JP2023095304A - Calibration method of x-ray measurement apparatus - Google Patents

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

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

Conventionally, an X-ray measuring device (X-ray CT device for measurement) can measure the three-dimensional shape of an object to be measured using X-rays. , and circuit pattern defects of electronic circuit components. However, in recent years, with the help of the spread of 3D printers, the demand for 3D dimension measurement inside processed products and its high precision is increasing. In order to meet such demands, there is a demand for an X-ray measuring apparatus with higher accuracy in dimensional measurement.

Reconfiguration of this X-ray measuring apparatus 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 measurement with an X-ray measuring apparatus with higher accuracy, it is important to perform various calibrations specific to the apparatus before starting measurement, as described in Japanese Patent Application Laid-Open No. 2002-200316.

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

Japanese Patent Application Laid-Open No. 2000-298105

However, there is a constraint that it cannot cope with the deformation of the calibration jig due to secular change, and that it must be an arrangement that facilitates geometric element measurement.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method for calibrating an X-ray measuring device that does not require prior high-precision three-dimensional measurement of a calibration jig for the X-ray measuring device. and

The invention according to claim 1 of the present application is a method for calibrating an X-ray measuring device for three-dimensional shape measurement of an object to be measured using X-rays, wherein the X-ray measuring device generates the X-rays a source, a rotary table on which the object to be measured is rotatably mounted, and an X-ray image detector for detecting the X-rays transmitted through the object to be measured, wherein projection onto the X-ray image detector a mounting step of mounting a calibration jig having a plurality of reference objects having shapes identifiable by an image and capable of being moved and arranged by M levels (M≧4) or more on the rotary table; a feature position calculation step of irradiating the calibration jig and specifying the position of the feature point of the projection image of each of the reference objects at M levels from the output of the X-ray image detector, and each of the reference objects at M levels a conversion matrix calculation step of calculating a conversion matrix including camera parameters for performing projective conversion to the detection plane of the X-ray image detector of the reference object from the positions and relative position intervals of the feature points of the projected image of , a parameter optimization step of optimizing the camera parameters so that the difference between the positions of the feature points of the projected image and the relative position intervals is small; and the relative positions of the feature points calculated using the optimized camera parameters. and a center position calculation step of calculating the rotation center position of the rotary table using .

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 for the camera parameters to determine 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 Im'(i, j)≈P×{X(j)+O(i)} ( 1)
A second step of finding a projection matrix P that satisfies and a third step of optimizing the camera parameters such that .

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

According to a fourth aspect of the present invention, after the camera parameters have converged in the third step, the projection matrix P in the second step is recalculated to repeat the optimization.

In the invention according to claim 5 of the present application, 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 combined in the optimization process. It is designed to be optimized for

In the invention according to claim 6 of the present application, when all of the reference objects are placed on only one plane in the calibration jig, the transformation matrix is a projective transformation matrix, and the reference object is a cubic In the case of original placement, N=6 and the transformation matrix is the projection matrix.

According to a seventh aspect of the present invention, in the center position calculating step, the rotation axis of the rotary table is calculated.

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

In the invention according to claim 9 of the present application, the position of the feature point of the projected image of the reference object is set as the barycentric position of the projected image.

According to the present invention, prior high-precision three-dimensional measurement of the calibration jig of the X-ray measuring apparatus is unnecessary.

1 is a schematic side view showing the basic configuration of an X-ray measuring device according to an embodiment of the present invention; FIG. Schematic top view showing only the main part of the X-ray measuring device of FIG. Diagrams showing the calibration jig in FIG. 1 (front view (A), top view (B)) FIG. 2 is a flow chart showing the calibration procedure of the X-ray measuring device according to the embodiment of the present invention; Detailed flowchart of an example of camera parameter optimization processing in FIG. Detailed flowchart of another example of optimization processing of camera parameters in FIG. Flow chart showing an example of the calibration procedure of the X-ray measuring device using the calibrated calibration jig in FIG. Detailed flowchart of processing for calculating the absolute position of the sphere in FIG. After calculating the absolute position of the X-ray source in FIG. 8, calculate the distance between the X-ray source and the X-ray image detector and the position of the foot of the perpendicular from the X-ray source to the X-ray image detector. flow chart A diagram showing an example of the relationship between the absolute position of the sphere and the absolute position of the X-ray source.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In addition, the present invention is not limited by the contents described in the following embodiments and examples. In addition, the configuration requirements in the embodiments and examples described below include those that can be easily assumed by those skilled in the art, those that are substantially the same, and those that fall 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.

