JP7757181B2 - Method for calibrating an X-ray measurement device - Google Patents

Description

The present invention relates to a method for calibrating an X-ray measurement device, and in particular to a method for calibrating an X-ray measurement device that does not require prior high-precision three-dimensional measurement of the calibration jig of the X-ray measurement device.

Traditionally, X-ray measurement systems (measuring X-ray CT systems) are capable of measuring the three-dimensional shape of an object 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 accuracy.

Reconstructing 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 device-specific calibrations before starting measurements, as described in Patent Document 1.

The calibration process for this purpose assumes that the three-dimensional positions of the calibration jig elements are known.

Japanese Patent Application Laid-Open No. 2000-298105

However, this method was unable to accommodate deformation of the calibration jig due to aging, and was also constrained by the need for a layout that made it easy to measure geometric elements.

The present invention was made to solve the above-mentioned problems of the conventional art, and aims to provide a method for calibrating an X-ray measurement device that does not require prior high-precision three-dimensional measurement of the calibration jig of the X-ray measurement device.

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, the calibration jig being movable and positionable at positions M or more (M≧4); a feature position calculation step of irradiating the calibration jig with X-rays and specifying positions of feature points of each of the projection images of the reference object 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 the 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 differences between the positions of the feature points of the projection images and the relative position intervals ; and a center position calculation step of rotating the turntable by a predetermined angle α using the relative positions of the feature points calculated using the optimized camera parameters to calculate a rotation center position at Q (Q≧3) or more rotation positions .

The invention according to claim 2 of the present application is characterized in that the parameter optimization step includes a first step of setting appropriate initial values to the camera parameters and determining the relative position O(i) of each reference object, and 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.

The invention according to claim 3 of the present application comprises a fourth step following the third step, in which the projection matrix P of the second step is recalculated using the camera parameters optimized in the third step, and the optimization process of the third step is repeated again until the difference in the feature point coordinates becomes small.

The invention of claim 4 of the present application is such that, after the camera parameters have converged in the third step, the projection matrix P of the second step is recalculated and optimization is repeated.

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

The invention of 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.

The invention according to claim 7 of the present application further comprises calculating the rotation axis of the rotary table in the center position calculation step.

The invention according to claim 8 of this application is such that the reference object is a sphere.

The invention according to claim 9 of the present application is such that the position of the feature point of the projected image of the reference object is set to the center of gravity of the projected image.

This invention eliminates the need for prior high-precision three-dimensional measurement of the calibration jig for the X-ray measurement device.

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. FIG. 2 is a schematic top view showing only the main parts of the X-ray measurement device of FIG. 2A and 2B are diagrams showing the calibration jig of FIG. 1 (front view (A) and top view (B)); FIG. 1 is a flowchart showing a calibration procedure of an X-ray measurement apparatus according to an embodiment of the present invention. A detailed flow diagram of an example of the camera parameter optimization process in FIG. A detailed flow diagram of another example of the camera parameter optimization process in FIG. FIG. 5 is a flow chart showing an example of a procedure for calibrating the X-ray measurement device using the calibrated calibration jig in FIG. A detailed flowchart of the process of calculating the absolute position of the sphere in FIG. 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. FIG. 1 is a diagram showing an example of the relationship between the absolute position of the sphere and the absolute position of the X-ray source.

Embodiments of the present invention will be described in detail below with reference to the drawings. It should be noted that the present invention is not limited to the contents of the following embodiments and examples. Furthermore, the constituent elements of the embodiments and examples described below include those that would 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 combined as appropriate, or may be selected and used as appropriate.

Figure 1 shows an embodiment of the present invention. In Figure 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.

The X-ray measurement device 100 is a device that uses X-rays to measure the three-dimensional shape of an object, and as shown in Figure 1, it comprises a main body 108, a host computer 128, and a motion controller 130.

1 and 2, a calibration jig 102 is placed on a rotary table 120 in place of the 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 of diameter D (e.g., 4 x 3, or N = 12) on a plate-like member 104 at known relative position intervals Pu and Pv (i.e., the spheres 106 are arranged at 12 locations with 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, 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, can also be said to be 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.

