JP4069204B2 - Displacement distribution measurement method using digital holography - Google Patents

Description

  The present invention relates to a displacement distribution measuring method using digital holography, and more particularly to a displacement distribution measuring method in which the influence of halation and speckle noise is reduced and a displacement distribution on an object surface can be obtained as phase information.

  Image measurement using an optical technique is a technique that can measure the shape, deformation, stress, strain, etc. of an object in a non-contact manner, and can be used in various fields such as information communication and medical care. Can do. As a method of measuring the displacement distribution or deformation distribution of the object surface, a measurement method using phase shift digital holography is known (for example, see Non-Patent Document 1). In this measurement method using phase shift digital holography, an interference image before and after displacement of an object is captured by a CCD camera, and the phase distribution of each part of the object surface is measured as digital data. Therefore, the deformation amount and displacement amount of the distribution surface can be measured at high speed, and the present invention can be applied to various applications that need to measure the minute displacement amount of the object surface at high speed.

On the other hand, in phase shift digital holography, since coherent light is projected toward the object surface and scattered light from the object surface is received by the CCD camera, a speckle pattern is likely to occur on the reproduction surface, and measurement errors are likely to occur. Has been pointed out. In particular, when a measurement target is a metal surface or a mirror surface, it is easily affected by a speckle pattern. As a method for solving this problem, a method has been proposed in which a digital phase value having the largest amplitude value among four adjacent pixels when reproducing a hologram is used as the phase value of four pixels (for example, Non-Patent Document 2).
Experimental Mechanics, Vol.3 No2, “Out-of-plane displacement measurement using phase-shift digital holography”, June 2003 Opt. Eng. 42 (5) “Measurement of surface shape and deformation by phase-shifting image digital holography”, May 2003

  In the method described in the above-mentioned paper, the phase value of the pixel having the largest back amplitude value of the four adjacent pixels is set to the phase value of the four pixels, so that noise due to the speckle pattern is reduced. However, there is a problem that the spatial resolution is lowered.

Accordingly, an object of the present invention is to eliminate the above-described drawbacks, and to reduce phase speckle noise and enable high-precision measurement even on an object surface where halation and speckle patterns are likely to occur. This is to realize a displacement distribution measuring method using the above.
Furthermore, another object of the present invention is to provide a displacement distribution measuring method capable of measuring the phase distribution on the object surface without reducing the resolution.
Furthermore, another object of the present invention is to provide an image reproducing method for reproducing a clear image from a digital hologram.

In the first state, the displacement distribution measuring method using phase shift digital holography according to the present invention captures an object image with a two-dimensional imaging device while sequentially shifting the phase of the reference light by a predetermined amount, and records interference fringes. And creating a digital hologram in the first state;
In the second state, which is deformed or displaced from the first state, the image of the object is picked up by the two-dimensional image pickup device while shifting the phase of the reference light by a predetermined amount, and the interference fringes are recorded and the second state is recorded. Creating a digital hologram;
Regenerating the digital hologram in the first state using a window function, and obtaining the intensity distribution and phase distribution in the first state for each of a plurality of window regions;
Reproducing the digital hologram in the second state using the same window function as the window function, and obtaining the intensity distribution and phase distribution of the second state for each of the plurality of window regions;
Obtaining an intensity sum of the intensity distribution of the first state and the intensity distribution of the second state in units of each window region for each pixel;
Obtaining a phase difference for each pixel between the phase distribution of the first state and the phase distribution of the second state;
A step of obtaining, for each pixel, a phase difference between the phase of the first state and the phase of the second state of the window region in which the obtained sum of intensity is maximum.

  In the present invention, when a digital hologram before and after deformation is reproduced, it is reproduced using a window function, and a phase distribution is created by using the phase difference before and after the deformation of the pixels in the window region where the sum of intensity is maximum for each pixel. Therefore, it is possible to obtain a displacement distribution before and after deformation with reduced influence of noise caused by the speckle pattern. As for the reproduced image, a clear reproduced image having no speckle pattern can be formed.

