Objective hologram quality evaluation method

Abstract

An objective hologram quality evaluation method is provided. The quality evaluation method, according to an embodiment of the present invention, receives an original holographic fringe pattern and a target holographic fringe pattern to be compared, calculates the respective angular spectra of the inputted original holographic fringe pattern and the inputted target holographic fringe pattern, and calculates a PSNR obtained from the calculated angular spectra as a quality value of the target holographic fringe pattern. Since the angular spectrum of the holographic fringe pattern has the same characteristics without change according to distance, even a diffraction wavefront positioned at an arbitrary distance as well as the position of the holographic fringe pattern has the same PSNR value, thereby enabling objective quality evaluation for the holographic fringe pattern.

Description

Objective Hologram Quality Evaluation Method

[0001] The present invention relates to a method for evaluating hologram quality, and more particularly, to an objective quality evaluation method for a holographic fringe pattern or a numerically restored holographic restoration image.

[0002] 1. Generation and numerical reconstruction of holographic fringe patterns

[0003] Figure 1 shows the hologram plane where the holographic fringe pattern (hologram) is located and the location for a 3D object. The 3D object can be regarded as a collection of points (point-cloud) with unique amplitude and unique phase, and the light emitted from each point is propagated to the hologram plane in the (x, y) plane. In the hologram plane, the wavefronts propagated from all points interfere with each other to form a holographic fringe pattern. The p-th point constituting the point-cloud has a 3D spatial location (x p ,y p ,z p ) with complex amplitude value A p =a p exp(jφ p ) can be expressed as a p is the characteristic amplitude, φ p represents the initial phase.

[0004] The holographic fringe pattern H(x,y) on the hologram plane (x,y) can be numerically generated by scalar diffraction, and the representative method, Rayleigh-Sommerfeld integral, can be expressed as follows.

[0005] [Formula 1]

[0006]

[0007] r here p is the distance between the pth point and (x,y) on the hologram plane , and R1(x,y) represents the reference wave for recording, k=2π / λ represents the wavenumber, and λ represents the wavelength. As shown in Equation 1, the holographic fringe pattern records 3D information (position, amplitude, phase, etc.) for each point and the wavelength information of the light used for recording, so it can be considered that 3D information is encoded in the holographic fringe pattern.

[0008] Recovering three-dimensional object information encoded from holographic fringe patterns is possible through scalar diffraction, such as the Fresnel approximation or the angular spectrum. For example, the Fresnel approximation can be expressed as in Equation 2.

[0009] [Formula 2]

[0010]

[0011] Here, Γ(x', y'; d) represents a numerical holographic reconstruction image on the plane (x', y') located at a distance d from the hologram plane, and R2 represents a reference wave for reconstruction. Generating a holographic fringe pattern encodes three-dimensional information about an object distributed in three-dimensional space onto a two-dimensional hologram plane, but the reconstruction process creates a two-dimensional reconstruction image on a plane located at an arbitrary distance d from the two-dimensional holographic fringe pattern on the hologram plane. A complete reconstruction method for three-dimensional space has not yet been presented. For this reason, most numerical reconstructions of holograms refer to two-dimensional images.

[0012] Due to these characteristics, a numerically reconstructed image at a specific distance d has clear reconstruction characteristics for an object located at that distance d, but as the distance increases, blurring increases for points or objects that are far from the plane located at that distance d. This is due to the out-of-focus effect. An example of this is shown in Fig. 2. Fig. 2 (a) shows a holographic fringe pattern generated by the Rayleigh-Sommerfeld integral, and Figs. 2 (b) to (e) show images numerically reconstructed at different distances from the holographic fringe pattern. Fig. 2 (b) is a back-focus reconstructed image, in which the back portion is clear, but blurring occurs in the other portions due to defocusing. Fig. 2 (c) is a front-focus reconstructed image, in which the front portion is in focus, so the front is clear, but blurring occurs in the back because it is out of the focus region. In addition, blurring occurs in all areas at a distance completely outside the range where a 3D object is located, and it can be seen that the blurring increases as the distance from the object position increases.

[0013]

[0014] 2. Trends in Holographic Fringe Pattern Quality Evaluation

[0015] PSNR (Peak Signal Noise Ratio) is the maximum signal-to-noise ratio, which represents the power of noise relative to the maximum power that a signal can have. The formulas for this are as follows: (3) and (4).

