  110  in the process direction P. During the printing operation, the support member  102  moves in a predetermined process direction path P that passes the printheads multiple times to form successive layers of a three-dimensional printed object, such as the object  150  that is depicted in  FIG. 1B . The printheads  104 A- 104 C and  108 A- 108 C also eject drops of material to form predetermined test patterns, such as the test patterns  192 A- 192 B and  194 A- 194 B depicted in  FIG. 1A  and the test patterns  184  and  186  depicted in  FIG. 1B . In some embodiments, multiple members similar to the member  102  pass the print zone  110  in a carousel or similar configuration. In the printer  100 , one or more actuators move the member  102  through the print zone  110  in the process direction P. In other embodiments, the actuators  120 A and  120 B or other actuators move the printheads  104 A- 104 C and  108 A- 108 C, respectively, along the process direction P to form the printed object on the support member  102 . 
     In the printer  100 , an actuator  124  also moves the support member  102  along the z-direction axis (z) away from the printheads in the print zone  110  after application of each layer of material to the support member. In some embodiments, the actuator  124  or other actuators that are operatively connected to the support member  102  are configured to adjust an angle of tilt of the support member  102  about the cross-process direction axis CP (tilt arrows  172  and  174 ) and the process direction axis P (tilt arrows  176  and  178 ). In another configuration, the actuators  120 A and  120 B move the printhead arrays  104 A- 104 C and  108 A- 108 C, respectively, upwards along the z-axis to maintain the separation between the printheads and a printed object. In the printer  100 , the actuators  124  and  120 A- 120 B are electromechanical actuators such as stepper motors that receive control signals from the controller  128  to move the support member  102  or printhead arrays  104 A- 104 C and  108 A- 108 C by predetermined distances along the z-axis. The illustrative embodiment of the printer  100  includes actuators that adjust the z-axis positions of both the support member  102  and the printhead arrays  104 A- 104 C and  108 A- 108 C, but alternative printer embodiments include actuators operatively connected to only the support member  102  or only to the printheads. The print zone  110  forms an additional layer to the three-dimensional printed object or objects on each member during each circuit through the path to form multiple sets of three-dimensional objects in parallel. 
     The printhead arrays including the printheads  104 A- 104 C and  108 A- 108 C that eject material toward the support member  102  to form layers of a three-dimensional printed object, such as the object  150  that is depicted in  FIG. 1B . Each of the printheads  104 A- 104 C and  108 A- 108 C includes a plurality of ejectors that eject liquefied drops of a build material or support material. In one embodiment, each ejector includes a fluid pressure chamber that receives the liquid build material, an actuator such as a piezoelectric actuator, and an outlet nozzle. The piezoelectric actuator deforms in response to an electric firing signal and urges the liquefied build material through the nozzle as a drop that is ejected toward the member  102 . If the member  102  bears previously formed layers of a three-dimensional object, then the ejected drops of the build material form an additional layer of the object. Each of the printheads  104 A- 104 C and  108 A- 108 C includes a two-dimensional array of the ejectors, with an exemplary printhead embodiment including 880 ejectors. During operation, the controller  128  controls the generation of the electrical firing signals to operate selected ejectors at different times to form each layer of the build material for the object. As described in more detail below, the controller  128  also generates firing signals for the ejectors in the printheads  104 A- 104 C and  108 A- 108 C to print test patterns that are used to identify a distance along the z-axis between each printhead and a substrate in the print zone  110 . The substrate can be the surface of the support member  102  or an upper layer of a three-dimensional printed substrate formed on the support member  102 . 
     While  FIG. 1A  and  FIG. 1B  depict two printhead arrays that eject drops of the build material, alternative embodiments can include three or more printhead arrays that form printed objects with additional build materials. Another embodiment includes only a single printhead array. While the printhead arrays  104 A- 104 C,  108 A- 108 C are each depicted as including three printheads, alternative configurations can include few printheads or a greater number of printheads to accommodate print zones with different sizes in the cross-process direction. Additionally, in rasterized three-dimensional object printer embodiments, one or more printheads move along the cross-process direction axis CP and optionally the process direction axis P during printing operations. 