As shown in FIG. 1, the main body 108 comprises, 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 measured object (not shown) is rotatably placed, and an X-ray image detector 124 that detects the X-rays 118 that have passed through the measured object. The X-ray source 116 is mounted on a radiation source support 114 on the base 112. The radiation source support 114 may be equipped with a linear motion mechanism that enables the X-ray source 116 to move in three axes (x, y, and z). The rotary table 120 is mounted on a table support 122 on the base 112. The table support 122 is equipped with a linear motion mechanism that enables the measured object to move in three axes (x, y, and z). Furthermore, the table support 122 may be equipped with a tilt mechanism that enables the tilt adjustment of the 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 (x, y, and z). The radiation beam of X-rays 118 from the X-ray source 116 expands in a cone shape in the z-axis direction, and is adjusted so that its center line intersects the rotation axis Ax of the rotary table 120 and is perpendicular to the detection surface 124A of the X-ray image detector 124.

The host computer 128 shown in FIG. 1 controls the radiation source support base 114, X-ray source 116, rotary table 120, table support base 122, X-ray image detector 124, and detector support base 126 of the main body 108. The host computer 128 can also automatically or semi-automatically perform the measurement operations and calibration of the X-ray measurement 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 measurement device 100, the host computer 128 reconstructs, for example, data of a projection image obtained by the X-ray image detector 124 to create three-dimensional volume data of the object to be measured.

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

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 multiple angular directions (for example, approximately 1,000 to 6,000 angular divisions). The collected projection images are reconstructed using a slice plane that horizontally crosses the object to be measured as the reference plane, creating three-dimensional volume data (three-dimensional images) of the object to be measured.

The calibration method according to the present invention is described below.

In calibrating the X-ray measurement device 100, the host computer 128 moves a calibration jig 102, on which a plurality of spheres 106 (3 × 4 = 12 in the figure) are arranged, as illustrated in FIG. 3, to four or more positions (also referred to as levels) on the XY plane of the three-dimensional coordinate measuring machine shown in FIGS. 1 and 2, and acquires a projection image, thereby calibrating the X-ray measurement device 100.

The specific implementation procedure is shown in Figure 4.

First, in step S2, the calibration jig 102 is moved to four or more positions (levels) on the XY plane of the three-dimensional coordinate measuring machine, and the center of gravity (an example of a feature point) of each sphere in the projected image is found. Here, the number of each sphere 106, the position coordinates of the calibration jig 102, and the sphere center of gravity coordinates are as follows:
Ball number i... 1 to N
Calibration jig position number j ... 1 to M (M ≥ 4)
Calibration jig position coordinates X(j)
Sphere center of gravity coordinates Im (i, j)

Next, in step S4, a projective transformation matrix (also referred to as 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 by 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)

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

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 if the aspect ratio of the pixels of the X-ray image detector 124 is different. Also, the skew S, which relates to image distortion, may be used in the first row and second column of the internal parameter matrix A, but in this embodiment, the skew S is set to 0.

Next, proceed to step S6, where the camera parameter A is used as the optimization parameter, and optimization is performed so that the difference E between the calculated image centroid Im'(i,j) of each sphere i and the actual image centroid Im(i,j) is minimized.

A specific example of the optimization process in step S6 is shown in Figure 5.

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

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

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)

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)

Next, proceed to step S66, recalculate the projection matrix P in step S62 using the optimized relative position O(i), and perform the optimization again in step S64.

Then, proceed to step S68, and repeat steps S64 and S66 until the residual error E of step S64 becomes smaller than a predetermined value.

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.

After the optimization process in Figure 5 is completed, return to step S8 in Figure 4 and calibrate the X-ray measurement device 100.

Specifically, the relative position of the sphere 106 determined in this invention is used to determine the rotation axis and center of rotation of the table, for example, using the method described below.

A specific example of the calibration procedure for the X-ray measurement device 100 in step S8 of Figure 4 will be described using Figures 7 to 10. Here, all calculations are performed by the host computer 128. Note that when k = 1, for example, the kth rotational position Posk indicates rotational position Pos1. Furthermore, at the kth rotational position Posk, when N = 12 and the number of spheres 106 is N, 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.

