Abstract:
A calibration and part inspection method for the inspection of ball grid array, BGA, devices. Two cameras image a precision pattern mask with dot patterns deposited on a transparent reticle. The precision pattern mask is used for calibration of the system. A light source and overhead light reflective diffuser provide illumination. A first camera images the reticle precision pattern mask from directly below. An additional mirror or prism located below the bottom plane of the reticle reflects the reticle pattern mask from a side view, through prisms or reflective surfaces, into a second camera and a second additional mirror or prism located below the bottom plane of the reticle reflects the opposite side view of the reticle pattern mask through prisms or mirrors into a second camera. By imaging more than one dot pattern the missing state values of the system can be resolved using a trigonometric solution. The reticle with the pattern mask is removed after calibration and the BGA to be inspected is placed with the balls facing downward, in such a manner as to be imaged by the two cameras. The scene of the part can thus be triangulated and the dimensions of the BGA are determined.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a continuation of pending application Ser. No. 09/351,892, filed Jul. 13, 1999, which is a continuation-in-part of application Ser. No. 09/008,243, filed Jan. 16, 1998, now issued as U.S. Pat. No. 6,072,898. The application Ser. No. 09/351,892 and U.S. Pat. No. 6,072,898 are incorporated by reference herein, in their entireties, for all purposes. 
     
    
     NOTICE REGARDING COPYRIGHT  
       [0002]     A portion of the disclosure of this patent document contains material that is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent disclosure, as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all copyright rights whatsoever.  
       FIELD OF THE INVENTION  
       [0003]     This invention relates to an apparatus for three dimensional inspection, a method of manufacturing electronic components using the apparatus, and and the electronic components produced according to the method. More particularly, this invention relates to three dimensional inspection of solder balls on ball grid arrays and solder bumps on wafer and die, and to calibration.  
       BACKGROUND OF THE INVENTION  
       [0004]     Prior art three dimensional inspection systems have involved laser range finding technology, moire interferometry, structured light patterns or two cameras. The laser range finding method directs a focused laser beam onto the Ball Grid Array, BGA, and detects the reflected beam with a sensor. Elements of the BGA are determined in the X, Y and Z dimensions utilizing a triangulation method. This method requires a large number of measurement samples to determine the dimensions of the BGA resulting in longer inspection times. This method also suffers from specular reflections from the smooth surfaces of the solder balls resulting in erroneous data.  
         [0005]     Moire interferometry utilizes the interference of light waves generated by a diffraction grating to produce a pattern of dark contours on the surface of the BGA. These contours are of known distance in the Z dimension from the diffraction grating. By counting the number of contours from one point on the BGA to another point on the BGA, the distance in the Z dimension between the two points can be determined. This method suffers from the problem of low contrast contour lines resulting in missed counting of the number of contours and resulting in erroneous data. This method also suffers from the contour lines merging at surfaces with steep slopes, such as the sides of the balls on the BGA, resulting in an incorrect count of the number of contours and resulting in erroneous data.  
         [0006]     Structured light systems project precise bands of light onto the part to be inspected. The deviation of the light band from a straight line is proportional to the distance from a reference surface. The light bands are moved across the part, or alternately the part is moved with respect to the light bands, and successive images are acquired. The maximum deviation of the light band indicates the maximum height of a ball. This method suffers from specular reflections due to the highly focused nature of the light bands resulting in erroneous data. This method further suffers from increased inspection times due to the number of images required.  
         [0007]     Two camera systems utilize one camera to view the BGA device in the normal direction to determine X and Y dimensions and the second camera to view the far edges of the balls from an angle. The two images are combined to determine the apparent height of each ball in the Z dimension utilizing a triangulation method. This method suffers from the need for a higher angle of view of the ball from the second camera resulting in looking at a point significantly below the top of the ball for BGA&#39;s having fine pitch. This method also suffers from limited depth of focus for the second camera limiting the size of BGA&#39;s that can be inspected. This system can only inspect BGA&#39;s and not other device types such as gullwing and J lead devices.  
         [0008]     The prior art does not provide two separate and opposite side views permitting larger BGA&#39;s to be inspected or nonlinear optics to enhance the separation between adjacent ball images in the side perspective view.  
         [0009]     It is therefore a motivation of the invention to improve the accuracy of the measurements, the speed of the measurements, the ability to measure all sizes and pitches of BGA&#39;s and to measure other devices including gullwing and J lead parts in a single system.  
       SUMMARY OF THE INVENTION  
       [0010]     The invention provides a calibration and part inspection method and apparatus for the inspection of BGA devices. The invention includes two cameras to image a precision pattern mask with dot patterns deposited on a transparent reticle to be inspected and provides information needed for calibration. A light source and overhead light reflective diffuser provide illumination that enhances the outline of the ball grid array. A first camera images the reticle precision pattern mask from directly below. An additional mirror or prism located below the bottom plane of the reticle reflects the reticle pattern mask from a side view, through prisms or reflective surfaces, into a second camera. A second additional mirror or prism located below the bottom plane of the reticle reflects the opposite side view of the reticle pattern mask through prisms or mirrors into a second camera. By imaging more than one dot pattern, the missing state values of the system can be resolved using a trigonometric solution. The reticle with the pattern mask is removed after calibration and a BGA to be inspected is placed with the balls facing downward, in such a manner as to be imaged by the two cameras. The scene of the part can thus be triangulated and the dimensions of the BGA are determined.  
         [0011]     The system optics are designed to focus images for all perspectives without the need for an additional focusing element. The optics of the side views may incorporate a nonlinear element to stretch the image in one direction to increase the apparent spacing between adjacent ball images allowing a lower angle of view and inspection of BGA&#39;s with closely spaced balls.  
         [0012]     The invention provides an apparatus for inspecting a ball grid array, wherein the apparatus is calibrated using a precision pattern mask with dot patterns deposited on a calibration transparent reticle. The apparatus for inspecting a ball grid array comprises a means for mounting the ball grid array and a means for illuminating the ball grid array to provide an outline of the ball grid array. A first camera is positioned to image the ball grid array to provide a first image of the ball grid array. A first means for light reflection is positioned to reflect the ball grid array through a second means for light reflection into a second camera, wherein the second camera provides a second image of the ball grid array. A third means for light reflection is positioned to reflect an opposite side view of the ball grid array into a fourth means for light reflection and into the second camera as part of the second image of the ball grid array. A means for image processing, such as a computer, microprocessor or digital signal processor, processes the first image and second image of the ball grid array to inspect the ball grid array.  
         [0013]     The invention also provides a method for three dimensional inspection of a lead on a part mounted on a reticle. The method comprises the steps of: locating a first camera to receive an image of the lead; transmitting an image of the lead to a first frame grabber; providing fixed optical elements to obtain two side perspective views of the lead; locating a second camera to receive an image of the two side perspective views of the lead; transmitting the two side perspective views of the lead to a second frame grabber; operating a processor to send a command to the first frame grabber and second frame grabber to acquire images of pixel values from the first camera and the second camera; and processing the pixel values with the processor to obtain three dimensional data about the lead.  
         [0014]     The invention also provides a method to inspect a ball grid array device comprising the steps of: locating a point on a world plane determined by a bottom view ray passing through a center of a ball on the ball grid array device; locating a side perspective view point on the world plane determined by a side perspective view ray intersecting a ball reference point on the ball and intersecting the bottom view ray at a virtual point where the side perspective view ray intersects the world plane at an angle determined by a reflection of the side perspective view ray off of a back surface of a prism where a value of the angle was determined during a calibration procedure; calculating a distance L, as a difference between a first world point, defined by an intersection of the bottom view ray with a Z=0 world plane, and a second world point, defined by the intersection of the side perspective view ray and the Z=0 a world plane, where a value Z is defined as a distance between a third world point and is related to L, as follows: 
 
