AU2008258180B2 - Method for determining printer characteristics - Google Patents

Description

S&F Ref: 883310 AUSTRALIA PATENTS ACT 1990 COMPLETE SPECIFICATION FOR A STANDARD PATENT Name and Address Canon Kabushiki Kaisha, of 30-2, Shimomaruko 3 of Applicant : chome, Ohta-ku, Tokyo, 146, Japan Actual Inventor(s): Ben Yip, Paul Joseph Ellis Address for Service: Spruson & Ferguson St Martins Tower Level 35 31 Market Street Sydney NSW 2000 (CCN 3710000177) Invention Title: Method for determining printer characteristics The following statement is a full description of this invention, including the best method of performing it known to me/us: 5845c(1896883_1) -1 METHOD FOR DETERMINING PRINTER CHARACTERISTICS TECHNICAL FIELD The present invention relates generally to printers and more particularly to the calibration and quality assurance of printers. 5 BACKGROUND In recent years, high quality colour printers have become a norm. In this regard, two significant and related factors are improvements in colour accuracy and improvements in resolution. For inkjet printers, typical resolutions are 1200dpi or higher, which translates into a printer ink dot size (and separation) of 20 microns or less. 10 In many systems, the inkjet printer may overprint regions multiple times to reduce the effect of printer defects, such as blocked printer head nozzles. The optical density of a printed colour can be very sensitive to the precise value of the displacement between overprinted regions. This means that (for high quality printers at least) the exact shift of the printer head relative to the printed medium between overprints must be controlled or 15 calibrated. Typically, the desired accuracy of this calibration is on the order of one micron. A number of techniques have been proposed for calibrating the movements of the medium being printed relative to the head size on the medium, but few techniques measure the effective head size as printed on the medium. 20 One method of measuring the effective head size on the medium is to print dots using predefined nozzles and then measuring the separation of the dots on the medium using a microscope. However, because printed dots on the medium could have a dimension of around 40 micrometers and may have irregular shapes, and because 883310(1879165_1) -2 microscopes with the desired accuracy are typically very expensive, such measurements are not always practical. SUMMARY 5 In accordance with an aspect of the invention, there is provided a method of determining a head size of a print head of a printer. The method comprises the steps of: printing using a print head onto a print medium a test pattern comprising at least two patches with a predetermined relationship to the print head, the at least two patches each comprising a plurality of colourant dots arranged to form a spread spectral pattern; 10 imaging at least a portion of the print medium with a two-dimensional reference pattern superimposed with the test pattern printed on the print medium, the two-dimensional reference pattern adapted to detect the location and orientation of the test pattern; locating in the image the at least two patches of the test pattern relative to the two dimensional reference pattern; and determining the head size from the at least two patch 15 locations. In accordance with another aspect of the invention, there is provided a method of determining a head size of a print head of a printer, the method comprising the steps of: printing using a print head onto a print medium a test pattern comprising a plurality of measurement patterns each having at least two patches with a predetermined relationship 20 to the print head, the at least two patches of a respective measurement pattern each comprising a plurality of colourant dots arranged to form a spread spectral pattern in one passage, each measurement pattern being separated from an adjacent measurement pattern by a print medium advance operation, a patch of the subsequent measurement pattern being located to minimise a distance measurement in a direction of interest 883310(1879165_1) -3 between the patch and one of the at least two patches of the previous measurement pattern; imaging at least a portion of the print medium with a two-dimensional reference pattern superimposed with the test pattern printed on the print medium, the two dimensional reference pattern adapted to detect the location and orientation of the test 5 pattern; calculating the minimised distance measurement; locating in the image a patch from one passage and another patch from another passage relative to the two-dimensional reference pattern; and determining the head size from the patch locations of the measurement patterns and the minimised distance measurement. Either of the foregoing methods may further comprise the step of statistically 10 combining head sizes to provide an overall spatial alignment characteristic dependent upon printing multiple measurement patterns on the print medium and calculating multiple head sizes. In accordance with still another aspect of the invention, there is provided a method of determining a spatial alignment characteristic of a printer. The method 15 comprises the steps of: printing using a print head onto the print medium a test pattern comprising a plurality of patches at predetermined measurement points, the patches each comprising a plurality of colourant dots arranged to form a spread spectral pattern; imaging at least a portion of the print medium with a two-dimensional reference pattern superimposed with the test pattern printed on the print medium, the two-dimensional 20 reference pattern adapted to detect the location and orientation of the test pattern; locating in the image the at least two patches relative to the two-dimensional reference pattern; and determining a spatial alignment characteristic from the at least two patch locations. 883310(1879165_1) -4 The test pattern may comprise patches printed in different print passages of the print head. The test pattern may comprise two patches, one patch printed vertically above the other patch on the print medium in the same print passage. 5 The test pattern may comprise three patches, two patches being printed by a nozzle bank so that one of the two patches is located vertically above the other of the two patches, and the remaining patch of the three patches being printed in the middle by a different nozzle bank, all patches being printed in the same passage. The test pattern may comprise three patches, two patches being printed by a 10 nozzle bank so that one of the two patches is located vertically above the other of the two patches, and the remaining patch of the three patches being printed in the middle with a different passage without advance of the print medium. In accordance with any method of the foregoing aspects, the locating step may comprise: extracting a region of the image to be analysed; calculating a simulated region 15 corresponding to the extracted region of the image dependent upon simulation parameters; correcting an affine transformation for coarse alignment dependent upon a shift between the extracted region and the simulated region; refining the simulation parameters dependent upon the shift; and determining reference pattern coordinates dependent upon the refined simulation parameters. The method may further comprise the 20 step of applying a mask to region to be extracted to neglect one or more portions of the region. In accordance with any method of the foregoing aspects, the two-dimensional reference pattern may comprise at least two registration marks for determining a location approximately and at least one special pattern for determining a location accurately. At 883310(1879165_1) -5 least two registration marks may each comprise a spiral mark, and the at least one special pattern each may comprise a two-dimensional pseudo-random noise pattern having a predetermined marking density with each marking having a predetermined size and shape. 5 In accordance with any method of the foregoing aspects, a transparent substrate with low coefficient of thermal expansion may embody the two-dimensional reference pattern. The transparent substrate embodying the two-dimensional reference pattern may comprise a glass substrate formed with chrome particles on or in the glass substrate. In accordance with still another aspect of the invention, there is provided an 10 apparatus, comprising: a memory for storing data and instructions for a central processing unit; a central processing unit coupled to the memory, the central processing unit performing the method according to any one of the foregoing aspects of the invention dependent upon the instructions and the data. In accordance with yet another aspect of the invention, there is provided a 15 computer program product comprising a tangible computer readable medium having a computer program recorded for execution by a computer to perform the method according to any one of the foregoing methods, computer program code modules implementing each step of the respective method. Other aspects of the invention are also disclosed. 20 BRIEF DESCRIPTION OF THE DRAWINGS Embodiments of the present invention are described hereinafter with reference to the drawings, in which: 883310(1879165_1) -6 Fig. 1 is a schematic block diagram of a general purpose computer on which the embodiments of the invention may be practised; Fig. 2a is a block diagram providing a simplified representation of the mechanical layout of an inkjet printer; 5 Fig. 2b is a block diagram providing a simplified representation of the mechanical layout of an inkjet printer; Fig. 3 is a block diagram illustrating a typical layout of ink ejection nozzles of an inkjet print head; Fig. 4 is a block diagram illustrating the action of two inks ejected from the print 10 head; Fig. 5 is a block diagram illustrating the action of two groups of inks ejected from the print head; Fig. 6 is a block diagram showing a measurement system that comprises a flat bed scanner, attached to a computer; 15 Fig. 7a is a block diagram showing an example of a two-dimensional pattern glass, including a magnified portion of the glass; Fig. 7b is a block diagram showing an example of a two-dimensional pattern glass having a plurality of special patterns; Fig. 8 is a plot of an example of a spiral showing the real part and the imaginary 20 part of a logarithmic radial harmonic function; Fig. 9 is a flow diagram of a method to determine an accurate position on the two-dimensional pattern glass of a feature; 883310(1879165_1) -7 Fig. 10 is a perspective view illustrating the relationship between the two dimensional pattern glass, the measurement system surface, and the surface to be measured; Fig. 11 is a side view of the placement of the head size measurement chart 5 printed on the print medium and the placement of the two-dimensional pattern glass on the scanner; Fig. 12 is a top plan view illustrating a set of displacement vectors which represent the fine alignment transform; Fig. 13 is a schematic flow diagram illustrating a method of determining the 10 location relative to the two-dimensional pattern glass of features in the scanned image; Fig. 14 is a flow diagram of a method to determine the affine transform using spirals; Fig. 15 is a schematic flow diagram illustrating a method of determining accurate coordinates relative to the reference pattern of a given location; 15 Fig. 16 is a schematic flow diagram illustrating a method to handle unwanted noise; Fig. 17 comprises images of a chart mark and a corresponding mask image; Fig. 18 is a schematic flow diagram illustrating the procedures of measuring the head size; 20 Fig. 19 is an example of a head size measurement chart; Fig. 20 is an image showing an example of a patch; Fig. 21 is a schematic flow diagram illustrating a method of estimating the displacement of two image regions by correlation. 883310(1879165_1) -8 Fig. 22 and Fig. 23 are block diagrams illustrating the printing process of a chart which may be used to measure the head size; Fig. 24 shows an example of a scanned image; Fig. 25 is a schematic flow diagram illustrating a method of analysing the 5 scanned image to determine the head size according to an embodiment of the invention; Fig. 26 is the head size measurement chart as depicted in Fig. 19, but each patch is labelled with a number and a character; Fig. 27 is a schematic flow diagram illustrating a method of analysing the scanned image to determine the head size according to another embodiment of the 10 invention; Fig. 28 is an example of a head size measurement chart; Fig. 29, 30 and 31 illustrate the printing process for a head size measurement chart; Fig. 32 is the head size measurement chart with each patch labelled by a number 15 and a character. Fig. 33 is a schematic flow diagram illustrating a method of analysing the scanned image to determine the head size according to a further embodiment of the invention; Fig. 34 shows an enlargement of a region of Fig. 32, and illustrates a 20 measurement chain. Fig. 35 illustrates one example of a possible selection of the D-vectors, the H vectors, the T-vectors and hence the selection of the measurement chains. Fig. 36 illustrates some examples of alternative selections of measurement chains 883310(1879165_1) -9 Fig. 37 is a schematic flow diagram illustrating a method for accurately measuring printer characteristics. Fig. 38 is a block diagram illustrating some examples of different types of printer characteristics. 5 Fig. 39 shows an implementation of the printer's line feed distance characteristic measurement chart. Fig. 40 shows an implementation of the printer's line feed distance characteristic measurement chart. Fig. 41 shows an implementation of the printer's head tilt characteristic 10 measurement chart. Fig. 42 shows an implementation of the printer's inter-nozzle alignment characteristic measurement chart. Fig. 43 illustrates the geometric relation of the patches, the head tile angle and the inter-nozzle alignment distance. 15 Fig. 44 shows an implementation of the printer's carriage alignment characteristics measurement chart. Fig. 45 illustrates the geometric relation of the patches, the head tile angle and the carriage alignment distance. 20 DETAILED DESCRIPTION Methods, apparatuses and computer program products are disclosed for determining a head size of a print head of a printer. Methods, apparatuses and computer program products are also disclosed for determining a spatial alignment characteristic of a printer. In the following description, numerous specific details, including particular 883310(1879165_1) -10 colourants, printing technologies, and sizes in terms of pixels, and the like are set forth. However, from this disclosure, it will be apparent to those skilled in the art that modifications and/or substitutions may be made without departing from the scope and spirit of the invention. In other circumstances, specific details may be omitted so as not 5 to obscure the invention. Where reference is made in any one or more of the accompanying drawings to steps and/or features, which have the same reference numerals, those steps and/or features have for the purposes of this description the same function(s) or operation(s), unless the contrary intention appears. 10 Methods of measuring the head size of an inkjet print head and the spatial characteristics of an inkjet printer using a two-dimensional measurement system, a relative position estimation of printed noise patches (or regions), and the design of these patches so as to enable accurate estimates based on cross-correlation. 