A filtered back-projection method to improve the quality of on-line circular trajectory tomographic reconstruction

Abstract

The application discloses a filtered back-projection method for improving online circle track tomography reconstruction quality, and belongs to the field of CT reconstruction. 1. For a group of projection images scanned by an online circle track tomography device, the group of images is subjected to preprocessing operation, and bit conversion, logarithmic transformation and angle weighting are sequentially performed, so that the projection images after preprocessing are obtained; 2. The projection images after preprocessing are sequentially subjected to back-projection reconstruction operation along a ray path, in the process, a different step angle difference between a detector and a ray source is corrected, so that the reconstructed volume data are obtained; 3. The volume data after reconstruction are subjected to secondary gray scale stretching post-processing operation, the first gray scale stretching converts 32-bit volume data into 8-bit volume data, and the second gray scale stretching expands voxels in the main gray scale range interval of the 8-bit volume data into [0, 255]. The application protects important low-frequency information in the horizontal direction of the reconstruction result slice, eliminates the artifact problem caused by the different step angle difference, and enhances the definition and contrast of the reconstruction result.

Description

Technical Field

[0001] This invention belongs to the field of industrial CT reconstruction technology, specifically relating to a filtered back projection method for improving the reconstruction quality of online circular trajectory tomography. Background Technology

[0002] Analytical and iterative methods are two commonly used algorithms in CT reconstruction. Compared to iterative methods, analytical methods are widely used in commercial CT equipment due to their lower computational cost and simpler implementation. The filtered backprojection algorithm is a type of analytical method; the filtered backprojection algorithm for cone-beam CT is also known as the FDK algorithm. The FDK algorithm first applies cosine weights to the projection data, then performs high-pass filtering on the projection image along the row direction, and finally obtains the three-dimensional volume data of the scanned object through a backprojection process.

[0003] In industrial assembly, cone-beam CT scanners typically use a fixed X-ray source and detector, with the object to be scanned moving in a circular motion between them. Unlike cone-beam CT, in-line circular trajectory tomography (CCT) requires the X-ray source and detector to move in a circular path with a 180° phase difference to achieve in-line scanning. The product to be scanned flows into one end of the path and remains stationary; after scanning, it flows out from the other end. Through reconstruction and detection algorithms, in-line detection of the product is achieved. In-line CCT focuses on detecting plate-like objects, such as printed circuit boards (PCBs) and electronic semiconductor chips. If cone-beam CT were used to scan these plate-like objects, accurate reconstruction results would not be obtained due to missing information in certain directions. Given that in-line CCT is used on production lines and requires high reconstruction speed, filtered back-projection algorithms are more suitable.

[0004] The traditional FDK algorithm is derived from the geometry of cone-beam CT. Due to the special geometry of online circular trajectory tomography equipment, applying the cone-beam FDK algorithm to online circular trajectory tomography has the following problems: (1) In the preprocessing stage, the cone-beam FDK algorithm often performs high-pass filtering on the projected image line by line to eliminate the blurring phenomenon after reconstruction. However, due to the special geometry of online circular trajectory CL, if the projected image of online circular trajectory tomography equipment is still subjected to directional high-pass filtering, the important low-frequency information in the horizontal direction of the reconstruction result will be severely lost, resulting in the loss of details in the reconstruction result and affecting the reconstruction quality; (2) Online circular trajectory tomography equipment performs online scanning of plate-shaped objects, which requires the X-ray source and detector to perform circular motion with a phase difference of 180° on their respective circular tracks. It is difficult to guarantee the synchronization of motion between the X-ray source and the detector. If reconstruction is performed using the back-projection step in the traditional cone-beam FDK algorithm, the asynchronous angle difference between the X-ray source and the detector will cause the projection path and the back-projection path to be inconsistent, resulting in severe ring artifacts in the reconstruction results and affecting the reconstruction quality; (3) Since the online circular trajectory tomography equipment uses the edge beam of the X-ray source to scan the plate-shaped object, the brightness of each projected image will be uneven, and the image part closer to the X-ray source will be brighter. After the projected image is reconstructed, the brightness contrast of each reconstructed slice will be greatly different, the slice contrast will be very low, and the reconstruction quality will be affected.