  First, the principle of phase shift digital holography will be described. FIG. 1 is a diagram showing an example of a recording optical system for carrying out an object surface displacement distribution measuring method using phase shift digital holography according to the present invention. A light beam is emitted from a laser light source 1 that generates coherent light. The light beam is converted into an expanded parallel light beam by the expander optical system 2 and the collimator lens 3. This light beam enters the prism 4 that functions as a beam splitter, is split by the half mirror 4a, and the reflected light beam enters the object 5 to be measured. The scattered light reflected by the surface of the object 5 is incident on the prism 4 again as object light, passes through the half mirror 4a, and propagates toward the CCD camera 6. On the other hand, the light beam transmitted through the half mirror 4 a is incident on a total reflection mirror 8 mounted on the PZT stage 7. The light beam reflected by the total reflection mirror 8 becomes reference light, enters the prism 4 again, is reflected by the half mirror 4a, and propagates toward the CCD camera 6. The object light and the reference light interfere with each other, and an interference fringe is imaged on the CCD camera 6. The interference fringes picked up by the CCD camera are recorded as digital digital, and the output data is transferred to a computer for signal processing.

  The PZT stage 7 is displaced by a minute distance in the optical axis direction of the optical system, and shifts the phase of the reference light. As the phase shift amount of the reference light, for example, four phase shift amounts of 0, π / 2, π, 3π / 2 can be selected. The interference fringes are recorded while the phase of the reference light is shifted, that is, first, the interference fringes are imaged and recorded as digital data with the phase shift amount being zero. Next, the reference light is shifted by the phase shift amount π / 2 and imaged and recorded as digital data. Then, this imaging operation is sequentially repeated by each phase shift amount, and four digital holograms in which the phase of the reference light is shifted by π / 2 are recorded as digital data.

Assuming that the amplitude distributions of the object light and the reference light are A ₀ (x, y) and A _r (x, y), the amplitude distributions of the object light and the reference light can be expressed by the following equations.
A _o (x, y) = a _o (x, y) exp {iφ _o (x, y)} (1)
A _r (x, y) = _ar (x, y) exp [i {φ _r (x, y) + α}] (2)
Here, a _o (x, y) and a _r (x, y) are amplitude distributions, φ _o (x, y) and φ _r (x, y) are phase distributions, and α is a mirror attached to the piezo stage. The phase shift amount of the reference light to be changed is α = 0, π / 2, π, 3π / 2.

この位相と振幅より記録面での複素振幅分布ｇ（ｘ，ｙ）を求めると次式のようになる。
ｇ（ｘ，ｙ）＝ａ_ｏ（ｘ，ｙ）ｅｘｐ｛ｉφ_ｏ（ｘ，ｙ）｝ （６） The intensity of interference fringes recorded by the CCD camera 6 and input to the computer can be expressed by the following equation.
I _a (x, y) = a _o (x, y) _ar (x, y) cos {φ _o (x, y) −φ _r (x, y) −α} (3)
Since the parallel light is used as the reference light, the amplitude on the recording surface is constant and the phase does not change, and the amplitude a _o (x, y) of only the object light on the recording surface is obtained from Equation (4). The phase φ _o (x, y) can be obtained from the relational expression 5). Here, x and y define the position coordinates on the recording surface.

When the complex amplitude distribution g (x, y) on the recording surface is obtained from the phase and amplitude, the following equation is obtained.
g (x, y) = a _o (x, y) exp {iφ _o (x, y)} (6)

ここで、ｕ（Ｘ，Ｙ）は再生面での複素振幅分布、Ｒは記録面と再生面の距離、ｋは波数（ｋ＝２π／λ）、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求めることで再生像を得ることができる。式（７）のｕ（Ｘ，Ｙ）について絶対値をとることにより、再生面における各画素の強度を得ることができ、偏角を求めることにより各画素の位相値が求められる。本発明では、再生処理において、記録面の強度分布及び位相分布を用い変位ないし変形前後の変位分布を位相情報として求める。 The complex amplitude distribution of the original object is obtained by Fresnel transforming and reproducing the expression g (x, y) representing the complex amplitude distribution of only the object light on the recording surface to the reproduction surface where the object is placed. be able to. It is also possible to reproduce using various approximation or conversion methods other than Fresnel conversion. FIG. 2 shows a conceptual diagram of a diffraction phenomenon for digital holography reproduction.
An expression indicating the complex amplitude on the reproduction surface obtained by Fresnel transformation is expressed as Expression (7). X and Y indicate position coordinates on the reproduction surface.

Here, u (X, Y) is a complex amplitude distribution on the reproduction surface, R is a distance between the recording surface and the reproduction surface, k is a wave number (k = 2π / λ), and F is an operator representing a Fourier transform. A reproduction image can be obtained by obtaining the intensity of the complex amplitude distribution on the reproduction surface. By taking the absolute value for u (X, Y) in equation (7), the intensity of each pixel on the reproduction surface can be obtained, and the phase value of each pixel is obtained by obtaining the declination. In the present invention, in the reproduction processing, the intensity distribution and the phase distribution on the recording surface are used to determine the displacement or the displacement distribution before and after deformation as phase information.