     The image sensor  116  includes an array of photodetectors that is arranged across the print zone  110  in the cross-process direction CP is configured to generate digitized image data that corresponds to light reflected from the build material and support material that is formed on the member  102 . In one embodiment, the photodetectors generate gray scale 8-bit image data with a total of 256 (0 to 255) levels that correspond to a level of reflected light that each photodetector receiver from the top-most layer of printed support material and printed build material. In other embodiments, the image sensor  116  incorporates multispectral photodetector elements such as red, green, blue (RGB) sensor elements. During operation, the image sensor  116  generates multiple image scanlines that correspond to printed patterns of material drops including printed test patterns formed on the support member  102  or on a substrate that is formed from layers of build material or support material. As the support member  102  moves past the image sensor  116 , the image sensor  116  generates two-dimensional scanned image data from a series of the scanlines. The controller  128  receives the scanned image data and performs further processing of the scanned image data to identify the z-axis direction distances between the printheads and the substrate with reference to scanned image date of printed test patterns. 
     The controller  128  is a digital logic device such as a microprocessor, microcontroller, field programmable gate array (FPGA), application specific integrated circuit (ASIC) or any other digital logic that is configured to operate the printer  100 . In the printer  100 , the controller  128  is operatively connected to the actuator  124  that controls the movement of the support member  102  and the actuators  120 A and  120 B that control the z-axis movement of the printhead arrays  104 A- 104 C and  108 A- 108 C. The controller  128  is also operatively connected to the printhead arrays  104 A- 104 C and  108 A- 108 C, the image sensor  116 , and a memory  132 . 
     In the embodiment of the printer  100 , the memory  132  includes volatile data storage devices such as random access memory (RAM) devices and non-volatile data storage devices such as solid-state data storage devices, magnetic disks, optical disks, or any other suitable data storage devices. The memory  132  stores programmed instructions  136 , 3D object image data  138 , test pattern data  140 , and a drop dispersion to z-axis distance profile  144  associated with each of the printheads  104 A- 104 C and  108 A- 108 C. The controller  128  executes the stored program instructions  136  to operate the components in the printer  100  to both form a three-dimensional printed object, such as the object  150  and to print test patterns that identify z-axis direction distances between the printheads and a substrate in the print zone  110 . The controller  128  also generates the drop dispersion to z-axis distance profiles for the printheads  104 A- 104 C and  108 A- 108 C as described in more detail below in the process  300 . In some configurations, the controller  128  also identifies an angle of tilt away from the z-axis of the surface of the support member  102  or another substrate in the print zone  110 . The 3D object image data  138  include, for example, a plurality of two-dimensional image data patterns that correspond to each layer of build material and support material that the printer  100  forms during the three-dimensional object printing process. The controller  128  ejects drops of material from the printheads  104 A- 104 C and  108 A- 108 C with reference to each set of two-dimensional image data to form each layer of the object  150 . The memory  132  also stores test pattern data  140  that correspond to predetermined patterns of marks that the ejectors in the printheads  104 A- 104 C and  108 A- 108 C form on substrates in the print zone  110 . 
       FIG. 1B  depicts the printer  100  during a three-dimensional object printing operation. In  FIG. 1B , the printheads  104 A- 104 C and  108 A- 108 C form a three-dimensional printed object  150 . The support member  102  includes a margin region that is configured to receive additional printed test patterns  184  from some or all of the printheads  104 A- 104 C and  108 A- 108 C. In the embodiment of  FIG. 1B , the upper surface of the printed object  150  also serves as a substrate that receives a printed test pattern  186  from the printhead  104 A. The image sensor  116  generates image data that include discernible printed marks in the test pattern  186  when the uppermost layer or layers of the object  150  is formed from an optically distinct material, such as a build material with a different color or support material that is ejected from the printheads  108 A- 108 C. In other configurations, the printheads  104 A- 104 C and  108 A- 108 C form structures from two different build materials or a build material and support material to form substrate structures that receives printed test patterns and that have a z-axis height that is similar to the height of the object  150 . The controller  128  uses the substrate structures to identify the z-axis distance between one or more of the printheads and the uppermost layer of the object  150 . 
       FIG. 2  depicts the printhead  104 A and the substrate  202  in a first z-axis direction position  240  and a second z-axis position  244 . As described above, the substrate  202  can be the surface of the support member  102  or upper surface of a printed structure that is formed on the support member  102 . In the illustrative example of  FIG. 2  the first z-axis direction position  240  places the printhead  104 A and substrate  202  closer together along the z-axis compared to the second position  244 , but the in another configuration the first position places the printhead  104 A and substrate  202  at a larger z-axis distance than the second position. In the configuration of  FIG. 2 , the controller  128  operates the actuator  124  to move the substrate along the z-axis between the first position  240  and second position  244 , while in other embodiments the actuator  120 A moves the printhead  104 A or the actuators  124  and  120 A move both the substrate  202  and printhead  104 A, respectively, along the z-axis. 
