JP2020190616A - Hologram recording/reproducing device and stereoscopic image reproducing method - Google Patents

Abstract

To acquire a high-quality reproduced image by reducing noise included in a hologram without reducing time resolution in incoherent holography.SOLUTION: In a hologram recording/reproducing device for reproducing a stereoscopic image by dividing incoherent light waves into first split light and second split light, imparting mutually different phase distributions, and then reconfiguring a hologram formed by permitting interference of the first split light and the second split light, space averaging processing including operation for averaging signal value of pixels and signal values of pixels existing in the adjacent area is performed to the photographed hologram or the respective pixels of a complex amplitude distribution obtained by analyzing the hologram, and a stereoscopic image is reproduced based on the hologram or the complex amplitude distribution where the space averaging processing has been performed.SELECTED DRAWING: Figure 1

Description

The present invention relates to a hologram recording / reproduction apparatus and a stereoscopic image reproduction method, and more particularly to a stereoscopic image recording / reproduction apparatus and a stereoscopic image reproduction method by incoherent holography.

In the incoherent holography technique, a hologram of an object can be recorded by using a low coherence light source such as sunlight or an LED (Light Emitting Diode) (Patent Document 1, Non-Patent Document 1). Because of this feature, incoherent holography is seen as a promising stereoscopic photography technique. However, in coherent holography, compared to holography using a high coherence light source such as a laser, the contrast of the hologram is very low, so it is easily affected by the noise of the image sensor, and the problem of low quality of the reproduced image remains. Has been done.

To solve this problem, in order to reduce the noise of incoherent holography and improve the quality of the reproduced image, a method of photographing a plurality of holograms and averaging them has been proposed (Non-Patent Document 2).

FIG. 16 shows a conceptual diagram of hologram averaging (time averaging). Here, a case where a 4-step phase shift method (Non-Patent Document 3) is used as a hologram photographing method is shown. Generally, by photographing four holograms having a phase shift amount of 0, π / 2, π, 3π / 2 rad with the image sensor 10, it is possible to photograph and reconstruct the object to be photographed. is there. However, in reality, the influence of noise from the image sensor cannot be ignored, and the captured hologram contains noise.

In order to reduce this noise, as shown in FIG. 16, n holograms having different phase shift amounts are photographed to obtain a hologram group. Since the noise contained in each hologram has a distribution that fluctuates with time, (“1st image” + “2nd image” + ... + “nth image”” with respect to the acquired hologram group. ) / N averaging signal processing can be applied to obtain holograms with reduced noise components. To obtain a complex amplitude distribution with reduced noise by analyzing four holograms obtained by averaging based on a four-step phase shift algorithm (for example, Non-Patent Document 3). In addition, high-quality three-dimensional information or reproduced images of objects can be reconstructed from this.

Special Table 2016-533542 Japanese Patent No. 6245551

J. Rosen and G. Brooker, "Non-scanning motionless fluorescence three-dimensional holographic microscopy", Nature Photonics, (2008), Vol. 2, pp. 190-195 B. Katz, D. Wulich, and J. Rosen, "Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution", Applied Optics, (2010), Vol. 49, No. 30, pp. 5757 −5763 I. Yamaguchi and T. Zhang, "Phase-shifting digital holography", Optics Letters, (1997), Vol. 22, No. 16, pp. 1268-1270 J. Hong and M. K. Kim, "Single-shot self-interference incoherent digital holography using off-axis configuration", Optics Letters, (2013), Vol. 38, No. 23, pp. 5196-5199 W. Qin, X. Yang, Y. Li, X. Peng, H. Yao, X. Qu, and BZ Gao, "Two-step phase-shifting fluorescence incoherent holographic microscopy", Journal of Biomedical Optics, (2014), Vol. 19, No. 6, 060503

However, the noise reduction technique for performing the above-mentioned averaging (time averaging) process has a problem that the shooting time is long because a plurality of shootings of 4 × n times are required for averaging. For example, the pixel division phase shift method (Patent Document 2), the off-axis method (Non-Patent Document 4), the 2-step phase shift method (Non-Patent Document 5), and the 3-step phase shift method (Non-Patent Document 1) are not used. When the averaging method of Patent Document 2 is used, the number of times of photographing is n times, n times, 2 × n times, 3 × n times, respectively, which is n times in all the methods.

As described above, in the prior art, it is necessary to photograph n holograms having different noise generation positions with the image sensor and apply the calculation of averaging over time. Therefore, at least the photographing time is required to reduce the noise. There is a problem that the time resolution is reduced by n times.

Therefore, an object of the present invention made in view of the above problems is to reduce noise contained in a hologram and obtain a high-quality reproduced image in incoherent holography without lowering the temporal resolution. It is an object of the present invention to provide a hologram recording / reproducing apparatus and a stereoscopic image reproducing method capable of capable of reproducing the hologram.

FIG. 1 shows a conceptual diagram of averaging (spatial averaging) of the hologram of the present invention. In the present invention, as shown in FIG. 1, for a hologram by incoherent light taken by the image sensor 10, the signal value of each pixel of each hologram is averaged with adjacent pixels (spatial average signal processing). The effect of noise reduction is obtained by introducing. In digital cameras and the like, spatial averaging (or pixel binning) signal processing is generally used to reduce noise, but in coherent holography, attempts to apply spatial averaging signal processing have not yet been reported.