15 [Processing Environment] Methods of determining head size of a printer described hereinafter may be implemented using a computer system 100, such as that shown in Fig. 1. Methods in accordance with embodiments of the invention may be implemented as software, such as one or more application programs executable within the computer system 100. In 20 particular, the steps of the methods of measuring head size are effected by instructions in the software that are carried out within the computer system 100. The instructions may be formed as one or more computer program code modules, each for performing one or more particular tasks. The software may also be divided into two separate parts, in which a first part and the corresponding code modules perform the measurement of the head 883310(1879165_1) -11 size and a second part and the corresponding code modules manage a user interface between the first part and the user. The software may be stored in a computer readable medium, including the storage devices described hereinafter, for example. The software is loaded into the computer system 100 from the computer readable medium, and then 5 executed by the computer system 100. A computer readable medium having such software or computer program recorded on the medium is a computer program product. The use of the computer program product in the computer system 100 preferably effects an advantageous apparatus for image processing, particularly for head size measurement. As seen in Fig. 1, the computer system 100 is formed by a computer 10 module 101, input devices such as a keyboard 102, a mouse pointer device 103 and a scanner 119, and output devices including a printer 115, a display device 114 and loudspeakers 117. An external Modulator-Demodulator (Modem) transceiver device 116 may be used by the computer module 101 for communicating to and from a communications network 120 via a connection 121. The network 120 may be a wide 15 area network (WAN), such as the Internet or a private WAN. Where the connection 121 is a telephone line, the modem 116 may be a traditional "dial-up" modem. Alternatively, where the connection 121 is a high capacity (eg: cable) connection, the modem 116 may be a broadband modem. A wireless modem may also be used for wireless connection to the network 120. 20 The computer module 101 typically includes at least one processor unit 105, and a memory unit 106 for example formed from semiconductor random access memory (RAM) and read only memory (ROM). The module 101 also includes an number of input/output (1/0) interfaces including an audio-video interface 107 that couples to the video display 114 and loudspeakers 117, an 1/0 interface 113 for the keyboard 102 and 883310(1879165_1) -12 mouse 103 and optionally a joystick (not illustrated), and an interface 108 for the external modem 116, scanner 119 and printer 115. In some implementations, the modem 116 may be incorporated within the computer module 101, for example within the interface 108. The computer module 101 also has a local network interface 111 which, 5 via a connection 123, permits coupling of the computer system 100 to a local computer network 122, known as a Local Area Network (LAN). As also illustrated, the local network 122 may also couple to the wide-area network 120 via a connection 124, which would typically include a so-called "firewall" device or a device with similar functionality. The interface 111 may be formed by an Etherneti" circuit card, a wireless 10 Bluetoothim or an IEEE 802.11 wireless arrangement. The networks 120 and 122 may represent sources of image data, and image data may also be sourced from the scanner 119. The scanner 119 may be a flatbed scanner for scanning documents, or a fingerprint scanner or an eye scanner for biometric scanning. The interfaces 108 and 113 may afford both serial and parallel connectivity, the 15 former typically being implemented according to the Universal Serial Bus (USB) standards and having corresponding USB connectors (not illustrated). Storage devices 109 are provided and typically include a hard disk drive (HDD) 110. Other devices such as a floppy disk drive and a magnetic tape drive (not illustrated) may also be used. An optical disk drive 112 is typically provided to act as a non-volatile source of 20 data. Portable memory devices, such optical disks (eg: CD-ROM, DVD), USB-RAM, and floppy disks for example may then be used as appropriate sources of data to the system 100. The components 105, to 113 of the computer module 101 typically communicate via an interconnected bus 104 and in a manner which results in a conventional mode of 883310(1879165_1) -13 operation of the computer system 100 known to those skilled in the relevant art. Examples of computers on which the described arrangements can be practised include IBM-PC's and compatibles, Sun Sparcstations, Apple Macm or alike computer systems evolved therefrom. 5 Typically, the application programs discussed above are resident on the hard disk drive 110 and read and controlled in execution by the processor 105. Intermediate storage of such programs and any data, such as image data, fetched from the networks 120 and 122 or scanner 119 maybe accomplished using the semiconductor memory 106, possibly in concert with the hard disk drive 110. In some instances, the 10 application programs may be supplied to the user encoded on one or more CD-ROMs and read via the corresponding drive 112, or alternatively may be read by the user from the networks 120 or 122. Still further, the software can also be loaded into the computer system 100 from other computer readable media. Computer readable media refers to any storage medium that participates in providing instructions and/or data to the computer 15 system 100 for execution and/or processing. Examples of such media include floppy disks, magnetic tape, CD-ROM, a hard disk drive, a ROM or integrated circuit, a magneto-optical disk, or a computer readable card such as a PCMCIA card and the like, whether or not such devices are internal or external of the computer module 101. Examples of computer readable transmission media that may also participate in the 20 provision of instructions and/or data include radio or infra-red transmission channels as well as a network connection to another computer or networked device, and the Internet or Intranets including e-mail transmissions and information recorded on Websites and the like. 883310(1879165_1) -14 The second part of the application programs and the corresponding code modules mentioned above may be executed to implement one or more graphical user interfaces (GUIs) to be rendered or otherwise represented upon the display 114. Through manipulation of the keyboard 102 and the mouse 103, a user of the computer system 100 5 and the application may manipulate the interface to provide controlling commands and/or input to the applications associated with the GUI(s). The methods to be described may also be implemented, at least in part, in dedicated hardware such as one or more integrated circuits performing the functions or sub functions to be described. Such dedicated hardware may include graphic processors, 10 digital signal processors, or one or more microprocessors and associated memories. [Inkjet printer and print head] Fig. 2a illustrates a simplified representation of the internal arrangement of an inkjet printer 200. The arrangement comprises a print head 210 having ink ejection 15 nozzles (not illustrated) organised into groups based on colour and/or ink volume. The print head 210 is mounted on a carriage 220 which transverses a print medium 230 and forms image swaths during a forward passage in a scan direction 240 and a back passage opposite to the scan direction 240, by controlling the ejection of ink from the ink ejection nozzles within the nozzle banks. The inkjet printer 200 further comprises a print medium 20 advance mechanism 250, which transports the print medium 230 in a direction 260 perpendicular to the print head scan direction 240. The distance that the print medium 230 is advanced is called the line feed distance. Fig. 2b illustrates a simplified representation of the internal arrangement of a full-width fixed head printer 270. The arrangement comprises a print head 210 having 883310(1879165_1) -15 ink ejection nozzles (not illustrated) organised into groups based on colour and/or ink volume. The print head 210 is stationary and forms image by controlling the ejection of ink from the ink ejection nozzles within the nozzle banks while the print medium advance mechanism 250 transports the print medium 230. The print head 210 extends 5 across the entire printable area of the printing medium 230 in one dimension. Otherwise, the configuration of this printer 270 is the same as that of printer 200 of Fig. 2a. Fig. 3 illustrates a typical layout 300 of the ink eject nozzle banks 310 (four in this embodiment) of the print head 210. Each nozzle bank 310 comprises-multiple ink ejection nozzles 320 extending perpendicularly to the print head scan direction 240. 10 For an inkjet printer to produce images that do not contain noticeable visual artefacts, alignment is required between the nozzle banks 310 used within the same passage and between the nozzle banks 310 used during the forward and back passages respectively. The print medium advance mechanism 250 of Figs. 2a and 2b must also be calibrated to advance the print medium 230 to correctly align swaths. 15 To produce optimal image quality, each individual printing system must be characterised, and components of that printing system must be calibrated accordingly. One important parameter to measure in the process of calibration is the head size. Fig. 4 illustrates the action of two inks ejected from the print head 210. The arrangement comprises a print head 210 having ink ejection nozzles 320 (only two are 20 depicted in Fig. 4), ejecting inks onto a print medium 230 and forming two ink dots 410. The physical distance on the print medium 230 between two ink dots 410 is denoted the head size 420. Because the print head 210 may not be exactly parallel to the print medium 230 and because the inks may not be ejected exactly perpendicularly to the print 883310(1879165_1) -16 medium 230, in general the head size 420 (indicated by arrow extending between ink dots 410) is not the same as the physical distance 430 between the two nozzles 320. Fig. 5 illustrates the action of two groups of ink dots 410 ejected from the print head 210. An alternative definition of the head size 420 is the average distance 510 on 5 the print medium 230 between corresponding ink dots 410 in each group, one group of ink dots 410 printed by a nozzle group 520and another group of ink dots 410 printed by a nozzle group 530. When the nozzle spacing is consistent, the distance 420 on the print medium 230 between two corresponding ink dots 410 should be the same as the average distance on the print medium 230 between two ink groups 510. 10 For the purposes of the following discussion, the head size is defined as the average distance between two ink groups 510. [Imaging system] Fig. 6 shows a measurement system 600 for determining a two-dimensional 15 position of a location on a surface 610 imaged by the system 600. The measurement system 600 comprises a flat bed scanner 620, attached to a computer 630. [Two-dimensional pattern glass] Due to spatial distortions introduced by the scanner 620, positions on the surface 20 610 imaged by the system 600 do not directly correspond with pixel positions of a digital image resulting from scanning the surface. To accurately determine the physical two-dimensional position of a feature of interest on the surface 610, the scanner surface 610 may be prepared with a reference 883310(1879165_1) -17 pattern. A feature of interest may then be located relative to the reference pattern rather than merely relying on the pixel position containing the feature. Such a reference pattern may also be manufactured on a separate transparent sheet, which could be placed between the scanner surface 610 and the object being 5 imaged. Fig. 7a illustrates an example of a two-dimensional pattern glass 710, comprising a transparent sheet prepared with a reference pattern 720, described in detail below, on one surface. The two-dimensional pattern glass substrate can be a material with a low 10 coefficient of thermal expansion such as fused silica and the reference pattern 720 is manufactured by forming chrome particles on the substrate. Since the two-dimensional pattern glass 710 is used as a reference, the accuracy of a measurement is determined in part by the accuracy of the two-dimensional pattern glass 710 manufacturing process. For a target measurement accuracy of 1 micron standard deviation using a measurement 15 system 600 with optical resolution of around 1600 dots per inch (15.875 microns/pixel), the reference pattern 720 may be manufactured onto the two-dimensional pattern glass substrate using a standard ultraviolet (UV) lithographic process with a minimum feature (mark) size of around 400 nm. The reference pattern can comprise registration marks 730 and 731 used to 20 determine a location (e.g. 740) approximately and a special pattern 750 used to determine a location accurately. In the embodiment of Fig. 7a, a registration mark 730, 731 is located in each corner of the square substrate. A spiral pattern can be used as the registration mark 730 and 731, described in detail below. Three of these spiral marks 730 are identical while the fourth spiral mark 883310(1879165_1) -18 731 is a negative image of spiral marks 730. As described below, these marks permit the estimation of the geometrical relationship between the digital image and the reference pattern 720. Other reference marks may be used instead. As illustrated in the enlargement 760, the special pattern 750 can comprise a 5 two-dimensional pseudo-random noise pattern having a marking density of approximately 4%, with each marking (e.g. 770) taking the form of a square 8 microns in size. Fig. 7a illustrates one special pattern 750 that is fabricated onto the two dimensional pattern glass 710. As shown in Fig, 7b, a plurality of special patterns 750 10 can be fabricated onto the two-dimensional pattern glass 710. [Logarithmic Radial Harmonic Function registration marks] As described previously, the reference pattern 720 can include four spiral registration marks 730 and 731. Each spiral is a bitmapped version of a logarithmic 15 radial harmonic function (LRHF). Mathematically, an LRHF is a complex-valued function defined on a plane. As an example, Fig. 8 shows an illustration of the real 810 and imaginary 820 parts of an LRHF. An LRHF has the properties of scale and rotation invariance, which means that if an LRHF is transformed by scaling or rotation the transformed LRHF is still an LRHF. 20 An LRHF has three parameters that may be adjusted. The first parameter is referred to as the Nyquist radius R, which is the radius at which the frequency of the LRHF becomes greater than -r radians per pixel (e.g., 830). The second parameter is referred to as the spiral angle o, which is the angle that the spiral arms (e.g., 840) make with circles centred at the origin (e.g., 850). The third parameter is referred to as the 883310(1879165_1) -19 phase offset 4. An LRHF may be expressed in polar coordinates (r, 0), in accordance with Formula (1) as follows: i(r,0) = ei'"""'"n (1)+O where the values of m and n may be determined in accordance with the following 5 Formulae (2): n = R7rcosa m = LRxsin r (2) Each spiral registration mark image is created as a bitmap, which samples the LRHF with the Nyquist radius R, the spiral angle u and the phase offset 4. In the preferred embodiments, each spiral bitmap is a square approximately 5 millimeters on 10 edge with square pixels 8 microns on edge. In accordance with the above definition of radius r and angle 0, the value of a pixel in the spiral bitmap with coordinates (r, 0) may be determined in accordance with Formula (3) as follows: {1 if r > R and Re(t(r,0))> (3) 0 otherwise 15 The adjustable parameters for the reference pattern spiral registration marks 730 and 731 can be as follows: (1) Nyquist radius, R = 6.33; (2) Spiral angle, a = -9.08*; and (3) Phase offset, # = 0* for marks 730 and 4= 180* for mark 731. 