FIG. 1 shows an embodiment of the invention. Note that in FIG. 1, the horizontal direction with respect to the paper surface is defined as the z-axis direction, the vertical direction with respect to the paper surface is defined as the y-axis direction, and the direction perpendicular to the paper surface is defined as the x-axis direction.

An X-ray measuring apparatus 100 is an apparatus for measuring the three-dimensional shape of an object to be measured using X-rays, and as shown in FIG.

1 and 2, the calibration jig 102 is placed on the rotary table 120 instead of the object to be measured. As shown in FIGS. 3A and 3B, the calibration jig 102 is made of a material (for example, aluminum) through which X-rays 118 can pass. ) 106 at known relative position intervals Pu and Pv (for example, 4×3 and N=12) (that is, the balls 106 are arranged at 12 locations at known relative position intervals Pu and Pv). there). In other words, all the balls 106 are placed only on one plane in the calibration jig 102 . At the same time, it can be said that the relative positions X(1-12) of the 12 spheres 106, in other words, the 12 spheres 106 are known (X(1-12) and X1-X12 mean the same thing, The same notation is used hereinafter). It should be noted that the sphere 106 has a simple shape and is a shape that can be easily identified by a projected image onto the X-ray image detector 124 . In FIG. 3A, the left-right direction with respect to the paper surface is defined as the u-axis direction, the vertical direction with respect to the paper surface is defined as the v-axis direction, and the direction perpendicular to the paper surface is defined as the w-axis direction.

As shown in FIG. 1, the main body 108 includes, on a base 112, an X-ray shielding cover 110 for preventing leakage of X-rays 118, an X-ray source 116 for generating X-rays 118, and an object to be measured (not shown). ) is rotatably mounted thereon, and an X-ray image detector 124 for detecting X-rays 118 transmitted through the object to be measured. An X-ray source 116 is mounted on a source support 114 on the base 112 . The radiation source support 114 can include a linear motion mechanism that allows the X-ray source 116 to move in the xyz three-axis directions. A rotary table 120 is provided on a table support 122 on the base 112 . The table support base 122 has a linear motion mechanism that allows the object to be measured to be moved in three axial directions of xyz. Furthermore, the table support base 122 may be provided with a tilt mechanism that enables tilt adjustment of the rotation axis Ax of the rotary table 120 . X-ray image detector 124 has a two-dimensional detection surface 124 A sensitive to X-rays 118 . X-ray image detector 124 is supported by detector support 126 on base 112 . The detector support 126 may also include a linear movement mechanism that allows the X-ray image detector 124 to move in the xyz three-axis directions. A radiation beam of X-rays 118 from the X-ray source 116 spreads conically in the z-axis direction, the center line of which intersects the rotation axis Ax of the rotary table 120, and the normal to the detection surface 124A of the X-ray image detector 124. is adjusted so that

The host computer 128 shown in FIG. 1 controls the radiation source support 114 , X-ray source 116 , rotary table 120 , table support 122 , X-ray image detector 124 and detector support 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 measuring apparatus 100 by reading out and executing a program stored in a storage unit (not shown). That is, in the measurement operation of the X-ray measuring apparatus 100, the host computer 128, for example, reconstructs projection image data 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 FIG. 1 is connected to the host computer 128 and controls the rotation/movement of the X-ray source 116 and the rotary table 120 of the main body 108 and various mechanisms.

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

A calibration method according to the present invention will be described below.

In the calibration of the X-ray measuring apparatus 100, the host computer 128 sets a calibration jig 102 having a plurality of (3×4=12 in the figure) spheres 106 arranged as an example in FIG. The X-ray measuring apparatus 100 is calibrated by moving four or more levels on the plane and acquiring projection images.

