Abstract:
Systems and methods for analyzing for images in an x-ray inspection system are provided. One embodiment is a system for analyzing images in an x-ray inspection system. Briefly described, one such system comprises: a means for receiving an image of an object that is generated by an x-ray inspection system, the image of the object having a first field of view (FOV); a means for determining whether the first FOV associated with the image of the object matches a reference FOV corresponding to design data that models the object being inspected by the x-ray inspection system; and a means for modifying the design data based on the difference between the first FOV and the reference FOV.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]    This application is a continuation of copending U.S. utility application entitled, “Z-Axis Elimination in an X-Ray Laminography System Using Image Magnification for Z Plane Adjustment,” having Ser. No.09/652,255 and filed Aug. 30, 2000, which is entirely incorporated herein by reference. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    The invention relates generally to the rapid, high resolution inspection of circuit boards using a computerized laminography system, and in particular, to systems which use electronic means to adjust the Z-axis location of the inspection site with respect to the circuit board.  
         BACKGROUND OF THE INVENTION  
         [0003]    Rapid and precise quality control inspections of the soldering and assembly of electronic devices have become priority items in the electronics manufacturing industry. The reduced size of components and solder connections, the resulting increased density of components on circuit boards and the advent of surface mount technology (SMT), which places solder connections underneath device packages where they are hidden from view, have made rapid and precise inspections of electronic devices and the electrical connections between devices very difficult to perform in a manufacturing environment.  
           [0004]    Many existing inspection systems for electronic devices and connections make use of penetrating radiation to form images which exhibit features representative of the internal structure of the devices and connections. These systems often utilize conventional radiographic techniques wherein the penetrating radiation comprises X-rays. Medical X-ray pictures of various parts of the human body, e.g., the chest, arms, legs, spine, etc., are perhaps the most familiar examples of conventional radiographic images. The images or pictures formed represent the X-ray shadow cast by an object being inspected when it is illuminated by a beam of X-rays. The X-ray shadow is detected and recorded by an X-ray sensitive material such as film or other suitable means.  
           [0005]    The appearance of the X-ray shadow or radiograph is determined not only by the internal structural characteristics of the object, but also by the direction from which the incident X-rays strike the object. Therefore, a complete interpretation and analysis of X-ray shadow images, whether performed visually by a person or numerically by a computer, often requires that certain assumptions be made regarding the characteristics of the object and its orientation with respect to the X-ray beam. For example, it is often necessary to make specific assumptions regarding the shape, internal structure, etc. of the object and the direction of the incident X-rays upon the object. Based on these assumptions, features of the X-ray image may be analyzed to determine the location, size, shape, etc., of the corresponding structural characteristic of the object, e.g., a defect in a solder connection, which produced the image feature. These assumptions often create ambiguities which degrade the reliability of the interpretation of the images and the decisions based upon the analysis of the X-ray shadow images. One of the primary ambiguities resulting from the use of such assumptions in the analysis of conventional radiographs is that small variations of a structural characteristic within an object, such as the shape, density and size of a defect within a solder connection, are often masked by the overshadowing mass of the solder connection itself as well as by neighboring solder connections, electronic devices, circuit boards and other objects. Since the overshadowing mass and neighboring objects are usually different for each solder joint, it is extremely cumbersome and often nearly impossible to make enough assumptions to precisely determine shapes, sizes and locations of solder defects within individual solder joints.  
           [0006]    In an attempt to compensate for these shortcomings, some systems incorporate the capability of viewing the object from a plurality of angles. One such system is described in U.S. Pat. No. 4,809,308 entitled “METHOD &amp; APPARATUS FOR PERFORMING AUTOMATED CIRCUIT BOARD SOLDER QUALITY INSPECTIONS”, issued to Adams et al. The additional views enable these systems to partially resolve the ambiguities present in the X-ray shadow projection images. However, utilization of multiple viewing angles necessitates a complicated mechanical handling system, often requiring as many as five independent, non-orthogonal axes of motion. This degree of mechanical complication leads to increased expense, increased size and weight, longer inspection times, reduced throughput, impaired positioning precision due to the mechanical complications, and calibration and computer control complications due to the non-orthogonality of the axes of motion.  
           [0007]    Many of the problems associated with the conventional radiography techniques discussed above may be alleviated by producing cross-sectional images of the object being inspected. Tomographic techniques such as laminography and computed tomography (CT) have been used in medical applications to produce cross-sectional or body section images. In medical applications, these techniques have met with widespread success, largely because relatively low resolution on the order of one or two millimeters (0.0425 to 0.08 inches) is satisfactory and because speed and throughput requirements are not as severe as the corresponding industrial requirements.  
           [0008]    In the case of electronics inspection, and more particularly, for inspection of electrical connections such as solder joints, image resolution on the order of several micrometers, for example, 20 micrometers (0.0008 inches) is preferred. Furthermore, an industrial solder joint inspection system must generate multiple images per second in order to be practical for use on an industrial production line. Laminography systems which are capable of achieving the speed and accuracy requirements necessary for electronics inspection are described in the following patents: 1) U.S. Pat. No. 4,926,452 entitled “AUTOMATED LAMINOGRAPHY SYSTEM FOR INSPECTION OF ELECTRONICS”, issued to Baker et al.; 2) U.S. Pat. No. 5,097,492 entitled “AUTOMATED LAMINOGRAPHY SYSTEM FOR INSPECTION OF ELECTRONICS”, issued to Baker et al.; 3) U.S. Pat. No. 5,081,656 entitled “AUTOMATED LAMINOGRAPHY SYSTEM FOR INSPECTION OF ELECTRONICS”, issued to Baker et al.; 4) U.S. Pat. No. 5,291,535 entitled “METHOD AND APPARATUS FOR DETECTING EXCESS/INSUFFICIENT SOLDER DEFECTS”, issued to Baker et al.; 5) U.S. Pat. No. 5,621,811 entitled “LEARNING METHOD AND APPARATUS FOR DETECTING AND CONTROLLING SOLDER DEFECTS”, issued to Roder et al.; 6) U.S. Pat. No. 5,561,696 “METHOD &amp; APPARATUS FOR INSPECTING ELECTRICAL CONNECTIONS”, issued to Adams et al.; 7) U.S. Pat. No. 55,199,054 entitled “METHOD AND APPARATUS FOR HIGH RESOLUTION INSPECTION OF ELECTRONIC ITEMS”, issued to Adams et al.; 8) U.S. Pat. No. 5,259,012 entitled “LAMINOGRAPHY SYSTEM AND METHOD WITH ELECTROMAGNETICALLY DIRECTED MULTIPATH RADIATION SOURCE”, issued to Baker et al.; 9) U.S. Pat. No. 5,583,904 entitled “CONTINUOUS LINEAR SCAN LAMINOGRAPHY SYSTEM AND METHOD”, issued to Adams; and 10) U.S. Pat. No. 5,687,209 entitled “AUTOMATIC WARP COMPENSATION FOR LAMINOGRAPHIC CIRCUIT BOARD INSPECTION”, issued to Adams. The entirety of each of the above referenced patents is hereby incorporated herein by reference.  
           [0009]    Several of the above referenced patents disclose devices and methods for the generation of cross-sectional images of test objects at a fixed or selectable cross-sectional image focal plane. In these systems, an X-ray source system and an X-Ray detector system are separated in the Z-axis direction by a fixed distance and the cross-sectional image focal plane is located at a predetermined specific position on the Z-axis which is intermediate the Z-axis locations of the X-ray source system and the X-ray detector system. The X-ray detector system collects data from which a cross-sectional image of features in the test object, located at the cross-sectional image focal plane, can be formed. In systems having a fixed cross-sectional image focal plane, it is necessary to postulate that the features desired to be imaged are located in the fixed cross-sectional image focal plane at the predetermined specific position along the Z-axis. Thus, in these systems, it is essential that the positions of the fixed cross-sectional image focal plane and the plane with respect to the object which is desired to be imaged, be configured to coincide at the same position along the Z-axis. If this condition is not met, then the desired image of the selected feature of the test object will not be acquired. Instead, a cross-sectional image of a plane with respect to the test object which is either above or below the plane which includes the selected feature will be acquired. Thus, mechanical motion of the test object along the Z-axis is often used to position the desired plane with respect to the test object which is to be imaged at the position of the fixed cross-sectional image focal plane of the inspection system.  
           [0010]    Since the laminographic image area (e.g., 2-3 cm 2 ) of a typical laminography system is substantially smaller than the area of a typical circuit board (e.g., 150-1,500 cm 2 ), a complete inspection of a circuit board includes multiple laminographic images, which, if pieced together would form an image of the entire circuit board or selected regions of the circuit board. Thus, in addition to having a Z-axis mechanical positioning system for placing the test object (circuit board) at a specific location along the Z-axis, a typical high resolution laminography system also includes X-axis and Y-axis mechanical positioning systems for placing the test object at specific locations along the X and Y axes. This is frequently achieved by supporting the test object on a mechanical handling system, such as an X, Y, Z positioning table. The table is then moved to bring the desired regions of the test object into the laminographic image area of the laminography system. Movement in the X and Y directions locates the region of the test object to be examined, while movement in the Z direction moves the test object up and down to select the plane with respect to the test object where the cross sectional image is to be taken. As used throughout this document, the phrase “board view” will be used to refer to the laminographic image of a particular region or area of a circuit board identified by a specific X, Y coordinate of the circuit board. Thus, each “board view” includes only a portion of the circuit board.  
           [0011]    Many inspections require that some of the board views include multiple images at different Z-axis levels of the circuit board. This may be accomplished by physically moving the circuit board up or down in the Z-axis direction using the X, Y, Z mechanical positioning table. However, this additional mechanical motion along the Z-axis direction can also lead to increased expense, increased size and weight, longer inspection times, reduced throughput, reduced image resolution and accuracy due to mechanical vibrations and impaired Z-axis positioning precision due to mechanical complications.  
