Calibration method for X-ray measurement equipment

Abstract

To dispense with prior highly accurate three-dimensional measurement of a calibration jig of an X-ray measurement apparatus.SOLUTION: A calibration method comprises: a placement step of placing on a rotary table 120 a calibration jig 102 which includes a plurality of reference objects (ball 106) and can be arranged so as to move by M standard (M≥4) or greater; a feature position calculation step of specifying a position (ball gravity center coordinates Im'(i,j)) of a feature point of a projection image of each reference object at the M standard from the output of an X-ray image detector 124 by irradiating the calibration jig 102 with X-ray 118; a transformation matrix calculation step of calculating a transformation matrix H(i) including a camera parameter A from the position of the feature point of the projection image of each reference object at the M standard and a relative position interval O(i); a parameter optimization step of optimizing the camera parameter A so as to reduce a difference E between the position of the feature point of the projection image and the relative position interval; and a center position calculation step of calculating a rotation center position Cp of the rotary table 120 by using the relative position of the feature point calculated by using the optimized camera parameter A.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a method for calibrating an X-ray measurement device, and more particularly to a method for calibrating an X-ray measurement device that does not require prior high-precision three-dimensional measurement of a calibration jig for the X-ray measurement device. [Background technology]

[0002] Traditionally, X-ray measurement systems (measuring X-ray CT systems) have been used to measure the three-dimensional shape of objects using X-rays, and have been used primarily for observation and inspection of defects that are difficult to detect from the outside, such as voids in cast parts, poor welding in welded parts, and defects in the circuit patterns of electronic circuit components. However, in recent years, aided by the spread of 3D printers, there has been an increasing demand for 3D dimensional measurement of the interior of processed products and for high-precision measurement. To meet this demand, there is a demand for X-ray measurement systems with even higher dimensional measurement precision.

[0003] Reconstruction of this X-ray measurement device requires information such as the position of the rotary table and the distance between the radiation source and the X-ray detector. Therefore, in order to perform dimensional measurements with an X-ray measurement device with higher accuracy, it is important to perform various calibrations specific to the device before starting measurement, as described in Patent Document 1.

[0004] The calibration process for this purpose assumes that the three-dimensional positions of the calibration jig elements are known. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2000-298105 Summary of the Invention [Problem to be solved by the invention]

[0006] However, this method is not able to deal with deformation of the calibration jig due to aging, and is also restricted by the need for a layout that makes it easy to measure geometric elements.

[0007] The present invention has been made to solve the above-mentioned conventional problems, and an object of the present invention is to provide a method for calibrating an X-ray measurement device that does not require prior high-precision three-dimensional measurement of a calibration jig for the X-ray measurement device. [Means for solving the problem]

[0008] The invention according to claim 1 of the present application is a method for calibrating an X-ray measurement apparatus that measures the three-dimensional shape of an object to be measured using X-rays, the X-ray measurement apparatus comprising: an X-ray source that generates the X-rays; a rotary table on which the object to be measured is rotatably placed; and an X-ray image detector that detects the X-rays that have passed through the object to be measured; and a plurality of reference objects having shapes that can be identified by images projected onto the X-ray image detector; M( M≧4) or more At the position a placing step of placing a movable and positionable calibration jig on the rotary table; and irradiating the calibration jig with X-rays and determining M from the output of the X-ray image detector. Position of the individual a feature position calculation step of identifying the positions of feature points of the projection images of each of the reference objects in M Position of the individual a transformation matrix calculation step of calculating a transformation matrix including camera parameters for performing a projective transformation of the reference object onto the detection surface of the X-ray image detector from the positions and relative position intervals of feature points of the projection images of the respective reference objects; a parameter optimization step of optimizing the camera parameters so that the difference between the positions of feature points of the projection images and the relative position intervals becomes small; and a parameter optimization step of optimizing the camera parameters using the relative positions of feature points calculated using the optimized camera parameters. , the rotary table is rotated by a predetermined angle α and at a rotation position of Q (Q≧3) or more, The above-mentioned problem is solved by including a center position calculation step of calculating the position of the rotation center.

