JP5354675B2 - Displacement distribution measuring method, apparatus and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a downsized displacement distribution measuring method, apparatus, and program capable of measuring a displacement distribution of a measurement object at a high speed. <P>SOLUTION: The displacement distribution measuring apparatus (1) includes a laser source (11) emitting light of a predetermined wavelength; a beam splitter (14) splitting the emitted light into object light and reference light; a mirrored PZT stage (20) shifting a phase of the reference light by a predetermined amount; pellicle beam splitters (17, 18) branching the phase-shifted reference light into a plurality; and CCD sensors (15, 16) photographing an interference pattern of the object light scattered by the measurement object (23) and the branched reference light. <P>COPYRIGHT: (C)2011,JPO&amp;INPIT

Description

  The present invention relates to a displacement distribution measuring method, apparatus, and program, and more particularly, to a displacement distribution measuring method, apparatus, and program for measuring a displacement distribution of a measurement object using a plurality of imaging elements by phase shift digital holography. .

  It is an important issue in many industrial fields to accurately measure stress, displacement, and strain of machine structures. In particular, it is important to efficiently inspect defects in infrastructure structures such as bridges, and development of techniques for measuring high-speed and efficient displacement distribution and strain distribution (hereinafter collectively referred to as “displacement distribution”). Is required.

  Phase-shifting digital holography (Phase-shifting Digital Holography, PSDH) is a new method capable of measuring minute displacement distribution and strain distribution of a measurement object without contact and without surface treatment. In this method, the interference fringes before and after the deformation of the measurement object can be imaged by a CCD camera, reproduced by a computer, and the process of developing the film can be omitted, so that the displacement amount of the measurement object surface can be measured at high speed ( For example, refer nonpatent literature 1).

  The displacement distribution measuring device using phase shift digital holography is less susceptible to external vibration due to its miniaturization, so that a measurement experiment can be performed outdoors without being on an optical test bench. For this reason, research on downsizing of the measuring apparatus has been conducted, and a portable displacement distribution measuring apparatus in which an optical system is made compact and integrated is desired.

  Under such circumstances, a technique is known that enables a measurement object to be irradiated with a laser from two directions and to measure the displacement in the in-plane direction and the out-of-plane direction of the measurement object with high accuracy (for example, see Patent Document 1). .

  However, in displacement distribution measurement by digital holography, in order to measure displacement in three directions, light reception information from three independent directions is required, and therefore, incident light of at least three light beams is necessary. In order to incorporate the device into a small apparatus, it is necessary to design a rather complicated optical system.

  Therefore, a laser beam is irradiated simultaneously from three directions as object light, components in each direction are extracted from a digital hologram photographed by seven phase shifts, and a three-dimensional displacement distribution and a two-dimensional strain distribution are obtained from the obtained components. Has been proposed (see, for example, Patent Document 2).

JP 2007-071584 A JP 2007-240465 A

Isao Takahashi and 4 others, “Out-of-plane displacement measurement using phase shift digital holography”, Experimental Mechanics, June 2003, Vol. 3, no. 2, p. 98-102

  However, the technique of Patent Document 1 takes a lot of time to measure the displacement distribution because a single image sensor mechanically uses a shutter to switch the irradiation direction in order and sequentially captures each image.

  On the other hand, although the technique of Patent Document 2 is more advantageous than the apparatus according to the invention of Patent Document 1 in terms of downsizing, there is room for further improvement because three optical systems for producing a laser light source and object light are required. ing. In addition, since the number of phase shifts required for shooting is seven or more, further improvement in the time required for shooting is desired.

  SUMMARY OF THE INVENTION An object of the present invention is to provide a displacement distribution measuring method, apparatus, and program by phase shift digital holography that can shorten the measuring time of the displacement distribution of a measurement object while reducing the size of the apparatus.

  The inventors of the present application have made extensive studies on the downsizing of the displacement distribution measuring device and the method for measuring the displacement distribution at high speed. As a result, the displacement distribution measuring device has a plurality of image sensors and has a single object beam. In general, the on-axis configuration in which the object light and the reference light are incident in parallel to the CCD sensor is changed to the off-axis configuration in which the object light and the reference light are not incident in parallel. It has been found that the measurement can be simplified and the displacement distribution and the like can be measured at high speed by reducing the number of phase shifts and omitting the shutter switching step with the miniaturization of the measuring device. That is, in digital holography, since the pixel pitch of the image sensor is larger than the particle size of the hologram dry plate, an on-axis optical system in which object light and reference light are in the same direction has been used. -Axis configuration is not essential, and it has been demonstrated that even an off-axis optical system can capture a hologram. In addition, in the off-axis optical system, the inventors of the present application actually have the measurement object obliquely forward rather than in front of the imaging element, but the reproduced image is captured by using Fourier transform for the calculation at the time of reproduction. Utilizing the fact that it appears in front of the element and using a plurality of image sensors for one light beam, it becomes possible to obtain the same number of received light information from different independent directions as the image sensor. Simplify.

