JP2015099145A - Diffraction ring analysis method and diffraction ring analyzer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a diffraction ring analysis method capable of analyzing a diffraction ring and improving accuracy even if the diffraction ring has a missing part.SOLUTION: A diffraction ring analysis method includes: irradiating a specific part of a measurement target with a beam exhibiting a diffraction property, and measuring a strain using a central angle α of a diffraction ring formed by a diffraction beam reflected by this specific part (S21, S22); performing Fourier transform on this measurement result (S23); and calculating at least either a stress or strain of the specific part from a result of this Fourier transform (S24).

Description

  The present invention irradiates a specific part of an object to be measured with a beam having the property of diffracting X-rays and Fourier transforms the deformation of the diffraction ring formed by the diffracted beam, thereby obtaining strain and stress of the specific part. The present invention relates to a diffraction ring analysis method and a diffraction ring analysis apparatus.

  With respect to conventional diffraction ring analyzers, there are an X-ray diffractometer disclosed in Patent Document 1, a triaxial stress measurement method disclosed in Patent Document 2, and the like.

  In Non-Patent Document 1, the cosα method, which is one of the X-ray stress measurement methods disclosed in Non-Patent Document 2, is developed to analyze the two-dimensional data of the diffracting ring, thereby obtaining a single plane stress component. A method of simultaneously measuring by X-ray irradiation is disclosed. The method will be described with reference to the drawings.

FIG. 30 is a diagram showing a coordinate system, incident X-rays, and a diffraction ring when X-rays are irradiated on the surface of the measurement object. As shown in the figure, an X-ray beam 1 is irradiated onto a specific portion 3 of a sample 2 that is a measurement object, and a diffraction ring 5 (Debye ring) is imaged on an imaging unit 6 by the diffraction beam 4. In the figure, ε _α represents the deformation of the diffraction ring at the circumferential angle α, and η is an additional angle of the diffraction angle θ determined by the crystal lattice spacing and the X-ray wavelength (that is, η is 90 ° -θ). Ψ ₀ is an angle formed by the normal line of the surface of the measurement object and the incident beam, and φ ₀ is an angle formed by the projection line of the X-ray beam onto the surface of the measurement object and the x axis of the measurement object.

  In the stress measurement using the diffraction ring 5, when the specific portion 3 of the sample 2 is strained, as shown in FIG. 31, the strain of the sample 2 is shifted to a position deviated from the circular diffraction ring 8 when there is no strain. As a result, an X-ray diffraction ring 9 which is deformed in accordance with is generated.

  The cos α method is to obtain the strain (stress state) of the sample 2 from the deformation of the diffraction ring 9. This method can be used for other than X-rays as long as the beam has a property of being diffracted by a crystal, such as a neutron beam.

In the cos α method, when the deformation measured at the point of the central angle α on the diffraction ring 9 is represented by ε _α , the central angles α, π + α, −α, π-α are obtained from the diffraction ring 9 as shown in FIG. The deformations ε _α , ε _{π + α} , ε _−α , and ε _π-α in four directions are measured. Then, from these four measured values, values of four parameters calculated by the following formulas (1) to (4) are obtained.

FIG. 33 to FIG. 36 show the relationship of the measured values of the four parameters with the vertical axis and cos α, sin α, cos 2α, and sin 2α on the horizontal axis. As can be seen from Figure 33, cos [alpha] and epsilon ^- _alpha clear that linear proportional relationship between (superscript bar) is observed. That is, when the parameter ε ⁻ _α (with the upper bar) of equation (1) is plotted with respect to cosα, a linear relationship is obtained, and by applying equation (9) of Non-Patent Document 1 to the slope of the straight line, Strain (stress state) can be obtained (in this example, stress σ _{x in the} x direction).

On the other hand, in (2) to (4), the linear relationship is not so clear (FIGS. 34 to 36). This is a cos [alpha] method epsilon ^- _alpha (superscript bar), epsilon ^~ _alpha (superscript tilde), E _1, E ₂ and cosα, sinα, cos2α, although the relationship between the sin2α is respectively a straight line, this assumption This is because the stress state of the object to be measured is limited to an ideal case. Actually, the stress state of the object to be measured deviates from an ideal case, and as a result, deviation from a straight line occurs as shown in FIGS. This deviation includes information on the physical state of the object to be measured, but it is difficult to handle the information by the cos α method for obtaining strain (stress state) from linear approximation.

In the cos α method, parameters are always calculated with a set of four points on the diffraction ring (FIG. 32), so that it is difficult to calculate stress in a diffraction ring with a part missing as shown in FIG. 37 (FIG. 37). In the example, ε ^- _α (with an upper bar), ε ^to _α (with an upper tilde), E ₁ and E ₂ parameters cannot be calculated.

  As an example of a missing diffraction ring, Non-Patent Document 3 shows a spotted diffraction ring (that is, a granularity). Non-Patent Document 3 discloses a software rocking method as an image processing method for accurately obtaining stress from a spotted diffraction ring. However, in the diffraction ring as shown in FIG. Application is difficult.

JP-A-2005-241308 JP 2011-27550 A

Toshihiko Sasaki and Yukio Hirose “Single-incidence X-ray stress measurement of all plane stress components using a two-dimensional X-ray detector imaging plate”, Materials Vol.44, No.504, pp.1138-1143, (1995) Shuji Hira, Keisuke Tanaka, Toshiharu Yamazaki “A Method of Stress Measurement for Fine Bundles and Its Application to Fatigue Crack Propagation Problems” Material Vol.27, pp.251-256, (1978) Toshihiko Sasaki, Yukio Hirose, Shoichi Yaskawa “X-ray Macro Stress Measurement of Coarse Grained Materials Using Imaging Plate”, Transactions of the Japan Society of Mechanical Science (A), 63, pp.533-541, (1997)

  According to Non-Patent Document 1 and Non-Patent Document 2, there are the following problems due to the numerical processing of the cos α method.

  First, when the diffraction ring is missing (for example, FIG. 37), the calculation accuracy of the stress deteriorates or cannot be calculated.

  Secondly, since the distortion at 4 points is added and subtracted, the parameter to be extracted always includes a measurement value error for 4 points. This degrades the S / N ratio.

  Thirdly, the strain information of the diffraction ring includes information on many stress states of the measurement object. However, since the information is aggregated into four parameters, a lot of information is lost.

  An object of the present invention is to provide a diffraction ring analysis method and apparatus for analyzing a diffraction ring and improving accuracy even when the diffraction ring is missing.

  The first diffraction ring analysis method of the present invention irradiates a specific part of an object to be measured with a beam having a diffracting property, measures a diffraction ring formed by the diffraction beam reflected from the specific part, The deformation of the ring is subjected to Fourier transform, and at least one of stress or strain at a specific portion is calculated from the result. With this configuration, it is possible to accurately determine the stress or strain of a specific part of the measurement object, and it is possible to analyze the strain (stress state) of the measurement object even when the diffraction ring is missing. .

To obtain the Fourier series specifically, create a list of the relationship between the diffraction ring deformation ε _α and the center angle α of the diffraction ring, and apply an algorithm such as Fast Fourier Transform (FFT) to it. Ask for. The coefficient of the Fourier series can also be obtained by calculating the correlation with cosα, sinα, cos2α, sin2α,.

  The second diffractive ring analysis method of the present invention is the same as the first diffractive ring analysis method, in addition to the Fourier series coefficient, the Young's modulus, the Poisson's ratio, the residual angle of the diffraction angle, and the method for the surface of the measurement object. An operation using the angle formed by the line and the incident beam may be performed on the measurement result. With this configuration, the stress or strain of a specific portion of the measurement object can be obtained more accurately.

  In the third diffraction ring analysis method of the present invention, in the first or second diffraction ring analysis method, when there is a missing part in a part of the diffraction ring, information on the measured diffraction ring and the center angle α of the missing part is obtained. From the above, a method of estimating the Fourier series of the diffraction ring when there is no omission using the properties of the Fourier series may be used. Thereby, even if the diffraction ring is missing, the strain (stress state) of the measurement object can be accurately analyzed.

  The fourth diffractive ring analysis method of the present invention uses at least coefficients from the 0th order to the second order among the Fourier series obtained as a result of the Fourier transform in the first, second or third diffractive ring analysis method. May be. Here, at least one of the first-order coefficient and the second-order coefficient may be used. With this configuration, it is possible to analyze the diffractive ring more accurately than in the conventional cos α method without using higher-order coefficients.

The fifth diffractive ring analysis method of the present invention is the first, second, third or fourth diffractive ring analysis method, wherein the coefficients of the first and second order Fourier series are a ₁ , b ₁ , a ₂ , When b ₂ is assumed, the stress of the object to be measured is assumed to be plane stress, and the vertical stresses σ _{x and} σ _y in the x-axis and y-axis directions are respectively
And the shear stress τ _xy
It may be calculated by at least one of the two formulas. Here, E is the Young's modulus, ν is the Poisson's ratio, η is the remainder of the diffraction angle, and ψ ₀ is the angle between the normal of the surface of the measurement object and the incident X-ray beam.

  With this configuration, the normal stress and the shear stress can be accurately obtained.

  The first diffractive ring analyzer of the present invention images a beam irradiation unit that irradiates a specific part of a measurement object with a beam having a diffracting property, and images a diffracted beam reflected from the specific part, and diffracts it on the imaging surface An imaging unit that forms a ring and a data processing unit that performs Fourier transform on a measurement result obtained by the imaging unit and calculates at least one of stress or strain of the specific part. With this configuration, it is possible to accurately determine the stress or strain of a specific portion of the measurement object, and it is possible to provide an apparatus for analyzing a diffraction ring even when the diffraction ring is missing.