A specific implementation procedure is shown in FIG.

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

Next, in step S4, the projective transformation matrix (also called homography matrix) H(i) of each sphere i is obtained. Specifically, for a certain sphere i, from the correspondence between the calibration jig position coordinates X(j) and the sphere center-of-gravity coordinates Im(i, j), a homography of, for example, 3 columns×3 rows that satisfies the following equation (2): Matrix H(i) can be determined.
H(i)×X(j)≈Im(i, j) (2)

Ｈ（ｉ）＝ Ａ ×［ｒ１（ｉ） ｒ２（ｉ） ｔ（ｉ）］ ・・・（４） Here, the homography matrix H(i) is composed of camera parameters (also called internal parameters) A expressed by the following equation (3), vectors r1(i) and r2(i) representing rotation, vector t Using (i), it can be expressed as in the following equation (4).

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 legs of the perpendicular from the X-ray source 116 to the X-ray image detector 124. . Note that the distance f in the first row and the first column of the internal parameter matrix A and the distance f in the second row and the second column of the intrinsic parameter matrix A have slightly different values when the aspect ratios of the pixels of the X-ray image detector 124 are different. . A skew S related to image distortion may be used in the first row and second column of the intrinsic parameter matrix A, but the skew S is set to 0 in this embodiment.

Next, in step S6, the camera parameter A is used as an optimization parameter, and the difference E between the calculated image center of gravity Im′(i,j) of each sphere i and the actual image center of gravity Im(i,j) becomes small. Optimize as follows.

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

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

The relative position O(i) of each sphere i to be obtained is expressed by the following equation using vectors r1(i) and r2(i) representing rotation, r3(i) derived therefrom, and vector t(i) representing translation. (5) and (6).
R(i)=[r1(i) r2(i) r3(i)] (5)
O(i)=−R(i)^−1×t(i) (6)

Next, in step S62, from the correspondence between the sphere position coordinates (=X(j)+O(i)) and the sphere center-of-gravity coordinates Im(i,j), projection Find the matrix P.
Im'(i,j)≈P×{X(j)+O(i)} (7)

Next, in step S64, the barycentric coordinates Im'(i,j) calculated using the projection matrix P obtained in step S62 are obtained, and Optimize the camera parameter A to
E=|Im(i,j)−P×{X(j)+O(i)}| → min
... (8)

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

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

During the optimization process, as in the other example shown in FIG. The projection matrix P may also be optimized together.

After the optimization process in FIG. 5 ends, the process returns to step S8 in FIG. 4 to calibrate the X-ray measuring apparatus 100. FIG.

Specifically, using the relative position of the ball 106 obtained by the present invention, the rotation axis and rotation center position of the table are obtained by, for example, the following method.

A specific example of the procedure for calibrating the X-ray measurement apparatus 100 in step S8 of FIG. 4 will be described with reference to FIGS. 7 to 10. FIG. Here, the host computer 128 is doing all the calculations. For example, when k=1, the k-th rotational position Posk indicates the rotational position Pos1. Further, when N=12 and the number of balls 106 is N at the k-th rotational position Posk, the center-of-gravity position ImPosk_Sphr_(1 to N) indicates the center-of-gravity positions ImPos1_Sphr_1 to ImPos1_Sphr_12 of the 12 balls 106, respectively.

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

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

Next, from the center-of-gravity position ImPosk_Sphr_(1 to 12) of the projection image of each of the 12 spheres 106 and the relative position X(1 to 12) of the sphere 106 to the detection surface 124A of the X-ray image detector 124 of the sphere 106, A projective transformation matrix Hk for projective transformation is calculated (step S110 in FIG. 7; transformation matrix calculation step).

Next, it is determined whether or not the number k of the rotational positions Posk is Q or more (three times or more in the present 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 rotary table 120 is rotated at a predetermined angle α (step S114 in FIG. 7). Then, the number k of the 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). When the number k of the 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 twice or more, and the characteristic position calculation process and the conversion matrix calculation process are repeated. In this embodiment, the predetermined angle α is, for example, a constant 30 degrees, but 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 the 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 details of this center position calculation process will be described in detail.