[0009] The invention according to claim 2 of the present application is characterized in that the parameter optimization step comprises a first step of setting appropriate initial values ​​to the camera parameters and obtaining the relative position O(i) of each reference object, and a second step of calculating the relative position O(i) of each reference object from the correspondence between the position coordinate X(j) of each reference object and the feature point coordinate Im(i,j) using the following equation: Im'(i,j)≒ P × {X(j)+O(i)} ···(1) and a third step of calculating feature point coordinates Im'(i, j) using the calculated projection matrix P and optimizing the camera parameters so that the difference between the calculated feature point coordinates Im'(i, j) and the actual feature point coordinates Im(i, j) becomes small.

[0010] The invention according to claim 3 of the present application is characterized in that in a fourth step subsequent to the third step, the projection matrix P of the second step is calculated again using the camera parameters optimized in the third step, and the process of again performing the optimization of the third step is repeated until the difference between the feature point coordinates becomes small.

[0011] According to the invention of claim 4 of the present application, after the camera parameters have converged in the third step, the projection matrix P in the second step is calculated again to repeat the optimization.

[0012] The invention according to claim 5 of the present application is such that in the third step, the projection matrix P in the second step is decomposed into camera parameters, a rotation matrix, and a translation matrix, and the projection matrix P is also optimized in the optimization process.

[0013] The invention according to claim 6 of the present application is such that when all of the reference objects are placed on only one plane in the calibration jig, the transformation matrix is ​​a projection transformation matrix, and when the reference objects are placed three-dimensionally, N=6 and the transformation matrix is ​​a projection matrix.

[0014] According to a seventh aspect of the present invention, the center position calculation step further calculates the rotation axis of the rotary table.

[0015] According to an eighth aspect of the present invention, the reference object is a sphere.

[0016] According to a ninth aspect of the present invention, the position of the feature point of the projected image of the reference object is set to the position of the center of gravity of the projected image. [Effects of the Invention]

[0017] According to the present invention, there is no need to perform high-precision three-dimensional measurement in advance of the calibration jig of the X-ray measurement device. [Brief explanation of the drawings]

[0018] [Figure 1] FIG. 1 is a schematic side view showing a basic configuration of an X-ray measurement apparatus according to an embodiment of the present invention. [Figure 2] A schematic top view showing only the main parts of the X-ray measurement device in Figure 1. [Figure 3] A diagram showing the calibration jig in Figure 1 (front view (A), top view (B)) [Figure 4] FIG. 1 is a flowchart showing a calibration procedure of an X-ray measurement apparatus according to an embodiment of the present invention. [Figure 5] A detailed flow diagram of an example of the camera parameter optimization process in FIG. [Figure 6] A detailed flow diagram of another example of the camera parameter optimization process in FIG. [Figure 7] FIG. 5 is a flow chart showing an example of a procedure for calibrating an X-ray measurement device using the calibrated calibration jig in FIG. [Figure 8] Detailed flow diagram of the process for calculating the absolute position of the ball in Figure 7 [Figure 9] 9 is a flowchart for calculating 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 after calculating the absolute position of the X-ray source in FIG. [Figure 10] A diagram showing an example of the relationship between the absolute position of the sphere and the absolute position of the X-ray source. DETAILED DESCRIPTION OF THE INVENTION

[0019] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Note that the present invention is not limited to the contents described in the following embodiments and examples. Furthermore, the constituent elements in the embodiments and examples described below include those that can be easily imagined by a person skilled in the art, those that are substantially the same, and those that are within the so-called equivalent range. Furthermore, the constituent elements disclosed in the embodiments and examples described below may be appropriately combined or appropriately selected for use.

[0020] An embodiment of the present invention is shown in Fig. 1. In Fig. 1, the left-right direction relative to the paper surface is the z-axis direction, the up-down direction relative to the paper surface is the y-axis direction, and the direction perpendicular to the paper surface is the x-axis direction.

[0021] The X-ray measurement apparatus 100 is an apparatus that measures the three-dimensional shape of an object to be measured using X-rays, and as shown in FIG. 1, includes a main body 108, a host computer 128, and a motion controller 130.