           [0012]    An alternative to mechanical Z-axis positioning is disclosed in U.S. Pat. No. 5,259,012 entitled “LAMINOGRAPHY SYSTEM AND METHOD WITH ELECTROMAGNETICALLY DIRECTED MULTIPATH RADIATION SOURCE”, issued to Baker et al. This patent describes a laminography system which electronically shifts the Z-axis location of the image plane with respect to the test object. In this device, the test object is interposed between a rotating X-Ray source and a synchronized rotating X-ray detector. A focal plane with respect to the test object is imaged onto the detector so that a cross-sectional image of a layer of the test object which coincides with the image focal plane is produced. The X-ray source is produced by deflecting an electron beam onto a target anode. The target anode emits X-ray radiation where the electrons are incident upon the target anode. The electron beam is produced by an electron gun which includes X and Y deflection coils for deflecting the electron beam in the X and Y directions. The X and Y deflection coils cause the X-ray source to rotate in a circular trace path. The voltages applied to the X and Y deflection coils are adjusted to change the radius of the circular trace path on the target anode resulting in a change in the Z-axis location of the image plane with respect to the test object. A characteristic of this type of electronic Z-axis positioning system is that images produced at different Z-axis positions have different magnification factors. The different magnification factors of the images complicates the analysis of the multiple images acquired during a complete inspection of the circuit board.  
           [0013]    In summary, the magnification of multiple board views at different Z levels is not changed when using systems of the type previously described wherein the X-ray source and detector are fixed at specific locations along the Z-axis and the circuit board is moved in the Z-axis direction to obtain laminographic images at the different Z levels of the circuit board. Alternatively, the magnification of different Z level board views does change with each change in Z level when using the previously described systems which electronically change the radius of the X-Ray source to obtain lamingraphic images at different Z levels of the circuit board. The different magnifications for different Z level board views in these systems presents difficulties in analyzing the images thus obtained.  
           [0014]    The present invention provides improvements which address the above listed specific problems. The present invention advantageously includes ease of use and improved accuracy of Z elevation determination, resulting in an improved technique for producing high resolution cross sectional images of electrical connections.  
         SUMMARY OF THE INVENTION  
         [0015]    The present invention comprises an improved computerized laminography system which accurately compensates for variable magnifications of different Z level board views in an efficient manner. This feature makes it feasible to eliminate the Z-axis mechanical motion of the circuit board along the Z-axis direction. Elimination of the Z-axis mechanical motion improves speed of the inspection as well as reliability of the inspection system.  
           [0016]    As used throughout this document, the phrase “field of view” or “FOV” will be used to refer to the size of a particular region or area of a circuit board which is included in a laminographic image of that particular region or area of the circuit board. For example, one particular configuration of the present invention has two preset magnification factors. A first magnification factor of 4.75 has a FOV of 0.8 inch×0.8 inch and an image size of 3.8 inches×3.8 inches. Thus, a board view at a particular x, y location of the circuit board at a magnification of 4.75 refers to a 3.8 inches×3.8 inches image of a 0.8 inch×0.8 inch region of the circuit board centered at location x, y on the circuit board. A second magnification factor of 19 has a FOV of 0.2 inch×0.2 inch and an image size of 3.8 inches×3.8 inches. Thus, a board view at a particular x, y location of the circuit board at a magnification of 19 refers to a 3.8 inches×3.8 inches image of a 0.2 inch×0.2 inch region of the circuit board centered at location x, y on the circuit board. Thus, four board views at the magnification of 19, each board view having a FOV of 0.2 inch×0.2 inch, are required to image the single corresponding board view at the magnification of 4.75, each board view having a FOV of 0.8 inch×0.8 inch. In terms of FOV, the FOV of the system operating at a magnification factor of 4.75 is 4 times larger than the FOV of the system operating at a magnification factor of 19.  
           [0017]    As described above, in addition to changing the magnification of the image, another side effect of changing the Z-axis location of the image plane electronically as opposed to mechanically is that the field of view (FOV) for different Z-axis locations of the image plane also changes as the magnification changes. In systems having a fixed Z-axis location of the image plane, the magnification and FOV are not dependent on which Z-level of the circuit board is being imaged since different Z-levels of the circuit board are mechanically positioned at the same fixed Z-axis location of the image plane of the system.  
           [0018]    There are several ways that this change in FOV with magnification can be accounted for and corrected in analyzing the images. In circuit board inspection systems, CAD data which describes the circuit board being inspected is utilized during the acquisition and analysis of the images of the circuit board. Thus, a first technique for compensating for variable image magnification factors and FOV&#39;s may be accomplished by magnifying or shrinking the acquired images to a “nominal” size (“nominal” being defined by a base FOV). Numerous algorithms for doing this are well documented in the technical literature. However, these techniques tend to be CPU intensive and may affect throughput of the system. A second and preferred technique for compensating for variable image magnification factors and FOV&#39;s may be accomplished more efficiently by using on-the-fly CAD data manipulation and on-the-fly FOV adjustments during the analysis of the images.  
           [0019]    In a first aspect, the present invention is a device for inspecting electrical connections on a circuit board comprising: a source of X-rays which emits X-rays through the electrical connection from a plurality of positions centered about a first radius and a second radius; an X-ray detector system positioned to receive the X-rays produced by the source of X-rays which have penetrated the electrical connection, the X-ray detector system further comprising an output which emits data signals; an image memory which combines the detector data signals to form an image database which contains information sufficient to form a first cross-sectional image of a cutting plane of the electrical connection at a first image plane at a first Z-axis location corresponding to the first X-ray source radius and a second cross-sectional image of a cutting plane of the electrical connection at a second image plane at a second Z-axis location corresponding to the second X-ray source radius; and a processor which controls the acquisition and formation of the cross-sectional images and analyzes the cross-sectional images, the image processor further comprising: a storage area for storing CAD data which describes a first cross-sectional design of the electrical connection at the first image plane at the first Z-axis location and CAD data for a second cross-sectional design of the electrical connection at the second image plane at the second Z-axis location; and a CAD data calculator section which determines a variance between the first cross-sectional image at the first image plane and the second cross-sectional image at the second image plane and uses the variance to modify, on an as-needed basis, portions of the CAD data which describe said electrical connection at the second image plane at the second Z-axis location thereby generating modified CAD data for the second image plane which describes the electrical connection at the second image plane as represented by the second cross-sectional image. In some configurations, the first cross sectional image has a first field of view and the second cross sectional image has a second field of view and the variance between the first cross-sectional image and the second cross-sectional image is determined by comparing the second field of view to the first field of view. In some configurations, the first cross sectional image has a first magnification factor and the second cross sectional image has a second magnification factor and the variance between the first cross-sectional image and the second cross-sectional image is determined by comparing the second magnification factor to the first magnification factor. In some configurations, the source of X-rays comprises a plurality of X-ray sources. In some configurations, the X-ray detector system comprises a plurality of X-ray detectors. In some configurations, the processor further comprises an image section which produces the cross-sectional images of the electrical connection from the image database.  
           [0020]    A second aspect of the present invention includes a method for analyzing laminographic images of an object at multiple Z-axis levels within the object comprising the steps of: determining a reference Z-axis position Z 1 , corresponding to a first Z level in the object; acquiring a first cross sectional image of the object at the reference Z-axis position Z 1 , which corresponds to the first Z level in the object and a second cross sectional image of the object at a second Z-axis position Z 2  which corresponds to a second Z level in the object; providing first Z level design data which describes the object and specific features within the object at the first Z level of the object and second Z level design data which describes the object and specific features within the object at the second Z level of the object; determining a variance factor which represents a difference between the first cross sectional image of the object at the first Z level and the second cross sectional image of the object at the second Z level; and modifying in real time or near real time, one or more portions of the second Z level design data with the variance factor while comparing the second cross sectional image of the object at the second Z level with the real time or near real time modified second Z level design data. In some implementations of the method, the first cross sectional image has a first field of view and the second cross sectional image has a second field of view and the variance factor which represents a difference between the first cross-sectional image and the second cross-sectional image is determined by comparing the second field of view to the first field of view. In some implementations of the method, the first cross sectional image has a first magnification factor and the second cross sectional image has a second magnification factor and the variance factor which represents a difference between the first cross-sectional image and the second cross-sectional image is determined by comparing the second magnification factor to the first magnification factor.  
           [0021]    A third aspect of the present invention includes a method for inspecting an electrical connection on a circuit board comprising: determining a first Z-axis position Z 1 , corresponding to a first Z level in the electrical connection; acquiring a first cross sectional image of the electrical connection at the first Z-axis position Z 1 , which corresponds to the first Z level in the electrical connection and a second cross sectional image of the electrical connection at a second Z-axis position Z 2  which corresponds to a second Z level in the electrical connection, wherein the first cross sectional image has a first magnification factor and the second cross sectional image has a second magnification factor; providing first Z level design data which describes the electrical connection and specific design features within the electrical connection at the first Z level of the electrical connection and second Z level design data which describes the electrical connection and specific design features within the electrical connection at the second Z level of the electrical connection; comparing the first and second magnification factors to determine a first field of view correction factor; and modifying in real time or near real time, one or more portions of the second Z level design data with the first field of view correction factor while comparing the second cross sectional image of the electrical connection at the second Z level with the real time or near real time modified second Z level design data.  
           [0022]    Some implementations of this method further comprise: providing third Z level design data which describes the electrical connection and specific design features within the electrical connection at a third Z level of the electrical connection; acquiring a third cross sectional image of the electrical connection at a third Z-axis position Z 3  which corresponds to the third Z level in the electrical connection wherein the third cross sectional image has a third magnification factor; comparing the first and third magnification factors to determine a second field of view correction factor; and modifying in real time or near real time, one or more portions of the third Z level design data with the second field of view correction factor while comparing the third cross sectional image of the electrical connection at the third Z level with the real time or near real time modified third Z level design data.  
           [0023]    These and other characteristics of the present invention will become apparent through reference to the following detailed description of the preferred embodiments and accompanying drawings. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0024]    [0024]FIG. 1 is a schematic representation of a laminography system illustrating the principles of the technique.  
         [0025]    [0025]FIG. 2 a  shows an object having an arrow, a circle and a cross embedded in the object at three different planar locations.  
         [0026]    [0026]FIG. 2 b  shows a laminograph of the object in FIG. 2 a  focused on the plane containing the arrow.  
         [0027]    [0027]FIG. 2 c  shows a laminograph of the object in FIG. 2 a  focused on the plane containing the circle.  