[0016] [Formula 3]

[0017]

[0018] [Formula 4]

[0019]

[0020] Here, I(i,j) is the original image, K(i,j) is the image containing noise, MAX is the maximum value that the image can have, and NM represents the vertical × horizontal number of pixels in the image. According to the above formula, PSNR represents the difference in pixel values ​​between two images as power. Since it can calculate the difference in pixel values, it is widely used in fields that calculate the difference in pixel values ​​that occurs according to the degree of loss after image lossy compression and restoration.

[0021] Recent technological advancements and expanded applications have led to efforts to compress or vary the bitrate of holographic fringe patterns. Because holographic fringe patterns contain a vast amount of data, various algorithms are being used to compress them for storage or transmission. Quality assessment is an essential part of these compression / reconstruction processes.

[0022] Methods for comparing the original holographic fringe pattern with the fringe pattern lost through compression and restoration are typically used for image or video quality assessment, such as PSNR and SSIM (Structural SIMilarity index). However, these methods were not proposed for comparing holographic fringe patterns and may therefore be unsuitable as criteria for evaluating holographic fringe patterns. Nevertheless, the background for using PSNR and SSIM in comparing holographic fringe patterns is that a suitable quality assessment method specifically for holographic fringe patterns has not yet been presented.

[0023] The present invention has been devised to solve the above problems, and the purpose of the present invention is to provide a method capable of objectively evaluating the quality of a holographic fringe pattern and a restored image using an angular spectrum and PSNR (Peak Signal Noise Ratio).

[0024] An objective quality evaluation method according to one embodiment of the present invention for achieving the above purpose includes the steps of: receiving an original holographic fringe pattern as input; receiving a target holographic fringe pattern as a comparison target; calculating angular spectra of the input original holographic fringe pattern and the target holographic fringe pattern respectively; and calculating a quality value of the target holographic fringe pattern from the calculated angular spectra.

[0025] The target holographic fringe pattern may be a holographic fringe pattern that has suffered loss from the original holographic fringe pattern due to bit rate adjustment or otherwise.

[0026] The target holographic fringe pattern may be a holographic fringe pattern that has suffered loss by restoring the original holographic fringe pattern after compression.

[0027] The quality value of the target holographic fringe pattern can be the same regardless of the position calculated from the holographic fringe pattern in the direction of the numerically restored image.

[0028] The objective quality evaluation method according to the present invention may further include a step of converting an input holographic fringe pattern into a holographic fringe pattern composed of complex amplitudes, if the input holographic fringe pattern is not a holographic fringe pattern composed of complex amplitudes having amplitude and phase.

[0029] If the holographic fringe pattern is not a holographic fringe pattern composed of complex amplitudes, it may be a holographic fringe pattern composed of only amplitudes or a holographic fringe pattern composed of only phases.

[0030] The calculation step can calculate the quality value of the target holographic fringe pattern by taking the absolute value of each of the produced angular spectra and calculating the PSNR value.

[0031] The output stage is,

[0032] Using the formula below, each Angular spectrum is calculated,

[0033]

[0034] A ref (f X ,f Y ) is the Angular spectrum of the original holographic fringe pattern,

[0035] A tar (f X ,f Y ) is the Angular spectrum of the target holographic fringe pattern,

[0036] H ref (x,y) is the original holographic fringe pattern,

[0037] H tar (x,y) is the target holographic fringe pattern,

[0038] f X Wow f Y can be a spatial frequency.

[0039] The calculation steps are:

[0040] The PSNR value is calculated using the following formula:

[0041]

[0042] MAX is the maximum value of the holographic fringe pattern,

[0043] The absolute value |A| for the complex amplitude A = α+jβ is is produced by,

[0044] NM can be vertical × horizontal pixels.

[0045] According to another aspect of the present invention, an objective quality evaluation system is provided, characterized by including: a processor for receiving an original holographic fringe pattern and a target holographic fringe pattern to be compared, calculating angular spectra of the input original holographic fringe pattern and the target holographic fringe pattern, and calculating a quality value of the target holographic fringe pattern from the calculated angular spectra; and a storage unit for providing storage space required by the processor.

[0046] As described above, according to embodiments of the present invention, the angular spectrum of a holographic fringe pattern is produced and the PSNR is calculated based on the angular spectrum. Since the angular spectrum has the same characteristics without change according to distance, the diffraction wavefront located at any distance as well as the holographic fringe pattern position has the same PSNR value, thereby enabling objective quality evaluation of the holographic fringe pattern.