  The second diffractive ring analyzer of the present invention is the first diffractive ring analyzer, wherein the imaging unit may be a solid X-ray imaging device or an imaging play using a semiconductor. With this configuration, the diffraction ring can be accurately measured.

  According to the diffraction ring analysis method and apparatus of the present invention, it is possible to analyze a diffraction ring and improve accuracy even when the diffraction ring is missing.

  In other words, first, even when there is a missing diffraction ring (for example, FIG. 37), the expansion into the Fourier series is possible, so that the stress calculation can be performed without degrading the calculation accuracy.

  Second, unlike the conventional method of adding / subtracting distortion at 4 points, the S / N ratio is reduced because it does not include the measured value error for 4 points by expanding all the portions where the diffraction rings exist into a Fourier series. Can be improved.

  Third, the coefficients up to the second order of the Fourier series enable analysis equivalent to the conventional method, and the coefficients of the third order and higher are more stresses included in the strain information of the diffraction ring than the conventional method. Allows analysis of the condition.

FIG. 1 is a block diagram illustrating a configuration example of the diffraction ring analyzer according to the first embodiment. FIG. 2 is a flowchart showing the diffraction ring analysis method according to the first embodiment. FIG. 3 is a graph showing the relationship between the measured value of the deformation ε _α of the diffraction ring and the approximate value of the deformation ε _α obtained by the second-order coefficient (upper diagram) and the residual (lower diagram). is there. FIG. 4 is a diagram showing an example (part) of deformation data of a diffraction ring and coefficients of Fourier series obtained therefrom. FIG. 5 is a diagram showing a comparison between the mechanically measured load and the stress σ _x obtained by the Fourier method of the first embodiment. FIG. 6 is a block diagram showing a configuration in a modification of the diffractive ring measuring apparatus in the first embodiment. FIG. 7 is a flowchart showing the operation of the diffraction ring measuring apparatus. FIG. 8A is a side view and FIG. 8B is a bottom view of the imaging unit in the first configuration example. FIG. 9 is a block diagram illustrating a configuration example of the solid-state imaging device of FIG. FIG. 10A is a side view and FIG. 10B is a bottom view of the imaging unit in the second configuration example. FIG. 11 is a diagram illustrating a pixel arrangement example of the solid-state imaging device of FIG. FIG. 12A is a side view and FIG. 12B is a bottom view of the imaging unit in the third configuration example. FIG. 13A is a side view and FIG. 13B is a bottom view of the imaging unit in the fourth configuration example. FIG. 14A is a side view and FIG. 14B is a bottom view of the imaging unit in the fifth configuration example. FIG. 15A is a side view and FIG. 15B is a bottom view of the imaging unit in the sixth configuration example. FIG. 16A is a (a) side view and (b) bottom view of the imaging unit in the seventh configuration example. FIG. 16B is a (a) side view and (b) bottom view of the imaging unit in the modification of FIG. 16A. FIG. 17A is a side view and FIG. 17B is a bottom view of the imaging unit in the eighth configuration example. FIG. 18A is a side view and FIG. 18B is a bottom view of the imaging unit in the ninth configuration example. FIG. 19A is a cross-sectional view and FIG. 19B is a bottom view of the imaging unit in the tenth configuration example. 20A is a cross-sectional view of the imaging unit in the eleventh configuration example, and FIG. 20B is a bottom view thereof. FIG. 21 is a diagram illustrating a matrix M of the formula (2.5) in the second embodiment. FIG. 22 is a diagram showing characteristics of the material used in the experiment in the second embodiment. FIG. 23 is a diagram showing an example of a mask for making a diffraction ring with a part missing in the second embodiment. FIG. 24 is a diagram showing a diffraction ring image when there is no mask and when the diffracted light is blocked by the mask in the second embodiment. FIG. 25 is a diagram showing the range of the circumferential angle α used for data analysis for each mask in the second embodiment. FIG. 26 is a diagram showing the m dependence of σx obtained by the method of formula (2.8) from the diffraction ring image with a part missing in Embodiment 2, and σx (broken line) obtained from the complete diffraction ring. is there. FIG. 27 is a diagram showing σx obtained by the conventional cos α method and σx obtained by the method of the present embodiment. FIG. 28 is an explanatory diagram when the diffraction ring is measured at eight points. FIG. 29 is a diagram showing estimated values of x1 to x5 from ε and ε ′. FIG. 30 is a diagram showing a coordinate system, incident X-rays, and a diffraction ring when X-rays are irradiated on the surface of the measurement object. FIG. 31 is a diagram illustrating an example of a diffraction ring in which a measurement object is distorted and a stress-free and strain-free diffraction ring (perfect circle). FIG. 32 is an explanatory diagram of four divisions in the conventional cos α method. FIG. 33 is a graph showing ε ^- _α (with an upper bar) obtained by the conventional cosα method on the vertical axis and cos α on the horizontal axis. Figure 34 is a E ₂ obtained by conventional cosα method on the vertical axis, shows a graph plotting the sin2α on the horizontal axis. Figure 35 is a E ₁ obtained by conventional cosα method on the vertical axis, shows a graph plotting the cos2α on the horizontal axis. FIG. 36 is a graph showing ε ^to _α (with an upper tilde) determined by the conventional cos α method on the vertical axis and sin2α on the horizontal axis. FIG. 37 is a diagram showing a state where there is a missing portion in the diffraction ring.

  Each of the embodiments described below shows a preferred specific example of the present invention. Numerical values, shapes, materials, constituent elements, arrangement positions and connection forms of constituent elements, steps, order of steps, and the like shown in the following embodiments are merely examples, and are not intended to limit the present invention.

(Embodiment 1)
<Configuration of diffraction ring analyzer>
FIG. 1 is a block diagram illustrating a configuration example of a diffraction ring analyzer according to the present embodiment. This apparatus analyzes a diffraction ring generated by X-ray diffraction. In the figure, 11 is a high-voltage power source, 12 is a cooling unit for cooling the X-ray irradiation unit, 13 is a control unit for controlling the operation of the entire diffractive ring analyzer, and 14 is an X-ray on a specific portion of the sample that is a measurement object X-ray irradiating unit 15, 15 is an imaging unit (for example, a solid-state imaging device such as a semiconductor) that images a diffraction ring (also called Debye ring or Debye-Scherrer ring) formed by diffracted light reflected from the sample , 17 is a data processing unit for analyzing the diffraction ring image captured by the imaging unit 15, and 18 is an output unit.

  Here, the X-ray irradiation unit 14 includes an apparatus that generates an X-ray by colliding an electron beam with a target, and an X-ray optical system that irradiates a measurement target object with the generated X-ray as a fine bundle of X-ray beams. I have. As an X-ray generator, for example, an X-ray tube (vacuum tube) for accelerating an electron beam at a high voltage and colliding with an anode to generate Cr-Kα characteristic X-rays, and an X-ray optical system, For example, it is a pinhole collimator that irradiates the generated X-rays with a narrow parallel beam.

  The angle formed by the surface of the measurement object and the X-ray beam may be set freely. The diameter of the irradiated X-ray beam may be as small as several hundred μm, for example. The energy of X-rays to be irradiated may be soft X-rays of about 4 to 20 keV.

  The imaging unit 15 images the diffraction ring formed by the diffracted beam from the measurement object. For this reason, the image sensor includes a solid-state imaging device such as a CCD image sensor, a MOS (Metal Oxide Semiconductor) image sensor, or an imaging plate. In the case of a solid-state imaging device, (a) a through-hole through which an X-ray beam passes is formed in the center, and the entire diffraction ring is imaged, or (b) a part or a plurality of portions of the diffraction ring is imaged 1 One or a plurality of solid-state imaging devices are provided. When an imaging plate is used for imaging, a reading device for reading the exposed diffraction ring image is provided.

The data processing unit 17 analyzes the diffraction ring image picked up by the image pickup unit 15. Specifically, the diffraction ring is discriminated from the captured image, and the deviation in the radial direction between the discriminated diffraction ring and the perfect circle is calculated as a deformation ε _α using the central angle α of the diffraction ring as a parameter. Expressed in Fourier series. The central angle α is a central angle formed by a reference line passing through the center of the diffraction ring and a point on the circumference of the diffraction ring, and is also referred to as a circumferential angle α. The Fourier series coefficients are called Fourier coefficients or simply coefficients. From the Fourier series, the stress of the test object is obtained according to the above theory (in the case of a plane stress state, equations (21) to (24) described later).

  The output unit 18 includes a display device and a storage unit, displays an analysis result by the data processing unit 17, and records data indicating the analysis result as a file in the storage unit.

  In addition, the measurement state of the X-ray irradiation part 14, the imaging part 15, and a sample is as showing in FIG.

<Details of data processing unit>
FIG. 2 shows a flowchart according to the diffraction ring analysis method of this embodiment.

  As shown in the figure, the present diffraction ring analysis method is a Fourier series diffraction ring analysis method, and the data processing unit 17 first determines a diffraction ring from a diffraction ring image picked up by the image pickup unit 15 (S21). .

Then, the radial deviation between the determined diffraction ring and the perfect circle in the radial direction is calculated as a deformation ε _α using the central angle α of the diffraction ring as a parameter ( S22).

Next, ε _α Fourier transform is performed on the deformation with the central angle α of the diffraction ring as a parameter, and the coefficient of this Fourier series is calculated (S23).

  If there is a missing portion in the discriminated diffractive ring, a Fourier series is calculated from the measured diffractive ring and the center angle α of the missing portion. This calculation makes use of the properties of the Fourier series and estimates the Fourier series when there would have been no omissions.

  Then, using this calculation result, at least one of stress or strain of a specific portion of the sample is calculated (S24).