  That is, a displacement distribution measuring method according to the present invention is a displacement distribution measuring method for measuring displacement due to deformation of a measurement object by phase shift digital holography in an off-axis optical system, and emitting a laser beam having a predetermined wavelength; Separating the emitted laser light into object light for irradiating the measurement object and reference light for generating interference fringes with the object light, and a phase of the reference light by a predetermined amount The phase-shifted reference light to be incident on each of a predetermined number of imaging elements whose optical axes are parallel to each other, and the object scattered by the measurement object The step of imaging the interference fringes between the light and each branched reference light by each image sensor, and the measurement from each of the interference fringes imaged by each image sensor Calculating a complex amplitude distribution in the body of the reproduced image and is characterized in that it comprises a step of measuring a displacement distribution of the measurement object from the phase difference of the complex amplitude distribution of the front and rear deformation of the measurement object.

  A displacement distribution measuring method according to the present invention is a displacement distribution measuring method for measuring displacement due to deformation of a measurement object by phase shift digital holography in an off-axis optical system, and emitting a laser beam of a predetermined wavelength; Separating the emitted laser light into object light for irradiating the measurement object and reference light for generating interference fringes with the object light, and a phase of the object light by a predetermined amount A step of shifting the reference light into a plurality of light beams so as to be incident on each of a predetermined number of imaging elements whose optical axes are parallel to each other, and the object that is phase-shifted and scattered by the measurement object The step of imaging the interference fringes between the light and each branched reference light by each image sensor, and the measurement from each of the interference fringes imaged by each image sensor Calculating a complex amplitude distribution in the body of the reproduced image and is characterized in that it comprises a step of measuring a displacement distribution of the measurement object from the phase difference of the complex amplitude distribution of the front and rear deformation of the measurement object.

  The displacement distribution measurement method according to the present invention further includes a step of obtaining a strain distribution from the obtained displacement distribution of the measurement object.

  The displacement distribution measuring method according to the present invention further includes a step of adjusting the position of a reproduced image obtained from the interference fringe for each of the interference fringes imaged by the imaging device. Is.

  A displacement distribution measuring apparatus according to the present invention is a displacement distribution measuring apparatus that measures displacement due to deformation of a measurement object by phase-shift digital holography in an off-axis optical system, and that emits laser light having a predetermined wavelength. Means, separation means for separating the object light for irradiating the measurement object with the generated laser light and reference light for generating interference fringes with the object light, and the phase of the reference light A phase shift means for shifting by a predetermined amount; a branch means for branching the phase-shifted reference light into a plurality of light beams so as to enter each of a predetermined number of imaging elements whose optical axes are parallel to each other; and the measurement object. Each of the interference fringes imaged by each of the plurality of image sensors that images the interference fringes of the scattered object light and each branched reference light with each image sensor Displacement distribution calculating means for calculating a complex amplitude distribution of a reproduced image of the measurement object and calculating a displacement distribution of the measurement object from a phase difference of the complex amplitude distribution before and after the deformation of the measurement object. To do.

A displacement distribution measuring apparatus according to the present invention is a displacement distribution measuring apparatus that measures displacement due to deformation of a measurement object by phase-shift digital holography in an off-axis optical system, and that emits laser light having a predetermined wavelength. Means, separation means for separating the object light for irradiating the measurement object with the generated laser light and reference light for generating interference fringes with the object light, and the phase of the object light Phase-shifting means for shifting by a predetermined amount; branching means for branching the phase-shifted reference light into a plurality of light beams so as to be incident on each of a predetermined number of imaging elements whose optical axes are parallel to each other; A plurality of image sensors that capture images of interference fringes between the object light scattered by the measurement object and each branched reference light;
The complex amplitude distribution of the reproduced image of the measurement object is calculated from each of the interference fringes imaged by each imaging device, and the displacement distribution of the measurement object is calculated from the phase difference of the complex amplitude distribution before and after the deformation of the measurement object. And a displacement distribution calculating means.

  The displacement distribution measuring apparatus according to the present invention further includes strain distribution analysis means for obtaining a strain distribution from the obtained displacement distribution of the measurement object.

  The displacement distribution measuring apparatus according to the present invention further includes reproduction image position adjusting means for adjusting the position of the reproduction image obtained from the interference fringe for each of the interference fringes photographed by the image sensor. It is characterized by.

  Moreover, the displacement distribution measurement program according to the present invention provides the interference fringes imaged by each image sensor on a computer configured as the displacement distribution calculation means in the displacement distribution measurement device according to any one of claims 5 to 8. A step of calculating a complex amplitude distribution of a reproduced image of the measurement object from each of the steps, and a step of calculating a displacement distribution of the measurement object from a phase difference of the complex amplitude distribution before and after the deformation of the measurement object. is there.

  According to the present invention, it is possible to reduce the size of the measuring device by simplifying the optical system with one light source, and reduce the displacement distribution and strain distribution of the measuring object by reducing the number of phase shifts and omitting the shutter switching process. It can measure at high speed.