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 rotary table 120 (step S130 in FIG. 8). Incidentally, FIG. 10A shows the predetermined angle α and the trajectory Fb of the ball 106 when the rotary table 120 rotates. FIG. 10B shows the locus Fs of the absolute position Xs of the X-ray source 116 assuming that the X-ray source 116 and the X-ray image detector 124 are rotated.

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

In the center position calculation step, when the absolute position Xs of the X-ray source 116 at Q points is calculated, the distance f between the X-ray source 116 and the X-ray image detector 124 and the distance from the X-ray source 116 A case where the leg position Cc of the perpendicular to the X-ray image detector 124 is unknown will be described below with reference to FIG.

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 X-ray image detection from the X-ray source 116 The position Cc (cx, cy) of the foot of the perpendicular to the container 124 is used as a variable (step S140 in FIG. 9). Then, the position on the trajectory Fs of the temporary perfect 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 projective transformation matrix Hk to the perfect circle and the absolute position of the X-ray source 116 A distance error from Xs is evaluated (step S142 in FIG. 9). Then, the distance f and the position Cc at which this distance error is the minimum error are calculated (step S144 in FIG. 9).

Specifically, for example, the distance f is tentatively determined as an appropriate value, the position Cc is changed, and the position Cc with the smallest distance error is calculated. Next, the position Cc at which the distance error is the smallest is tentatively determined, and the distance f is changed this time to calculate the distance f at which the distance error is the smallest. Also, the distance f that provides the minimum distance error is tentatively determined, the position Cc is changed, and the position Cc that provides the minimum distance error is calculated. Also, the position Cc at which the distance error is the smallest is tentatively determined, the distance f is changed again, and the distance f at which the distance error is the smallest is calculated. By repeating this several times, the distance f and the position Cc with the smallest distance error can be calculated, and the distance f and the position Cc can be optimized.

Next, returning to FIG. 7, from the change in the absolute position Xa (1 to N) of the X-ray source 116, the center position Cp of the trajectory Fs fitted with a perfect circle (=provisional perfect circle) is calculated, and the center position Let Cp be the rotation center position Cp of the rotary table 120 . More specifically, the absolute positions Xs of the X-ray sources 116 at Q points 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 by, for example, the method of least squares. If Q=3, for example, the central position Cp of the perfect circle is calculated by simultaneous equations.

Then, for example, the angle of inclination of the trajectory Fs fitted with a perfect circle from the horizontal plane (xz plane) is calculated. Then, the rotation center position Cp and the rotation axis Ax of the rotary table 120 are calculated (step S122 in FIG. 7). At this point, the host computer 128 can also calculate the center positions Cp of the perfect circles and their trajectories 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 by averaging the inclinations of the trajectories Fb from the horizontal plane, the inclination of the rotation axis Ax is calculated. The angle can be calculated, and the rotation axis Ax can also be calculated.

As described above, in this embodiment, the rotary table 120 is provided with the calibration jig 102 having 12 spheres 106 each having a shape that can be identified by the projection image onto the X-ray image detector 124 at known relative position intervals Pu and Pv. It is possible to calculate the rotation center position Cp of the turntable 120 by a very simple series of steps of mounting, adjusting the turntable 120 to three rotation angles, and taking projection images of the calibration jig 102 . can. That is, in this embodiment, it is not necessary to create three-dimensional volume data to calculate the rotation center position Cp.

Further, in this embodiment, since all the balls 106 are placed only on one plane in the calibration jig 102, the detection surface 124A of the X-ray image detector 124 of the ball 106 at the k-th rotational position Posk A transformation matrix for performing the projective transformation to is defined as the projective transformation matrix Hk. Therefore, the rotation center position Cp of the rotary table 120 can be calculated by using only four balls 106 out of the 12 balls 106 as calculation targets in each process, and the calibration time can be further shortened. In addition, in this embodiment, not only the four balls 106 but also all twelve balls 106 are used as calculation targets in each process, so that the rotation center position Cp of the rotary table 120 can be calculated very accurately. .