20 883310(1879165_1) -20 [Determining the accurate location of a feature on a surface] A method 900 for determining an accurate position on the two-dimensional pattern glass 710 of a feature of interest on a surface is described with reference to Fig. 9. The method 900 begins at step 910 where the two-dimensional pattern glass 710 5 is placed on the measurement system surface 610. The pattern glass 710 can usually be placed in the middle of the measurement system surface 610, where the scanners tested typically demonstrated the highest optical resolution. The pattern glass 710 and the measurement system surface 610 are preferably clean and free from dust, fingerprints etc. In the following step 920, the chart to be measured is placed on the pattern glass 10 710. The chart embodies a test pattern. Fig. 10 illustrates the relationship between the two-dimensional pattern glass 710, the measurement system surface 610 and the chart to be measured 1010. The two dimensional pattern glass 710 is oriented to place the reference pattern 720 on the surface immediately adjacent to the surface to be measured 1010. The optical resolution and 15 other performance characteristics of a measurement system 600 are not usually the same in all orientations on the measurement system surface 610. As the orientation of the surface to be measured on the measurement system surface 610 is changed, the accuracy of a measurement typically also changes. The optimal orientation depends on the particular characteristics of the measurement system 600 and the measurement being 20 made and should be determined empirically for a particular system. The surface to be measured should be flat and that the gap between the surface to be measured and the two-dimensional pattern glass 710 should be as small as practicable. There are many possible ways to achieve this. As illustrated in Fig. 11, in the preferred embodiments of the invention, a flat weight 1110 may be placed on top of 883310(1879165_1) -21 the surface to be measured 1010. Too light a weight may not serve the purpose, while too heavy a weight may bend the measurement system surface 610, possibly impairing system accuracy. The suitable weight can be determined empirically. Returning to Fig. 9, in the next step 930 of the method 900, a scanned image is 5 acquired. A position measurement is performed in the measurement system 600 of Fig. 6 by scanning, thus imaging, the surface 1010 to be measured through the reference pattern 720 manufactured onto the surface of the two-dimensional pattern glass 710. With the relationship between the surface 1010 to be measured, the pattern glass 710, and the measurement system surface 610 being that illustrated in Fig. 10, any position on the 10 surface 1010 to be measured has a corresponding position relative to the reference pattern 720 and hence the two-dimensional pattern glass 710. The digital image resulting from the scan, henceforth denoted the "scanned image" or "scan", is transferred to the computer 100 where the scanned image is stored. In the step 940 of the method 900, the scanned image is processed. The image is 15 analysed to determine the measurement result. This analysis typically entails the determination of locations in the pattern glass 710 of features in the scanned image. The pixels of the scanned image include information resulting from the reference pattern 720. To determine the spatial position relative to the two-dimensional pattern glass 710 of a feature in the scanned image, an application program is executed within the computer 20 100. The executed application program detects and analyses the properties of the pattern 720 around the pixel position of that feature and uses the detected properties to determine the corresponding spatial position on the pattern glass 710. This process is described in detail below. The method 900 then ends. 883310(1879165_1) -22 [Two-stage alignment] As a result of distortions in the measurement system 600, locating a reference pattern mark (e.g. 770) in the digital image can be problematic. This locating task can be accomplished using a combination of "coarse alignment" and "fine alignment". 5 Coarse alignment represents an approximate mapping between the location of a mark in the reference pattern 720 and the location of the mark in the scanned image. The coarse alignment may use an affine transformation. The coarse-alignment affine transform is specified by a matrix A and a vector b and transforms coordinates (x, y) in the reference pattern 720 to coordinates (xs, ys) in the 10 scan according to Formula (4), below: (xs =A~j +b. (4) Ys ) y) Since the mapping between locations in the two-dimensional pattern glass and locations in the scanned image is usually more complicated than an affine transform, coarse alignment may not adequately represent the actual transformation. To represent 15 this transformation more accurately, a fine alignment transform may be used to apply corrections to locations determined using the coarse alignment transform. As illustrated in Fig. 12, the fine alignment transform may be represented as a set of displacement vectors (e.g. 1210). Each displacement vector is associated with a location (e.g. 1220) in the scanned image 1230, and measures the amount of shift 20 between the coarsely-aligned reference pattern image and the scanned image at that location. Such a set of displacement vectors may be referred to as a "displacement map", d. 883310(1879165_1) -23 The displacement vectors can be arranged on a regular grid (e.g. 1240) in the scanned image. As shown in Fig. 12, the exterior border of the grid 1240 should contain at least the region of interest (e.g. 1250) in the scanned image. The grid step size, P, may be varied. A smaller value of P gives more spatial detail but may reduce the accuracy to 5 which a displacement vector can be determined. As an example, if the region of interest in the scanned image is a square, 400 pixels on edge, P may be set to 256 and displacement map grid of three points in each direction, as illustrated in Fig. 12, may be used. The coarse and fine alignment steps may be combined into a single "warp map", 10 w. If (x, y) are the coordinates of a mark in the reference pattern 720, the warp map w maps (x, y) to a corresponding location in the scanned image in accordance with Formula (5) as follows: w(x, y) = AH + bli + d [A~x + bI (5) However, the displacement map d(x, y) is only defined at a few places, namely 15 the grid point locations (e.g., 1220). To determine a value for Formula (5) at other locations, the displacement map d is interpolated. Many methods of interpolation are known in the art. Depending on the number of points in each direction, appropriate methods of interpolation along a particular grid axis might be linear, quadratic or cubic interpolation. Cubic interpolation may be used if there are at least four points available; 20 if there are three points, quadratic interpolation may be used, and otherwise linear interpolation may be used. 883310(1879165_1) -24 [Determine locations on the pattern glass] Fig. 13 is a schematic flow diagram illustrating a method 1300 of determining the location relative to the two-dimensional pattern glass 710 of features in the scanned image. 5 In step 1310, the affine transform is determined. The coarse-alignment affine transform described above is determined from the locations of the spiral registration marks 730 and 731. Referring now to the schematic flow diagram Fig. 14, a method 1400 of determining the affine transform using the spiral registration marks is described. 10 The method 1400 begins at step 1410, where the processor 105 generates a spiral template image, within the digital memory 106, for example. Each pixel in the spiral template image is complex-valued. Each value is stored as a pair of double precision floating point numbers representing the real and imaginary parts of the pixel. The spiral template image has height and width equal to T,, the template size. The 15 template size T, may vary. The template size T, may be chosen to make the spiral template image approximately the same size as the spirals in the scanned image. In one example, T, = 256. Polar coordinates (r, 0) in the spiral template are defined, with the origin in the centre of the template. The pixel value at polar coordinates (r, 0) in the spiral template 20 image may be determined in accordance with Formula (6) as follows: e j(mE)+ nIn r) if r>R(6 0 otherwise' 883310(1879165_1) -25 where m and n are defined by Formulae (2) above and the Nyquist radius R and the spiral angle a have the values used in the generation of the reference pattern 720. At step 1420, the processor 105 generates a correlation image. The processor performs a correlation between the scanned image and the complex-valued spiral 5 template image to generate the correlation image. The correlation of two images I, and 12 is a correlation image I,. The correlation image I, may be determined in accordance with Formula (7) below: 1. (X, Y)= 11,(X', Y')12(X'+ X, Y'+ Y). (7) The sum of Formula (7) ranges over all x' and y' where I is defined, and, in the 10 image 12, the values of pixels outside the image are considered to be zero. If either of the images I, or 12 is complex-valued, the correlation image I, may be complex-valued too. The resulting correlation image I, contains peaks (i.e., pixels with large modulus relative to neighbouring pixels), at the locations of spirals 730 and 731 in the scanned image. The phase of the pixel value of a peak is related to the phase # of a corresponding 15 spiral (e.g. 731) that was included in the reference pattern 720. The three spirals 730 that were generated with # = 0 have peaks with similar phase, while the one spiral 731 that was generated with # = 7r typically has a peak with opposite phase to the peaks of the other three spirals. Since the underlying LRHF of the spirals is scale-invariant and rotation-invariant, detection is robust to rotation and differences between the resolution 20 of the scanned image and the resolution employed in the fabrication of the pattern glass 710. 883310(1879165_1) -26 At step 1430, the processor 105 locates the peaks in the correlation image, examines the correlation image resulting from step 1420 and locates the four peaks corresponding to each of the spirals 730 and 731 in accordance with the known arrangement of the spirals in reference pattern 720. 5 At step 1440, the processor 105 calculates the affine transform. In particular, the processor calculates parameters A and b that minimise the error between the known coordinates of the spirals 730 and 731 in the reference pattern, transformed to scanned image coordinates according to Formula (4), above and the corresponding scanned image locations determined in the step 1430. 10 Referring to Fig. 13, in decision step 1320, a check is made to determined if scanned image locations remain to be processed. In steps 1320, 1330, 1340 and 1350,the method 1300 iterates over a set of scanned image locations for which the corresponding pattern glass 710 location is desired. In step 1320, the processor 105 determines if there is any scanned image 15 location for which the corresponding pattern glass 710 location has not yet been determined. If there is such a location (YES), the method 1300 proceeds to step 1330. If there is no such location (NO), the method 1300 ends. In step 1330, the processor 105 obtains the next scanned image location. In step 1340, the processor 105 locates the feature on the pattern glass. The 20 scanned image location is found in the pattern glass 710 according to a method 1500 described in detail hereinafter. In step 1350, the pattern glass location is output. The location can be saved for subsequent processing. The method 1300 then returns to the step 1320. 883310(1879165_1) -27 [Simulate scanned image pixel] Fig. 15 is a schematic flow diagram illustrating a method 1500 of determining accurate coordinates relative to the reference pattern 720 of a given location in a digital image produced by imaging a chart through the two-dimensional pattern glass 710 using 5 the measurement system 600. As described in detail hereinafter, in step 1530, the processor 105 calculates a simulated version of part of the scanned image from the known reference pattern 720 and a set of parameters used to model the process of image acquisition using the measurement system 600. Before describing method 1500, the simulation process is first 10 detailed. The appearance in the simulated image of each marking (e.g. 770) in the special pattern 750 can be modelled using a two-dimensional Gaussian function. As described previously, the location in the simulated image of a marking (e.g. 770) may be calculated using a warp map. Specifically, the simulation parameters comprise: 15 (1) the value of a scanned image pixel distant from any reference pattern marks (the "background" level), B; (2) the value of a scanned image pixel distant from any unmarked region of the reference pattern (the "foreground" level), F; (3) the standard deviation of the Gaussian function in the horizontal and vertical 20 directions, or, and a,, respectively; (4) the coarse alignment parameters, namely the affine matrix, A, and vector, b; and (5) the fine alignment parameters, namely the displacement map, d. 883310(1879165_1) -28 Let R denote an image of the reference pattern, where R(x, y)=l indicates the presence of a mark at location (x, y) and R(x, y)=O indicates the absence of a mark. Then, given the simulation parameters mentioned above, the value, S, of the pixel at location (xs, ys) in the simulated image may be calculated according to Formula (8) below: S(xs,ys) = B+ 5 e (w(x,,)xx,,,,>)aiag~o.,Y,>-'l2, (8) (F - B) f fR(x,y) |rto go, J,(x,y)| dy dx ( where: w(x, y) is the warp map calculated according to Formula (5), above; diag(au, ay) represents a 2x2 matrix with main diagonal coefficients ax and ay; represents the Euclidean norm; and 10 J,(x,y)l is the determinant of the Jacobian matrix of w at (x, y). The reference image, R, can be stored as a raster array, RA, in the digital memory of the computer 100, with each pixel the same size and shape as a special pattern marking (e.g. 770): a square 8 microns in size. If the number of pixels in the x and y directions are Nx and N, respectively, R and RA are related according to Formula (9) below: 5 R(\ A(RAYA) if 0 xA<NandOsyA<N 0 otherwise where XA and YA are defined as follows: xA = + (10) 8 pm 2 883310(1879165_1) -29 YA = 8 pm, 2_ In this case, S may be calculated according to Formula (11) below: S(xs,ys) = B+ N,- N,-I -1(W(x,y)-(xs,ys))diag(a,,ayy'/2 (F-B)Z ZR(x,y)e 2|ru o IJ,(x,y)|x 64pm 2 XA=0 YA= 0 y where x and y are defined as follows: 5 x=xA x 8pm (12) Y=YA x 8pm [Converting scan coordinates to pattern glass coordinates] 10 The method 1500 of determining accurate coordinates relative to the reference pattern 720 of a given location in a digital image produced by imaging a chart through the two-dimensional pattern glass 710 using the measurement system 600 is described with reference to Fig. 15. As described above, a warp map, w, provides a mapping from coordinates in the 15 reference pattern 720 to coordinates in the scanned image. To determine accurate coordinates relative to the reference pattern of a given location in the scanned image, the method 1500 first generates a warp map relating a region in the reference pattern to a region including the location of interest in the scanned image and determines the location in the reference pattern mapping to the location of interest. 883310(1879165_1) -30 In the subsequent discussion, approximate values of the simulation parameters B, F, a, A and b, described previously, are assumed to be known. For the purposes of the following discussion, (1) let these approximate values be denoted BO, FO, oo, Ao and bo, respectively; and (2) define a uniformly zero displacement map, do, according to Formula 5 (13), below: do(x, y) =(O, 0) , (13) The method 1500 begins at step 1510, where the processor 105 determines a window width, W, and height, H, in scanned image pixels for subsequent processing. The parameters W and H typically correspond to distances in the range of 700 microns to 10 5000 microns. At step 1520 a region, Io, of the digital image that is W pixels wide and H pixels high, centred on the input digital image coordinates, is extracted from the scanned image to be analysed. If the coordinates of the first pixel, in scanline order, of the region 1 are denoted (xo, yo), the pixels of Io are related to the pixels of I according to Formula (14), 15 below: Io(x, y) = I(x + xo, y + yo). (14) In step 1530, a new image region, So, also W pixels wide and H pixels high, is calculated in the digital memory 106 of computer 100. Each pixel, So(x, y), of this image is calculated using the simulation parameters BO, FO, uo, AO, bo, and do as described 20 above, according to Formula (15), as follows: So(x,y)=S(x+xo,y+yo) .