tan σ 1   =Z/L   1  
 
 Z=L   1  tan θ 1  
 
 wherein Z is computed based on the angle; computing an offset E as the difference between the virtual point defined by the intersection of the bottom view ray and the side perspective view ray and a crown of a ball at a crown point that is defined by the intersect ion of the bottom view ray with the crown of the ball, and can be calculated from a knowledge of the angle and ideal dimensions of the ball where a final value of Z for the ball 
 
 Z   Final   =Z−E.  
 
         [0015]     The invention also provides a method for finding a location and dimensions of a ball in a ball grid array from a bottom image comprising the steps of: defining a region of interest in the bottom image of an expected position of a ball where a width and a height of the region of interest are large enough to allow for positioning tolerances of the ball grid array for inspection; imaging the ball, wherein the ball is illuminated to allow a spherical shape of the ball to present a donut shaped image, wherein the region of interest includes a perimeter of the ball wherein the bottom image comprises camera pixels of higher grayscale values and where a center of the bottom image comprises camera pixels of lower grayscale value and wherein a remainder of the region of interest comprises camera pixels of lower grayscale values; finding an approximate center of the ball by finding an average position of pixels having pixel values that are greater than a predetermined threshold value; converting the region of lower grayscale pixel values to higher grayscale values using coordinates of the approximate center of the ball; and finding the center of the ball.  
         [0016]     The invention also provides a method for finding a reference point on a ball in an image of a side perspective view of a ball grid array comprising the steps of: defining a region of interest in the image from an expected position of a ball wherein a width and a height of the region of interest are large enough to allow for positioning tolerances of the ball grid array; imaging the ball, wherein the ball is illuminated to allow a spherical shape of the ball to present a crescent shaped image having camera pixels of higher grayscale values, and wherein a remainder of the region of interest comprises camera pixels of lower grayscale values; computing an approximate center of the crescent shaped image by finding an average position of pixels that are greater than a predetermined threshold value; using coordinates of the approximate center of the crescent; determining a camera pixel as a seed pixel representing a highest edge on a top of the crescent shaped image; and determining a subpixel location of the reference point based on the camera pixel coordinates of the seed pixel that define coordinates of a region of interest for the seed pixel.  
         [0017]     Electronic components are produced according to manufacturing methods that provide for three dimensional inspection of the electronic componenets. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0018]     To illustrate this invention, a preferred embodiment will be described herein with reference to the accompanying drawings.  
         [0019]      FIG. 1A  shows the apparatus of the invention for system calibration.  
         [0020]     FIGS.  1 B 1 ,  1 B 2 , and  1 B 3  show an example calibration pattern and example images of the calibration pattern acquired by the system.  
         [0021]      FIG. 2A  shows a flow chart of a method of the invention used for calibration of the bottom view.  
         [0022]      FIG. 2B  shows a flow chart of a method of the invention used for determining the state values, and the X and Y world coordinates, of the bottom view of the system.  
         [0023]      FIG. 2C  shows a flow chart of a method of the invention used for calibration of the side perspective views.  
         [0024]      FIG. 2D  shows a flow chart of a method of the invention used for determining the state values of the side perspective views of the system.  
         [0025]      FIG. 2E  shows the relationship of a side perspective angle to the ratio of the perspective dimensions to the non-perspective dimensions.  
         [0026]     FIGS.  2 F 1  and  2 F 2  show a bottom view and a side perspective view of precision dots used in the method for determining a side perspective view angle.  
         [0027]      FIG. 3A  shows the apparatus of the invention for part inspection.  
         [0028]     FIGS.  3 B 1 ,  3 B 2 , and  3 B 3  show example images of a part acquired by the system.  
         [0029]      FIG. 4  shows a method of the invention for the three dimensional inspection of balls on a ball grid array.  
         [0030]      FIGS. 5A and 5B  together show a flow chart of the three dimensional inspection method of the invention.  
         [0031]      FIGS. 6A and 6B  show an example ball of a ball grid array and associated geometry used in a method of the invention for determining the Z position of the ball.  
         [0032]      FIG. 7A  shows one example of an image used in the grayscale blob method of the invention.  
         [0033]      FIG. 7B  shows one example of an image used with the method of the invention to perform a subpixel measurement of the ball reference point.  
         [0034]      FIG. 8A  shows a side perspective image of the calibration pattern magnified in one dimension.  
         [0035]      FIG. 8B  shows a side perspective image of the balls on a BGA, magnified in one dimension.  
         [0036]      FIG. 9  shows an apparatus for presenting a BGA for inspection.  
         [0037]      FIGS. 10A and 10B  show an example ball of a ball grid array with associated geometry as used with a method of the invention for determining the Z position of a ball using two side perspective views.  
         [0038]      FIG. 11A  shows the apparatus of the invention for system calibration, utilizing a single side perspective view.  
         [0039]     FIGS.  11 B 1 ,  11 B 2 , and  11 B 3  show an example calibration pattern and example images of a calibration pattern acquired by the system, utilizing a single side perspective view, of the invention.  
         [0040]      FIG. 12A  shows the apparatus of the invention for ball inspection utilizing a single side perspective view.  
         [0041]     FIGS.  12 B 1 ,  12 B 2 , and  12 B 3  show an example ball grid array and example images of the ball grid array for three dimensional inspection, utilizing a single side perspective view.  
         [0042]      FIG. 13  shows the apparatus of the invention for the three dimensional inspection of ball grid array devices, gullwing devices and J lead devices.  
         [0043]      FIG. 14  shows the apparatus of the invention for the three dimensional inspection of parts utilizing three cameras.  
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0044]     In one embodiment of the invention, the method and apparatus disclosed herein is a method and apparatus for calibrating the system by placing a pattern of calibration dots of known spacing and size on the bottom plane of a calibration reticle. From the precision dots the missing state values of the system are determined allowing for three dimensional inspection of balls on ball grid array devices, BGA devices or balls on wafers or balls on die. In one embodiment of the invention the system may also inspect gullwing and J lead devices as well as ball grid arrays.  
         [0045]     Refer now to  FIG. 1A  which shows the apparatus of the invention configured with a calibration reticle for use during calibration of the state values of the system. The apparatus obtains what is known as a bottom image  50  of the calibration reticle  20 . To take the bottom image  50  the apparatus includes a camera  10  with a lens  11  and calibration reticle  20  with a calibration pattern  22  on the bottom surface. The calibration pattern  22  on the reticle  20  comprises precision dots  24 . The camera  10  is located below the central part of the calibration reticle  20  to receive an image  50  described in conjunction with FIGS.  1 B 1 ,  1 B 2 , and  1 B 3 . In one embodiment the camera  10  comprises an image sensor. The image sensor may be a charged coupled device array. The camera  10  is connected to a frame grabber board  12  to receive the image  50 . The frame grabber board  12  provides an image data output to a processor  13  to perform a two dimensional calibration as described in conjunction with  FIG. 2A . The processor  13  may store an image in memory  14 . The apparatus of the invention obtains an image of a pair of side perspective views and includes using a camera  15  with a lens  16  and a calibration reticle  20 . The camera  15  is located to receive an image  60 , comprising a pair of side perspective views, described in conjunction with FIGS.  1 B 1 ,  1 B 2 , and  1 B 3 . Fixed optical elements  30 ,  32  and  38  provide a first side perspective view and fixed optical elements  34 ,  36 ,  38  for a second side perspective view. The fixed optical elements  30 ,  32 ,  34 ,  36  and  38  may be mirrors or prisms. As will be appreciated by those skilled in the art additional optical elements may be incorporated. The camera  15  is connected to a frame grabber board  17  to receive the image  60 . The frame grabber board  17  provides an image data output to a processor  13  to perform a two dimensional inspection as described in conjunction with  FIG. 2B . The processor  13  may store an image in memory  14 . In one embodiment of the invention, the apparatus may contain a nonlinear optical element  39  to magnify the side perspective image  60  in one dimension as shown in  FIG. 8A . In another embodiment of the invention optical element  38  may be a nonlinear element. The nonlinear optical elements  38  and  39  may be a curved mirror or a lens.  