It is a block diagram of the displacement distribution measuring device of Example 1 by the present invention. It is a figure which shows the diffraction phenomenon of the object light and reference light in a phase shift digital holography interferometry. It is a figure which shows the correspondence of the complex amplitude distribution in a hologram surface and a reproduction | regeneration surface. It is a schematic diagram of the interference fringe pattern on each pixel of the image sensor at the time of phase shift with respect to (a) on-axis configuration and (b) off-axis configuration. It is a figure which shows the positional relationship of the arrangement | positioning of two CCD sensors, an object, and a reproduction image. It is a conceptual diagram of reproduction in a space adjacent to the reproduction plane in the in-plane direction. It is a figure which shows the movement of the optical axis in a hologram surface and a reproduction | regeneration surface. It is a figure which shows the movement of the reproduction | regeneration image on a reproduction | regeneration surface by the optical axis adjustment by this invention. It is a measurement sample used in the in-plane displacement measurement experiment by Example 1 of this invention. In Example 1 of this invention, it is a figure which shows the reproduction image before a deformation | transformation obtained by (a) CCD sensor 15 and (b) CCD sensor 16. FIG. In Example 1 of this invention, it is a figure which shows the phase difference before and behind a deformation | transformation obtained by (a) CCD sensor 15 and (b) CCD sensor 16. FIG. It is a figure which shows the displacement distribution of the x direction after the deformation | transformation obtained by Example 1 of this invention. It is a figure which shows the distortion distribution of the x direction after the deformation | transformation obtained by Example 1 of this invention. It is a block diagram of the displacement distribution measuring device of Example 2 by the present invention. (A)-(d) is a figure which shows the structural example of the image pick-up element (CCD sensor) in the displacement distribution measuring apparatus of Example 1 and 2 by this invention.

  First, an apparatus for measuring the displacement distribution and strain distribution of the measurement object according to the first embodiment of the present invention will be described.

  FIG. 1 is a block diagram showing the configuration of the displacement distribution measuring apparatus according to the first embodiment of the present invention. The displacement distribution measuring device 1 includes a laser light source 11, a spatial filter 12, a convex lens 13, a beam splitter 14, an image sensor (for example, CCD sensors 15 and 16 of a two-dimensional image sensor), a pellicle beam splitter 17, and 18, a half mirror 19, a PZT stage 20 with a mirror, an ND filter 21, a mirror 22, and a displacement distribution calculation device 24.

  The laser light source 11 can be a He—Ne laser light source having a wavelength of 632.8 nm and an output of 5 mW, for example, and emits a laser beam for recording and reproducing a hologram having a predetermined wavelength.

  The spatial filter 12 removes spatial noise from the laser light emitted from the laser light source 11 and outputs it to the convex lens 13.

  The convex lens 13 outputs the laser light output from the spatial filter 12 as parallel light.

  The beam splitter 14 is an object beam for irradiating the measurement object 23 with the parallel light from the convex lens 13 and a reference beam used as a reference for calculating the phase difference of the complex amplitude distribution before and after the deformation of the measurement object 23 on the reproduction surface. And to separate.

  The mirror-attached PZT stage 20 shifts the phase of the reference light that has passed through the half mirror 19 by a predetermined amount and reflects it to the half mirror 19.

  The ND filter 21 adjusts and outputs a predetermined amount so that the intensity of the reference light reflected by the half mirror 19 is approximately the same as the intensity of the object light.

  The pellicle beam splitter 17 is adjusted in intensity by the ND filter 21, reflects a part of the reference light to the CCD sensor 15 and reflects the light reflected by the mirror 22 to the pellicle beam splitter 18.

  The pellicle beam splitter 18 reflects a part of the reference light transmitted through the pellicle beam splitter 17 to the CCD sensor 16.

  The CCD sensors 15 and 16 obtain, as a hologram, interference fringes between the reference light reflected by the pellicle beam splitters 17 and 18 and the object light separated by the beam splitter 14 and reflected by the measurement object 23 as a hologram. It is sent to the distribution calculation device 24.

  The displacement distribution calculation device 24 has a phase difference analysis function 24a, a displacement analysis function 24b, and a distortion analysis function 24c. For each of the interference fringes acquired from the CCD sensors 15 and 16, a reproduced image from the interference fringes is obtained. And the displacement distribution of the measurement object 23 is calculated from the phase difference of the complex amplitude distribution before and after the deformation of the measurement object 23. Incidentally, interference fringes acquired as holograms by the CCD sensors 15 and 16 can be recorded in a memory (not shown).

  The phase difference analysis function 24a is a function for calculating the phase difference on the reproduction surface from the interference fringes between the object light and the reference light before and after the deformation of the measurement object 23 recorded as a hologram by the CCD sensors 15 and 16.

  The displacement analysis function 24b is a function for analyzing the displacement of the measurement object 23 from the phase difference on the reproduction surface obtained by the phase difference analysis function 24a.

  The strain analysis function 24c is a function for calculating strain from the displacement of the measurement object 23 obtained by the displacement analysis function 24b.

  As described above, the displacement distribution measuring apparatus 1 according to the present invention can simplify the optical system because there is one light source, reduce the size of the measuring apparatus, and reduce the number of phase shifts. And strain distribution can be measured at high speed.

  In the displacement distribution measuring apparatus 1, the object light and the reference light are emitted from the laser source 11 and separated into the object light and the reference light by the beam splitter 12, and the reference light is phase-shifted by a predetermined amount by the mirrored PZT stage 20, and the pellicle beam splitters 17 and 18 are used. Thus, the light enters the CCD sensor 15 and the CCD sensor 16 from the front.

