Calibration method for X-ray measuring devices

Abstract

This invention provides a calibration method for an X-ray measuring device, comprising the following steps: a placement step, in which a calibration fixture is placed on a rotary stage; a feature position calculation step, in which X-rays are irradiated onto the calibration fixture, and the center of gravity position is determined based on the output of an X-ray image detector; a transformation matrix calculation step, in which a projection transformation matrix is ​​calculated based on the center of gravity position and a known relative position interval; a rotation detection step, in which the rotary stage is rotated at least twice by a predetermined angle, and the feature position calculation step and the transformation matrix calculation step are repeated; and a center position calculation step, in which the rotation center position of the rotary stage is calculated based on the projection transformation matrix. Thus, the rotation center position of a rotary stage on which the object to be measured is placed in a rotatable manner can be easily calculated through simple steps.

Description

[0001] Cross-reference of related applications

[0002] The entire contents of Japanese Patent Application 2020-111821, filed on June 29, 2020 (including the description, drawings and claims) are incorporated herein by reference. Technical Field

[0003] This invention relates to a calibration method for an X-ray measuring device, and more particularly to a calibration method for an X-ray measuring device that can easily calculate the rotation center position of a rotary stage on which the object to be measured is rotatably mounted through a simple procedure. Background Technology

[0004] Previously, X-ray measuring devices (X-ray CT measuring devices) could use X-rays to perform three-dimensional shape measurements on the object being measured. They were primarily used to observe and inspect features that were difficult to detect visually, such as porosity in cast parts, poor welding in welded components, and defects in circuit patterns in electronic components. However, in recent years, due to the widespread adoption of 3D printing, the demand for high-precision 3D dimensional measurement of the internal dimensions of processed products has also increased. To address this demand, there is a need for X-ray measuring devices to further improve the accuracy of dimensional measurements.

[0005] In order to enable the X-ray measuring device to perform dimensional measurements with higher accuracy, as described in Patent Document 1, it is important to perform various calibrations inherent to the device before the measurement begins. Summary of the Invention

[0006] The problem the invention aims to solve

[0007] However, in the calibration method described in Japanese Patent Application Publication No. 2000-298105, for example, in order to determine the position of the rotation center of the rotary stage, after rotating the calibration fixture 180 degrees to calculate the center channel on the detection surface of the X-ray detector corresponding to the rotation center, it is necessary to calculate the distance between the X-ray source and the rotation center position through a different process. That is, in the past, the calculation of the rotation center position of the rotary stage was complex and difficult.

[0008] The present invention was made to solve the aforementioned problems, and its objective is to provide a calibration method for an X-ray measuring device that can easily calculate the rotation center position of a rotary stage on which the object to be measured is rotatably mounted through a simple procedure.

[0009] Solution for solving the problem

[0010] The first invention of this application solves the aforementioned problem by a calibration method for an X-ray measuring device, namely, a calibration method for an X-ray measuring device that uses X-rays to perform three-dimensional shape measurement on an object to be measured. The X-ray measuring device comprises: an X-ray source that generates the X-rays; a rotating stage that rotatably mounts the object to be measured; and an X-ray image detector that detects the X-rays transmitted through the object to be measured. The calibration method includes the following steps: a mounting step in which a calibration fixture is mounted on the rotating stage, the calibration fixture being capable of arranging a reference object at N or more known relative positional intervals, the shape of which can be determined by a projection onto the X-ray image detector. The process involves determining the following steps: a feature position calculation step, where N ≥ 4; irradiating the calibration fixture with X-rays and determining the positions of feature points of the projected images of the reference object at N positions based on the output of the X-ray image detector; a transformation matrix calculation step, calculating a transformation matrix based on the positions of the feature points of the projected images of the reference object at N positions and the known relative position intervals, the transformation matrix being used to transform the projection of the reference object onto the detection surface of the X-ray image detector; a rotation detection step, rotating the rotary table at a predetermined angle more than twice, repeating the feature position calculation step and the transformation matrix calculation step; and a center position calculation step, calculating the rotation center position of the rotary table based on the transformation matrix.

