Abstract:
A method for the detection of an irregularity in an object based on an image of the object that includes the steps of binarizing the image at a plurality of binarization thresholds to obtain a plurality of binarized images, extracting information from each of the binarized images, estimating the regular object resulting from the binarization at the respective binarization threshold of an image of a version of the object in which the irregularity is absent, combining the information extracted from each of the binarized images, and detecting the irregularity based on the combined information. A method for the detection of a defect in a solder element based on an X-ray image of the solder element. This aspect includes the steps of binarizing the image at a plurality of binarization thresholds to obtain a plurality of binarized images, extracting information from each of the binarized images, combining the information extracted from each of the binarized images, and detecting the defect based on the combined information.

Description:
BACKGROUND OF INVENTION 
     1. Field of Invention 
     This invention concerns methods for the detection of an irregularity in an object based on an image of the object. One embodiment is related generally to systems and methods for the detection of a defect in a solder element based on an X-ray image of the solder element. 
     2. Discussion of Related Art 
     Surface mount technology (“SMT”) is an electronic circuit assembly process in which surface-mount devices, components, or parts, such as resistors, capacitors, integrated circuit packages, and the like, are soldered onto the surface of a printed circuit board (“PCB”). This differs from “leaded” or “through-hole” technology, in which leads of the device are inserted into holes in the PCB. 
     Among the variety of existing surface-mount packages for integrated circuits (“ICs”) is the Ball Grid Array (“BGA”). While other surface-mount IC packages have pins extending from the sides of the package (e.g., the Dual In-line Package and the Quad Flat Package), BGA packages employ an array of spheres or balls of solder attached to the bottom surface of the package as external electrical interconnects. The solder balls can lie over all or a portion of the bottom surface of the package. 
     To assemble the BGA package on a printed circuit board, the BGA solder balls are first placed on corresponding solder pads on the PCB surface, such as by use of a pick-and-place machine. The PCB is then placed in a reflow oven, in which the solder balls are caused to melt. The solder balls then cool and solidify, soldering the BGA package to the PCB. 
     A common defect in BGA solder balls is the presence of bubbles of gas, known as voids, in the solder. Depending on the quantity of voids in the solder ball, their size relative to the size of the solder ball, and their location in the solder ball, voids can affect the quality and/or reliability of the resulting solder joints. In order to ensure the quality of the solder joints, therefore, it is necessary to inspect solder balls to detect occurrences of voids and measure their characteristics. Characteristics of interest may include position, diameter, depth, area, volume, and the like. 
     Due to the fact that they are hidden below the surface of the solder ball, voids cannot be detected by visual or optical inspection. For this reason, X-ray imaging may be used to inspect solder balls for voids. 
     SUMMARY OF THE INVENTION 
     One aspect of the invention provides a method for the detection of an irregularity in an object based on an image of the object. In this aspect, the method includes the steps of binarizing the image at a plurality of binarization thresholds to obtain a plurality of binarized images, extracting information from each of the binarized images, estimating the regular object resulting from the binarization at the respective binarization threshold of an image of a version of the object in which the irregularity is absent, combining the information extracted from each of the binarized images, and detecting the irregularity based on the combined information. 
     This first aspect of the invention may further include the additional step of estimating the non-defective solder element resulting from the binarization, at the respective binarization threshold, of an X-ray image of a version of the solder element in which the defect is absent. 
     Another aspect of the invention provides a method for the detection of a defect in a solder element based on an X-ray image of the solder element. This aspect includes the steps of binarizing the image at a plurality of binarization thresholds to obtain a plurality of binarized images, extracting information from each of the binarized images, combining the information extracted from each of the binarized images, and detecting the defect based on the combined information. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. In the drawings: 
         FIG. 1A  is a side view of an exemplar BGA package; 
         FIG. 1B  is a bottom view of the BGA package of  FIG. 1A ; 
         FIG. 2  is a schematic drawing of an exemplar X-ray inspection station; 
         FIG. 3  is a schematic drawing illustrating an X-ray sample and a grayscale image generated from the sample; 
         FIG. 4  is a mock-up of an X-ray image of a BGA solder ball. 
