JP2020139829A - Three-dimensional image generation device and coefficient calculation method for three-dimensional image generation device - Google Patents

Abstract

To generate a three-dimensional image of a test object by using X-rays generated from the test object.SOLUTION: A three-dimensional image generation device includes: an irradiation section configured to irradiate a test object with an excitation beam; an X-ray detector configured to detect X-ray emitted from the test object irradiated with the excitation beam; an inclination calculation section configured to calculate an inclination of a surface of the test object from an output of the X-ray detector; and a three-dimensional image generation section configured to generate a three-dimensional image of the test object by using the inclination information obtained by the inclination calculation section by using the three-dimensional reconstruction.SELECTED DRAWING: Figure 9

Description

The present invention detects X-rays generated from a test object irradiated with an excitation beam, calculates inclination information on the surface of the test object, and generates a three-dimensional image of the test object by three-dimensional reconstruction. The present invention relates to a three-dimensional image generator and a method for calculating a coefficient of an arithmetic expression used in the three-dimensional image generator.

Conventionally, as shown in Patent Document 1, a plurality of secondary electron detectors are provided in a scanning electron microscope, and the inclination of the surface of the test object is obtained from the difference values of the output signals of the plurality of secondary electron detectors. It is considered to obtain the three-dimensional shape of the surface of the test object by integrating.

JP-A-63-218804

On the other hand, the inventor of the present application generates a three-dimensional image of the test object by detecting X-rays obtained by irradiating the test object with an excitation beam instead of secondary electrons generated from the test object. It was investigated. Then, as a result of diligent studies described later, a three-dimensional image generation device according to the present invention was made, and the problem is to generate a three-dimensional image of the test object using X-rays generated from the test object. is there.

That is, the three-dimensional image generator according to the present invention includes an irradiation unit that irradiates an object with an excitation beam, an X-ray detector that detects X-rays generated from the object irradiated with the excitation beam, and the above. A tilt calculation unit that calculates information on the surface tilt of the test object from the output of the X-ray detector, and a three-dimensional reconstruction of the test object using the tilt information obtained by the tilt calculation unit. It is characterized by including a three-dimensional image generation unit that generates an image.

In such a case, the inclination calculation unit calculates information on the inclination of the surface of the test object from the output of the X-ray detector, and the three-dimensional image generation unit uses the inclination information obtained by the inclination calculation unit. Since the three-dimensional image of the test object is generated by the three-dimensional reconstruction, the three-dimensional image of the test object can be generated by using the X-rays generated from the test object.

First, the coordinate system is defined as shown in FIG. When an excitation beam such as an electron beam is incident on the surface of an object, the Z axis is considered in a direction substantially coincident with the irradiation direction of the excitation beam with the irradiation position of the excitation beam as the origin, and the XY plane is set as a plane perpendicular to the Z axis. Is assumed. Generally, it is considered that the horizontal plane is often the XY plane.

It is assumed that the tangent plane of the surface of the test object at the irradiation position of the excitation beam is tilted by an inclination angle θ in an arbitrary direction with respect to the XY plane. At this time, the intensity of X-rays observed by the X-ray detector installed in the direction of the extraction angle ψ with respect to the XY plane is at least a function of the inclination angle θ, and as shown in the following equation (1), It can be written in the form of the product of two functions E and D.

The plane including the X-ray detector and the Z axis is defined as the XZ plane. That is, it is assumed that the point where the detection position of the X-ray detector is projected on the XY plane along the Z axis is on the X axis.

Here, E is a function representing the ratio of the generated X-ray intensity, and D is a function representing the attenuation rate (more accurately, the ratio of the attenuation rate) at which the X-rays passing through the test object are absorbed. is there. Further, _Im (0) is the output of the X-ray detector when the tangent plane of the surface of the test object is parallel to the XY plane in FIG. 2A (a), that is, when θ = 0. Therefore, the function E and the function D are functions that represent the change from the time when θ = 0 as a ratio.

In the above equation (1), the function E representing the ratio of the generated X-ray intensities will be considered.
When the tangent plane of the surface of the test object is tilted by an inclination angle θ from the XY plane, the generated X-ray intensity changes. At this time, the generated X-ray intensity is governed by the inclination angle θ (scalar value) regardless of the inclination direction of the surface of the test object. Therefore, the function E representing the ratio of the generated X-ray intensities (ratio to the time when θ = 0) is the function E (θ) of the inclination angle θ.

Next, the relationship between the change in the inclination angle θ of the tangent plane and the function E (θ) will be considered.
The case where the excitation beam incident on the surface of the test object has a circular cross section having a diameter d will be described as an example. In the case of FIG. 2A (a) in which the tangent plane of the surface of the test object is parallel to the XY plane (when θ = 0, the excitation beam is incident at right angles to the tangent plane), the diameter d on the surface of the test object. The circular region of is illuminated by the excitation beam.

However, when the surface of the test object is tilted by the inclination angle θ from the XY plane as shown in FIG. 2A (b), the elliptical region having the major axis d / cos θ and the minor axis d becomes the irradiation region of the excitation beam. Therefore, as the inclination angle θ of the tangent plane becomes larger, the major axis of the ellipse becomes longer, and the area irradiated by the excitation beam on the surface of the test object increases. Therefore, the energy supplied to the test object by the excitation beam decreases monotonically as the inclination angle θ increases, considering the intensity per unit area. Then, when the inclination angle θ of the tangent plane reaches π / 2, the major axis of the elliptical shape becomes infinite, so that the energy per unit area of the excitation beam becomes zero. This corresponds to the fact that the excited beam to be irradiated cannot reach because the excitation beam itself is shielded by the test object.

Therefore, the function E (θ) representing the ratio of the generated X-ray intensity has a maximum value E (0) = 1 when the inclination angle of the tangent plane is θ = 0, and the absolute value of the inclination angle θ of the tangent plane increases. It must be a function that decreases monotonically with respect to E (± π / 2) = 0 at θ = ± π / 2. That is, the function E (θ) is an even function with respect to the inclination angle θ of the tangent plane.

In addition, X-rays are generated depending on the rate at which the function E (θ) decreases monotonically with respect to the increase in the absolute value of the tilt angle θ of the tangent plane, and how the function E (θ) changes with respect to the tilt angle θ. It changes depending on the element to be used. This is because the amount of X-rays generated is non-linear with respect to the energy supplied from the excitation beam and the like, and the degree thereof differs for each element. In addition, it should be noted that not all of the energy of the excitation beam applied to the surface of the test object penetrates inside the test object, and some of it is reflected. That is, as the inclination angle θ of the tangent plane increases, the energy ratio of the reflected excitation beam also increases. Moreover, it is known that the change in the ratio of reflected energy with respect to the inclination angle θ differs for each element. Therefore, the function E (θ) representing the ratio of the generated X-ray intensities must include at least "m1 which is a material-specific coefficient determined by the element that generates X-rays".