[0022] 1 and 2, a calibration jig 102 is placed on a rotary table 120 instead of an object to be measured. As shown in FIGS. 3A and 3B, the calibration jig 102 is made of a material (e.g., aluminum) that is transmissive to X-rays 118, and has a plurality of spheres (reference objects) 106 with a diameter D (e.g., 4 spheres × 3 spheres, or N = 12 spheres) on a plate-like member 104 at known relative position intervals Pu and Pv (i.e., the spheres 106 are arranged at 12 locations at known relative position intervals Pu and Pv). In other words, all of the spheres 106 in the calibration jig 102 are placed on only one plane. At the same time, it can be said that the relative positions X(1 to 12) of the 12 spheres 106, or in other words, the relative positions X(1 to 12) of the 12 spheres 106 at the 12 locations, are known (X(1 to 12) and X1 to X12 mean the same thing, and the same notation will be used hereinafter). The sphere 106 has a simple shape that can be easily identified by the image projected onto the X-ray image detector 124. In Fig. 3(A), the left-right direction relative to the paper surface is the u-axis direction, the up-down direction relative to the paper surface is the v-axis direction, and the direction perpendicular to the paper surface is the w-axis direction.

[0023] As shown in FIG. 1 , the main body 108 includes, on a base 112, an X-ray shielding cover 110 that prevents leakage of X-rays 118, an X-ray source 116 that generates X-rays 118, a rotary table 120 on which a measurement object (not shown) is rotatably placed, and an X-ray image detector 124 that detects the X-rays 118 that have passed through the measurement object. The X-ray source 116 is mounted on a radiation source support 114 on the base 112. The radiation source support 114 may include a linear motion mechanism that can move the X-ray source 116 in three axial directions (x, y, z). The rotary table 120 is mounted on a table support 122 on the base 112. The table support 122 includes a linear motion mechanism that can move the measurement object in three axial directions (x, y, z). Furthermore, the table support 122 may be provided with a tilt mechanism that can adjust the tilt of a rotation axis Ax of the rotary table 120. The X-ray image detector 124 has a two-dimensional detection surface 124A that is sensitive to X-rays 118. The X-ray image detector 124 is supported by a detector support table 126 on the base 112. The detector support table 126 may also be equipped with a linear motion mechanism that enables the X-ray image detector 124 to move in three axes directions of x, y, and z. The radiation beam of X-rays 118 from the X-ray source 116 spreads in a cone shape in the z-axis direction, and is adjusted so that its center line intersects with the rotation axis Ax of the rotary table 120 and is perpendicular to the detection surface 124A of the X-ray image detector 124.

[0024] 1 controls the radiation source support base 114, the X-ray source 116, the rotary table 120, the table support base 122, the X-ray image detector 124, and the detector support base 126 of the main body 108. The host computer 128 can also automatically or semi-automatically perform the measurement operation and calibration of the X-ray measurement apparatus 100 by reading and executing a program stored in a storage unit (not shown). That is, in the measurement operation of the X-ray measurement apparatus 100, the host computer 128 reconstructs, for example, data of a projection image obtained by the X-ray image detector 124, and creates three-dimensional volume data of the object to be measured.

[0025] The motion controller 130 shown in FIG. 1 is connected to a host computer 128, and controls the rotation and movement of the X-ray source 116 of the main body 108 and the rotary table 120, as well as various mechanisms.

[0026] During measurement, the object to be measured is rotated on the rotary table 120 while X-rays 118 are generated, and projection images are collected from a plurality of angular directions (for example, at an angular division number of about 1000 to 6000). The collected projection images are reconstructed using a slice plane that horizontally crosses the object to be measured as a reference plane, to create three-dimensional volume data (three-dimensional image) of the object to be measured.

[0027] The calibration method according to the present invention will now be described.

[0028] In the calibration of the X-ray measurement device 100, the host computer 128 uses a calibration jig 102 on which a plurality of spheres 106 (3×4=12 in the figure) are arranged, as shown in FIG. , as shown in Figs. Three-dimensional coordinate measuring machine XY On a plane 4 or more above At the position (also called the level) The X-ray measurement device 100 is calibrated by moving and acquiring projection images.