[0005] Currently, online circular trajectory tomography technology is largely controlled by foreign companies, such as VISCOM from Germany and ORMON and SAKI from Japan, with ORMON being a leader in the industry. The online inspection equipment for the domestic SMT and electronic semiconductor industries is basically monopolized by foreign companies. With the localization of X-ray sources and detectors in recent years, the transformation of domestic offline CT scanning equipment to online systems is a trend. Therefore, solving the problems of applying the traditional FDK algorithm to online circular trajectory tomography equipment and improving reconstruction quality is of great significance for breaking the foreign monopoly and thus promoting the development of the domestic electronics manufacturing industry. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a filtered backprojection method to improve the reconstruction quality of online circular trajectory tomography. This method performs high-pass filtering on the projected images in both row and column directions during the preprocessing stage, and then superimposes the results. In the backprojection stage, an online circular trajectory tomography backprojection formula based on angle difference correction is proposed. In the post-processing stage, the reconstructed volume data undergoes secondary grayscale stretching. Compared to traditional cone-beam filtering backprojection algorithms, this method preserves important low-frequency information in the reconstruction results, eliminates artifacts caused by asynchronous angle differences, and improves the clarity and contrast of the volume data.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A filtered back projection method for improving the reconstruction quality of online circular trajectory tomography includes the following steps:

[0009] Step A: For a set of projection images scanned by the online circular trajectory tomography imaging device, preprocessing operations are performed on the set of projection images. The preprocessing operations include bit conversion, logarithmic transformation, angle weighting and filtering. During the filtering process, high-pass filtering is performed on the projection images in the horizontal and vertical directions respectively. Then the results are superimposed to obtain the preprocessed projection images.

[0010] Step B: Perform backprojection reconstruction on each preprocessed projection image along the ray path in sequence; during this process, correct the asynchronous angle difference between the detector and the ray source to obtain the reconstructed volume data.

[0011] Step C: Perform a second grayscale stretching post-processing operation on the reconstructed volume data. The first grayscale stretching converts the 32-bit volume data into 8-bit volume data; the second grayscale stretching expands the voxels in the main grayscale range of the 8-bit volume data to [0,255].

[0012] The specific steps of step A are as follows:

[0013] Step A01: For a projection image in a set of projection images scanned by an online circular trajectory tomography device, the projection image P0 is obtained by successively performing bit conversion, logarithmic transformation, and angle weighting.

[0014] Step A02: Perform Fourier transform on the projected image P0 row by row to obtain the first frequency domain image R1. Multiply the first frequency domain image R1 row by row by the high-pass filter weight w. Perform inverse Fourier transform on the weighted first frequency domain image to obtain the time domain image I1.

[0015] Step A03: Transpose the projected image P0 to obtain the transposed projected image T1. Perform Fourier transform on the transposed projected image T1 row by row to obtain the second frequency domain image R2. Multiply the second frequency domain image R2 row by row by the high-pass filter weight w. Perform inverse Fourier transform on the weighted second frequency domain image to obtain the second time domain image. Transpose this second time domain image to obtain the transposed time domain image I2.

[0016] Step A04: Add the time-domain image I1 to the transposed time-domain image I2 to obtain the preprocessed projection image P1; perform the above processing on each projection image in the group to complete the preprocessing of all projection images in the group.

[0017] The specific steps of step B are as follows:

[0018] Step B01: Determine the sizes of the three dimensions of the volume data to be reconstructed as xSize, ySize, and zSize, and allocate memory of size xSize*ySize*zSize*4 bytes for the volume data; the volume data is represented as F0, and the data type in F0 is a 32-bit floating-point type;

[0019] Step B02: Iterate through the positions (x, y) of the volume data F0 in the world coordinate system. v ,y v ,z v Each voxel of ) For each location, the coordinates before interpolation are obtained according to the back projection formula.