Summarizing the above considerations, the function E representing the ratio of the X-ray intensity generated in the equation (1) is a function of the inclination angle θ and is a material-specific coefficient determined by the element that generates the X-ray m1. It becomes a function E (m1, θ) having. As a boundary condition for the inclination angle θ, the maximum value E (m1,0) = 1 when θ = 0, and it decreases monotonically with the increase of the absolute value of θ, and E (m1) at θ = ± π / 2. , ± π / 2) = 0. The material-specific coefficient m1 may be analytically derived for each element from a more detailed theoretical study, or may be numerically analyzed using a well-known simulation technique such as the Monte Carlo method. Alternatively, it may be determined experimentally by the method described later.

As a specific example of the function E (m1, θ) satisfying the above conditions, the following equation (2) can be used.

The specific value of m1 is a real number of about 0 to 2. For example, when using the M line of an element such as W (tungsten) or Au (gold), the value is close to 0.8. On the other hand, for elements such as Ni (nickel) and Ti (titanium), the value is about 0.5 when the K line is used, but exceeds 0.8 when the L line is used. ..

Since the X-rays generated inside the test object have a large penetrating power to the substance in this way, they pass through the test object and travel linearly, reach the X-ray detector, and are detected. However, even though the penetrating power is large, the X-rays passing through the test object are absorbed and attenuated. Moreover, it is known that it decays exponentially (rapidly) with respect to the distance it passes through the test object. Therefore, regarding the function D representing the attenuation rate at which X-rays are absorbed in the equation (1), it is necessary to consider the distance through which the X-rays pass through the test object.

First, consider the case shown in FIG. 2B (a) in which X-rays are generated at a unit depth when the tangent plane of the surface of the test object is parallel to the XY plane, that is, when θ = 0. FIG. 2B (a) is a cross-sectional view of the XZ plane centered on the position where the excitation beam is irradiated. X-rays generated at a position where the depth inside the test object is 1, pass through the test object for a distance L ₀ = cosec ψ, and then are installed in the direction of the extraction angle ψ with respect to the XY plane. Reach the vessel. The X-ray intensity detected by the X-ray detector at this time is given by the following equation (3).

Here, I _o (0) is the intensity of X-rays generated at a unit depth (not the ratio of intensities). Further, m2 is a coefficient that determines the degree of exponential decay of X-rays passing through the test object, and is a material-specific coefficient determined by at least an element that generates X-rays and an element that absorbs X-rays. Is.

Next, the state of FIG. 2B (a) and the state of FIG. 2B (b) are compared. FIG. 2B (b) shows a state in which the tangent plane of the surface of the test object is rotated clockwise with respect to the XY plane and is inclined by θ _y . In FIG. 2B (b), it can be seen that the distance generated X-rays proceeds with a test substance in is shortened by L _1. This shortened distance L ₁ depends on the Y-axis component θ _y of the inclination angle θ of the tangent plane and the extraction angle ψ of the X-ray detector.

Similarly, given the state of FIG. 2C which tangential plane of the surface of the test object is rotated counterclockwise about the Y axis (a), the distance generated X-rays proceeds with a test substance in becomes longer by L ₂ You can see that. This increasing distance L ₂ also depends on the Y-axis component θ _y of the inclination angle θ of the tangent plane and the extraction angle ψ of the X-ray detector.

Therefore, the function D representing the attenuation rate at which X-rays are absorbed in the equation (1) is a function D (θ _y ) of the Y-axis component θ _y of the inclination angle θ of the tangent plane. Further, since it depends on the extraction angle ψ of the X-ray detector, the function D (θ _y , ψ) including the extraction angle ψ is obtained. The most important thing to pay attention to here is the distinction between the inclination angle θ of the tangent plane and its Y-axis component θ _y . That is, the function E representing the ratio of the X-ray intensities generated in the equation (1) is a function of the inclination angle θ, and the direction of the inclination angle θ does not matter. On the other hand, the function D representing the attenuation rate at which X-rays are absorbed in the equation (1) is a function of the Y-axis component θ _y of the inclination angle θ. For example, considering the case where the tangent plane is rotated by θ _x around the X-axis from the state of FIG. 2B (a), the ratio of the generated X-ray intensity is from E (m1, 0) to E (m1, θ _x). ), But the attenuation rate at which X-rays are absorbed does not change. This is because θ _y = 0 remains.

Next, the relationship between the change in the Y-axis component θ _y of the inclination angle θ of the tangent plane and the function D (θ _y , ψ) will be considered.
The state of FIG. 2B (a) is θ = 0, and therefore θ _y = θ _x = 0. In this case, consistent because it is the left side I _{m (theta)} is the output of the X-ray detector when the theta = 0 in formula (1), the right side of I _{m (0).} Further, since the function E representing the ratio of the generated X-ray intensity is E (m1,0) = 1, the function D representing the attenuation rate at which X-rays are absorbed is D (0, ψ) = 1. Just do it.

Next, when the tangent plane of the surface of the test object is tilted clockwise by θ _y (θ _y is a positive value) with respect to the XY plane, it occurs as shown in FIG. 2B (b). distance the X-ray travels specimen in is shortened by L _1. Since this distance L ₁ increases monotonically as θ _y increases, the function D (θ _y , ψ) representing the attenuation rate at which X-rays are absorbed also monotonically increases. Then, when the maximum value of θ _y is reached, π / 2, the X-rays generated in the test object reach the X-ray detector without being attenuated. At this time, the function D representing the attenuation rate at which X-rays are absorbed must be D (π / 2, ψ) = exp (m2 · cosec ψ). Then, the equation (1) can be an equation that does not include the attenuation term as shown in the following equation (4) in consideration of the equation (3).

The above discussion is the result of consideration for determining the boundary condition of the function D. In reality, θ = θ _y = π / 2, so E (m1, π / 2) = 0. , _Im (π / 2) = 0.

Next, when the tangent plane of the surface of the test object is tilted counterclockwise by θ _y (θ _y is a negative value) with respect to the XY plane, as shown in FIG. 2C (a). distance generated X-rays proceeds with a test substance in becomes longer by L _2. Since this distance L ₂ increases monotonically as θ _y decreases (absolute value increases), the function D (θ _y , ψ) representing the attenuation rate at which X-rays are absorbed decreases monotonically. Then, in the state of FIG. 2C (b) when θ _y = −ψ is reached, the generated X-rays are shielded by the test object, so that the X-ray intensity reaching the X-ray detector is almost zero. .. Therefore, D (−ψ, ψ) = 0 should be set.

Summarizing the above considerations, in Eq. (1), the function D representing the attenuation rate (more accurately, the ratio of the attenuation rate) at which X-rays passing through the test object are absorbed is the Y-axis component θ of the inclination angle θ. It is a function of _y . Further, since the distance through which the X-ray passes depends on the extraction angle ψ of the X-ray detector, it is a function including the extraction angle ψ. Further, as can be seen from the definition of Eq. (3), the function D (m2, θ _y , ψ) has “a coefficient that determines the degree of exponential decay of X-rays passing through the test object” m2. .. As boundary condition of θ _y, θ _y = minimum value D when the -ψ (m2, -ψ, ψ) = 0 , and the monotonically increasing with increasing theta _y, D when theta _y = 0 It must be a function such that (m2,0, ψ) = 1. Further continued to increase monotonically with increasing theta _y, it reaches the _{θ y = π / 2 D (} m2, π / 2, ψ) = a become function exp (m2 · cosecψ). Here, since m2 and ψ take positive values, exp (m2 · cosec ψ)> 1 and D (m2, π / 2, ψ) is a finite value larger than 1.