[0029] The specific implementation procedure is shown in Figure 4.

[0030] First, in step S2, the calibration jig 102 is attached to the three-dimensional coordinate measuring machine. XY On a plane 4 or more above At the position (level) The center of gravity (an example of a feature point) of each sphere in the projected image is found by moving the sphere. Here, the number of each sphere 106, the position coordinates of the calibration jig 102, and the coordinates of the center of gravity of the sphere are as follows: Ball number i … 1~N Calibration jig position number j … 1 to M (M≧4) Calibration jig position coordinates X(j) Sphere centroid coordinates Im(i,j)

[0031] Next, in step S4, a projective transformation matrix (also called a homography matrix) H(i) for each sphere i is calculated. Specifically, for a certain sphere i, a homography matrix H(i) of, for example, 3 columns x 3 rows that satisfies the following formula (2) can be calculated from the correspondence between the calibration jig position coordinate X(j) and the sphere center of gravity coordinate Im(i,j). H(i)× X(j)≒ Im(i,j) ···(2)

[0032] Here, the homography matrix H(i) can be expressed as in the following equation (4) using the camera parameters (also called internal parameters) A expressed by the following equation (3), vectors r1(i) and r2(i) representing rotation, and vector t(i) representing translation.

number

[0033] In equation (3), f is the distance between the X-ray source 116 and the X-ray image detector 124, and cx and cy are the positions of the feet of the perpendicular line from the X-ray source 116 to the X-ray image detector 124. Note that the distance f in the first row and first column of the internal parameter matrix A and the distance f in the second row and second column will have slightly different values ​​when the aspect ratio of the pixels of the X-ray image detector 124 is different. Also, although the skew S related to image distortion may be used in the first row and second column of the internal parameter matrix A, in this embodiment, the skew S is set to 0.

[0034] Next, proceeding to step S6, the camera parameter A is used as an optimization parameter, and optimization is performed so that the difference E between the calculated image center Im'(i,j) of each sphere i and the actual image center Im(i,j) becomes small.

[0035] A specific example of the optimization process in step S6 is shown in FIG.

[0036] First, in step S60, an appropriate initial value is set for the camera parameter A, and the relative position O(i) is determined.

[0037] The relative position O(i) of each sphere i to be determined can be expressed as the following equations (5) and (6) using the vectors r1(i) and r2(i) representing rotation, r3(i) which can be derived from them, and the vector t(i) representing translation. R(i)=[r1(i) r2(i) r3(i)] ···(5) O(i)= -R(i)^-1 × t(i) ···(6)

[0038] Next, in step S62, a projection matrix P that satisfies the following equation (7), which is the same as the above equation (1), is found from the correspondence between the sphere position coordinates (=X(j)+O(i)) and the sphere center of gravity coordinates Im(i,j). Im'(i,j)≒ P × {X(j)+O(i)} ···(7)

[0039] Next, proceed to step S64, calculate the center of gravity coordinate Im'(i,j) using the projection matrix P obtained in step S62, and optimize the camera parameter A so that the difference E from the actual center of gravity coordinate Im(i,j) becomes small. E=|Im(i,j)- P × {X(j)+O(i)}| → min ···(8)

[0040] Next, the process proceeds to step S66, where the projection matrix P of step S62 is recalculated using the optimized relative position O(i), and the optimization of step S64 is performed again.

[0041] Then, the process proceeds to step S68, and the processes of steps S64 and S66 are repeated until the residual error E of step S64 becomes smaller than a predetermined value.

[0042] In addition, during the optimization process, as in another example shown in Figure 6, in step S66', the projection matrix P calculated in step S62 may be decomposed into A × [R t], and the projection matrix P may also be optimized during the optimization process.

[0043] After the optimization process in FIG. 5 is completed, the process returns to step S8 in FIG.

[0044] Specifically, the relative position of the sphere 106 determined in the present invention is used to determine the rotation axis and center of rotation of the table, for example, by the method described below.