         [0046]     FIGS.  1 B 1 ,  1 B 2  and  1 B 3  show an example image  50  from camera  10  and an example image  60  from camera  15  acquired by the system. The image  50 , a bottom view of dot pattern  22 , shows dots  52  acquired by camera  10 . The dot pattern contains precision dots  24  of known dimensions and spacing. The precision dots  24  are located on the bottom surface of the calibration reticle  20 . The image  60  shows two side perspective views of the dot pattern  22 . A first side perspective view in image  60  contains images  62  of dots  24  and is obtained by the reflection of the image of the calibration reticle dot pattern  22  off of fixed optical elements  30 ,  32  and  38  into camera  15 . A second side perspective view in image  60  contains images  66  of dots  24  and is obtained by the reflection of the image of the calibration reticle dot pattern  22  off of fixed optical elements  34 ,  36  and  38  into camera  15 .  
         [0047]     Optical element  36  is positioned to adjust the optical path length of a second side perspective view to equal the optical path length of a first side perspective view. Those skilled in the art will realize that any number of perspective views can be utilized by the invention. In one embodiment of the invention, the maximum depth of focus of a side perspective view includes an area of the reticle including the center row of dots. This allows for a fixed focus system to inspect larger parts, with one perspective view imaging half of the part and the second perspective view imaging the other half of the part.  
         [0048]      FIG. 2A  shows a flow diagram for the calibration of the bottom view of the system. The method starts in step  101  by providing a transparent reticle  20  having a bottom surface containing a dot pattern  22 , comprising precision dots  24  of known dimensions and spacing. The method in step  102  provides a camera  10  located beneath the transparent reticle  20  to receive an image  50 . In step  103  the processor  13  sends a command to a frame grabber  12  to acquire an image  50 , comprising pixel values from the camera  10 . The method then proceeds to step  104  and processes the pixel values with a processor  13 .  
         [0049]      FIG. 2B  shows a flow diagram for determining the state values of the bottom view of the system. In step  111  the method begins by finding the dots  52  in image  50 , corresponding to the calibration dots  24 . The processor finds a dimension and position for each dot visible in image  50  in subpixel values using well known grayscale methods and stores these values in memory  14 . By comparing these results to known values stored in memory, the processor calculates the missing state values for the bottom calibration in steps  112  and  113 . In step  112  the processor  13  calculates the optical distortion of lens  11  and the camera roll angle with respect to the dot pattern  22 . Step  113  calculates the pixel width and pixel height by comparing the subpixel data of dots  52  with the known dimensions of the precision dot pattern  22 . The pixel aspect ratio is determined from the pixel width and pixel height. In step  114  the processor defines the X and Y world coordinates and the Z=0 plane from the image  50  of the precision dot pattern  22 . The processor then stores these results in memory. These results provide conversion factors for use during analysis to convert pixel values to world values.  
         [0050]      FIG. 2C  shows a flow diagram for the calibration of the side perspective views of the system. The method starts in step  121  by providing a transparent reticle  20  having a bottom surface containing a dot pattern  22 , comprising precision dots  24  of known dimensions and spacing. The method in step  122  provides fixed optical elements  30 ,  32 ,  34 ,  36  and  38  to reflect two perspective images of the precision dot pattern  22  into camera  15 . The method in step  123  provides a camera  15  located to receive an image  60 . In step  124  the processor  13  sends a command to a frame grabber  12  to acquire an image  60 , comprising pixel values from the camera  15 . The method then proceeds to step  125  and processes the pixel values with a processor  13 .  
         [0051]      FIG. 2D  shows a flow diagram for determining the state values of the side perspective views of the system. In step  131  the method begins by finding dots  62  in image  60 , corresponding to the calibration dots  24 . The processor finds a dimension and position for each dot visible, comprising the group of dots  62 , in image  60  for a first side perspective view in subpixel values and stores these values in memory  14 . By comparing these results to known values stored in memory, the processor calculates the missing state values for a side perspective view, comprising the group of dots  62 , in steps  132  and  133 . In step  132  the processor  13  calculates the optical distortion of lens  16  and the camera roll angle with respect to the dot pattern  22 . In step  133  the processor  13  calculates the pixel width and pixel height by comparing the subpixel data of dots  62  with the known dimensions of the precision dots  24 . The pixel aspect ratio is determined from the pixel width and pixel height. In step  134  the processor defines the X and Y world coordinates and the Z=0 plane from the dots  62  in image  60  of the dot pattern  22 . The processor then stores these results in memory. These results provide conversion factors for use during analysis to convert pixel values to world values. In step  135  the method of the invention computes the side view angle. In step  136  the method is repeated for a second side perspective view using the dots  66  in image  60 .  
         [0052]      FIG. 2E  shows the relationship of a side perspective angle to the ratio of the perspective dimension to the non-perspective dimension. Ray  171 ,  172 , and  173  defining point  181  is parallel to ray  174 ,  175  and  176  defining point  182 . Point  181  and point  182  lie on a plane  170  parallel to a plane  180 . The intersection of ray  175  and ray  176  define point  186 . The intersection of ray  176  and ray  172  define point  184 . The intersection of ray  173  and ray  172  define point  187 . The intersection of ray  174  and ray  172  define point  183 . The reflecting plane  179  intersecting plane  180  at an angle D is defined by ray  172  and ray  175  and the law of reflectance. Ray  172  and ray  175  intersect plane  170  at an angle  177 . Referring to  FIG. 2E  it can be shown: 
 tan θ= C/D   B      C /sin  A=L /sin  A  Therefore: C=L  cos θ= D   S   /L=D   S   /C      C=D   S /cos θ Substituting:  tan θ=( D   S /cos θ)/ D   B   =D   S   /D   B  cos θ (tan θ)(cos θ)= D   S   /D   B =sin θ θ=arcsin( D   S   /D   B )  
         [0053]     FIGS.  2 F 1  and  2 F 2  show a bottom view and a side perspective view of precision dots used in the method for determining a side perspective view angle  177  as shown in  FIG. 2E  of the system. A bottom view image  200  comprising precision dots  201 ,  202  and  203  of known spacing and dimensions from the calibration method described earlier can be used to provide a reference for determination of a side perspective view angle  177 . The value D H  and D B  are known from the bottom view calibration. A side perspective view image  210  comprising precision dots  211 ,  212  and  213 , corresponding to bottom view dots  201 ,  202  and  203  respectively, of known spacing and dimensions D s  and D h  from the calibration method described earlier, can be used to determine the side view perspective angle. The ratio of (D h /D H ) from the bottom image  200  and the side perspective image  210  can be used in the bottom view to calibrate DB in the same units as the side perspective view as follows: 
 