         [0028]    [0028]FIG. 2 d  shows a laminograph of the object in FIG. 2 a  focused on the plane containing the cross.  
         [0029]    [0029]FIG. 2 e  shows a conventional, two-dimensional X-ray projection image of the object in FIG. 2 a.    
         [0030]    [0030]FIG. 3 a  is a diagrammatic cross-sectional view of a circuit board inspection laminography system showing how the laminographic image is formed and viewed by a camera.  
         [0031]    [0031]FIG. 3 b  shows a top view enlargement of an inspection region shown in FIG. 3 a.    
         [0032]    [0032]FIG. 3 c  is a perspective view of the circuit board inspection laminography system shown in FIG. 3 a.    
         [0033]    [0033]FIGS. 4 and 5 are schematic views of a laminography system in accordance with the present invention.  
         [0034]    [0034]FIGS. 6 and 7 illustrate the manner in which a laminographic system in accordance with the present invention is utilized to produce a Z-axis shaft of the imaged region of the object plane with respect to the object.  
         [0035]    [0035]FIG. 8 illustrates a possible configuration of a X-ray target anode which may be used with the present invention.  
         [0036]    [0036]FIG. 9 illustrates how the magnification of an image is related to the distance between an image plane and an X-ray detector.  
         [0037]    [0037]FIG. 10 illustrates how the FOV and magnification changes in a first implementation of the present invention.  
         [0038]    [0038]FIG. 11 shows a perspective view of the test object  10  shown in FIG. 2 a  mounted on a circuit board.  
         [0039]    [0039]FIG. 12 shows a cross sectional view of the test object  10  mounted on the circuit board shown in FIG. 11.  
         [0040]    [0040]FIGS. 13A, 13B, and  13 C show CAD data for the test object  10  shown in FIGS. 2, 11 and  12 .  
         [0041]    [0041]FIGS. 14A, 14B, and  14 C show laminographic images of the test object  10  shown in FIGS. 2, 11 and  12  corresponding to the CAD data in FIGS. 13A, 13B and  13 C.  
         [0042]    [0042]FIG. 15 is a flow chart showing a process for performing on-the-fly CAD data manipulations for the analysis of laminographic images.  
       REFERENCE NUMERALS IN DRAWINGS  
       [0043]    [0043]                                                        10   object under inspection            20   source of X-rays            30   X-ray detector            40   common axis of rotation            50   central ray            52   X-ray projection            60   image plane in object 10            60a   arrow image plane            60b   circle image plane            60c   cross image plane            62   plane of source of X-rays            64   plane of X-ray detecto            70   point of intersection            81   arrow test pattern            82   circle test pattern            83   cross test pattern           100   image of arrow 81           102   blurred region           110   image of circle 82           112   blurred region           120   image of cross 83           122   blurred region           130   image of arrow 81           132   image of circle 82           134   image of cross 83           200   X-ray tube           210   printed circuit board           212   electronic components           214   electrical connections           220   support fixture           230   positioning table           240   rotating X-ray detector           250   fluorescent screen           252   first mirror           254   second mirror           256   turntable           258   camera           260   feedback system           262   input connection           263   sensor           264   output connection           265   position encoder           270   computer           276   input line           278   output line           280   rotating source spot           281   deflection coils           282   X-rays           283   region of circuit board           284   X-rays           285   rotating electron beam           286   light           287   target anode           290   granite support table           292   load/unload port           294   operator station           296   laser range finder           310   laminography system           312   source of X-rays           314   object           315   analysis system           316   rotating X-ray detector           318   electron gun           320   electrodes           322   coils           324   target anode           330   electron beam           332   X-ray spot           334   X-rays           340   fluorescent screen           342   first mirror           344   second mirror           346   turntable           348   platform           349   granite table           350   axis           352   plane           356   camera           357   video terminal           360   focus coil           362   steering yoke/deflection coil           363   look up table (LUT)           410   first plane of object 414           412   second plane of object 414           414   object under inspection           416   cone of X-rays           418   cone of X-rays           420   image of cross 472           424   scan circle with radius R1           425   scan circle with radius R2           426   cone of X-rays           428   cone of X-rays           430   image of arrow 470           470   arrow test pattern           472   cross test pattern           550   target anode           560   X-rays           620   circuit board           640   Field of View (FOV)           720cd   CAD data for test object 10 at Level 1           720id   image data for test object 10 at Level 1           750cd   CAD data for test object 10 at Level 2           750id   image data for test object 10 at Level 2           780cd   CAD data for test object 10 at Level 3           780id   image data for test object 10 at Level 3           810   flow chart process block           820   flow chart process block           830   flow chart process block           840   flow chart process block           850   flow chart process block           860   flow chart process block                        
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0044]    As used throughout, the term “radiation” refers to electromagnetic radiation, including but not limited to the X-ray, gamma and ultraviolet portions of the electromagnetic radiation spectrum.  
         [0045]    Cross-sectional Image Formation  
         [0046]    [0046]FIG. 1 shows a schematic representation of a typical laminographic geometry used with the present invention. An object  10  under examination, for example, a circuit board, is held in a stationary position with respect to a source of X-rays  20  and an X-ray detector  30 . Synchronous rotation of the X-ray source  20  and detector  30  about a common axis  40  causes an X-ray image of the plane  60  with respect to the object  10  to be formed on the detector  30 . The image plane  60  is substantially parallel to planes  62  and  64  defined by the rotation of the source  20  and detector  30 , respectively. The image plane  60  is located at an intersection  70  of a central ray  50  from the X-ray source  20  and the common axis of rotation  40 . This point of intersection  70  acts as a fulcrum for the central ray  50 , thus causing an in-focus cross-sectional X-ray image of the object  10  at the plane  60  to be formed on detector  30  as the source and detector synchronously rotate about the intersection point  70 . Structure with respect to the object  10  which lies outside of plane  60  forms a blurred X-ray image on detector  30 .  
         [0047]    In the laminographic geometry shown in FIG. 1, the axis of rotation of the radiation source  20  and the axis of rotation of the detector  30  are coaxial. However, it is not necessary that these axes of rotation of the radiation source and the detector  30  be coaxial. The conditions of laminography are satisfied and a cross-sectional image of the layer  60  will be produced as long as the planes of rotation  62  and  64  are mutually parallel, and the axes of rotation of the source and the detector are mutually parallel and fixed in relationship to each other. Coaxial alignment reduces the number of constraints upon the mechanical alignment of the apparatus.  
         [0048]    [0048]FIGS. 2 a - 2   e  show laminographs produced by the above described laminographic technique. The object  10  shown in FIG. 2 a  has test patterns in the shape of an arrow  81 , a circle  82  and cross  83  embedded within the object  10  in three different planes  60   a,    60   b  and  60   c,  respectively.  
         [0049]    [0049]FIG. 2 b  shows a typical laminograph of object  10  formed on detector  30  when the point of intersection  70  lies in plane  60   a  of FIG. 2 a . An image  100  of arrow  81  is in sharp focus, while the images of other features within the object  10 , such as the circle  82  and cross  83  form a blurred region  102  which does not greatly obscure the arrow image  100 .  
         [0050]    Similarly, when the point of intersection  70  lies in plane  60   b,  an image  110  of the circle  82  is in sharp focus as seen in FIG. 2 c . The arrow  81  and cross  83  form a blurred region  112 .  
         [0051]    [0051]FIG. 2 d  shows a sharp image  120  formed of the cross  83  when the point of intersection  70  lies in plane  60   c.  The arrow  81  and circle  82  form blurred region  122 .  
         [0052]    For comparison, FIG. 2 e  shows an X-ray shadow image of object  10  formed by conventional projection radiography techniques. This technique produces sharp images  130 ,  132  and  134  of the arrow  81 , circle  82  and cross  83 , respectively, which overlap one another. FIG. 2 e  vividly illustrates how multiple characteristics contained within the object  10  may create multiple overshadowing features in the X-ray image which obscure individual features of the image.  
         [0053]    [0053]FIG. 3 a  illustrates a schematic diagram of a typical laminographic apparatus used with the present invention. In this configuration, an object under inspection is a printed circuit board  210  having multiple electronic components  212  mounted on the board  210  and electrically interconnected via electrical connections  214  (See FIG. 3 b ). Typically, the electrical connections  214  are formed of solder. However, various other techniques for making the electrical connections  214  are well know in the art and even though the invention will be described in terms of solder joints, it will be understood that other types of electrical connections  214  including, but not limited to, conductive epoxy, mechanical, tungsten and eutectic bonds may be inspected utilizing the invention. FIG. 3 b , which is a top view enlargement of a region  283  of the circuit board  210 , more clearly shows the components  212  and solder joints  214 .  
         [0054]    The laminographic apparatus acquires cross-sectional images of the solder joints  214  using the previously described laminographic method or other methods capable of producing equivalent cross-sectional images. The cross sectional images of the solder joints  214  are automatically evaluated to determine their quality. Based on the evaluation, a report of the solder joint quality is presented to the user.  
         [0055]    The laminographic apparatus, as shown in FIG. 3 a , comprises an X-ray tube  200  which is positioned adjacent printed circuit board  210 . The circuit board  210  is supported by a fixture  220 . The fixture  220  is attached to a positioning table  230  which is capable of moving the fixture  220  and board  210  along three mutually perpendicular axes, X, Y and Z. A rotating X-ray detector  240  comprising a fluorescent screen  250 , a first mirror  252 , a second mirror  254  and a turntable  256  is positioned adjacent the circuit board  210  on the side opposite the X-ray tube  200 . A camera  258  is positioned opposite mirror  252  for viewing images reflected into the mirrors  252 ,  254  from fluorescent screen  250 . A feedback system  260  has an input connection  262  from a sensor  263  which detects the angular position of the turntable  256  and an output connection  264  to X and Y deflection coils  281  on X-ray tube  200 . A position encoder  265  is attached to turntable  256 . The position sensor  263  is mounted adjacent encoder  265  in a fixed position relative to the axis of rotation  40 . The camera  258  is connected to a computer  270  via an input line  276 . The computer  270  includes the capability to perform high speed image analysis. An output line  278  from the computer  270  connects the computer to positioning table  230 . A laser range finder  296  is positioned adjacent the circuit board  210  for creating a Z-map of the surface of the circuit board  210 .  