[0045] A specific example of the calibration procedure of the X-ray measurement apparatus 100 in step S8 of Fig. 4 will be described with reference to Figs. 7 to 10. Here, all calculations are performed by the host computer 128. Note that, for example, when k = 1, the k-th rotational position Posk indicates the rotational position Pos1. Furthermore, when N = 12 and the number of spheres 106 is N at the k-th rotational position Posk, the center of gravity positions ImPosk_Sphr_(1 to N) indicate the center of gravity positions ImPos1_Sphr_1 to ImPos1_Sphr_12 of the 12 spheres 106, respectively.

[0046] First, the calibration jig 102 having a plurality of spheres 106 at known relative position intervals Pu and Pv is placed on the rotary table 120 (step S102 in FIG. 7; placing step). Then, the state in which the rotary table 120 is not yet rotated is set to k=1 (step S104 in FIG. 7).

[0047] Next, X-rays 118 are irradiated onto the calibration jig 102 (step S106 in FIG. 7), and the center of gravity positions (positions of feature points) ImPosk_Sphr_(1 to 12) of the projection images of each of the N (N=12) spheres 106 are identified from the output of the X-ray image detector 124 (step S108 in FIG. 7; steps S106 to S108 are the feature position calculation process).

[0048] Next, a projection transformation matrix Hk is calculated from the center of gravity positions ImPosk_Sphr_(1 to 12) of the projection images of the 12 spheres 106 and the relative positions X(1 to 12) of the spheres 106 to perform projection transformation of the spheres 106 onto the detection surface 124A of the X-ray image detector 124 (step S110 in FIG. 7; transformation matrix calculation process).

[0049] Next, it is determined whether the number k of rotation positions Posk is Q or more (three or more in this embodiment) (step S112 in FIG. 7). If the number k of rotation positions Posk is not Q (Q≧3) or more (No in step S112 in FIG. 7), the turntable 120 is rotated by a predetermined angle α (step S114 in FIG. 7). Then, the number k of rotation positions Posk is incremented by one (step S116 in FIG. 7), and steps S106 to S112 are repeated (steps S106 to S116; rotation detection step). If the number k of rotation positions Posk is Q (Q≧3) or more (Yes in step S112 in FIG. 7), the process proceeds to step S118. That is, in the rotation detection step, the turntable 120 is rotated by the predetermined angle α two or more times, and the feature position calculation step and the transformation matrix calculation step are repeated. In this embodiment, the predetermined angle α is set to a constant value of, for example, 30 degrees, but is not particularly limited to this value, and may be a smaller angle, or the predetermined angle α may be changed each time.

[0050] Next, the rotation center position Cp and rotation axis Ax of the turntable 120 are calculated based on the projective transformation matrix Hk (k=1 to Q) (center position calculation step). The center position calculation step will be described in detail.

[0051] First, as shown in Fig. 8, it is assumed that the X-ray source 116 and the X-ray image detector 124 rotate instead of the turntable 120 (step S130 in Fig. 8). Incidentally, Fig. 10(A) shows the predetermined angle α and the trajectory Fb of the sphere 106 when the turntable 120 rotates. Fig. 10(B) shows the trajectory Fs of the absolute position Xs of the X-ray source 116 when it is assumed that the X-ray source 116 and the X-ray image detector 124 rotate.

[0052] Next, the absolute position Xs of the X-ray source 116 at each rotation of a predetermined angle α, that is, at Q positions, is calculated based on the projective transformation matrix Hk (k=1 to Q) (step S132 in FIG. 8).

[0053] In the above-described central position calculation process, when the absolute position Xs of the X-ray source 116 at point Q is calculated, a case where the distance f between the X-ray source 116 and the X-ray image detector 124 and 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 will be described below with reference to FIG. 9.

[0054] First, when calculating the absolute position Xs of the X-ray source 116 at the kth 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 from the X-ray source 116 to the X-ray image detector 124 are used as variables (step S140 in FIG. 9). Then, the absolute position Xs of the X-ray source 116 at the kth assumed rotation position, calculated based on the projection transformation matrix Hk, is fitted to a perfect circle, and the distance error between the position on the locus Fs of the provisional perfect circle and the absolute position Xs of the X-ray source 116 is evaluated (step S142 in FIG. 9). Then, the distance f and position Cc that minimize this distance error are calculated (step S144 in FIG. 9).