Further, in the present embodiment, the rotation axis Ax of the rotary table 120 is further calculated in the center position calculation step. Therefore, even if it is initially assumed that the rotation axis Ax of the rotary table 120 does not need to be calibrated, the need for calibration is properly evaluated by comparing the result of actually calculating the rotation axis Ax of the rotary table 120. can do.

Further, in the present embodiment, it is assumed that the X-ray source 116 and the X-ray image detector 124 rotate instead of the turntable 120 in the center position calculation step, and from the projection transformation matrix Hk, By calculating the absolute position Xs of the X-ray source 116, the rotation center position Cp of the rotary table 120 is calculated. 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 projective transformation matrix Hk, as a result, the amount of calculation can be reduced, and calibration can be realized quickly. Alternatively, the rotation center position Cp of the rotary table 120 may be calculated by calculating the absolute position Xa of the ball 106 .

Further, in the present embodiment, when the rotary table 120 is rotated at the predetermined angle α four times or more to calculate the absolute position Xs of the X-ray source 116 at Q points, the X-ray source 116 and the X-ray image detector 124 are and the foot position Cc (cx, cy) of the perpendicular from the X-ray source 116 to the X-ray image detector 124 are variables. Then, the position on the trajectory Fs of the temporary perfect circle obtained by fitting the absolute position Xs of the X-ray source 116 at Q points calculated based on the projective transformation matrix Hk (k=1 to Q) to the perfect circle and the X at the Q points A distance error from the absolute position Xs of the radiation source 116 is evaluated. Thereby, the distance f between the X-ray source 116 and the X-ray image detector 124 and the foot position Cc (cx, cy) of the perpendicular line from the X-ray source 116 to the X-ray image detector 124 are calculated. Therefore, an attempt is made to calibrate the distance f between the X-ray source 116 and the X-ray image detector 124 and the leg position Cc (cx, cy) of the perpendicular line from the X-ray source 116 to the X-ray image detector 124. Then, these values can be calculated and more accurate calibration can be performed.

Further, in the present 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 Let Cp be the rotation center position Cp of the rotary table 120 . That is, by fitting with a perfect circle, the total number Q of rotational positions can be reduced, and the center position Cp can be uniquely calculated. Note that the rotation center position Cp of the rotary table 120 may be calculated by other methods without being limited to this.

Further, in this embodiment, when calculating the rotation axis Ax of the rotary table 120, the inclination angle from the horizontal plane of the trajectory Fs fitted with a perfect circle is calculated, and the inclination angle and the rotation center position Cp are calculated. , the rotation axis Ax is calculated. Therefore, since only one ball 106 is required to calculate the rotation axis Ax, the process of calculating the rotation axis Ax can be simplified and can be performed in a short time. However, the present invention is not limited to this, and for example, a trajectory Fs fitted with 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.

Also, in this embodiment, the reference object on the calibration jig 102 is the sphere 106 . Therefore, the sphere 106 has a circular contour when projected from any direction. That is, the sphere 106 is the shape most easily identifiable by projection onto the X-ray image detector 124 as the reference object. Note that the reference object is not limited to this, and may be, for example, a polyhedron including a regular polyhedron or a deformed rhomboid, or a shape including a curved surface such as an ellipsoid or a cone.

Further, in this embodiment, the position of the feature point of the projected image of the sphere 106, which is the reference object, is the position of the center of gravity of the projected image. Since the projected image of the sphere 106 is a circle, the position of the center of gravity can be easily calculated with a small positional error. Note that the position of the feature point of the projected image of the sphere 106, which is the reference object, may be the central position. Alternatively, if the reference object is not a sphere but has locally characteristic recesses or protrusions, the characteristic recesses or protrusions may be associated with the feature points of the projected image.

That is, in the present embodiment, it is possible to easily calculate the rotation center position Cp of the rotation table 120 on which the object to be measured is rotatably mounted through a simple process.

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

The host computer 128 uses the following equation (10) related to the projection matrix Pk instead of the equation (9) to obtain the X-ray source 116 , the absolute position Xs of can be calculated.