 D   Bcal   =D   B ( D   h   /D   H ) 
 
 Substituting into the equation for the side perspective view angle  177  described earlier yields: 
 
θ=arcsin( D   S   /D   B )=arcsin( D   S   /D   Bcal ) 
 
θ=arcsin( D   S   D   H   /D   B   D   h ) 
 
         [0054]      FIG. 3A  shows the apparatus of the invention for a three dimensional inspection of the balls of a ball grid array. The apparatus of the invention includes a part  70  to be inspected. The apparatus further includes a camera  10  with a lens  11 , located below the central area of part  70 , to receive a bottom image  80 , described in conjunction with FIGS.  3 B 1 ,  3 B 2 , and  3 B 3 , of part  70 . The camera  10  is connected to a frame grabber board  12  to receive the image  80 . The frame grabber board  12  provides an image data output to a processor  13  to perform a two dimensional inspection as described in conjunction with  FIG. 3A . The processor  13  may store an image in memory  14 . The apparatus of the invention obtains an image of a pair of side perspective views with a camera  15  and a lens  16 . The camera  15  is located to receive an image  90 , comprising a pair of side perspective views, described in conjunction with FIGS.  3 B 1 ,  3 B 2 , and  3 B 3  and utilizing fixed optical elements  30 ,  32  and  38  for a first side perspective view and fixed optical elements  34 ,  36  and  38  for a second side perspective view. In one embodiment of the invention, the apparatus may contain a nonlinear optical element  39  to magnify the side perspective image  60  in one dimension as shown in  FIG. 8B . In another embodiment of the invention optical element  38  may be the nonlinear element. The fixed optical elements  30 ,  32 ,  34 ,  36  and  38  may be mirrors or prisms. As will be appreciated by those skilled in the art additional optical elements may be incorporated without deviating from the spirit and scope of the invention. The camera  15  is connected to a frame grabber board  17  to receive the image  90 . The frame grabber board  17  provides an image data output to a processor  13  to calculate the Z position of the balls, described in conjunction with  FIG. 32 . The processor  13  may store an image in memory  14 .  
         [0055]     FIGS.  3 B 1 ,  3 B 2 , and  3 B 3  show an example image  80  from camera  10  and an example image  90  from camera  15  acquired by the system. The image  80  shows the bottom view of the balls located on the bottom surface of a part  70 . The image  90  shows two side view perspectives of the balls located on part  70 . A first side perspective view in image  90  contains images of balls  91  and is obtained by the reflection of the image of the part  70  off of fixed optical elements  30 ,  32  and  38  into camera  15 . A second side perspective view in image  90  contains images of balls  92  and is obtained by the reflection of the image of the part  70  off of fixed optical elements  34 ,  36  and  38  into camera  15 . Optical element  36  is positioned to adjust the optical path length of a second side perspective view to equal the optical path length of a first side perspective view. In one embodiment of the invention, the maximum depth of focus of a side perspective view just includes an area of the part including the center row of balls. This allows for a fixed focus system to inspect larger parts, with one perspective view imaging at least half of the part and the second perspective view imaging at least the other half of the part. Those skilled in the art will realize that any number of perspective views can be utilized by the invention. In another embodiment of the invention, all of the balls are in focus from both side perspective views resulting in two perspective views for each ball. This permits two Z calculations for each ball as shown in conjunction with  FIGS. 10A and 10B .  
         [0056]      FIG. 4  shows a flow diagram for the three dimensional inspection of balls on a ball grid array. The method starts in step  141  by providing a part  70  having balls  71  facing down. The method in step  142  provides a camera  10  located beneath the part  70  to receive an image  80 . In step  143  a frame grabber  12  is provided to receive the image  80  from camera  10 . In step  144 , fixed optical elements are provided for obtaining two side perspective views of the part  70 . A first optical path is provided by optical elements  30 ,  32  and  38 . A second optical path is provided by optical elements  34 ,  36  and  38 . A second camera  15  receives an image  90  of two side perspective views in step  145 . In step  146  a second frame grabber board  17  is provided to receive the image  90  from camera  15 . A processor  13  sends a command to frame grabbers  12  and  17  to acquire images  80  and  90  comprising pixel values from cameras  10  and  15 . The method then proceeds to step  147  and processes the pixel values with a processor  13  to obtain three dimensional data about part  70 .  
         [0057]     The invention contemplates the inspection of parts that have ball shaped leads whether or not packaged as a ball grid array. The invention also contemplates inspection of leads that present a generally curvilinear profile to an image sensor.  
         [0058]      FIGS. 5A and 5B  together show a flow chart of the three dimensional inspection method of the invention. The process begins in step  151  by waiting for an inspection signal. When the signal changes state, the system initiates the inspection. The processor  13  sends a command to frame grabber boards  12  and  17  to acquire images  80  and  90  respectively of part  70  having balls  71 . In step  152 , camera  10  captures an image  80  comprising pixel values and camera  15  captures an image  90  comprising pixel values and the processor stores the images in memory  14 . The images comprise information from both a bottom view and two side perspective views as shown in FIGS.  3 B 1 ,  3 B 2 , and  3 B 3 . In step  153 , the inspection system sends a signal to a part handler shown in  FIG. 9  to allow the part handler to move the part out of the inspection area and allows the next part to be moved into the inspection area. The handier may proceed with part placement while the inspection system processes the stored image data.  