  In FIG. 2, the deviation from the perfect circle of the diffractive ring is expanded to the Fourier series. Instead, or in addition thereto, changes in the width of the diffractive ring and the intensity of the diffractive ring are expanded to the Fourier series. May be. As a result, more multi-faceted analysis can be performed on the information included in the diffraction ring.

  As a feature of the present embodiment, first, even if there is a deficiency in the diffraction ring, it can be expanded into a Fourier series, so that stress calculation is possible without degrading calculation accuracy.

  Secondly, unlike the conventional method of adding and subtracting the strain at 4 points, the S / N ratio is not included because it does not include the measured value error for 4 points by expanding all the parts where the diffraction ring exists into a Fourier series. Can be improved.

  Third, the coefficients up to the second order of Fourier series enable analysis equivalent to the conventional method, and more than the third order coefficient, more stress included in the strain information of the diffraction ring than the conventional method. Allows analysis of the condition.

  For the Fourier series, the data processing unit 17 calculates at least coefficients from the 0th order to the second order among the coefficients of the Fourier series. Here, at least one of the first-order coefficient and the second-order coefficient may be calculated. For example, coefficients from the 0th order to the 2nd order may be calculated, or coefficients of the 3rd order or higher may be calculated.

  The data processing unit 17 for analyzing the diffraction ring by Fourier series may be configured by a microcomputer including a memory and a processor, or may be configured by a general-purpose personal computer. In that case, the processing shown in FIG. 2 is executed by the processor executing the software in the memory. In other words, the function of the data processing unit 17 may be realized by the processor executing software.

  Further, the Fourier series in the present embodiment may be an equivalent orthogonal series, and the conversion to a Fourier series or an equivalent orthogonal series is called Fourier transformation.

<Fourier series expansion of diffraction rings>
Next, the contents of the Fourier series expansion of the diffraction ring will be described.

The positional relationship between the incident beam and the test object, the imaging device, and the diffraction ring is as shown in FIG. η is the remainder angle of the diffraction angle θ determined by the lattice spacing of the crystal and the X-ray wavelength (that is, η is 90 ° −θ). Ψ ₀ is an angle formed by the normal line of the surface of the measurement object and the incident beam, and φ ₀ is an angle formed by the projection line of the X-ray beam onto the surface of the measurement object and the x axis of the measurement object.

In general, if the vertical strains in the x, y, and z axes of the test object are ε _x , ε _y , ε _z , and the shear strains are γ _xy , γ _yz , and γ _zx , respectively, the diffraction ring at the circumferential angle α The deformation ε _α of
It is represented by However n _1, n _2, n ₃ is the strain epsilon _alpha direction of direction cosines, (a reasonable set in the following discussion) When set to phi ₀ = 0 in FIG. 30
It is represented by On the other hand, if the deformation ε _α is expressed in the form of a Fourier series,
It is. By comparing the equation (8) into the equation (7) and the equation (9), the distortion of the measurement object and the Fourier series of the distortion of the diffraction ring can be related. In particular
become that way. The coefficients for k> = 3 are all 0, but if the strain of the test object is not uniform within the irradiation area of the beam, one of ε _x , ε _y , ε _z , γ _xy , γ _yz or All are functions of α, and k> = 3 components are observed.

As described above, the stress angle and distortion of the test object can be accurately obtained by determining the circumferential angle α and deformation ε _α of the diffraction ring, and using the Fourier transform and relating the coefficients of the Fourier series. Can do.

<Plane stress state>
In Equations (10) to (14), there are 6 variables, but since there are 5 equations, it cannot be solved as it is. Therefore, the measurement is usually performed assuming the stress state of the test object. Consider a plane stress state as a relatively simple example. This is approximate in many cases on the assumption that the stress does not change in the depth direction of the test object, and is industrially important. Specifically, using Young's modulus E, Poisson's ratio v, stress components σ _x , σ _y and τ _xy
and
It is expressed as

Substituting Equation (15) and Equation (16) into Equations (11)-(14)
Thus, the relational expression between the coefficient of the Fourier series and the stress is obtained. However, a ₀ is omitted because it does not use the determination of stress.

From equation (17), σ _x is
It is calculated as follows. Using this σ _x and equation (19), σ _y is
It is required as follows. Similarly, from Equation (18) and Equation (20)
As shown, τ _xy is calculated independently.

<Example of stress measurement>
In order to verify the Fourier method of the present invention, a mechanical load (four-point bending) was applied to the JIS-SS400C material, and the mechanical stress measured by the strain gauge affixed to the back surface was compared with the measured value by the present Fourier method. An X-ray (Cr-Kα ray) was used for the diffraction beam, and an imaging plate (IP) was used for acquiring the diffraction image. Since the diffraction angle θ is 78.44 degrees, η is 11.56 degrees. The distance between the test object and the IP was 39 mm and Ψ ₀ = 35 degrees.

<Fourier coefficient extraction>
FIG. 3 is a diagram showing the relationship between the circumferential angle of the diffraction ring and the deformation. Specifically, a diagram illustrating an example of a deformation epsilon _alpha diffraction rings obtained when a load of 10 MPa. Circumferential angle of the horizontal axis of FIG diffraction ring alpha, and the vertical axis represents the deformation epsilon _alpha. When the measured value of ε _α (shown by the solid line in the upper diagram of FIG. 3) is expanded into a Fourier series with respect to α and the strain is approximated by a coefficient of second order or lower of the coefficient of each term, It looks like a dashed line. Here, the coefficients are obtained by fast Fourier transform (FFT), and the figure shows coefficients up to the fourth order (actually higher order coefficients are also found).

The lower diagram in FIG. 3 shows the residual between the solid line (actually measured value) and the broken line (approximate calculated value) in the upper diagram. The second-order approximation is an approximation obtained by substituting only a ₁ , b ₁ , a ₂ , and b _{2 in} FIG. 3 into the equation (7), and the residual is a difference between the actually measured value and the approximate value.

  As apparent from the figure, the error between the actually measured value and the calculated value is slight, which proves the effect of the diffraction ring analysis method and the apparatus. It should be noted that the residual shown in the lower figure of the figure is that the approximation of the plane stress state of Equations (13) and (14) does not hold completely, and the position of the diffraction peak when determining strain is determined. The error is considered to be the cause.

<Determination of stress>
FIG. 4 is a diagram showing a result of measuring a Fourier series coefficient by measuring the deformation ε _α of the diffraction ring in a state where a mechanical load is applied to the test object at 10 MPa. In the figure, the coefficients a ₁ , b ₁ , a ₂ , and b ₂ correspond to the equations (1) to (4), respectively. As is apparent from FIG. 4, the diffraction ring analysis method and apparatus according to the present embodiment obtain up to higher-order coefficients a ₃ , b ₃ , a ₄ , and b ₄ that cannot be obtained by the conventional cos α method. Is possible. In the present embodiment, this is because the relationship with the actual measurement value is clearly theorized as described above.

FIG. 5 shows stress σ _x obtained by the Fourier method of this embodiment while mechanically applying loads of 10, 43, 73, 106, 140, 174, and 209 MPa to the test object. The horizontal axis in the figure is the stress due to the mechanical load, and the vertical axis is the stress σ _x obtained by the Fourier method of the present invention. The average and standard deviation of the stress were obtained from the Fourier coefficient for each load, and the stress σ _{x in the} load direction was determined from Equation (21). In this figure, the proportionality coefficient between the stress due to the mechanical load and the stress σ _x obtained by the Fourier method of the present invention is almost 1, and it can be seen that the stress can be accurately measured by the Fourier method of the present embodiment.

<Influence of the crystal plane spacing d _0>
The error factor of the stress measurement method (Fourier method) of the present invention will be examined. The first factor is the influence of the error of the crystal plane distance d ₀ . The crystal diffraction phenomenon depends on the value of the crystal plane distance d ₀ , but the value cannot be obtained only from the measurement of the test object, and must be obtained separately. Since the error in the determination becomes an error in the stress measurement value, it is necessary to evaluate the influence.

The deformation ε _{α of the} diffractive ring is obtained from Equation (14)
It is expressed. If this is partially differentiated by the crystal plane spacing d ₀ ,
Therefore, the error error δε _{α on} ε _{α due} to the error δd _{0 of} d ₀ is
It becomes. Since δd ₀ / d ₀ can be regarded as a constant, the influence on each coefficient of (7) is due to the nature of the Fourier series.
and
It becomes. In normal measurements, the effect is small enough.

<Influence of change in diffraction angle θ>
Was assumed here to is constant without change by _α is a complementary angle of the diffraction angle θ η (η = 90 ° -θ ) is epsilon. However, in practice, the crystal plane distance d is changed by strain, and η is also affected by the change. Along with this, the direction cosine of equation (8) also changes. In the following, the impact is considered within the scope of the verification experiment results.

According to Equation (14) in Non-Patent Document 2, if the diffraction angle θ in the unstrained state becomes θ + Δθ due to strain, the deformation ε _{α of the} diffraction ring is
It is expressed. From this, η is
You can see that it only changes.

On the other hand, in the verification experiment from Fig. 4, the coefficients of Fourier series (9) other than a ₁ and a ₂ are small.
And approximate. From this and equation (31)
and
Is obtained. Applying equations (31) and (32) to equations (5) and (6) and ignoring the higher order terms of a ₁ and a ₂ (because they are minute)
It is possible to estimate the impact on a ₁ as.

In the verification experiment, σ _y was estimated to be 150 MPa from Equation (22), so the effect of the change in the diffraction angle θ on the coefficient of the Fourier series is
It becomes. The effect of this on stress measurements is negligible.