         FIG. 5  is a flowchart illustrating steps associated with one embodiment of the invention; 
         FIG. 6A  is an representative image resulting from the thresholding step in a first iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 6B  is an representative image of a convex envelope in a first iteration the embodiment reflected in  FIG. 5 ; 
         FIG. 6C  is an image representative of inner blobs obtained in a first iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 6D  is an image representative the accumulation obtained in a first iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 7A  is an representative image resulting from the thresholding step in a second iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 7B  is an representative image of a convex envelope in a second iteration the embodiment reflected in  FIG. 5 ; 
         FIG. 7C  is an image representative of inner blobs obtained in a second iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 7D  is an image representative the accumulation obtained in a second iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 8A  is an representative image resulting from the thresholding step in a third iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 8B  is an representative image of a convex envelope in a third iteration the embodiment reflected in  FIG. 5 ; 
         FIG. 8C  is an image representative of inner blobs obtained in a third iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 8D  is an image representative the accumulation obtained in a third iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 9A  is an representative image resulting from the thresholding step in a fourth iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 9B  is an representative image of a convex envelope in a fourth iteration the embodiment reflected in  FIG. 5 ; 
         FIG. 9C  is an image representative of inner blobs obtained in a fourth iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 9D  is an image representative the accumulation obtained in a fourth iteration of the embodiment reflected in  FIG. 5 ; 
         FIG. 10  is a flowchart illustrating steps associated with another embodiment of the invention; 
         FIG. 11A  is an representative image resulting from the thresholding step in a first iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 11B  is an representative image of a convex envelope in a first iteration the embodiment reflected in  FIG. 10 ; 
         FIG. 11C  is an image representative of inner blobs obtained in a first iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 11D  is an image representative the accumulation obtained in a first iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 12A  is an representative image resulting from the thresholding step in a second iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 12B  is an representative image of a convex envelope in a second iteration the embodiment reflected in  FIG. 10 ; 
         FIG. 12C  is an image representative of inner blobs obtained in a second iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 12D  is an image representative the accumulation obtained in a second iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 13A  is an representative image resulting from the thresholding step in a third iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 13B  is an representative image of a convex envelope in a third iteration the embodiment reflected in  FIG. 10 ; 
         FIG. 13C  is an image representative of inner blobs obtained in a third iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 13D  is an image representative the accumulation obtained in a third iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 14A  is an representative image resulting from the thresholding step in a fourth iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 14B  is an representative image of a convex envelope in a fourth iteration the embodiment reflected in  FIG. 10 ; 
         FIG. 14C  is an image representative of inner blobs obtained in a fourth iteration of the embodiment reflected in  FIG. 10 ; 
         FIG. 14D  is an image representative the accumulation obtained in a fourth iteration of the embodiment reflected in  FIG. 10 ; and 
         FIG. 15  illustrates the grayscale X-ray image of  FIG. 4 , in which the boundaries of blobs identified as voids have been identified. 
     
    
    
     DETAILED DESCRIPTION 
     This invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” “having,” “containing,” “involving,” and variations thereof, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. 
     In one embodiment, the present method addresses the problem of accurately detecting and/or characterizing the occurrences of voids in materials. As used herein, “characterizing” means determining physical characteristics of a void, such as, but not limited, to the position, diameter, depth, area, volume, etc. of the void. 
     The invention is described below in the context of detecting and characterizing voids in BGA solder balls. As will be discussed, however, the method is not limited to BGA solder balls, solder, or any other specific material, and it may be extended to various other applications. 
       FIGS. 1A-1B  depict side and bottom views, respectively, of an exemplar BGA package  10  prior to mounting on a PCB. The package  10  includes a die  20  bonded to a substrate  30  to which are attached a number of solder balls  40 . In the illustrated BGA package  10 , the die  20  is bonded to the substrate  30  via wire bonds  50 . 
     As shown schematically in  FIG. 2 , an X-ray imaging system  100  suitable for use with the invention may include an X-ray source  110  and an X-ray detector  120  placed on either side of a sample  130 , such as the BGA package  10  shown in  FIG. 1 , under inspection. The X-ray source  110  may emit X-rays  115  that travel through the sample  130  and are then collected by the X-ray detector  120 . The amount of X-rays  115  that exit the sample  130  for collection by the X-ray detector  120  is a function of the thickness of the sample  130  and of the X-ray absorption properties of the materials composing the sample. 