[0011] The second invention of this application is that, when all the reference objects are placed on only one plane on the calibration fixture, the transformation matrix is ​​set as a projection transformation matrix; when the reference objects are placed in three dimensions on the calibration fixture, N is set to 6 and the transformation matrix is ​​set as a projection matrix.

[0012] The third invention of this application is that, in the center position calculation step, the rotation axis of the rotary table is also calculated.

[0013] The fourth invention of this application is that, in the center position calculation step, it is assumed that the X-ray source and the X-ray image detector rotate in place of the rotary table, and the absolute position of the X-ray source is calculated based on the transformation matrix each time the specified angle is rotated, thereby calculating the rotation center position of the rotary table.

[0014] The fifth invention of this application is that, when the rotary table is rotated more than four times at the specified angle and the absolute position of the X-ray source is calculated, the distance between the X-ray source and the X-ray image detector, and the position of the foot of the perpendicular line from the X-ray source to the X-ray image detector are set as variables. The distance error between the position on the trajectory of the virtual circle obtained by fitting the absolute position of the X-ray source calculated based on the transformation matrix to a perfect circle and the absolute position of the X-ray source is evaluated. The distance between the X-ray source and the X-ray image detector, and the position of the foot of the perpendicular line from the X-ray source to the X-ray image detector are calculated thereby.

[0015] The sixth invention of this application is that, in the center position calculation step, the center position of the trajectory obtained by fitting a perfect circle is calculated based on the change in the absolute position of the X-ray source, and the center position is set as the rotation center position of the rotary table.

[0016] The seventh invention of this application is that, when calculating the rotation axis of the rotary table, the tilt angle of the trajectory relative to the horizontal plane is calculated, and the rotation axis is calculated based on the tilt angle and the position of the rotation center.

[0017] The eighth invention of this application is to set the reference object as a sphere.

[0018] The ninth invention of this application is to set the position of the feature point of the projected image of the reference object as the centroid position of the projected image.

[0019] The effects of the invention

[0020] According to the present invention, the rotation center position of a rotary table on which the object to be measured is rotatably placed can be easily calculated through a simple procedure.

[0021] These and other novel features and advantages of the present invention will become apparent from the following detailed description of preferred embodiments. Attached Figure Description

[0022] Preferred embodiments will be described with reference to the accompanying drawings, in which the same reference numerals denote the same elements throughout the drawings.

[0023] Figure 1 This is a schematic side view showing the basic structure of the X-ray measuring device according to an embodiment of the present invention.

[0024] Figure 2 Is only shown Figure 1 A top-view summary of the main parts of the X-ray measuring device.

[0025] Figure 3A It is shown Figure 1 The front view of the calibration fixture.

[0026] Figure 3B It is shown Figure 1 Top view of the calibration fixture.

[0027] Figure 4 This is a flowchart illustrating the calibration process of the X-ray measuring apparatus involved in the embodiments of the present invention.

[0028] Figure 5 yes Figure 4 A detailed flowchart of the process for calculating the absolute position of the X-ray source.

[0029] Figure 6 It was carried out Figure 5 The flowchart shows the process of calculating the distance between the X-ray source and the X-ray image detector, as well as the position of the foot of the perpendicular line from the X-ray source to the X-ray image detector, after calculating the absolute position of the X-ray source.

[0030] Figure 7A It is a diagram showing the trajectory of the ball as the turntable rotates at a specified angle.

[0031] Figure 7B It is a diagram showing the trajectory of the absolute position of the X-ray source when the X-ray source and the X-ray image detector are assumed to have rotated. Detailed Implementation

[0032] Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. Furthermore, the present invention is not limited to the contents described in the following embodiments and examples. Additionally, the constituent elements of the embodiments and examples described below include constituent elements that can be easily conceived by those skilled in the art, substantially the same constituent elements, i.e., constituent elements within the same range. Moreover, the constituent elements disclosed in the embodiments and examples described below can be appropriately combined or selected for use.

[0033] exist Figure 1 Embodiments of the present invention are shown in the figure. Furthermore, in Figure 1 In this example, the left-right direction relative to the paper is defined as the z-axis, the up-down direction relative to the paper is defined as the y-axis, and the direction perpendicular to the paper is defined as the x-axis.

[0034] X-ray measuring device 100 is a device that uses X-rays to measure the three-dimensional shape of an object being measured, such as... Figure 1 As shown, it includes a main body 108, a host computer 128, and an action controller 130.

