Abstract:
An optical system including a plurality of selectably directable mirrors ( 38 ) each arranged to direct a laser beam ( 41 ) to a selectable location within a field, a plurality of mirror orientation sensors ( 45 ) operative to sense the orientation of the plurality of selectably directable mirrors and to provide mirror orientation outputs and an automatic calibration subsystem ( 47 ) for automatically calibrating the plurality of selectably directable mirrors, the automatic calibration subsystem including a target ( 40 ) being operative to provide an optically visible indication of impingement of a laser beam thereon; the target being rewritable and having optically visible fiducial markings ( 54, 56 ), a target positioner ( 42 ) for selectably positioning the target, an optical sensor ( 44 ) operative to view the target following impingement of the laser beam thereon and to provide laser beam impingement outputs and a correlator ( 36 ) operative to provide a calibration output.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a National Stage of International Application No. PCT/IL2009/000041 filed Jan. 11, 2009, claiming priority based on U.S. Patent Application No. 61/020,273 filed Jan. 10, 2008, the contents of all of which are incorporated herein by reference in their entirety. 
     Reference is made to U.S. Provisional Patent Application Ser. No. 61/202,273, filed Jan. 10, 2008 and entitled Multiple Laser Beam Positioning and Energy Delivery System, the disclosure of which is hereby incorporated by reference and priority of which is hereby claimed pursuant to 37 CFR 1.78(a) (4) and (5)(i). 
     This application is related to the PCT Patent Application titled “Multiple Beam Drilling System,” filed on even date, which is assigned to the assignee of the present invention and which is also incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The present invention relates generally to apparatus calibration, and specifically to calibration of multiple steering mirrors used to direct laser beams. 
     BACKGROUND OF THE INVENTION 
     For a number of years laser beams have been used in fabrication systems, operating on an object such as a substrate, for such purposes as drilling, fusion, or ablation of the object. In order to reduce the time of fabrication, the systems may use multiple laser beams, and the requirements for the accuracy of such multi-beam systems is constantly increasing. 
     U.S. Pat. No. 6,615,099 to Müller et al., whose disclosure is incorporated herein by reference, describes a process for calibrating a laser processing machine, operating using a “deflection device.” The process first generates an image of a calibration plate to determine imaging errors caused by the deflection device. The calibration plate is replaced by a test plate, upon which a test pattern is written and measured to determine an optical offset. Workpieces are processed in the machine by compensating for the imaging errors and the optical offset. 
     SUMMARY OF THE INVENTION 
     The present invention provides an improved system and method for calibration of multiple mirrors used to direct a laser beam. 
     There is thus provided in accordance with a preferred embodiment of the present invention an optical system including a plurality of selectably directable mirrors each arranged to direct a laser beam to a selectable location within a field, a plurality of mirror orientation sensors operative to sense the orientation of the plurality of selectably directable mirrors and to provide mirror orientation outputs and an automatic calibration subsystem for automatically calibrating the plurality of selectably directable mirrors, the automatic calibration subsystem including a target having an area at least as large as the field of each of the selectably directable mirrors and being operative to provide an optically visible indication of impingement of a laser beam thereon; the target being rewritable and having optically visible fiducial markings, a target positioner for selectably positioning the target in the fields of respective ones of the selectably directable mirrors while each respective one of the selectably directable mirrors directs the laser beam to a selectable location thereon, an optical sensor operative to view the target following impingement of the laser beam thereon and to provide laser beam impingement outputs and a correlator operative in response to the mirror orientation outputs and the laser beam impingement outputs to provide a calibration output. 
     In accordance with a preferred embodiment of the present invention the optical system may be operative in a calibration phase and in a production phase. 
     Preferably, the calibration phase includes orienting each of the plurality of mirrors in a first orientation, using the plurality of sensors to sense the first orientation of each of the plurality of mirrors and to provide a plurality of mirror orientation outputs, fixing the target to the target positioner, for each one of the plurality of selectably directable mirrors selectably positioning the target, by positioning the target positioner, in the field of the one of the plurality of selectably directable mirrors while the one of the plurality of selectably directable mirrors directs the laser beam to a selectable location thereon, generating laser beam impingement markings thereon, viewing the target following impingement of the laser beam thereon and providing laser beam impingement outputs for the one of the plurality of selectably directable mirrors and erasing the laser beam impingement markings and correlating the plurality of mirror orientation outputs and the laser beam impingement outputs to provide a calibration output for each of the plurality of selectably directable mirrors. 
