JP4025878B2 - Apparatus for obtaining reproduced image of object, phase shift digital holographic displacement distribution measuring apparatus, and parameter identifying method - Google Patents

Description

  The present invention relates to an apparatus for recording an image of an object as a digital hologram by phase shift digital holography to obtain a reproduced image. The present invention further relates to a displacement distribution measuring apparatus that records an image of an object as a digital hologram by phase shift digital holography and measures the displacement distribution or deformation distribution of the object as phase information from the recorded digital hologram. The present invention relates to an enlarged displacement distribution measuring apparatus. The invention further relates to a method for identifying parameters in these devices.

There are various methods such as speckle interferometry, moire interferometry, digital image correlation, and holographic interferometry as displacement measurement methods for optically measuring displacement distribution and strain distribution of structures and the like with high accuracy. Among them, the holographic interferometry is troublesome in the development processing of the recording plate, but because it can measure the displacement, deformation, shape, etc. of rough surface objects in a non-contact, high sensitivity, full field of view, machine industry, automobile industry, It is used in various fields such as nondestructive inspection and medicine in the acoustic machinery industry. In displacement measurement by holographic interferometry, interference fringes representing the displacement of an object can be obtained by double exposure on the recording plate of two images before and after displacement with different phases. You can know the amount. In recent years, with the improvement of computer processing capacity and the high resolution and high pixel count of CCD elements, holograms are recorded on a CCD camera instead of film, captured in a computer, and reproduced by Fresnel transformation, one of the light diffraction methods. Shift digital holographic interferometry has been devised. Phase shift digital holography is characterized in that not only the intensity of light but also the phase can be obtained as digital information, and research on applying it to measurement of minute displacement of an object is being actively conducted.
Measurement of deflection distribution by phase shift digital holography, Isao Takahashi, Proceedings of the Japan Society for Experimental Force, p122-125, No2, (2002) Measurement of three-dimensional surface shape and deformations using phase stepping speckle interferometry, Liu-Sheng Wang, Society of Photo-Optical Instrumentation, p2333-2340, (1996)

  Non-Patent Document 1 describes the reproduction principle of phase shift digital holography. The normal reproduction range can be expanded by increasing the distance between the CCD and the object. However, if the distance between the object and the CCD is increased, there is a problem in terms of accuracy. In speckle interferometry as described in Non-Patent Document 2, the displacement of an object is measured by imaging the object on the CCD surface. At this time, the measurement range is derived from the lens imaging formula. Therefore, the measurement range can be changed by changing the lens arrangement and focal length. On the other hand, since the lens is imaged, the positions of the object, the lens, and the CCD are fixed.

  In view of the above, the present invention provides a phase shift digital holography displacement distribution measuring device that can reduce the restriction of the phase shift digital holography measurement range, enables a wide range of measurement, and does not require the CCD to be fixed to the imaging plane. The purpose is to provide. The present invention further provides a method for identifying parameters in these devices.

  The displacement distribution measuring apparatus according to the present invention comprises a laser light source means for generating laser light, a beam splitting means for splitting the laser light generated by the laser light source means in two directions, and a laser beam split by the beam splitting means. Reference light forming means for forming reference light from one side and imaging means are provided, and the other of the laser beams divided by the beam splitting means is reflected by an object and incident on the imaging means as object light, and the reference In the displacement distribution measuring apparatus configured to form a digital hologram from the object light and the reference light, light is also incident on the imaging means, and the object light is interposed between the imaging means and the object. A concave lens through which is passed is arranged. Another embodiment of the displacement distribution measuring apparatus of the present invention is characterized by further comprising means for collimating the laser light emitted by the laser light source means.

  According to the present invention, by adding a concave lens to the optical system, the restriction of the phase shift digital holography measurement range is reduced, a wide range of measurement is possible, and the CCD is fixed to the imaging surface to reproduce a virtual image. There is provided a phase shift digital holographic displacement distribution measuring apparatus which is not necessary.