[0055] Specifically, for example, distance f is temporarily set to an appropriate value, position Cc is changed, and the position Cc that results in the smallest distance error is calculated. Next, the position Cc that results in the smallest distance error is temporarily set, and distance f is then changed, and the distance f that results in the smallest distance error is calculated. Furthermore, distance f that results in the smallest distance error is temporarily set, and position Cc is changed, and the position Cc that results in the smallest distance error is calculated. Furthermore, the position Cc that results in the smallest distance error is temporarily set, and distance f is again changed, and the distance f that results in the smallest distance error is calculated. By repeating this process several times, it is possible to calculate the distance f and position Cc that result in the smallest distance error, and it is possible to optimize distance f and position Cc.

[0056] 7, the center position Cp of the trajectory Fs fitted to a perfect circle (= provisional perfect circle) is calculated from the change in the absolute position Xa (1 to N) of the X-ray source 116, and this center position Cp is set as the rotation center position Cp of the turntable 120. More specifically, the absolute position Xs of the X-ray source 116 at Q locations is fitted to a perfect circle (step S120 in FIG. 7). At this time, if Q>3 or more, the center position Cp of the perfect circle is calculated by, for example, the least squares method. If Q=3, the center position Cp of the perfect circle is calculated by, for example, simultaneous equations.

[0057] Then, for example, the tilt angle of the trajectory Fs fitted to the perfect circle from the horizontal plane (xz plane) is calculated. Then, the rotation center position Cp and rotation axis Ax of the turntable 120 are calculated (step S122 in FIG. 7). At this point, the host computer 128 can also calculate the center position Cp of the perfect circle and its trajectory Fb for each of the N=12 spheres 106. Therefore, by averaging the center positions Cp of the perfect circles of the 12 spheres 106 to calculate the rotation center position Cp and averaging the tilts of these trajectories Fb from the horizontal plane, the tilt angle of the rotation axis Ax can be calculated, and the rotation axis Ax can also be calculated.

[0058] As described above, in this embodiment, the rotation center position Cp of the turntable 120 can be calculated through a series of extremely simple steps of placing the calibration jig 102, which includes 12 spheres 106 with known relative position intervals Pu and Pv, each sphere having a shape that can be identified by a projected image onto the X-ray image detector 124, on the turntable 120, adjusting the turntable 120 to three rotation angles, and taking projected images of the calibration jig 102. In other words, in this embodiment, there is no need to create three-dimensional volume data to calculate the rotation center position Cp.

[0059] Furthermore, in this embodiment, since all of the spheres 106 in the calibration jig 102 are placed on only one plane, the transformation matrix for performing projective transformation of the spheres 106 at the kth rotation position Posk onto the detection surface 124A of the X-ray image detector 124 is the projective transformation matrix Hk. Therefore, it is possible to calculate the rotation center position Cp of the turntable 120 by using only four of the twelve spheres 106 as the calculation targets in each process, further reducing the calibration time. Note that in this embodiment, by using all twelve spheres 106 as the calculation targets in each process, rather than just four spheres 106, the rotation center position Cp of the turntable 120 can be calculated extremely accurately.

[0060] Furthermore, in this embodiment, the center position calculation step further calculates the rotation axis Ax of the turntable 120. Therefore, even if it is initially assumed that calibration is not required for the rotation axis Ax of the turntable 120, the necessity of calibration can be properly evaluated by comparing with the result of actually calculating the rotation axis Ax of the turntable 120.

[0061] Furthermore, in this embodiment, in the center position calculation step, it is assumed that the X-ray source 116 and the X-ray image detector 124 rotate instead of the turntable 120, and the absolute position Xs of the X-ray source 116 for each rotation of the predetermined angle α is calculated from the projection transformation matrix Hk, thereby calculating the rotation center position Cp of the turntable 120. That is, instead of calculating the absolute position Xa of the sphere 106, the absolute position Xs of the X-ray source 116 is calculated. Therefore, by directly using the projection transformation matrix Hk, the amount of calculation can be reduced and calibration can be performed quickly. However, this is not limiting, and the rotation center position Cp of the turntable 120 may be calculated by calculating the absolute position Xa of the sphere 106.