         [0059]     The inspection system processes the pixel values of the stored image  80  in step  154  to find a rotation, and X placement and Y placement of the part relative to the world X and Y coordinates. The processor determines these placement values finding points on four sides of the body of the part. In step  155 , the processor employs a part definition file that contains values for an ideal part.  
         [0060]     By using the measurement values from the part definition file and the placement values determined in step  154 , the processor calculates an expected position for each ball of the part for the bottom view contained in image  80 .  
         [0061]     The processor employs a search procedure on the image data to locate the balls  81  in image  80 . The processor then determines each ball&#39;s center location and diameter in pixel values using grayscale blob techniques as described in  FIG. 7A . The results are stored in memory  14 .  
         [0062]     The processor proceeds in step  156  to calculate an expected position of the center of each ball in both side perspective views in image  90  using the known position of each side view from calibration. The processor employs a subpixel edge detection method described in  FIG. 72  to locate a reference point on each ball in step  157 . The results are stored in memory  14 .  
         [0063]     Now refer to  FIG. 5B . In step  158  the processor converts the stored pixel values from steps  154  and  157  into world locations by using pixel values and parameters determined during calibration. The world locations represent physical locations of the balls with respect to the world coordinates defined during calibration.  
         [0064]     In step  159  the Z height of each ball is calculated in world coordinates in pixel values. The method proceeds by combining the location of the center of a ball from the bottom view  80  with the reference point of the same ball from a side perspective view in image  90  as described in  FIGS. 6A and 6B . The processor then converts the world values to part values using the calculated part rotation, and X placement and Y placement in step  160  to define part coordinates for the ideal part. The part values represent physical dimensions of the balls such as ball diameter, ball center location in X part and Y part coordinates and ball height in Z world coordinates.  
         [0065]     In step  161  these part values are compared to the ideal values defined in the part file to calculate the deviation of each ball center from its ideal location. In one example embodiment of the invention the deviation values may include ball diameter in several orientations with respect to the X and Y part coordinates, ball center in the X direction, Y direction and radial direction, ball pitch in the X direction and Y direction and missing and deformed balls. The Z world data can be used to define a seating plane, using well known mathematical formulas, from which the Z dimension of the balls with respect to the seating plane can be calculated. Those skilled in the art will recognize that there are several possible definitions for seating planes from the data that may be used without deviating from the spirit and scope of the invention.  
         [0066]     In step  162  the results of step  161  are compared to predetermined thresholds with respect to the ideal part as defined in the part file to provide an electronic ball inspection result. In one embodiment the predetermined tolerance values include pass tolerance values and fail tolerance values from industry standards. If the measurement values are less than or equal to the pass tolerance values, the processor assigns a pass result for the part. If the measurement values exceed the fail tolerance values, the processor assigns a fail result for the part. If the measurement values are greater than the pass tolerance values, but less than or not equal to the fail tolerance values, the processor designates the part to be reworked. The processor reports the inspection result for the part in step  163 , completing part inspection. The process then returns to step  151  to await the next inspection signal.  
         [0067]      FIGS. 6A and 6B  show an example ball of a ball grid array and associated geometry used in a method of the invention for determining the Z position of the ball. The method determines the Z position of a ball with respect to the world coordinates defined during calibration. Using parameters determined from the calibration procedure as shown in  FIGS. 2B and 2D  to define a world coordinate system for the bottom view and the two side perspective views, comprising world coordinate plane  250  with world coordinate origin  251  and world coordinate axis X  252 , Y  253  and Z  254  shown in  FIG. 6A , and a pair of images  80  and  90  as shown in FIGS.  3 B 1 ,  3 B 2 , and  3 B 3 , the processor computes a three dimensional location.  
         [0068]     Now refer to  FIG. 6A . The processor locates a point  258  on the world plane  250  determined by a bottom view ray  255  passing through the center  257  of a ball  71  on a part  70 . The processor locates a side perspective view point  260  on the world plane  250  determined by a side perspective view ray  256  intersecting a ball reference point  259  on ball  71  and intersecting the bottom view ray  255  at a virtual point  261 . Ray  256  intersects the world plane  250  at an angle  262  determined by the reflection of ray  256  off of the back surface  263  of prism  30 . The value of angle  262  was determined during the calibration procedure.  
         [0069]     Now refer to  FIG. 6B . The distance L.sub.1 is calculated by the processor as the difference between world point  258 , defined by the intersection of ray  255  with the Z=0 world plane  250 , and world point  260 , defined by the intersection of ray  256  and the Z=0 world plane  250 . The value Z is defined as the distance between world point  261  and  258  and is related to L 1  as follows: 
 
tan θ1= Z/L   1  
 
 Z can be computed by processor  13  since the angle  262  is known from calibration. The offset E  265  is the difference between the virtual point  261  defined by the intersection of ray  255  and ray  256  and the crown of ball  71  at point  264 , defined by the intersection of ray  255  with the crown of ball  71 , and can be calculated from the knowledge of the angle  262  and the ideal dimensions of the ball  71 . The final value of Z for ball  71  is: 
 