     In the case of the inspection of a BGA package, the package may be placed right side up (with the solder balls facing downward) or upside down (with the solder balls facing upwards) relative to the X-ray source  110 . The viewing direction  125  is typically perpendicular to the top and bottom surfaces of the BGA package, but this is not a requirement. 
     In a digital X-ray system, the X-ray detector  120  generates a grayscale image of the sample, in which the brightness or grayscale intensity of a pixel is a function of the thickness and the coefficient of absorption of the sample along the corresponding X-ray path. In some cases, an 8-bit grayscale intensity format may be employed, such that the “darkest” pixel is represented by a grayscale intensity of 0 and the “brightest” pixel is represented by a grayscale intensity of 255. 
     In one embodiment, the thicker the sample, or the higher its absorption coefficient along the X-ray path, the darker the corresponding pixel in the resulting grayscale X-ray image (i.e., the lower the grayscale intensity of the pixel). In the example shown in  FIG. 3 , the portions of the image  340  that are darker indicate portions of the sample  320  that are “thicker,” while the portions of the image  340  that are lighter shades correspond to portions of the sample  320  that are “thinner.” Thicker or thinner in this context refers to relative amounts of material lying in the paths of the X-rays  310  corresponding to a given pixel in the image. 
       FIG. 4  shows an exemplary grayscale X-ray image of a single solder ball  40 . The X-ray image of  FIG. 4  may be, for example, a portion of a larger X-ray image of an entire BGA package generated by the above-described X-ray imaging system. As can be seen in  FIG. 4 , the image exhibits generally elliptical regions of pixels of slightly higher grayscale intensity than the surrounding pixels. Examples of these elliptical regions are indicated by reference numerals  42 ,  44 , and  46 . These lighter regions  42 ,  44 , and  46  correspond to voids in the imaged solder ball. 
     The presence of one or more voids (bubbles of gas replacing what should be solder) along an X-ray path means a smaller effective thickness of solder along the X-ray path and therefore results in a higher (lighter) grayscale intensity at the corresponding pixel in the X-ray image. Furthermore, the contrast between the void region and the surrounding area is a useful measure of the importance of the void(s) in the viewing direction relative to that of the solder ball. 
     In general, voids in solder balls may be difficult to accurately detect and characterize due to the very small contrast between the void regions and their surrounding area, the non-uniform grayscale intensity over the area of the solder ball, the fact that the exact geometry/shape of the solder ball is unknown, and the noisy nature of X-ray imaging. All of these factors make it difficult to find a binarization threshold that will isolate all the voids. The generally spherical shape of the solder ball means that the thickness of the solder ball is highest at the center of the solder ball and decreases in a radial direction towards the inner boundary of the solder ball. Thus, in the grayscale X-ray image of the solder ball (e.g.,  FIG. 4 ), the grayscale intensity of the pixels increases (i.e., the pixels become lighter) radially towards the inner boundary of the solder ball. For various reasons, in practice, this is only apparent near the boundaries of the solder ball. 
       FIG. 5  describes the steps of an embodiment of the invention relating to the detection of voids in a solder ball. This illustrative embodiment begins with a grayscale X-ray image of a single solder ball, such as that of  FIG. 4 . 
     At step  520 , an appropriate set of binarization threshold values, with which to successively binarize the grayscale X-ray image, is selected. The set of binarization threshold values can be represented, for example, as a combination of a range [Tmin, Tmax] and a step size ΔT. 
     In some embodiments, the range of binarization threshold values [Tmin, Tmax] is selected based on the grayscale intensity values of the set of pixels in the grayscale X-ray image corresponding to the solder ball. For example, the lowest and highest grayscale intensity values among the set of solder ball pixels can be selected as the minimum binarization threshold value, Tmin, and the maximum binarization threshold value, Tmax, respectively. The set of pixels in the grayscale X-ray image corresponding to the solder ball can be determined, for example, by binarizing the grayscale X-ray image and locating in the binarized image a group (“blob”) of pixels having the same binary intensity. 