[0062] Furthermore, in this embodiment, the turntable 120 is rotated four or more times at a predetermined angle α, and when calculating the absolute position Xs of the X-ray source 116 at location Q, 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 used as variables. Then, the absolute position Xs of the X-ray source 116 at location Q, which is calculated based on the projection transformation matrix Hk (k=1 to Q), is fitted to a perfect circle, and a distance error between the position on the locus Fs of a virtual perfect circle and the absolute position Xs of the X-ray source 116 at location Q is evaluated. In this way, 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 attempting to calibrate 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, these values ​​can be calculated, allowing for more accurate calibration.

[0063] Furthermore, in this embodiment, in the center position calculation step, the center position Cp of the trajectory Fs fitted with a perfect circle (= provisional perfect circle) is calculated from 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 turntable 120. In other words, by fitting with a perfect circle, the total number Q of rotation positions can be reduced, and the center position Cp can be calculated uniquely. However, without being limited to this, the rotation center position Cp of the turntable 120 may be calculated by other methods.

[0064] Furthermore, in this embodiment, when calculating the rotation axis Ax of the turntable 120, the tilt angle of the trajectory Fs fitted to a perfect circle from the horizontal plane is calculated, and the rotation axis Ax is calculated from the tilt angle and the rotation center position Cp. Therefore, only one sphere 106 is required to calculate the rotation axis Ax, so the process of calculating the rotation axis Ax can be simplified and completed in a short time. However, this is not limiting, and for example, the trajectory Fs fitted to a perfect circle may be calculated for each sphere 106, and the rotation axis Ax may be calculated from the deviation of the center position.

[0065] Furthermore, in this embodiment, the reference object on the calibration jig 102 is a sphere 106. Therefore, the outline of the sphere 106 is a circle when projected from any direction. That is, the sphere 106 is the shape that can be most easily identified as the reference object by the image projected onto the X-ray image detector 124. However, the reference object is not limited to this, and may be, for example, a polyhedron including a regular polyhedron or a deformed rhombic body, or may have a shape including a curved surface such as an ellipsoid or a cone.

[0066] Furthermore, in this embodiment, the position of a feature point of the projected image of the sphere 106, which is the reference object, is set to the position of the center of gravity of the projected image. Because the projected image of the sphere 106 is circular, it is easy to calculate the position of the center of gravity, and it can be calculated with little position error. However, this is not limiting, and the position of the feature point of the projected image of the sphere 106, which is the reference object, may be the center position. Alternatively, if the reference object is not a sphere but has locally characteristic concave or convex portions, the characteristic concave or convex portion may be associated with the feature point of the projected image.

[0067] That is, in this embodiment, the rotation center position Cp of the turntable 120 on which the object to be measured is rotatably placed can be easily calculated through a simple process.

[0068] In the above embodiment, all of the spheres 106 are placed on only one plane in the calibration jig 102, but the present invention is not limited to this. For example, all of the spheres 106 may not be placed on one plane in the calibration jig 102, but may be placed three-dimensionally. In this case, there are at least six spheres 106, and a projection matrix Pk shown in the following equation (10) is used instead of the projection transformation matrix Hk shown in the following equation (9). Hk=A[rk1 rk2 Tk] (9) Pk=A[rk1 rk2 rk3 Tk] ···(10)

[0069] The host computer 128 can calculate the absolute position Xs of the X-ray source 116 from the 3-row x 4-column projection matrix Pk of the kth assumed rotational position by using the following equation (10) related to the projection matrix Pk instead of equation (9).

[0070] In this case, by using the projection matrix Pk, accurate calibration can be performed even if the plane accuracy of the calibration jig 102 is not good.

[0071] In the above embodiment, the number of spheres 106 is at least four (or six), but the present invention is not limited to this. For example, the calibration jig 102 may be configured so that two spheres 106 are movable and positioned at at least four (or six) locations.