In order to solve the above problems, the hologram recording / reproducing device according to the present invention divides an incoherent light wave into a first divided light and a second divided light, imparts different phase distributions to each other, and then applies the first divided light and the above. In a hologram recording / reproducing device that reproduces a stereoscopic image by reconstructing a hologram formed by interfering with the second divided light, each pixel of the photographed hologram or a complex amplitude distribution obtained by analyzing the hologram is On the other hand, a spatial averaging process including an operation of averaging the signal values of the pixels and the signal values of pixels existing in the adjacent region is performed, and a stereoscopic image is performed based on the hologram or the complex amplitude distribution obtained by the spatial averaging process. It is characterized by playing.

Further, in the hologram recording / reproducing device, the spatial averaging process has an number of n _x × n _y pixels in the horizontal direction n _x and the number of pixels in the vertical direction n _y (n _x , n _y > 1) before averaging. It is desirable to include an operation of averaging the signal value for each pixel, and then an operation of increasing the number of pixels by n _x × n _y times to make the number of pixels and the pixel pitch the same before and after the averaging.

Further, in the hologram recording / reproducing device, the spatial averaging process has an number of n _x × n _y pixels in the horizontal direction n _x and the number of pixels in the vertical direction n _y (n _x , n _y > 1) before averaging. It is desirable to include a convolution integral with a spatial filter that has a number of elements.

Further, it is desirable that the hologram recording / reproducing device applies low-pass filtering having a spatial frequency band corresponding to the reciprocal of the number of pixels used for averaging after the spatial averaging process.

Further, the hologram recording / reproducing device provides information on at least the focal length of the optical elements constituting the hologram recording / reproducing device, the effective aperture diameter, the wavelength of the light source, the distance between the optical elements, and the distance from the object to be imaged to the image sensor. Therefore, it is desirable to set the number of pixels in the adjacent region used for the space averaging process.

Further, the hologram recording / reproducing device sets the number of horizontal pixels n _x and the number of vertical pixels n _y (n _x , n _y > 1) in the adjacent region used for the spatial averaging process to the wavelength λ of the light source and the interference fringes. focal length z _r, the diameter D _h of the interference fringes, as a pixel pitch p of the image sensor, it is desirable to set the following λz _r / D _h p.

In order to solve the above problems, the stereoscopic image reproduction method according to the present invention is formed by interfering with the first divided light and the second divided light which are divided from the incoherent light waves and given different phase distributions. In a stereoscopic image reproduction method of reconstructing a hologram and reproducing a stereoscopic image, for each pixel of the photographed hologram or a complex amplitude distribution obtained by analyzing the hologram, the signal value of the pixel and its adjacent region. It is characterized in that a spatial averaging process for averaging the signal values of the pixels existing in is performed, and a stereoscopic image is reproduced based on the hologram or the complex amplitude distribution to which the spatial averaging process is performed.

Further, in the stereoscopic image reproduction method, it is desirable to apply low-pass filtering having a spatial frequency band corresponding to the reciprocal of the number of pixels used for averaging after the spatial averaging process.

According to the hologram recording / reproducing device and the stereoscopic image reproducing method of the present invention, it is possible to reduce noise contained in a hologram and obtain a high-quality reproduced image in incoherent holography without lowering the temporal resolution. It becomes. Moreover, the contrast of the reproduced image can be improved.

It is a conceptual diagram of the averaging (spatial averaging) of the hologram of this invention. It is a figure which shows the optical system of incoherent holography based on a single optical path interferometer. It is a conceptual diagram of hologram averaging (spatial averaging) by averaging signal values. It is a conceptual diagram of averaging (spatial averaging) of holograms by a spatial filter. A hologram and its reproduced image for explaining the effect of spatial averaging. This is an example of a hologram taken by incoherent holography. It is a figure which shows the optical system of the incoherent holography based on another interferometer. It is a figure which shows the optical system of the incoherent holography used for the verification of the effect. It is a reproduced image reconstructed by processing a hologram under various conditions. It is an enlarged view of FIG. 9 (d) and the enlarged view of FIG. 9 (g). It is a figure which shows the evaluation result of the contrast ratio and smoothness with respect to the average number of sheets. It is a figure which shows the relationship of the required sampling interval with respect to the recording position of the object to be photographed. It is a figure which compares the evaluation result of the optical transfer function of a reproduced image. It is a figure which shows the optical system of incoherent holography using a reflective object. It is a figure which shows the result of reconstructing the reproduced image after applying various spatial averaging. It is a conceptual diagram of the averaging (time averaging) of the hologram of the prior art.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

(Embodiment)
FIG. 2 shows an optical system for incoherent holography based on a single optical path interferometer. The optical system includes each optical element of a point light source 1, a lens 2, a polarizer 3, a spatial light modulator 4, a polarizer 5, a bandpass filter 6, an image pickup element 10, and a signal processing device 20. Hereinafter, the details of the noise reduction means according to the present invention will be described by taking hologram imaging using the single optical path interferometer of FIG. 2 as an example.