<Comparison between Fourier method and cosα method (1)>
The stress determination method (Fourier) of the present invention is compared with the conventional method (cos α method). Assuming that the strain of the test object is uniform in the X-ray (beam) irradiation region, ε _α is
It can be expressed as This is the basic formula of the conventional cos α method (re-posted from formulas (1) to (4))
Assign to
Is obtained. As apparent from the equation (39), the coefficient of Fourier series is simply calculated in the conventional cos α method. Thus Fourier method and conventional cosα methods of the present invention in the case of strain epsilon _alpha is described by equation (37) it can be said to be equivalent.

<Comparison between Fourier method and cosα method (2)>
Next, consider the case where the cos α method and the Fourier method of the present invention are not equivalent. Since the strain is not completely uniform in the actual test object, the deformation ε _α of the diffraction ring of Equation (9) includes a term of k> = 3. Here for the sake of simplicity
And Substituting this into equation (38)
Is obtained. These equations have higher-order terms compared to equation (39). Actually, higher order terms of 5th order or higher are included. In the conventional method, since each equation (41) is approximated by a straight line, it is difficult to remove the influence of higher-order terms. On the other hand, in the Fourier method of the present invention, the influence of higher order terms can be separated, so that it can be expected that stress can be measured with higher accuracy than before.

  The Fourier method has been described above as the diffraction ring analysis method of the present invention.

<Modification of diffraction ring analyzer>
Next, a modification of the diffractive ring analyzer to which the Fourier method of the present invention can be effectively applied will be described.

  FIG. 6 is a block diagram showing a configuration of a modified example of the diffraction ring analyzer according to the present embodiment. Compared with the diffraction ring analyzer shown in FIG. 1, the diffraction ring analyzer shown in FIG. 1 has a point that an image processing unit 16 is added, and the imaging unit 15 has (a) a through-hole through which an X-ray beam passes. It has a single solid-state imaging device that has a central part and images the entire diffraction ring, or (b) a plurality of solid-state imaging elements that image a part or a plurality of parts of the diffraction ring. There is no difference. This is because the Fourier method of the present invention can be effectively applied in that the Fourier method of the present invention can be analyzed with high accuracy even when imaging a part or a plurality of parts of the diffraction ring of (b) above. Because. Hereinafter, the configuration of the modified example illustrated in FIG. 6 will be described focusing on differences from the configuration illustrated in FIG.

  The image processing unit 16 generates a diffraction ring image representing the diffraction ring imaged by the imaging unit 15. The process of generating a diffraction ring image includes: (a) a first solid-state imaging device that has a through-hole through which X-rays pass in the center and images the diffraction ring; and (b) the diffraction ring It differs depending on which of the plurality of second solid-state imaging devices that images different portions.

  In the case of (b), the image processing unit 16 forms an image from the pixel signal sequence obtained from the plurality of second solid-state imaging devices, and further performs a process of synthesizing these images into one diffraction ring image. In the synthesized diffraction ring image, a part of the diffraction ring is missing. In addition, the image processing unit 16 may perform processing for converting into polar coordinates when the coordinate system of the image obtained from the imaging unit 15 is orthogonal coordinates. In the case of (a), the image processing unit 16 generates a diffraction ring image from the pixel signal sequence obtained from the first solid-state imaging device. This diffraction ring image represents a diffraction ring having no omission. In this case, the image processing unit 16 is freed from the process of combining a plurality of images into one diffraction ring image.

  FIG. 7 is a flowchart showing the operation of the diffractive ring measuring apparatus in the present embodiment.

  The diffraction ring measuring apparatus 10 first irradiates the measurement target with an X-ray beam from the X-ray irradiation unit 14 and simultaneously images the diffraction ring by the imaging unit 15 (step S10). Next, the image processing unit 16 generates one diffraction ring image from the pixel signal sequence from the imaging unit 15 (step S20). Further, the data processing unit 17 analyzes the diffraction ring image generated by the image processing unit 16 (step S30). In this analysis step, the data processing shown in FIG. 2, that is, analysis of the diffraction ring by the Fourier method is performed. The output unit 18 outputs the analysis result obtained by the data processing unit 17 (step S40).

  The four steps S10 to S40 may be processed in series, or may be parallelized by pipeline processing for higher speed (higher frame rate).

  Subsequently, first to eleventh configuration examples will be described with respect to a more specific configuration of the imaging unit 15.

<First Configuration Example of Imaging Unit>
In the first configuration example, the imaging unit 15 includes a one-chip first solid-state imaging device. The first solid-state imaging device has a through hole through which X-rays pass and a circular imaging area.

  8A is a side view and FIG. 8B is a bottom view of the imaging unit in the first configuration example of the imaging unit 15. As shown in the figure, the imaging unit 15 includes a base 151 and a solid-state imaging device 200 (first solid-state imaging device).

  The base 151 has a through-hole 152 through which the X-ray beam from the X-ray irradiator 14 passes, and the solid-state imaging device 200 is disposed on the lower surface. The diameter of the through-hole 152 may be selected according to the crystal state and measurement area of the measurement object, and may be larger than that when the diameter of the X-ray beam is about 1 to 2 mm. In FIG. 9, the through hole 152 is greatly drawn for clarity.

  The solid-state imaging device 200 has a circular imaging area 201 and a through-hole 202 through which an X-ray beam from the X-ray irradiation unit 14 passes in the center, and diffraction formed by X-rays diffracted by the measurement object. It is an image sensor that images the ring. The imaging area 201 has a size equal to or larger than the diameter of the diffraction ring to be imaged. For example, when the pixel size of the imaging unit 15 is about 10 μm, the distance between the measurement target and the imaging unit 15 may be about 10 mm. In this case, although the size of the diffraction ring depends on the object to be measured, the radius is about 4 to 9 mm, so the size (short side or inner diameter) of the imaging area 201 may be about 10 to 20 mm.

  The diameter of the through hole 202 may be the same as the diameter of the through hole 152.

  If the distance between the measurement object and the imaging unit 15 is reduced, the size of the imaging area 201 and the intensity of the X-ray can be reduced. In this regard, the distance between the measurement object and the imaging unit 15 is preferably about 30 mm or less, although it depends on the pixel size of the imaging unit 15 and the size of the diffraction angle.

  FIG. 10 is a block diagram illustrating a configuration example of the solid-state imaging device 200 of FIG. In the figure, the configuration of the imaging area 201 of the solid-state imaging device 200 is shown. The imaging area 201 includes a plurality of R transfer units 101 that transfer charges in the radius R direction, a plurality of photoelectric conversion units 102, and a single θ transfer unit 103 that transfers charges in the circumferential direction.

  The plurality of photoelectric conversion units 102 are arranged along polar coordinates with the through hole as the center, and are configured of, for example, a photodiode including a PN junction. The light receiving areas of the plurality of photoelectric conversion units 102 are larger than the light receiving areas of the photoelectric conversion units 102 inside the polar coordinates. For example, the light receiving area of the photoelectric conversion unit 102 may be proportional to the radius.

  The plurality of R transfer units 101 are formed radially around the through hole. Each of the plurality of R transfer units 101 is a CCD that simultaneously receives signal charges from the photoelectric conversion units 102 arranged in the radial direction and sequentially transfers the signal charges toward the center in the radial direction.

  The θ transfer unit 103 is a CCD that simultaneously receives signal charges from a plurality of R transfer units 101 and transfers the signal charges in the θ direction (that is, the circumferential direction of the θ transfer unit 103). An amplifier is formed at the final stage of the θ transfer unit 103. This amplifier converts the signal charge of the final stage transferred in the θ direction by the θ transfer unit 103 into a voltage and outputs the voltage.

  Comparing the solid-state imaging device 200 with an orthogonal CCD image sensor having photodiodes arranged two-dimensionally orthogonally, a plurality of R transfer units 101 correspond to a plurality of vertical CCDs of the orthogonal CCD image sensor, and a θ transfer unit Reference numeral 103 corresponds to the horizontal CCD of the orthogonal CCD image sensor.

  The entire circumference of the diffraction ring (that is, a complete diffraction ring without a missing portion) can be imaged by one solid-state imaging device 200.

  Since the image processing unit 16 in the first configuration example obtains a diffraction ring image representing the entire circumference of the diffraction ring from the imaging unit 15, the image processing unit 16 is free from the process of combining a plurality of images.

  Since the photoelectric conversion unit 102 is arranged along the polar coordinates, the data processing unit 17 in the first configuration example does not require a process of converting from the orthogonal coordinates to the polar coordinates when calculating the radius of the diffraction ring. Processing is simple and accuracy can be improved. Further, since the photoelectric conversion unit 102 has a light receiving area proportional to the radius, it is easy or unnecessary to correct the luminance with respect to the distance to the measurement object and the diffraction angle. Thus, the processing load of the data processing unit 17 is small and good accuracy can be obtained.

  Note that the photoelectric conversion unit 102 in FIG. 9 has a rectangular shape, but may have a fan shape or an arc shape.

  The solid-state image sensor 200 may be a MOS type solid-state image sensor.

<Second Configuration Example of Imaging Unit>
In the first configuration example, the example in which the imaging area of the first solid-state imaging device is circular has been described. In the second configuration example, an example in which the imaging area of the first solid-state imaging device is rectangular will be described.

  FIG. 10A is a side view and FIG. 10B is a bottom view of the imaging unit in the second configuration example. As shown in the figure, the imaging unit 15 includes a base 151 and a solid-state imaging device 300 (first solid-state imaging device).

  The base 151 has a through-hole 152 that allows the X-ray beam from the X-ray irradiation unit 14 to pass through at the center, and the solid-state imaging device 300 is disposed on the lower surface.

  The solid-state imaging device 300 has a rectangular imaging area 301 and a through-hole 302 through which an X-ray beam from the X-ray irradiation unit 14 passes in the center, and is formed by X-rays diffracted by a measurement object. It is an image sensor that images a diffraction ring.