[0020] Where FDD is the vertical distance between the focal point of the X-ray source and the center of the detector; DOD is the vertical distance between the focal plane and the center of the detector; FOD is the vertical distance between the focal point of the X-ray source and the focal plane. θ is the angle between the line connecting the focal point of the X-ray source and the center of the detector and the Z-axis; θ is the angle of rotation of the X-ray source and detector relative to their initial positions, with clockwise being positive and counterclockwise being negative; α is the angle between the initial position of the X-ray source and the positive half-axis of the X-axis, used to adjust the initial positions of the X-ray source and detector; β is the asynchrony angle difference between the detector and the X-ray source; D is the system magnification; p w It is the width of the projected image P1; p h It is the height of the preprocessed projection image P1;

[0021] Step B03: The obtained coordinates (u, v) are of floating-point type. Integer coordinates (u1, v1) are obtained through bilinear interpolation, where 0 ≤ u1 <p w ,0≤v1 <p h ; Take the pixel value p at integer coordinates (u1, v1) on the preprocessed projected image P1 and accumulate it into the volume data F0 at position (x). v ,y v ,z v On the voxels of ), when the complete individual data position is traversed, the back projection of the projected image at one angle is completed; the back projection operation is performed on the projected images at all angles in sequence to complete the reconstruction and obtain the reconstructed 32-bit voxel data F1.

[0022] The specific steps of step C are as follows:

[0023] Step C01: Traverse each layer of the reconstructed 32-bit voxel data F1, and obtain the minimum and maximum values ​​of voxels in F1, respectively f min and f max ;Calculate the value of each voxel in F1 according to the formula Scaling to the range [0,255], i = 0, 1, ..., xSize*ySize*zSize-1, we get the 8-bit volume data F2;

[0024] Step C02: Let the grayscale statistics array of the grayscale histogram of the 8-bit volumetric data F2 be I0, with a size of 256, initialized to 0; traverse the z-direction slice S of the 8-bit volumetric data F2. j j = 0, 1, ..., zSize-1, statistic S j The grayscale histogram grayscale statistics array is T. j I0 = I0 + T j The grayscale statistics of each slice are accumulated into I0 to obtain the grayscale statistics array I0 of the entire 8-bit volumetric data F2; the maximum value in I0 is i. max ; through formula Scale each value in I0 to [0, 255] to obtain the grayscale statistics array J0;

[0025] Step C03: In the grayscale statistics array J0, find the index of the first non-zero grayscale value from left to right, denoted as left; find the index of the first non-zero grayscale value from right to left, denoted as right; thus obtaining the sub-interval [left, right] of [0, 255]; iterate through each voxel of the 8-bit volume data F2, when... hour, when hour, when hour, k=0,1,…,xSize*ySize*zSize-1, where, It is the voxel value at index k of the 8-bit volume data F2. The value at index k of the volume data after grayscale stretching is used to obtain the post-processed 8-bit volume data F. res .

[0026] The technical solution of this invention has the following technical effects:

[0027] 1. In the projection image preprocessing stage, the method of this invention abandons the traditional row-by-row high-pass filtering method and uses a row-column filtering superposition method. This method can retain important low-frequency information in both the row and column directions of the projection image, while simultaneously suppressing overall low-frequency information. This protects important low-frequency information in the horizontal direction (such as the outlines of some electronic components) in the reconstruction result and overcomes the blurring phenomenon that occurs without filtering, resulting in richer details in the reconstruction result.

[0028] 2. Computer simulation experiments have verified that in online circular trajectory tomography equipment, the asynchronous angular difference (even a few tenths of a degree) between the detector and the X-ray source can severely affect the reconstruction results, specifically manifesting as severe ring artifacts and blurred volumetric data. This invention, through its proposed backprojection method based on angular difference correction in the backprojection stage, corrects the inconsistency between the projection path and the backprojection path, thereby eliminating artifacts in the reconstruction results, improving the clarity of the reconstruction results, and significantly enhancing the quality of the reconstructed volumetric data.

[0029] 3. In the post-processing stage, the volume data undergoes a first grayscale stretch to overcome the problem of inconsistent contrast in volume data slices caused by uneven brightness in the projected image. A second grayscale stretch of the volume data extends the grayscale values ​​within the main grayscale distribution range, improving the contrast of the volume data and making defect information in industrial products easily distinguishable from other information, facilitating subsequent defect location and detection.

[0030] This invention presents a filtered back-projection method for improving the reconstruction quality of online circular trajectory tomography, significantly enhancing the quality of the reconstruction results. Comparative experiments, using average gradient and spatial frequency as quantitative indicators and combined with subjective evaluation, show that the reconstruction quality of this method surpasses that of the German commercial software VGStudio. Attached Figure Description

[0031] Figure 1 In the image, (a) and (b) are the projected image of the first input angle and its preprocessed image, respectively.