     Preferably, the step size, ΔT, should be small enough that no significant void information is missed. In some embodiments, the step size may be selected based on the desired or required precision and processing speed. For example, if the contrast between the void region(s) and the surrounding area is small, a smaller step size should be selected. Of course, a smaller step size will increase the degree of processing required. In some embodiments, the user may select the step size. For example, the user may be given the option to choose between a step size of 1 and a step size of 3; using a step size of 1, every single grayscale intensity value within the range [Tmin, Tmax] is selected. 
     At step  530 , a binarization threshold variable is initialized to the maximum binarization threshold value, Tmax. According to the present embodiment, at each iteration of the loop, the binarization threshold variable is decremented according to the step size, ΔT, until the minimum binarization threshold value, Tmin, has been processed. It should be understood, however, that the binarization threshold values can be processed in any order. 
     At step  540 , the grayscale X-ray image of the solder ball is binarized using the current value of the binarization threshold variable. In one embodiment, this consists of setting all pixels having a grayscale intensity value larger than the binarization threshold to white in the binarized image, while setting the remaining pixels to black. 
       FIG. 6A  illustrates the binary image obtained by binarizing the grayscale X-ray image of  FIG. 4  at a particular binarization threshold value, i.e., during a particular iteration of the loop. 
     Because the grayscale intensity of the pixels forming the solder ball in the grayscale X-ray image increases as you move radially outward toward the boundary of the solder ball, the solder ball appears in an “eroded” form (with a smaller radius) in the binarized image. 
       FIGS. 7A ,  8 A, and  9 A illustrate the binarized images obtained at step  540  during subsequent iterations of the loop, i.e., for decreasing binarization threshold values. As the binarization threshold is decreased at each iteration of the loop, the solder ball appears increasingly eroded (with a smaller and smaller radius), in the binarized X-ray images, until the shape of the solder ball is completely lost (not shown). 
     Step  550  estimates the non-voided solder ball object that would result from binarizing, at the current value of the binarization threshold variable, a grayscale X-ray image of a version of the solder ball in which the voids are absent. 
     In one embodiment, step  550  is achieved by identifying the voided solder ball object in the binarized image and determining the convex envelope of the identified voided solder ball object. The convex envelope of an object can be thought of as the boundary an elastic band stretched around the object would define. A number of methods are known in the art to determine the convex envelope of a set of points. In  FIGS. 6A-B ,  7 A-B,  8 A-B, and  9 A-B, the voided solder ball objects are indicated by reference numerals  610 ,  710 ,  810 , and  910 , respectively, and their convex envelopes are indicated by reference numerals  620 ,  720 ,  820 , and  920 , respectively. 
     In another embodiment (not shown), step  550  may be achieved by identifying a set of points belonging to the boundary of the voided solder ball object and fitting a pre-defined geometric shape to the set of boundary points. The pre-defined shape may be, but is not limited to, any one of a circle, ellipse, paraboloid, etc. In one embodiment, fitting a pre-defined geometric shape to a set of points consists of determining the parameters of the pre-defined shape that best fits the set of points. A number of methods are known in the art to accomplish the fitting operation. 
     In other embodiments, the step  550  of estimating the regular object may be performed using any of a number of geometric properties of the voided solder ball object and/or the set of boundary points. Such properties may include convexity, concavity, dimensions such as a length or width, the area, centers of gravity, or circumscribed, inscribed, or fitted shapes, such as but not limited to one or more circles, ellipses, paraboloids, and polygons. 
     At step  560 , the pixels corresponding to a void (“void pixels”) within the estimated non-voided solder ball object determined at step  550  are identified. For example, in the embodiment illustrated in  FIGS. 6B-C , all white pixels  630  inside the convex envelope  620  are identified. In  FIGS. 7B-C ,  8 B-C, and  9 B-C, the identified void pixels are indicated by reference numerals  730 ,  830 , and  930 , respectively. FIGS.  6 C,  7 C,  8 C, and  9 C illustrate binary images in which all identified void pixels are set to white and the remaining pixels are set to black. 