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.

In addition, although the number of balls 106 is at least four (or six) in the above embodiment, the present invention is not limited to this. For example, the calibration jig 102 may be configured such that two balls 106 are moved to at least four (or six) locations.

Also, the reference object is not limited to a sphere, and the position of the feature point is not limited to the barycentric position.

INDUSTRIAL APPLICABILITY The present invention can be widely applied to the calibration of X-ray measuring devices.

DESCRIPTION OF SYMBOLS 100... X-ray measuring device 102... Calibration jig 104... Plate-shaped member 106... Ball 108... Body part 110... X-ray shielding cover 112... Base 114... Radiation source support base 116... X-ray source 118... X-ray 120... Rotation Table 122 Table support base 124 X-ray image detector 124A Detection surface 126 Detector support base 128 Host computer 130 Motion controller i Ball number j Calibration jig position number X(j) Calibration jig Tool position coordinates Im (i, j), Im' (i, j) ... Ball center of gravity coordinates H (i), Hk ... Projective transformation matrix (homography matrix)
A... camera (internal) parameter O(i)... relative position of each sphere r1(i), r2(i), r3(i)... vector representing rotation t(i)... vector representing translation P, Pk... projection queue

Claims (9)

A method for calibrating an X-ray measuring device for three-dimensional shape measurement of an object to be measured using X-rays,
The X-ray measuring device includes an X-ray source that generates the X-rays, a rotary table 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. equipped with a vessel and
A calibration jig having a plurality of reference objects having a shape identifiable by a projected image onto the X-ray image detector and capable of being moved and arranged by at least M levels (M≧4) is placed on the rotary table. a placing step;
a feature position calculation step of irradiating the calibration jig with the X-ray and specifying the position of the feature point of the projected image of each of the reference objects at the M level from the output of the X-ray image detector;
A transformation matrix including camera parameters for projectively transforming the positions and relative position intervals of the feature points of the projection images of the reference object at M levels to the detection plane of the X-ray image detector of the reference object. a conversion matrix calculation step of calculating
a parameter optimization step of optimizing the camera parameters so that the difference between the position of the feature point of the projected image and the relative position interval is small;
a center position calculation step of calculating a rotation center position of the rotary table using the relative positions of the feature points calculated using the optimized camera parameters;
A method for calibrating an X-ray measuring device, comprising: In claim 1,
The parameter optimization step includes:
First, a first step of determining the relative position O(i) of each reference object by setting appropriate initial values for the camera parameters;
From the correspondence between the position coordinates X(j) of each reference object and the feature point coordinates Im(i,j), the following equation Im'(i,j)≈P×{X(j)+O(i)}
a second step of finding a projection matrix P that satisfies
The feature point coordinates Im′(i, j) calculated using the obtained projection matrix P are obtained, and the camera parameters are optimized so that the difference from the actual feature point coordinates Im(i, j) becomes small. 3 steps;
A method for calibrating an X-ray measuring device, comprising: In claim 2,
In a fourth step following the third step,
The projection matrix P in the second step is recalculated using the camera parameters optimized in the third step, and the process of performing the optimization in the third step again is performed so that the difference in the feature point coordinates is small. A method for calibrating an X-ray measuring device, characterized by repeating until In claim 2,
A method for calibrating an X-ray measuring apparatus, wherein the projection matrix P in the second step is recalculated and optimization is repeated after the camera parameters have converged in the third step. In claim 2,
X characterized in 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. A method of calibrating a line measuring device. 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 projective transformation matrix, and when the reference object is placed three-dimensionally 3. A method of calibrating an X-ray measuring apparatus, wherein N=6 and said transformation matrix is a projection matrix. In any one of claims 1 to 6,
A method for calibrating an X-ray measuring device, wherein the center position calculating step further includes calculating a rotation axis of the rotary table. In any one of claims 1 to 7,
A calibration method for an X-ray measuring device, wherein the reference object is a sphere. In any one of claims 1 to 8,
A method for calibrating an X-ray measuring apparatus, wherein 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.

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