         [0056]    A perspective view of the laminographic apparatus is shown in FIG. 3 c.  In addition to the X-ray tube  200 , circuit board  210 , fluorescent screen  250 , turntable  256 , camera  258 , positioning table  230  and computer  270  shown in FIG. 3 a , a granite support table  290 , a load/unload port  292  and an operator station  294  are shown. The granite table  290  provides a rigid, vibration free platform for structurally integrating the major functional elements of the laminographic apparatus, including but not limited to the X-ray tube  200 , positioning table  230  and turntable  256 . The load/unload port  292  provides a means for inserting and removing circuit boards  210  from the machine. The operator station  294  provides an input/output capability for controlling the functions of the laminographic apparatus as well as for communication of inspection data to an operator.  
         [0057]    In operation of the laminographic apparatus as shown in FIGS. 3 a  and  3   c,  high resolution, cross-sectional X-ray images of the solder joints  214  connecting components  212  on circuit board  210  are acquired using the X-ray laminographic method previously described in reference to FIGS. 1 and 2. Specifically, X-ray tube  200 , as shown in FIG. 3 a , comprises a rotating electron beam spot  285  which produces a rotating source  280  of X-rays  282 . The X-ray beam  282  illuminates a region  283  of circuit board  210  including the solder joints  214  located within region  283 . X-rays  284  which penetrate the solder joints  214 , components  212  and board  210  are intercepted by the rotating fluorescent screen  250 .  
         [0058]    Dynamic alignment of the position of the X-ray source  280  with the position of rotating X-ray detector  240  is precisely controlled by feedback system  260 . The feedback system correlates the position of the rotating turntable  256  with calibrated X and Y deflection values stored in a look-up table (LUT). Drive signals proportional to the calibrated X and Y deflection values are transmitted to the steering coils  281  on the X-ray tube  200 . In response to these drive signals, steering coils  281  deflect electron beam  285  to locations on an annular shaped target anode  287  such that the position of the X-ray source spot  280  rotates in synchronization with the rotation of detector  240  in the manner previously discussed in connection with FIG. 1. X-rays  284  which penetrate the board  210  and strike fluorescent screen  250  are converted to visible light  286 , thus creating a visible image of a single plane within the region  283  of the circuit board  210 . The visible light  286  is reflected by mirrors  252  and  254  into camera  258 . Camera  258  typically comprises a low light level closed circuit TV (CCTV) camera which transmits electronic video signals corresponding to the X-ray and visible images to the computer  270  via line  276 . The image analysis feature of computer  270  analyzes and interprets the image to determine the quality of the solder joints  214 .  
         [0059]    Computer  270  also controls the movement of positioning table  230  and thus circuit board  210  so that different regions of circuit board  210  may be automatically positioned within inspection region  283 .  
         [0060]    The laminographic geometry and apparatus shown and described with reference to FIGS.  1 - 3  are typical of that which may be used in conjunction with the present invention. However, specific details of these systems are not critical to the practice of the present invention, which addresses an alternate and/or additional technique for adjusting the Z-axis location of the image plane within the circuit board  210 . For example, the number of computers and delegation of tasks to specific computers may vary considerably from system to system as may the specific details of the X-ray source, detector, circuit board positioning mechanism, etc.  
         [0061]    Electronic Z-axis Laminography System  
         [0062]    [0062]FIG. 4 illustrates a schematic diagram of a laminography system  310  in accordance with the present invention. The system  310  comprises a source of X-rays  312  positioned above an object  314  to be viewed, and a rotating X-ray detector  316 , positioned below the object  314 , opposite the X-ray source  312 . The object  314  may, for example, be an electronic item such as a circuit board, a manufactured item such as an aircraft part, a portion of a human body, etc.  
         [0063]    The invention acquires X, Y plane cross-sectional images of the object  314  under inspection using multipath laminography geometries which enables multiple locations of the object  314  to be sequentially viewed without requiring mechanical movement of the object  314 . Movement in various scan circles produces laminographs at the desired X, Y coordinate locations and various Z planes without the need for mechanical movement of the viewed object  314 . In one embodiment, the invention may be interfaced with an analysis system  315  which automatically evaluates the cross-section image generated by the system  310  and provides a report to the user that indicates the results of the evaluation.  
         [0064]    The source  312  is positioned adjacent the object  314 , and comprises an electron gun  318 , a set of electrodes for electron beam acceleration and focus  320 , a focus coil  360 , and a steering yoke or deflection coil  362 , and a substantially flat target anode  324 . An electron beam  330  emitted from the electron gun  318  is incident upon the target  324 , producing an X-ray spot  332  which serves as an approximately point source of X-rays  334 . The X-rays  334  originate in the target  324  from the point where the electron beam  330  impinges upon the target  324  and, as described below, illuminate various regions of the object  314 .  
         [0065]    The object  314  is typically mounted on a platform  348  which may be affixed to a granite table  349 , so as to provide a rigid, vibration-free platform for structurally integrating the functional elements of the system  310 , including the X-ray source  312  and turntable  346 . It is also possible that the platform  348  comprises a positioning table that is capable of moving the object  314  relatively large distances along three mutually perpendicular axes X, Y, and Z.  
         [0066]    The rotating X-ray detector  316  comprises a fluorescent screen  340 , a first mirror  342 , a second mirror  344 , and a turntable  346 . The turntable  346  is positioned adjacent to the object  314 , on the side opposite to the X-ray source  312 . A camera  356  is positioned opposite the mirror  344 , for viewing images reflected into the mirrors  342 ,  344  from the fluorescent screen  340 . The camera  356  typically comprises a low light level closed circuit television or CCD camera that produces a video image of the X-ray image formed on the fluorescent screen  340 . The camera  356  may, for example, be connected to a video terminal  357  so that an operator may observe the image appearing on the detector  340 . The camera  356  may also be connected to the image analysis system  315 .  
         [0067]    The laminography system  310  is advantageously encased by a supporting chassis (not shown) which acts to prevent undesired emissions of X-rays, as well as facilitating the structural integration of the major elements of the system  310 .  
         [0068]    In operation, X-rays  334  produced by the X-ray source  312  illuminate and penetrate regions of the object  314  and are intercepted by the screen  340 . Synchronous rotation of the X-ray source  312  and detector  316  about an axis  350  causes an X-ray image of a plane  352  (see FIG. 5) within the object  314  to be formed on the detector  316 . Although the axis of rotation  350  illustrated is the common axis of rotation for both the source  312  and detector  316 , one skilled in the art will recognize that it is not necessary for the axes of rotation to be collinear. In practice, it is sufficient that the axes of rotation be parallel. X-rays  334  which penetrate the object  314  and strike the screen  340  are converted into visible light reflected by the mirrors  342 ,  344  and into the camera  356 .  
         [0069]    Referring to FIG. 5, the electron beam  330  is emitted from the electron gun  318  and travels in a region between the electrodes  320  and steering coils  322 . The electrodes  320  and coils  322  produce electromagnetic fields which interact with the electron beam  330  to focus and direct the beam  330  onto the target  324  forming an electron beam spot  332  from which X-rays are emitted. Preferably, the size of the electron beam spot  332  on the target is on the order of 0.02 to 10 microns in diameter. The steering coils  322  enable the X-ray source  312  to provide X-rays  334  from the X-ray spots  332  wherein the location of the spots  332  move in a desired pattern around the target  324 . Preferably, the steering coils  322  comprise separate X and Y electromagnetic deflection coils  360 ,  362  which deflect the electron beam  330  discharged from the electron gun  318  in the X and Y directions, respectively. Electrical current flowing in the steering yoke  362  creates a magnetic field which interacts with the electron beam  330  causing the beam  330  to be deflected. However, one skilled in the art will also recognize that electrostatic deflection techniques could also be used to deflect the electron beam  330 .  
         [0070]    Preferably, a LUT  363  outputs voltage signals which, when applied to the X and Y deflection coils  360 ,  362  cause the electron beam spot  332  to rotate, thus producing a circular pattern on the surface of the target  324 . In one embodiment, the LUT  363  provides the output voltages in response to addressing signals from a master computer (not shown) which may be included within the image analysis system  315 . The output voltages are advantageously predetermined using a calibration technique which correlates the position of the turntable  346 , and the position of the X-ray beam spot  332 .  
         [0071]    The present invention provides a method and apparatus for processing laminographic images of various Z-axis levels of the object  314  which requires little or no physical movement of the object  314  or the supporting table  348 . In accordance with the present invention, desired Z-axis levels of the object are brought within the field of view of the system electronically as opposed to mechanically. This is accomplished by moving the location of the pattern traced by the X-ray beam spot  332  on the target  324 . In this manner, various Z-axis levels of the object  314  are brought within the field of view and images are produced of a specific Z-axis level of the object coinciding with the field of view. In accordance with the present invention, the voltages applied to the X and Y deflection coils  360 ,  362  are varied in order to produce rotating X-ray beam paths of distinct radii having distinct x, y locations on the target  324 .  
         [0072]    Referring to FIG. 6 and FIG. 7, the present invention further provides a laminography system having a geometry which can be utilized to effect a shift or change in the Z-axis position of the object plane  60  (see FIG. 1) within a test object  414  without moving the test object. FIG. 6 illustrates an object  414  having the patterns of an arrow  470  and a cross  472  located therein. The cross pattern  472  is located in a first plane  410  and the arrow pattern  470  is located in a second plane  412 , wherein the first plane  410  lies above and is parallel to the second plane  412 . The X-ray beam spot  332  traces a scan circle  424  having a radius R1, defining a family of cones including cones  416 ,  418 .  
         [0073]    The intersection of the cones formed as the X-ray beam spot  332  travels around the circle  424 , including cones  416 ,  418 , forms an image region substantially centered about the cross pattern  472 , such that the first plane  410  is defined as the object plane  60 . As the X-ray spot  332  and detector  316  rotate in synchronization, a distinct image  420  of the cross pattern  472  is produced on the surface of the detector  316 . The image of the arrow  470 , which lies in the second plane  412  and is outside the object plane  410  defined by the cones  416 ,  418 , is not stationary on the detector  316  during the entire rotation of the detector  316  and thus, appears blurred.  