     Alternatively, the calibration phase includes orienting each of the plurality of mirrors in a first orientation, using the plurality of sensors to sense the first orientation of each of the plurality of mirrors and to provide a plurality of mirror orientation outputs, fixing the target to the target positioner, selectably positioning the target, by positioning the target positioner, in the fields of respective ones of the plurality of selectably directable mirrors while each respective one of the plurality of selectably directable mirrors directs the laser beam to a selectable location thereon, viewing the target following impingement of the laser beam thereon and providing laser beam impingement outputs and correlating the plurality of mirror orientation outputs and the laser beam impingement outputs to provide a calibration output for each of the plurality of selectably directable mirrors. 
     Preferably, the production phase includes at least one of a laser drilling phase, a laser ablation phase and a laser machining phase. 
     In accordance with a preferred embodiment of the present invention the target includes a substrate, a photochromic layer formed on an upper surface of the substrate, a transparent layer overlaid on the photochromic layer, a metallic layer formed on a lower surface of the substrate and a thermoelectric cooler coupled to a lower surface of the metallic layer. Additionally, the visible fiducial markings are formed within the photochromic layer. 
     Preferably, the optical system also includes a plurality of adjustable mirror mounts including the plurality of mirror orientation sensors. Additionally, each of the plurality of mirror mounts has two degrees of rotational freedom. Additionally or alternatively, the plurality of mirror mounts include galvanometric motors to which the plurality of mirrors are attached. 
     In accordance with a preferred embodiment of the present invention the optical system also includes a laser generating the laser beam. 
     There is also provided in accordance with another preferred embodiment of the present invention a method for calibrating a plurality of selectably directable mirrors arranged to direct a laser beam to a selectable location within a field, the method including orienting each of the plurality of mirrors in a first orientation, sensing the first orientation of each of the plurality of mirrors and providing a plurality of mirror orientation outputs, fixing a target to a target positioner, the target having an area at least as large as the field of each of the plurality of selectably directable mirrors and being operative to provide an optically visible indication of impingement of a laser beam thereon, the target being rewritable and having optically visible fiducial markings, for each one of the plurality of selectably directable mirrors selectably positioning the target, by positioning the target positioner, in the field of the one of the plurality of selectably directable mirrors while the one of the plurality of selectably directable mirrors directs the laser beam to a selectable location thereon, generating laser beam impingement markings thereon, viewing the target following impingement of the laser beam thereon and providing laser beam impingement outputs for the one of the plurality of selectably directable mirrors and erasing the laser beam impingement markings and correlating the plurality of mirror orientation outputs and the laser beam impingement outputs to provide a calibration output for each of the plurality of selectably directable mirrors. 
     Preferably, the method also includes, for each one of the plurality of selectably directable mirrors, cooling the target subsequent to the erasing. 
     There is also provided in accordance with another preferred embodiment of the present invention a method for calibrating a plurality of selectably directable mirrors arranged to direct a laser beam to a selectable location within a field, the method including orienting each of the plurality of mirrors in a first orientation, sensing the first orientation of each of the plurality of mirrors and providing a plurality of mirror orientation outputs, fixing a target to a target positioner, the target having an area at least as large as the field of each of the plurality of selectably directable mirrors and being operative to provide an optically visible indication of impingement of a laser beam thereon, the target being rewritable and having optically visible fiducial markings, selectably positioning the target, by positioning the target positioner, in the fields of respective ones of the plurality of selectably directable mirrors while each respective one of the plurality of selectably directable mirrors directs the laser beam to a selectable location thereon, viewing the target following impingement of the laser beam thereon and providing laser beam impingement outputs and correlating the plurality of mirror orientation outputs and the laser beam impingement outputs to provide a calibration output for each of the plurality of selectably directable mirrors. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings, a brief description of which follows. 