[0035] In addition, Figure 1 , Figure 2In this process, the calibration fixture 102 is placed on the rotary table 120 instead of the object being measured. The calibration fixture 102 is as follows: Figure 3A , Figure 3B As shown, the plate member 104 is made of a material (e.g., aluminum) that allows X-rays 118 to pass through. Multiple (e.g., 4 x 3, or N = 12) spheres (reference objects) 106 of diameter D are arranged at known relative intervals Pu and Pv on the plate member 104. In other words, the spheres 106 are arranged at 12 positions with known relative intervals Pu and Pv. That is, in the calibration fixture 102, all the spheres 106 are placed on only one plane. Furthermore, it can be said that the relative positions X(1-12) of the 12 spheres 106, or in other words, the spheres 106 at 12 positions, are known (X(1-12) has the same meaning as X1-X12, and will be described the same way below). Moreover, the shape of the spheres 106 is simple and can be easily determined by the projected image projected onto the X-ray image detector 124. Furthermore, in Figure 3A In this explanation, the left-right direction relative to the paper is defined as the u-axis, the up-down direction relative to the paper is defined as the v-axis, and the direction perpendicular to the paper is defined as the w-axis.

[0036] like Figure 1 As shown, the main body 108 includes an X-ray shield 110 to prevent X-ray leakage 118, an X-ray source 116 that generates X-ray 118, a rotary stage 120 that rotatably mounts the object to be measured (not shown), and an X-ray image detector 124 that detects the X-ray 118 that has passed through the object to be measured, all mounted on a base 112. The X-ray source 116 is mounted on a radiation source support 114 on the base 112. The radiation source support 114 may have a linear motion mechanism that allows the X-ray source 116 to move in the three axial directions of x, y, and z. The rotary stage 120 is mounted on a worktable support 122 on the base 112. Furthermore, the worktable support 122 has a linear motion mechanism that allows the object to be measured to move in the three axial directions of x, y, and z. Additionally, a tilting mechanism that can tilt the rotation axis Ax of the rotary stage 120 may also be provided on the worktable support 122. The X-ray image detector 124 has a two-dimensional detection surface 124A sensitive to X-rays 118. The X-ray image detector 124 is supported on a detector support stage 126 on a base 112. The detector support stage 126 may also have a linear motion mechanism that allows the X-ray image detector 124 to move in the three axial directions of x, y, and z. The radiation beam of X-rays 118 from the X-ray source 116 is adjusted to diffuse in a conical shape in the z-axis direction, and the centerline of the radiation beam intersects the rotation axis Ax of the rotary stage 120 and becomes a perpendicular line to the detection surface 124A of the X-ray image detector 124.

[0037] Figure 1The main computer 128 shown controls the X-ray source support 114, X-ray source 116, rotary stage 120, worktable support 122, X-ray image detector 124, and detector support 126 of the main body 108. Furthermore, the main computer 128 can automatically or semi-automatically perform the measurement operations and calibration of the X-ray measuring device 100 by reading and executing programs stored in a storage unit (not shown). In other words, during the measurement operations of the X-ray measuring device 100, the main computer 128, for example, reconstructs the data of the projected image obtained by the X-ray image detector 124 to create three-dimensional volume data of the object being measured.

[0038] Then, during the calibration of the X-ray measuring device 100, the host computer 128, for example assuming that the X-ray source 116 rotates in place of the rotary stage 120, can use the relationships expressed by the series of formulas shown below to calculate the absolute position Xs of the X-ray source 116 at the k-th assumed rotation position, based on the 3x3 projection transformation matrix (transformation matrix) Hk of the k-th (1≤k≤Q; Q≥3) rotation position Posk of the rotary stage 120. Figure 7A , Figure 7B Then, the host computer 128 calculates the rotation center position Cp of the rotary table 120 (that is, the host computer 128 calculates the rotation center position Cp of the rotary table 120 based on the projection transformation matrix Hk).