         [0074]    [0074]FIG. 7 illustrates that by adjusting the gain of the voltages output from the LUT  363  to the deflection coils  360 ,  362 , thereby changing the amplitude of sine and cosine signals driving the coils, the radii of the scan circles  424 ,  425  traced by the X-ray spot  332  can be varied to produce images of regions within distinct Z-axis planes in the object  414 . With the adjustment of the gain applied to the output from the LUT  363 , the scan circle  424  is increased in radius by a value ΔR to a radius R2, thereby forming a scan circle  425  defining a second family of cones including the cones  426 ,  428 . Because of the larger radius R2 of the second scan circle  425 , the set of points defined by the intersection of a second family of cones, including cones  426 ,  428 , is displaced in the negative Z direction relative to the region imaged when the X-ray source  332  follows the path  424  (FIG. 6). Thus, the object plane  60  is lowered by an amount ΔZ to the second plane  412 , and the image region is substantially centered about the arrow pattern  470 . As the X-ray spot  332  and detector  316  rotate, a distinct image  430  of the arrow pattern  470  is then produced on the detector  316 , while the image of the cross pattern  472 , lying outside the object plane  412 , appears blurred. The amplitude of the gain adjustment made to the voltages applied to the deflection coils  360 ,  362  is proportional to the direction and amount of the shift ΔZ in the position of the object plane  60 ,  410 ,  412 . For example, a large increase in the gain would result in a relatively large movement of the object plane  60  in the downward (i.e., negative Z) direction, while a small decrease in the gain would result in a relatively small movement of the object plane  60  in the upward (i.e., positive Z) direction. In this manner, the geometry utilized in the laminographic system of the present invention further allows various planes in the object  414  to be imaged upon the detector  316  without mechanical movement of any of the system components.  
         [0075]    It will be understood that different configurations of the target anode  324  may be used in accordance with the present invention. For example, FIG. 8 illustrates an embodiment of a target anode that may be used in accordance with the present invention. FIG. 8 shows a cross-sectional view of this embodiment of the target. In the embodiment shown in FIG. 8, a target  550  comprises multiple concentric rings which are formed so that X-rays  560  are produced when the electron beam  330  is incident upon the surface of the target  550 . Each of the rings has a different radius so that objects in different focal planes along the Z-axis are imaged when the electron beam  330  is deflected to trace a path on selected ones of the rings of the target  550 .  
         [0076]    Laminographic and Magnification Geometries  
         [0077]    [0077]FIG. 1 shows the parameters referred to in the following discussion and equations regarding the laminographic geometry of the present method and device. The radius of the circular path followed by the rotating X-ray detector  30  is “R 0 ” and maintains a constant value. Similarly, the Z-axis distance between the rotating X-ray source  20  (X-ray tube target) and the rotating X-ray detector  30  is “Z 0 ” and maintains a constant value. The radius of the circular path followed by the rotating source of X-rays  20  is “r” and is a variable in the geometry used for the present invention. The central X-ray path  50  from the X-ray source  20  forms an angle “θ” with the common axis of rotation  40 . The Z-axis distance between the image plane  60  in object  10  and the X-ray detector  30  is “z”. The distance “z” is determined by the intersection  70  of the central X-ray path  50  with the common axis of rotation  40 . Thus, a change in the radius “r” of the circular path followed by the rotating source of X-rays  20  also results in changes in the angle “θ”, the Z-axis location of the image plane  60 , i.e., the point of intersection  70 , and the Z-axis distance “z” between the image plane  60  and the X-ray detector  30 . The equations to determine the radius “r” required for a specified distance “z” are straightforward as follows: 
           z=R   0 /tan θ=( R   0   /r )( Z   0   −z )  (1) 
         [0078]    Solving equation (1) for the radius “r” in terms of the Z-axis distance “z” results in the following:  
             r   =         -     (       R   0     /   z     )            (       Z   0     -   z     )       =       R   0            (       Z   0     -   1     )     Z                 (   2   )                               
 
         [0079]    In one configuration of the present invention, the radius “r” of the circular path followed by the rotating source of X-rays  20  is adjusted in accordance with equation (2) to electronically change the position of the Z-axis location “z” of the image plane  60  with respect to the X-ray detector  30 . This results in a laminography system which does not require a mechanical system to change the Z-axis location “z” of the image plane  60  with respect to the X-ray detector  30 . For example, in the laminographic inspection of a circuit board, cross-sectional images of different Z-axis positions of the circuit board (including both top and bottom surfaces and any other slices), may be brought into the image plane  60 , by electronically shifting the radius of rotation “r” of the rotating source of X-rays  20  as opposed to mechanically moving the circuit board in the Z-axis direction.  
         [0080]    Changing the Z-axis position “z” of the circuit board image plane  60  by changing the radius of rotation “r” of the rotating source of X-rays  20 , also results in changing the Field of View (FOV) of the image formed on detector for different values of “r” and “z”. As previously discussed, the phrase “Field of View” or “FOV” as used herein refers to the size of a particular region or area of a circuit board which is included in a laminographic image of that particular region or area of the circuit board. Thus, the size of the image changes with respect to the region or area of the circuit board being inspected, i.e., the magnification of the image changes when “r” and “z” change. This change in FOV and hence magnification factor must be accurately and efficiently accounted for in a circuit board inspection laminography system.  
         [0081]    There are several ways that these changes in FOV with magnification can be accounted for and corrected in analyzing the images. In circuit board inspection systems, CAD data which describes the circuit board being inspected is utilized during the acquisition and analysis of the images of the circuit board. Thus, a first technique for compensating for variable image magnification factors and FOV&#39;s may be accomplished by magnifying or shrinking the acquired images to a “nominal” size (“nominal” being defined by a base FOV). Numerous algorithms for doing this are well documented in the technical literature. However, these techniques tend to be CPU intensive and may affect throughput of the system. A second and preferred technique for compensating for variable image magnification factors and FOV&#39;s may be accomplished more efficiently by using on-the-fly CAD data manipulation and on-the-fly FOV adjustments during the analysis of the images.  
         [0082]    [0082]FIG. 9 illustrates how the magnification of an image is related to the distance “z” between the image plane  60  and the X-ray detector  30 . Image magnification is defined as the ratio of the size of the image to the size of the object which forms the image. For example, FIG. 9 shows an object being imaged in the form of an arrow having a linear dimension “2a” in the image plane  60 . The image of the arrow is shown in the plane of the X-ray detector  30  and has a linear dimension “2A”. Thus, the magnification is given by “A/a”. The arrow object is positioned in the XZ plane such that the common axis of rotation  40  bisects the arrow in the X-axis direction. Thus, half the length of the arrow, “a”, lies on a first side of the axis  40  and the other half lies on a second side of the axis  40 . The following equations show how the magnification of the image is related to geometric parameters of the inspection system. As previously shown in FIG. 1, the radius of the path followed by the X-ray source  20  about the common axis of rotation  40  is “r”, the angle formed between a central ray  50  from X-ray source  20  and the common axis of rotation is “θ”, the Z-axis distance between the X-ray source  20  and the plane of the X-ray detector  30  is “Z 0 ”, the Z-axis distance between the image plane  60  and the plane of the X-ray detector  30  is “z”, and the Z-axis distance between the X-ray source  20  and the image plane  60  is “(Z 0  z)”. A reference angle “φ” with respect to the vertical axis of rotation  40  is formed between an X-ray projection  52  from the X-ray source  20  to a first end of the arrow object. The derivation of the magnification of the image, “A/a”, in terms of “A”, “a”, “Z 0 ”, and “z” is as follows:  
               tan                 φ     =         a   +   r         Z   0     -   z       =       A   +     R   0     +   r       Z   0                 (   3   )                               
 ( a+r ) Z   0 =( A+R   0   +r )( Z   0   −Z )  (4) 
           a Z   0   +r Z   0   =A ( Z   0   −z )+ R   0 ( Z   0   −z )+ r ( Z   0   −z )  (5) 
           aZ   0   =A ( Z   0   −z )+ R   0 ( Z   0   −z )− rz   (6) 
         [0083]    Using equation (2) for “r” in terms of “z”, equation (6) becomes: 
           a Z   0   =A ( Z   0   −z )+ R   0 ( Z   0   −z )− R   0 ( Z   0   /z− 1)  (7) 
         [0084]    Which results in a magnification factor A/a of:  
               A   a     ·       Z   0         Z   0     -   z               (   8   )                               
 
         [0085]    It is to be understood that the above discussion, although presented in terms of one dimension for purposes of illustration, applies equally to the second dimension of the image plane  60  and the plane  64  of the X-ray detector  30 . Since square or rectangular electronic detectors are more readily available than circular detectors, corresponding square or rectangular images are selected for analysis. Additionally, square or rectangular patterns are more readily adapted to computer analysis than are other shapes, e.g., circular patterns. However, the present invention is also applicable to systems which use detectors and images which are not square or rectangular, including circular detectors and images.  
         [0086]    The following specific example of a system having two pre-defined magnifications further illustrates the geometry discussed above. In this example, a square portion of the image formed on the X-ray detector  30  is selected. The selected square image has a length and a width of “2A”, which in this example is selected to be approximately equal to 3.8 inches. The FOV corresponding to the 2A by 2A (3.8 inches×3.8 inches) image, i.e., the particular region in the image plane  60  of the object being inspected, e.g., a circuit board, has a length and width of “2a”, the size of which varies with the size of the radius “r”. Other fixed dimensions for this example include the radius of the circular path followed by the rotating X-ray detector  30 , “R 0 ”, which is selected to be approximately equal to 5.8 inches, and the Z-axis distance between the rotating X-ray source  20  (X-ray tube target) and the rotating X-ray detector  30 , “Z 0 ”, which is selected to be approximately equal to 12.5 inches. A first magnification factor, MAG 1, of approximately 19× is achieved at a radius “r” of approximately 0.32 inches. The first magnification factor, MAG 1, has an FOV of approximately of 0.2 inches×0.2 inches in image plane  60  and a Z-axis distance between the image plane  60  and the plane  64  of the X-ray detector  30  “z” of approximately 11.84 inches. Similarly, a second magnification factor, MAG 2, of approximately 4.75× is achieved at a radius “r” of approximately 1.55 inches. The second magnification factor, MAG 2, has an FOV of approximately of 0.8 inches×0.8 inches in image plane  60  and a Z-axis distance between the image plane  60  and the plane  64  of the X-ray detector  30 , “z”, of approximately 8.87 inches. The MAG 1 and MAG 2 configurations are summarized in Table 1 below.  