  On the other hand, the object light passes between the CCD sensors 15 and 16 and irradiates the object 18 from the front, and the scattered light reflected by the surface of the object 18 enters the CCD sensors 15 and 16. The interference fringes of the incident object light and reference light are recorded as holograms in both the CCD sensors 15 and 16.

  Here, the operation of the displacement distribution calculating device 24 that analyzes the displacement and distortion of the measurement object 23 from the interference fringes photographed by the CCD sensors 15 and 16 will be described in detail.

FIG. 2 shows how object light and reference light interfere with each other in phase shift digital holography interferometry. Assuming that the coordinates on the recording surface of the image sensor (CCD sensors 15 and 16) are (X, Y), the complex amplitude A _O (X, Y) of the object light on the surface of the image sensor, and the complex amplitude A _r (X of the reference light) , Y) can be expressed as follows:
Here, a _O (X, Y) and a _r (X, Y) are amplitude distributions of object light and reference light, respectively, and Φ _O (X, Y) and Φ _r (X, Y) are respectively referred to object light and reference light. The phase distribution of light, α is the phase shift amount of the reference light. From the equations (1) and (2), the interference fringes I (X, Y, α) recorded by the CCD sensors 15 and 16 can be expressed as follows.
The interference fringes thus obtained are recorded as a hologram.

Since parallel light is used as the reference light, it can be considered that the amplitude on the recording surface of the CCD sensors 15 and 16 is constant and there is no phase change, and a _r (X, Y) = 1, Φ _r (X, Y ) = 0, no problem. Accordingly, the amplitude a _O (X, Y) and the phase Φ _O (X, Y) of only the object light on the recording surfaces of the CCD sensors 15 and 16 are obtained by the phase shift method in which α is changed to a plurality of values. Can do. From this phase and amplitude, the complex amplitude distribution g (X, Y) on the recording surface of the CCD sensors 15 and 16 is
Thus, the complex amplitude distribution of only the object light on the recording surfaces of the CCD sensors 15 and 16 can be obtained.

Next, a complex amplitude distribution on the reproduction surface is obtained. As shown in FIG. 3, the complex amplitude distribution on the surface of the measurement object 23 gives the distance (reproduction distance) R to the measurement object 23 from the complex amplitude distribution g (X, Y) on the recording surface of the CCD sensors 15 and 16. Thus, it can be obtained by performing the Fresnel transformation shown in Equation (5).
Here, u (x, y) is a complex amplitude distribution on the reproduction surface, R is a reproduction distance (distance between the recording surface and the reproduction surface), k is a wave number, and F is an operator representing a Fourier transform. A reproduced image can be obtained by calculating the intensity of the complex amplitude distribution u (x, y) on the reproduction surface thus obtained.

  Further, the change in the optical path length can be obtained by obtaining the phase difference of the complex amplitude distribution before and after the deformation of the measurement object 23, and the displacement distribution, the strain distribution, etc. of the measurement object 23 are obtained from the obtained change in the optical path length. Is possible.

  Subsequently, in-plane displacement distribution measurement by the off-axis optical system used in the present invention will be described.

  FIG. 4 schematically shows a pattern of interference fringes on each pixel of the image sensor at the time of phase shift. FIGS. 4A and 4B show interference fringes (indicated by dotted lines) in the case of an on-axis configuration and an off-axis configuration, respectively. In the imaging device, since the light receiving surface of each pixel has a predetermined area, the integrated value of the intensity on the light receiving surface is output as the luminance value of the pixel. In FIG. 4, a vertical line represents a boundary between pixels, and a horizontal solid line represents an output value of luminance at the pixel.

  As shown in FIG. 4A, in the case of on-axis, since the pitch of the interference fringes is larger than the size of one pixel, the output value of the luminance of each pixel is spatially related to the intensity distribution of the interference fringes. The change is almost the same, and the same change with the same amplitude as the intensity distribution of the interference fringes is shown for the phase shift.

  On the other hand, as shown in FIG. 4B, in the case of off-axis, since the pitch of the interference fringes is smaller than the size of one pixel, a plurality of interference fringes appear in one pixel. As a result, the luminance output value of each pixel does not spatially represent the change in the original interference fringes. However, when viewed in one pixel, the amplitude of the CCD sensor output shows a change in the intensity of one period of the interference fringes according to the four phase shifts. That is, as described above, since the integrated value of the intensity of interference fringes on the light receiving surface of each pixel is output as the luminance value of that pixel, vibrations of a plurality of periods appear in each pixel as shown in FIG. In this case, although the detection accuracy of the displacement due to the deformation of the measurement object 23 is reduced, when attention is paid to the boundary of each pixel, the interference fringes are caused by four phase shifts as in the case of on-axis in FIG. It can be seen that the vibration intensity changes by one cycle. Therefore, even in the case of off-axis, it is possible to obtain a phase distribution by the phase shift method.

  Further, in the reproduction calculation by the discrete Fourier transform represented by the equation (5), whether the object light is in front of the CCD sensors 15 and 16 even when the object light comes from a position shifted from the optical axis by the same size as the reproduction range. It is played as follows. This is because the discrete Fourier transform is an operation that repeats spatially. Therefore, as shown in FIG. 5, if the two CCD sensors 15 and 16 are arranged to be shifted to the left and right by the size of the reproduction range and the object is irradiated from the front through the object light therebetween, The reproduced image is reproduced as if it were in front of the respective CCD sensors 15 and 16.