         FIG. 1  is a simplified schematic diagram of a mirror calibration apparatus, according to an embodiment of the present invention; 
         FIGS. 2A and 2B  are simplified schematic diagrams of a target used in the apparatus, according to an embodiment of the present invention; 
         FIG. 3  is a simplified schematic diagram of different stages of operation of the apparatus in a first mode of calibration, according to an embodiment of the present invention; 
         FIG. 4  is a simplified schematic diagram of the target showing markings, according to an embodiment of the present invention; 
         FIG. 5  is a simplified flowchart showing steps performed by a processing unit of the apparatus in generating calibration tables or equations, according to an embodiment of the present invention; 
         FIG. 6  is a simplified schematic diagram illustrating a second calibration mode of the apparatus, according to embodiments of the present invention; and 
         FIG. 7  is a simplified flowchart of steps performed by the processing unit to implement the second mode, according to embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Reference is now made to  FIG. 1 , which is a simplified schematic diagram of a mirror calibration apparatus  20 , according to an embodiment of the present invention. Apparatus  20  comprises an optical system which is under the overall control of a processing unit  36 , and which is typically operated by a human controller of the apparatus. 
     Processing unit  36  typically comprises a general-purpose computer processor, which is programmed in software to carry out functions that are described herein. The software may be downloaded to the processor in electronic form, over a network, for example. Alternatively or additionally, the software may be provided on tangible media, such as optical, magnetic, or electronic storage media. Further alternatively, at least some of the functions of the processor may be carried out by dedicated or programmable hardware. 
     Apparatus  20  comprises a set of selectably directable mirrors  38 , the orientation of each of the directable mirrors being individually controlled by instructions generated by processing unit  36 , the instructions enabling the processing unit to select each mirror to be oriented. The directable mirrors are also herein termed orientable mirrors, and act as steering mirrors for beams which impinge upon them. Apparatus  20  includes an optical sensor  44 , herein assumed to comprise a camera, which is used as part of an automatic calibration subsystem  47  of the apparatus to calibrate the orientation of each of the mirrors. In addition to sensor  44 , also referred to herein as camera  44 , the elements of subsystem  47  comprise a movable table  42 , a rewritable target  40 , and processing unit  36  acting as a correlator. The functions of the elements of automatic calibration subsystem  47  are described in more detail below. 
     Typically, once the mirrors have been calibrated, camera  44  is not required in the apparatus, and the camera may be removed. Alternatively, the camera may be left in position. Once the orientable mirrors have been calibrated, apparatus  20  may be used as a laser drilling facility  21 , wherein the multiple orientable mirrors are used to direct respective laser sub-beams to drill multiple holes in a material (not shown in  FIG. 1 ) mounted on movable table  42 , in a production phase of the apparatus. In addition to drilling, it will be understood that in the production phase facility  21  may be used for operations similar to drilling, such as ablation and/or machining of material. Consequently, as will be apparent from the description below, some elements of apparatus  20  perform a dual function, a first function corresponding to the elements being used to calibrate orientable mirrors  38  during a calibration phase of the apparatus, a second function corresponding to the elements being used for laser drilling in the production phase of the apparatus. As is also described below, the calibration phase of apparatus  20  may be implemented in a number of different modes. 
     Apparatus  20  comprises a laser  22 , which is typically a solid-state laser generating a single laser beam  24  of pulses at an ultra-violet wavelength. The parameters of the beam are set according to instructions received from processing unit  36 . In one embodiment of the present invention, the beam comprises approximately 30 ns pulses produced at a repetition rate of approximately 100 kHz, each pulse having an energy of the order of 100 μJ, so that an average power of the beam is approximately 10 W. Beam  24  passes through a cylindrical lens  26 , which focuses the beam to a substantially collimated beam that is transmitted to an acousto-optic deflector (AOD)  28 . Approximately the full energy of the laser pulses may be used in the production phase. In the calibration phase described herein, the laser pulse energy is typically reduced sufficiently to avoid damage to the target. 