 Z   Final   =Z−E  
 
         [0070]      FIG. 7A  shows one example of an image used in the grayscale blob method of the invention. The image processing method finds the location and dimensions of a ball  71  from a bottom image  80 . From the expected position of a ball  71 , a region of interest in image  80  is defined as (X1, Y1) by (X2,Y2). The width and height of the region of interest are large enough to allow for positioning tolerances of part  70  for inspection. Due to the design of the lighting for the bottom view, the spherical shape of balls  71  of part  70  present a donut shaped image where the region  281 , including the perimeter of the ball  71 , comprises camera pixels of higher grayscale values and where the central region  282  comprises camera pixels of lower grayscale values. The remainder  283  of the region of interest  280  comprises camera pixels of lower grayscale values.  
         [0071]     In one embodiment of the invention the processor  13  implements image processing functions written in the C programming language.  
         [0072]     The C language function “FindBlobCenter”, as described below, is called to find the approximate center of the ball  71  by finding the average position of pixels that are greater than a known threshold value. Using the coordinates of the approximate center of the ball  71 , the region  282  of lower grayscale pixel values can be converted to higher grayscale values by calling the C language function “FillBallCenter”, as described below. The exact center of the ball  71  can be found by calling the C language function “FindBallCenter” which also returns an X world and Y world coordinate. The diameter of the ball  71  can be calculated by the C language function, “Radius=sqrt(Area/3.14)”. The area used in the diameter calculation comprises the sum of pixels in region  281  and  282 .  
         [0073]      FIG. 7B  shows one example of an image used with the method of the invention to perform a subpixel measurement of the ball reference point. The method of the invention finds a reference point on a ball  71  in an image  90  of a side perspective view as shown in FIGS.  3 B 1 ,  3 B 2 , and  3 B 3 . From the expected position of a ball  71 , a region of interest  290  in image  80  is defined as (X3, Y3) by (X4, Y4). The width and height of the region of interest are large enough to allow for positioning tolerances of part  70  for inspection. Due to the design of the lighting for a side perspective view, the spherical shape of balls  71  of part  70  present a crescent shaped image  291  comprising camera pixels of higher grayscale values and where the remainder  293  of the region of interest  290  comprises camera pixels of lower grayscale values.  
         [0074]     The C language function “FindBlobCenter” is called to compute the approximate center of the crescent image  291  by finding the average position of pixels that are greater than a known threshold value. Using the coordinates of the approximate center of the crescent image  291 , the C language function “FindCrescentTop” is called to determine the camera pixel, or seed pixel  292  representing the highest edge on the top of the crescent. The camera pixel coordinates of the seed pixel are used as the coordinates of a region of interest for determining the subpixel location of the side perspective ball reference point.  
         [0075]     One example of grayscale blob analysis and reference point determination implemented in the C language is presented as follows:  
                                   ////////////////////////////////////////////////////////////       //       // FindBlobCenter - finds the X,Y center of the pixels that have a       value greater than       THRESHOLD in the region (x1,y1) to (x2,y2)       ////////////////////////////////////////////////////////////       //       long FindBlobCenter(int x1,int y1,int x2,int y2, double* pX,double* pY)       {        int x,y;        long Found = 0;        long SumX = 0;        long SumY = 0;        for (x=x1;x&lt;=x2;x++)        {         for (y=y1;y&lt;=y2;y++)         {          if (Pixel [x] [y] &gt; THRESHOLD)          {           SumX += X;           SumY += y;           Found ++;          }         }        }        if (Found &gt; 0)        {         *pX = (double)SumX / (double)Found;         *pY = (double)SumY / (double)Found;        }        return Found;       }       ////////////////////////////////////////////////////////////       //       // FillBallCenter - fills the center of the BGA “donut”       ////////////////////////////////////////////////////////////       //       void FillBallCenter(double CenterX,double CenterY,double Diameter)       {        int x,y;        int x1 = (int) (CenterX − Diameter / 4.0);        int x2 = (int) (CenterX + Diameter / 4.0);        int y1 = (int) (CenterY − Diameter / 4.0);        int y2 = (int) (CenterY + Diameter / 4.0);        for (x=x1;x&lt;=x2;x++)        {         for (y=y1;y&lt;=y2;y++)         {          Pixel [x] [y] = 255;         }        }       }       ////////////////////////////////////////////////////////////       //       // FindBallCenter - finds the X,Y center of the a BGA ball       //  using the grayscale values       ///////////////////////////////////////////////////////////       //       long FindBallCenter(int x1,int y1,int x2,int y2, double* pX,double* pY,             double* pRadius)       {        int x,y;        long Found = 0;        long Total = 0;        long SumX = 0;        long SumY = 0;        for (x=x1;x&lt;=x2;++)        {         for (y=y1;y&lt;=y2;y++)         {          if (Pixel [x] [y] &gt; THRESHOLD)          {           SumX += x*Pixel [x] [y];           SumY += y*Pixel [x] [y];           Total += Pixel [x] [y];           Found ++;          }         }        }        if (Found &gt; 0)        {         *pX = (double)SumX / (double)Total;         *pY = (double)SumY / (double)Total;         *pRadius = sqrt((double)Found / 3.14159279);        }        return Found;       }       /////////////////////////////////////////////////////////////       //       // FindCresentTop - finds the X,Y top position of a BGA cresent       ////////////////////////////////////////////////////////////       //       void FindCresentTop(int CenterX,int CenterY,int Diameter,       int* pX,int* pY)       {        int x,y,Edge,Max,TopX,TopY;        int x1 = CenterX − Diameter / 2;        int x2 = CenterX + Diameter / 2;        int y1 = CenterY − Diameter / 2;        int y2 = CenterY;        *pY = 9999;        for (x=x1;x&lt;=x2;x++)        {         Max = −9999;         for (y=y1;y&lt;=y2;y++)         {          Edge = Pixel [x] [y] − Pixel [x] [y−1];          if (Edge &gt; Max)          {           Max = Edge;           TopY = y;           TopX = x;          }         }         if (TopY &lt; *pY)         {          *pX = TopX;          *pY = TopY;         }        }       (c) 1997 Scanner Technologies Inc.                  
 