Here, Fresnel diffraction integration is used for the complex amplitude distribution of the hologram by the object light in the space adjacent to the normal reproduction surface in the in-plane direction, and the complex amplitude distribution (reproduction image) on the reproduction surface is converted to the front surface of the CCD sensor surface. A method for calculating the reproduced image will be described. FIG. 6 shows a conceptual diagram. The complex amplitude distribution of the object light on the CCD sensor surface is g (X, Y), the complex amplitude distribution of the actual object light on the reproduction surface is u _h (x, y), the hologram and the center on the CCD sensor surface Let u (x ′, y) be the reproduction complex amplitude distribution reproduced in the front space sharing the axis. The coordinate system of both distributions on the reproduction surface has a relationship of x = x ′ + h. The light propagation equation from point Q on the CCD sensor surface to point P ′ on the reproduction surface is
It can be expressed. Here, k is the wave number, k = 2π / λ, and r ′ is the distance between the points (x ′, y) and (X, Y). The integration range of X is −H _Y or more and H _Y or less, and the integration range of _Y is −H _Y or more and H _Y or less.

In reproduction of phase shift digital holography, distance approximation is performed in order to use Fresnel diffraction. If the distance between the CCD sensor surface and the playback surface is R,
It can be expressed. Since R is sufficiently large compared to (x′−X) and (y−Y),
Can be approximated. Substituting equation (8) into equation (6),

The light propagation equation from point P on the reproduction surface to point Q on the CCD sensor surface is:
It can be expressed. This r is similarly
Can be approximated.

Substituting equations (10) and (11) into equation (9),
It can be expressed. Here, substituting x = x ′ + h into equation (12) and rearranging,
It becomes.

Further, the integration portion is discretely expressed using sampling intervals on the CCD sensor surface, the number of pixels on the reproduction surface, and discrete coordinates p and Y corresponding to coordinates X on the CCD sensor surface. Since the reproduction range on the reproduction surface is h = λR / ΔX,
Is required. Therefore, from (13) and (14), the discrete representation of the reproduced image complex amplitude distribution u (x ′, y) is u (p ′, q), and the actual complex amplitude distribution u _h (x, y) = u _h. When the discrete expression of (x ′ + h, y) is expressed discretely as u (p, q) = u (p ′ + N _x , q),
And the phase of the complex amplitude distribution reproduced in the space in front of the hologram is obtained by adding −k ((p′ΔX + N _x ΔX) N _x ΔX / 2R + R) to the phase of the complex amplitude distribution of the object light in the adjacent space. It was led to appear as a thing. This phase term is a constant phase for each sampling point of the reproduced image.

  In FIG. 5, unless the two CCD sensors 15 and 16 are strictly arranged, the positions of the reproduced images of the holograms obtained by the respective CCD sensors 15 and 16 do not become the same position in the reproduced images. In practice, it is difficult to physically fine tune it. Therefore, in the present invention, the position of the reproduced image is adjusted by software by the optical axis adjustment method described later. When displacement measurement is performed with one light source and a plurality of image sensors (CCD sensors 15 and 16) as in the present invention, the center of the object light is shifted from the central axis of the CCD sensors 15 and 16, so A reproduced image may be reproduced, and the coordinates on the reproduction surface reproduced by each camera need to be matched. Next, an optical axis adjustment technique for moving the reproducing surface on the xy plane by moving the optical axis on the hologram for reproduction will be described.

As described above, the reproduction of the phase shift digital holography uses the Fourier transform for the Fresnel diffraction integration as shown in the equation (5). In actual reproduction, since the complex amplitude distribution is discrete data for each pixel of the CCD sensor on the surface of the CCD sensor, fast discrete Fourier transform (FFT) is used for Fourier transform. Therefore, the relationship between the sampling interval on the CCD sensor surface and the sampling interval on the reproduction surface is examined. Expressing equation (5) discretely,
It can be expressed. Here, F is a fast discrete Fourier transform operator. Further, (m, n) and (p, q) represent discrete coordinates of the CCD sensor surface and the reproduction surface, respectively. ΔX and ΔY are sampling intervals at the CCD sensor, and Δx and Δy are sampling intervals at the reproduction surface. Usually, when the fast discrete Fourier transform image g (p, q) of _{N X} pixels × _{N Y} pixels to u (m, n), the sampling interval of the spatial frequency [Delta] [mu, .DELTA..nu respectively,
It can be expressed. In the Fresnel transform, the spatial frequencies μ and ν at the time of Fourier transform are set as shown in the equation (17).
It can be expressed. Therefore, the sampling interval of the Fresnel transformation from Equation (17) and Equation (18) is
It can be expressed. From Expression (19), it can be seen that the sampling intervals Δx and Δy of the reproduction surface in the Fresnel diffraction integration are proportional to the wavelength λ and the reproduction distance R, and inversely proportional to the sampling intervals ΔX and ΔY of the CCD sensors 15 and 16.