[0039] Specifically, the intrinsic parameter matrix A, expressed by equation (1), is defined based on the distance f between the X-ray source 116 and the X-ray image detector 124, and the position Cc(cx, cy) of the foot of the perpendicular line from the X-ray source 116 to the X-ray image detector 124. Furthermore, the values ​​of the distance f in the first row and first column of the intrinsic parameter matrix A and the distance f in the second row and second column are slightly different when the aspect ratio of the pixels of the X-ray image detector 124 is different. Additionally, there is a case where the first row and second column of the intrinsic parameter matrix A uses a skew S related to image distortion, but in this embodiment, the skew S is set to 0.

[0040] [Number 1]

[0041]

[0042] At this point, the rotation matrix Rk of the kth assumed rotation position is a 3-row x 3-column matrix consisting of 3 column vectors rk1, rk2, and rk3, which can be expressed as in equation (2).

[0043] Rk=[rk1 rk2 rk3] (2) Here, by using the translation matrix Tk (translation vector of column 1) of the kth assumed rotation position, equations (1) and (2), the projection transformation matrix Hk can be decomposed into equation (3).

[0044] Hk=A[rk1 rk2 Tk] (3)

[0045] According to equation (3), the absolute position Xs of the X-ray source 116 at the k-th assumed rotation position can be calculated as shown in equation (4). Furthermore, the symbol -inv() denotes the inverse matrix.

[0046] Xs=-inv(Rk)*Tk (4)

[0047] Furthermore, the main computer 128 can use the internal parameter matrix A and the projection transformation matrix Hk to calculate the absolute position Xa (1 to N) of the sphere 106. On the image, using the known relative position intervals Pu, Pv, distance f, and position Cc (cx, cy) of the sphere 106, each sphere 106 is spatially arranged, and the coordinate transformation is performed using the rotation and translation information contained in the projection transformation matrix Hk to transform it to the actual position, thereby enabling the calculation of the absolute position Xa (1 to N) of the sphere 106.

[0048] Furthermore, when the distance f between the X-ray source 116 and the X-ray image detector 124, and the position Cc(cx, cy) of the foot of the perpendicular line from the X-ray source 116 to the X-ray image detector 124 are unknown, the host computer 128 uses the distance f and the position Cc(cx, cy) as variables, substitutes them with appropriate values, and uses Equation (4), that is, based on the projection transformation matrix Hk (k = 1 to Q), to calculate the Q absolute positions Xs of the X-ray source 116. The host computer 128 fits a circle (virtual circle) to the calculated Q absolute positions Xs of the X-ray source 116, for example, using the least squares method. Then, the host computer 128 evaluates the distance error between the position on the trajectory of the virtual circle and the Q absolute positions Xs of the X-ray source 116, and calculates the distance f and position Cc(cx, cy) with the minimum distance error. In addition, at this time, the total number of rotation positions Q is 4 or more, that is, the rotary table 120 is rotated 4 times or more at a specified angle α.

[0049] Figure 1 The motion controller 130 shown is connected to the host computer 128 to control the rotation and movement of the X-ray source 116 and the rotary table 120 of the main body 108, as well as various mechanisms.

[0050] Next, the measurement operation of the X-ray measuring device 100 will be briefly explained.

[0051] During the measurement, the object under test on the rotating stage 120 is rotated while generating X-rays 118, and projection images are collected from multiple angle directions (e.g., the number of angle divisions is about 1000 to 6000). The collected projection images are reconstructed using the horizontally transverse slice plane of the object under test as a reference plane to create three-dimensional volume data (three-dimensional image) of the object under test.

[0052] Next, use Figures 4 to 7B The calibration process of the X-ray measuring device 100 will be explained below. All calculations are performed in the main computer 128. Furthermore, for example, when k = 1, the k-th rotational position Posk represents the rotational position Pos1. Additionally, at the k-th rotational position Posk, when N = 12 and the number of balls 106 is N, the centroid positions ImPosk_Sphr_(1~N) represent the centroid positions ImPos1_Sphr_1~ImPos1_Sphr_12 of the 12 balls 106, respectively.

[0053] Initially, a calibration fixture 102, comprising multiple spheres 106 spaced at known relative intervals Pu and Pv, is placed on a rotary table 120. Figure 4 Step S2; loading process). Then, set the state where the rotary table 120 has not yet rotated to k=1 ( Figure 4 Step S4).