  First, the principle of phase shift digital holography will be described. FIG. 1 is a diagram showing an example of the configuration of a recording / reproducing optical system of phase shift digital holography. The phase shift digital holography uses an on-axis optical system in which object light and reference light are incident on a CCD coaxially. The recording / reproducing optical system 1 includes a laser light source 2 that generates a laser beam, a spatial filter 4 that passes only a specific spatial frequency component of the laser light generated by the laser light source 2, and a laser beam that has passed through the spatial filter 4 in parallel. A collimator lens 6, a beam splitter 8 that splits the laser light paralleled by the collimator lens 6 in two directions, and a diaphragm 10 that allows only one part of the laser light split by the beam splitter 8 to pass through; It includes a neutral density filter 12 that attenuates the laser light that has passed through the diaphragm 10, a PZT stage 14 with a mirror that reflects the laser light attenuated by the neutral density filter 12 while phase-shifting, and a CCD camera 16. The other of the laser beams divided by the beam splitter 8 is reflected by an object to be measured, passes through the beam splitter 8 and enters the CCD camera 16 as object light. The laser light reflected by the mirrored PZT stage 14 passes through the neutral density filter 12 and the diaphragm 10 again, is reflected toward the CCD camera 16 by the beam splitter 8, and enters the CCD camera 16 as reference light.

と表すことができる。ここでａ_ｏ（Ｘ，Ｙ）、ａ_ｒ（Ｘ，Ｙ）はそれぞれ物体光と参照光の振幅分布である。またΦ_ｏ（Ｘ，Ｙ）、Φ_ｒ（Ｘ，Ｙ）はそれぞれ物体光と参照光の位相分布である。αはミラー付きＰＺＴステージでシフトさせる参照光の位相シフト量で、それぞれ０、π／２、π、３π／２である。αの値を０、π／２、π、３π／２でとシフトさせた４枚のデジタルホログラムＩ_０（Ｘ，Ｙ）、Ｉ_１（Ｘ，Ｙ）、Ｉ_２（Ｘ，Ｙ）、Ｉ_３（Ｘ，Ｙ）はそれぞれ、

となる。位相シフトデジタルホログラフィでは、式（２）〜式（５）を位相シフト法の計算式

に代入して計算をおこない、ＣＣＤ面における物体光の複素振幅分布を求める。ここで、参照光に平行光を用いるため、ＣＣＤ面における参照光の振幅分布と位相分布は一定で定数とすることができる。したがって、位相シフト法により求めたＣＣＤ面における複素振幅分布ｇ（Ｘ，Ｙ）は

となり、ＣＣＤ面における物体光のみの複素振幅分布を求めることができる。 When the coordinates on the CCD surface are (X, Y), the interference fringes I (X, Y, α) recorded by the CCD are

It can be expressed as. Here, a _o (X, Y) and a _r (X, Y) are amplitude distributions of the object light and the reference light, respectively. Φ _o (X, Y) and Φ _r (X, Y) are phase distributions of the object light and the reference light, respectively. α is a phase shift amount of the reference light shifted by the PZT stage with a mirror, and is 0, π / 2, π, and 3π / 2, respectively. Four digital holograms I ₀ (X, Y), I ₁ (X, Y), I ₂ (X, Y), I with the value of α shifted by 0, π / 2, π, 3π / 2 ₃ (X, Y)

It becomes. In phase shift digital holography, equations (2) to (5) are calculated using the phase shift method.

To calculate the complex amplitude distribution of the object light on the CCD surface. Here, since parallel light is used as the reference light, the amplitude distribution and phase distribution of the reference light on the CCD surface can be constant and constant. Therefore, the complex amplitude distribution g (X, Y) on the CCD surface obtained by the phase shift method is

Thus, the complex amplitude distribution of only the object light on the CCD surface can be obtained.

で表せるフレネル回折積分により、元の物体の複素振幅分布ｕ（ｘ，ｙ）を求める。図２は、回折現象の概念を示す線図である。ここで、Ｒは記録面と再生面の距離、ｋは波数、ｆ［］はフーリエ変換を表す演算子である。この再生面の複素振幅分布の強度をもとめることで再生像を得ることができる。 When the coordinates on the reproduction surface are (x, y), the complex amplitude distribution of only the object light on the CCD surface is reached to the reproduction surface on which the object is placed.

The complex amplitude distribution u (x, y) of the original object is obtained by Fresnel diffraction integration expressed as follows. FIG. 2 is a diagram showing the concept of the diffraction phenomenon. Here, R is the distance between the recording surface and the reproducing surface, k is the wave number, and f [] is an operator representing the Fourier transform. A reproduction image can be obtained by obtaining the intensity of the complex amplitude distribution on the reproduction surface.