  FIG. 11 is a diagram illustrating a pixel arrangement example of the solid-state imaging device 300 of FIG. The solid-state imaging device 300 includes a plurality of pixels 111 arranged orthogonally in a two-dimensional shape. However, the pixel 111 is not disposed near the through hole 302.

  The solid-state imaging device 300 includes, for example, a CCD image sensor having an upper half (upper one-dot chain line) pixel 111 and a CCD image sensor having a lower half (lower one-dot chain line) pixel 111 on one semiconductor substrate. Is provided. By configuring the circuits of the upper and lower CCD image sensors symmetrically, it is possible to share drive signals such as vertical transfer pulses and horizontal transfer pulses. Since signal charges from the pixels of the upper and lower CCD image sensors can be read simultaneously, they can be read out at substantially double speed.

  In this case, the image processing unit 16 generates a diffraction ring image by combining two images obtained from the upper and lower CCD image sensors. In this diffraction ring image, the entire circumference of the diffraction ring without any omission is expressed.

  In FIG. 11, the configuration in which two upper and lower CCD image sensors are formed on one semiconductor substrate has been described. However, two CCD image sensors may be configured on the left and right sides, and two in the diagonal direction. A plurality of CCD image sensors that share all the conversion units may be configured. Further, the solid-state imaging device 300 may be configured by a MOS image sensor instead of a CCD image sensor.

<Third Configuration Example of Imaging Unit>
In the third configuration example, the imaging unit 15 includes a plurality of second solid-state imaging elements. The plurality of second solid-state imaging devices are arranged on a plane orthogonal to the X-rays with the X-rays irradiated from the X-ray irradiation unit as the center. Here, an example in which there are two second solid-state imaging devices will be described.

  FIG. 12A is a side view and FIG. 12B is a bottom view of the imaging unit in the third configuration example. As shown in the figure, the imaging unit 15 includes a base 151 and solid-state imaging devices 400a and 400b (two second solid-state imaging devices).

  The base 151 has a through-hole 152 that allows the X-ray beam from the X-ray irradiation unit 14 to pass through in the center thereof, and the solid-state imaging devices 400a and 400b are disposed on the lower surface.

  The solid-state imaging device 400a has an imaging area 401a. The solid-state imaging device 400b has an imaging area 401b.

  In the third configuration example, since the solid-state imaging devices 400a and 400b do not have through holes, the manufacturing cost can be reduced as compared with the first solid-state imaging device having through holes.

  Further, the image processing unit 16 in the third configuration example generates a diffraction ring image by synthesizing images captured by the two second solid-state imaging elements. Although the diffraction ring image is missing in the diffraction ring image, depending on the analysis method of the data processing unit 17, the lack can be sufficiently allowed.

<Fourth Configuration Example of Imaging Unit>
In the third configuration example, two examples of the plurality of second solid-state imaging devices have been described, but four examples will be described.

  FIG. 13A is a side view and FIG. 13B is a bottom view of the imaging unit in the fourth configuration example. As shown in the figure, the imaging unit 15 includes a base 151 and solid-state imaging devices 500a to 500d (four second solid-state imaging devices).

  The base 151 has a through-hole 152 through which the X-ray beam from the X-ray irradiating unit 14 passes in the center, and the solid-state imaging devices 500a to 500d are arranged on the lower surface.

  The solid-state imaging device 500a has an imaging area 501a. Similarly, the solid-state imaging devices 500b to 500d have imaging areas 501b to 501d, respectively.

  In the fourth configuration example, none of the solid-state imaging devices 500a to 500d has a through hole, so that the manufacturing cost can be reduced as compared with the first solid-state imaging device having the through hole.

  The image processing unit 16 in the fourth configuration example generates a diffraction ring image by synthesizing images captured by the four second solid-state imaging elements. Although the diffraction ring image is missing in the diffraction ring image, depending on the analysis method of the data processing unit 17, the lack can be sufficiently allowed.

<Fifth Configuration Example of Imaging Unit>
In the fourth configuration example, four examples of the plurality of second solid-state imaging elements have been described. In the fifth configuration example, ten examples are described.

  FIG. 14A is a side view and FIG. 14B is a bottom view of the imaging unit in the fifth configuration example. As shown in the figure, the imaging unit 15 includes a base 151 and solid-state imaging devices 600a to 600j (10 second solid-state imaging devices).

  The base 151 has a through-hole 152 that allows the X-ray beam from the X-ray irradiation unit 14 to pass through at the center, and the solid-state imaging devices 600a to 600j are arranged on the lower surface.

  The solid-state imaging device 600a has an imaging area 601a. Similarly, the solid-state imaging devices 600b to 600j have imaging areas 601b to 601j, respectively.

  In addition, the image processing unit 16 in the fifth configuration example generates a diffraction ring image by synthesizing images captured by the ten second solid-state imaging elements.

<Sixth Configuration Example of Imaging Unit>
In the fifth configuration example, the example in which the plurality of second solid-state imaging elements is 10 has been described, but in the sixth configuration example, 12 examples will be described.

  FIG. 15A is a side view and FIG. 15B is a bottom view of the imaging unit in the sixth configuration example. As shown in the figure, the imaging unit 15 includes a base 151 and solid-state imaging devices 700a to 700l (12 second solid-state imaging devices).

  The base 151 has a through-hole 152 that allows the X-ray beam from the X-ray irradiation unit 14 to pass through in the center thereof, and the solid-state imaging devices 700a to 700l are disposed on the lower surface.

  The solid-state imaging device 700a has an imaging area 701a. Similarly, the solid-state imaging devices 700b to 700l have imaging areas 701b to 701l, respectively.

  Further, the image processing unit 16 in the sixth configuration example generates a diffraction ring image by synthesizing images captured by the 12 second solid-state imaging elements.

<Seventh Configuration Example of Imaging Unit>
In the seventh configuration example, the imaging unit 15 includes a plurality of second solid-state imaging elements, and each of the plurality of second solid-state imaging elements includes a fan shape including a fan center from a fan shape centering on the through hole. An imaging area having a shape excluding the portion is included. The plurality of second solid-state imaging devices have a plurality of photoelectric conversion units arranged along polar coordinates centered on the through hole. Furthermore, the light receiving area of each of the plurality of photoelectric conversion units is larger than the light receiving area of the photoelectric conversion unit inside the polar coordinates.

  FIG. 16A is a (a) side view and (b) bottom view of the imaging unit in the seventh configuration example. As shown in the figure, the imaging unit 15 includes a base 151 and solid-state imaging devices 800a to 800d (four second solid-state imaging devices).

  The base 151 has a through-hole 152 through which the X-ray beam from the X-ray irradiation unit 14 passes, and the solid-state imaging devices 800a to 800d are arranged on the lower surface.

  The solid-state imaging device 800a has an imaging area 801a. Similarly, the solid-state imaging devices 800b to 800d have imaging areas 801b to 801d, respectively.

  The imaging area 801a has a shape in which a fan-shaped portion including the fan center is excluded from a fan-shaped shape centered on the through hole, and has a plurality of photoelectric conversion units arranged along polar coordinates centered on the through hole. The imaging area 801a has the same circuit configuration as a portion corresponding to approximately 1/4 (approximately 90 degrees) in the polar coordinate CCD image sensor shown in FIG. The same applies to the imaging areas 801b to 801d. For example, since there is a gap in the arrangement of the solid-state imaging devices 800a to 800d, the imaging area 801a is slightly smaller than 1/4 (90 degrees) of the CCD image sensor shown in FIG.

  The image processing unit 16 generates a diffraction ring image from images captured by the plurality of second solid-state imaging elements.

  In the seventh configuration example, although the diffraction ring image is missing in the diffraction ring image, since it is polar coordinates, the same effect as the first configuration example can be obtained, and the cost can be reduced more than in the first configuration example. it can.

  Note that the outer shape of the solid-state imaging devices 800a to 800d shown in FIG. 16A is rectangular, but the shape and arrangement shown in FIG. 16B may be used. In FIG. 16B, a part corresponding to the central part of the solid-state imaging devices 810a to 810d is cut out in a fan shape. In this way, the arrangement gap between the solid-state imaging devices 810a to 810d can be reduced to 0 or can be reduced. The loss of the diffraction ring imaged by the imaging areas 811a to 811d in FIG. 16B can be reduced as compared with FIG. 16A.

  In addition, the notch of FIG. 16B does not need to be a fan shape and may be 45 degrees diagonally.

<Eighth Configuration Example of Imaging Unit>
In the eighth configuration example, an example in which the plurality of second solid-state imaging devices are five or more line sensors will be described. Five or more line sensors are arranged radially around the through hole. The image processing unit forms a diffraction ring image from images picked up by five or more line sensors.

  FIG. 17A is a side view and FIG. 17B is a bottom view of the imaging unit in the eighth configuration example. As shown in the figure, the imaging unit 15 includes a base 151 and 16 line sensors 900a to 900p.

  The base 151 has a through-hole 152 through which the X-ray beam from the X-ray irradiation unit 14 passes, and 16 line sensors 900a to 900p are arranged radially on the lower surface.

  The line sensor 900a has a plurality of photoelectric conversion units (photodiodes) arranged in a straight line. The light receiving areas of the plurality of photoelectric conversion units are formed larger than the light receiving areas of the radially inner photoelectric conversion units. For example, the light receiving area of the photoelectric conversion unit may be proportional to the radius. The same applies to the line sensors 900b to 900p.

  In the seventh configuration example, although the diffraction ring image is missing in the diffraction ring, the same effect as the first configuration example can be obtained, and the cost can be reduced as compared with the first configuration example.