ここで、λは計測光の波長である。 Next, the principle of holographic interferometry will be briefly described.
A conceptual diagram of the holographic interferometry is shown in FIG. If the object light before deformation or displacement is A _o (x, y) and the object light after deformation is A ′ _o (x, y), they can be expressed by the following equations, respectively.
A _o (x, y) = a _o (x, y) exp {iφ _o (x, y)} (8)
A ′ _o (x, y) = a ′ _o (x, y) exp {iφ ′ _o (x, y)} (9)
If the applied deformation is minute, it can be considered that there is no change in the amplitude of the object light before and after the deformation and only the phase is changed, and the amplitude and the phase can be expressed by the following equations, respectively.
a ′ _o (x, y) = a _o (x, y) (10)
φ ′ _o (x, y) = φ _o (x, y) + Δφ (x, y) (11)
Here, φ _o (x, y) represents a phase distribution before deformation, φ ′ _o (x, y) represents a phase distribution after deformation, and Δφ (x, y) represents a phase change amount before and after deformation. Show the distribution. Further, the relationship between the displacement d before and after the deformation of the object surface and the phase change can be expressed by the following equation.

Here, λ is the wavelength of the measurement light.

  Thus, by obtaining the difference in phase distribution before and after deformation for each pixel, the deformation amount or displacement amount before and after deformation of each part (each pixel) of the object can be obtained as the phase amount. Furthermore, in order to obtain a reproduced image, the reproduced image of the object can be obtained by calculating the intensity of the complex amplitude distribution on the reproduction surface shown in Expression (7), that is, the absolute value for each pixel.

  Next, a method for reducing speckle noise will be described. In the present invention, a window function is used to reduce speckle noise. In Expression (7) indicating the complex amplitude distribution on the reproduction surface, a term g (X, Y) indicating the complex amplitude on the recording surface is multiplied by the window function W (X, Y) to define a plurality of window regions, An intensity distribution and a phase distribution are obtained for each window region. Various window functions such as a rectangular function, a Hamming function, and a Hanning function can be used as the window function to be used. Next, with each window region as a unit, the sum of the intensity before and after deformation at the position (X, Y) is calculated for each pixel, and among all the window regions, the window region having the maximum intensity sum is selected, The phase difference Δφ (X, Y) between the phase value before deformation and the phase value after deformation of the selected window region is calculated, and the obtained phase difference is set as the phase difference of the pixel (X, Y). The calculation for obtaining the phase difference is executed for all the pixels. With this process, a displacement distribution with reduced speckle noise can be obtained. The reason for using the phase difference of the window area having the maximum intensity sum among all the window areas is that the data of the window area having the maximum intensity sum is the brightest and the least noise. . The gist of the present invention is to obtain an intensity distribution and a phase distribution for each window region by applying a window function. And based on various experimental results, the same effect can be obtained even if one of the intensity values before and after deformation is used instead of the intensity sum. The reason is that in the case of minute deformation, the reproduced speckle pattern is substantially the same before and after the deformation.

また、以下に示す式に基づき、強度和を重み付けに用いて平均をとる方法を用いることもできる。

As a method of determining the phase difference Δφ (X, Y) before and after deformation, the average of the top m pieces of intensity sum can be used as the phase difference.

Further, based on the following formula, a method of averaging by using the sum of intensity for weighting can also be used.

  Next, a specific example of displacement measurement using phase shift digital holography will be described. FIG. 4 is a flowchart of a displacement distribution measuring method using digital holography according to the present invention. As a first step, the optical system shown in FIG. 1 is used to image an object in the first state before deformation while phase-shifting, and interference fringes are recorded as a digital hologram of digital data. In this example, four phase shift amounts of 0, π / 2, π, and 3π / 2 are used as the phase shift amounts (step 1).

  Next, in the second state in which the object is deformed, the object is imaged while the phase is similarly shifted, and the digital hologram in the second state is recorded as digital data (step 2).

  Next, reproduction processing is executed using the window function W (X, Y), and an intensity distribution and a phase distribution are obtained for each window region (step 3). In this example, a rectangular function is used as a window function, and 16 window areas of 4 × 4 are defined.

  Next, in the second state in which the object is deformed, the object is imaged while similarly shifting the phase, and the digital hologram in the second state is recorded as digital data (step 3).

  Next, reproduction processing is executed from the digital hologram in the second state using the same window function as in step 2, and the intensity distribution and phase distribution in the second state after deformation are obtained (step 4).