     The printhead  104 A includes a plurality of ejectors that are arranged along the cross-process direction axis CP. In some embodiments, the printhead  104 A includes diagonal arrangements of ejectors that are staggered across the face of the printhead  104 A in a two-dimensional arrangement. As described above, the controller  128  only operates a portion of the ejectors in the printhead  104  to form a single set of marks in a row set of the test pattern.  FIG. 2  depicts only a subset of ejectors in the printhead  104 A that eject the drops to form a single row set and the printhead  104 A includes four ejectors separating each of the adjacent activated ejectors in the cross-process direction CP to form the test pattern  600  of  FIG. 6 . For example, in  FIG. 2  the ejectors  220  and  224  form adjacent marks in one row of a printed test pattern but four additional ejectors separate the ejectors  220  and  224  in the cross-process direction. The controller  128  operates the intermediate ejectors to form other row sets in the predetermined test pattern  600 . In different test pattern configurations, the controller  128  operates ejectors to form marks in a single row set with at least one ejector positioned between the activated ejectors in the cross-process direction. 
       FIG. 3  depicts a block diagram of a process  300  for generation of a profile between the z-axis distance between a printhead and a substrate and a level of dispersion of drop placement along the cross-process direction from a printhead in a three-dimensional object printer. In the description below, a reference to the process  300  performing an action or function refers to the operation of a controller in a printer to execute stored program instructions to perform the function or action with other components in the printer. The process  300  is described in conjunction with the printer  100  and  FIG. 1A - FIG. 1B ,  FIG. 2 ,  FIG. 6 , and  FIG. 7  for illustrative purposes. 
     Process  300  begins as the printer  100  places a printhead and the substrate in a first position with a first distance of separation along the z-axis (block  304 ). For example, the controller  128  operates one or both of the actuators  120 A and  124  to place the printhead  104 A and a substrate in a first position along the z-axis. As described above, the substrate is either the support member  102  or an upper surface of a build material or support material structure that forms a print substrate. For example, in the printer  100  the controller  128  optionally operates the printheads  108 A- 108 C to form a structure of a second build material or support material having a uniform substrate surface that is optically distinct from the material that is ejected from the printhead  104 A. The controller  128  forms the printed test pattern on the surface of the structure instead of the surface of the support member in some configurations. 
     The process  300  continues as the controller  128  operates the printhead  104 A to form a first predetermined test pattern on the surface of the substrate (block  308 ). The controller  128  generates firing signals for the ejectors in the printhead  104 A to form the predetermined test pattern with a plurality of row sets. As used herein, the term “row set” refers to a plurality of printed marks that a printer forms on the surface of the substrate in a predetermined arrangement extending in the cross-process direction. A row set includes at least one set of the printed marks arranged in a single “row” along the cross-process direction, although some test patterns include row sets with multiple rows of the printed marks that are formed as a set of distinct marks extending along the process direction. The printer  100  forms multiple printed rows in some row sets to reduce the effects of random cross-process material drop placement errors during identification of the dispersion in the cross-process direction locations of marks in the printed test pattern. The printed test pattern  600  in  FIG. 6  includes five row sets  602 A- 602 E that each include a single row of marks arranged along the cross-process direction axis CP. The controller  128  operates only a portion of the ejectors in the printhead to form each row set in the test pattern. The test pattern  600  includes five row sets because the controller  128  forms adjacent marks in each row set using a set of ejectors in the printhead  104 A where four intermediate ejectors lie between each pair of ejectors that form adjacent marks in the row set. In some embodiments, the controller  128  forms a test pattern that includes multiple instances of the test pattern  600  or another similar test pattern in different regions of the substrate surface. In other test pattern embodiments, the row sets include multiple rows of the printed marks. For example, in some embodiments each row set includes a series of two or more rows of the printed marks formed by a single portion of the ejectors in the printhead  104 A. The controller  128  forms the printed test pattern with multiple rows in each row set to reduce the effects of random drop placement errors in the identification of dispersions between the locations of printed marks in the cross-process direction. 