                                         TABLE 1                                   MAG 1   MAG 2                                    Field of View - FOV (2a × 2a)   0.2″ × 0.2″   0.8″ × 0.8″       Z-axis Distance between Image   0.32″   1.55″       plane 60 X-ray Detector Plane 30 (z)       Magnification Factor (A/a)   19×   4.75×       Detected Image Size (2A × . 2A)   3.8″ × . 3.8″   3.8″ × 3.8″       Rotating X-ray Detector Radius (R 0)     5.8″   5.8″       Distance between X-ray Source and   12.5″   12.5″       X-ray Detector (Z 0 )                  
 
         [0087]    Circuit Board Inspection Using Electronic Z-axis Laminography Systems  
         [0088]    There are two primary options for using the above described electronic Z-axis laminography system for inspection of electrical connections (e.g., solder joints) on circuit boards. The first option supports the circuit board at a single fixed Z-axis position in the system and varies the radius of the X-ray source to obtain laminographic images at all other Z-axis locations of interest. The second option provides mechanical supports for the circuit board at multiple fixed Z-axis positions in the system and varies the radius of the X-ray source to obtain laminographic images at Z-axis locations intermediate the fixed locations.  
         [0089]    The first option includes a laminography system having a mechanical support for the circuit board which is located at a single, i.e., fixed, Z-axis position in the system. While the circuit board support does not allow for movement of the circuit board along the Z-axis of the system, it does provide for precise positioning of the circuit board along the X and Y axes of the system, wherein the XY plane is substantially parallel to the plane of the circuit board. In this system, one base or “central” FOV in a single fixed image plane  60  corresponding to the fixed Z-axis location is selected. Laminographic images of portions of the electrical connections on the circuit board which are either above or below the fixed Z-axis image plane are acquired by changing the radius of the rotating X-ray source as described above. Thus, perturbations to the fixed base or central FOV at the fixed Z-axis location allows for acquisition of laminographic cross-sectional images of regions above and below the fixed Z-axis position.  
         [0090]    An example of the first option is illustrated in FIG. 10. The circuit board is positioned in the laminography system such that an approximate midpoint thickness level of the region of the circuit board (or electrical connection on the circuit board) being inspected approximately coincides with the fixed image plane referred to as Level 1 in FIG. 10. The Z-axis distance between the rotating X-ray source positions  20 . 1 ,  20 . 2 ,  20 . 3  and the plane  64  of the X-ray detector  30  is “Z 0 ”, the Z-axis distance between the image plane  60  and the plane  64  of the X-ray detector  30  is “z”, and the Z-axis distance between the X-ray source positions  20 . 1 ,  20 . 2 ,  20 . 3  and the image plane  60  is “(Z 0 -z)”. The base or “central” FOV in fixed image plane  60 , i.e., Level 1, is located at a distance z 1 , from the plane  64  of the X-ray detector  30  and is characterized by: a first magnification factor; a first radius “r l ,” of the rotating X-ray source  20 . 1 ; a first FOV having dimensions of 2a 1 ,×2a 1 , in image plane  60 ; and a Z-axis distance between the image plane  60  and the plane of the rotating X-ray source  20 . 1  of “(Z 0- z 1 ,)”. A second FOV, i.e., Level 2, is located above Level 1 at a distance Z 2  from the plane  64  of the X-ray detector  30  and is characterized by: a second magnification factor; a second radius “r 2 ” of the rotating X-ray source  20 . 2 ; a second FOV having dimensions of 2a 2 ×2a 2  in image plane  60 ; and a Z-axis distance between the image plane  60  and the plane of the rotating X-ray source  20 . 2  of “(Z 0 -z 2 )”. A third FOV, i.e., Level 3, is located below Level 1 at a distance Z 3  from the plane  64  of the X-ray detector and is characterized by: a third magnification factor; a third radius “r 3 ” of the rotating X-ray source  20 . 3 ; a third FOV having dimensions of 2a 3 ×2a 3  in image plane  60 ; and a Z-axis distance between the image plane  60  and the plane of the rotating X-ray source  20 . 3  of “(Z 0 -Z 3 )”. Similarly, laminographic images at levels intermediate Levels 1 and 2 and Levels 1 and 3 may be acquired by selecting the appropriate radius of the rotating X-ray source  20  in accordance with equation (2).  
         [0091]    Applying the above example to a typical circuit board further illustrates this system. In this specific example, the base or “central” FOV, is selected to correspond to the specific system configuration referred to as MAG 2 as summarized in Table 1. The Z-axis levels of interest for a typical electrical connection inspection are generally located within a range of approximately ±60 mils (0.060 inch) centered about a central Z-axis level. Equation (2) is used to derive the value of the X-ray source radius for each specific Z-axis level. Equation (8) is used to derive the value of the Magnification factor for each specific Z-axis level. Examples of specific parameters for Levels 1, 2 and 3 of this configuration are presented in Table 2. Laminographic images at levels intermediate Levels 1 and 2 and Levels 1 and 3 may be acquired by selecting the appropriate radius of the rotating X-ray source  20  between 1.50 inches and 1.59 inches in accordance with equation (2). Similarly, laminographic images at levels above Level 2 and/or below Level 3 may be acquired by selecting the appropriate radius of the rotating X-ray source  20  in accordance with equation (2).  
                           TABLE 2                           Level 2   Level 1   Level 3                   FOV (2a × 2a)   0.78″ × 0.78″   0.80″ × 0.80″   0.82″ × 0.82″       X-ray Radius (4)   1.50″   1.55″   1.59″       Image Plane-to-   9.93″   9.87″   9.81″       Detector (z)       Magnification Factor   4.86×   4.75×   4.65×       (A/a)       Image Size (2A × 2A)   3.8″ × . 3.8″   3.8″ × . 3.8″   3.8″ × . 3.8″       X-ray Detector Radius   5.8″   5.8″   5.8″       (R 0)         X-ray Source-to-   12.5″   12.5″   12.5″       Detector (Z 0)                    
 
         [0092]    The second option includes a laminography system which provides mechanical supports for the circuit board at multiple fixed Z-axis positions in the system and varies the radius of the X-ray source to obtain laminographic images at Z-axis locations intermediate the fixed locations. An example of the second option involves a simplified Z-axis that allows 2 or more discreet “stops” so that multiple FOVs can be used for magnification purposes. For example, fine pitch devices often require higher magnification than larger discreet components like passive devices (e.g., chip capacitors and resistors). Using the specific example illustrated in Table 1, this type of system could have a first fixed position which magnifies the image by a factor of 4.75 for inspections of the large components on the circuit board and a second fixed position which magnifies the image by a factor of 19 for inspections of the smaller fine pitch devices on the circuit board. Thus, this simplified dual-position design still provides for inspections at any value of Z within the designed inspection range of the system, but no longer requires on-the-fly accurate high-speed Z positioning at any continuous value of Z within the designed inspection range of the system.  
         [0093]    On-the-fly CAD Data Manipulation  
         [0094]    Circuit board inspection systems typically include data files that describe the positions, size, pin locations, and other important design data for all inspected solder joints and other features in all board views. As previously stated, the phrase “board view” refers to the laminographic image of a particular region or area of the circuit board identified by a specific X, Y coordinate of the circuit board. A complete inspection of a circuit board typically includes multiple board views. Additionally, some board views include multiple slices, i.e., cross-sectional images acquired at different Z height locations or layers of the circuit board.  
         [0095]    In prior art inspection systems, the image plane of the inspection system may include several fixed Z-axis locations, one for each calibrated FOV, and the multiple image slices of the circuit board within one of the FOV&#39;s at different Z-levels with respect to the circuit board are acquired by mechanically moving the circuit board along the inspection system Z-axis such that the desired Z-level slice of the circuit board coincides with the fixed inspection system Z-axis location of the image plane for that FOV. Since the inspection system Z-axis location of the image plane is fixed, and the multiple image slices of the circuit board at different Z-levels with respect to the circuit board are positioned at this fixed inspection system Z-axis location, all of the images acquired at this fixed inspection system Z-axis location have the same FOV and magnification. However, as previously described, the present invention replaces the mechanical movement of the circuit board along the Z-axis of the inspection system with electrically controlled relocation of the image plane along the Z-axis of the inspection system. As previously described, this results in image planes positioned at different Z-axis locations of the inspection system having different FOV&#39;s and magnifications. The present invention compensates for these changes in FOV and magnification by modifying the CAD design data on-the-fly to match the magnification of the current image.  
         [0096]    In the present context, “on-the-fly” data analysis refers to real time or near real time modification of the CAD data on as-needed basis for analysis of the current image as opposed to modifying the CAD data in advance and storing it for later recall and utilization. Analysis of the image is then carried out in the normal manner, i.e., comparing the acquired image data with the CAD design data, using the modified CAD data. For example, one situation where on-the-fly CAD data modification is advantageous is where surface mapping of the boards before inspection reveals that each new circuit board is likely to have different Z heights with respect to the inspection system for the same specific Z level within a specific solder joint. These variations in Z heights with respect to the inspection system from board to board are most commonly due to variations in board warpage measured by laser range finder readings from board to board. In other words, board warpage causes a Z level referenced to the circuit board surface to be located at different Z-axis levels of the laminographic inspection system. Thus, electronic relocation of the image plane with respect to the inspection system coupled with on-the-fly CAD data modification provides a processor time and data storage resource efficient means for acquiring images at the desired Z levels of the circuit board and analyzing these images by recalling, modifying and applying the CAD data for use on an as needed basis.  
         [0097]    On-the-fly CAD data manipulation requires that various CAD data fields be modified. The CAD data fields requiring modification depends on the current FOV. Examples of specific CAD files which often require modification are discussed below. The CAD data files discussed below are included to illustrate the procedure and are not to be considered as limiting which files may be subject to modification when practicing the present invention. The present invention is applicable to virtually any type of CAD data which may be required for laminographic electrical connection or solder joint inspection.  