(15) 883310(1879165_1) -31 In step 1540, the regions 1o and So are compared to determine a shift, i.e., a two dimensional integer-coordinate translational offset Ao, from Io to So. Many methods to achieve this are well known. The phase-only correlation can be used. In step 1550, the affine transform is corrected for shift. The affine transform 5 vector is adjusted to account for the offset between the scan and simulated scan images 1o, So according to Formula (16): b= bo-Ao .(16) The method 1500 continues at step 1560, where the processor 105 refines the simulation parameters. The difference between Io and the simulated image is minimised 10 by varying the simulation parameters B, M, a, and d. More specifically, the error function, E, to be minimised may be the squared residual error calculated according to Formula (17) as follows: W-1 H-1 E = E (Io(x,y)- S(x+ xo,y yo)) . .(17) x=O y=O Non-linear minimisation requires initial conditions for the variables which are 15 being varied. These initial conditions are defined as follows: B: Approximate value, Bo; F: Approximate value, Fo; a: Approximate value, ao; and d: Zero displacement map, do. 20 The affine transform parameters are not varied by the minimisation process, but have fixed values as follows: 883310(1879165_1) -32 A: Approximate value, Ao; and b: Adjusted value, bi. A non-linear least-squares minimisation scheme, known as the Levenberg Marquardt method, can be used, and many other such methods are well known. 5 The minimisation is performed in step 1560. In step 1570, the processor 105 determines the reference pattern coordinates. The desired reference image coordinates corresponding to the input digital image coordinates are determined using the refined simulation parameters. Let the value of the displacement map d corresponding to the minimum value of 10 E be denoted di. Then the refined warp map, wi, may be calculated according to Formula (18) as follows: wi(x, y)= Ao(x, y) T + bi + di(Ao(x, y)T + ai). (18) To determine the desired reference image coordinates (XR, YR) from wi and the input digital image coordinates (xi, y,), a second minimisation process is used. The error 15 function, c, to be minimised in this step may be calculated according to Formula (19), below: 6 =||w,(xI ,yR)_X I I11 219 The initial value of (XR, YR) may be calculated from the affine component of wI according to Formula (20) as follows: 20 (xR, yR)o - A((xI, y8) - bi1). (20) 883310(1879165_1) -33 The error function E can be minimised by varying (xR, yR) using the Simplex algorithm of Nelder and Mead. Other well known methods may also be practiced. The desired reference image coordinates (XR, YR), correspond to the minimum value of c (expected to be 0). 5 Following step 1570, method 1500 concludes. [Pixel masking and dust, hair etc. rejection] The method 1500 is based on the assumption that the digital image region, Io, being analysed may be modelled as dark-coloured reference pattern marks on a uniform 10 light-coloured background. However, other marks on the chart often obscure the reference pattern marks in some subregion of Io. In addition, dust, hair, etc. between the chart and the two-dimensional pattern glass 710 or between the pattern glass and the measurement system surface 610 is often imaged along with the pattern glass and the chart. 15 In such cases, the accuracy of the reference pattern coordinates determined by method 1500 may be improved by neglecting pixels affected by chart marks, dust or hair, etc. This can be accomplished using a mask image, M, with the same dimensions as 1 o, stored in the digital memory of computer 100. The pixels of the mask image M are set according to Formula (21), below: [0 if pixel (x,y) is to be neglected 20 M(x, y)= h*(21) 1 otherwise For the purposes of the subsequent discussion, if the mask image indicates that a given pixel is to be neglected, the pixel is termed a "masked" pixel and has a mask image 883310(1879165_1) -34 value of zero. All other pixels are termed "unmasked" and have a mask image value of one. A method 1600 of determining accurate coordinates relative to the reference pattern 720 of a given location in a scanned image produced by imaging a chart through 5 the two-dimensional pattern glass 710 using the measurement system 600 in the case where some pixels in the region of interest of the digital image are affected by chart marks, dust, hair etc. is described with reference to Fig. 16 and Fig. 17. The method 1600 begins at step 1610 where the processor 105 sets the mask M to exclude chart marks. The mask M, shown as mark 1710 in Fig. 17, is set to 0 where 10 the corresponding pixel in the digital image region 1 o, 1720 is determined to be sufficiently close to a chart mark (e.g. 1730) or is set to 1 otherwise (e.g. 1740). All pixels of M may be I if no pixels are to be neglected in the analysis initially. At step 1620, the processor 105 corrects the shift and refines simulation parameters. Refined simulation parameters are determined. Step 1620 is identical to 15 steps 1510 to 1560, inclusive, of method 1500 described previously, save for the following modifications: (1) in step 1540, the comparison of 1 o and So neglects any pixels in Io for which the corresponding pixel in M has value 0; (2) in step 1560, the error function, E, to be minimised is calculated according to 20 Formula (22) as follows: W-1 H-I E = J (zo(x,y)- S(x+xo,y + yo")) 2 M(x,y). (22) x=O y=O 883310(1879165_1) -35 In decision 1630, a check is made to determine if dust, hair, etc. is to be excluded. If it is desired to exclude additional pixels affected by dust etc. (YES), the method 1600 proceeds to step 1640. Otherwise (NO), the method 1600 proceeds to step 1680. 5 In step 1640, the processor 105 calculates a residual image, D. Each pixel in D is the difference between the corresponding pixels in Io and the image S simulated with the refined simulation parameters, according to Formula (23), as follows. D(x, y) =I0 (x, y) - S(x + x 0 , y + y 0 )| (23) In step 1650, the processor 105 determines the fraction, 0, of pixels to exclude. 10 A typical value of 0 can be 0.1. In step 1660 the processor 105 sets the mask M to exclude pixels with large residuals. The unmasked pixels in D are sorted in decreasing order of magnitude. If the initial number of unmasked pixels is denoted n, the pixels in M corresponding to the first L x nJ pixels in the sorted pixels of D are set to 0. 15 Step 1670 of method 1600 is identical to the step 1620 described previously. The shift is corrected, and the simulation parameters are refined. Step 1680 is identical to the step 1570 of method 1500, described previously. In step 1680, the reference pattern coordinates are determined. Following step 1680, method 1600 concludes. 20 [First Embodiment] Fig. 18 is a schematic flow diagram illustrating a method 1800 for accurately measuring the head size 510. 883310(1879165_1) -36 The method 1800 begins at step 1810, where a head size measurement chart is printed. The design of the chart and the chart printing process are described in detailed below. In step 1820, the two-dimensional pattern glass is placed on the measurement 5 surface 610 as described previously for the step 910 of the method 900. In step 1830, the head size measurement chart is placed on the two-dimensional pattern glass, as described above for the step 920 of the method 900. In step 1840, the scanned image is acquired, as described for the step 930 above. In step 1850, the scanned image is processed to determine the desired head size 10 510. This step is described in detail below. The step of placing the two-dimensional pattern glass on the measurement surface 610 could be performed prior to step 1810. Further, the step 1810 could be eliminated if the two-dimensional pattern 750 were fabricated onto the glass of the scanner. 15 [Chart design for the first embodiment] Fig. 19 shows an example of a head size measurement chart 1900. The chart 1900 has four LRHF spiral registration marks 1910, 1920, 1930 and 1940 and at least two "patches" 1950, described below. The chart 1900 is a test pattern that can be printed 20 on a print medium using the print head of the printer, of which the head size is to be determined. As used hereinafter, the phrase "head size measurement chart" refers to a test pattern. The chart spiral registration marks 1910, 1920, 1930, 1940 are generated as described previously with respect to the reference pattern spiral registration marks 730 and 731 of Fig. 7, but with different adjustable parameters for ease of distinguishing two 883310(1879165_1) -37 dimensional pattern glass spirals from chart spirals. The adjustable parameters for the chart spiral registration marks 1910, 1920, 1930 and 1940 can be as follows: (1) Nyquist radius, R = 3.82; (2) Spiral angle, o = 300; and 5 (3) Phase offset, < = 180*, 1200, 600, and 00 for marks 1910, 1920, 1930 and 1940, respectively. The spiral registration marks 1910, 1920, 1930 and 1940 are used to detect the location and the orientation of the chart 1900. Other types of spirals or even other types of marks (e.g. crosses) can be used to detect the location and the orientation of the chart 10 1900. Furthermore, the location and the orientation of the chart can be detected using the known pattern and location of the patches. [Patch design] Fig. 20 shows a detailed example of a patch 1950. A patch 1950 comprises a 15 group of printed ink dots, with the dots being arranged such that the patch has both wide spatial and wide spectral support so as to form a spread spectral pattern. When correlated with a similar patch, this results in a distinct, sharp correlation peak. The patches are printed by the nozzles of the to-be-measured head 210. The colour or colours on the patches depends on the colour or colours of the ink ejected by 20 the nozzles. The colourants may be CMYK inks, but other colours could be used. In one example, the patch is a square that is 3 mm on edge, formed from cyan and magenta ink dots. 883310(1879165_1) -38 [Describe correlation] One aspect of the analysis of the head size measurement chart 1900 is the calculation of the relative locations of pairs of patches. Many methods of performing this calculation are known Phase-only correlation can be used, with the correlation peak 5 located to subpixel resolution by Fourier interpolation. Other shift estimation methods such as gradient based shift estimation could be used instead. In such cases, the patch 1950 could be re-designed to ensure the best performance for the alternative shift estimation method. Fig. 21 is a schematic flow diagram illustrating a method 2100 of estimating the 10 displacement of two equal-sized image regions by correlation. For the purposes of the following discussion, let the image regions be denoted I, and 12 and the calculated average displacement between corresponding features in the image regions be denoted d. Further, let the width in pixels of each image region be denoted w, let the height in pixels be denoted h, and let the uppermost leftmost pixel of each image region have coordinates 15 (0, 0) with the first, x, coordinate increasing to the right and the second, y, coordinate increasing downward. The method 2100 starts at 2110 where a two-dimensional Fourier transform is applied to input images I, and I2 to form the spectra Si and S2 respectively, according to Formulae (23b), below: w-I h-I 21' + S,(k,l) = X I I,(x,y) e w h,and 20 X=O = (23b) w-I h- 2M + S2 (k, 1) = 12 (x,y) e x=O y=O 883310(1879165_1) -39 Both spectra Si and S 2 are two-dimensional, complex-valued images of the same size as I, and I2, but with the uppermost leftmost pixel coordinate of (-Lw/2J,-Lh/2J). In step 2120, a conjugated first spectrum SO* is formed from spectrum S 1 . This is done by negating the imaginary part of each pixel according to Formula (23c) as 5 follows: S, (x, y) = (S, (x, y)) (23c) In the following step 2130, the two complex spectra S,* and S 2 are combined by multiplying on a pixel-by-pixel basis to form a correlation spectrum E according to Formula (23d), below: 10 E(x, y) = S, (x, y) S 2 (x,y) (23d) The correlation spectrum E is further processed in the next step 2140 is normalised. Each pixel of the complex-valued correlation spectrum E is scaled to an amplitude of one to form a normalised correlation spectrum Z according to Formula (23e), below: E(x,y) if|E(x,y)| >0 15 E(x,y)= |E(x,y)| (23e) 1 0 otherwise In step 2150, a two-dimensional inverse Fourier transform is applied to the normalised correlation spectrum Z to form a correlation image C according to Formula (23f), as follows: 883310(1879165_1) -40 C(x,y)= L LE(k,1) e . (23f) k=-2 J /=-['] In step 2160, the peak in the correlation image C is found to estimate the displacement. The pixel with the largest absolute amplitude in the correlation image C is located. If the width of image C in pixels is denoted w and the height in pixels is denoted 5 h, the coordinates (mr, my) in image C of this pixel are converted to a first estimate do, in image pixels, of the displacement of features in image 12 relative to corresponding features in image I, according to Formula (23g), as follows: do =(m, - w [ ,, - ! . (23g) w h In step 2170, this initial estimated displacement is refined to sub-pixel resolution 10 using a maximisation process. Given a displacement d, initially equal to the value do calculated in the previous step 2160, the function, y, to be maximised in this step is the Fourier-interpolated correlation image C at location d. The function y may be calculated according to Formula (23h), below: w-1I_ h-1-r 15 -Kx,y)= E(k,l) e w h (23h) k=-[w '=-L'i The function y can be maximised by varying d using the Simplex algorithm of Nelder and Mead, but many other methods known in the art may also be practised. Following step 2170, method 2100 concludes. 883310(1879165_1) -41 The essence of the correlation process 2100 is to determine the displacement between the two images. There are other alternative correlation processes, for example, gradient based shift estimation that could be used instead. In addition, the patch 1950 could also be re-designed to ensure the best performance for the alternative correlation 5 process. [Print the head size measurement chart] Fig. 22 and Fig. 23 illustrate the process 1810 in Fig. 18 of printing a chart which may be used to measure the head size 510. 10 Referring first to Fig. 22, the print head 210 makes a passage 2210 across the printing medium 230, which is in a first position and records (prints) a number of patches, e.g. 2220, arranged according to the patch layout shown in Fig. 19. An LRHF spiral registration mark 1910 is located to the left of patch 2220. As described previously with reference to Fig. 5, the distance between the patches is the desired head size 510. 15 Referring now to Fig. 23, the printing medium advance mechanism 250 moves the printing medium 230 to a second position, and a second passage 2310 of the print head 210 records further patches, e.g. 2320. The complete measurement chart 1900 is printed after four passages. The printing process may be different for different printers, for example, the passages 2210 and 2310 may be forward passages, backward passages 20 or a combination of forward and backward passages. [Acquire the scanned image] Fig. 24 illustrates a scan 2400 of the head size measurement chart 1900 imaged through the two-dimensional pattern glass 710. In the scanned image 2400, the reference 883310(1879165_1) -42 pattern 720 is superimposed on the head size measurement chart 1900. The scan can acquired at a resolution of 2400 dpi, although other resolutions may be practised. [Analyse the scanned image to determine the head size] 5 The schematic flow diagram Fig. 25 illustrates the method 1850 of analysing the scanned image 2400 to determine the head size 510. The method 1850 begins at step 2510 where the affine transform of the measurement chart is obtained. An affine transform between the coordinates of the measurement chart 1900 and the coordinates of the scanned image 2400 is determined. 