[0072] Furthermore, the reference object is not limited to a sphere, and the positions of the feature points are not limited to the positions of the centers of gravity. [Industrial Applicability]

[0073] The present invention can be widely applied to the calibration of X-ray measurement devices. [Explanation of symbols]

[0074] 100...X-ray measurement device 102...Calibration jig 104...Plate-shaped member 106…ball 108...Main body 110...X-ray shielding cover 112...base 114…Radiation source support stand 116...X-ray source 118...X-ray 120...Rotary table 122...Table support 124...X-ray image detector 124A…Detection surface 126...Detector support stand 128...host computer 130...Motion controller i...ball number j...Calibration jig position number X(j)…Calibration jig position coordinates Im(i,j), Im'(i,j)...Sphere centroid coordinates H(i), Hk...projection transformation matrix (homography matrix) A...Camera (internal) parameters O(i)...Relative position of each ball r1(i), r2(i), r3(i)...Vector representing rotation t(i)...vector representing translation P, Pk...Projection matrix

Claims

1. 1. A method for calibrating an X-ray measurement apparatus that measures a three-dimensional shape of an object to be measured using X-rays, comprising: the X-ray measurement device includes an X-ray source that generates the X-rays, a rotary table on which the object to be measured is rotatably placed, and an X-ray image detector that detects the X-rays that have passed through the object to be measured, a placing step of placing a calibration jig on the rotary table, the calibration jig having a plurality of reference objects each having a shape that can be identified by a projected image onto the X-ray image detector, the calibration jig being movable and positionable at M or more positions (M≧4); a feature position calculation step of irradiating the calibration jig with the X-rays and identifying the positions of feature points of the projection images of each of the reference objects at M positions from the output of the X-ray image detector; a transformation matrix calculation step of calculating a transformation matrix including camera parameters for performing projective transformation of the reference object onto the detection surface of the X-ray image detector from the positions and relative position intervals of feature points of each of the projection images of the reference object at M positions; a parameter optimization step of optimizing the camera parameters so as to reduce a difference between the positions of the feature points of the projected images and the relative position intervals; a center position calculation step of calculating a rotation center position at a rotation position equal to or greater than Q (Q≧3) by rotating the rotary table by a predetermined angle α using the relative positions of the feature points calculated using the optimized camera parameters; 1. A method for calibrating an X-ray measurement device, comprising:

2. In claim 1, The parameter optimization step A first step of setting appropriate initial values ​​for the camera parameters and determining the relative position O(i) of each reference object; From the correspondence between the position coordinates X(j) of each reference object and the feature point coordinates Im(i, j), the following equation is obtained: Im'(i,j)≒P × [X(j)+O(i)] A second step of obtaining a projection matrix P that satisfies a third step of calculating feature point coordinates Im'(i, j) using the obtained projection matrix P, and optimizing the camera parameters so that the difference between the calculated feature point coordinates Im'(i, j) and the actual feature point coordinates Im(i, j) becomes small; 1. A method for calibrating an X-ray measurement device, comprising:

3. In claim 2, In a fourth step following the third step, a method for calibrating an X-ray measurement device, comprising: calculating the projection matrix P in the second step again using the camera parameters optimized in the third step; and repeating the process of optimizing the third step again until the difference in the feature point coordinates becomes small.

4. In claim 2, a projection matrix P calculated in the second step after the camera parameters have converged in the third step, and optimization is repeated.

5. In claim 2, a third step of decomposing the projection matrix P from the second step into camera parameters, a rotation matrix, and a translation matrix, and optimizing the projection matrix P during the optimization process.

6. In any one of claims 1 to 5, When all of the reference objects are placed on only one plane in the calibration jig, the transformation matrix is ​​a projection transformation matrix, and when the reference objects are placed three-dimensionally, wherein N=6 and the transformation matrix is ​​a projection matrix.

7. In any one of claims 1 to 6, The method for calibrating an X-ray measurement apparatus, wherein the center position calculation step further comprises calculating a rotation axis of the rotary table.

8. In any one of claims 1 to 7, 2. A method for calibrating an X-ray measurement apparatus, wherein the reference object is a sphere.

9. In any one of claims 1 to 8, A method for calibrating an X-ray measurement apparatus, wherein the position of the feature point of the projection image of the reference object is set to the position of the center of gravity of the projection image.

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