When the z-axis is moved by a certain amount on the CCD sensor surface, the amount of movement becomes equal to the amount of movement on the reproduction surface. Accordingly, the reproduced image can be moved by an arbitrary amount of movement by moving the optical axis. On the other hand, as shown in FIG. 7, consider the position of the reproduction surface in the case where the optical axis D _X pixels in the X-axis direction on the CCD sensors 15 and 16 face moves D _Y parallel to the Y-axis direction. At this time, when the D _x pixel is moved in the _x- axis direction and the Dy pixel is moved in the y-axis direction on the reproduction surface, Expression (20) is established.
Here, ΔX and ΔY represent sampling intervals of the CCD sensor, and Δx and Δy represent sampling intervals of the reproduction surface. Rewriting equation (20),
It becomes. Here, ΔX and ΔY represent the pixel pitch of the CCD sensor in the X direction and the Y direction, respectively, and Δx and Δy represent the pixel spacing on the reproduction surface in the x direction and the y direction, respectively. ΔX / Δx and ΔY / Δy are ratios between the size of the hologram surface and the size of the reproduction surface, and therefore generally take a value from a fraction to a few ten. Therefore, if the hologram is shifted with a resolution of one pixel on the hologram surface, the reproduced image can be shifted with a resolution of a fraction of a pixel to several tens of pixels on the reproduction surface.

Further, when Expression (19) is substituted into Expression (20), Expression (22) is obtained.
In this way, the amount of movement (D _X pixel, _DY pixel) of the CCD sensors 15 and 16 when it is desired to move the reproduction plane (D _x pixel, D _y pixel) using the equation (21) is calculated. Can do. Also, consider a reproduction image when the reproduction surface is moved. The spatial frequency of the reproduced image on the reproduction surface is finite. The maximum spatial frequency here is half the number of pixels of the CCD sensor (N _X / 2 pixels, N _Y / 2 pixels). Therefore, the reproduction plane when there is an object at the point O _r in FIG. 7 is as shown in FIG. When the optical axis of the reproduction surface is not moved, a reproduction image in the area A is obtained. When the optical axis is moved from the point O _r to the point O _r ′ in FIG. 8, a reproduced image in the region B is obtained.

  Thus, by performing the optical axis adjustment in units of pixels on the hologram surface, the optical axis can be adjusted in units of a fraction of the pixels on the reproduction surface. By utilizing this, in the present invention, it is possible to accurately perform pixel alignment of reproduced images obtained by a plurality of image sensors.

Next, as shown in FIG. 5, the angles from the center of the measurement object 23 to the centers of the CCD sensors 15 and 16 are θ ₁ and θ ₂ , respectively. Assuming that the phase differences before and after deformation obtained at the respective pixels of the CCD sensors 15 and 16 are Δφ ₁ and Δφ ₂ , respectively, the displacements d _x and d _z in the x direction and the z direction are expressed by the equations (23) and (23), respectively. It can be expressed as shown in equation (24).
Here, λ is the wavelength of the light source.

  Thus, the displacement in the in-plane direction of the measurement object 23 can be obtained from the phase difference before and after the deformation of the measurement object 23.

  Here, the result of the in-plane displacement measurement experiment by the displacement distribution measuring apparatus according to the first embodiment of the present invention will be described.

  In the two CCD sensors 15 and 16 in FIG. 1, elements having a pixel pitch of 4.65 μm, a pixel number of 1280 × 960 pixels, and a gradation number of 256 were used. 960 × 960 pixels were cut out from the photographed image and used.

  A He—Ne laser having a wavelength of 632.8 nm and an output of 5 mW was used as a light source, and parallel light was formed by a spatial filter and a convex lens. The reference light separated by the beam splitter was phase-shifted by the mirror of the PZT stage 20 with a mirror, and entered the CCD sensors 15 and 16 from the front by the pellicle beam splitter.

  On the other hand, the object light passes between the two CCD sensors 15 and 16 and is irradiated onto the measurement object 23 from the front. Scattered light reflected from the surface of the measurement object 23 enters the respective CCD sensors 15 and 16, and interference fringes with the reference light are recorded as holograms. The phase shift digital hologram is photographed by the CCD sensors 15 and 16 while the phase shift is performed four times every π / 2 by the PZT stage 20 with a mirror.

In the arrangement of FIG. 1, the distance between the optical axis of the CCD sensors 15 and 16 and the optical axis of the object light was 40.0 mm and 36.5 mm, respectively, at a reproduction distance R = 300 mm. Thus, an off-axis optical system having angles of θ ₁ = 7.6 deg and θ ₂ = 6.9 deg is obtained. In this case, the reproduction range at the reproduction distance R = 300 mm is 40.8 mm.

  As a sample of the measurement object 23, an aluminum cantilever beam having a 5 mm square and a length of 25 mm was used as shown in FIG. The cantilever was displaced by 12 μm in the y direction at a position 20 mm from the fixed end.

  FIG. 10 shows a reproduction image before deformation obtained from a phase shift digital hologram photographed by each CCD sensor. Thus, it can be confirmed that a reproduced image can be obtained even with an off-axis configuration.