[0032] Figure 2 This is a schematic diagram of the angle weighting relationship during the preprocessing process.

[0033] Figure 3 This is a flowchart of the filtering process during preprocessing.

[0034] Figure 4 This is a geometric diagram of an online circular trajectory tomography system during the back projection process.

[0035] Figure 5 This is a diagram defining the angle difference during the back projection process.

[0036] Figure 6 This is a flowchart of the post-processing procedure.

[0037] Figure 7 (a), (b), (c), and (d) are comparison charts of the reconstruction results at each step.

[0038] Figure 8 (a) and (b) are comparison charts of the reconstruction results and the commercial software VGStudio, respectively. Detailed Implementation

[0039] The specific details of each step of the present invention will be described in detail below with reference to the accompanying drawings.

[0040] This invention proposes a filtered back projection method to improve the reconstruction quality of online circular trajectory tomography, specifically including the following steps:

[0041] Step A: Perform preprocessing on a set of projection images scanned by the online circular trajectory tomography device. For example... Figure 1 (a) and Figure 1 As shown in (b), this is the first of 32 projected images obtained by scanning a ball grid array (BGA) once with a tomographic imaging device. Preprocessing operations were performed on this projected image, including bit conversion, logarithmic transformation, angle weighting, and filtering. During the filtering process, high-pass filtering was applied to the projected image in both the horizontal and vertical directions. The results were then superimposed to obtain the preprocessed projected image.

[0042] Step A involves the following steps:

[0043] Step A01: In order to capture richer X-ray energy decay information, the projection after detector scanning is generally a 16-bit image with a value range of [0, 65535], such as... Figure 1 The projected image is shown in (a). Since the subsequent backprojection operation is an accumulation process, in order to prevent numerical overflow errors in the subsequent backprojection operation, the pixel values ​​of the projected image need to be converted into 32-bit floating-point type.

[0044] right Figure 1 (a) The formula for type conversion is:

[0045] Where P u,v It is the pixel value at position (u,v) in the 16-bit projected image before type conversion; It is the pixel value at the same position on the 32-bit projected image after type conversion.

[0046] Based on the properties of the log function, it can stretch the low-gray-value parts of an image to a larger extent and the high-gray-value parts to a smaller extent. Applying a log transform to a projected image can make defect information in a product more apparent.

[0047] The formula for logarithmic transformation is as follows:

[0048] in After logarithmic transformation, the pixel value at position (u,v) in the projected image. Defects in industrial products have relatively low density values, which are reflected as a relatively high density in the projected image. Inverting the result can darken the defect information, making it more noticeable.

[0049] Based on the geometric characteristics of online circular trajectory tomography, it utilizes X-ray imaging at the large cone angle of the X-ray source. According to the properties of the cone-shaped beam of the X-ray source, the further away from the center of rotation the large cone angle, the weaker the incident X-ray energy. Weighted corrections are then applied to the cone angle at each position in the projected image. For example... Figure 2 This is a schematic diagram of the positional relationship of the weighted correction of the projected data, where each pixel value of the projected image is multiplied by the cosine value of the indicated cone angle.

[0050] The weighted correction formula is:

[0051] in It is the pixel value at position (u,v) in the projected image after weighted correction, FOD is the distance from the focal point of the ray source to the center of rotation, and t x It is the x-coordinate of the ray source under the rotation angle θ, t y It is the y-coordinate of the ray source under the rotation angle θ, t z It is the z-coordinate of the ray source under the rotation angle θ. It is the distance from the focal point of the X-ray source to the point (u,v) on the projected image;

[0052] Step A02: As Figure 3 The diagram illustrates the process of row-column superposition filtering on the angle-weighted projected image P0. The first frequency domain image R1 is obtained by performing a Fourier transform row by row on the projected image P0. The first frequency domain image R1 is then multiplied row by row by a high-pass filter weight w. The weighted first frequency domain image is then subjected to an inverse Fourier transform to obtain the time domain image I1. The projected image P0 is then transposed to obtain the transposed projected image T1. The second frequency domain image R2 is obtained by performing a Fourier transform row by row on T1. The second frequency domain image R2 is then multiplied row by row by a high-pass filter weight w. The weighted second frequency domain image is then subjected to an inverse Fourier transform to obtain the second time domain image T2. This second time domain image is then transposed to obtain the transposed time domain image I2.