  A phase shift digital holographic displacement distribution measuring apparatus according to the present invention will be described. FIG. 3 is a diagram showing an example of the configuration of the phase shift digital holographic displacement distribution measuring apparatus according to the present invention. The phase shift digital holographic displacement distribution measuring device 21 includes a laser light source 22, a spatial filter 23, a collimator lens 24, a beam splitter 26, a half mirror 28, a neutral density filter 30, a diaphragm 32, and a PZT stage with a mirror. 34, a glass plate 36, a CCD camera 38, a half mirror 40, and a concave lens 42. The laser light emitted from the laser light source 22 transmits only a specific spatial frequency component through the spatial filter 23, and the laser light that has passed through the spatial filter 23 is collimated by the collimator lens 24 and enters the beam splitter 26. The laser light incident on the beam splitter 26 is divided in two directions, one toward the half mirror 28 and the other toward the half mirror 40. One part of the laser light that has passed through the half mirror 28 is attenuated by the neutral density filter 30, and only a part of the laser light enters the mirror-attached PZT stage 34 by the diaphragm 32. The laser beam reflected while being phase-shifted by the PZT stage with mirror 34 passes through the diaphragm 32 and the neutral density filter 30 again, and is reflected toward the glass plate 36 by the half mirror 28. The laser light incident on the glass plate 36 is reflected toward the CCD camera 38 and enters the CCD camera 38 as reference light. The other part of the laser light directed toward the half mirror 40 is reflected by the half mirror 40 and travels toward the object 44 to be measured. The laser light reflected by the object 44 passes through the half mirror 40, passes through the concave lens 42, passes through the glass plate 36, and enters the CCD camera 38 as object light.

凹レンズによって結像された像は実際の物体よりも小さくなる。このときの像の倍率はＦ_１／Ｆ_２となる。よって物体が縮小した状態で再生され、限られ再生範囲内により多くの範囲を再生することが可能になる。 In phase shift digital holography interferometry, the complex amplitude distribution on the reproduction surface is obtained by using Fresnel transform. When a concave lens is placed between the CCD and the object, the back propagation of light due to Fresnel conversion becomes an optical path bent by the lens. FIG. 4 is a diagram for explaining the relationship between the object and the reproduction surface. The optical path bent by the concave lens is indicated by a dotted line in FIG. The reconstructed image at this time is obtained as a virtual image by the concave lens. The reproduction distance is not the distance between the CCD and the object, but the distance from the CCD to the virtual image. The position of the virtual image at this time is obtained from the imaging formula of the concave lens. Equation (10) shows the lens imaging formula. F ₁ is the distance from the lens to the virtual image, and F ₂ is the distance from the lens to the object. R ₁ is the distance from the lens to the imaging position. R ₂ is the distance from the CCD to the object.

The image formed by the concave lens is smaller than the actual object. The image magnification at this time is F ₁ / F ₂ . Therefore, the object is reproduced in a reduced state, and a larger range can be reproduced within the limited reproduction range.

となる。ここで、ＦＦＴ［］は高速離散フーリエ変換の演算子である。また、（ｍ，ｎ）と（ｐ，ｑ）はそれぞれ再生面とＣＣＤ面の離散的な座標を表している。ΔＸ、ΔＹとΔｘ、ΔｙはそれぞれＣＣＤと再生面のサンプリング間隔である。通常、Ｎ_ｘ画素×Ｎ_ｙ画素の画像ｇ（ｐ，ｑ）をｕ（ｍ，ｎ）に高速離散フーリエ変換したとき、空間周波数のサンプリング間隔Δμ、Δνは、それぞれ

となる。フレネル変換では、フーリエ変換するときの空間周波数をμ、νとし、波長λ、再生距離Ｒを用いて

と表す。離散的な空間周波数は

となる。よって、式（１２）と式（１４）よりフレネル変換のサンプリング間隔は

となる。ここで図５に示すように、記録面と再生面の間に凹レンズを設置する場合を考える。図５は計測範囲の拡大を説明する線図である。記録面と凹レンズとの距離をＦ_０とする。虚像の位置における再生範囲をＷ_１、物体の位置における再生範囲をＷ_２とする。虚像の位置における再生範囲Ｗ_１、物体の位置における再生範囲Ｗ_２は、ＣＣＤ面のサンプリング間隔をｐとしたとき式（１５）より

と表せる。Ｗ_１の領域にはレンズによってＦ_１／Ｆ_２倍された像が再生される。したがって再生範囲はＦ_２／Ｆ_１倍されることになる。よってレンズを置いたことによる再生範囲の倍率は