  As described above, in the reproduction calculation by Fourier transform, the actual object is reproduced as if it were at a position shifted by the size of the reproduction range, that is, in front of each CCD sensor. However, since each actual CCD sensor is not strictly arranged, a deviation occurs between the CCD sensor 15 and the CCD sensor 16. Therefore, the CCD sensor 15 hologram is moved by −280 pixels in the i direction and +170 pixels in the j direction so that the reproduced images of the CCD sensor 15 and the CCD sensor 16 are reproduced at the same position in the image. By doing so, the reproduced image was moved by +1.30 mm in the x direction and by −0.91 mm in the y direction.

  Next, the phase difference before and after deformation is shown in FIG. This phase difference is subjected to noise removal by a phase difference averaging method using 256 window functions (see, for example, JP-A-2007-071589).

  FIG. 12 shows a displacement distribution in the x direction obtained as a measurement result. FIG. 13 shows the strain distribution in the x direction obtained as a measurement result. This is obtained by performing a spatial differentiation in the x direction on the displacement distribution of FIG. It can be seen that the upper side of the cantilever is compressed and negative strain is generated, and the lower side is expanded and positive strain is generated as a distribution.

  As described above, the displacement distribution measuring apparatus 1 according to the present embodiment including a plurality of imaging elements can obtain a reproduced image of the measurement object even in the off-axis optical system, and can measure the in-plane displacement and strain distribution. I understand.

  In the displacement distribution measuring apparatus 1 shown in FIG. 1, the phase shift by the mirrored PZT stage 20 is performed on the “reference light”, but can be performed on the “object light” instead of the reference light. A displacement distribution measuring apparatus in this case is shown in FIG. The displacement distribution measuring apparatus 2 according to the second embodiment of the present invention is the same as the displacement distribution measuring apparatus 1 in FIG. 1 in terms of the components and functions of each component, but uses object light instead of reference light as described above. The difference is in the phase shift. That is, the object light separated by the beam splitter 14 is reflected by the half mirror 19, is phase-shifted by the PZT stage 20 with a mirror, passes through the half mirror 19, and is irradiated on the measurement object 23. On the other hand, the separated reference light passes through the ND filter 21, is reflected by the mirror 22, and enters the CCD sensor 15 and the CCD sensor 16 from the front by the pellicle beam splitters 17 and 18. Other processes are the same as those of the displacement distribution measuring apparatus 1.

  By configuring in this way, similarly to the displacement distribution measuring apparatus 1 of the first embodiment, since there is one light source, the optical system can be simplified, the measuring apparatus can be miniaturized, and the number of phase shifts can be reduced. Therefore, the displacement distribution and strain distribution of the measurement object 23 can be measured at high speed.

  In the first and second embodiments, the displacement distribution measuring devices 1 and 2 include the two imaging devices 15 and 16, but the imaging device may be further added. An example of the configuration of the image sensor (CCD sensor) viewed from the measurement object 23 is shown in FIG. (A) is an example in which four CCD sensors (3a-1 to 3a-4) are arranged two by two in the x and y directions. With such a configuration, the displacement of the measurement object 23 in the x and y directions is reduced. The detection sensitivity is uniform and the detection accuracy is improved. Moreover, according to the arrangement | positioning convenience of an apparatus, you may comprise the structure of (a) like (b) (3b-1-3b-4). (C) is a case where three CCD sensors (3c-1 to 3c-3) are provided, and the entire apparatus can be reduced in size. (D) is an example in which a CCD sensor is further added to obtain eight (3d-1 to 3d-8). Since the detection sensitivity of the displacement of the measurement object 23 is improved, the noise can be reduced.

  In the first and second embodiments described above, the entire components shown in FIGS. 1 and 14 are integrated to form a portable displacement distribution measuring device, which can be carried and measured outdoors, for example.

  In addition, although the CCD sensors 15 and 16 and the displacement analysis device 24 are separately configured, they can be integrated as one device.

  Furthermore, as one aspect of the present invention, the displacement distribution measuring device 1 can be configured as a computer that functions as each device. A program for causing a computer to realize each of the above-described components is stored in a storage unit provided inside or outside each computer. Such a storage unit can be realized by an external storage device such as an external hard disk or an internal storage device such as ROM or RAM. The control unit provided in each computer can be realized by control of a central processing unit (CPU) or the like. In other words, the CPU can appropriately read from the storage unit a program in which the processing content for realizing the function of each component is described, and realize the function of each component on the computer. Here, you may implement | achieve the function of each component by all or a part of hardware.

  Although the present invention has been described in detail with specific examples, it will be apparent to those skilled in the art that various modifications and changes can be made without departing from the scope of the claims of the present invention. For example, the displacement in three directions can be measured by increasing the number of image sensors. Therefore, the present invention is not limited to the above embodiment.

  According to the present invention, by using a plurality of image sensors, the optical system can be simplified and the apparatus can be miniaturized, and the displacement distribution and strain distribution of the measurement object can be measured at high speed.・ Strain distribution measurement test, 2) Defect inspection of steel structure, concrete structure, resin / ceramic structure, etc. 3) Material test 4) Micromachine material test / characteristic evaluation test, etc. .