     Process  300  continues as the image sensor  116  generates scanned image data of the substrate and the first printed test pattern formed on the substrate (block  312 ). In the printer  100 , the controller  128  receives the scanned image data from the image sensor  116 . The controller  128  identifies the a first dispersion in the cross-process direction locations of the printed marks with reference to the cross-process direction locations and corresponding cross-process direction distances that separate the printed marks in the scanned image of the test pattern (block  316 ). As used herein, the term “dispersion” refers to differences in the cross-process direction locations between printed marks in scanned image data of the printed test pattern in comparison to the predetermined locations of the printed marks for a test pattern that is printed with ejectors that exhibit no deviation from the z-axis. For example, in  FIG. 6  the test pattern  600  depicts an idealized arrangement of marks where the cross-process direction distance between adjacent marks is equal for each of the row sets  602 A- 602 E. The printed test pattern  650  depicts scanned image data of marks that are printed with the printhead  104 A. Since at least some of the ejectors in the printhead  104 A eject material drops at varying angles along the cross-process direction other than the z-axis, the cross-process distances between adjacent printed marks in the row sets  652 A- 652 E in the test pattern  650  exhibit dispersions compared to the test pattern  600 . 
     In one embodiment, the controller  128  identifies the dispersions in the cross-process locations of the marks with reference to the standard deviation in the cross-process direction distances between marks compared to an average cross-process direction distance between the marks in the row sets of the printed test pattern. In one configuration, the controller  128  identifies the dispersion with reference to the average cross-process direction distance between marks empirically from the scanned image data of the printed test pattern (e.g. the average distance between marks in the scanned image data of the test pattern  650 ), and subsequently identifies the standard deviation with reference to the empirical average. In another configuration, the controller  128  uses the predetermined cross-process direction separation between marks in the predetermined test pattern (e.g. the cross-process direction separation between marks in the test pattern  600 ) as the average and identifies the standard deviation with reference to the predetermined average. In another configuration, the controller  128  identifies the standard deviation based on pairs of printed marks. The controller  128  identifies the standard deviation between the cross-process direction distance that separates adjacent printed marks in the test pattern and the average predetermined separation distance between the marks in the predetermined test pattern. In another configuration, the controller  128  identifies the average cross-process direction distance between adjacent groups of marks, and subsequently identifies the standard deviation with reference to the empirical average of the group to which each dash belongs. 
     The controller  128  identifies a dispersion, such as the standard deviation, for the cross-process distances between the printed marks in the scanned image data of each row set in the printed test pattern. In another embodiment, the printer  100  forms the printed test pattern during multiple passes of the support member  102  through the print zone. When the printer  100  prints different rows of marks in the test pattern during different passes, the dispersion for individual row sets in the scanned image data of each pass includes an artifact since only a portion of the ejectors in the printhead  104 A forms each row of the printed test pattern. Because the ejection angle in the cross process direction for each ejector is random, and each row samples a different subset of the ejectors, the dispersion between rows is often unequal. For example, if printer forms the marks in row sets  652 A and  652 C when the printhead to support member spacing was at the same fixed distance, the standard deviation metric for row set  652 A could differ from the standard deviation metric for row set  652 C. 
     In a single-pass embodiment, the printer  100  forms the row sets in the printed test pattern with process direction spaces formed between the different row sets to enable the image sensor  116  to generate scanned image data of different row sets that are formed on the substrate. In a multi-pass configuration of the printer  100 , the standard deviation or other dispersion metric experiences variations between passes of the support member  102  through the print zone  110 . In either embodiment, the printer  100  identifies the standard deviation from sets of generated image data that include a periodic signal. A frequency of the periodic signal depends on either the relative process direction spacing between repeated sets of marks formed by the ejectors in the printhead on the substrate or upon a pass number in a multi-pass configuration. The periodic signal includes an artifact that is introduced due to the dependence of the standard deviation metric on the particular row since different rows have somewhat different standard deviation metrics. The regular repetition of rows in the generated image data of one or more test patterns introduces the artifact signal into the standard deviation metric signal. In some embodiments, the controller  128  applies a notch filter to the dispersion results from each row to generate a filtered plurality of dispersions from the dispersions identified for each of the row sets in the image data. The controller  128  applies the notch filter with a center frequency corresponding to the predetermined number of row sets in the first predetermined test pattern, such as five row sets in the illustrative test patterns  600  and  650  of  FIG. 6 . 