<Ninth Configuration Example of Imaging Unit>
In the eighth configuration example, the example in which the plurality of second solid-state imaging devices are 16 line sensors has been described. In the ninth configuration example, the plurality of second solid-state imaging devices has 32 line sensors. An example will be described.

  FIG. 18A is a side view and FIG. 18B is a bottom view of the imaging unit in the eighth configuration example. As shown in the figure, the imaging unit 15 includes a base 151 and 16 line sensors 901 to 932.

  The base 151 has a through-hole 152 through which the X-ray beam from the X-ray irradiating unit 14 passes in the center, and 32 line sensors 901 to 932 are radially arranged on the lower surface.

  The line sensor 901 is, for example, a CCD linear image sensor having a plurality of photoelectric conversion units (photodiodes) arranged in a straight line and a CCD arranged in parallel therewith.

  The light receiving areas of the plurality of photoelectric conversion units are formed larger than the light receiving areas of the radially inner photoelectric conversion units. For example, the light receiving area of the photoelectric conversion unit may be proportional to the radius. The same applies to the line sensors 902 to 932.

  Note that the line sensors 901 to 932 are not limited to the CCD linear image sensor, and may be composed of a MOS linear image sensor.

  In the ninth configuration example, the diffraction ring image is missing in the diffraction ring, but the same effect as that of the first configuration example is obtained, and the cost can be reduced as compared with the first configuration example.

<Tenth Configuration Example of Imaging Unit>
In the tenth configuration example, an example will be described in which the attachment angle of the line sensor to the base in the eighth configuration example is inclined.

  FIG. 19A is a cross-sectional view and FIG. 19B is a bottom view of the imaging unit in the tenth configuration example. (A) of the figure is a cross-sectional view taken along the line AA of (b) of the figure. As shown in the figure, the base 152 has a conical inner surface on the lower surface, and has a through hole at the apex of the conical shape through which X-rays irradiated from the X-ray irradiation unit pass.

  Compared to the eighth configuration example, the tenth configuration example can improve the accuracy of the diffraction ring image because the angle between the diffracted X-ray from the measurement object and the line sensor approaches 90 degrees. .

<Eleventh configuration example of imaging unit>
In the tenth configuration example, an example having 16 line sensors has been described. In the eleventh configuration example, an example having 32 line sensors will be described.

  20A is a cross-sectional view of the imaging unit in the eleventh configuration example, and FIG. 20B is a bottom view thereof. (A) of the figure is a cross-sectional view taken along the line AA of (b) of the figure. As shown in the figure, the base 152 has a conical inner surface on the lower surface, and has a through hole at the apex of the conical shape through which X-rays irradiated from the X-ray irradiation unit pass.

  The eleventh configuration example can further improve the accuracy of the diffraction ring image as compared to the tenth configuration example.

  In the tenth and eleventh configuration examples, the tilt of the line sensor (the tilt of the conical lower surface) may be set according to the direction in which the diffraction ring appears, the type of measurement object, and the like. The base 152 may include a mechanism that can arbitrarily set the inclination of the lower surface. For example, it is good also as a structure like the umbrella which made the line sensor respond | corresponded to the bone | frame centering on X-ray irradiation tube. In this case, the umbrella bone and the line sensor may be linear or may be curved along the inner surface of the sphere. Also, the shape of the first or second solid-state imaging device shown in FIGS. 8 to 20 may be a shape that follows a conical inner surface or a spherical inner surface.

  In FIG. 19 or FIG. 20, the number of line sensors may be two or more, and more preferably five or more for handling as a diffraction ring.

  Further, the imaging unit 15 may be configured to be removable. For example, (a) a first solid-state imaging device that has a through-hole through which an X-ray beam passes, and that images a diffraction ring, and (b) a plurality of second that images different portions of the diffraction ring. Instead of either one of the solid-state imaging devices, a configuration in which both are provided and can be selected or exchanged may be employed. Moreover, it is good also as a structure which comprises two or more image pick-up parts of said 1st-11th structural example, and can be selected or replaced | exchanged.

  According to the modification of the diffractive ring analyzer described above, since the diffractive ring is imaged by the first solid-state imaging device having the through holes or the plurality of second solid-state imaging devices, the analysis from the imaging of the diffractive ring is performed. Can be done in real time. Furthermore, even if a part of the diffraction ring is missing, it can be accurately analyzed by the Fourier method of the present invention.

(Embodiment 2)
Next, an X-ray diffraction analysis method and apparatus according to Embodiment 2 will be described.

  First, desirable improvements in the conventional technique and the first embodiment will be described.

  The X-ray diffraction analysis method (diffraction ring analysis method) in the first embodiment discloses a method for obtaining strain and stress of an object to be measured by utilizing information of an annular diffraction ring (Debye ring) for the entire circumference. Yes. Conventionally, acquisition of a Debye ring by X-ray diffraction is disclosed in Non-Patent Document 2, and a method using an imaging plate (IP) developed in Non-Patent Document 1 is generally used. In the method using an element (CCD, MOS sensor, etc.), it is expected that the configuration of the analyzer (diffraction ring measuring device) becomes simple and the measurement can be performed at high speed.

  However, in order to accurately measure stress and strain using the X-ray diffraction ring, it is necessary to take a diffraction image from the X-ray irradiation direction (FIG. 30), and a hole is inevitably formed in the center of the image sensor of the diffraction image. There is a need. This was not a problem with image sensors such as photographic film and IP, but to achieve with solid-state image sensors, a new solid-state image sensor was designed or a hole was made in the center of the manufactured solid-state image sensor. Special work such as this is required, which leads to an increase in development and production costs. On the other hand, in a method in which general rectangular solid-state image sensors are arranged around the X-ray beam (for example, FIG. 12, FIG. 13, etc.), a gap is inevitably formed between the solid-state image sensors. If the analysis methods of Non-Patent Document 1, Non-Patent Document 2 and Patent Document 1 are applied as they are, an error occurs in the obtained stress value.

  From the above, in order to realize a low-cost X-ray strain and stress analyzer using a solid-state imaging device, a part of the missing diffraction ring obtained from a solid-state imaging device with a gap is used. There is a need for a method for accurately analyzing stress.

  In the present embodiment, the following points are improved with respect to the diffraction ring analyzer and method in the first embodiment.

  In this regard, in the first embodiment, the stress / strain analysis method (cos α method) of the conventional method using the diffraction ring cannot calculate the stress / strain at all if a part or a plurality of parts of the diffraction ring is missing. It was pointed out that the error would increase even if it could be calculated. Further, it is suggested that the stress / strain can be calculated accurately even in such a case by using the analysis method of the first embodiment.

  As a case where a part or a plurality of parts of the diffractive ring are missing, firstly, the case may be caused by the property of the object to be measured. As an example, a case where the crystal grains are coarse as in Non-Patent Document 3 can be given. Non-Patent Document 3 proposes a sample plane swing method in which measurement is performed while moving the object to be measured little by little as a countermeasure in such a case. In this method, a mechanism for mechanically moving the sample is proposed. Is required, and the measuring apparatus becomes large. In addition, the measurement time becomes longer than in the case of normal single X-ray irradiation.

  As a second case where a part or a plurality of parts of the diffraction ring is missing, there is a case where the diffraction ring is imaged by a solid-state imaging device (CCD, MOS sensor, etc.) as shown in FIGS. Conventionally, imaging with an imaging plate (IP) has been common, but in the case of IP, it is necessary to irradiate and read a laser beam after imaging, so an optical system for that purpose and a mechanism for rotating the IP are necessary. This is disadvantageous in terms of both cost and measurement time. On the other hand, when a solid-state imaging device is used, reading time can be shortened and a reading mechanism can be simplified. However, in the measurement of stress and strain by X-rays, it is necessary to make a hole in the center of the solid-state imaging device (FIG. 30), which is disadvantageous in terms of cost. Therefore, a method (for example, FIG. 12, FIG. 13, etc.) of reading a diffraction ring by arranging a number of general rectangular solid-state image sensors can be considered. And the diffraction ring becomes incomplete.

  With respect to the points to be improved as described above, in the second embodiment, a method for accurately calculating stress / strain even when a part or a plurality of parts of a diffraction ring is missing will be described.

(Outline of Embodiment 2)
Next, an outline of the second embodiment will be described.

  In the first embodiment, when the deformation of the diffraction ring is ε (α) as a function of the central angle α, there is a correspondence between the coefficient of the Fourier series of ε (α) (hereinafter referred to as Fourier coefficient) and the stress / strain. did. Therefore, even when a part or a plurality of parts of the diffraction ring is missing, if the Fourier coefficient can be estimated with high accuracy, the stress / strain can be obtained with high accuracy.

  In general, when ε (α) is expanded into a Fourier series, stress / strain information is concentrated on the terms with small coefficients of α, especially the four terms cosα, sin α, cos 2α, and sin 2α. In many cases, a term having a large coefficient of α can be regarded as having a coefficient of zero. Therefore, accurate approximation is possible by truncating the Fourier series with an appropriate term in accordance with the number of observation points.

Specifically, when ε (α) is measured at 2k points or 2k + 1 points on the diffraction ring, the Fourier series expansion is used.
2k or 2k + 1 coefficients can be determined. On the other hand, when a plane stress state is established in the object to be measured, the stress can be completely determined if the Fourier coefficient is determined from the first embodiment to the coefficient (a ₄ ) of the term sin 2α. Therefore, the stress can be determined by measuring ε (α) at least at five points even in a diffraction ring lacking a part or a plurality of parts.

  That is, the diffraction ring analysis method in the present embodiment irradiates a specific part of a measurement object with a beam having a diffracting property, measures the deformation of the diffraction ring formed by the diffraction beam reflected from the specific part, The diffraction ring is analyzed by performing a Fourier transform that converts the measurement result into a Fourier series or an equivalent orthogonal series. Here, in the above measurement, the number of measurement points may be determined, and in the above analysis, the diffraction ring may be approximated by a Fourier series having the number of terms corresponding to the number of measurement points, and the stress and strain of the measurement object may be obtained. .