The material-specific coefficient m2 may be analytically derived for each element from a more detailed theoretical study, or may be numerically analyzed using a well-known simulation technique such as the Monte Carlo method. Alternatively, it may be determined experimentally by the method described later.

As a specific example of the function D (m2, θ _y , ψ) satisfying the above conditions, the following equation (5) can be used.

The specific value of m2 is a real number of about 0 to 2. For example, when using the M line of an element such as W (tungsten) or Au (gold), the value is close to 0.9. On the other hand, for elements such as Ni (nickel) and Ti (titanium), the value is about 0.3 when using the K line, but exceeds 1.0 when using the L line. ..

As shown in FIG. 3, the three-dimensional image generator of the present invention has a first X-ray detector and a first X-ray detector which are opposed to each other with the excitation beam interposed therebetween and whose detection direction is orthogonal to the Y axis. a second X-ray detector, the inclination calculation unit, using the ratio of the output I _{m ^1,} I _m ² of said first and second X-ray detector, the rotational angle (the tilt angle θ It is desirable to calculate the Y-axis component) θ _y .

Rewriting the output _I ^m _{1, I} ^{m 2} of the formula (1) Two X-ray detector, is as follows.

By taking the ratio of the two, the inclination angle θ can be eliminated as shown in the following equation (6).

This equation (6) is solved to obtain the rotation angle (Y-axis component of the inclination angle θ) θ _y around the Y-axis. For that purpose, it is necessary to define a function D (m2, θ _y , ψ) representing the attenuation rate at which X-rays are absorbed, but a function that matches the experimental results may be prepared.

Equation (6) holds only in the range of −ψ <θ _y <ψ. This is because when the tilt angle θ becomes large and the tilt angle θ _y exceeds the X-ray extraction angle ψ, the output of the X-ray detector cannot be obtained because the test object blocks the X-rays. In such a case, the invention described later is used.
In the equation (6), the extraction angles of the two X-ray detectors are the same, but different extraction angles ψ ₁ ≠ ψ ₂ may be used.

Further, as shown in FIG. 4, the three-dimensional image generator of the present invention further includes a third X-ray detector provided in a direction orthogonal to the first and second X-ray detectors. The inclination calculation unit calculates the X-ray component θ _x of the inclination angle θ by using the ratio of the output of the first or second X-ray detector to the output of the third X-ray detector. Is desirable.

Rewriting the output I _{m ^1,} I _m ³ of the two X-ray detector which is orthogonal equation (1), it becomes less.

By taking the ratio of the two, the inclination angle θ can be eliminated as shown in the following equation (7).

When the rotation angle θ _y around the Y-axis is known using the above equation (6) or the like, the rotation angle θ _x around the X-axis can be obtained by solving the equation (7). As the function D (m2, θ _x , ψ) representing the attenuation rate at which X-rays are absorbed, the same function as in the above equation (6) may be used.
Since the equation (7) holds in the range of −ψ <θ _x <90 deg, there is an effect that it can correspond to a range of a wider inclination angle θ than when the above equation (6) is used.

Further, if a fourth X-ray detector (fourth X-ray detector) is added as described later, the range of −90 deg <θ _x <90 deg can be supported. At this time, the X-ray detector that takes the ratio on the left side of the equation (7) should be selected as follows.
An output I _m ¹ of the first X-ray detector a second larger output of the X-ray detector I _m ² selects the denominator of Equation (7).
The larger output of the third X-ray detector _Im ³ and the output of the fourth X-ray detector _Im ⁴ are selected as the numerator of the formula (7).

The three-dimensional image generator of the present invention faces the first X-ray detector and the second X-ray detector provided so as to sandwich the excitation beam, and faces the first X-ray detector. The first and second X-ray detectors are provided with a third X-ray detector and a fourth X-ray detector provided in directions orthogonal to each other, and the inclination calculation unit is two-dimensionally scanned. The output of the four X-ray detectors at each irradiation position of the excitation beam is used to calculate the normal vector at each irradiation position, and the three-dimensional image generation unit calculates the normal at each irradiation position. It is desirable to integrate the vectors to generate a three-dimensional image of the test object.

Specifically, the inclination calculation unit includes the output of either the first X-ray detector or the second X-ray detector, and either the third X-ray detector or the fourth X-ray detector. It is desirable to calculate the normal vector at each irradiation position using one of the outputs and the geometric relational expression regarding the inclination.

Equation (1) can be rewritten for the four orthogonal X-ray detectors as follows.

Further, from the geometrical relationship, the following equation (9) holds.

As described above, the three unknowns theta _x, theta _y, relative theta, since at least three equations is satisfied, by solving this, all unknowns theta _x, theta _y, a theta can be determined.

Further, the normal vector N = (N _x , N _y , N _z ) can be obtained by the following equation.

Therefore, it can be easily obtained.

In order to solve the equations (8x) (8y) and (9), in addition to the function D (m2, θ _y , ψ) representing the attenuation rate at which X-rays are absorbed, the ratio of the generated X-ray intensity is calculated. It is necessary to determine the function E (m1, θ) to be represented, but it is sufficient to prepare a function that matches the experimental results.

In addition, it is preferable to select from the outputs of the four X-ray detectors as follows.
The larger of the output of the first X-ray detector and the output of the second X-ray detector is selected in the equation (8y).
The larger of the output of the third X-ray detector and the output of the fourth X-ray detector is selected in the equation (8x).

Here, the one with the larger output is the X-ray detector with the shorter attenuation distance. That is, since an output having a high SN ratio can be selected, more accurate calculation becomes possible. By selecting the outputs of the four X-ray detectors in this way, the outputs of the X-ray detectors in two directions orthogonal to each other can be obtained. Therefore, −90 deg <θ _x , θ _y. , Θ <90 deg, and the detectable angle can be greatly expanded.
In the equations (8x) and (8y), the extraction angles ψ of the four X-ray detectors are the same, but different extraction angles may be used for each X-ray detector.

In the present invention, the tilt calculation unit calculates the normal vector at each irradiation position using the outputs of the four X-ray detectors, and the three-dimensional image generation unit calculates the normal vector at each irradiation position. When the line vector is integrated to generate a three-dimensional image of the test object, it is desirable to configure it as follows.
That is, in the three-dimensional image generator, the output of the first and second X-ray detectors is less than the predetermined value, or the output of the third and fourth X-ray detectors is less than the predetermined value. It is desirable to exclude the non-existent region and perform the above integration.