     At step  570 , for each identified void pixel, the corresponding accumulator in an accumulator array is incremented. In one embodiment, the size of the accumulator array is equal to the size of the X-ray image, such that each pixel in the X-ray image has a corresponding accumulator in the array, in a one-to-one manner. In other embodiments, however, the accumulator array may be smaller than the X-ray image (i.e., several pixels are assigned to a single accumulator), although with a loss of precision. 
     In one embodiment, over several iterations of the loop, the value accumulated by an accumulator of the accumulator array is equal to the number of times the corresponding pixel in the binarized X-ray images was identified as a void pixel. The accumulator array may itself be viewed as a grayscale image, in which the grayscale intensity of a pixel corresponds to the number of times the corresponding pixel in the binarized X-ray image was identified as a void pixel.  FIGS. 6D ,  7 D,  8 D, and  9 D illustrate the accumulator image obtained at step  570  for the different iterations of the loop. 
     At step  580 , if there are still binarization threshold values that have not been processed, the method proceeds to step  590 . At step  590 , the binarization threshold variable is decremented according to the step size, ΔT. Steps  540  through  570  are then repeated using the new value of binarization threshold variable. 
     At step  595 , once all binarization threshold values have been processed, the accumulator array or image is analyzed to detect the voids and, optionally, characterize the voids. As illustrated in  FIGS. 6-9 , each of the binarized images in  FIGS. 6A ,  7 A,  8 A, and  9 A contributes different information, in the form of the void pixels  630 ,  730 ,  830 , and  930 , about the voids  42 ,  44 , and  46  illustrated in  FIG. 4 . Once all binarization threshold values have been processed, the accumulator array or image provides comprehensive information regarding the voids  42 ,  44 , and  46  that cannot be extracted from any one of the binarized images alone. 
     In some embodiments, step  595  may include a first step of filtering out noise from the accumulator image. As mentioned previously, in one embodiment, the grayscale intensity of a pixel in the accumulator image is equal to the number of times the corresponding pixel in the binarized images was identified as a void pixel. Accordingly, pixels in the accumulator image having relatively small grayscale intensities correspond to pixels that were identified as voids at relatively few binarization threshold values; these pixels are more likely to correspond to noise, than to significant voids. Therefore, in one embodiment, noise may be filtered out of the accumulator image and significant voids may be selected. First, only values in the accumulator image over an adequate threshold can be considered. For example, the threshold value may be selected to select voids which have a minimal corresponding thickness. Then, the selected values may be analyzed to form groups of connected pixels or blobs. These blobs can be further analyzed and discarded based on their size for example, or any other of their properties. 
     In the de-noised accumulator image, pixels having a non-zero grayscale intensity are assumed to belong to voids. Finally, if desired, characteristics of the voids can be determined from the de-noised accumulator image, such as position, diameter, depth, area, volume, etc. 
       FIG. 15  illustrates the grayscale X-ray image of  FIG. 4 , in which the boundaries  1510 ,  1512  and  1514  of blobs identified as voids according to step  595  have been identified. 
       FIG. 10  illustrates the main steps in an alternative embodiment of the method. Steps  1020 - 1050  are identical to steps  520 - 550  of  FIG. 5 . The embodiments differ starting at step  1060 . 
     In step  560  of the embodiment of  FIG. 5 , all void pixels (white pixels) within the estimated non-voided solder ball object were identified. In the alternative embodiment of  FIG. 10 , at step  1060 , all the pixels (white or black) within the estimated non-voided solder ball object (again, determined using the convex envelope or by fitting a pre-defined geometric shape, for example) are identified. As explained previously, the estimated non-voided solder ball object estimates the result of binarizing, at the current value of the binarization threshold variable, a grayscale X-ray image of a version of the solder ball in which the voids are absent. The pixels identified at step  1060  for different iterations of the loop are indicated with reference numerals  1130 ,  1230 ,  1330 , and  1430  in  FIGS. 11C ,  12 C,  13 C, and  14 C, respectively. 
     At step  1070 , for each of the identified pixels, the corresponding accumulator in the accumulator array is incremented. In this embodiment, the accumulator array does not accumulate void pixels over different binarization threshold values, but accumulates all pixels of the estimated non-voided solder ball object over different binarization threshold levels. Again, the accumulator array can be viewed as an accumulator image.  FIGS. 11D ,  12 D,  13 D, and  14 D illustrate the accumulator image obtained at step  1070  for the different iterations of the loop. 