     AOD  28  receives radio-frequency (RF) driving input from processing unit  36 , the RF input causing the incident collimated laser beam to be diffracted into one or more sub-beams  29 . Sub-beams  29  are typically generated to be in a two-dimensional plane. Processing unit  36  may select the number of the sub-beams, and the distribution of energy between the sub-beams, by varying parameters of the RF input into AOD  28 . An AOD which may be used in embodiments of the present invention is the part MQ180-A0,2-UV produced by AA Optoelectronic of Saint-Rémy-Lès-Chevreuse, France. 
     Sub-beams  29  are transferred by a relay lens  30  to a first set of mirrors  32 . Mirrors  32  are oriented to reflect their respective incident beams, as a three-dimensional set of sub-beams  41 , to a second set of mirrors  34 . For clarity, in  FIG. 1  only a path  39  of one of the three-dimensional set of sub-beams is shown. In the following description, each sub-beam of set  41  is distinguished, as required, by a letter suffix. Thus, if as illustrated in  FIG. 1  there are twenty mirrors  34  and twenty mirrors  38 , set  41  comprises sub-beams  41 A,  41 B, . . .  41 T. As appropriate, in the following description the corresponding letter is also appended to elements requiring differentiation. For example, sub-beam  41 B is initially generated from sub-beam  29 B, and sub-beam  41 B is then reflected by mirrors  32 B and  34 B, and is subsequently reflected by an orientable mirror  38 B. Mirrors  32  and  34  are typically fixed in position and orientation, and are configured so that the three-dimensional set of sub-beams reflected from mirrors  34  are generally parallel to each other. 
     The three-dimensional set of sub-beams reflected from mirrors  34  is transmitted to orientable mirrors  38 . Between mirrors  32 , mirrors  34 , and mirrors  38  are beam conditioning and relay optics, illustrated schematically for purposes of clarity in  FIG. 1  by a lens  35 . The beam conditioning and relay optics ensure that the sub-beams reflected by mirrors  38  are collimated and narrow. In the following description, the elements of apparatus  20  generating set  41  of sub-beams, i.e. elements  22 ,  26 ,  28 ,  30 ,  32 ,  34 , and  35 , are also referred to herein as a sub-beam generating system  33 . 
     Each mirror of set  38  is coupled to a respective steering assembly, herein termed an adjustable mount  43 , in a set of mounts. Each mount  43  of the set is individually controlled by processing unit  36 , which is able to direct the orientation of a specific mount, and thus the orientation of the mirror coupled to the mount, within limits according to characteristics of the mount. Each mount comprises a sensor  45  which senses the orientation of the mount, and thus the orientation of the mirror coupled to the mount, and the sensor provides a corresponding output to processing unit  36  so that the processing unit is aware of the orientation of the mount and its mirror. 
     Although not a requirement for embodiments of the present invention, for simplicity it is assumed herein, by way of example, that processing unit  36  may change the orientation of each mirror by generally the same overall solid angle. In addition, each mount is typically initially set so that its “null orientation,” i.e., the direction of the mount about which processing unit  36  changes its orientation, is approximately the same, and so that its respective reflected sub-beam is approximately orthogonal to movable table  42 . Each mount  43  is assumed, by way of example, to have two degrees of rotational freedom, and to be able to rotate its attached mirror by two independent angles, θ, φ, in respective orthogonal planes that intersect in the null orientation direction of the mirror. Typically, mounts  43  use galvanometric motors, to which are attached mirrors  38 , to implement the two-axis mirror steering required. 
     Table  42  may move, according to commands received from processing unit  36 , in orthogonal x, y, and z directions. In the calibration phase of apparatus  20  described herein, processing unit  36  typically configures beam generating system  33  to radiate only one sub-beam at a time onto rewritable target  40 , which is mounted on table  42 . As illustrated in an inset  48 , table  42  moves target  40  from position to position for each of mirrors  38 , each position of the target corresponding to a respective field of operation of a different mirror. 
     As explained above, each mirror  38  receives a respective sub-beam  41 . Each mirror  38  then reflects its respective sub-beam  41  according to the orientation of the mirror. Because of the different physical locations of the mirrors, while the null orientation for each mirror may be generally the same, the reflected sub-beam from each mirror  38  covers a different respective field of operation. 