[0054] Next, X-rays 118 were irradiated onto the calibration fixture 102. Figure 4 Step S6), then, based on the output of the X-ray image detector 124, determine the centroid position (feature point position) of the projection image of each of the N (N=12) spheres 106. Figure 4 Step S8; in addition, steps S6 to S8 are feature position calculation processes.

[0055] Next, based on the centroid positions ImPosk_Sphr_(1~12) of the projected images of the 12 spheres 106 and the relative positions X(1~12) of the spheres 106, the projection transformation matrix Hk that transforms the projection of the spheres 106 onto the detection surface 124A of the X-ray image detector 124 is calculated. Figure 4 Step S10; Transformation matrix calculation process).

[0056] Next, determine whether the number of rotation positions, Posk, k, is greater than or equal to Q (in this embodiment, 3 times or more is sufficient). Figure 4 Step S12). If the number of rotation positions, Posk, k is not greater than or equal to Q (Q≥3) ( Figure 4 Step S12: "No"), then the rotary table 120 is rotated by a specified angle α. Figure 4Step S14). Then, increase the number of rotation positions Posk k by 1 ( Figure 4 Step S16), and repeat steps S6 to S12 (steps S6 to S16; rotation detection process). When the number of rotation positions Posk k becomes Q (Q≥3) or more ( Figure 4 Step S12: "Yes"), proceed to step S18. That is, in the rotation detection process, the rotary table 120 is rotated at least twice by a specified angle α, and the feature position calculation process and the transformation matrix calculation process are repeated. In addition, in this embodiment, the specified angle α is set to, for example, a fixed 30 degrees, but it is not particularly limited. The specified angle α can also be a smaller angle, or the specified angle α can be changed each time.

[0057] Next, the rotation center position Cp and rotation axis Ax of the rotary table 120 are calculated based on the projection transformation matrix Hk (k = 1 to Q) (center position calculation process). The details of this center position calculation process are explained in detail.

[0058] First, such as Figure 5 As shown, it is assumed that the X-ray source 116 and the X-ray image detector 124 rotate in place of the rotary stage 120. Figure 5 Step S30). Incidentally, in Figure 7A The diagram shows the predetermined angle α and the trajectory Fb of the ball 106 when the rotary table 120 rotates. Furthermore, in... Figure 7B The document records the trajectory Fs of the absolute position Xs of the X-ray source 116 when the X-ray source 116 and the X-ray image detector 124 are assumed to have rotated.

[0059] Next, based on the projection transformation matrix Hk (k = 1 to Q), the absolute position Xs of the X-ray source 116 is calculated each time it rotates by a specified angle α, that is, the Q absolute positions Xs of the X-ray source 116. Figure 5 Step S32).

[0060] In addition, the following uses Figure 6 This document explains the situation where, during the calculation of the Q absolute positions Xs of the X-ray source 116 in the aforementioned center position calculation process, the distance f between the X-ray source 116 and the X-ray image detector 124, as well as the position Cc of the foot of the perpendicular line from the X-ray source 116 to the X-ray image detector 124, are unknown.

[0061] First, when calculating the absolute position Xs of the X-ray source 116 at the k-th assumed rotation position, the distance f between the X-ray source 116 and the X-ray image detector 124, and the position Cc(cx, cy) of the foot of the perpendicular line from the X-ray source 116 to the X-ray image detector 124 are set as variables. Figure 6Step S40). Then, evaluate the position on the trajectory Fs of the virtual circle obtained by fitting the absolute position Xs of the X-ray source 116 at the k-th assumed rotation position calculated based on the projection transformation matrix Hk to a circle, and the distance error between the position and the absolute position Xs of the X-ray source 116. Figure 6 Step S42). Then, calculate the distance f and position Cc where the distance error is minimized. Figure 6 Step S44).

[0062] Specifically, for example, the distance f is tentatively set to an appropriate value, and the position Cc is changed. The position Cc that minimizes the distance error is then calculated. Next, this position Cc that minimizes the distance error is tentatively set again, and the distance f is changed again, and the distance f that minimizes the distance error is calculated. Then, this distance f that minimizes the distance error is tentatively set again, and the position Cc is changed again, and the position Cc that minimizes the distance error is calculated. This process is repeated several times, and the distance f and position Cc that minimize the distance error can be calculated, thus achieving optimization of distance f and position Cc.