When the output I _{m ^1,} I _m ² of the first and second X-ray detector is less than a predetermined value, it is difficult to determine the inclination angle theta _y around the Y axis (or calculation can But the accuracy is poor). Further, when the output of the third and fourth X-ray detector I _{m ^3,} I _m ⁴ is less than a predetermined value, it is difficult to determine the inclination angle theta _x around the X-axis. Therefore, points that satisfy these conditions are excluded from the integration process.

The inclination calculation unit calculates an individual normal vector for each element contained in the test object at each irradiation position of the excitation beam, and weights and adds the individual normal vector corresponding to each element. It is desirable to calculate the composite normal vector. At this time, the three-dimensional image generation unit integrates the composite normal vector to generate a three-dimensional image of the test object.

An X-ray analyzer to which the three-dimensional image generator of the present invention can be applied detects X-rays generated from a test object with an X-ray detector, and detects the test object from the spectrum of characteristic X-rays or fluorescent X-rays. It is an analyzer that performs qualitative analysis or quantitative analysis of the elements contained in. That is, in a test object composed of M elements, the intensity distribution of each element can be obtained two-dimensionally, and M X-ray images can be measured from each of the above-mentioned X-ray detectors. Therefore, since the normal vector N (x, y) _i (i = 1 to M) can be calculated for each element by a predetermined method, the synthetic normal vector N (x, y) can be calculated by the following formula. Can be sought.

Here, _Wi is a weight for the i-th element. Incidentally, the weight W _i may be determined according to the content of the element. Further, the weight _Wi may be set to 1 only for the element having the highest content, and may be set to zero for other elements.
By obtaining the synthetic normal vector in this way, a correct three-dimensional reconstruction result can be obtained even if the test object is composed of a plurality of elements and the component ratio differs depending on the location. Further, even when a foreign substance composed of a different element is partially adhered on a test object composed of a predetermined element, a correct three-dimensional reconstruction result can be obtained.

The two-dimensional scanning direction and scanning range of the excitation beam may be arbitrary. For example, as shown in FIG. 5, a coordinate system X', Y'axis rotated by α = 45 degrees around the Z axis is set with respect to the X and Y axes determined by the arrangement of four X-ray detectors, and X' A square area may be scanned two-dimensionally along the Y'axis. Mutual coordinate conversion between the X and Y axes and the X'and Y'axis can be easily performed using a known rotating coordinate conversion formula.

For example, the normal vector N (x, y) = (N _x , N _y , N _z ) on the surface of the test object is a normal vector with respect to the X and Y axes, but N _x '= N _x cos α-N. Converted to _y sin α, N _y '= N _x sin α + N _y cos α, and the normal vector N (x', y') = (N _x' , N _y' , N _z ) seen from the X', Y'axes. Can be calculated immediately.

Generally, when displaying an image of the output of an X-ray detector, it is desirable to display the vertical-horizontal relationship with reference to the two-dimensional scanning directions X'and Y'axis. On the other hand, when obtaining the normal vector of the surface of the test object from the output of the X-ray detector (since equation (1) and the like are used), it is necessary to use the X and Y axes. Here, the X and Y axes are directions connecting two X-ray detectors facing each other with the excitation beam in between, and do not always coincide with the X'and Y'axes. As described above, the coordinate conversion formula between both coordinate axes may be used.

When two-dimensional scanning of the excitation beam is performed, it may be necessary to correct the output of the X-ray detector according to the scanning position. If the effective detection area of the X-ray detector is small, such correction is not necessary. However, when an X-ray detector having a large effective detection area is used for the purpose of increasing the detection sensitivity, the output of the X-ray detector must be corrected according to the operating position of the excitation beam.
This is because the solid angle facing the effective detection region of the X-ray detector changes three-dimensionally according to the distance between the position where the excitation beam is checked and the X-ray detector. That is, the closer the position where the excitation beam is examined to the X-ray detector, the larger the solid angle. As the solid angle increases, the number of effective X-rays that reach the X-ray detector out of the X-rays that are generated at that position and spread uniformly in all directions increases, so the detected X-ray intensity also increases.
The correction method may be performed as follows. That is, a plane subject made of a single element is placed parallel to the XY plane (in the direction orthogonal to the excitation beam). In this state, a predetermined area is two-dimensionally scanned with an excitation beam, and the X-ray output at each point is recorded. Since the shape of the test object is flat, it is possible to know the change in the output of the X-ray detector with respect to the distance from each point to the X-ray detector according to the scan position of the excitation beam. Normally, it is proportional to the distance, so the proportionality coefficient may be determined by the least squares method or the like.

By the way, when a large-area X-ray detector is used, the detection efficiency of X-rays is high, but the average value of X-rays projected in various directions is measured. Even in such a case, the method of finding the slope of the object tangent plane from the output of the X-ray detector, the method of finding constants such as the material constants required for that, and the method of integrating the slopes to create a three-dimensional shape. The method of calculating is exactly the same. Simply, one point in the X-ray detector may be treated as a representative detection position. For example, in the X-ray detector, the X-ray extraction angle ψ changes between the end on the side closer to the test object and the end on the far side. However, the central position of both may be used as the representative detection position, and the X-ray detector may be treated as if there is a point detection type X-ray detector at this position. The representative detection position may be a geometric center position, or may be arbitrarily determined such as an area center position (a position where the area is even) and an angle center position (a point where the angle is halved).

Further, the coefficient calculation method of the three-dimensional image generator according to the present invention is the calculation method of the coefficients m1 and m2 in the three-dimensional image generator described above, and the two X-ray detectors so that the detection directions are orthogonal to each other. The coefficients m1 and m2 are calculated using the outputs obtained by the two X-ray detectors in a state where the test object having a known shape is tilted or rotated at two or more different known angles. ..

As shown in FIGS. 6 and 7, the tangent plane of the surface of the test object rotates (inclines) only around the Y axis, so that θ _x = 0 and two X-ray detections are performed so that the detection directions are orthogonal to each other. The output of the device (for example, the first X-ray detector and the third X-ray detector in the above) is as follows.

Since two or more different rotation angle theta output of the third X-ray detector relative _y I _m ³ has been found, the function E which represents the ratio of the X-ray intensity generated (m1, theta) material-specific in relation to The coefficient m1 can be determined from the equation (10), and the function E (m1, θ) can be determined. Note that FIG. 6 is an example of θ _y = 30 deg and θ _x = 0 deg, and FIG. 7 is an example of θ _y = 15 deg and θ _x = 0 deg.

Further, the output of the first X-ray detector recorded at the same time is obtained by substituting the equation (10) into the equation (11).

Therefore, the material-specific coefficient m2 related to the function D (m2, θ _y , ψ) representing the attenuation rate at which X-rays passing through the test object are absorbed can be determined from Eq. (12). , The function D (m2, θ _y , ψ) can be defined.

At this time, the number of times the planar test object is rotated (tilted) may be equal to or greater than the number of (undecided) coefficients included in the function E (θ) or D (θ _y , ψ). When the number of times the flat object is rotated (tilted) exceeds the number of (undecided) coefficients, the (undecided) coefficient may be determined by using the least squares method or the like. The number of undetermined coefficients varies depending on how the function E (θ) or D (θ _y , ψ) is determined, but the equation (1) is used.