       FIGS. 2A and 2B  are simplified schematic diagrams of target  40 , according to an embodiment of the present invention.  FIG. 2A  shows a top view of the target.  FIG. 2B  shows a partial cross-section of the target. The target is set to have an area at least as large as the field of operation of each of the mirrors at table  42 . The shape and dimensions of target  40  are typically chosen to be greater than the largest of such fields of operation. In the following description, target  40  is assumed, by way of example, to be circular, with an approximate diameter of 50 mm. 
     Target  40  is a multi-layered target constructed on a substrate  64 . Substrate  64  is typically a low thermal expansion material such as Zerodur™ glass, so that within operating temperatures of apparatus  20 , dimensions of the target, and of elements within the target, are substantially invariant. A metallic layer  66  is formed on the lower surface of substrate  64 , and a thermoelectric cooler  68  (TEC) is coupled to the lower surface of layer  66 . TEC  68  is used by processing unit  36  to heat and cool target  40  as required. 
     A photochromic layer  62  is formed on the upper surface of substrate  64 , and a protective transparent layer  60  is overlayed on photochromic layer  62 . Layer  60  protects the photochromic layer from photochemical deterioration, by minimizing the interaction of the photochromic layer with the oxygen of the air. The photochromic layer  62  is transparent to visible light, until irradiated with radiation from laser  22 . The radiation causes a photochromic reaction to occur at the regions of the photochromic material upon which the radiation impinges. The reaction renders the impinged regions substantially opaque in a specific spectral band, typically in the visible range of the spectrum and typically few tens of nm wide, so that the radiation effectively writes visible marks or indications on target  40  at the regions of impingement. 
     The photochromic layer  62  preserves the visible marks written on the target for a long enough time before the marks fade by thermal decay. The decay typically follows a simple Arrhenius law, where the decay rate is proportional to 
               exp   ⁡     (     -       E   a     kT       )       ,         
where E a  is the activation energy of the material, k is Boltzmann&#39;s constant, and T is the absolute temperature. Typically the decay time is designed to be hours. The marks can be erased by application of a moderate amount of heat to the target, using TEC  68 , the consequent elevated temperature increasing the decay rate significantly. After erasure of the marks, the target is typically then cooled by TEC  68  so that it is able to be rewritten with new visible marks by another irradiation of the target. Cooling is typically required to preserve the long life-time of the marks, as indicated above.
 
     Fiducial marks  50 F, are also formed on target  40 , and are used as described below. Typically, fiducial marks  50 F are formed by overlaying a metal, such as chromium, on the upper surface of substrate  64  and within photochromic layer  62 . An example of the structure of the fiducial marks within target  40  is shown in  FIG. 2B , wherein fiducial marks  54 ,  56 , included in marks  50 F, are shown in cross-section. 
     Target  40  is configured so that both the fiducial marks and the marks written in the photochromic layer may have a high contrast, as measured with respect to their immediate surroundings. The examining radiation used by sensor  44  is typically selected so as to generate the high contrast. High contrast of the marks is typically achieved by using an LED illumination with its peak emission wavelength at or near the peak of the photochromic material absorption band in its colored form. Substrate  64  is typically configured to be generally diffusive, so as to ensure the high contrast. 
       FIG. 3  is a simplified schematic diagram of different stages of operation of apparatus  20  in a first mode of calibration, according to an embodiment of the present invention. In the first mode of calibration, table  42  acts as a target positioner by moving target  40  sequentially, so that in each position it includes the field of operation of each mirror  38 . For each mirror the target is irradiated by a sub-beam reflected from the mirror, which directs the sub-beam to a selectable location within the field of operation of the mirror. After all mirrors have been irradiated, table  42  moves the target out of the fields of operation of the mirrors, and into the field of view of sensor  44 . 
       FIG. 3  corresponds to inset  48  of  FIG. 1 , and shows target  40  as it is sequentially positioned by table  42  into four different positions P 1 , P 2 , P 3 , and P 4 . Each position corresponds to the field of operation of a different mirror, assumed by way of example to be the first four mirrors in the calibration sequence. The first four mirrors that are irradiated are assumed, by way of example, to be mirrors  38 G,  38 F,  38 P, and  38 Q, and are also referred to herein as mirrors M 1 , M 2 , M 3 , and M 4 . As required, in the following description a given mirror  38  may also be referred to herein as mirror Mn, where n is a positive integer. 