First, the calibration jig 102, which has multiple spheres 106 at known relative position intervals Pu and Pv, is placed on the rotary table 120 (step S102 in Figure 7; placement process). Then, the state in which the rotary table 120 is not yet rotating is set to k = 1 (step S104 in Figure 7).

Next, X-rays 118 are irradiated onto the calibration jig 102 (step S106 in Figure 7), and the center of gravity positions (feature point positions) ImPosk_Sphr_(1 to 12) of the projected 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 Figure 7; steps S106 to S108 are the feature position calculation process).

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

Next, it is determined whether the number k of rotational positions Posk is equal to or greater than Q (three or more times is sufficient in this embodiment) (step S112 in FIG. 7). If the number k of rotational positions Posk is not equal to or greater than Q (Q≧3) (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 rotational positions Posk is incremented by one (step S116 in FIG. 7), and steps S106 to S112 are repeated (steps S106 to S116; rotation detection process). If the number k of rotational positions Posk is equal to or greater than Q (Q≧3) (Yes in step S112 in FIG. 7), the process proceeds to step S118. That is, in the rotation detection process, the turntable 120 is rotated by the predetermined angle α two or more times, and the feature position calculation process and the transformation matrix calculation process are repeated. In this embodiment, the predetermined angle α is set to a constant value of, for example, 30 degrees, but this is not particularly limited and may be a smaller angle, or the predetermined angle α may change each time.

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 process). The details of this center position calculation process will be explained in detail below.

First, as shown in Figure 8, it is assumed that the X-ray source 116 and the X-ray image detector 124 rotate instead of the rotary table 120 (step S130 in Figure 8). Incidentally, Figure 10(A) shows the predetermined angle α and the trajectory Fb of the sphere 106 when the rotary table 120 rotates. Then, Figure 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.

Next, the absolute position Xs of the X-ray source 116 at each rotation of a predetermined angle α, i.e., at location Q, is calculated based on the projection transformation matrix Hk (k = 1 to Q) (step S132 in Figure 8).

Note that, in the above-mentioned central position calculation process, when the absolute position Xs of the X-ray source 116 at location Q is calculated, a case in which 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 explained below using Figure 9.

First, when calculating the absolute position Xs of the X-ray source 116 at the kth assumed rotational 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 rotational position calculated based on the projection transformation matrix Hk is fitted to a perfect circle, and the distance error between the position on the trajectory 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).

Specifically, for example, distance f is tentatively set to an appropriate value, position Cc is changed, and the position Cc that results in the smallest distance error is calculated. Next, position Cc that results in that smallest distance error is tentatively set, and distance f is changed again, and the distance f that results in the smallest distance error is calculated. Again, distance f that results in the smallest distance error is tentatively set, and position Cc is changed, and the position Cc that results in the smallest distance error is calculated. Again, position Cc that results in the smallest distance error is tentatively set, and distance f is changed again, 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, thereby optimizing distance f and position Cc.

Next, returning to FIG. 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 rotary table 120. Explaining this in more detail, the absolute positions Xs of the X-ray source 116 at Q locations are 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, for example, by the least squares method. If Q = 3, the center position Cp of the perfect circle is calculated, for example, by a system of simultaneous equations.

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 Figure 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 balls 106. Therefore, by averaging the center positions Cp of the perfect circles of the 12 balls 106 to calculate the rotation center position Cp, and averaging the tilt 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.

In this way, in this embodiment, the rotation center position Cp of the turntable 120 can be calculated through a series of extremely simple steps: a calibration jig 102 having 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, is placed on the turntable 120, the turntable 120 is adjusted to three rotation angles, and a projected image of the calibration jig 102 is taken. In other words, in this embodiment, there is no need to create three-dimensional volume data to calculate the rotation center position Cp.

Furthermore, in this embodiment, since all of the spheres 106 in the calibration jig 102 are placed on only one plane, the transformation matrix used to perform the projection 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 projection transformation matrix Hk. Therefore, it is possible to calculate the rotation center position Cp of the turntable 120 using only four of the twelve spheres 106 as the calculation target in each process, further reducing the calibration time. Note that in this embodiment, by using all twelve spheres 106 as the calculation target in each process, rather than just four spheres 106, the rotation center position Cp of the turntable 120 can be calculated extremely accurately.