An object illuminated by incoherent light or an object that generates incoherent light can be regarded as a collection of a plurality of point light sources. Therefore, a hologram of an arbitrary three-dimensional object can be considered as a sum of holograms formed by each point light source. Here, it is assumed that the object to be photographed is composed of one point light source 1, and the process of photographing the hologram will be described.

Light of wavelength λ propagating from a point light source is incident on a lens 2 having a focal length f ₀ and an aperture diameter D ₀ arranged at a distance z _s . The use of this lens 2 is optional, but it is used to increase the light efficiency and to adjust the image magnification and the field of view. The light after passing through the lens 2 passes through the polarizer 3 and becomes linearly polarized light whose polarization state is tilted at 45 degrees. The horizontal linear polarization component and the vertical linear polarization component of the 45-degree linear polarization are used as the first division light and the second division light required for self-interference in incoherent holography.

In each phase distribution of the first division light and the second division light, the phases of the focal lengths f _d1 and f _{d 2} are used by using the spatial light modulator 4 having an effective aperture diameter D _slm arranged at a distance of z _l from the lens. Give a distribution. As the spatial light modulator 4, a liquid crystal having birefringence, a diffractive optical element, a metasurface, or the like is used. The first-division light and the second-division light to which the spatial light modulators 4 have different phases are the image pickup surfaces of the image sensor 10 having a pixel pitch p and an effective aperture diameter D _sensor z _h away from the spatial light modulator 4. (The solid line and the broken line are the images of the first division light and the second division light).

A polarizing element 5 is arranged again between the spatial light modulator 4 and the image pickup element 10, and the polarized light is changed to 45 degrees by passing the first divided light and the second divided light through the polarizer 5. They match with linearly polarized light and form interference fringes on the surface of the image pickup element. This interference fringe is photographed as a hologram by using the image sensor 10.

In this embodiment, the spatial light modulator 4 gives four phase shift amounts of 0, π / 2, π, and 3π / 2 rad to obtain four holograms (FIG. 1). When the wavelength width of light is wide and interference fringes cannot be obtained, the bandpass filter 6 is used to narrow the wavelength width and enhance the temporal coherence. The hologram taken by the image sensor 10 contains artifacts of a 0th-order light (direct image) component and a conjugate image component. To remove this, the complex amplitude distribution of light is obtained by the phase shift method or the off-axis method as described later.

In the present invention, spatial averaging signal processing (spatial averaging processing) is applied to the photographed hologram in the signal processing device 20.

FIG. 3 is a conceptual diagram of hologram averaging (spatial averaging) by averaging signal values of a plurality of adjacent pixels. The horizontal and vertical coordinates of the hologram image data I taken by the image sensor 10 are assigned as 1, 2, 3, ... From the upper left, and are used as the luminance signals I (i, j) at each pixel position. After applying the spatial averaging calculation for each n _x x n _y (n _x , n _y > 1) pixels, where the number of pixels in the horizontal direction is n _x and the number of pixels in the vertical direction is n _y before averaging. The image data I'(i', j') is given by the following equation (1). Here, n _x × n _y pixel regions are one adjacent region.

When averaging as shown in FIG. 3, the number of pixels in the horizontal and vertical directions of the image data after averaging is 1 / n _x times and 1 / n _y times, respectively, and the pixel pitch in the horizontal and vertical directions is They are n _x times and n _y times, respectively. If the number of pixels in the horizontal / vertical direction of the image data I before averaging is not divisible by n _x or n _y , zero padding, linear / non-linear complementation, and periodicity are taken into consideration in the captured image data I. Image processing such as complementation is applied to expand the image data and then average it.

Furthermore, the number of pixels of the image data by the averaging before and after, in order to equalize the pixel pitch, the image data after averaging, n _x × n _y times the nearest neighbor, bilinear -, such as bi-cubic method It is desirable to apply image processing technology to increase the number of pixels in the image data (the number of pixels before averaging). If it is desired to reduce the amount of data or the amount of calculation, it is not necessary to apply the above-mentioned image processing of n _x × n _y times magnification.

Other methods may be used for the processing of hologram averaging (spatial averaging). FIG. 4 shows a conceptual diagram of hologram averaging (spatial averaging) by a spatial filter. For example, a moving average is performed by convolution integration with a spatial filter having an number of n _x × n _y elements (the coefficient of each element is 1 / n _x n _y ). Further, I'may be obtained by using a weighted average, a median filter, or the like. In this case, the range of the spatial filter is the adjacent area for the central pixel.

By the above spatial averaging calculation, it is possible to remove noise components that are independently distributed for each adjacent pixel in the captured hologram.

A hologram taken by an image sensor generally contains a direct image component and a conjugate image component. Therefore, as shown in FIG. 1, after the spatial averaging calculation, the hologram is subjected to a phase shift algorithm (for example, Patent Document 2, Non-Patent Document 1, Non-Patent Document 5), or an off-axis method (for example, , It is desirable to obtain a complex amplitude distribution that does not include the direct image component and the conjugate image component by analysis in Non-Patent Document 4). If the direct image component and the conjugate image component have a minor effect on the quality of the reproduced image, it is not necessary to acquire the complex amplitude distribution.

After that, a reproduced image can be obtained by applying propagation calculation such as Fresnel diffraction integration or angular spectral method, or correlation calculation to the hologram or complex amplitude distribution from which the noise component has been removed.