[0053] The overall filtering formula is:

[0054] P1 = F -1 (F row (P0)*w)+F -1 (F col (P0)*w), where P1 is the result of passing through (P0)*w), where P1 is the result of passing Figure 3 Filtered projection image; F -1 F represents the inverse Fourier transform of the image. rowThis indicates that a Fourier transform is performed on the image row by row, F col This indicates that the image is subjected to a Fourier transform along the columns, and w represents the high-pass filter weights multiplied along the rows of the image.

[0055] In the implementation of the method of this invention, the filtering formula for w can be selected in the following three ways:

[0056] The Ram-Lak ramp filter, where u is the column index of each row of the image and n is the column number in the spectrum, produces the clearest result of all pre-filters. However, this is sometimes not ideal because it introduces noise;

[0057] Shepp-Logan filters can attenuate high-frequency information to a certain extent, and compared with Ram-Lak ramp filters, they can effectively reduce noise.

[0058] The Hann filter is more effective at attenuating high-frequency signals than the Shepp-Logan filter. The more high-frequency information is removed, the smoother the result and the less noise is generated, but the edges in the final reconstruction are also less sharp. The filter can be flexibly selected according to needs.

[0059] Finally, the time-domain image I1 is added to the transposed time-domain image I2 to obtain the preprocessed projection image P1, as shown below. Figure 1 As shown in (b), compared to the original projected image, the preprocessed projected image shows more obvious bubble defect information in the solder balls, and the image outline is more distinct.

[0060] Step B: Perform backprojection reconstruction on each preprocessed projection image along the ray path in sequence; during this process, correct the asynchronous angle difference between the detector and the ray source to obtain the reconstructed volume data.

[0061] Step B involves the following steps:

[0062] Step B01: Establish a geometric coordinate system for the online circular trajectory tomography system. For example... Figure 4The diagram shows the geometric structure of an online circular trajectory tomography system. The X-ray source and detector undergo linear circular motion within their respective planes. S is the focal point of the X-ray source, D is the center point of the detector, and O is the origin of the coordinate system, which is also the center point of the object to be reconstructed. S, O, and D are collinear. The XYZ coordinate system is the world coordinate system of the object, and the X′Y′Z′ coordinate system is the rotating coordinate system of the X-ray source and detector. The X′Y′Z′ coordinate system rotates relative to the XYZ coordinate system around the Z-axis as the X-ray source and detector rotate, with a rotation angle of θ. UV is the image coordinate system, with its origin located at the upper left corner of the image. The U-axis is positive horizontally to the right, and the V-axis is positive vertically downwards. The angle φ between the straight line SD and the Z-axis is called the oblique angle. The angle α between the initial position of the X-ray source and the positive half-axis of the X-axis is called the initial angle. The phase difference between the detector and the X-ray source is always maintained at 180°. The vertical distance between the X-ray source focus S and the origin O is FOD, the vertical distance between the detector center point D and the origin is DOD, and the vertical distance between the X-ray source focus and the detector center is FDD.

[0063] Define the asynchronous angular difference β between the radiation detector and the radiation source. For example... Figure 5 The diagram shows the asynchronous angular difference of an online circular trajectory tomography system. The inner circle represents the rotation trajectory of the X-ray source, and the outer circle represents the rotation trajectory of the detector. Point O is the origin of the world coordinate system, and point S is the focal point of the X-ray source. The initial position of the X-ray source is located on the positive half-axis of the X-ray axis. Without an angular difference, the detector's initial position should be at position D1, 180° relative to the X-ray source. However, this is difficult to guarantee during mechanical assembly. Point D2 represents the detector's initial position with an angular difference. The angular difference between D2 and D1 is defined as β. Therefore, the initial angle of the detector relative to the positive half-axis of the X-ray axis is 180° + β.