  Next, the sum of the intensity distribution in the first state and the intensity distribution in the second state is obtained for each pixel, and the intensity sum is calculated. Then, for the 16 window areas, the pixel of the window area that maximizes the intensity sum is selected. Next, the phase difference before and after the deformation of the selected pixel is calculated, and this process is executed for all the pixels to obtain the distribution of the phase difference before and after the deformation of the object (step 5).

  Note that the amount of deformation or displacement of the object surface is obtained by substituting the phase difference of each pixel into equation (12) and calculating.

  Next, an image reproduction method in which the influence of speckle patterns and halation is reduced will be described. FIG. 5 is a diagram showing an example of an image reproducing method according to the present invention. As described above, an object image is picked up by a CCD camera while sequentially shifting the phase of the reference light by a predetermined amount, and interference fringes are recorded as digital data to create a digital hologram. Next, in the reproduction process, a window function is applied to the digital hologram to create a plurality of window areas, and an intensity distribution is obtained for each pixel using the window area as a unit or for each window area. Next, for each pixel, the intensity of the window region where the intensity is maximum is selected, and the intensity distribution is obtained for the entire image to be a reproduced image. In this way, when reproducing a digital hologram, by applying a window function and selecting a value that maximizes the intensity of the pixels in each window region to obtain a reproduced image, the entire image is a set of pixels with the least noise. Therefore, it is possible to obtain a reproduced image in which the influence of the speckle pattern or the like is greatly reduced.

Next, a modification of the digital hologram imaging optical system will be described. FIG. 6 is a diagram for explaining the principle of the imaging optical system of this example. In this example, the semiconductor laser performs phase shift using the characteristic that the oscillation wavelength changes according to the current value. A semiconductor laser has a characteristic that an oscillation wavelength changes according to a current value applied to a semiconductor element due to a structure of laser oscillation. In the phase shift method using a semiconductor laser as a light source, an optical system having an optical path difference shown in FIG. 6 is used. The relationship between the wavelength λ in interference, the optical path difference ΔL, and the phase φ of the interference fringes can be expressed by the following equation: φ = 2πΔL / λ
The phase φ ′ of the interference fringes when the wavelength after changing the injection current is λ + Δλ can be expressed by the following equation.
φ ′ = 2πΔL / (λ + Δλ)
Phase φ and phase φ ′ are phases before and after changing the injection current, respectively. The phase amount Δφ that shifts by changing the injection current is a phase difference between the phase φ and the phase φ ′.
Δφ = φ−φ ′
= 2πΔL [1 / λ−1 / (λ + Δλ)]
It can be expressed as. Therefore, since Δλ is determined by the amount of change in the injection current, it is possible to shift the phase without mechanically displacing the optical element that generates the reference light due to the change in the injection current. In the present invention, a phase shift digital hologram is created by recording interference fringes while phase shifting is performed by a phase shift method using a change in the injection current of a semiconductor laser, and the image reproduction of a minutely changing object surface is performed using this digital hologram. Alternatively, a minute displacement of the object surface is measured.

  7A and 7B show a specific configuration of the optical system. Laser light generated from the semiconductor laser 10 is converted into an expanded parallel light beam by the expander optical system 11. This parallel beam is incident on the glass wedge 12 and uses the reflected light reflected by the surface as reference light. The transmitted light is reflected by the object 13 to become object light, passes through the wedge 12 again, and enters the CCD camera 14. Then, interference fringes between the object light and the reference light are imaged by the CCD camera, and a digital hologram is formed. Next, imaging is performed by changing the injection current value of the semiconductor laser 10 and changing the injection current so that, for example, the phase changes by π / 2. As described above, the phase shift can be performed only by changing the injection current of the semiconductor laser, and the phase shift hologram can be imaged without using the PZT stage which is a mechanical structure.