     When target  40  is in position P 1 , processing unit  36  activates sub-beam  41 G, typically with a reduced pulse energy as stated above, and ensures that the other sub-beams  41  are not activated. While sub-beam  41 G is activated, processing unit  36  rotates mirror M 1 , using its coupled mount  43 , into a small number of different known orientations a 1 , a 2 , . . . with respect to its incident sub-beam. It will be understood that each specific orientation is a combination of the two rotational angles θ, φ, of the mount  43  attached to mirror M 1 , so that orientation a 1  could be more fully written as an ordered pair (θ(a 1 ), (φ(a 1 )). However, except as necessary, for simplicity in the following description each orientation is represented by a letter and a subscript. 
     Herein it is assumed, by way of example, that the number of different known orientations is five, so that the different orientations comprise {a 1 , a 2 , . . . , a 5 }, also written as {α 1 }. For each orientation in {α 1 } the beam from M 1  is reflected at an angle to the z-axis and is in a plane containing the z-axis. Processing unit  36  maintains the mirror fixed for a period of time for each of the known different orientations, during which period target  40  is irradiated by the reflected sub-beam. The irradiation at the different orientations {a 1 , a 2 , . . . , a 5 } makes respective marks { 1 x 1 ,  1 x 2 , . . . ,  1 x 5 }, also written as { 1 X}, in layer  62  ( FIG. 2B ). Typically the orientations of {α 1 } are selected so that marks { 1 X} are approximately evenly distributed over the whole field of operation of mirror M 1 . Processing unit  36  selects the period of time to be as short as possible, but long enough so that the marks formed by the reflected sub-beam have sufficient contrast to be easily identified by sensor  44 . For the exemplary laser described above, a typical period of time allows approximately ten pulses for making each mark, so that the period is approximately 100 μs. 
     After marks { 1 X} have been made, processing unit  36  switches off sub-beam  41 G, and positions table  42  to locate target  40  into position P 2 , wherein the field of operation of mirror M 2  is encompassed by the target. When target  40  is in position P 2 , processing unit  36  activates sub-beam  41 F, and ensures that the other sub-beams  41  are not activated. While sub-beam  41 F is activated, processing unit  36  rotates mirror M 2  into a set of a small number of different known orientations, {α 2 }, with respect to its incident sub-beam. Typically, as assumed herein, the number of different orientations of set {α 2 } is the same as that of set {α 1 }. However, there is no necessity for the numbers to be the same, and in some embodiments the numbers may be different. 
     The orientations of set {α 2 } are selected so that marks { 2 x 1 ,  2 x 2 , . . . ,  2 x 5 }, also written as { 2 X}, made by the reflection of sub-beam  41 F onto target  40  are separated from marks { 1 X}. The separation is selected to be sufficient so that sensor  44  is able to distinguish each mark { 1 X} from each mark { 2 X}. Marks { 2 X} are formed in substantially the same manner as marks { 1 X}. After marks { 2 X} have been formed, processing unit  36  moves table  42  to position target  40  into position P 3 , wherein the target includes the field of operation of mirror M 3 , and then into position P 4 , wherein the target includes the field of operation of mirror M 4 . 
     Marks { 3 x 1 ,  3 x 2 , . . . ,  3 x 5 } for mirror M 3 , also written as { 3 X}, and marks { 4 x 1 ,  4 x 2 , . . . ,  4 x 5 } for mirror M 4 , also written as { 4 X}, are formed substantially as described above for marks { 1 X}, using sub-beams  41 P and  41 Q respectively. 
     In  FIG. 3 , for clarity each set of marks { 1 X}, [ 2 X}, { 3 X}, and { 4 X} is shown using the same symbol for a given set, but different symbols between sets. The shape of the actual marks made by the sub-beams is under the control of processing unit  36 . In some embodiments all marks, regardless of whether they are in the same set or in different sets, have substantially the same shape. For example, all marks may be effectively single points on target  40 , the point for a particular mark being formed by irradiation at the respective orientation, with the mirror not being moved during the irradiation. The points typically have diameters in a range between approximately 20 μm and approximately 70 μm. 