[0064] The sizes of the three dimensions of the volume data to be reconstructed are determined as xSize, ySize, and zSize, respectively. Memory of size xSize*ySize*zSize*4 bytes is allocated for the volume data. The initial volume data is represented as F0, and the data type in F0 is a 32-bit floating-point type, initialized to 0.

[0065] Step B02: Iterate through the positions (x, y) in the F0 intrinsic world coordinate system. v ,y v ,z v Each voxel of ) For each location, according to Figure 4 Based on the geometric structure shown, the back projection formula of the online circular trajectory tomography system is derived, and the floating-point coordinates (u,v) of the projected image before interpolation are obtained.

[0066] The derivation of the back projection formula is as follows:

[0067] Let the resolution of the detector be s. d The resolution s of the sample volume data to be reconstructed v Based on geometric relationships, the formula for calculating the system's magnification D is: Convert the units (mm) of FOD and DOD to pixels: Ideally, according to geometric relationships, the coordinates of the ray source focus in the XYZ coordinate system are S(x). s ,y s ,z s ) is: S: When there is an angular difference, the coordinates D(x) of the detector center in the XYZ coordinate system are... d ,y d ,z d D: Let the coordinates of the point to be reconstructed in the world coordinate system XYZ be V(x v ,y v ,z v The equation of the ray passing from the focal point S of the ray source through the point V to be reconstructed can be expressed as: The core purpose of back projection is to calculate the back projection address, that is, to calculate the horizontal and vertical coordinates of all points on the detector plane, and to set z = z d Substituting into the ray equation, we can obtain the back-projection address: The world coordinates (x, y) of the projected image need to be converted to coordinates (u, v) in the image coordinate system. Let the width of the projected image be p. w , height is p h The conversion process is as follows:

[0068] Therefore, the final back projection formula is:

[0069]

[0070] in θ is the angle between the line connecting the focal point of the X-ray source and the center of the detector and the Z-axis; θ is the angle of rotation of the X-ray source and detector relative to their initial positions, clockwise is positive and counterclockwise is negative; α is the angle between the initial position of the X-ray source and the positive half-axis of the X-axis, which can be used to adjust the initial positions of the X-ray source and detector; β is the asynchrony angle difference between the detector and the X-ray source; D is the system magnification; p w It is the width of the projected image P1; p h It is the height of the projected image P1;

[0071] Step B03: Obtain the back-projected coordinates (u, v) as floating-point type, and use bilinear interpolation to obtain integer coordinates (u1, v1), where 0 ≤ u1 <p w ,0≤v1 <p h; Take the pixel value p at (u1, v1) on the preprocessed projected image P1 and add it to the volume data F0 at position (x). v ,y v ,z v On the voxels of the data; when the complete individual data position is traversed, the back projection of the projected image at one angle is completed; following the above steps, the back projection operation is performed on the projected images at all angles in sequence to complete the reconstruction and obtain the reconstructed volume data F1.

[0072] Step C: As Figure 6 This is a flowchart of the secondary grayscale stretching post-processing operation on the reconstructed volume data. The first grayscale stretching converts the 32-bit volume data into 8-bit volume data; the main grayscale distribution range of the 8-bit volume data is calculated; based on the grayscale distribution range, the second grayscale stretching expands the voxels within the main grayscale range of the 8-bit volume data to [0, 255].

[0073] Step C involves the following steps:

[0074] Step C01: Traverse each layer of the reconstructed 32-bit voxel data F1 to obtain the minimum value of each voxel in F1, and the maximum values ​​are f. min f max ;Calculate the value of each voxel in F1 according to the formula Scaling to the range [0,255], i = 0, 1, ..., xSize*ySize*zSize-1, we get the 8-bit volume data F2;

[0075] Step C02: Let the grayscale statistics array of the grayscale histogram of F2 be I0, with a size of 256, initialized to 0; traverse the z-direction slice S of the 8-bit volumetric data F2. j j = 0, 1, ..., zSize-1, statistic S j The grayscale histogram grayscale statistics array is T. j I0 = I0 + T j The grayscale statistics of each slice are accumulated into I0 to obtain the grayscale statistics array I0 of the entire 8-bit volumetric data F2; the maximum value in I0 is i. max ; through formula i = 0, 1, ..., 255, scale each value in I0 to [0, 255] to obtain the grayscale statistics array J0;

[0076] Step C03: In the grayscale statistics array J0, find the index of the first non-zero grayscale value from left to right, denoted as left; find the index of the first non-zero grayscale value from right to left, denoted as right; thus obtaining the sub-interval [left, right] of [0, 255]; iterate through each voxel of the 8-bit volume data F2, when... season when season when season k=0,1,…,xSize*ySize*zSize-1, where, It is the voxel value at index k of the 8-bit volume data F2. The value at index k of the volume data after grayscale stretching is used to obtain the post-processed 8-bit volume data F. res .