         [0076]      FIG. 8A  shows a side perspective image of the calibration pattern magnified in one dimension.  FIG. 8A  shows a side perspective image  300  of a reticle calibration pattern where the space  303  between dot  301  and dot  302  is magnified, increasing the number of lower value grayscale pixels when compared to a non magnified image.  
         [0077]      FIG. 8B  shows a side perspective image of the balls on a BGA, magnified in one dimension. In  FIG. 8B  a side perspective image  310  of two views are shown where the space  313  between ball image  311  and ball image  312  is magnified, increasing the number of lower value grayscale pixels when compared to a non magnified image. The increased number of lower grayscale value pixels allows for the successful application of the subpixel algorithm.  
         [0078]     In another embodiment of the invention, the method and apparatus disclosed herein is a method and apparatus for calibrating the system by placing a pattern of calibration dots of known spacing and dimensions on the bottom plane of a calibration reticle and for providing for two side perspective views of each ball for the three dimensional inspection of parts. From the precision dots the missing state values of the system are determined allowing for three dimensional inspection of balls on BGA devices or balls on wafers or balls on die.  
         [0079]      FIG. 9  shows an example apparatus for presenting a BGA to the system for inspection. An overhead light reflective diffuser  5  includes a vacuum cup assembly  6 . The vacuum cup assembly may attach to a BGA part  70  having balls  71  and suspend the BGA part  70  below the overhead light reflective diffuser  5 .  
         [0080]      FIGS. 10A and 10B  show an example ball on a ball grid array and associated geometry for use with the method of the invention for determining the Z position of a ball with respect to the world coordinates defined during calibration, using two perspective views for each ball. Using parameters determined from the calibration procedure as shown in  FIGS. 2B and 2D  to define a world coordinate system for the bottom view and the two side perspective views, comprising world coordinate plane  700  with world coordinate origin  701  and world coordinate axis X  702 , Y  703  and Z  704  shown in  FIG. 10A  and  FIG. 10B , and a pair of images  80  and  90  as shown in FIGS.  3 B 1 ,  3 B 2 , and  3 B 3 , the processor computes a three dimensional location.  
         [0081]     Now refer to  FIG. 10A . The processor locates a point  709  on the world plane  700  determined by a bottom view ray  705  passing through the center  708  of a ball  717 . The processor locates a first side perspective view point  711  on the world plane  700  determined by a side view ray  706  intersecting a ball reference point  710  on ball  717  and intersecting the bottom view ray  705  at a virtual point  714 . Ray  706  intersects the world plane  700  at an angle  715  determined by the reflection of ray  706  off of the back surface of prism  30 . The value of angle  715  was determined during the calibration procedure. The processor locates a second side perspective view point  713  on the world plane  700  determined by a side view ray  707  intersecting a ball reference point  712  on ball  717  and intersecting the bottom view ray  705  at a virtual point  718 . Ray  707  intersects the world plane  700  at an angle  716  determined by the reflection of ray  707  off of the back surface of prism  34 . The value of angle  716  was determined during the calibration procedure.  
         [0082]     Now refer to  FIG. 10B . The distance L 1  is calculated by the processor as the distance between world point  709  and world point  711 . The distance L 2  is calculated by the processor as the distance between world point  713  and world point  709 . The value Z 1  is defined as the distance between world point  714  and  709  and is related to L 1  as follows: 
 
tan θ 1   =Z   1   /L   1  
 
 Z   1 =L 1  tan θ 1  
 
 The value Z 2  is defined as the distance between world point  718  and  709  and is related to L 2  as follows: 
 
tan θ 2   =Z   2   /L   2  
 
 Z   2   =L   2  tan θ 2  
 
 The average of Z 1  and Z 2  are calculated and used as the value for Z of the ball. This method is more repeatable and accurate than methods that use only one perspective view per ball. 
 