In the case of, each one of the material-specific coefficients m1 and m2 becomes an undetermined coefficient. In addition, the observed value _Im (0) of the X-ray detector with respect to the XY plane may also be an undetermined coefficient. However, when _Im (0) is determined, the measurement is performed in a state where θ _x = θ _y = 0, that is, a state in which the planar object is parallel to the XY plane (a state orthogonal to the excitation beam). It is better to do it.

Further, when the planar test object is orthogonal to the excitation beam, the outputs of the four X-ray detectors are the same.
Utilizing this, it is also possible to determine the origin of the rotation angle of the test object. That is, the inclination may be adjusted so that the outputs of the four X-ray detectors are the same with respect to the flat object, and the posture may be the origin of the object rotation angle.

Further, the excitation beam may be scanned in a predetermined range in the XY plane, and the X-rays generated from each scanning position may be sequentially recorded. By averaging the recording results corresponding to all scanning positions, the influence of measurement noise such as random noise can be eliminated.

When scanning the excitation beam, the shape of the test object may be unknown. This is because if the outputs of the four X-ray detectors are the same, the tangent plane of the test object at that position is parallel to the XY plane. After searching for a position where the outputs of the four X-ray detectors are the same, the test object may be rotated (tilted) and the output of the X-ray detectors at that position may be used.

By applying this, even if the object has an unknown shape, at least the observed value _Im (0) of the X-ray detector with respect to the XY plane can always be measured (without rotating the object). It turns out that there is. That is, the excitation beam may be scanned in a predetermined range in the XY plane to search for a position where the outputs of the four X-ray detectors are the same. From equation (13), the observed value _Im (0) of the X-ray detector with respect to the XY plane can be calculated immediately. Taking the average value at a plurality of positions is more convenient because the influence of measurement noise such as random noise can be eliminated.

As another application example, for example, when a cylindrical test object is used, its ridgeline can be obtained. Even if the shape such as the diameter is unknown, the tangent plane is parallel to the XY plane on the ridgeline of the cylindrical surface, so that the outputs of the four X-ray detectors are the same. Therefore, the ridgeline of the cylindrical surface can be obtained by searching for a position where the outputs of the four X-ray detectors are the same.

Further, the coefficient calculation method of the three-dimensional image generator according to the present invention is the calculation method of the coefficients m1 and m2 in the above-mentioned three-dimensional image generator, and the two X-ray detectors so that the detection directions are orthogonal to each other. Is arranged, and a cylindrical test object is installed with its axial direction provided in a direction orthogonal to the excitation beam and in a direction toward the detection direction of one X-ray detector, and the excitation beam is scanned. Therefore, the coefficients m1 and m2 are calculated using the outputs obtained by the two X-ray detectors at each scanning position.

With this method, the tangent plane (see FIG. 8) at each point in the circumferential direction of the cylinder can secure the same situation as the above-mentioned calculation method (plane rotated around the Y axis), so that the test is performed. Results for a large number of angles can be obtained in a single measurement over a wide angle range of -90 deg to 90 deg without the trouble of tilting an object, and material-specific coefficients m1 and m2 can be determined with high accuracy. Further, since the values of E (m1, θ) and D (m2, θ _y , ψ) for a large number of angles over a wide angle range can be obtained, E (m1, θ) and D (m2, θ _y ) for the angle θ can be obtained. , Ψ) reference table can be prepared. Therefore, it is not necessary to assume specific functions of E (m1, θ) and D (m2, θ _y , ψ).

Further, it is desirable to average the output of the X-ray detector and process the points having the same circumferential coordinates of the cylindrical test object. If the circumferential coordinates of the cylinder are the same, the inclination θ _y around the Y axis will be the same even if the positions are different in the axial direction (Y axis direction). That is, since the same measurement conditions are satisfied, the influence of measurement noise and the like can be eliminated by averaging.

According to the present invention described above, a three-dimensional image of a test object can be generated using X-rays generated from the test object.

It is a figure which shows the definition of the coordinate system of this invention. It is a figure for demonstrating the derivation of E (m1, θ) and D (m2, θ _y , ψ). It is a figure for demonstrating the derivation of E (m1, θ) and D (m2, θ _y , ψ). It is a figure for demonstrating the derivation of E (m1, θ) and D (m2, θ _y , ψ). It is a figure for _{demonstrating} the calculation method of the rotation angle θ _y about the Y axis. It is a figure for _{demonstrating} the calculation method of the rotation angle θ _x around the X axis. It is a figure which shows the XY'axis rotated 45 degrees around the Z axis with respect to the XY axis determined by the arrangement of the X-ray detector. It is a figure for demonstrating the calculation method of the coefficient m1 and m2. It is a figure for demonstrating the calculation method of the coefficient m1 and m2. It is a figure for demonstrating another calculation method of coefficients m1 and m2. It is an overall schematic diagram of the 3D image generation apparatus which concerns on one Embodiment of this invention. It is a figure which shows the example of three-dimensional reconstruction (tungsten W, a cylinder with a diameter of 1 mm). It is a figure which shows the example of three-dimensional reconstruction (tungsten W, a cylinder with a diameter of 1 mm). It is a figure which shows the measurement result of the 3rd X-ray detector when the averaging process is not performed. It is a figure which shows the measurement result of the 3rd X-ray detector when the averaging process is performed. It is a figure which shows the measurement result of the 1st X-ray detector when the averaging process is performed.

Hereinafter, the three-dimensional image generator according to the embodiment of the present invention will be described with reference to the drawings.

<Overall configuration>
As shown in FIG. 9, the three-dimensional image generator 100 of the present embodiment has an irradiation unit 2 that irradiates the test object S with the excitation beam EB and X-rays generated from the test object S irradiated with the excitation beam EB. The tilt calculation unit 4 and the tilt calculation unit 4 calculate information on the surface tilt of the test object S from the outputs of the four X-ray detectors 31 to 34, and the four X-ray detectors 31 to 34. It is provided with a three-dimensional image generation unit 5 that generates a three-dimensional image of a test object by three-dimensional reconstruction using the obtained tilt information. The number of X-ray detectors 3 is not limited to four, and one or more X-ray detectors may be provided. The tilt calculation unit 4 and the three-dimensional image generation unit 5 of the present embodiment are composed of a computer including a CPU, an internal memory, an input / output interface, an AD converter, input means such as a keyboard and a mouse, and a display.

Each part will be described below.

The irradiation unit 2 includes an electron gun 21 that irradiates the test object S with an electron beam as the excitation beam EB, and a scanning unit 22 that two-dimensionally scans the excitation beam EB from the electron gun 21.

The four X-ray detectors 31 to 34 face each other with the excitation beam EB sandwiched between the first X-ray detector 31 and the second X-ray detector 32 provided so as to face each other with the excitation beam EB interposed therebetween. , The first and second X-ray detectors 31 and 32 are composed of a third X-ray detector 33 and a fourth X-ray detector 34 provided in a direction orthogonal to each other.