     Process  300  continues as the printer  100  adjusts the controller  128  operates one or both of the printhead actuator  120 A and support member actuator  124  to move the printhead  104 A and substrate by a predetermined distance along the z-axis to a second position with a second separation distance along the z-axis (block  320 ). The controller  128  operates the printhead  104 A to form a second predetermined printed test pattern in the second position (block  324 ), generates second scanned image data of the second printed test pattern with the image sensor  116  (block  328 ), and identifies a second dispersion in the cross-process direction distances between marks in the second scanned image data (block  332 ). The printer  100  performs the processing of blocks  324 - 332  in substantially the same manner as the processing of blocks  308 - 316 , respectively. During process  300 , the controller  128  identifies a different second dispersion for the cross-process direction distances between printed marks in the second test pattern in comparison to the first dispersion of the first test pattern because the printer  100  adjusts the z-axis distance between the printhead  104 A and the substrate. For example, if the printer  100  increases the z-axis distance between the printhead  104 A and the substrate in the second position, then the dispersion level increases because the drops of ejected material from the printhead travel for a longer linear distance to the surface of the substrate. If, however, the second position has a shorter z-axis distance than the first position, then the dispersion decreases because the drops of ejected material from the printhead travel for a shorter linear distance to the surface of the substrate. 
     As depicted in  FIG. 2 , the level of dispersion between the locations of printed material drops and marks on the substrate surface  202  increases as the z-axis distance between the printhead  104 A and the substrate  202  increases. In the embodiment of  FIG. 2 , the material drops travel along relatively linear paths after emission from the ejectors in the printhead  104 A. Due to manufacturing dispersions in the printhead  104 A, at least some of the ejectors emit the material drops with an angle in the cross-process direction, and the material drops do not follow a path that is parallel to the z-axis to reach the substrate  202 . For example, the ejectors  220 ,  224 ,  226 , and  228  emit material drops at an angle that is not parallel to the z-axis. 
     As depicted in  FIG. 2 , the level of dispersion between the cross-process direction locations of the drops of material ejected from the printhead  104 A increases as the z-axis distance between the printhead  104 A and the substrate  202  increases. In practical operation, the ejected material drops travel along substantially linear paths between the printhead  104 A and the substrate  202 . Thus, the degree of drop position dispersion along the cross-process direction axis CP for material drops from a given ejector increases as the z-axis direction distance between the printhead  104 A and the substrate  202  increases. In the first position  240 , the drops  250  and  252  that are emitted from the ejectors  220  and  224 , respectively, land on positions that are closer together in the cross-process direction than the nominal cross-process direction distance between adjacent printed marks when both ejectors emit material drops in parallel with the z-axis. Other ejectors, such as the ejectors  226  and  228  emit the material drops  254  and  256 , respectively, which land farther apart in the cross-process direction axis than the nominal cross-process direction separation between adjacent printed marks when both ejectors emit material drops in parallel with the z-axis. In the second position  244 , the same types of dispersion in cross-process direction drop placement occur, but the degree of dispersion increases due to the longer z-axis distance between the printhead  104 A and the substrate  202 . For example, the material drops  260  and  262  are closer together than the corresponding drops  250  and  252  in the first position  240 , while the material drops  264  and  266  are farther apart than the corresponding drops  254  and  256  in the first position  240 . The precise dispersion in material drop placement depends upon the characteristics of each printhead and the process  300  identifies the dispersion empirically. 
     Referring again to  FIG. 3 , process  300  continues as the controller  128  generates a profile for the printhead  104 A including a relationship between the between z-axis distance and the first and second dispersions in cross-process direction distances between printed marks and the predetermined z-axis distance between the first position and the second position (block  336 ). In one embodiment, the controller  128  identifies the relationship as a linear relationship between the first and second dispersion levels on one axis and the predetermined displacement distance along the z-axis between the first and second positions along another axis. The controller  128  stores the generated profile in the memory  132  with the drop dispersion to z-axis distance profile data  144  in association with the printhead  104 A. 
       FIG. 7  depicts a graph  700  of an example of a printhead profile relationship. The graph  700  includes the line  732  that fits the rise  728  corresponding to the predetermined change in the printhead and substrate distances and the run  730  corresponding to the change in identified cross-process direction drop placement dispersions between the first position dispersion  720  and the second position dispersion  724 . The graph  700  also includes additional identified dispersion levels that are generated at different z-axis distances between the printhead and the substrate, and the controller  128  generates the linear relationship  732  as a best-fit line through the different dispersion levels. While  FIG. 7  depicts a linear relationship for the printhead profile, alternative profile embodiments can include curves, splines, or other relationships between the cross-process direction dispersion levels and z-axis distance. 