10 This is accomplished according to the method 1400 as described previously, except that the LHRF registration mark adjustable parameters and locations used are those for the chart spiral registration marks 1910, 1920, 1930 and 1940 rather than the reference pattern spiral registration marks 730 and 731. The parameters of the affine transform are the matrix Ac and the vector bc. The 15 affine transform relates coordinates in the measurement chart 1900, (xc, yc) to coordinates in the scanned image 2400, (xs, ys) according to Formula (24), below: xs) = Ac~ c +bc -(24) As described previously, the parameters of the affine transformation could also be calculated using other marks on the measurement chart such as the patches, e.g. 1950. 20 Referring again to Fig. 25, at step 2520, the processor 105 locates the patches in the scanned image. The coordinates of each patch in the scanned image 2400 are calculated. 883310(1879165_1) -43 Fig. 26 shows again the head size measurement chart 1900 of Fig. 19, but with each patch labelled with a number and a character. The number indicates the passage in which a given patch is printed. The character indicates which nozzles of the print head 210 are used to print the patch. For example, 'A' may refer to the nozzle group 520 and 5 'B' to the nozzle group 530 in Fig. 5. Lines are drawn between patches that are printed at the same time. The distance between a patch printed by nozzle group 'A' and the patch printed at the same time by nozzle group 'B' is the head size 510. In step 2520, the processor 105 locates the patches in the scanned image 2400, according to the following steps: 10 (1) Calculate an estimated location for each patch using the known location of the patch in the chart and the affine transform determined in the previous step 2510; (2) For each patch, extract an image region that contains the patch. For a patch size of 3 mm, the region size could be 200 pixels at 1200 dpi; (3) Perform sub-pixel shift estimation between the extracted region of an 'A' 15 patch to the extracted region of the corresponding 'B' patch; and (4) Adjust the location of the 'B' patch by the estimated shift. Alternatively, step 2520 may be accomplished according to the following steps: (1) Calculate an estimated location for each patch using the known location of the patch in the chart and the affine transform determined in the previous step 2510; 20 (2) For each patch, extract an image region that contains the patch. For a patch size of 3 mm, the region size could be 200 pixels at 1200 dpi; (3) Perform sub-pixel shift estimation between the extracted region of each patch and the known theoretical pattern of the patch; and (4) Adjust the location of the patch by the estimated shift. 883310(1879165_1) -44 After determining the location of each patch in step 2520, the next step 2530 determines the accurate coordinates of each patch relative to the two-dimensional pattern glass 710. This may be accomplished according to the method 1300 described previously. In step 2540, the head size is calculated from the two-dimensional pattern glass 5 coordinates of each patch. Because the two-dimensional pattern glass is rigid and not sensitive to thermal expansion, the distance between two patches in two-dimensional pattern glass 710 coordinates corresponds to the physical distance between the patches on paper. Consequently, if two patches on paper are printed with a displacement of one head size 510, then the head size may be determined by measuring the distance in two 10 dimensional pattern glass 710 coordinates between the patches. Such two patches are known as a measurement pattern. Referring again to Fig. 26, in this embodiment, there are 32 pairs of patches with each pair separated by a distance of the head size. For a given chart layout, let N denote the number of patch pairs and let X 1 , X 2 , ... , XN denote the physical distances measured for the pairs. Then the desired head size 510 may be 15 calculated as the average distance according to Formula (25). 1 N head size =- X, (25) N i=1 [Second Embodiment] A second embodiment of the invention is described with reference to the 20 schematic flow diagram Fig. 27 illustrating an alternative method 2700 for accurately measuring the head size 510. As can be seen with reference to Fig. 18, the steps in method 2700 are the same as those for the corresponding method 1800 in first embodiment. The method 2700 883310(1879165_1) -45 differs from the method 1800 in the design of the test chart and the method of analysing the scanned image. The method 2700 begins at step 2710, where a head size measurement chart is printed. The design of the chart and the chart printing process are described in detailed 5 below. In step 2720, the two-dimensional pattern glass is placed on the measurement surface 610 as described previously for the step 910 of the method 900. In step 2730, the head size measurement chart is placed on the two-dimensional pattern glass as described above for the step 920 of the method 900. 10 In step 2740, the scanned image is acquired as described for step 930 above. In step 2750, the scanned image is processed to determine the desired head size 510. This step is described in detail below. [Chart design and printing for the second embodiment] 15 Fig. 28 shows an example of a head size measurement chart 2800. Like the previous example chart 1900, the chart 2800 has four spirals 1910, 1920, 1930, 1940and has two or more patches 1950, but the layout of the patches is different. Figs. 29, 30 and 31 illustrate the process of printing the chart 2800 which may 20 be used to measure the head size 210. Referring first to Fig. 29, the print head 210 makes a passage 2910 across the printing medium 230 and records (prints) a number of patches, e.g. 2920, with the patches arranged according to the patch layout shown in Fig. 28. As described previously with reference to Fig. 5, the distance between the patches is the desired head size 510. 883310(1879165_1) -46 As illustrated in Fig. 30, the printing medium advance mechanism 250 moves the printing medium 230 to a second position, and a second passage 3010 of the print head 210 records further patches, e.g. 3020. The distance moved by the printing medium 230 is carefully chosen so that the lower patches printed in the first passage 2910, e.g. 5 3030 are roughly aligned with the upper patches printed in the second passage 3010, e.g. 3040. Fig. 31 illustrates a third printing passage 3110. As for the second passage 3010, the distance moved by the printing medium 230 is carefully chosen so that the lower patches printed in the second passage, e.g. 3120, are roughly aligned with the 10 upper patches printed in the third passage, e.g. 3130. Fig. 26 shows again the head size measurement chart 1900 but with each patch labelled with a number and a character. The number indicates the passage in which a given patch is printed. The character indicates which nozzles of the print head 210 are used to print the patch. For example, 'A' may refer to the nozzle group 520 and 'B' to 15 the nozzle group 530 in Fig. 5. Lines are drawn between patches that are printed at the same time. The distance between a patch printed by nozzle group 'A' and the patch printed at the same time by nozzle group 'B' is the head size 510. Such pair of patches is known as a measurement pattern. Fig. 32 shows again the head size measurement chart 2800 with each patch 20 labelled by a number and a character. As described previously with respect to Fig. 26 for the first embodiment, the number indicates the passage in which a given patch is printed and the character indicates which nozzles of the print head 210 are used to print the patch. As for Fig. 26, lines are drawn between patches that are printed at the same time. 883310(1879165_1) -47 [Analyse the scanned image in the second embodiment] The different measurement chart 2800 design compared to the measurement chart 1900 permits an advantageous method of analysis to determine the desired head size 510. 5 Referring now to the schematic flow diagram Fig. 33, the method 2750 of analysing the scanned image in the second embodiment to determine the head size 510 is described. The method 2750 begins at step 3310 where an affine transform between the coordinates of the measurement chart 1900 and the coordinates of the scanned image is 10 obtained. This is accomplished according to the method of step 2510 of the method 1850 described previously for the first embodiment. [Define T, H and D vectors] Fig. 34 shows an enlargement of a region of Fig. 32, with additional arrows 15 drawn. Each arrow represents a displacement vector from the centre point of one patch to the centre point of the other patch. For the purposes of the following discussion, three different types of displacement vectors, namely H-vectors, D-vectors and T-vectors are defined. The arrow 3410 represents a H-vector from the patch labelled "2,A" to the patch 20 labelled "2,B". H-vectors correspond to the displacement between an "A" patch and a "B" patch printed at the same time and thus correspond to the head size 510. There are seven H-vectors shown in Fig. 34, specifically, the displacement vectors: (1) from "1,A" to "1,B"; (2) from "2,A" to "2,B"; (3) from "3,A" to "3,B"; (4) from "4,A" to "4,B"; (5) from "5,A" to "5,B"; (6) from "6,A" to "6,B"; and (7) from "7,A" to "7, B". 883310(1879165_1) -48 The arrow 3420 represents a D-vector from the patch labelled "5,B" to the patch labelled "6,A". There are six D-vectors shown in Fig. 34, specifically, the displacement vectors: (1) from "1,B" to "2,A"; (2) from "2,B" to "3,A"; (3) from "3,B" to "4,A"; (4) from "4,B" to "5,A"; (5) from "5,B" to "6,A"; and (6) from "6,B" to "7,A". The vertical 5 component of each D-vector is related to the head size and the distance of the print medium 230 advance between print passages. The arrow 3430 represents a T-vector from the patch labelled "1,A" to the patch labelled "7,B". A T-vector represents the total displacement between the "A" patch in the first passage to the corresponding "B" patch in the last passage. There is one T 10 vector shown in Fig. 34. Let the term "measurement chain" refer to a set of H-vectors, D-vectors and a T vector such that the destination patch of the T-vector could be reached from the origin patch of the T-vector by successively following the chain of H-vectors and D-vectors. For example, the H-vectors, the D-vectors and the T-vector in Fig. 34 form one 15 measurement chain. If T is the T-vector, H is i-th of NH H-vectors and Di is the i-th of ND D-vectors in a measurement chain, then by the rule of vector addition, the equation in Formula (26) holds for every measurement chain. N,, ND T=ZH, +ED, (26) i=1 i=1 In the example of Fig. 34, NH=7 and ND=6. 20 Rearranging Formula (26), yields Formula (27): 1 N,, I N, ZH,= (T -ED,) (27) N NH i=1 883310(1879165_1) -49 Formula (27) implies that the average of the H-vectors (and thus the average head size) may be calculated from the T-vector and the D-vectors. Let the average head size 510 thus determined be denoted "HC". Rewriting Formula (27), HC may be determined according to Formula (28), below: 1 ND 5 HC= (T - D;) (28) NH In general, for a given measurement chart, numerous combinations of a T vector, H-vectors and D-vectors exist that form a measurement chain. Fig. 35 illustrates one example of possible selections. The H-vectors, e.g. 3510, and D-vectors, e.g. 3520, are represented with lines. The patches used in the T-vectors, e.g. 3530, are circled. 10 There are four measurement chains shown in Fig. 35. Referring again to Fig. 33, after obtaining the location of each patch 3340, the next steps are to calculate the T-vectors 3350, and the D-vectors 3360. [Measure the T-vectors and D-vectors] 15 Referring again to Fig. 33, the next step 3320 of the method 2750 calculates the T-vectors. This is accomplished according to the method of steps 2520 and 2530 of method 1850 described previously, except that instead of analysing a pair of "A" and "B" patches separated by one head distance, the origin and destination patches of the T-vector are 20 used, for example, patches "1,A" and "7,B", respectively in Fig. 34. At the next step 3330, the D-vectors are calculated. These vectors may be calculated using a similar method to that employed in the previous step 3320. 883310(1879165_1) -50 Alternatively, these vectors may be calculated using the correlation method of step 2520 of method 1850 and scaling the resulting vector using the known scanned image resolution. The use of a simple correlation technique is possible because the print medium 5 advance for the head size measurement chart 2800 is carefully chosen so that the vertical component of a D-vector (in the same direction as the head size) is expected to be close to zero and thus less sensitive to scaling errors. This component is more significant for the final result than the horizontal component. As a result, typically the D-vectors can be calculated much faster and possibly more accurately without using the reference pattern 10 720. If the D-vectors are calculated without using reference pattern 720, the reference pattern 720 is only needed for the calculation of the T-vectors. In this case, the special pattern 750 can be omitted in other regions. Fig. 7b shows an example of such a two dimensional pattern glass 710. 15 [Calculate the head size] In step 3340 of Fig. 33, the head size is calculated. The average head size for each measurement chain is calculated according to Formula (28), above. In this embodiment, the final head size measured from the measurement chart is 20 calculated as the average of the head sizes calculated from each measurement chain, according to Formula (29), as follows: 1 N, head size =- EHC, (29) N, i= where Nc is the number of measurement chains. In the example of Fig. 35, Nc=4. 883310(1879165_1) -51 [Other selections of H, D, T vectors] Fig. 35 illustrated one example of a possible selection of the measurement chains. Some examples of alternative selections are shown in Fig. 36. As before, the D 5 vectors and H-vectors are represented as lines and the patches used in the T-vectors are circled. Referring to the measurement chains 3610, the selection of D-vectors is not limited to one side. D-vectors can be on the either side as shown. More than one measurement chain can be defined for a single T-vector. The group labelled 3620 can be 10 understood as two overlapped measurement chains. Referring to the measurement chain 3630, a measurement chain need not start from the first print passage, and/or need not finish at the last print passage. When some measurement chains of a measurement chart are longer/shorter, or when the measurement chain overlaps, a weighted average may be used to calculate the 15 desired head size 510. [Printer characteristics of inkjet printers] Fig. 37 is a schematic flow diagram illustrating a method 3700 for accurately measuring many different types of printer characteristics. 