For example, the complex amplitude distribution O (x, y) is analyzed by the phase shift method or the like from the hologram from which the noise component is removed by the spatial averaging process, and the obtained O (x, y) is obtained by the following equation (2). Apply the propagation calculation of.

Here, FT [...] and FT ^-1 [...] are two-dimensional Fourier transform operators and two-dimensional inverse Fourier transform operators, where i is an imaginary number, z _r is a distance, and λ is a wavelength. , U, v are spatial frequency variables. By this calculation, the image O'(x, y; z _r ) of the object at the distance z _r can be reproduced in the reproduction system.

According to the present invention, a high-quality reproduced image with reduced noise can be obtained. Further, even if spatial averaging is performed on a normal image obtained by an image sensor, noise (roughness of the image) is simply reduced and the contrast does not change. However, in the incoherent holography of the present invention, it will be described later. As shown, the spatial averaging has an effect different from other images in that the contrast of the obtained reproduced image is increased.

(Improved embodiment)
As described above, the effect of reducing noise in the reproduced image can be obtained by introducing the spatial average for the signal value of each adjacent pixel of each hologram, but the signal processing of the spatial average is simply introduced into the incoherent holography. As a result, there is concern that the following two problems will occur.

FIG. 5 shows a hologram and a reproduced image thereof for explaining the influence of the spatial average. 5 (a) and 5 (b) are holograms and their reproduced images when spatial averaging is not performed, and FIGS. 5 (c) and 5 (d) are spatial averaging. It is a hologram of time and its reproduced image.

The first problem is that the quality of the reproduced image deteriorates due to the occurrence of aliasing in the captured hologram, and a false reproduced image is generated. By applying the spatial averaging signal processing to the concentric hologram of FIG. 5 (a), as shown in FIG. 5 (c), the high frequency component of the hologram is lost and a plurality (upper and lower, left and right, diagonal). Concentric holograms will be obtained. By applying the propagation calculation or the reconstruction calculation to this hologram, a plurality of false point images that should not originally exist can be obtained as in the reproduced image of FIG. 5D. This problem is peculiar to incoherent holography, which requires propagation calculation or reconstruction calculation to obtain an image.

Another problem is that the diameter of the effective hologram becomes smaller and the spatial resolution of the reproduced image deteriorates. In the hologram after spatial averaging in FIG. 5C, a plurality of concentric holograms are formed, and at the same time, the diameter of the hologram in the central portion is reduced. The smaller diameter of the hologram corresponds to the lower NA of the lens, and as shown in FIG. 5D, the point image reproduced from the hologram is blurred and the diameter becomes larger. As a result, the spatial resolution of the reproduced image deteriorates due to the spatial averaging as in a normal digital camera.

As a further improvement in the present invention, regarding the problem of generation of false images, which is a side effect when applying spatial average signal processing to a hologram, the spatial frequency corresponding to the reciprocal of the number of pixels used for spatial average signal processing is dealt with. Reduced by low-pass filtering of bandwidth. Regarding the problem of deterioration of spatial resolution, by referring to the parameters of the optical element of the hologram recording device of incoherent holography and the information of the arrangement distance of the object to be photographed, only noise is reduced without deteriorating the spatial resolution. It enables the acquisition of high-quality reproduced images.

First, countermeasures against the occurrence of false images will be described. Low-pass filtering is performed on the spatial frequencies of the hologram or complex amplitude distribution to remove the false images resulting from the aliasing caused by the spatial averaging. The low-pass filtering is performed as a process in the signal processing device 20, and a signal process is performed in which the hologram or complex amplitude distribution is Fourier transformed, converted into a spatial frequency, and then the high frequency component is cut. The pass band (spatial frequency band) of low-pass filtering is the number of pixels used for averaging (number of pixels in the horizontal direction n _x , number of pixels in the vertical direction n _y ), where N _x × N _y is the number of pixels in the hologram or complex amplitude distribution. By setting N _x / n _x and N _y / n _y corresponding to the reciprocal of), there is no signal loss and a false image can be reduced. Further, when the hologram does not contain high frequency components or when the influence of the false image is slight, the application of low-pass filtering is optional.

The method of reconstructing the reproduced image from the hologram or the complex amplitude distribution after applying the above processing is the same as that of the conventional incoherent holography technique (Patent Documents 1, 2, Non-Patent Documents 1, 2, 4, 5). Therefore, it is possible to obtain a high-quality reproduced image on an arbitrary reproduction surface by applying propagation calculation such as Fresnel diffraction integration or holographic method, or correlation calculation.

Next, measures against deterioration of spatial resolution will be described. In the present invention, when n _x × n _y becomes large, that is, when the number of pixels used for averaging increases, the high frequency component of the image data of the hologram taken by the image sensor disappears, and as a result, the spatial resolution of the reproduced image becomes high. There is concern that it will decline. Therefore, in the present invention, the information of the optical parameters and the like (λ, f ₀ , D ₀ , z _l , f _d1 , f _d2 , D _slm , z _h , p, D _sensor ) of the hologram recording device described above is referred to. By appropriately setting the number of pixels n _x × n _y for spatial averaging according to these values, only noise is reduced without lowering the spatial resolution. The conditions required for the number of pixels n _x , n _y used for spatial averaging will be described below in order to reduce only noise without sacrificing spatial resolution.