         [0083]     In still another embodiment of the invention, the method and apparatus disclosed herein is a method and apparatus for calibrating the system by placing a pattern of calibration dots of known spacing and dimensions on the bottom plane of a calibration reticle and for providing a single side perspective view for the three dimensional inspection of parts. From the precision dots the missing state values of the system are determined allowing for three dimensional inspection of balls on BGA devices or balls on wafers or balls on die.  
         [0084]      FIG. 11A  shows the apparatus of the invention for system calibration, utilizing a single side perspective view. The method and apparatus for calibration of the bottom view is identical to the method and apparatus described earlier in  FIGS. 2A and 2B  for the two side perspective views method. The apparatus for an image of a side perspective view includes a camera  15  with a lens  18  and a calibration reticle  20 . The camera  15  is located to receive an image  64  of a side perspective view comprising dots  65 , described in conjunction with FIGS.  11 B 1 ,  11 B 2 , and  11 B 3 , and utilizing fixed optical elements  40  and  42 . The fixed optical element  40  may be a mirror or prism. The fixed optical element  42  is a nonlinear element that magnifies the image in one direction. In another embodiment fixed optical element  40  may be this nonlinear element. As will be appreciated by those skilled in the art additional optical elements may be incorporated. The camera  15  is connected to a frame grabber board  17  to receive the image  64 . The frame grabber board  17  provides an image data output to a processor  13  to perform a two dimensional inspection as described in conjunction with  FIG. 2B . The processor  13  may store an image in memory  14 .  
         [0085]     FIGS.  11 B 1 ,  11  B 2 , and  11  B 3  show an example calibration pattern and example images of a calibration pattern acquired by the system, utilizing a single side perspective view, of the invention. FIGS.  11 B 1 ,  11 B 2 , and  11 B 3  show an example image  50  from camera  10  and an example image  64  from camera  15  acquired by the system. The image  50  showing dots  52  acquired by camera  10  includes a bottom view of the dot pattern  22 , containing precision dots  24  of known dimensions and spacing, located on the bottom surface of the calibration reticle  20 . The image  64  shows a side perspective view of the dot pattern  22 , containing precision dots  24  of known dimensions and spacing, located on the bottom surface of the calibration reticle  20 . A side perspective view in image  64  contains images of dots  65  and is obtained by the reflection of the image of the calibration reticle dot pattern  22  off of fixed optical element  40 , passing through nonlinear element  42  and into camera  15 .  
         [0086]     The side perspective calibration is identical to the method shown in  FIG. 2C  except the fixed optical elements may have different properties.  
         [0087]     The determination of the state values for the side perspective view is identical to the method shown in  FIG. 2D  except the fixed optical elements may be different and there is only one side perspective view. The principles and relationships shown in  FIG. 2E ,  FIG. 2F   1 , and  FIG. 2F   2  apply.  
         [0088]     In still another embodiment employing a single side perspective view, the invention does not include the nonlinear element  42 .  
         [0089]      FIG. 12A  shows the apparatus of the invention for ball inspection utilizing a single side perspective view. The apparatus of the invention includes a part  70  to be inspected. The apparatus further includes a camera  10  with a lens  11 , located below the central area of part  70 , to receive a bottom image  80 , described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3 , of part  70 . The camera  10  is connected to a frame grabber board  12  to receive the image  80 . The frame grabber board  12  provides an image data output to a processor  13  to perform a two dimensional inspection as described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3 . The processor  13  may store an image in memory  14 . The apparatus for an image of a single side perspective view includes a camera  15  with a lens  18 . The camera  15  is located to receive an image  94 , comprising a single side perspective view, described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3  and utilizing fixed optical element  40  and nonlinear, fixed optical element  42 , to magnify the side perspective view in one dimension. In another embodiment of the invention optical element  40  may be the nonlinear element. The fixed optical element  40  may be a mirror or prism. As will be appreciated by those skilled in the art additional optical elements may be incorporated. The camera  15  is connected to a frame grabber board  17  to receive the image  94 . The frame grabber board  17  provides an image data output to a processor  13  to calculate the Z position of the balls, described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3 . The processor  13  may store an image in memory  14 .  
         [0090]     FIGS.  12 B 1 ,  12 B 2 , and  12 B 3  show an example ball grid array and example images of the ball grid array for three dimensional inspection, utilizing a single side perspective view. FIGS.  12 B 1 ,  12 B 2 , and  12 B 3  show an example image  80  from camera  10  and an example image  94  from camera  15  acquired by the system. The image  80  shows the bottom view of the balls  71  located on the bottom surface of a part  70 . The image  94  shows a side perspective view of the balls  71  located on part  70 . The side perspective view in image  94  contains images of balls  95  and is obtained by the reflection of the image of the part  70  off of fixed optical element  40  and passing through the nonlinear fixed element  42  into camera  15 .  
         [0091]     In an alternate embodiment of the invention, the system can be used to inspect other types of electronic parts in three dimensions, such as gullwing and J lead devices. By utilizing only one camera and adding an additional set of prisms on the reticle  400  these other devices may be inspected. The advantage of being able to inspect different devices with the same system includes savings in cost, and floor space in the factory. Additionally this design allows more flexibility in production planning and resource management.  
         [0092]      FIG. 13  shows the apparatus of the invention for the three dimensional inspection of ball grid array devices, gullwing devices and J lead devices. The apparatus described in  FIG. 13  allows the inspection of BGA, gullwing and J lead devices all on the same system. The apparatus includes a part  402  to be inspected located over the central area of a transparent reticle  400  with prisms  401  glued to the top surface to receive side perspective views of part  402 . A gullwing and J lead inspection device  21  may be integrated into the ball grid array inspection device. One example embodiment of such a gullwing and J lead inspection device is the “UltraVim” scanner from Scanner Technologies of Minnetonka, Minn. The apparatus further includes a camera  10 A with a lens  11 A, located below the central area of part  402  and reticle  400  to receive a bottom view and side perspective views of part  402 . The camera  10 A is connected to a frame grabber board  12 A to receive an image. The frame grabber board  12 A provides an image data output to a processor  13 A to perform a three dimensional inspection of part  402 . The processor  13 A may store an image in memory  14 A. These components comprise the hardware of the gullwing and J lead inspection device  21  and are shared by the ball grid array inspection device as described herein.  
         [0093]     The UltraVim is described in U.S. patent application Ser. No. 08/850,473 entitled THREE DIMENSIONAL INSPECTION SYSTEM by Beaty et al., filed May 5, 1997 which is incorporated in its entirely by reference thereto.  
         [0094]     Refer now to  FIG. 14 . In still another embodiment of the invention, the system may use three cameras to image directly the bottom view and two side perspective views as shown in  FIG. 14 .  FIG. 14  shows the apparatus of the invention for a three dimensional inspection of the balls of a BGA. The apparatus of the invention includes a part  70 , with balls  71  to be inspected. The apparatus further includes a camera  10  with a lens  11 , located below the central area of part  70 , to receive a bottom image  80 , described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3 , of part  70 . The camera  10  is connected to a frame grabber board  12  to receive the image  80 . The frame grabber board  12  provides an image data output to a processor  13  to perform a two dimensional inspection as described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3 . The processor  13  may store an image in memory  14 . The apparatus for an image of a first side perspective view includes a camera  15  with a lens  19 . The camera  15  is located to receive an image  94 , comprising a single side perspective view, described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3  and utilizing fixed optical element  38 , to magnify the side perspective view in one dimension. The camera  15  is connected to a frame grabber board  17  to receive the image  94 . The frame grabber board  17  provides an image data output to a processor  13  to calculate the Z position of the balls, described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3 . The processor  13  may store an image in memory  14 . The apparatus for an image of a second side perspective view includes a camera  15  with a lens  19 . The camera  15  is located to receive an image similar to  94 , comprising a single side perspective view, described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3  and utilizing fixed optical element  38 , to magnify the side perspective view in one dimension. The camera  15  is connected to a frame grabber board  17  to receive the image similar to  94 . The frame grabber board  17  provides an image data output to a processor  13  to calculate the Z position of the balls, described in conjunction with FIGS.  12 B 1 ,  12 B 2 , and  12 B 3 . The processor  13  may store an image in memory  14 . In another embodiment, the nonlinear fixed optical element  38  may be missing. In still another embodiment of the invention, only one side perspective view may be utilized.  
         [0095]     The invention has been described herein in considerable detail in order to comply with the Patent Statutes and to provide those skilled in the art with the information needed to apply the novel principles and to construct and use such specialized components as are required. However, it is to be understood that the invention can be carried out by specifically different equipment and devices, and that various modifications, both as to the equipment details and operating procedures, can be accomplished without departing from the scope of the invention itself.