         [0098]    Conversions: Pixels to Mils and Mils to Pixels  
         [0099]    Conversion of image units, e.g., pixels, to physical dimensionals, e.g., mils, is accomplished by dividing the physical size of the current FOV by the number of pixels included in an image frame buffer width as follows: 
         PixelsToMils=Current FOV in mils/Frame Buffer Width in pixels  (9) 
         [0100]    This is illustrated by a specific example where the number of pixels in an image is 2048×2048 and the image corresponds to a region of an object having physical dimensions of 800 mils×800 mils (0.8 inches×0.8 inches). The PixelsToMils conversion factor for this example is determined from equation (9) by dividing 800 mils by 2048 pixels, yielding a PixelsToMils conversion factor which is approximately equal to 0.391 mils. Thus, the width of each pixel in the image corresponds to a width of approximately 0.391 mils on the object shown in the image.  
         [0101]    Similarly, the inverse conversion from physical dimensionals, e.g., mils, to image units, e.g., pixels, is accomplished by dividing the number of pixels included in an image frame buffer width by the physical size of the current FOV as follows: 
         MilsTopixels=Frame Buffer Width in pixels/Current FOV in mils  (10) 
         [0102]    Using the previous specific example where the number of pixels in the image is 2048×2048 and the image corresponds to a region of an object having physical dimensions of 800 mils×800 mils, the MilsToPixels conversion factor is determined from equation (10) by dividing 2048 pixels by 800 mils, yielding a MilsToPixels conversion factor which is approximately equal to 2.56 pixels. Thus, a width of approximately 1 mil on the object corresponds to approximately 2.56 pixels in the image of the object.  
         [0103]    Conversion of CAD Coordinates to Pixels  
         [0104]    It is generally advantageous to perform on-the-fly calculations for coordinating and comparing CAD data with image data in pixel coordinate format. However, the primary format for CAD data received by the inspection facility is generally in physical dimensions format (e.g., mils). Thus, the physical dimensions format CAD data is converted to pixel format using equation for the conversion of Mils-To-Pixels. Since coordination and comparison of the CAD data with the image data is generally performed in pixel coordinate format, the following discussion is presented in terms of pixel coordinate format. However, if physical dimensions format is preferred for a particular application, the present invention may also be practiced in physical dimension format.  
         [0105]    FOV Correction Factor  
         [0106]    A “nominal FOV” or reference FOV refers to a field of view which is used as a reference for calibration of other FOV&#39;s of the laminography inspection system. For example, a laminography inspection system may be configured such that the nominal/reference FOV corresponds to an image having a specific magnification factor of an area in the image plane having a specific size. In certain situations, it may be advantageous for a laminography inspection system to have multiple configurations and corresponding multiple nominal FOVs or reference FOVs. For example, referring to the example of a specific laminography system summarized in Table 1, this system has a first nominal/reference FOV (MAG 1) which creates a 3.8 inch×3.8 inch image on  5  a detector which corresponds to an area in the image plane which is 0.2 inch×0.2 inch in size. Thus, this first nominal/reference FOV has a magnification factor of 19. Similarly, this system also has a second nominal/reference FOV (MAG 2) which creates a 3.8 inch×3.8 inch image on a detector which corresponds to an area in the image plane which is 0.8 inch×0.8 inch in size. Thus, this second nominal/reference FOV has a magnification factor of 4.75.  
         [0107]    The fields of view and magnification factors for Z-axis locations which are different from the Z-axis location for a nominal/reference FOV are referred to in this discussion as a “current FOV”. Thus, if an image is acquired at a “current FOV” which does not coincide with a “nominal FOV”, the CAD data must be adjusted to reflect the differences (e.g., magnification, etc.) between the nominal FOV and the current FOV before the image data in the current FOV can be compared to the CAD design data. This FOV conversion of the CAD data from a nominal FOV to a current FOV is done on-the-fly and uses a conversion factor referred to as “FOV Correction” which is calculated as follows: 
         FOVCorrection=NominalFOV/CurrentFOV  (11) 
         [0108]    A specific example, shown in FIGS. 11, 12,  13  and  14 , is used in the following discussion to illustrate the application of on-the-fly CAD data modification for analysis of laminographic circuit board images using the FOVCorrection conversion factor, location conversion factors, and length conversion factors. FIGS. 11 and 12 show a perspective view and a cross sectional view, respectively, of the test object  10  (see FIG. 2 a ) mounted on a circuit board  620 . Three corners of the test object  10  are located at circuit board coordinates (x 1 ,y 1 ,), (x 2 ,y 1 ,) and (x 1 ,y 2 ). The center of the test object  10  is located at circuit board coordinates (x Pc ,y Pc ). Referring to FIGS. 10 and 12, the circle image plane  60   b  in the test object  10  is located at the distance z, from the plane  64  of the X-ray detector  30  (Level 1); the arrow image plane  60   a  in the test object  10  is located at the distance Z 2  from the plane  64  of the X-ray, detector  30  (Level 2); and the cross image plane  60   c  in the test object  10  is located at the distance Z 3  from the plane  64  of the X-ray detector  30  (Level 3). As shown in FIG. 11, coordinates (x BV ,y BV ) identify a first board view location on circuit board  620 .  
         [0109]    For purposes of this example, the test object  10  has been selected to have the following physical characteristics: a length of approximately 413 mils; a width of approximately 213 mils; a height of approximately 240 mils; the circle image plane  60   b  (Level 1) positioned in the middle of the height dimension; the arrow image plane 60 a  (Level 2) positioned 60 mils above Level 1; and the cross image plane  60   c  (Level 3) positioned 60 mils below Level 1. Additionally, the laminography system selected for the inspection of the test object  10  having these physical characteristics is the specific example system summarized in Table 2.  
         [0110]    As previously stated, it is often more efficient to store the design CAD data for a particular circuit board in pixel format. In one implementation of the present invention, it has been found that on-the-fly calculation times can be minimized if the CAD data is stored in the analysis system in a pixel format which corresponds to a specific nominal/reference FOV. Additionally, inspection procedures may be defined for each particular circuit board. These inspection procedures include defining specific board views and objects or features (e.g., solder joints) to inspect in each board view.  
         [0111]    For example, one inspection procedure designed to check the position and dimensions of the test object  10  on circuit board  620  and the features of the circle  82 , arrow  81  and cross  83  in the test object  10  at Levels 1, 2 and 3, respectively, includes the following steps. First, determine a first board view location at board coordinates (x Bv ,y Bv ) such that Level 1, 2 and 3 board views at this location include the test object  10 . Second, define a first board view centered at board coordinates (x Bv ,y Bv ) at the first Z-axis level z 1 , (Level 1) and select the FOV of the first board view as the nominal FOV. Third, define a second board view centered at board coordinates (x BV ,y BV ) at the second Z-axis level Z2 (Level 2) and select the FOV of the second board view as the first current FOV. Fourth, define a third board view centered at board coordinates (x BV ,y Bv ) at the third Z-axis level Z 3  (Level 3) and select the FOV of the third board view as the second current FOV.  
         [0112]    Implementation of this procedure to check the position and dimensions of the test object  10  on circuit board  620  and the features of the circle  82 , arrow  81  and cross  83  in the test object  10  at Levels 1, 2 and 3, respectively, includes creating a pixel format CAD database which describes the features of the test object  10  from the physical dimensions CAD database for the test object  10 . An example of a pixel format CAD database  720   cd  corresponding to the first board view centered at board coordinates (x BV ,y BV ) at the first Z-axis level z 1 , (Level 1) and the nominal FOV is shown in FIG. 13A. The CAD data  720   cd  for Level 1 shows the center of the first board view, corresponding to the first board view dimensional coordinates (x BV ,y BV ), located at pixel coordinates  0   024 , 1024 ). Additionally, the CAD data  720   cd  for Level 1 shows:  
         [0113]    a) the three corners of the test object  10  corresponding to the dimensional coordinates (x 1 y 2 ), (x 1 ,y 1 ), and (x 2 ,y 1 ), located at pixel coordinates ( 195 , 920 ),  0   253 , 920 ) and ( 1253 , 375 ), respectively; and b) the center of the test object corresponding to the dimensional coordinates (x PC ,y PC ), located at pixel coordinates ( 724 , 648 ).  
         [0114]    A first laminographic image or board view  720   id  corresponding to the first board view location (x BV ,y BV ) at the first Z-axis level z, (Level 1) of test object  10  is shown in FIG. 14A. The image data  720   id  for Level 1 shows the center of the first board view, corresponding to the first board view dimensional coordinates (x BV ,y BV ), located at image pixel coordinates ( 1024 , 1024 ). The field of view (FOV) of the first board view image data  720   id  at Level 1, i.e., the portion of the circuit board  620  at the first Z-axis level z 1 , centered at the first board view location (x BV ,y BV ) which is included in the first laminographic board view image  720   id,  is represented by the dashed line perimeter  640  in FIG. 11.  
         [0115]    In this example, the FOV  640  at the dashed line position is selected as the “nominal FOV and has a size of approximately 800 mils×800 mils (see Table 10).  
         [0116]    In a typical circuit board inspection system according to the present invention, the CAD data which describes features in the first field of view  640  (e.g., the location and dimensions of the test object  10 , the circles within the plane  60   b  of the test object  10 , etc.) are available to the analysis portion of the inspection system in pixel format. As shown in the first board view image data  720   id  in FIG. 14A: a) the test object  10  forms an image having corners at pixel locations ( 205 , 920 ), ( 1263 , 920 ) and ( 1263 , 375 ) corresponding to the corners (x 1 ,y 2 ), (x 1 ,y 1 ) and x 2 ,y 1 ), respectively, of the test object  10 ; and b) the center of the test object  10  forms an image at pixel locations ( 734 , 648 ) corresponding to the center (x PC ,y PC ) of the test object  10 . Since the FOV  640  was selected as the “nominal FOV”, the first board view image data at level z 1 ,  720   id  (FIG. 14A) may be compared directly to the pixel format test object  10  CAD data at level z 1 , (FIG. 13A) corresponding to the first board view centered at board coordinates (x Bv ,y Bv ) at the first Z-axis level z 1 . This comparison of the image data  720   id  (FIG. 14A) with the corresponding CAD data  720   cd  (FIG. 13A) reveals that the test object  10  is shifted in the positive x direction by 10 pixels and is positioned correctly in the y direction.  