FIG. 6 is an example of a hologram photographed by incoherent holography. In the optical system of FIG. 2, when the point light source 1 is arranged at the center of the optical axis, interference fringes as shown in FIG. 6 are formed on the image pickup surface of the image pickup device 10. This interference pattern is equivalent to the Fresnel lens, the size of the focal distance z _r from light propagation based on phase modulation effect and the Fresnel diffraction integral in the lens 2 is expressed by the following equation (3). In order to obtain a focused image, z _r of Eq. (2) is set so as to satisfy the following Eq. (3).

Here, z _d is the following equation (4), and z _s is the distance from the lens 2 to the object 1 to be photographed.

Further, the diameter D _{h of the} interference fringes can be expressed by the following equation (5) by similarly considering the propagation of light waves and considering the effective aperture diameter of each optical element.

Here, MIN {...} is an operator for extracting the term of the minimum value, and D _l is Eq. (6).

That is, the first term in MIN {...} of Eq. (5) is the diameter of the first dividing light given the phase distribution of the focal length f _d1 , and the second term is the focal length f _d2. It is the diameter of the second division light given the phase distribution of, and the third term is the effective aperture diameter of the image sensor. The diameter D _{h of the} interference fringes is determined by these smallest ones.

The condition of the sampling interval in which the interference fringes are photographed by the image sensor so that aliasing does not occur is obtained by the equation (7) from the sampling theorem. Therefore, if the pixel pitch p of the captured image is selected so as to satisfy the condition of the equation (8), the information on the high frequency component of the interference fringes is not lost.

When the spatial averaging calculation shown in FIGS. 3 and 4 is performed, it is equivalent to the pixel pitch being n _x p or n _y p. Therefore, when the pixel pitch p of the image sensor is determined, if n _x and n _y are selected so as to satisfy the conditions of the following equations (9) and (10), the information of the interference fringes disappears. No, that is, only noise can be reduced without reducing spatial resolution.

That is, n _x and n _y are set to λ _{z r} / D _h p or less.

In the above example, the case where the spatial averaging calculation is applied to the hologram taken by the imaging element has been described, but the target of the averaging calculation is not the hologram but the phase shift method or the off-axis method. Spatial averaging operations may be applied to the complex amplitude distribution obtained after the analysis.

Further, the image sensor used in the present technology is not limited to a single color, and a color filter may be mounted.

(Other embodiments)
The hologram recording / reproducing device for carrying out the present invention is not limited to the single optical path interferometer shown in FIG. For example, various interferometers as shown in FIG. 7 can be used for hologram recording.

FIG. 7A is a Michelson interferometer, which includes a lens 2, a beam splitter 7, two concave mirrors 8, and an image sensor 10. The light wave passes through the lens 2, is split into two by the beam splitter 7, is given a curvature by the concave mirror 8, and a hologram is generated on the element surface of the image sensor 10.

FIG. 7B is a Mach-Zehnder interferometer, which includes two lenses 2, two beam splitters 7, two mirrors 9, and an image sensor 10. The light wave passes through the lens 2 and is split into two by the beam splitter 7. One split light is reflected by the mirror 9 via the lens 2, and the other split light is reflected by the mirror 9 without passing through the lens and is incident on the second beam splitter 7 on the element surface of the image pickup element 10. Generate a hologram.

FIG. 7C is a triangular optical path interferometer, which includes three lenses 2, a beam splitter 7, two mirrors 9, and an image sensor 10. The light wave passes through the lens 2 and is split into two by the beam splitter 7, travels clockwise and counterclockwise through the lens 2, mirror 9, mirror 9, and lens 2, respectively, and is incident on the beam splitter 7 again for imaging. A hologram is generated on the element surface of the element 10.

In this way, the light wave from the object can be separated into two, different phase distributions can be given to the first divided light and the second divided light, and finally these can be interfered with each other on the image sensor surface to form a hologram. Any form may be used as long as it is an optical system. Further, an additional lens may be inserted in each optical path of the optical system shown in FIG. 2 or FIG.

(Verification of effect)
Optical experiments were carried out to verify the effectiveness of the present invention. The optical system used in the experiment is shown in FIG. This optical system realizes the single optical path interferometer shown in FIG. 2 by using the reflection type spatial light modulator 4.

The light (incoherent light) generated by the light emitting diode (LED) 11 forms an optical pattern on the USAF test target 12, passes through a bandpass filter 6, a lens 2, and a polarizer 3, and then passes through a bandpass filter 6, a lens 2, and a polarizer 3, and then a horizontal linearly polarized light component and a vertically linearly polarized light. It becomes the first division light and the second division light composed of each of the components. The two split lights that have passed through the beam splitter 7 are given different phases by the spatial light modulator 4, are incident on the beam splitter 7 again, are reflected, and are directed toward the image pickup element 10 and are transmitted through the polarizer 5. , The polarization states match, and interference fringes are formed on the image pickup element surface. This interference fringe is photographed as a hologram by using the image sensor 10.