DESCRIPTION OF SYMBOLS 1 Displacement distribution measuring device 2 Displacement distribution measuring device 3a-1 to 3a-4, 3b-1 to 3b-4, 3c-1 to 3c-3, 3d-1 to 3d-8 CCD sensor 11 Laser light source 12 Spatial filter 13 Convex lens 14 Beam splitter 15, 16 CCD sensor 17, 18 Pellicle beam splitter 19 Half mirror 20 PZT stage with mirror 21 ND filter 22 Mirror 23 Measuring object 24 Displacement distribution calculation device 24a Phase difference analysis function 24b Displacement analysis function 24c Distortion analysis function

Claims (9)

A displacement distribution measurement method for measuring displacement due to deformation of a measurement object by phase shift digital holography in an off-axis optical system,
Emitting a laser beam of a predetermined wavelength;
Separating the emitted laser light into object light for irradiating the measurement object and reference light for generating interference fringes with the object light;
Shifting the phase of the reference light by a predetermined amount;
Branching the phase-shifted reference light into a plurality of light beams so as to be incident on each of a predetermined number of imaging elements having optical axes parallel to each other;
Imaging each interference fringe between the object light scattered by the measurement object and each branched reference light with each imaging element;
The complex amplitude distribution of the reproduced image of the measurement object is calculated from each of the interference fringes imaged by each image sensor, and the displacement distribution of the measurement object is measured from the phase difference of the complex amplitude distribution before and after the deformation of the measurement object. And steps to
A displacement distribution measuring method characterized by comprising: A displacement distribution measurement method for measuring displacement due to deformation of a measurement object by phase shift digital holography in an off-axis optical system,
Emitting a laser beam of a predetermined wavelength;
Separating the emitted laser light into object light for irradiating the measurement object and reference light for generating interference fringes with the object light;
Shifting the phase of the object light by a predetermined amount;
Branching the reference light into a plurality of light beams so as to be incident on each of a predetermined number of image sensors having optical axes parallel to each other;
Imaging each interference fringe between the object light that is phase-shifted and scattered by the measurement object and each branched reference light with each imaging device;
The complex amplitude distribution of the reproduced image of the measurement object is calculated from each of the interference fringes imaged by each image sensor, and the displacement distribution of the measurement object is measured from the phase difference of the complex amplitude distribution before and after the deformation of the measurement object. And steps to
A displacement distribution measuring method characterized by comprising:   The displacement distribution measuring method according to claim 1, further comprising a step of obtaining a strain distribution from the obtained displacement distribution of the measurement object.   4. The method according to claim 1, further comprising a step of adjusting a position of a reproduced image obtained from the interference fringe for each of the interference fringes imaged by the imaging element. The displacement distribution measuring method described in 1. A displacement distribution measuring device for measuring displacement due to deformation of a measurement object by phase shift digital holography in an off-axis optical system,
Light irradiation means for generating laser light of a predetermined wavelength;
Separating means for separating the generated laser light into object light for irradiating the measurement object and reference light for generating interference fringes with the object light;
Phase shift means for shifting the phase of the reference light by a predetermined amount;
Branching means for branching the phase-shifted reference light into a plurality of light beams so as to be incident on each of a predetermined number of imaging elements whose optical axes are parallel to each other;
A plurality of image sensors that capture images of interference fringes between the object light scattered by the measurement object and each branched reference light;
The complex amplitude distribution of the reproduced image of the measurement object is calculated from each of the interference fringes imaged by each imaging device, and the displacement distribution of the measurement object is calculated from the phase difference of the complex amplitude distribution before and after the deformation of the measurement object. Displacement distribution calculating means for
A displacement distribution measuring device comprising: A displacement distribution measuring device for measuring displacement due to deformation of a measurement object by phase shift digital holography in an off-axis optical system,
Light irradiation means for generating laser light of a predetermined wavelength;
Separating means for separating the generated laser light into object light for irradiating the measurement object and reference light for generating interference fringes with the object light;
Phase shift means for shifting the phase of the object light by a predetermined amount;
Branching means for branching the phase-shifted reference light into a plurality of light beams so as to be incident on each of a predetermined number of imaging elements whose optical axes are parallel to each other;
A plurality of image pickup devices that pick up images of interference fringes between the object light that is phase-shifted and scattered by the measurement object and the branched reference lights,
The complex amplitude distribution of the reproduced image of the measurement object is calculated from each of the interference fringes imaged by each imaging device, and the displacement distribution of the measurement object is calculated from the phase difference of the complex amplitude distribution before and after the deformation of the measurement object. Displacement distribution calculating means for
A displacement distribution measuring device comprising:   The displacement distribution measuring apparatus according to claim 5 or 6, further comprising strain distribution analysis means for obtaining a strain distribution from the obtained displacement distribution of the measurement object.   The reproduction image position adjusting means for adjusting the position of the reproduction image obtained from the interference fringe for each of the interference fringes photographed by the image pickup device is further provided. The displacement distribution measuring apparatus according to any one of the above. A computer configured as the displacement distribution calculating means in the displacement distribution measuring device according to any one of claims 5 to 8,
Calculating a complex amplitude distribution of a reproduced image of the measurement object from each of the interference fringes imaged by each imaging device;
Calculating a displacement distribution of the measurement object from a phase difference of the complex amplitude distribution before and after the deformation of the measurement object;
Displacement distribution measurement program to execute.