It is a diagram which shows an example of the optical system for enforcing the displacement distribution measuring method using the phase shift digital holography by this invention. It is a conceptual diagram which shows the diffraction phenomenon at the time of reproducing | regenerating a hologram. It is a diagram for explaining the principle of holographic interferometry. It is a diagram which shows a series of displacement measurement processes. It is a diagram for explaining an image reproduction method according to the present invention. It is a diagram which shows the principle of the modification of an imaging optical system. It is a diagram which shows the specific example of the modification of an imaging optical system.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Laser light source 2 Expander 3 Collimator lens 4 Beam splitter 5 Object 6 CCD camera 7 PZT stage 8 Mirror 10 Semiconductor laser 11 Expander optical system 12 Wedge 13 Object 14 CCD camera 15 Beam splitter

Claims (6)

In a displacement distribution measuring method of recording an object image 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,
In the first state, while the phase of the reference light is sequentially shifted by a predetermined amount, an image of an object, by the interference fringes is recorded as digital data using a two-dimensional imaging device, the digital hologram in the first state Imaging for each phase ;
In the second state where the object is deformed or displaced from the first state, the phase of the reference light is sequentially shifted by a predetermined amount , and the image of the object is converted into digital data using a two-dimensional imaging device as interference fringes. Recording the digital hologram in the second state for each phase by recording;
By multiplying the digital hologram in the first state by a predetermined plurality of window functions that define a plurality of spatial window regions, the intensity distribution and phase distribution of the pixel group in the first state can be obtained . Regenerating for each of the window regions ;
Wherein the digital hologram of the second state, by multiplying said predetermined plurality of window functions, said plurality of windows of the intensity distribution and phase distribution of the pixel group in the second state, the plurality of window functions to define Regenerating for each of the regions ;
Was regenerated by respectively multiplying the same window function, and the phase distribution of the pixel group of the first state, the phase difference of corresponding pixels between the phase distribution of the pixel groups of the second state, said plurality Determining for each of the window regions of
Based on the intensity distribution of the pixel group in the first state and / or the intensity distribution of the pixel group in the second state for each of the plurality of window regions, each of the window regions defining the phase difference is Selecting for each pixel;
Using the phase difference defined by the selected window region for each pixel to generate a new phase difference distribution composed of the pixel;
A displacement distribution measuring method characterized by comprising: The displacement distribution measuring method according to claim 1,
The step of selecting the window region defining the phase difference for each pixel includes the intensity distribution of the pixel group in the first state and the intensity of the pixel group in the second state for each of the plurality of window regions. A displacement distribution further comprising a step of obtaining an intensity sum of corresponding pixels between the distribution and selecting a window region defining the phase difference for each pixel based on the obtained intensity sum Measurement method. The displacement distribution measuring method according to claim 1,
The step of selecting the window region defining the phase difference for each pixel includes the intensity distribution of the pixel group in the first state or the intensity of the pixel group in the second state for each of the plurality of window regions. A window area corresponding to the intensity distribution of the top m (m is a natural number greater than or equal to 1) among the distributions is selected for each pixel.
The step of generating the new phase difference distribution uses the average value of the phase differences defined by the m window regions for each pixel to generate a new phase difference distribution composed of the pixels. Displacement distribution measuring method characterized by the above. In the displacement distribution measuring method according to claim 2 ,
The step of selecting the window region defining the phase difference for each pixel includes the intensity distribution of the pixel group in the first state and the intensity of the pixel group in the second state for each of the plurality of window regions. For each pixel, a window region corresponding to an intensity distribution that gives the intensity sum of the top m intensities (m is a natural number of 1 or more) is selected for each pixel .
The step of generating the new phase difference distribution uses the average value of the phase differences defined by the m window regions for each pixel to generate a new phase difference distribution composed of the pixels. Displacement distribution measuring method characterized by the above. A step of reproducing the intensity distribution and phase distribution of the pixel group of the first state, and in the step of reproducing the intensity distribution and the phase distribution of the pixel groups of the second state, the complex amplitude of the recording surface from the recorded digital hologram distribution determined, determine the complex amplitude distribution in the reproduction surface with Fresnel transform the complex amplitude distribution obtained, and obtains the intensity distribution and phase distribution from the complex amplitude distribution in the reproduction plane obtained, 4 claim 1 The displacement distribution measuring method according to any one of the preceding items. In an image reproduction method for recording an object image as a digital hologram by phase shift digital holography and obtaining a reproduction image of the object from the recorded digital hologram,
While the phase of the reference light is sequentially shifted by a predetermined amount, an image of an object, by the interference fringes is recorded as digital data using a two-dimensional image pickup device, a step of imaging for each phase of the digital hologram,
To the digital hologram, a step by multiplying a predetermined plurality of window function defining a plurality of spatial window area, the intensity distribution of the pixel group, to play for each of the plurality of window regions,
For each of the plurality of window regions , a step of selecting, for each pixel, a window region having a maximum intensity value among the intensity distribution of the pixel group ;
Using the intensity value of the pixel defined by the selected window region for each pixel, and reproducing the entire image of a new intensity distribution composed of the pixel;
An image reproduction method comprising:

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