Here, the distance between the lens and the spatial light modulator is 100 mm, and the distance between the spatial light modulator and the image sensor is 260 mm. The effective aperture diameter of the lens 2 is 12 mm, the effective aperture diameter of the spatial light modulator 4 is 10.65 mm, the effective aperture diameter of the image sensor 10 is 13.3 mm, and the image sensor 10 has a pixel size of 6.5 μm. Using. As a light source, an LED 11 having a center wavelength of 625 nm and a wavelength width of 18 nm was used. Further, in order to increase the coherence length of the light source, a bandpass filter 6 having a center wavelength of 633 nm and a wavelength width of 3 nm was used.

First, it is an object of the present invention to clarify whether the influence of noise and a false image can be reduced, and whether the noise reduction effect changes depending on the size of the number of pixels n _x × n _y used for averaging. As a result, a shooting experiment of a transmissive USAF test target was carried out.

The USAF test target 12 was placed at a position 400 mm away from the lens 2, and a hologram was photographed by the image sensor 10. Further, in order to remove the direct image component and the conjugate image component in the hologram by the 4-step phase shift method, four holograms having a phase shift amount of 0, π / 2, π, and 3π / 2 were obtained. Spatial averaging signal processing based on Eq. (1) was applied to each of the four holograms. The average number of pixels n _x × n _y was set to 3 types of 2 × 2, 4 × 4, 8 × 8.

The reproduced images created under various conditions are collectively displayed in FIG. FIG. 9A shows a reproduced image reconstructed without applying averaging. Further, in FIGS. 9 (b), 9 (c), and 9 (d), a reproduced image reconstructed by performing an averaging calculation of 2 × 2, 4 × 4, 8 × 8 pixels and reconstructing without applying low-pass filtering. Is shown. 9 (e), (f), and (g) show the results of averaging the number of pixels 2 × 2, 4 × 4, 8 × 8 and applying low-pass filtering to acquire a reproduced image. From a qualitative point of view, it can be seen that the reproduced image becomes clear by applying the spatial averaging with or without low-pass filtering.

Further, in order to confirm the existence of the false image, a part of the reproduced image of each of FIGS. 9 (d) and 9 (g) is enlarged, and an image in which the contrast is adjusted is shown in FIG. 10 (a) is an enlarged view of FIG. 9 (d), and FIG. 10 (b) is an enlarged view of FIG. 9 (g). When low-pass filtering is not applied (FIG. 10 (a)), unnecessary components (false images) are generated around "0" and the linear structure, but when low-pass filtering is applied. (FIG. 10 (b)) shows that these false images have been removed.

In order to quantitatively compare the quality of these reproduced images, the contrast ratio (CR: Contrast Ratio) and the smoothness (S: Smoothness) were evaluated. The contrast ratio CR is an index for evaluating the ratio of the brightness of the bright part and the dark part in the image, and is given by the following equation (11).

μ _b and μ _d are the average value of the intensity of the rectangular region (bright region) of the broken line in the reproduced image of FIG. 9, and the average value of the intensity of the rectangular region (dark region) of the alternate long and short dash line, respectively. Since the USAF target used in this experiment is a transmissive type, the intensity should ideally be 0 in the dark part of the reproduced image of the USAF test target. Therefore, it can be said that the larger the value of the contrast ratio CR, the higher the quality of the reproduced image.

On the other hand, the smoothness S corresponds to the reciprocal of the coefficient of variation and is given by the following equation (12).

σ _b is the standard deviation of the intensity within the dashed rectangular region (bright region) in the reproduced image. The higher this value S, the less speckle-like noise and the smoother the distribution, so it can be said that the reproduced image is of high quality.

The evaluation results of CR and S are shown at the bottom of each reproduced image in FIG. Since CR and S are improved as the number of averaged pixels increases, it was found that noise can be reduced and a high-quality reproduced image can be obtained by using the spatial averaging of the present invention. Further, it can be seen that by applying the low-pass filtering in the spatial frequency band, CR and S are improved as compared with the case where the low-pass filtering is not applied, which is effective for obtaining a higher quality reproduced image.

In addition, for a comparative experiment, a photographing experiment of a USAF test target was carried out using the time average described in Non-Patent Document 2. For this experiment, 64 holograms of each of the four types required for the four-step phase shift method were taken. The number of averaged sheets was changed from 2 to 64, and reproduced images were obtained for each. 9 (h), (i), and (j) show time-averaged reproduction images and evaluation results of CR and S when the average number of sheets is 4, 16, and 64, respectively.

Further, FIG. 11 shows the evaluation results of CR and S for the averaged number of sheets 2 to 64 (time average). FIG. 11A plots the average number of sheets on the horizontal axis and the contrast ratio CR value on the vertical axis, and FIG. 11B shows the average number of sheets on the horizontal axis and the smoothness S on the vertical axis. It is a plot of the values. Further, in FIG. 11, for comparison, the evaluation result of the reproduced image subjected to the spatial averaging process is also presented. Since the spatial averaging can be considered as the averaging of the number of holograms for the number of pixels, the low-pass filtering shown in FIGS. 9 (e) to 9 (g) is performed and the number of pixels is 2 × 2, 4 × 4. The evaluation results of CR and S when the 8 × 8 averaging is applied are plotted as data when the averaging number is 4, 16 and 64.