  In the above analysis, the deformation of the diffraction ring is expressed as a matrix by Fourier series, and the inverse matrix is used to analyze the Fourier series coefficient (hereinafter referred to as Fourier coefficient), the stress and strain state of the measurement object. May be.

  Here, in the above analysis, when a part or a plurality of parts of the diffraction ring are missing, the lines corresponding to the angles of the missing parts are removed from the matrix expressing the diffraction ring, and the same number of stresses A matrix in which a column having a small influence on the strain measurement is removed may be created, and the Fourier coefficient, stress, and strain may be calculated using the inverse matrix. A column with less influence is a column with less influence than other columns that are not removed. Also, the number of columns removed may not be the same as the number of rows removed.

  Generalized the above Fourier series determination method, disclosed a specific calculation method to determine the coefficient of ε (α) from the measurement data of any number of points on the diffraction ring, and also the calculation accuracy estimation method in that case Is also disclosed.

  According to the diffraction ring analysis method of the second embodiment, the following effects are obtained. That is, even when the diffraction ring is missing due to the property of the object to be measured, the stress / strain can be analyzed and the accuracy can be improved. In addition, it is possible to obtain stress and strain with high accuracy from a diffraction ring in which a general-purpose solid-state imaging device or the like is arranged with a gap. This makes it possible to configure a stress / strain analyzer by X-ray diffraction more flexibly than the present, which can reduce the price and shorten the measurement time.

  Further, according to the calculation method disclosed in the present embodiment, since the error of the Fourier coefficient calculated from the state where the diffraction ring is missing can be calculated as compared with the case of the complete diffraction ring, it is finally obtained. It is possible to evaluate the reliability of stress and strain.

(Details of Embodiment 2)
The configuration of the diffractive ring analyzer in the present embodiment is the same as that in the first embodiment, and is applicable to each of the first to eleventh configuration examples. Therefore, the diffractive ring analysis method is mainly described in detail while avoiding repeated description of the configuration of the diffractive ring analysis apparatus.

<Debye ring matrix display>
In this embodiment, first, matrix display is introduced as a derivation of the Fourier series expansion of the Debye ring disclosed in the first embodiment. This display itself can be used as a stress calculation method from the Debye ring.

Now the Fourier series of Debye ring deformation ε (α) is
It shall be represented by When measuring this ε (α) at n measuring points with a central angle α1 ... αn
It is. However, when the circumference is divided at equal intervals, α1 = 0, α2 = 2π / n,..., Αn = 2π (n−1) / n (unit: radians). Equation (2.4) is obtained by using an n × n matrix M as shown in FIG.
It can be expressed as. Where ε and x are
An n-dimensional vector represented by Equation (2.5) is a matrix display of the Debye ring introduced in this embodiment. Since the Fourier series is an orthogonal basis, there is an inverse matrix in M, and x
Usually, Fast Fourier Transform (FFT) that can be calculated at higher speed is used. Thus, the first n coefficients of the equation (2.3) can be determined, and the stress / strain of the object to be measured can be obtained.

<Reproduction of missing Debye ring>
Next, the case where the diffraction ring is missing will be described. It is assumed that measured values at k locations {αi1, αi2,..., Αik} (k <n) of the diffraction ring cannot be obtained. At this time, an nk-dimensional vector ε ′ obtained by removing {εi1, εi2,..., Ikik} from ε, and {i1, i2,..., Ik} rows of the matrix M are removed (nk). Consider a matrix n ₁ with row n columns
It is. Because the inverse matrix of the matrix M ₁ is not present can not be solved by the inverse matrix of equation (2.7).

Make an assumption about x to solve equation (2.7). In the diffraction ring of a sample in an ideal plane stress state, x _k = 0 (k> 5), and in many cases, k is sufficiently larger than 5 and x _k should be regarded as 0.

Therefore an m-dimensional vector
When introducing
It can be expressed as. However, the matrix _{M 3} represents a removal of m + 1 subsequent columns of the matrix M1 (n-k) rows and m columns of the matrix (m ≦ n-k). Although there is no inverse matrix of the matrix M ₃ , if a pseudo inverse matrix (that is, a general inverse matrix) M ₃ ⁻ is used,
From which x 'can be obtained and the stress of the sample can be estimated. For example, using x2 = a1, from equation (21)
Thus, the stress σx in the longitudinal direction of the sample can be obtained. Here, E and ν are X-ray Young's modulus and Poisson's ratio, and η and Ψ 0 are angles determined by the measurement system.

<Experiment>
In order to verify the diffractive ring analysis method in this embodiment, a mask for missing a diffractive ring was created by placing it in front of an imaging plate (IP) for taking a diffractive ring image, and a stress measurement experiment was performed. The sample used was an α-Fe 2 stress test piece manufactured by Proto, and details are shown in FIG. The X-ray elastic constant in the figure uses the X-ray Young's modulus E and Poisson's ratio ν.
It is represented by The rated value of the stress_x of the sample is
Thus, similar values were obtained by measurement using Rigaku MSF-3 and Cr-Kα.

Next, the stress of the sample used in FIG. 22 was measured by the method of the first embodiment. The apparatus used for the measurement is μ-X360 manufactured by Pulse Tech Co., and the characteristic X-ray used for the measurement is Cr-Kα. The resolution of the diffraction ring image is 0.72 ° in the circumferential direction and 50 μm in the radial direction. From this diffraction ring image, ε (α) is determined with an accuracy of about 10 ⁻⁴ . For Ψ ₀ (see FIG. 30), Ψ ₀ = 45 °. In addition, a mask was made of cardboard and placed just before the IP in order to create a diffraction ring with a part missing. When two sheets of 0.35 mm thick paper were stacked, the diffraction X-rays could be completely blocked. The mask actually used is shown in FIG. For example, Mask B corresponds to FIG. Any of these masks is used for copying the measurement by the configuration of the diffractive ring analyzer including a plurality of solid-state imaging elements in the first embodiment. The measurement using each mask was performed 10 times for 150 seconds, and the average value and the standard deviation were obtained. FIG. 24 shows diffraction ring images when there is no mask and when diffraction is blocked by the mask. For each mask, the range of α used for data analysis is as shown in FIG.

First, the value of FIG. 22 is used from the complete diffraction ring image, and σx is obtained according to the diffraction ring analysis method of the first embodiment.
Met. This result is equivalent to the rated value of equation (2.10).

  Next, the data was removed from this complete diffraction ring image so as to have the same shape as the diffraction ring image of mask A, and ε ′ was simulated, and x ′ was obtained from equation (2.8) while changing the value of m. FIG. 26 shows a comparative example of the σx obtained from the σx obtained from the complete diffraction ring. In this example, when m = 5, the difference between the two becomes the smallest.

  The tendency was the same for the other measurement data, and the stress value closest to the value obtained from the complete diffraction ring image was obtained when m = 5. Since the same tendency was observed for other mask shapes, the discussion will proceed with the stress value obtained as m = 5 unless otherwise specified. In FIG. 26, since σx is measured by one measurement, a value different from the average value of the equation (2.11) is taken.

  FIG. 27 shows the result of applying the above processing to the measurement data of each mask. The column of μ-X360 in the figure is a display value of the software attached to μ-X360, which calculates the stress value by the cos α method, but is general when a part of the diffraction ring is missing. Data is supplemented with a simple complement method. The stress value of the method of this embodiment (sequence of Proposed technique) was calculated from the equations (2.2) and (2.9) with m = 5. In addition, “Specification” in the figure indicates the nominal value of the stress standard, and “No Mask” indicates the analysis value when the diffraction ring is complete.

  The stress value by the software attached to the μ-X360 does not agree with the nominal value or “No mask” value even if an error is taken into consideration when a part of the diffraction ring is missing. On the other hand, in the proposed method, the value of “Mask A” is slightly smaller than the nominal value, but otherwise, it is equivalent to the case where the nominal value or the diffraction ring is complete. When the stress by the software attached to μ-X360 is compared with the proposed method, the value of the method of this embodiment is closer to the nominal value in any case.

<Summary>
In the present embodiment, a method for estimating stress when a part of a diffraction ring is missing is disclosed using the Fourier series expansion of distortion of the diffraction ring. That is, the diffraction ring analysis method in the present embodiment irradiates a specific part of a measurement object with a beam having a diffracting property, measures the deformation of the diffraction ring formed by the diffraction beam reflected from the specific part, The diffraction ring is analyzed by performing a Fourier transform that converts the measurement result into a Fourier series or an equivalent orthogonal series. At this time, in the above measurement, the number of measurement points is determined, and in the above analysis, the diffraction ring is approximated by a Fourier series having the number of terms corresponding to the number of measurement points, and the stress and strain of the measurement object are obtained. In the above analysis, if some or more parts of the diffraction ring are missing, the matrix corresponding to the angle of the missing part is removed from the matrix representing the diffraction ring, and the same number of stress / strain measurements are taken. Create a matrix with the least affected columns removed, and use the pseudo-inverse matrix (that is, the generalized inverse matrix) to calculate the Fourier coefficient, stress, and strain. Note that the number of columns to be removed may not be the same as the number of rows to be removed. If the number is the same, this pseudo matrix becomes a square matrix, and if it is not the same number, it does not become a square matrix. That is, this pseudo inverse matrix may not be a square matrix.

  Further, a diffraction ring image in which a part of the stress test piece was actually missing was taken, and the stress σx in the longitudinal direction was obtained by applying the diffraction ring analysis method of the second embodiment. As a result, it was possible to estimate an appropriate stress value in many cases, and to obtain a better result than the estimation by the combination of a simple interpolation method and the cos α method.