     Alternatively, in other embodiments, marks may be formed to have two or more different shapes. Marks having structure are formed as groups of single points, by processing unit  36  moving the mirror about its particular orientation so that the reflected sub-beam from the mirror forms a pre-defined pattern on the target. Examples of patterns that may be used include part of the sides and/or vertices of a triangle or a rectangle, but any other convenient pattern may also be used. Forming a mark as a group of points typically allows a more accurate determination of the position of points, and therefore a more accurate calibration of the mirrors. 
     Processing unit  36  applies the process that has been described above for the first four mirrors to all mirrors  38 . Thus, each mirror  38  generates a set of marks on target  40 , processing unit  36  positioning the marks so that they are separated from other marks. The separation is sufficient so that when target  40  is inspected by sensor  44 , the sensor, in conjunction with processing unit  36 , can distinguish the different marks. 
       FIG. 4  is a simplified schematic diagram of target  40 , according to an embodiment of the present invention. Target  40  shows exemplary marks made after twenty mirrors  38 A,  38 B, . . .  38 T have been used to irradiate the target, as described above, wherein each mirror generates five marks on the target. In  FIG. 4  it is assumed that the marks are single points, but it will be understood that some or all of the marks could be groups of points, as described above. 
     Returning to  FIG. 1 , once all mirrors  38  that are to be calibrated have been used to irradiate target  40 , table  42  moves the target to be in the field of view of sensor  44 . Processing unit  36  uses the image of target  40  formed by sensor  44  to form calibration tables for each mirror  38 , as described below with reference to  FIG. 5 . 
       FIG. 5  is a simplified flowchart  100  showing steps performed by processing unit  36  in generating calibration tables or equations for each mirror  38 , according to an embodiment of the present invention. The description of the steps of flowchart  100  is assumed to follow the description of the operation of apparatus  20 , as described above, and corresponds to the first mode of calibration of apparatus  20 . 
     In a first positioning step  102 , target  40  is fixed to table  42 , and processing unit  36  positions the table so that the target is in the field of operation of mirror M 1 . 
     In a first irradiation step  104 , processing unit  36  activates the appropriate sub-beam, in this case sub-beam  41 G. The processing unit then orients mirror M 1  to its predetermined positions, so as to form marks on the target. For mirror M 1  the marks are { 1 X}. 
     A subsequent positioning step  106  repeats the operation described in step  102 , processing unit  36  positioning the table so that the target is in the field of operation of another of mirrors  38 . 
     A subsequent irradiation step  108  repeats the operations of step  104  for the mirror that has been positioned in step  106 . 
     In a decision step  110 , processing unit  36  checks to see if all mirrors  38  have been through the calibration process of the steps described above. If some mirrors have not been through the process, processing unit  36  returns to step  106 . 
     If all mirrors have been through the calibration process, in a target translation step  112  processing unit  36  moves table  42  so that target  40  is in the field of view of sensor  44 , and processing unit  36  uses sensor  44  to acquire an image of target  40  and its marks. 
     In an analysis step  114 , using the acquired images of the fiducial marks of the target, the processing unit determines actual (x,y) values of each mark on target  40 , and correlates the actual values with the theoretical expected values of { 1 X}, { 2 X}, . . . , herein also written as E{ 1 X}, E{ 2 X}, . . . . The correlation may be performed automatically by processing unit  36 . For example, for each expected value of { 1 X}, { 2 X}, . . . the mark having an actual (x,y) that is closest to the expected value is assumed to be the corresponding mark. Alternatively, the operator of apparatus may at least partly assist processing unit  36  to perform the correlation. 