From the evaluation results of FIGS. 9 (h) to 9 (j) and 11 in FIG. 11, CR and S are improved as the number of averaged sheets increases even in the time average, and noise is reduced as reported in Non-Patent Document 2. It is possible. Comparing the noise reduction effects of the time average and the space average, the space average is superior in terms of contrast ratio CR and the time average is superior in terms of smoothness S, and the tendency of improvement of CR and S is different. This means that the types of noise that can be reduced differ between the time average and the spatial average. It can be considered that the time average is effective in removing the noise component that fluctuates with time, while the spatial average is effective in removing the noise component that fluctuates in space. Although there is a difference in the amount of noise reduction between the time average and the spatial average, the spatial average does not require multiple hologram shots, and the effect of improving the quality of the reproduced image is comparable to the time average from the viewpoint of CR. It turned out to be.

Next, when the present invention was applied, the effectiveness of the conditions that did not deteriorate the spatial resolution represented by the formulas (9) and (10) was confirmed by experiments. In the present invention, there is a concern that the spatial resolution deteriorates as the number of averaging pixels increases, but when the conditions of the equations (9) and (10) are satisfied, the spatial resolution does not deteriorate and the spatial frequency does not deteriorate. The response should not change. FIG. 12 shows a plot of the relationship (Equation (7)) between the imaging position z _{s of the} object and the required sampling interval p _s based on the parameters of the optical system used in this experiment. In this experiment, since the object to be photographed is arranged at the position of z _s = 400 [mm], it is predicted that the spatial resolution will not deteriorate if the sampling interval is 18.16 μm or less.

In this experiment, since the pixel size of the image sensor is 6.5 μm, the 2 × 2 average corresponds to the pixel size, that is, the sampling interval of 13 μm, and the spatial frequency response should not change. On the other hand, the 4 × 4 average and the 8 × 8 average correspond to the pixel sizes of 26 μm and 52 μm, the spatial resolution should be deteriorated, and the high frequency component of the spatial frequency response should be decreased. In order to confirm the validity of these predictions, the optical transfer function (OTF) of the reproduced image before and after averaging was evaluated. The purpose of this experiment is to evaluate the spatial frequency response. In order to remove noise components from the reproduced image as much as possible and perform more accurate evaluation, 64 holograms are time-averaged and then averaged. Based on the present invention, spatial averaging and low-pass filtering with 2 × 2, 4 × 4, 8 × 8 pixels were performed.

Since the USAF test target to be photographed is composed of a line-shaped mask having various spatial frequency components, the spatial frequency response, that is, OTF can be investigated by evaluating the contrast of the line-shaped image. .. The theoretical spatial resolution (Rayleigh's resolution) of the optical system of FIG. 8 used in the experiment is 31.24 μm, and when this is converted into a spatial frequency, it becomes 16.01 lp / mm (lp: line pair). Therefore, the contrast of the linear image of Group0 Element1 with the lowest spatial frequency of 1.00 lp / mm to Group4 Element3 with the spatial frequency of 20.16 lp / mm of the USAF test target was used in the experiment. It is possible to evaluate the OTF in the entire pass frequency band of the optical system.

FIG. 13 shows the results of comparing the optical transfer functions (OTF) of the reproduced images. It can be seen that there is almost no difference in OTF between the case where the averaging is not applied and the case where the number of pixels 2 × 2 averaging is applied, and the same characteristics are exhibited. On the other hand, it can be seen that by applying the 4 × 4 averaging and the 8 × 8 averaging, the contrast of the high-frequency component decreases and the OTF changes significantly. Further, as shown in FIG. 9E, the quality of the reproduced image can be improved by averaging 2 × 2. Therefore, from the above experimental results, if the condition of the number of pixels used for averaging is appropriately set according to the condition of the equation (7), that is, the spatial averaging is performed under the condition of the region on the left side of the broken line in FIG. By applying, it is possible to reduce only noise and improve the quality of the reproduced image without lowering the spatial resolution.

Finally, it was verified whether the quality of the reproduced image could be improved by spatial averaging by photographing the reflecting object. In the experiments so far, only the USAF test target, which is a transparent object, was photographed, but by photographing the reflective object, it will be clarified whether the quality of the reproduced image can be improved by using the spatial average.

In this experiment, the optical system shown in FIG. 14 was used. The specifications of the optical element are the same as those of the optical system of FIG. 8, but only the arrangement of the LED 11 which is the illumination light is changed in order to photograph the reflecting object 13. The light (incoherent light) generated by the LED 11 is reflected by the reflecting object 13 to become object light, and is incident on the bandpass filter 6. The following is the same as the optical system of FIG.

FIG. 15 shows the result of reconstructing the reproduced image after photographing the coin and applying the spatial averaging. 15 (a) is a reproduced image without averaging, (b) is a reproduced image with 2 × 2 pixels, (c) is a 4 × 4 pixel, and (d) is an averaged 8 × 8 pixel. In order to quantitatively evaluate the quality of the reproduced image, the CR between the broken line area (on the coin) and the alternate long and short dash line area (upper right background) was evaluated using the equation (11). The result is shown at the top of each reproduced image. Since the surface of the reflective object is rough and a speckle-like image is generally obtained, the reproduced image by S for evaluating the smoothness is not evaluated.