で表すことができる。Ｍは再生範囲の倍率とする。またこのときの虚像面における再生範囲Ｈは

と表すことができる。ここで再生範囲Ｈを求めるためにはＲ_１、Ｆ_１、Ｆ_２の３個の未知数を求める必要がある。この未知数を求めるための方法を示す。レンズを除いた状態での物体の再生画像とレンズを置いた状態での虚像の再生画像を得る。このときの再生距離よりＲ_１、Ｒ_２が求められる。また再生画像の対応する場所の画素数を調べ、倍率Ｍを求める。求めた値を式（１８）に代入することにより拡大を行った再生範囲が求められる。

The phase shift digital holography can be reproduced by using Fourier transform for Fresnel transformation. In actual reproduction, since the complex amplitude distribution on the CCD surface is discrete data, high-speed discrete Fourier transform is used for Fourier transform. Here, the relationship between the sampling interval on the CCD surface and the sampling interval on the reproduction surface will be described. Expressing the Fresnel transform discretely

It becomes. Here, FFT [] is an operator of fast discrete Fourier transform. Further, (m, n) and (p, q) represent discrete coordinates on the reproduction surface and the CCD surface, respectively. ΔX, ΔY and Δx, Δy are sampling intervals of the CCD and the reproduction surface, respectively. Usually, when an image g (p, q) of N _x pixels × N _y pixels is subjected to fast discrete Fourier transform to u (m, n), the spatial frequency sampling intervals Δμ and Δν are respectively

It becomes. In the Fresnel transform, the spatial frequency for Fourier transform is μ and ν, and the wavelength λ and the reproduction distance R are used.

It expresses. The discrete spatial frequency is

It becomes. Therefore, the sampling interval of the Fresnel transformation is based on the equations (12) and (14).

It becomes. Here, as shown in FIG. 5, consider a case where a concave lens is installed between the recording surface and the reproducing surface. FIG. 5 is a diagram illustrating the expansion of the measurement range. The distance between the recording surface and a concave lens to F _0. The reproduction range at the virtual image position is W ₁ , and the reproduction range at the object position is W ₂ . The reproduction range W _{1 at} the position of the virtual image and the reproduction range W _{2 at} the position of the object are expressed by Equation (15) when the sampling interval on the CCD surface is p.

It can be expressed. The area of the W _{1 F 1} / _{F 2} times by image by the lens is played. Thus the reproduction range will be ₁ × _F 2 / _F. Therefore, the magnification of the playback range by placing the lens is

It can be expressed as M is the magnification of the reproduction range. The reproduction range H in the virtual image plane at this time is

It can be expressed as. Here, in order to obtain the reproduction range H, it is necessary to obtain three unknowns R ₁ , F ₁ and F ₂ . A method for obtaining this unknown will be described. A reproduced image of the object with the lens removed and a reproduced image of the virtual image with the lens placed are obtained. R ₁ and R ₂ are obtained from the reproduction distance at this time. Further, the number of pixels at the corresponding location of the reproduced image is checked to obtain the magnification M. By substituting the obtained value into Expression (18), the expanded reproduction range is obtained.

これらの式を連立させて解くことにより、パラメータｆ、ａ、ｂをそれぞれ求めることができる。 It is difficult to accurately measure the optical distance from the CCD to the concave lens. Also, the actual focal length of the lens may deviate from the nominal value. Therefore, a method for obtaining these values from a reproduced image obtained by an actual optical system will be described. FIG. 6 is a diagram illustrating a method for identifying these parameters. Place the reference object at the position of R ″. A phase shift digital hologram is photographed in each of the case where there is no concave lens and the case where a concave lens is installed. In each case, the reproduction distances R ″ and R ′ that are in focus are found by repeatedly performing reproduction while changing the reproduction distance minutely. Whether or not the focus is in focus is calculated by calculating the standard deviation of the intensity of the reproduced image and obtaining it as the maximum reproduction distance. Next, the size of the reproduced object in the reproduced image is obtained. By obtaining these ratios, the enlargement ratio M of the reproduction range can be obtained. The reproduction distances R ″ and R ′ and the magnification M are expressed as follows by the focal length f of the concave lens, the distance a between the recording surface and the concave lens, and the distance b between the concave lens and the reproduction surface, respectively.

By simultaneously solving these equations, the parameters f, a, and b can be obtained.

  In the above embodiment, the parallel laser light is used as the object light and the reference light, but the same effect can be obtained even when the non-parallel laser light is used.