         [0117]    In accordance with the present invention, inspection of the arrow image plane  60   a  (Level 2 at Z 2 ) positioned 60 mils above Level 1; and the cross image plane  60   c  (Level 3 at Z 3 ) positioned 60 mils below Level 1, is accomplished by changing the radius of the X-ray source as summarized in Table 2. Thus, to change from Level 1 to Level 2, the radius of the X-ray source is changed from approximately 1.55 inches to approximately 1.50 inches which also changes the FOV from approximately 800 mils×800 mils to approximately 780 mils×780 mils. A second laminographic image or board view  750   id  corresponding to the first board view location (x Bv ,y Bv ) at the second Z-axis level Z 2  (Level 2) of test object  10  is shown in FIG. 14B. The image data  750   id  for Level 2 shows the center of the first board view, corresponding to the first board view dimensional coordinates (x BV ,y BV ), located at image pixel coordinates ( 1024 , 1024 ). The field of view (FOV) of the first board view image data  750   id  at Level 2, i.e., the portion of the circuit board  620  at the second Z-axis level Z 2  centered at the first board view location (x BV ,y BV ) which is included in the second laminographic board view image  750   id  , is selected as the first “current FOV” and has a size of approximately 780 mils×780 mils (see Table 2). Similarly, to change from Level 1 to Level 3, the radius of the X-ray source is changed from approximately 1.55 inches to approximately 1.59 inches which also changes the FOV from approximately 800 mils×800 mils to approximately 820 mils×820 mils. A third laminographic image or board view  780   id  corresponding to the first board view location (x BV ,y BV ) at the third Z-axis level Z 3  (Level 3) of test object  10  is shown in FIG. 14C. The image data  780   id  for Level 3 shows the center of the first board view, corresponding to the first board view dimensional coordinates (x BV ,y BV ), located at image pixel coordinates ( 1024 , 1024 ). The field of view (FOV) of the first board view image data  780   id  at Level 3, i.e., the portion of the circuit board  620  at the third Z-axis level Z3 centered at the first board view location (x BV ,y BV ) which is included in the third laminographic board view image  780   id,  is selected as the second “current FOV” and has a size of approximately 820 mils×820 mils (see Table 2).  
         [0118]    The FOV Correction factor previously defined in equation  11 , is used to perform the on-the-fly conversion of specific X, Y coordinates in the CAD data from a NominaIFOV to a CurrentFOV as follows: 
         Current X =(Nominal X −ImageCenter X )*FOVCorrection+ImageCenter X   
         Current Y =(Nominal Y −ImageCenter Y )*FOVCorrection+ImageCenter Y   (12) 
         [0119]    The FOVCorrection factor is also used to perform on-the-fly conversion of specific dimensions in the X-axis and Y-axis directions, AX and DY, in the CAD data from a NominaIFOV to a CurrentFOV as follows: 
         CurrentΔ X =NominalΔ X *FOVCorrection 
         CurrentΔ Y =NominaIΔ Y *FOVCorrection  (13) 
         [0120]    Examples of on-the-fly conversion of the nominal FOV CAD database  720   cd  for test object  10  at Level 1 shown in FIG. 13A to the first current view at Level 2 and the second current view at Level 3 are shown in FIGS. 13B and 13C, respectively. For example, equations  12  convert the CAD data of Level 2 at the nominal FOV of Level 1 to the first current FOV of Level 2 (FIG. 13B) as follows: a) the three corners of the test object  10  corresponding to the dimensional coordinates (x 1 ,y 2 ), (x 1 ,y 1 ) and (x 2 ,y 1 ), are located at pixel coordinates ( 176 , 918 ), ( 1258 , 918 ) and ( 1258 , 360 ), respectively, in the first current FOV; and b) the center of the test object  10  corresponding to the dimensional coordinates (x PC ,y PC ), is located at pixel coordinates ( 717 , 639 ) in the first current FOV. Similarly, equations  12  convert the CAD data of Level 3 at the nominal FOV of level 1 to the second current FOV of Level 3 (FIG. 13C) as follows: a) the three corners of the test object  10  corresponding to the dimensional coordinates (x 1 ,y 2 ), (x 1 ,y 1 ) and (x 2 ,y 1 ), are located at pixel coordinates ( 212 , 922 ), ( 1248 , 922 ) and ( 1248 , 389 ), respectively, in the second current FOV; and b) the center of the test object  10  corresponding to the dimensional coordinates (x PC ,y PC ), is located at pixel coordinates ( 730 , 656 ) in the second current FOV. Thus, analysis of the laminographic image for Level 2 (FIG. 14B) is accomplished using the first current FOV on-the-fly converted CAD data for Level 2 (FIG. 13B) and analysis of the laminographic image for Level 3 (FIG. 14C) is accomplished using the second current FOV on-the-fly converted CAD data for Level 3 (FIG. 13C). Equations  13  are employed in a similar manner to convert lengths in the CAD data of Level 1 (FIG. 13A) at the nominal FOV to the first current FOV of Level 2 (FIG. 13B) and the second current FOV of Level 3 (FIG. 13C) for comparison to the corresponding laminographic images at Levels 1, 2 and 3.  
         [0121]    Examples of specific parameters which are often used for inspection of solder joints/electrical connections include pad locations, pin locations, and pad dimensions. On-the-fly conversion of the CAD fields/data for these parameters may be accomplished as follows: 
         Pad X Location=(NominaIPad X−X lmageCenter)*FOVCorrection+ X lmageCenter 
         Pad Y Location=(NominaIPad Y−Y lmageCenter)*FOVCorrection+ Y lmageCenter  (14) 
         Pin X Location=(NominaIPin X−X lmageCenterl*FOVCorrection+ X lmageCenter 
         Pin Y Location=(NominaIPin Y−Y lmageCenter)*FOVCorrection+ Y lmageCenter  (15) 
         PadD x =NominaIPadD x *FOVCorrection 
         PadD y =NominaIPadD y *FOVCorrection 
         PinD x =NominaIPinD x *FOVCorrection 
         PinD y =NominaIPinD y *FOVCorrection  (16) 
         [0122]    These coordinate translations and scaling are performed for each slice of each board view for each board inspected, based on the current Z height which determines the current FOV and magnification.  
         [0123]    As presented in the above discussion and specific examples, the coordinates of features on the circuit board are referenced to the selected board view. Thus, the same features, referenced to a different board view would have different coordinates. Many such issues arise in the specific application of the present invention and do not limit the scope of the present invention, as its teachings can be readily adapted to numerous analysis conventions.  
         [0124]    The process for performing on-the-fly CAD data manipulations for the analysis of laminographic images according to the present invention is summarized in the flow chart shown in FIG. 15. In block  810 , a “Nominal or Reference Image Plane” at a Z-axis location “z 1 ,” in the object being inspected is determined. In block  820 , the size of the “Nominal FOV” corresponding to the Reference/Nominal Image Plane at Z-axis location “z 1 ” is determined. In block  830 , a “First Current Image Plane” at a Z-axis location “z s ” in the object being inspected is determined. In block  840 , the size of the First “Current FOV” corresponding to the First Current Image Plane at Z-axis location “Z 2 ” is determined. In block  850 , an FOVCorrection Factor for the First Current Image Plane is determined by using the sizes of the “Nominal FOV”; the First “Current FOV” and Equation (11). In block  860 , the FOVCorrection Factor is used to adjust the CAD data on-the-fly as needed for the analysis of the cross-sectional laminographic image at Z-axis location “Z 2 ”. While the above discussion has been in terms of an FOVCorrection factor based on relative sizes of the fields of view at different Z-axis locations, a similar and equivalent procedure could also be performed using other parameters, for example, the magnification factors for the different Z-axis locations. These and other such modifications are considered to be included within the scope of the present invention.  
         [0125]    Other Issues and Considerations  
         [0126]    Since the present system supplies cross-sectional images at various Z heights, a common use is to take multiple slices of a solder joint and correlate data between slices. Although the distances between slices are generally small, a few mils, for most surface mount devices, more substantial distances can be encountered for certain specific device types. For example, BGA devices are sometimes imaged at both the top and bottom of the ball, which is a distance of approximately 25 mils. Plated Through Hole (PTH) devices are imaged on both the top and bottom pads, which will be the entire board thickness, which is a distance of approximately 70 mils. For these larger distances, some measurements must be corrected.  
         [0127]    For example, a locator algorithm is usually run at the center of the ball for BGA devices. The x and y coordinates it finds will correspond to different x and y locations on different slices, such as the pad slice and the top package slice.  
         [0128]    Similarly a PTH location found in the barrel may need to be adjusted on the top and bottom pad. These can be cleverly handled by correcting these locations in a software module, which maintains and distributes these located positions to the algorithms. Similar magnification corrections to those discussed above to correct CAD locations can be applied to the locator positions at runtime as well.  
         [0129]    Similarly, size measurement may need normalization depending on the Z-height of the slice used to gather the measurement. For example, any measurements in units of pixel distances, if they exist, must be converted to mils using the current perturbed FOV before any comparison or use on different slices.  
       Summary, Ramifications and Scope  
       [0130]    Accordingly, the reader will see that the present invention solves many of the specific problems encountered when inspecting solder connections on circuit boards. Particularly important is that it removes the need for a mechanical means to move the circuit board along the Z-axis without impeding the analysis of the laminographic images at various Z-axis levels in the circuit board. Furthermore, the electronic relocation of the image plane with respect to the inspection system coupled with on-the-fly CAD data modification provides a processor time and data storage resource efficient means for acquiring images at the desired Z levels of the circuit board and analyzing these images by recalling, modifying and applying the CAD data for use on an as needed basis.  
         [0131]    Although the description above contains many specificities, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of this invention. For example, alternative techniques and image parameters may be used to determine how to convert the CAD data at the nominal FOV for use at a current FOV. Additionally, alternative CAD data parameters may be used for image analysis; alternative techniques may be used to acquire the cross sectional images; alternative methods may be used for changing the Z-axis level at which images are acquired; etc.  
         [0132]    The invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims and their legal equivalents, rather than by the foregoing description and specific examples given. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.