     In some embodiments, either or both of the first position and second position along the z-axis are at a predetermined measured distance (e.g. 0.5 mm and 1 mm) between the printhead and the substrate. In these embodiments, the controller  128  can use the profile data to identify an absolute distance between the printhead  104 A and the substrate, and identify if the z-axis distance is too small or too great for printing operations. However, the printer  100  can generate the profile without absolute z-axis distance measurements between the printhead and the substrate surface. Instead, the controller  128  generates the profile with a known z-axis displacement between the first position and the second position of the printhead and substrate along the z-axis. The controller  128  uses the profile corresponding to the relative z-axis distance between the printhead and the substrate to identify if the printhead is too close or too far from the substrate along the z-axis. 
     As described above, the process  300  generates a profile to identify the z-axis distance between a printhead and a substrate in the three-dimensional object printer based on changes in the dispersion of cross-process material drop placement at different z-axis distances between the printhead and the substrate. In some embodiments, the printer  100  performs the process  300  for each of the printheads  104 A- 104 C and  108 A- 108 C to identify profiles for each printhead since the dispersions in cross-process direction drop placement depend upon individual dispersions in the manufacture of each printhead. In other embodiments, the differences in the dispersion levels between different printheads are small compared to the sensitivity of the measurement needed, and the printer  100  uses a profile that is generated for a single printhead to identify the z-axis distances between the substrate and each of the printheads  104 A- 104 C and  106 A- 106 C. While process  100  describes placement of the printhead and substrate in two positions with two different separation distances along the z-axis, alternative embodiments of the process  300  form the predetermined test pattern at three or more z-axis positions to generate the profile. 
       FIG. 4  depicts a block diagram of a process  400  for identification of a distance between a printhead and a substrate along a z-axis in a three-dimensional object printer. In the description below, a reference to the process  400  performing an action or function refers to the operation of a controller in a printer to execute stored program instructions to perform the function or action with other components in the printer. The process  400  is described in conjunction with the printer  100  and  FIG. 1B  for illustrative purposes. The process  400  is described in conjunction with the printhead  104 A for illustrative purposes, but the printer  100  performs the same process for some or all of the printheads  104 A- 104 C and  108 A- 108 C. 
     Process  400  begins as the controller  128  operates the printhead  104 A to form a three-dimensional printed object (block  404 ). During operation in the printer  100 , the controller  128  operates the printhead  104 A and the other printheads  104 B- 104 C and  108 A- 108 C to form a printed object, such as the printed object  150  that is depicted in  FIG. 1B . During the printing process, the controller  128  operates the ejectors in the printhead  104 A to form the predetermined printed test pattern on the surface of the support member  102 , such as the test patterns  184 , or another substrate formed on the support member  102  (block  408 ). In the example of  FIG. 1B , the upper layer of the object  150  forms a substrate using an optically distinct material from the printheads  108 A- 108 C to form a surface that contrasts with the printed test pattern  186  from the printhead  104 A. In other embodiments, the printheads  104 A- 104 C and  108 A- 108 C form separate substrate structures that correspond to the height of the three-dimensional printed object along the z-axis. During process  400  the controller  128  operates the ejectors in the first printhead  104 A to form either the same test pattern that is formed during the process  300  or another test pattern that includes row sets with the same relative cross-process direction spacing between marks in the test pattern. 
     The process  400  continues as the printer  100  generates scanned image data of the printed test patterns with the image sensor  116  (block  412 ) and the controller  128  identifies dispersions in the cross-process direction locations of the printed marks in the test pattern with reference to the scanned image data (block  416 ). The controller  128  performs the processing of blocks  412  and  416  in a similar manner to the test pattern scanning and dispersion identification described above in blocks  312  and  316 , respectively, or  324  and  328 , respectively, in the process  300 . 
     During process  400 , the controller  128  uses the identified dispersion in the cross-process direction locations of marks in the printed test pattern and the dispersion to z-axis distance profile data  144  stored in the memory  132  to identify the z-axis distance between the printhead  104 A and the substrate (block  420 ). As described above with regards to  FIG. 7 , the controller  128  uses the previously generated linear relationship to identify a distance along the z-axis distance between the printhead  104 A and the substrate, such as the support member  102  or the upper layer of the object  150 . If the identified z-axis distance between the printhead and the substrate is within a predetermined tolerance range (block  424 ) then the printer  100  continues to use the printhead  104 A to form the three-dimensional printed object and the controller  128  optionally performs the process  400  again at a later stage of the printing process. If, however, the z-axis distance between the printhead  104 A and the substrate is either too small or too large, then the controller  128  operates either or both of the actuators  120 A and  124  to adjust the z-axis distance between the printhead  104 A and the substrate to be within the predetermined tolerance range (block  428 ). For example, in the embodiment of the printer  100  the acceptable z-axis distance is in a range of approximately 0.4 mm to 3.0 mm, although the z-axis distance varies for different three-dimensional object printer embodiments. 