[0077] The following is a combination of... Figure 1 The BGA reconstruction results illustrate the effectiveness of the filtered back projection method used to improve the reconstruction quality of online circular trajectory tomography:

[0078] like Figure 7 As shown in (d), the volumetric data F of the reconstruction result is obtained by the filtered back projection method used to improve the reconstruction quality of online circular trajectory tomography. res A slice of the central layer. With Figure 7 Compared to (d), Figure 7 In (a), step C was not used, which indicates that step C, by performing a second grayscale stretching post-processing on the volume data, can effectively improve the contrast of the volume data, making the information on saturation defects in the solder balls well distinguishable from other information, facilitating subsequent location and detection of BGA defects; and Figure 7 Compared to (b), Figure 7 In the backprojection stage, the angle difference β was corrected by 0.17° in (d), which can be seen... Figure 7 (d) eliminated Figure 7 The severe annular artifacts at the edge of the solder ball in (b) improve the clarity of the reconstruction results, which shows that the back projection method based on angle difference correction in step B can greatly improve the quality of the reconstructed volume data. Figure 7 In the preprocessing stage, (c) traditional row-wise high-pass filtering is used. Figure 7 In step (d), the filtering process from step A is used in the preprocessing stage. It can be seen that... Figure 7 In image (c), there are strip-shaped black artifacts in the horizontal direction, indicating a loss of detail in the horizontal direction. The edges of the solder balls are not clearly defined, and the image is blurry. This suggests that... Figure 3 The filtering process can protect important low-frequency information in the horizontal direction of the reconstruction result, enrich image detail information, and enhance image clarity. Figure 7 The mean gradient MG and spatial frequency SF are the highest in (d), at 6.4649 and 12.2927 respectively, which indicates that the filtered back projection method used to improve the reconstruction quality of online circular trajectory tomography is effective. Figure 1 The reconstructed dataset has better image clarity and richer texture detail.

[0079] Figure 8 (a) shows a filtered back-projection method used to improve the reconstruction quality of online circular trajectory tomography. Figure 1 The reconstruction result of BGA is the data center layer. Figure 8 (b) is the commercial software VGStudio. Figure 1 The reconstructed data center layer of the BGA. Figure 8 In (a), the average gradient MG and spatial frequency SF are 6.4649 and 12.2927, respectively. Figure 8 The average gradient MG and spatial frequency SF in (b) are 5.5334 and 9.8794, respectively, which shows that compared with the commercial software VGStudio, the filtered back projection method of the present invention for improving the reconstruction quality of online circular trajectory tomography has better image clarity and richer image texture details.