20 The method 3700 begins at step 3710, where a printer characteristics measurement chart is printed. The design of the chart and the chart printing process are described in detailed below. In step 3720, the two-dimensional pattern glass is placed on the measurement surface 610 as described previously for the step 910 of the method 900. 883310(1879165_1) -52 In the following step 3730, the printer characteristics measurement chart is placed on the two-dimensional pattern glass as described above for the step 920 of the method 900. In step 3740, the scanned image is acquired as described for the step 930 above. 5 In step 3750, the measurement chart affine transform is obtained. The chart orientation is calculated as described for step 2510 above. In step 3760, the patches in the scanned image are located as described above for the step 2520 of Fig. 25. In the next step 3770, the accurate coordinates of the patches are calculated as 10 described for step 2530 of Fig. 25. In step 3780, the scanned image is processed to determine the printer characteristics. This step is described in detail below. The method 3700 then ends. As is illustrated in Fig. 38, the printer characteristics determined in method 3700 may be grouped as follows: line feed distance 3810, horizontal alignment 3820, and head 15 tilt measurement 3830. The horizontal alignment 3820 may further be categorized into the inter-nozzle alignment 3840 and uni-directional and bi-directional carriage alignment 3850. For each printer characteristic, the design of the chart, the printing and the processing are different. Each is described separately in detail below. The head size and all the above-mentioned printer characteristics, or any subset thereof, can be measured in 20 one chart. [Embodiment 3 - Measure long line feed] 883310(1879165_1) -53 Fig. 39 shows an implementation of the printer's line feed distance characteristic measurement chart. The chart has four LRHF spiral registration marks 1910, 1920, 1930 and 1940 and at least two patches 3950, described below. The printer line feed distance is a measure of how far the print medium is 5 advanced by the line feed mechanism of the ink jet printer 115. The patches labelled 1 are printed in one passage of the print head. The patches labelled 2 are printed by another passage, which is separated by an advance of the print medium 3960. The patches labelled A are printed by a set of nozzles, for example, the nozzle group 520 in Fig. 5. Referring back to Fig. 37, following the step 3710 of printing a printer 10 characteristic measurement chart as illustrated in Fig. 39, the following steps 3720, 3730, 3740, 3750, 3760, and 3770 are the same as the steps 920, 930, 940, 2510, 2520 and 2530, respectively, described previously. In the final step 3780 of the method 3700, the accurate patch coordinates determined in the previous step 3770 are used to determine the desired line feed values. 15 Let P(r, c) denote the accurate patch coordinate calculated in step 3770 for the patch in row r and column c of the measurement chart in Fig. 39 and let LF(r) denote the rth line feed distance. Then LF(r) may be calculated according to Formula (30), as follows: LF(r) = IIP(r, c) - P(r + 1, c)| , (30) Nc= 20 Where Nc denotes the number of columns, and 11.11 denotes a two-dimensional distance function, also known as a L2 norm. A line feed value calculated according to the method described above may be affected by the horizontal alignment of the patches. In the case where there are at least 883310(1879165_1) -54 two columns, an alternative way to calculate the line feed distance independently of the horizontal alignment is described hereinafter. Let BFL(r) denote the line of best fit for the points {P(r, c): c = I to Nc}. Let PLD(p, 1) denote the closest distance of a point p to a line 1. Then the line feed may be 5 calculated according to Formula (31), below: I Nc LF(r)= -JPLD(P(r, c), BFL(r +1)). (31) Ncl [Embodiment 4 - Measure short line feed] The line feed measurement chart described in Fig. 39 is suitable for measuring a 10 line feed distance that is larger than the height of a patch. Fig. 40 describes a line feed measurement chart suitable for measuring line feed distance shorter than a patch. The chart has four LRHF spiral registration marks 1910, 1920, 1930 and 1940and at least two patches 4050, described below. The printer line feed distance is a measure of how far the print medium is 15 advanced by the line feed mechanism of the ink jet printer 115. The patches labelled 1 are printed in one passage of the print head. The patches labelled 2 are printed by another passage, which is separated by an advance of the print medium 4060. The patches labelled A are printed by a set of nozzles, for example, the nozzle group 520 in Fig. 5. Referring back to Fig. 37, following the step 3710 of printing a printer 20 characteristic measurement chart as illustrated in Fig. 40, the following steps 3720, 3730, 3740, 3750, 3760, and 3770 are the same as the steps 920, 930, 940, 2510, 2520 and 2530, respectively, described previously. In the final step 3780 of the method 3700, the 883310(1879165_1) -55 accurate patch coordinates determined in the previous step 3770 are used to determine the desired line feed values. Let P(rc) denote the accurate patch coordinate calculated in step 3770 for the cth patch printed in passage r of the measurement chart in Fig. 40. One way to calculate the 5 line feed is to project P(rc) and P(r+1,c) onto the medium advance direction, and calculate the distance of projected points. The steps involved are: (1) Calculate the accurate coordinates of the spirals as described in step 1500; (2) Calculate the best fit vertical line of the four spirals; (3) Calculate the rth line feed distance, denoted by LF(r) according to Formula 10 (32) below: LF(r) = I PP(r, c) - PP(r + 1, c)1 (32) NC c=1 where PP(rc) denotes the coordinate of the point P(rc) projected onto the best fit vertical line; Nc denotes the number of printed patches per row; and 11.11 denotes a two dimensional distance function, also known as a L2 norm. 15 In the case where there are at least two patches printed per row, an alternative way to calculate the line feed distance is described hereinafter. Let BFL(r) denote the line of best fit for the points {P(r, c): c = I to Nc}. Let PLD(p, 1) denote the closest distance of a point p to a line 1. The line feed may be calculated according to Formula (33), below: 20 LF(r) = - E PLD(P(r, c), BFL(r + 1)) (33) Nc c= 883310(1879165_1) -56 [Embodiment 5 - Measure head tilt] Fig. 41 shows an implementation of the printer's head tilt characteristic measurement chart. The chart has four LRHF spiral registration marks 1910, 1920, 1930 and 1940and at least two patches 4150, described below. 5 The patches labelled 1 are printed in one passage. The patches labelled A are printed by a first set of nozzles, for example, the nozzle group 520 in Fig. 5. Patches labelled B are printed by a different set of nozzles, for example, the nozzle group 530 in Fig. 5, with both nozzle groups in the same nozzle bank. Head tilt 4160 refers to the angle between the actual direction 4170 of the nozzle 10 banks and the designed direction 4180 of the nozzle banks, which is perpendicular to the direction of the print passage. Without loss of generality, the angle is defined positive when the head is tilted clockwise and negative for an anti-clockwise tilt. Referring back to Fig. 37, following the step 3710 of printing a printer 15 characteristic measurement chart as illustrated in Fig. 41, the following steps 3720, 3730, 3740, 3750, 3760, and 3770 are the same as the steps 920, 930, 940, 2510, 2520 and 2530, respectively, described previously. In step 3780, the accurate patch coordinates determined in the previous step 3770 are used to determine the desired head tilt values. Let A(r,c) denote the accurate patch coordinate calculated in step 3770 for the cth 20 A-patch printed in passage r of the measurement chart in Fig. 41. Let B(rc) denote the accurate patch coordinate calculated in step 3770 for the cth B-patch printed in passage r of the measurement chart in Fig. 41. Let L(rc) be a straight line that goes through A(r,c) and B(r,c). Let AngleBetween(L1, L2) denote a function that calculates the acute angle in radians from the line L1 to the line L2. The angle is defined to be positive when the 883310(1879165_1) -57 angle is clockwise and negative when the angle anti-clockwise. The head tilt may be calculated according to the following steps: (1) Calculate the accurate coordinates of the spirals as described in step 1500; (2) Calculate the best fit vertical line of the coordinates of the four spirals, 5 denoted BFVL; (3) Calculate the head tilt, denoted HT, according to Formula (34) below: 1 1 Nc NR HT =- AngleBetween(BFVL,L(r,c)), (34) NC NR c=I r=I where Nc and NR denotes the number of columns and the number of passages. If there are at least two columns, an alternative way to calculate the head tilt is 10 described hereinafter. Let BFL(r) denote the line of best fit for the points {A(r, c): c = 1 to Nc). The Head tilt (H) may be calculated according to Formula (35) below: 1 i Nc Nr I HT =(-AngieBetween(BFL(r), L(r, c))) - -. (35) NC N c=1 r=1 2 15 [Embodiment 6 - inter-nozzle alignment] Fig. 42 shows an implementation of a printer inter-nozzle alignment characteristic measurement chart. The chart has four LRHF spiral registration marks 1910, 1920, 1930 and 1940 and at least two patches 4250, described below. The patches labelled 1 are printed in one passage. The patches labelled A are 20 printed by a first set of nozzles, for example, the nozzle group 520 in Fig. 5. Patches labelled B are printed by a different set of nozzles, for example, the nozzle group 530 in 883310(1879165_1) -58 Fig. 5, where with both nozzle groups are in the same nozzle bank. Patches labelled C are printed by yet another set of nozzles by a different nozzle bank and are separated from the nozzles used to print the patches labelled A and B. Inter-nozzle alignment distance 4260 refers to the distance, in the carriage scan direction, required to align 5 separate nozzle banks in the print head. Referring back to Fig. 37, following the step 3710 of printing a printer characteristic measurement chart as illustrated in Fig. 42, the following steps 3720, 3730, 3740, 3750, 3760, and 3770 are the same as the steps 920, 930, 940, 2510, 2520 and 2530, respectively, described previously. In step 3780, the accurate patch coordinates 10 determined in the previous step 3770 are used to determine the desired inter-nozzle alignment distance. Let A(rc) denote the accurate patch coordinate calculated in step 3770 for the cth A-patch printed in passage r of the measurement chart in Fig. 42. Let B(rc), C(rc) be similarly defined for the B-patches and C-patches. 15 Fig. 43 illustrates the geometric relation between A(r,c), B(r,c), C(r,c), the head tilt angle 4160 and the inter-nozzle alignment distance 4260. The calculation of the head tilt angle is previously described. Fig. 43 illustrates three examples. With the given coordinates of the point A, B and C, and the head tilt angle 4160, the inter-nozzle alignment distance 4260 is calculated by coordinate geometry. Let X(r, c) denote the 20 inter-nozzle alignment distance calculated in passage r and column c. The inter-nozzle alignment distance (INAD) of the entire measurement chart may be calculated according to Formula (36) below: I 1 NC NR INAD = N - N 1 X(r,c) (36) NC NR c=1 r=1 883310(1879165_1) -59 [Embodiment 7 - Bi-directional and uni-directional carriage alignment] Fig. 44 shows an implementation of a printer carriage alignment characteristic measurement chart. This chart may be used for both bi-directional and uni-directional 5 carriage alignment. The difference being the carriage passage direction in which the particular patches are printed. The chart has four LRHF spiral registration marks 1910, 1920, 1930 and 1940and at least two patches 4450, described below. The patches labelled 1 are printed in one passage. The patches labelled 2 are printed by another passage with no advance in the print medium. The patches labelled A 10 are printed by a first set of nozzles, for example, the nozzle group 520 in Fig. 5. The patches labelled B are printed by a different set of nozzles, for example, the nozzle group 530 in Fig. 5. Patches labelled C are printed by yet another set of nozzles and are separated from the nozzles used to print the patches labelled A and B. All the patches in Fig. 44 are printed by the same nozzle bank. 15 For uni-directional alignment, all the patches in Fig. 44 are printed in the same carriage passage direction, for example, the default forward direction. For bi-directional alignment, the patches labelled 1 and the patches labelled 2 are printed in different direction, for example the forward direction, and the backward direction. The carriage alignment distance 4460 refers to the distance, in the carriage scan direction, required to 20 align the patches printed in different print passage. Referring back to Fig. 37, following the step 3710 of printing a printer characteristic measurement chart as illustrated in Fig. 44, the following steps 3720, 3730, 3740, 3750, 3760, and 3770 are the same as the steps 920, 930, 940, 2510, 2520 and 2530, respectively, described previously. In step 3780 of the method 3700, the accurate 883310(1879165_1) -60 patch coordinates determined in the previous step 3770 are used to determine the desired inter-nozzle alignment distance. Let A(r,c) denotes the accurate patch coordinate calculated in step 3770 for the cth A-patch printed in passage r of the measurement chart in Fig. 43. Let B(rc), C(rc) be 5 similarly defined for the B-patches and C-patches. Fig. 45 illustrates the geometric relation between A(r,c), B(r, c), C(r,c), the head tile angle 4160 and the carriage alignment distance 4460. The calculation of the head tilt angle is previously described. Fig. 45 illustrates three examples. With the given coordinates of the point A, B and C, and the head tilt angle 4160, the carriage alignment 10 distance 4460 is calculated by coordinate geometry, for example. Let X(rc) denotes the carriage alignment distance calculated in passage r and column c. The carriage alignment distance (CAD) of the entire measurement chart may be calculated according to Formula (37) below: CAD = N N 1 1 X(r,c) (37) C R c=1 r=1 15 Methods, apparatuses and computer program products have been disclosed for determining a head size of a print head of a printer. Methods, apparatuses and computer program products have also been disclosed for determining a spatial alignment characteristic of a printer. The foregoing describes only some embodiments of the 20 present invention, and modifications and/or changes can be made thereto without departing from the scope and spirit of the invention, the embodiments being illustrative and not restrictive. 883310(1879165_1) -61 In the context of this specification, the word "comprising" means "including principally but not necessarily solely" or "having" or "including", and not "consisting only of'. Variations of the word "comprising", such as "comprise" and "comprises" have correspondingly varied meanings. 5 883310(1879165_1)