It is a diagram which shows an example of a structure of the recording and reproducing optical system of a phase shift digital holography. It is a diagram which shows the concept of a diffraction phenomenon. It is a diagram which shows an example of a structure of the phase shift digital holography displacement distribution measuring apparatus by this invention. It is a diagram explaining the relationship between an object and a reproduction surface. It is a diagram explaining expansion of a measurement range. It is a diagram explaining the method of identifying a parameter.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Recording / reproducing optical system 2,22 Laser light source 4,23 Spatial filter 6,24 Collimator lens 8,26 Beam splitter 10,32 Aperture 12,30 Neutral filter 14,34 PZT stage with mirror 16,38 CCD camera 21 Phase shift Digital holographic displacement distribution measuring device 28, 40 Half mirror 36 Glass plate 42 Concave lens

Claims (6)

An apparatus for recording an image of an object as a digital hologram by phase shift digital holography to obtain a reproduced image, a laser light source means for generating laser light, and a beam for dividing the laser light generated by the laser light source means in two directions A splitting unit; a reference beam forming unit that forms reference beam from one of the laser beams split by the beam splitting unit; and an imaging unit. The other of the laser beams split by the beam splitting unit is applied to an object. In the apparatus configured to reflect and enter the imaging means as object light, the reference light also enters the imaging means, and the imaging means forms a digital hologram from the object light and the reference light. An apparatus characterized in that a concave lens through which the object light passes is disposed between an imaging means and an object.   2. The apparatus according to claim 1, further comprising means for collimating the laser light emitted by the laser light source means. A method for obtaining a focal length of the concave lens, a distance between a recording surface of the imaging unit and the concave lens, and a distance between the concave lens and the hologram reproducing surface in the apparatus according to claim 1,
Placing a reference object at a distance R ″ from the lens;
In each case of the state without the concave lens and the state of installing the concave lens, a step of photographing a phase shift digital hologram;
In each case, reproduction is repeated while slightly changing the reproduction distance, and the reproduction distance R ″ that is in focus is set to the reproduction distance that maximizes the standard deviation calculated by calculating the standard deviation of the intensity of the reproduction image. And obtaining as R ′ ;
Determining the size of the reproduced object in the reproduced image;
By obtaining these ratios, the step of obtaining the expansion rate M of the reproduction range;
Reproduction distances R ″ and R ′, magnification M is the focal length f of the concave lens, distance a between the recording surface and the concave lens, and distance b between the concave lens and the reproduction surface is

A process represented by
A method comprising: obtaining f, a, and b by solving these equations simultaneously.   A displacement distribution measuring device for recording an image of an object as a digital hologram by phase shift digital holography, and measuring the displacement distribution or deformation distribution of the object as phase information from the recorded digital hologram, comprising: a laser light source means for generating laser light; A beam splitting unit for splitting the laser beam generated by the laser light source unit in two directions, a reference beam forming unit for forming a reference beam from one of the laser beams split by the beam splitting unit, and an imaging unit. The other of the laser beams split by the beam splitting unit is reflected by an object and enters the imaging unit as object light, the reference light also enters the imaging unit, and the imaging unit In the displacement distribution measuring apparatus configured to form a digital hologram from reference light, the imaging means and the object During the displacement distribution measuring apparatus characterized in that a concave lens where the object light passes.   2. The displacement distribution measuring apparatus according to claim 1, further comprising means for collimating the laser light emitted by the laser light source means. A method for obtaining a focal length of the concave lens, a distance between a recording surface of the imaging means and the concave lens, and a distance between the concave lens and the hologram reproducing surface in the displacement distribution measuring apparatus according to claim 4 or 5,
Placing a reference object at a distance R ″ from the lens;
In each case of the state without the concave lens and the state of installing the concave lens, a step of photographing a phase shift digital hologram;
In each case, reproduction is repeated while slightly changing the reproduction distance, and the reproduction distance R ″ that is in focus is set to the reproduction distance that maximizes the standard deviation calculated by calculating the standard deviation of the intensity of the reproduction image. And obtaining as R ′ ;
Determining the size of the reproduced object in the reproduced image;
By obtaining these ratios, the step of obtaining the expansion rate M of the reproduction range;
Reproduction distances R ″ and R ′, magnification M is the focal length f of the concave lens, distance a between the recording surface and the concave lens, and distance b between the concave lens and the reproduction surface is

A process represented by
A method comprising: obtaining f, a, and b by solving these equations simultaneously.

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