As can be seen from the evaluation result of the contrast ratio CR in FIG. 15, it can be seen that the spatial averaging calculation increases the contrast ratio, improves the quality of the reproduced image, and makes it clear.

As described above, according to the present invention, it is possible to reduce noise, obtain a high-quality hologram, and obtain a high-quality reproduced image without lowering the time resolution. Further, in the present invention, the generation of a false image can be solved by applying low-pass filtering according to the number of pixels used for spatial averaging, and the problem of deterioration of spatial resolution is configured as a hologram recording device. The spatial resolution is deteriorated by appropriately setting the calculation conditions for spatial averaging by referring to the optical parameters and placement distance of the element to be imaged, the distance between the object to be imaged and the image pickup element, and the wavelength information of the light source. Only noise can be reduced without causing it. Further, since the number of pixels of the image data can be reduced by spatial averaging, it is effective in improving the data processing speed, reducing the arithmetic processing, and reducing the data storage capacity.

In the above-described embodiment, the configuration and operation of the hologram recording / playback device have been described, but the present invention is not limited to this, and may be configured as a stereoscopic image reproduction method for reproducing a stereoscopic image. That is, for each pixel of the photographed hologram or the complex amplitude distribution obtained by analyzing the hologram, a spatial averaging process for averaging the signal value of the pixel and the signal value of the pixel existing in the adjacent region is performed. It may be configured as a stereoscopic image reproduction method in which the stereoscopic image is reproduced based on the hologram or the complex amplitude distribution subjected to the spatial averaging process.

Although the above embodiments have been described as typical examples, it will be apparent to those skilled in the art that many modifications and substitutions can be made within the spirit and scope of the present invention. Therefore, the present invention should not be construed as being limited by the above embodiments, and various modifications and modifications can be made without departing from the scope of claims. For example, it is possible to combine the plurality of constituent blocks described in the embodiment into one, or to divide one constituent block into one.

1 Point light source 2 Lens 3 Polarizer 4 Spatial light modulator 5 Polarizer 6 Bandpass filter 7 Beam splitter 8 Concave mirror 9 Mirror 10 Imaging element 11 LED
12 USAF test target 13 Reflective object 20 Signal processing circuit

Claims (8)

The incoherent light wave is divided into the first divided light and the second divided light, and after giving different phase distributions, the hologram formed by interfering the first divided light and the second divided light is reconstructed. In a hologram recording / reproducing device that reproduces a stereoscopic image,
Spatial averaging processing including an operation of averaging the signal value of the pixel and the signal value of the pixel existing in the adjacent region for each pixel of the photographed hologram or the complex amplitude distribution obtained by analyzing the hologram. A hologram recording / reproducing apparatus, which reproduces a stereoscopic image based on the hologram or the complex amplitude distribution that has undergone the spatial averaging process. In the hologram recording / playback apparatus according to claim 1, the spatial averaging process is performed with n _x × n as the number of pixels in the horizontal direction n _x and the number of pixels in the vertical direction n _y (n _x , n _y > 1) before averaging. It is characterized by including an operation to average the signal value for each _y pixels, and then an operation to increase the number of pixels by n _x × n _y times to make the number of pixels and the pixel pitch the same before and after averaging. Hologram recording / playback device. In the hologram recording / playback apparatus according to claim 1, the spatial averaging process is performed with n _x × n as the number of pixels in the horizontal direction n _x and the number of pixels in the vertical direction n _y (n _x , n _y > 1) before averaging. _A hologram recording / playback apparatus characterized by including a convolution integral with a spatial filter having _y elements. The hologram recording / playback apparatus according to any one of claims 1 to 3 is characterized in that after the spatial averaging process, low-pass filtering having a spatial frequency band corresponding to the reciprocal of the number of pixels used for averaging is applied. A hologram recording / playback device. In the hologram recording / reproducing device according to any one of claims 1 to 4, at least the focal length, effective aperture diameter, light source wavelength, distance between optical elements, and photographing of the optical elements constituting the hologram recording / reproducing device. A hologram recording / reproducing device, characterized in that the number of pixels in an adjacent region used for the spatial averaging process is set according to information on the distance from an object to an image sensor. In the hologram recording / reproducing apparatus according to any one of claims 1 to 4, the number of horizontal pixels n _x and the number of vertical pixels n _y (n _x , n _y > 1) in the adjacent region used for the spatial averaging process. Is set to λ z _r / D _h p or less as the wavelength λ of the light source, the focal distance z _{r of} the interference fringes, the diameter D _{h of the} interference fringes, and the pixel pitch p of the image pickup device. .. In a stereoscopic image reproduction method for reconstructing a stereoscopic image by reconstructing a hologram formed by interference between a first division light and a second division light divided from an incoherent light wave and given different phase distributions to each other.
Spatial averaging processing is performed on each pixel of the photographed hologram or the complex amplitude distribution obtained by analyzing the hologram to average the signal value of the pixel and the signal value of the pixel existing in the adjacent region. A method for reproducing a stereoscopic image, which comprises reproducing a stereoscopic image based on the hologram or the complex amplitude distribution subjected to the spatial averaging process. The stereoscopic image reproduction method according to claim 7, wherein after the spatial averaging process, low-pass filtering having a spatial frequency band corresponding to the reciprocal of the number of pixels used for averaging is applied. ..