     For each mirror  38 , processing unit  36  selects the actual (x,y) values of the marks of the mirror. From the selected values, processing unit  36  acts as a correlator to generate a relationship for each mirror between orientations of the mirror, and the actual (x,y) values formed by reflection of the mirror&#39;s sub-beam. Processing unit  36  typically generates the relationship using processes of interpolation and/or extrapolation that are well known in the art. Processing unit  36  may store the relationships determined for the mirrors in any convenient form, such as in a calibration table for each mirror, and/or as an equation for each mirror having a general form:
 
( x,y )= f   Mn (θ,φ)  (1)
 
     where f Mn  is a function for mirror Mn determined by the processing unit. 
     It will be understood that the values of (x,y) for each table or equation may take account of the different physical positions of each mirror Mn. 
     After completion of step  114 , flowchart  100  typically ends. Optionally, as illustrated by broken line  116 , in an erase step  118  the marks on target  40  may be erased so that the target is available for further calibrations of apparatus  20 . 
     From the description of the first calibration mode above, it will be appreciated that all mirrors  38  may be automatically calibrated using one inspection and analysis of target  40 , as described in step  114  above. Consequently, the time taken to calibrate all mirrors  38  is small. 
       FIG. 6  is a simplified schematic diagram illustrating a second calibration mode of apparatus  20 , and  FIG. 7  is a simplified flowchart  150  of steps performed to implement the second mode, according to embodiments of the present invention. Apart from the differences described below, the second calibration mode is generally similar to that the first calibration mode, so that elements indicated by the same reference numerals in both  FIG. 1  and  FIG. 6  are generally similar in construction and in operation. 
     Unlike the first calibration mode, in the second calibration mode each mirror is separately calibrated using target  40 . After each mirror has been calibrated, marks of the target that have been used for the calibration are erased, and the target is used to calibrate another mirror. 
     In flowchart  150 , a positioning step  152  is substantially the same as step  102  ( FIG. 5 ). 
     A first irradiation step  154  is generally the same as step  104 . However, since only one mirror is calibrated at a time, the number of marks used for each calibration may be significantly enlarged. For example, in place of the five marks used in the exemplary description above of the first calibration mode, a typical number of marks used in the second calibration mode is approximately 100. 
     In a translation step  156 , processing unit  36  moves table  42  so that target  40  is in the field of view of sensor  44 , and processing unit  36  uses sensor  44  to acquire an image of target  40  and its marks. 
     In an erase step  158 , processing unit  36  activates thermoelectric cooler  68  ( FIG. 2B ) to heat the target sufficiently to erase the marks made in step  154 . Once the marks have been erased, the processing unit typically activates TEC  68  to cool the target, so that it is in a condition to be marked for subsequent irradiations, as explained above. 
     In a decision step  160 , processing unit  36  checks to see if all mirrors have been processed, i.e., if steps  154 ,  156 , and  158  have been applied to each mirror. 
     If all mirrors have not been processed, in a translation step  162  processing unit  36  moves the table, with target  40  attached, so that the target is in the field of another mirror, and the flowchart returns to the beginning of step  154 . 
     If decision step  160  returns that all mirrors have been processed, then in an analysis step  164  processing unit  36  analyzes each of the images acquired in step  156 . Analysis step  164  is generally similar to analysis step  114  described above. From the analysis, processing unit  36  generates a relationship for each mirror, typically in the form of a calibration table and/or equation for each mirror. 
     Flowchart  150  then ends. 
     The description above has described two modes of calibration of mirrors  38  by apparatus  20 . The first mode enables all mirrors of the apparatus to be calibrated using one pass of target  40  between the fields of the mirrors and the field of view of sensor  44 . In the second mode, multiple passes of the target between the fields of the mirrors and the field of view of sensor  44  are required. The first mode of calibration enables all mirrors  38  to be calibrated within a relatively short time period. The second mode of calibration typically requires more time than the first mode, but the calibration provided by the second mode typically has greater accuracy. 
     It will be understood that the two modes described above are exemplary, and other modes of calibration may be implemented by apparatus  20 . For example, mirrors  38  may be organized into groups, and the mirrors in each group may be calibrated substantially as described above for the first mode, but using more than the exemplary number of five marks for each mirror. The target may then be erased, and a subsequent group of mirrors may be calibrated as in the first mode. Organizing the mirrors into groups allows the operator of apparatus to select a desired level of accuracy of the calibration and a time taken for the calibration. 
     It will be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.