Furthermore, in this embodiment, the rotation axis Ax of the turntable 120 is also calculated in the center position calculation process. Therefore, even if it is initially assumed that calibration of the rotation axis Ax of the turntable 120 is not required, the necessity of calibration can be properly evaluated by comparing it with the results of actually calculating the rotation axis Ax of the turntable 120.

In addition, in this embodiment, in the center position calculation process, 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 is calculated for each rotation of a predetermined angle α from the projection transformation matrix Hk to calculate the rotation center position Cp of the turntable 120. In other words, 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 achieved quickly. However, this is not limited to this, and the rotation center position Cp of the turntable 120 may also be calculated by calculating the absolute position Xa of the sphere 106.

In this embodiment, the rotary table 120 is rotated at a predetermined angle α four or more times to calculate the absolute position Xs of the X-ray source 116 at location Q. The variables used are 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. The absolute position Xs of the X-ray source 116 at location Q, calculated based on the projection transformation matrix Hk (k = 1 to Q), is fitted to a perfect circle to form a virtual circle, and the distance error between the position on the trajectory Fs and the absolute position Xs of the X-ray source 116 at location Q is evaluated. This allows 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 to be 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.

Furthermore, in this embodiment, in the center position calculation process, the center position Cp of the trajectory Fs fitted with a perfect circle (= provisional perfect circle) is calculated from changes 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, this is not limited to this, and the rotation center position Cp of the turntable 120 may be calculated using other methods.

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 this 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 limited to this, and for example, the trajectory Fs fitted to a perfect circle for each sphere 106 can be calculated, and the rotation axis Ax can be calculated from the deviation of its center position.

In addition, in this embodiment, the reference object on the calibration jig 102 is a sphere 106. Therefore, the outline of the sphere 106 is circular regardless of the direction from which it is projected. In other words, the sphere 106 is the shape that can be most easily identified as a 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.

In addition, in this embodiment, the position of a feature point in the projected image of the sphere 106, which is the reference object, is taken as the center of gravity of the projected image. Because the projected image of the sphere 106 is circular, the center of gravity can be calculated easily and with little positional error. However, this is not limited to this, and the position of a feature point in the projected image of the sphere 106, which is the reference object, may also 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.

In other words, in this embodiment, the rotation center position Cp of the rotary table 120 on which the object to be measured is rotatably placed can be easily calculated through a simple process.

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)

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 using the following equation (10) for the projection matrix Pk instead of equation (9).

In this case, by using the projection matrix Pk, accurate calibration can be performed even if the planarity accuracy of the calibration jig 102 is poor.

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

Furthermore, the reference object is not limited to a sphere, and the position of the feature point is not limited to the center of gravity.

This invention can be widely applied to the calibration of X-ray measurement devices.

100...X-ray measurement device 102...calibration jig 104...plate-shaped member 106...sphere 108...main body 110...X-ray shielding cover 112...base 114...radiation source support base 116...X-ray source 118...X-ray 120...rotary table 122...table support base 124...X-ray image detector 124A...detection surface 126...detector support base 128...host computer 130...motion controller i...sphere number j...calibration jig position number X(j)...calibration jig position coordinates Im(i,j), Im'(i,j)...sphere center of gravity coordinates H(i), Hk...projection transformation matrix (homography matrix)
A...Camera (internal) parameters O(i)...Relative position of each sphere r1(i), r2(i), r3(i)...Vector representing rotation t(i)...Vector representing translation P, Pk...Projection matrix

Claims (9)

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, which has a plurality of reference objects having shapes that can be identified by the projection images onto the X-ray image detector, and which can be moved and placed at M or more positions (M≧4), on the rotary table;
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: 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 coordinate X(j) of each reference object and the feature point coordinate Im(i, j), the following equation Im'(i, j) ≈ P × [X(j) + O(i)] is obtained.
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: 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. 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. 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. In any one of claims 1 to 5,
A method for calibrating an X-ray measurement device, characterized in 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. 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. 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. 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.