Claims

1. A filtered back projection method for improving the reconstruction quality of online circular trajectory tomography, characterized in that: Includes the following steps: Step A: For a set of projection images scanned by the online circular trajectory tomography imaging device, preprocessing operations are performed on the set of projection images. The preprocessing operations include bit conversion, logarithmic transformation, angle weighting and filtering. During the filtering process, high-pass filtering is performed on the projection images in the horizontal and vertical directions respectively. Then the results are superimposed to obtain the preprocessed projection images. Step B: Perform backprojection reconstruction on each preprocessed projection image along the ray path sequentially; during this process, correct the asynchronous angle difference between the detector and the ray source to obtain the reconstructed volume data; the specific steps are as follows: Step B01: Determine the sizes of the three dimensions of the volume data to be reconstructed as xSize, ySize, and zSize, and allocate memory of size xSize*ySize*zSize*4 bytes for the volume data; the volume data is represented as... , The data type in the file is a 32-bit floating-point type; Step B02: Iterate through the volume data sequentially. Position in the intrinsic world coordinate system ( , , Each voxel of ) , , For each location, the coordinates before interpolation are obtained according to the back projection formula. , ,in FDD It is the vertical distance between the focal point of the radiation source and the center of the detector; DOD It is the vertical distance between the focal plane and the center of the detector; FOD It is the perpendicular distance between the focal point of the radiation source and the focal plane; It is the angle between the line connecting the focal point of the radiation source and the center of the detector and the Z-axis; It is the angle of rotation between the radiation source and the detector relative to their initial positions, with clockwise being positive and counterclockwise being negative; β is the angle between the initial position of the X-ray source and the positive half-axis of the X-axis, used to adjust the initial position of the X-ray source and the detector; β is the asynchrony angle difference between the detector and the X-ray source. D It is the system amplification factor; It is a projected image The width; It is the preprocessed projection image Height; Step B03: Obtained coordinates ( u , v The coordinates are of type floating-point, and integer coordinates are obtained through bilinear interpolation. ),in , ; Take the preprocessed projection image upper integer coordinates ( pixel value at ) p Accumulated into body data Middle position ( , , On the voxels; after traversing the complete individual data positions, the backprojection of the projected image at one angle is completed; the backprojection operation is performed on the projected images at all angles in sequence to complete the reconstruction and obtain the reconstructed 32-bit voxel data. ; Step C: Perform a second grayscale stretching post-processing operation on the reconstructed volume data. The first grayscale stretching converts the 32-bit volume data into 8-bit volume data; the second grayscale stretching expands the voxels in the main grayscale range of the 8-bit volume data to [0,255].

2. The filtered back projection method for improving the reconstruction quality of online circular trajectory tomography as described in claim 1, characterized in that: The specific steps of step A are as follows: Step A01: For a projection image from a set of projection images scanned by an online circular trajectory tomography device, the projection image is obtained by successively performing bit conversion, logarithmic transformation, and angle weighting. ; Step A02: Project the image The first frequency domain image is obtained by performing Fourier transform line by line. For the first frequency domain image Multiply each row by the high-pass filter weight w, and then perform an inverse Fourier transform on the weighted first frequency domain image to obtain the time domain image. ; Step A03: Project the image Transpose the image to obtain the transposed projection image. For the transposed projection image The second frequency domain image is obtained by performing Fourier transforms line by line. For the second frequency domain image The weighted second frequency domain image is obtained by multiplying each row by the high-pass filter weight w and then performing an inverse Fourier transform. This second time domain image is then transposed to obtain the transposed time domain image. ; Step A04: Convert the time-domain image With transposed time domain image Add them together to obtain the preprocessed projected image. ; The above processing is performed on each projected image in the group to complete the preprocessing of all projected images in the group.

3. The filtered back projection method for improving the reconstruction quality of online circular trajectory tomography as described in claim 1, characterized in that: The specific steps of step C are as follows: Step C01: Traverse the reconstructed 32-bit volume data Each layer, obtain The minimum and maximum values ​​of the middle voxels are respectively ;Will Each voxel value is calculated using the formula Scale to the range [0, 255] i =0,1,…,xSize*ySize*zSize-1, to obtain 8-bit volume data. ; Step C02: Set 8-bit volume data The grayscale statistics array of the grayscale histogram is Its size is 256, initialized to 0; iterate through the 8-bit data. z-direction slice , j =0,1,…,zSize-1, Statistical The grayscale histogram grayscale statistics array is , = + The grayscale statistics of each slice are accumulated to... Thus, the entire 8-bit volume data is obtained. Gray-scale statistical array ;beg The maximum value in is ; through formula , i =0,1,…,255, will Each value is scaled to [0, 255] to obtain a grayscale statistics array. ; Step C03: In the grayscale statistical array In the process, find the index of the first non-zero grayscale value from left to right, denoted as `left`; find the index of the first non-zero grayscale value from right to left, denoted as `right`; thus obtaining the sub-interval [left, right] of [0, 255]; traverse the 8-bit volume data. Each voxel, when hour, =0; when hour, =255; when hour, , k =0,1,…,xSize*ySize*zSize-1, where... It is 8-bit volume data index k voxel values ​​at the location, It is a volume data index after grayscale stretching. k The voxel values ​​at the specified locations are used to obtain the post-processed 8-bit voxel data. .

Images