The tilt calculation unit 4 uses the outputs of the four X-ray detectors 31 to 34 at each irradiation position of the two-dimensionally scanned excitation beam EB, and tilt information (specifically, a normal vector) at each irradiation position. ) Is calculated.

Specifically, the inclination calculation unit 4 calculates information on the inclination of the surface of the test object S by using the following equation (1).

Here, θ is an inclination angle formed by the tangent plane of the test object S at the irradiation position of the excitation beam EB and the XY plane orthogonal to the Z axis which is the irradiation direction of the excitation beam EB (see FIG. 1).
ψ is the X-ray extraction angle of the X-ray detectors 31 to 34 with respect to the XY plane (see FIG. 1).
θ _y is a rotation angle around the Y axis (inclination angle of the tangent plane) with the direction orthogonal to the plane including the detection directions of the X-ray detectors 31 and 32 and the irradiation direction (Z axis) of the excitation beam EB as the Y axis. (Y-axis component of θ) (see FIG. 3). The X-axis component of the inclination angle θ of the tangent plane is θ _x (see FIG. 4).
E (m1, θ) is a function representing the ratio of the generated X-ray intensity, and D (m2, θ _y , ψ) is the ratio of the attenuation rate at which the X-ray passing through the test object S is absorbed. Is a function that represents.
m1 is a material-specific coefficient determined by an element that generates X-rays, and m2 is a material-specific coefficient that is determined by at least an element that generates X-rays and an element that absorbs X-rays.
_Im (0) is the output of the X-ray detectors 31 to 34 when the surface of the test object is parallel to the XY plane.

Here, specific examples of Im are the following equations using the equations (2) and (5).

More specifically, the tilt calculation unit 4 has the output of either the first X-ray detector 31 or the second X-ray detector 32 (the following equation (8y)) and the third X-ray detection. Each irradiation is performed using the output of either the device 33 or the fourth X-ray detector 34 (the following formula (8x)) and the geometric relational expression regarding the inclination (the following formula (9)). Calculate θ _x , θ _y , and θ at the position.

Then, the slope calculation unit 4 calculates the normal vector N = (N _x , N _y , N _z ) at each irradiation position using the following equation.

The three-dimensional image generation unit 5 integrates the normal vector N = (N _x , N _y , N _z ) at each irradiation position obtained by the inclination calculation unit 4 and reconstructs the three-dimensional object S. Generate a three-dimensional image of.

Here, if the output I _{m ^1,} I _m ² of the first and second X-ray detector 31, 32 is less than the predetermined value, it is difficult to determine the inclination angle theta _y around the Y axis (Alternatively, the calculation is possible but the accuracy is poor). Also, if the output _I ^m _{3, I} ^{m 4} of the third and fourth X-ray detector 33, 34 is less than the predetermined value, it is difficult to determine the inclination angle theta _x around the X-axis.

Therefore, the three-dimensional image generating unit 5, a region where the output _I ^m _{1, I} ^{m 2} of the first and second X-ray detector 31, 32 is less than a predetermined value, or the third and fourth X it is also possible to output I _{m ^3,} I _m ⁴ line detector 33 performs the integration process by excluding an area less than the predetermined value (3D reconstruction).

FIG. 10 shows an example in which a cylinder of tungsten W having a diameter of 1 mm is three-dimensionally reconstructed. In this example, the output I _m ¹ ~I _m ⁴ of the four X-ray detectors 3 to 34 is not less than a predetermined value, a three-dimensional reconstruction result of the integration process for every region.

On the other hand, FIG. 11 also, although an example in which three-dimensional reconstruction of the cylinder diameter 1mm tungsten W, a region where the output _I ^m 1 _~I ^{m 4} of the four X-ray detectors 3 to 34 is less than a predetermined value Yes, this is the result of three-dimensional reconstruction in which the region is excluded and the integration process is performed.

<Calculation method of coefficients m1 and m2>
Next, an example of the calculation method of the coefficients m1 and m2 of the above formula (1) will be described.
The calculation method of the coefficients m1 and m2 is as follows: At least two X-ray detectors (first X-ray detector in FIG. 6) arranged in directions in which the detection directions are orthogonal to each other (X-ray direction and Y-axis direction in FIG. 6). A device 31 and a third X-ray detector 33) are arranged, and two X-ray detectors 31 and 33 are used in a state in which a test object having a known shape is tilted or rotated at two or more different known angles. The coefficients m1 and m2 are calculated using the obtained outputs _Im ¹ and _Im ³ .

As shown in FIGS. 6 and 7, the tangent plane of the surface of the test object rotates (inclines) only around the Y axis, so that θ _x = 0 and two X-ray detections are performed so that the detection directions are orthogonal to each other. The outputs _Im ¹ and _Im ³ of the device (first X-ray detector 31 and third X-ray detector 33) are as follows. Note that FIG. 6 is an example of θ _y = 30 deg and θ _x = 0 deg, and FIG. 7 is an example of θ _y = 15 deg and θ _x = 0 deg.

Since two or more different rotation angle theta output of the third X-ray detector relative _y I _m ³ has been found, the function E which represents the ratio of the X-ray intensity generated (m1, theta) material-specific in relation to The coefficient m1 can be determined from the equation (10), and the function E (m1, θ) can be determined.

Further, the output I _m ¹ of the first X-ray detectors simultaneously recorded,

Therefore, the material-specific coefficient m2 related to the function D (m2, θ _y , ψ) representing the attenuation rate at which X-rays passing through the test object are absorbed can be determined from Eq. (12). , The function D (m2, θ _y , ψ) can be defined.

At this time, the number of times the planar test object is rotated (tilted) may be equal to or greater than the number of (undecided) coefficients included in the function E (θ) or D (θ _y , ψ). When the number of times the flat object is rotated (tilted) exceeds the number of (undecided) coefficients, the (undecided) coefficient may be determined by using the least squares method or the like. The number of undetermined coefficients varies depending on how the function E (θ) or D (θ _y , ψ) is determined, but the equation (1) is used.

In the case of, each one of the material-specific coefficients m1 and m2 becomes an undetermined coefficient. In addition, the observed value _Im (0) of the X-ray detector with respect to the XY plane may also be an undetermined coefficient. However, when _Im (0) is determined, the measurement is performed in a state where θ _x = θ _y = 0, that is, a state in which the planar object is parallel to the XY plane (a state orthogonal to the excitation beam). It is better to do it.

In a state where flat specimen is perpendicular to the excitation beam, the output _I ^m 1 _~I ^{m 4} of the four X-ray detectors 31 to 34 are the same (Formula (13)). Utilizing this, it is also possible to determine the origin of the rotation angle of the test object. That is, the plane shape of the test object, the four output I _m ¹ of the X-ray detector 31 to 34 ~I _m ⁴ adjusts the inclination such that the same becomes the origin of the object rotation angle posture thereof And it is sufficient.