<Simple example>
In order to facilitate understanding of the diffraction ring analysis method in the present embodiment, a calculation method will be described using a simple example. First, an example of the number of measurement points in the measurement of the diffraction ring is shown in FIG. FIG. 28 is an explanatory diagram when the diffraction ring is measured at eight points of α = 0, π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4. This figure shows a case where ε (α) is measured by dividing the diffraction ring into n = 8.

Next, consider the case where the number of measurement points is n = 16 and the diffraction ring is divided into 16 to measure ε (α). If we take measurement points at regular intervals
It is. The unit is radians. From this, the matrix M in equation (2.4) is
Of 16 × 16 matrix. Also
If
It is. Similarly, ε is
It is. However, in order to simulate the rounding error of the measurement, the value of ε was rounded to 3 digits after the decimal point.

Since M, x, and ε in equations (2.15), (2.16), and (2.17) satisfy equation (2.5), from equation (2.6)
X can be estimated as follows. This result closely reproduces the initial setting of equation (2.16).

  Next, consider a case where a part of the diffraction ring is missing.

The distortion of the diffractive ring is expressed as ε (α) as a function of the circumferential angle α. However, when a part of the diffractive ring is missing, the window function h (α) is used.
It expresses like this. However, h (α) is
When the diffraction ring cannot be measured, it is assumed that ε ′ (α) = 0.

Now window function
Then, the (1,2,3,4,5,13,14,15,16) -th element of ε is missing. From this, ε´ is
And M1 in equation (2.7) is
7 × 16 matrix. However, the value of element mi, j of M1 is as defined in equation (2.15). There is no inverse matrix of M1, but a 7 × 7 symmetric matrix M2 with the eighth and subsequent columns removed
Has an inverse matrix, and from this the first 7 elements x 'of x
It becomes. Compared equations (2.21) and (2.16) and (2.18), it can be seen that the accuracy of (2.21) has deteriorated (approximately 30% x _2). This is because the absolute value of the smallest eigenvalue of M is about 3, whereas the absolute value of the smallest eigenvalue of M2 is as small as 0.01, so that the calculation error has increased.

One reason for the deterioration of accuracy is that x is evaluated up to 7 terms in equation (2.21). Ie
This approximates the diffraction ring. On the other hand, according to the first embodiment, the plane stress state can be reproduced if the first five terms of x can be evaluated, so the 7 × 5 matrix in which the first five columns of M2 are extracted.
Should be used.

Although there is no inverse matrix of M3, if a pseudo inverse matrix (general inverse matrix) is used, x ′ can be estimated from equation (2.8). The method will be described below. M3
Singular value decomposition can be performed as follows. W and V ^T are symmetric matrices of 7 × 7 and 5 × 5, respectively, and satisfy W ^T = W ⁻¹ and V ^T = V ⁻¹ . S is the singular value of M3 (k ₁ , k ₂ , k ₃ , k ₄ , k ₅ ) (k ₁ ≧ k ₂ ≧ k ₃ ≧ k ₄ ≧ k ₅ ).
Is a 7 × 5 matrix. Using the above W, V and S, the pseudo inverse matrix (general inverse matrix) of M3 is
Is required. However, S- ¹ is
Is a 5 × 7 matrix. Actually calculating the pseudo inverse matrix according to equation (2.22) and substituting it into equation (2.8)
The first five terms of x can be estimated as follows. This estimated value is clearly closer to the default value equation (2.16)) than equation (2.21).

FIG. 29 summarizes the above results. This shows the estimated values of x ₁ to x ₅ from ε and ε ′ in the equations (2.17) and (2.20). The first level is the estimated value from the complete diffraction ring, which reproduces the initial setting of equation (2.16). On the other hand, the second and subsequent stages are estimated values from a missing diffraction ring, the second stage is an estimated value using the inverse matrix of M2, and the third stage is a general inverse of M3 with strict assumptions on x. An estimated value from a matrix (that is, a pseudo inverse matrix). As is clear from the figure, better results are obtained by the estimation using the general inverse matrix.

  As described above, according to the diffraction ring analysis method of the second embodiment, stress / strain can be analyzed and accuracy can be improved even when the diffraction ring is missing due to the properties of the object to be measured. In addition, it is possible to obtain stress and strain with high accuracy from a diffraction ring in which a general-purpose solid-state imaging device or the like is arranged with a gap. This makes it possible to configure a stress / strain analyzer by X-ray diffraction more flexibly than the present, which can reduce the price and shorten the measurement time.

  Further, according to the diffraction ring analysis method disclosed in the present embodiment, the error of the Fourier coefficient calculated from the state where the diffraction ring is missing can be calculated as compared with the case of a complete diffraction ring. It becomes possible to evaluate the reliability of the stress and strain obtained in the above.

  The present invention is useful for nondestructive inspection in general such as residual stress of industrial materials such as metals and ceramics. It is also useful for non-destructive inspection equipment using X-rays and the like and for stress analysis of thin films such as metals.

2 samples (measurement object)
5, 8, 9 Diffraction ring 10 Diffraction ring analyzer 11 High voltage power supply 12 Cooling unit 13 Control unit 14 X-ray irradiation unit 15 Imaging unit 16 Image processing unit 19 Measurement object 101 R transfer unit 102 Photoelectric conversion unit 111 Pixel 151, 155 Base 152 Through-hole 200, 300 Solid-state imaging device 201 Imaging area 202 Through-hole 302 Through-hole 303 θ transfer unit 300, 400a, 400b, 500a-500d, 600a-600j Solid-state imaging device 700a-700l, 800a-800d, 810a- 810d Solid-state imaging device 301, 401a, 401b, 501a to 501d, 601a to 601j Imaging area 701a to 701l, 801a to 801d, 811a to 811d Imaging area 900a to 900p, 901 to 932 Line sensor

Claims (12)

Irradiate a specific part of the measurement object with a diffracting beam,
Measuring the deformation of the diffraction ring formed by the diffracted beam reflected from the specific part;
A diffraction ring analysis method for analyzing a diffraction ring by performing a Fourier transform for converting a measurement result into a Fourier series or an equivalent orthogonal series. The diffraction ring analysis method according to claim 1, wherein in the analysis of the diffraction ring, at least one of stress and strain of the specific portion is calculated from the result of the Fourier transform. In the analysis of the diffraction ring, in addition to the Fourier series coefficient, calculation is performed using Young's modulus, Poisson's ratio, diffraction angle remainder angle, and the angle between the normal to the measurement object surface and the incident beam. The diffraction ring analysis method according to claim 2, wherein at least one of the stress and the strain is calculated. Further, when there is a missing part in a part of the diffraction ring, the Fourier series of the diffraction ring in the absence of the missing part is estimated using mathematical properties from information on the measured diffraction ring and the central angle α of the missing part. The diffraction ring analysis method according to any one of claims 1 to 3. 5. The analysis according to claim 1, wherein in the analysis of the diffraction ring, at least one of a first-order coefficient and a second-order coefficient is used among the Fourier series obtained as a result of the Fourier transform. Diffraction ring analysis method. In the analysis of the diffraction ring, assuming that the first and second order coefficients of the Fourier series are a ₁ , b ₁ , a ₂ , b ₂ , the stress of the measurement object is assumed to be plane stress, x-axis and y-axis direction stress σx and σy respectively
Is calculated by equation (1) and the shear stress τxy is
Calculate with at least one of the equations (2)
a ₁ is a coefficient of cos α of the first order coefficients of the Fourier series, a ₂ is a coefficient of sin ₂ α of the second order coefficients of the Fourier series, and b ₁ is a coefficient of sin α of the first order coefficients of the Fourier series. , B ₂ is a coefficient of cos 2α of the second-order coefficients of the Fourier series, α is a central angle of the diffraction ring, E is a Young's modulus, ν is a Poisson's ratio, η is an additional angle of the diffraction angle, and ψ ₀ is the measurement The diffraction ring analysis method according to any one of claims 1 to 5, which represents an angle formed by a normal of a surface of an object and an incident X-ray beam. In the measurement, determine the number of measurement points,
The diffraction ring analysis method according to claim 1, wherein in the analysis, the diffraction ring is approximated by a Fourier series having a number of terms corresponding to the number of measurement points, and the stress and strain of the measurement object are obtained. 2. In the analysis, the deformation of the diffraction ring is expressed as a matrix by Fourier series, and the inverse matrix is used to analyze the Fourier series coefficient (hereinafter referred to as Fourier coefficient), the stress and strain state of the measurement object. Or the diffraction ring analysis method according to 7. In the above analysis, when a part or a plurality of parts of the diffraction ring is missing, a row corresponding to the angle of the missing part is removed from the matrix representing the diffraction ring, and the column having a small influence on the stress / strain measurement is removed. The diffraction ring analysis method according to claim 8, wherein a matrix is created by removing the, and the Fourier coefficient, stress, and strain are calculated using the pseudo inverse matrix. A beam irradiation unit that irradiates a specific part of the measurement object with a beam having a diffracting property;
An imaging unit that images the diffracted beam reflected from the specific part and forms a diffraction ring on the imaging surface;
A diffraction ring analyzer including a data processing unit that calculates at least one of stress or strain of the specific portion by performing Fourier transform on a measurement result obtained by the imaging unit. The diffraction ring analyzer according to claim 10, wherein the imaging unit is a solid-state X-ray imaging device or an imaging plate using a semiconductor. The diffraction ring according to claim 10 or 11, wherein the imaging unit includes two solid-state imaging elements, and is arranged so that the beam passes through a gap between the two solid-state imaging elements above and below the diffraction ring. Analysis equipment.