     The process  400  described above enables the printer  100  to identify a z-axis distance between a printhead and a single region of the substrate that includes the printed test pattern. In some instances, however, the substrate, such as the support member  102  or a three-dimensional printed structure supported by the substrate  102 , experiences tilt away from an angle that is parallel to the faces of the printheads  104 A- 104 C and  108 A- 108 C in the printer  100 . The tilt in the substrate can produce errors in the printed three-dimensional object, and  FIG. 5A  and  FIG. 5B  depict processes  500  and  550 , respectively, which identify and correct substrate tilt in the printer  100 . In the description below, a reference to the processes  500  or  550  performing an action or function refers to the operation of a controller in a printer to execute stored program instructions to perform the function or action with other components in the printer. The processes  500  and  550  are described in conjunction with the printer  100  and  FIG. 1A - FIG. 1B  for illustrative purposes. 
       FIG. 5A  depicts a process  500  for identification of tilt about the cross-process direction axis CP. For example, in  FIG. 1A  and  FIG. 1B , the arrows  172  and  174  depict potential tilt of the support member  102  about the cross-process direction axis CP. The tilt produces a slope of the support member  102  and a corresponding change in the z-axis distance between the support member  102  and the printheads  104 A- 104 C and  108 A- 108 C along the length of the process direction axis P. 
     During process  500 , the printer  100  identifies the z-axis distance between at least one printhead, such as the printhead  104 A, and the substrate, such as the support member  102 , in a first region of the substrate (block  504 ). The printer  100  identifies first the z-axis distance to the first region of the support member  102  using the process  400  and the stored profile data  144  associated the printhead  104 A that is generated during the process  300 . The printhead  104 A generates a printed test pattern on a first region of the substrate  102 , such as the printed test patter  192 A formed on the support member  102  in  FIG. 1A . The printer  100  also identifies the z-axis distance between the printhead  104 A and the support member  102  in a second region of the support member that is separated from the first region by a predetermined distance in the process direction P (block  508 ). The printer  100  also identifies the z-axis distance to the second region of the support member using the process  400  and the stored profile data  144  associated the printhead  104 A that is generated during the process  300 . In  FIG. 1A , the printhead  104 A forms the printed test pattern  192 B on a second region of the support member  102  that is separated from the first region including the first test pattern  192 A by a predetermined distance in the process direction P. 
     During process  500 , the controller  128  identifies an angle of tilt about the cross-process direction axis CP with reference to a difference between the first z-axis distance, the second z-axis distance and the predetermined process direction separation between the first region of the support member  102  including the first test pattern  192 A and the second region of the support member  102  including the second test pattern  192 B (block  512 ). For example, the controller  128  identifies a tilt angle θ with reference to the following equation: 
             θ   =     atan   ⁡     (         z   1     -     z   2       D     )             
where z 1  and z 2  are the first and second identified z-axis distances, respectively, and D is the predetermined process direction separation between the first and second printed test patterns. The value of θ indicates the magnitude of any tilt and the sign (positive or negative) indicates the direction of the tilt.
 
     If the angle of identified tilt is zero or is sufficiently small to be within a predetermined operating threshold for the printer  100  (block  516 ) then the printer  100  continues three-dimensional object printing operations using the support member  102  (block  520 ). If, however, the identified tilt exceeds the predetermined threshold (block  516 ), then the controller  128  operates an actuator, such as the actuator  124  or another actuator that is operatively connected to the support member  102 , to reduce or eliminate the identified tilt about the cross-process direction axis (block  524 ). The printer  100  continues with a printing operation with the support member  102 . In an alternative embodiment, the printer  100  ceases operation and generates an output alert to an operator that indicates the tilt, and a manual realignment process realigns the support member  102  to reduce or eliminate the tilt. 