[0063] Next, return to Figure 4 Based on the changes in the absolute positions Xs (1~N) of the X-ray source 116, the center position Cp of the trajectory Fs obtained by fitting a perfect circle (= virtual perfect circle) is calculated, and this center position Cp is set as the rotation center position Cp of the rotary table 120. To explain in more detail, the Q absolute positions Xs of the X-ray source 116 are fitted into a perfect circle (… Figure 4 (Step S20). At this point, if Q > 3, the center position Cp of the circle is calculated, for example, by the least squares method. If Q = 3, the center position Cp of the circle is calculated, for example, by solving a system of equations.

[0064] Then, for example, calculate the tilt angle of the trajectory Fs obtained by fitting a perfect circle relative to the horizontal plane (xz plane). Then, calculate the rotation center position Cp of the rotary table 120 and the rotation axis Ax. Figure 4 (Step S22). At this point in time, the main computer 128 can also calculate the center position Cp of the perfect circle and its trajectory Fb for each of the N=12 balls 106. Therefore, by averaging the center positions Cp of the perfect circles of the 12 balls 106, the rotation center position Cp can be calculated, and by averaging the inclination of their trajectories Fb relative to the horizontal plane, the tilt angle of the rotation axis Ax can be calculated, thereby also calculating the rotation axis Ax.

[0065] Thus, in this embodiment, the rotation center position Cp of the rotary stage 120 can be calculated through a very simple series of steps. These steps consist solely of placing a calibration fixture 102, equipped with 12 spheres 106 at known relative positional intervals Pu and Pv, on the rotary stage 120 and adjusting the rotary stage 120 to three rotation angles to obtain a projection image of the calibration fixture 102. The shape of the spheres 106 can be determined by the projection image projected onto the X-ray image detector 124. In other words, in this embodiment, it is not necessary to create three-dimensional volume data for calculating the rotation center position Cp.

[0066] Furthermore, in this embodiment, since all the balls 106 are placed on only one plane in the calibration fixture 102, the transformation matrix for projecting the balls 106 at the k-th rotation position Posk onto the detection surface 124A of the X-ray image detector 124 is set as the projection transformation matrix Hk. Therefore, it is possible to calculate the rotation center position Cp of the rotary stage 120 by using only 4 out of the 12 balls 106 as the calculation objects in each process, thereby further shortening the calibration time. In addition, in this embodiment, by using all 12 balls 106, not just 4, as the calculation objects in each process, the rotation center position Cp of the rotary stage 120 can be calculated with extremely high accuracy.

[0067] Furthermore, in this embodiment, the rotation axis Ax of the rotary table 120 is also calculated during the center position calculation process. Therefore, even if it is originally assumed that the rotation axis Ax of the rotary table 120 does not need to be calibrated, the necessity of calibration can be properly evaluated by comparing it with the result obtained from actually calculating the rotation axis Ax of the rotary table 120.

[0068] Furthermore, in this embodiment, during the center position calculation step, it is assumed that the X-ray source 116 and the X-ray image detector 124 rotate in place of the rotary stage 120. The absolute position Xs of the X-ray source 116 at each rotation angle α is calculated based on the projection transformation matrix Hk, thereby calculating the rotation center position Cp of the rotary stage 120. That is, the absolute position Xs of the X-ray source 116 is calculated instead of the absolute position Xa of the sphere 106. Therefore, by directly using the projection transformation matrix Hk, the computational load can be reduced and calibration can be achieved quickly. Moreover, this is not a limitation; the rotation center position Cp of the rotary stage 120 can also be calculated by calculating the absolute position Xa of the sphere 106.