Further, the excitation beam may be scanned in a predetermined range in the XY plane, and the X-rays generated from each irradiation position may be sequentially recorded. By averaging the recording results corresponding to all irradiation positions, the influence of measurement noise such as random noise can be eliminated.

When scanning the excitation beam, the shape of the test object may be unknown. If four output _I ^m 1 of the X-ray detector 31 to 34 _~I ^{m 4} are the same, the tangent plane of the object at that position is because parallel to the XY plane. Four output _I ^m 1 _~I ^{m 4} of the X-ray detector 31 to 34 is to search the position at which the same rotates the test object (slope), the X-ray detector 31 to 34 in that position may be utilized output _I ^m 1 _~I ^{m 4.}

By applying this, even if the object has an unknown shape, at least the observed value _Im (0) of the X-ray detector with respect to the XY plane can always be measured (without rotating the object). It turns out that there is. That is, the excitation beam by scanning in a predetermined range in the XY plane, may be searching for a position where the four output _I ^m 1 _~I ^{m 4} of the X-ray detector 31 to 34 is the same. From equation (13), the observed value _Im (0) of the X-ray detector with respect to the XY plane can be calculated immediately. Taking the average value at a plurality of positions is more convenient because the influence of measurement noise such as random noise can be eliminated.

As another application example, for example, when a cylindrical test object is used, its ridgeline can be obtained. Even if the diameter is unknown, the tangent plane is parallel to the XY plane on the ridgeline of the cylindrical surface, so that the outputs of the four X-ray detectors are the same. Therefore, the ridgeline of the cylindrical surface can be obtained by searching for a position where the outputs of the four X-ray detectors are the same.

Further, as another example of the calculation method of the coefficients m1 and m2, the following may be performed.
As shown in FIG. 8, the calculation method of the coefficients m1 and m2 is as follows: two X-ray detectors (in the above example, the first X-ray detector 31 and the third X) so that the detection directions are orthogonal to each other. A line detector 33) is arranged so that the columnar object is orthogonal to the excitation beam and is in the detection direction of one X-ray detector (third X-ray detector 33 in FIG. 8). toward the direction (Y axis direction) laid with its center axis direction, by scanning the electron beam EB, the output I _{m 1} obtained by the two X-ray detectors 31, 32 at each irradiation ^position, I _m ^The coefficients m1 and m2 are calculated using ³ .

With this method, the tangent plane (see FIG. 8) at each point in the circumferential direction of the cylinder can secure the same situation as the above-mentioned calculation method (plane rotated around the Y axis), so that the test is performed. Results for a large number of angles can be obtained in a single measurement over a wide angle range of -90 deg to 90 deg without the trouble of tilting an object, and material-specific coefficients m1 and m2 can be determined with high accuracy. Further, since the values of E (m1, θ) and D (m2, θ _y , ψ) for a large number of angles over a wide angle range can be obtained, E (m1, θ) and D (m2, θ _y ) for the angle θ can be obtained. , Ψ) reference table can be prepared. Therefore, it is not necessary to assume specific functions of E (m1, θ) and D (m2, θ _y , ψ).

Further, it is desirable to average the output of the X-ray detector and process the points having the same circumferential coordinates of the cylindrical test object. If the circumferential coordinates of the cylinder are the same, the rotation angle (inclination) θ _y around the Y axis is the same even if the positions are different in the axial direction (Y axis direction). That is, since the same measurement conditions are satisfied, the influence of measurement noise and the like can be eliminated by averaging.

FIG. 12 shows the measurement result of the third X-ray detector 33 when the averaging process is not performed. The output of the third X-ray detector 33 at each position of the rotation angle (tilt) θ _y around the Y axis shown on the horizontal axis is plotted with a circle. It can be seen that the measurement noise is very large.

FIG. 13 shows the measurement result of the third X-ray detector 33 when the averaging process is performed in the axial direction (Y-axis direction). It can be seen that the measurement noise can be significantly reduced. The result of fitting (regressing) E (m1, θ _y ) of the equation (10) using the least squares method is shown by a dotted line. It can be seen that the two are in perfect agreement. That is, the validity of using the function shown in Eq. (2) can be confirmed as the function E (m1, θ) representing the ratio of the generated X-ray intensities.

Further, FIG. 14 shows the measurement result of the first X-ray detector 31 when the averaging process is performed. Further, the function E (m1, θ _y ) representing the ratio of the generated X-ray intensities obtained from the measurement result of FIG. 13 is shown by a dotted line. Since FIGS. 13 and 14 are data measured at the same time, the generated X-ray intensities are the same. Fitting D (m2, θ _y , ψ) of equation (12) to the measurement result (measurement result of 31 of the first X-ray detector) shown by a circle in FIG. 14 using the least squares method ( Regression). The ratio (relative value) of the X-ray intensity actually observed is the product of the function E (m1, θ) and the function D (m2, θ _y , ψ), which is shown by a solid line in FIG. It can be seen that this also agrees well with the measurement results. That is, the validity of using the function shown in Eq. (5) can be confirmed as the function D (m2, θ _y , ψ) representing the attenuation rate at which X-rays passing through the test object are absorbed.

<Effect of this embodiment>
According to the three-dimensional image generation device 100 of the present embodiment, the inclination calculation unit 4 calculates information on the inclination of the surface of the test object from the outputs of the four X-ray detectors 31 to 34, and the three-dimensional image generation unit 5 Generates a three-dimensional image of the test object by three-dimensional reconstruction using the slope information (specifically, the normal vector) obtained by the slope calculation unit 4, so that X-rays generated from the test object are used. A three-dimensional image of the test object can be generated.

At this time, since the tilt information is integrated to generate a three-dimensional image, the position of each pixel of the X-ray image obtained by two-dimensionally scanning the excitation beam is in the Z-axis direction of the surface of the test object. You can know the relative height. Therefore, the unevenness of the surface of the test object can be measured as a cross-sectional shape along an arbitrary direction, and the height of the step can be easily measured. Furthermore, it is possible to evaluate the quality of the cross-sectional shape and the surface shape such as "surface roughness" and "waviness".

Further, in the three-dimensional image generation device 100 of the present embodiment, since individual X-ray images can be acquired for a plurality of elements, the difference between the elements at the positions of each pixel can be identified. As a result, it is possible to reliably determine whether the unevenness of the test object is due to the adhesion of a foreign substance (a substance whose contained element is different from that of the test object), or whether it is a defect or scratch on the surface. Furthermore, since the type of foreign matter can be identified, it is possible to estimate the cause of the foreign matter adhering. With the conventionally known "device that generates a three-dimensional image using multiple secondary electron detectors", even if the unevenness of the test object can be confirmed, the difference in elements cannot be identified, so it is a foreign substance or a scratch. I can't even judge.

<Other modified embodiments>
The present invention is not limited to the above embodiment.

For example, in the above-described embodiment, four X-ray detectors are used, but any X-ray detector may be used as long as it has one or more X-ray detectors.

Further, the inclination calculation unit 4 calculates an individual normal vector for each element contained in the test object at each irradiation position of the excitation beam, and weights and adds the individual normal vector corresponding to each element. It may be the one that calculates the composite normal vector. At this time, the three-dimensional image generation unit 5 integrates the composite normal vector to generate a three-dimensional image of the test object.