     The process  550  in  FIG. 5B  identifies a tilt of the substrate, such as the support member  102 , about the process direction axis P with reference to changes in the z-axis distances between two regions of the support member  102  and two printheads in the printer  100 , such as the printheads  104 A and  104 C. For example, in  FIG. 1A  and  FIG. 1B , the arrows  176  and  178  depict potential tilt of the support member  102  about the process direction axis P. The tilt produces a slope of the support member  102  and a corresponding change in the z-axis distance between the support member  102  and the printheads  104 A- 104 C and  108 A- 108 C along the length of the cross-process direction axis CP. 
     During the process  550 , the printer  100  identifies the z-axis distance between a first printhead, such as the printhead  104 A, and the substrate, such as the support member  102 , in a first region of the substrate (block  554 ). The printer  100  identifies first the z-axis distance to the first region of the support member  102  using the process  400  and the stored profile data  144  associated the printhead  104 A that is generated during the process  300 . The printhead  104 A generates a printed test pattern on a first region of the substrate  102 , such as the printed test patter  194 A formed on the support member  102  in  FIG. 1A . The printer  100  also identifies the z-axis distance between the second printhead  104 C and the support member  102  in a second region of the support member that is separated from the first region by a predetermined distance in the cross-process direction CP (block  558 ). The printer  100  also identifies the z-axis distance to the second region of the support member using the process  400  and the stored profile data  144  associated the printhead  104 C that is generated during the process  300 . In  FIG. 1A , the printhead  104 C forms the printed test pattern  194 B on a second region of the support member  102  that is separated from the first region including the first test pattern  194 A by a predetermined distance in the cross-process direction CP. 
     In another embodiment, the printer  100  identifies two or more dispersion levels for different groups of marks that are formed from two or more sets of ejectors in a single printhead instead of using test patterns that are formed by two different printheads. For example, the test pattern  186  in  FIG. 1B  is formed from ejectors in a single printhead, but the controller  128  optionally identifies two different dispersion values for a first portion and a second portion of the printed marks in the test pattern  186 . The first portion of the printed marks is separated from the second portion of the printed marks by a predetermined distance in the cross-process direction CP. In one embodiment, the controller  128  divides the image data of the printed marks in half along the process direction axis P to group the image data into two groups that are separated along the cross-process direction axis. The controller  128  identifies first and second dispersion values for the first and second groups of the marks. Examples of printers that use the single printhead embodiment of the process  550  include the printer  100  and in printers that include wider printheads including “full width” printheads where a single printhead extends across most or all of the cross-process direction width of the print-zone  110 . 
     During process  550 , the controller  128  identifies an angle tilt about the process direction axis P with reference to a difference between the first z-axis distance, the second z-axis distance and the predetermined cross-process direction separation between the first region of the support member  102  including the first test pattern  194 A and the second region of the support member  102  including the second test pattern  194 B (block  562 ). For example, the controller  128  identifies a tilt angle ϕ with reference to the following equation: 
             ϕ   =     atan   ⁡     (         z     p   ⁢           ⁢   1       -     z     p   ⁢           ⁢   2         C     )             
where z p1  is the z-axis distance between the first printhead  104 A and the first region of the support member  102 , z p2  is the z-axis distance between the second printhead  104 C and the second region of the support member  102 , and C is the predetermined cross-process direction separation between the first and second printed test patterns or the predetermined cross-process direction separation between the two sections of a single test pattern used to extract the z-axis distance. The value of ϕ indicates the magnitude of any tilt and the sign (positive or negative) indicates the direction of the tilt.
 
     If the angle of identified tilt is zero or is sufficiently small to be within a predetermined operating threshold for the printer  100  (block  566 ) then the printer  100  continues three-dimensional object printing operations using the support member  102  (block  570 ). If, however, the identified tilt exceeds the predetermined threshold (block  566 ), then the controller  128  operates an actuator, such as the actuator  124  or another actuator that is operatively connected to the support member  102 , to reduce or eliminate the identified tilt about the cross-process direction axis (block  574 ). The printer  100  continues with a printing operation with the support member  102 . In an alternative embodiment, the printer  100  ceases operation and generates an output signal to an operator that indicates the tilt, and a manual realignment process realigns the support member  102  to reduce or eliminate the tilt. 
     It will be appreciated that variants of the above-disclosed and other features and functions, or alternatives thereof, may be desirably combined into many other different systems, applications or methods. Various presently unforeseen or unanticipated alternatives, modifications, dispersions or improvements may be subsequently made by those skilled in the art that are also intended to be encompassed by the following claims.