[0069] Furthermore, in this embodiment, when the rotary table 120 is rotated at a predetermined angle α more than 4 times and the Q absolute positions Xs of the X-ray source 116 are calculated, the distance f between the X-ray source 116 and the X-ray image detector 124, and the position Cc(cx, cy) of the foot of the perpendicular line from the X-ray source 116 to the X-ray image detector 124 are set as variables. Moreover, the distance error between the position on the trajectory Fs of the virtual circle obtained by fitting the Q absolute positions Xs of the X-ray source 116 calculated based on the projection transformation matrix Hk (k = 1 to Q) to a perfect circle and the distance of the Q absolute positions Xs of the X-ray source 116 is evaluated. Therefore, the distance f between the X-ray source 116 and the X-ray image detector 124, and the position Cc(cx, cy) of the foot of the perpendicular line from the X-ray source 116 to the X-ray image detector 124 are calculated. Therefore, when calibrating the distance f between the X-ray source 116 and the X-ray image detector 124, and the position Cc(cx, cy) of the foot of the perpendicular line from the X-ray source 116 to the X-ray image detector 124, their values ​​can be calculated, thereby enabling more accurate calibration.

[0070] Furthermore, in this embodiment, during the center position calculation process, the center position Cp of the trajectory Fs obtained by fitting a perfect circle (=virtual perfect circle) is calculated based on the change in the absolute position Xs of the X-ray source 116, and this center position Cp is set as the rotation center position Cp of the rotary table 120. That is, by fitting a perfect circle, the total number of rotation positions Q can be reduced, and the center position Cp can be uniquely calculated. However, this is not a limitation; other methods can also be used to calculate the rotation center position Cp of the rotary table 120.

[0071] Furthermore, in this embodiment, when calculating the rotation axis Ax of the rotary table 120, the tilt angle of the trajectory Fs obtained by fitting a perfect circle relative to the horizontal plane is calculated, and the rotation axis Ax is calculated based on this tilt angle and the rotation center position Cp. Therefore, only one ball 106 is needed to calculate the rotation axis Ax, thus simplifying the process of calculating the rotation axis Ax and enabling the process to be performed in a short time. Moreover, this is not a limitation; for example, the trajectory Fs obtained by fitting a perfect circle can be calculated for each ball 106, and the rotation axis Ax can be calculated based on the offset of its center position.

[0072] Furthermore, in this embodiment, the reference object on the calibration fixture 102 is a sphere 106. Therefore, regardless of the direction from which the sphere 106 is projected, its outline is always circular. That is, the sphere 106, as a reference object, is the shape most easily determined by the projected image projected onto the X-ray image detector 124. Moreover, this is not a limitation; the reference object may, for example, be a polyhedron including a regular polyhedron, a rhombic prism obtained by deformation, or a shape including curved surfaces such as an ellipse or a cone.

[0073] Furthermore, in this embodiment, the position of the feature point of the projected image of the sphere 106, which serves as the reference object, is set as the centroid position of the projected image. Since the projected image of the sphere 106 is a circle, the centroid position is easy to calculate, and the calculation can be performed with less positional error. However, this is not a limitation; the position of the feature point of the projected image of the sphere 106, which serves as the reference object, can also be the center position. In other words, the reference object does not necessarily have to be a sphere. For example, a characteristic recess or protrusion provided in a part of the calibration fixture 102 can be set as the reference object, and this characteristic recess or protrusion can be associated with the feature point of the projected image.

[0074] That is, in this embodiment, the rotation center position Cp of the rotary table 120, on which the object to be measured is placed in a rotatable manner, can be easily calculated through a simple process.

[0075] Furthermore, in the above embodiment, all the spheres 106 are placed on a single plane in the calibration fixture 102, but the present invention is not limited to this. For example, in the calibration fixture 102, it is not necessary to place all the spheres 106 on a single plane, but rather to place all the spheres 106 in three dimensions. In this case, there are at least 6 spheres 106, and a projection matrix Pk is used instead of the projection transformation matrix Hk. The host computer 128 can use the following equation (5) related to the projection matrix Pk instead of equation (3) to calculate the absolute position Xs of the X-ray source 116 based on the 3x4 projection matrix Pk of the kth assumed rotation position.

[0076] Pk=A[rk1 rk2 rk3 Tk] (5)

[0077] In this case, accurate calibration can be performed even if the plane accuracy of the calibration fixture 102 is not high by using the projection matrix Pk.

[0078] Furthermore, in the above embodiments, at least four (or six) balls 106 are used, but the present invention is not limited to this. For example, the calibration fixture 102 may also have a structure in which one ball 106 is moved and configured in at least four (or six) positions.