Specifically, the slope producing unit 4 calculates the normal vector N (x, y) _i (i = 1 to M) for each element, and the synthetic normal vector N (x, y) is as follows. Obtained by the formula.

Here, _Wi is a weight for the i-th element. Incidentally, the weight W _i may be determined according to the content of the element. Further, the weight _Wi may be set to 1 only for the element having the highest content, and may be set to zero for other elements.
By obtaining the synthetic normal vector in this way, a correct three-dimensional reconstruction result can be obtained even if the test object is composed of a plurality of elements and the component ratio differs depending on the location. Further, even in the case where a foreign substance composed of a different element is partially adhered on the test object composed of a predetermined element, a correct three-dimensional reconstruction result can be obtained.

In addition, various embodiments may be modified or combined as long as it does not contradict the gist of the present invention.

100 ・ ・ ・ Three-dimensional image generator S ・ ・ ・ Subject 2 ・ ・ ・ Irradiation part EB ・ ・ ・ Excitation beam 31 ・ ・ ・ First X-ray detector 32 ・ ・ ・ Second X-ray detector 33 ・ ・ ・ Third X-ray detector 34 ・ ・ ・ Fourth X-ray detector 4 ・ ・ ・ Tilt calculation unit 5 ・ ・ ・ Three-dimensional image generation unit

Claims (12)

An irradiation part that irradiates the test object with an excitation beam,
An X-ray detector that detects X-rays generated from the subject irradiated with the excitation beam, and
An inclination calculation unit that calculates information on the inclination of the surface of the test object from the output of the X-ray detector,
A three-dimensional image generation device including a three-dimensional image generation unit that generates a three-dimensional image of the test object by three-dimensional reconstruction using the inclination information obtained by the inclination calculation unit. Let θ be the inclination angle formed by the tangent plane of the test object at the irradiation position of the excitation beam and the XY plane orthogonal to the Z axis which is the irradiation direction of the excitation beam.
Let ψ be the X-ray extraction angle of the X-ray detector with respect to the XY plane.
The rotation angle around the Y axis (the Y axis of the inclination angle θ of the tangent plane) is defined as the direction orthogonal to the plane including the detection direction of the X-ray detector and the irradiation direction (Z axis) of the excitation beam. If the component) is θ _y ,
The three-dimensional image generation device according to claim 1, wherein the inclination calculation unit calculates information on the inclination of the surface of the test object by using the following formula (1).
Here, E (m1, θ) is a function representing the ratio of the generated X-ray intensity, and D (m2, θ _y , ψ) is the attenuation at which the X-ray passing through the test object is absorbed. It is a function that expresses the ratio of rates. Further, m1 is a material-specific coefficient determined by an element that generates X-rays, and m2 is a material-specific coefficient that is determined by at least an element that generates X-rays and an element that absorbs X-rays. Further, _Im (0) is the output of the X-ray detector when the surface of the test object is parallel to the XY plane. The inclination calculation unit is an even function with respect to the inclination angle θ of the tangent plane as a function E (m1, θ) representing the ratio of the X-ray intensity generated by the equation (2), and is a maximum value E at θ = 0. (M1,0) = 1, and it decreases monotonically with the increase of the absolute value of the inclination angle θ, and E (m1, ± π / 2) = 0 at θ = ± π / 2, using a function. The three-dimensional image generation device according to claim 2, which calculates information regarding the inclination of the surface of the test object. The inclination calculation unit is an inclination angle of the tangent plane as a function D (m2, θ _y , ψ) representing the ratio of the attenuation rate at which X-rays passing through the test object of the equation (2) are absorbed. relative theta of Y-axis component θ _y, θ = D in -ψ (m2, -ψ, ψ) = 0 , and the monotonically increasing with increasing theta _y, in θ _y = 0 D (m2 , 0, ψ) = 1, and at θ _y = π / 2, D (m2, π / 2, ψ) = A (A is a finite value greater than 1). The three-dimensional image generator according to claim 2, which calculates information regarding the inclination of the surface of the above. It is provided with a first X-ray detector and a second X-ray detector which are opposed to each other with the excitation beam in between and are provided so that the detection direction is orthogonal to the Y axis.
The three-dimensional image according to any one of claims 1 to 4, wherein the inclination calculation unit calculates the rotation angle θ _y by using the ratio of the outputs of the first and second X-ray detectors. Generator. Further, a third X-ray detector provided in a direction orthogonal to the first and second X-ray detectors is provided.
The inclination calculation unit calculates the X-ray component θ _x of the inclination angle by using the ratio of the output of the first or second X-ray detector to the output of the third X-ray detector. The three-dimensional image generator according to claim 5. A first X-ray detector and a second X-ray detector provided so as to face each other across the excitation beam,
It is provided with a third X-ray detector and a fourth X-ray detector that face each other with the excitation beam in between and are provided in a direction orthogonal to the first and second X-ray detectors.
The inclination calculation unit calculates a normal vector at each irradiation position by using the outputs of the four X-ray detectors at each irradiation position of the excitation beam scanned two-dimensionally.
The three-dimensional image generation device according to any one of claims 1 to 6, wherein the three-dimensional image generation unit integrates normal vectors at each irradiation position to generate a three-dimensional image of the test object. The inclination calculation unit includes the output of either the first X-ray detector or the second X-ray detector, and the output of either the third X-ray detector or the fourth X-ray detector. The three-dimensional image generator according to claim 7, wherein a normal vector at each irradiation position is calculated using an output and a geometric relational expression relating to inclination. In the three-dimensional image generator, the output of the first and second X-ray detectors is less than a predetermined value, or the output of the third and fourth X-ray detectors is less than a predetermined value. The three-dimensional image generator according to claim 7 or 8, wherein the integration is performed excluding a region. The inclination calculation unit calculates an individual normal vector for each element contained in the examination object at each irradiation position of the excitation beam as information regarding the inclination of the surface of the examination object, and corresponds to each element. The three-dimensional image generation apparatus according to any one of claims 1 to 9, wherein a composite normal vector obtained by weighting and adding individual normal vectors is calculated. The method for calculating the coefficients m1 and m2 in the three-dimensional image generator according to any one of claims 2 to 4.
Two X-ray detectors are placed so that the detection directions are orthogonal to each other.
A method of calculating coefficients m1 and m2 using the outputs obtained by the two X-ray detectors in a state where a test object having a known shape is tilted or rotated at two or more different known angles. The method for calculating the coefficients m1 and m2 in the three-dimensional image generator according to any one of claims 2 to 4.
Two X-ray detectors are placed so that the detection directions are orthogonal to each other.
A cylindrical test object is installed with its axial direction provided in a direction orthogonal to the excitation beam and in a direction toward the detection direction of one of the X-ray detectors.
A method in which the excitation beam is scanned and the coefficients m1 and m2 are calculated using the outputs obtained by the two X-ray detectors at each scanning position.