Claims (16)

1. A method of determining a head size of a print head of a printer, said 5 method comprising the steps of: printing using a print head onto a print medium a test pattern comprising at least two patches with a predetermined relationship to said print head, said at least two patches each comprising a plurality of colourant dots arranged to form a spread spectral pattern; imaging at least a portion of said print medium with a two-dimensional reference 10 pattern superimposed with said test pattern printed on said print medium, said two dimensional reference pattern adapted to detect the location and orientation of said test pattern; locating in said image said at least two patches of said test pattern relative to said two-dimensional reference pattern; and 15 determining said head size from said at least two patch locations.

2. A method of determining a head size of a print head of a printer, said method comprising the steps of: printing using a print head onto a print medium a test pattern comprising a plurality of measurement patterns each having at least two patches with a predetermined 20 relationship to said print head, said at least two patches of a respective measurement pattern each comprising a plurality of colourant dots arranged to form a spread spectral pattern in one passage, each measurement pattern being separated from an adjacent measurement pattern by a print medium advance operation, a patch of the subsequent measurement pattern being located to minimise a distance measurement in a direction of 883310(1879165_1) -63 interest between said patch and one of said at least two patches of the previous measurement pattern; imaging at least a portion of said print medium with a two-dimensional reference pattern superimposed with said test pattern printed on said print medium, said two 5 dimensional reference pattern adapted to detect the location and orientation of said test pattern; calculating said minimised distance measurement; locating in said image a patch from one passage and another patch from another passage relative to said two-dimensional reference pattern; and 10 determining said head size from said patch locations of said measurement patterns and said minimised distance measurement.