[0079] Furthermore, in the above embodiments, such as Figure 3A , Figure 3B As shown, spheres 106 are arranged at fixed relative positional intervals Pu and Pv in the u and v axes, respectively, but the present invention is not limited thereto. For example, the relative positional intervals Pu and Pv can be different between the spheres 106, and do not need to be arranged in the u and v axes. This is not only the case of spheres 106 being arranged in two dimensions on a plane, but also the case of spheres 106 being arranged in three dimensions.

[0080] This invention can be widely applied to the calibration of X-ray measuring devices.

[0081] Those skilled in the art will understand that the above embodiments are merely illustrative, illustrating the application of the principles of the invention. Without departing from the spirit and scope of the invention, those skilled in the art can readily design numerous other different configurations.

Claims

1. A calibration method of an X-ray measuring apparatus that uses X-rays to perform a three-dimensional shape measurement of a measured object, the calibration method of the X-ray measuring apparatus characterized by, the X-ray measuring apparatus having: an X-ray source that generates the X-rays; a rotary stage that rotatably mounts the measured object; and an X-ray image detector that detects the X-rays that have passed through the measured object, the calibration method of the X-ray measuring apparatus including the following steps: A placing step of placing a calibration jig on the rotary table, the calibration jig being capable of arranging a reference object at N or more positions at a known relative position interval, the reference object being capable of being determined by a projection image projected to the X-ray image detector, wherein N≥4； a characteristic position calculation step of irradiating the calibration jig with the X-rays and determining positions of characteristic points of projection images of each of the reference objects at N positions from an output of the X-ray image detector; a transformation matrix calculation step of calculating a transformation matrix for projecting and transforming the reference objects to a detection surface of the X-ray image detector from the positions of the characteristic points of the projection images of each of the reference objects at the N positions and the known relative position intervals; a rotation detection step of repeatedly performing the characteristic position calculation step and the transformation matrix calculation step while rotating the rotary stage by a prescribed angle two or more times; and a center position calculation step of calculating a rotation center position of the rotary stage based on the transformation matrix.

2. The calibration method of the X-ray measuring apparatus according to claim 1, characterized in that, in a case where all of the reference objects are mounted on only one plane on the calibration jig, the transformation matrix is set to a projection transformation matrix, and in a case where the reference objects are three-dimensionally mounted on the calibration jig, N = 6 and the transformation matrix is set to a projection matrix.

3. The calibration method of the X-ray measuring apparatus according to claim 1, characterized in that, in the center position calculation step, a rotation axis of the rotary stage is also calculated.

4. The calibration method of the X-ray measuring apparatus according to claim 1, characterized in that, in the center position calculation step, an absolute position of the X-ray source at a time of rotating by the prescribed angle each time is calculated based on the transformation matrix assuming that the X-ray source and the X-ray image detector instead of the rotary stage are rotated, and thereby a rotation center position of the rotary stage is calculated.

5. The calibration method of the X-ray measuring apparatus according to claim 4, characterized in that, in a case where the rotary stage is rotated by the prescribed angle four or more times and the absolute position of the X-ray source is calculated, a distance of the X-ray source from the X-ray image detector and a position of a foot of a perpendicular line from the X-ray source to the X-ray image detector are set as variables, a distance error of a position on a locus of a virtual circle obtained by fitting the absolute position of the X-ray source calculated based on the transformation matrix into a true circle is evaluated, and thereby the distance of the X-ray source from the X-ray image detector and the position of the foot of the perpendicular line from the X-ray source to the X-ray image detector are calculated.

6. The calibration method of the X-ray measuring apparatus according to claim 4, characterized in that, ​ In the center position calculation step, a center position of the locus fitted as a perfect circle is calculated based on a change in the absolute position of the X-ray source, and the center position is set as the rotation center position of the rotary table.

7. The calibration method of an X-ray measurement apparatus according to claim 6, wherein In the center position calculation step, an inclination angle of the locus with respect to a horizontal plane is also calculated, and the rotation axis of the rotary table is calculated based on the inclination angle and the rotation center position.

8. The calibration method of an X-ray measurement apparatus according to claim 1, wherein The reference object is provided as a sphere.

9. The calibration method of an X-ray measurement apparatus according to claim 1, wherein The position of the feature point of the projection image of the reference object is provided as a barycentric position of the projection image.

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