     At step  1080 , once all the binarization threshold values have been processed, the accumulator image provides an approximation of a grayscale X-ray image of a non-voided version of the solder ball. 
     At step  1095 , the accumulator image is subtracted from the original grayscale X-ray image of the solder ball. The result is a void accumulator image similar to that obtained in the previous embodiment once all the binarization threshold values have been processed. 
     In some embodiments, at step  1095  the accumulator image may be subtracted from a modified version of the original grayscale X-ray image in which the grayscale intensity of all pixels not within the boundary of the solder ball is set to 0, i.e., are set to black. 
     In this embodiment, if the step size ΔT is equal to 1, all grayscale intensity values found within the boundary of the solder ball in the original X-ray image of the solder ball will be selected as a binarization threshold level. If the step size ΔT is not equal to 1, before subtracting the accumulator image from the grayscale image of the solder ball at step  1185 , the grayscale intensities in the grayscale image of the solder ball may be quantized according to the step size ΔT, and/or the grayscale intensities in the accumulator image may be scaled (e.g., multiplied by 3 for a step size of 3). 
     In addition, in this embodiment, prior to subtracting the accumulator image from the grayscale image of the solder ball at step  1095 , a grayscale intensity offset equal to the minimum grayscale intensity value found within the boundary of the solder ball in the original X-ray image (and equal to Tmin) may either be added to the accumulator image or subtracted from grayscale image of the solder ball. 
     At step  1098 , the void accumulator array or image is analyzed to detect the voids and, optionally, characterize the voids, as described above in connection with the embodiment of  FIG. 5 . 
     In the embodiments described with reference to  FIGS. 5 and 10 , the difference in grayscale intensity between any two consecutive binarization threshold values was constant over the set of binarization threshold values. In other embodiments, however, the difference in grayscale intensity between consecutive binarization threshold values may vary over the set of binarization threshold values. An advantage of this is that more binarization threshold values can be selected in ranges of binarization threshold values that are more likely to provide significant void information, and fewer binarization threshold values can be selected in the remaining ranges. 
     Also, in the embodiments described with reference to  FIGS. 5 and 10 , the value by which an accumulator is incremented at steps  570  and  1070  was constant over the set of binarization threshold values. In other embodiments, however, each binarization threshold value may be assigned an increment amount (e.g., by means of a look-up table, a parameterized function, etc.) and, at steps  570  and  1070 , the accumulator may be incremented according to the assigned increment amount of the respective binarization threshold value. In one embodiment, the increment amount assigned to a particular binarization threshold value may be equal to the difference in grayscale intensity between the particular binarization threshold value and the previous or subsequent binarization threshold value in the set of binarization threshold values. In another embodiment, the increment amount may be based on a relationship between a grayscale intensity in the grayscale X-ray image and an effective thickness of the solder ball. 
     As noted above, the inventive methods may be employed in a number of applications other than the detection of voids in solder balls. 
     Some embodiments, for example, may be used in the analysis of solder components or elements other than solder balls or spheres, including solder bumps and/or wafer bumps. In one particular application, these methods may be used in the inspection of “flip chips,” assemblies resulting from a method of mounting integrated circuits or other semiconductor devices without the use of wire bonds such as those indicated by reference numeral  50  in  FIG. 1 . The method may also be applied in the context of the detection of irregularities in a solder used to join pieces of material. 
     In other embodiments, the methods described above may be used to detect the presence or absence of defects other than voids, including, in particular, the presence or absence of foreign bodies or impurities in a sample. Other embodiments may be employed to detect the presence or absence of things other than defects, such as, for example, the presence or absence of desirable structures. 
     In other embodiments, the methods disclosed herein may be used to inspect articles or materials other than solder for the presence or absence of desirable or undesirable structures or characteristics. In one embodiment, for example, these methods may be employed to inspect X-ray images of fruits or vegetables for the presence or absence of seeds. 
     In still further embodiments, the methods described above may be employed to analyze images other than X-ray images, including grayscale or color images of any desired resolution or depth. In some embodiments, for example, the methods may be employed to analyze range data images to locate one or more features of interest. 
     Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description and drawings are by way of example only.