3. The method according to claim 1 or 2, further comprising the steps of statistically combining head sizes to provide an overall spatial alignment characteristic dependent upon printing multiple measurement patterns on said print medium and 15 calculating multiple head sizes.

4. A method of determining a spatial alignment characteristic of a printer, the method comprising the steps of: printing using a print head onto said print medium a test pattern comprising a plurality of patches at predetermined measurement points, said patches each comprising a 20 plurality of colourant dots arranged to form a spread spectral pattern; imaging at least a portion of said print medium with a two-dimensional reference pattern superimposed with said test pattern printed on said print medium, said two dimensional reference pattern adapted to detect the location and orientation of said test pattern; 883310(1879165_1) -64 locating in the image said at least two patches relative to said two-dimensional reference pattern; and determining a spatial alignment characteristic from said at least two patch locations.

5 5. The method according to claim 4, wherein said test pattern comprises patches printed in different print passages of said print head.

6. The method according to claim 4, wherein said test pattern comprises two patches, one patch printed vertically above the other patch on said print medium in the same print passage. 10

7. The method according to claim 4, wherein said test pattern comprises three patches, two patches being printed by a nozzle bank so that one of the two patches is located vertically above the other of the two patches, and the remaining patch of said three patches being printed in the middle by a different nozzle bank, all patches being printed in the same passage. 15

8. The method according to claim 4, wherein said test pattern comprises three patches, two patches being printed by a nozzle bank so that one of the two patches is located vertically above the other of the two patches, and the remaining patch of said three patches being printed in the middle with a different passage without advance of said print medium. 20

9. The method according to claim 1, 2 or 4, wherein said locating step comprises: extracting a region of said image to be analysed; calculating a simulated region corresponding to said extracted region of said image dependent upon simulation parameters; 883310(1879165_1) -65 correcting an affine transformation for coarse alignment dependent upon a shift between said extracted region and said simulated region; refining said simulation parameters dependent upon said shift; and determining reference pattern coordinates dependent upon said refined simulation 5 parameters.

10. The method according to claim 9, further comprising the step of applying a mask to region to be extracted to neglect one or more portions of said region.

11. The method according to claim 1, 2 or 4, wherein said two-dimensional reference pattern comprises at least two registration marks for determining a location 10 approximately and at least one special pattern for determining a location accurately.

12. The method according to claim 11, wherein: said at least two registration marks each comprise a spiral mark, and said at least one special pattern each comprises a two-dimensional pseudo-random noise pattern having a predetermined marking density with each marking having a 15 predetermined size and shape.

13. The method according to any one of the preceding claims, wherein a transparent substrate with low coefficient of thermal expansion embodies said two dimensional reference pattern.

14. The method according to claim 13, wherein said transparent substrate 20 embodying said two-dimensional reference pattern comprises a glass substrate formed with chrome particles on or in said glass substrate.

15. An apparatus, comprising: a memory for storing data and instructions for a central processing unit; 883310(1879165_1) -66 a central processing unit coupled to said memory, said central processing unit performing the method according to any one of claims 1 -14 dependent upon said instructions and said data.

16. A computer program product comprising a tangible computer readable 5 medium having a computer program recorded for execution by a computer to perform the method according to any one of claims 1 -14. Dated this Seventeenth day of December 2008 CANON KABUSHIKI KAISHA 10 Patent Attorneys for the Applicant SPRUSON&FERGUSON 883310(1879165_1)