[0047] Figure 1. Relationship between the hologram plane and the object plane

[0048] Figure 2. Numerical reconstruction images at different distances restored by holographic fringe pattern and Fresnel approximation.

[0049] Figure 3. (a) Diffraction wavefront propagation image (numerically reconstructed image) at each position of the holographic fringe pattern and at propagation distances d1 and d2 from the holographic fringe pattern, (b) Fourier spectrum at each position, (c) angular spectrum at each position.

[0050] Figure 4. Objective quality assessment method for existing holographic fringe patterns.

[0051] Fig. 5. Objective quality evaluation method for holographic fringe patterns using angular spectrum according to one embodiment of the present invention.

[0052] Fig. 6. Objective quality evaluation method for holographic fringe patterns using angular spectrum according to another embodiment of the present invention.

[0053] Fig. 7. Holographic fringe pattern, numerical reconstruction, and PSNR for the angular spectrum.

[0054] Fig. 8. An objective quality evaluation system for a holographic fringe pattern using an angular spectrum according to another embodiment of the present invention.

[0055] Hereinafter, the present invention will be described in more detail with reference to the drawings.

[0056] An embodiment of the present invention proposes an objective hologram quality assessment method. This technology objectively assesses the quality of a holographic fringe pattern or a numerically reconstructed hologram image.

[0057]

[0058] 1. Objective quality assessment requirements for holographic fringe patterns and numerical reconstruction images.

[0059] To objectively evaluate the quality of holographic fringe patterns, the following requirements must be met:

[0060] (1) Objective quality assessment of holographic fringe patterns or numerically reconstructed images must be performed regardless of the holographic display. Because holographic fringe patterns contain specific parameters of the holographic display system (e.g., wavelength, pixel interval), compatibility of holographic content between holographic displays with different system parameters is low.

[0061] (2) The quality assessment methods for holographic fringe patterns and numerically reconstructed images must be identical, and the same results must be obtained. Since holographic fringe patterns and numerically reconstructed images contain identical information about three-dimensional objects, the quality assessment methods for these two images must be identical, and the quality assessment results must also be identical.

[0062] (3) The objective quality evaluation results must show the same results regardless of the location from which they are evaluated, from the holographic fringe pattern to an infinite distance in the direction of the numerical restoration image.

[0063] (4) Any type of holographic fringe pattern, including complex amplitude holograms, amplitude holograms, and phase holograms, must be capable of quality evaluation.

[0064]

[0065] 2. Characteristics of Angular Spectrum

[0066] The Fourier spectrum is the frequency spectrum of a two-dimensional plane with an arbitrary pattern, and it shows that it can be expressed as a combination of various harmonic waves with unique amplitudes and frequencies. A similar method, the angular spectrum, shows that a two-dimensional plane with an arbitrary pattern can be expressed as a combination of various plane waves with a single wavelength, unique amplitudes, and incident angles.

[0067] A typical optoelectronic holographic display system displays a holographic fringe pattern on a spatial light modulator and incidents a reference wave onto the spatial light modulator. The incident reference wave is diffracted by the fringe pattern to form a three-dimensional object in free space. The angular spectrum A(α / λ, β / λ; 0) for the holographic fringe pattern H(x, y; 0) displayed on the spatial light modulator can be expressed as in Equation 5.

[0068] [Formula 5]

[0069]

[0070] Here, λ represents the wavelength of the plane wave, (α,β,γ) represent the direction cosines, and f X Wow f Y means spatial frequency, and has the following relationship with the direction cosine.

[0071] [Formula 6]

[0072]

[0073] The angular spectrum A(α / λ,β / λ;d) at a distance d from the holographic fringe pattern can be expressed as follows.

[0074] [Formula 7]

[0075]

[0076] The diffraction wavefront or numerically reconstructed image H(x,y;d) at a distance d from the holographic fringe pattern can be expressed by the following equation.

[0077] [Formula 8]

[0078]

[0079] Here represents the circle function.

[0080]

[0081] 3. Objective hologram quality evaluation method

[0082] A holographic fringe pattern is composed of a pattern for diffracting light, and is generated using scalar diffraction such as the Rayleigh-Sommerfeld integral so that the diffracted wavefront can form a three-dimensional object at an arbitrary distance. When a reference wave is incident on a holographic fringe pattern generated or acquired by a camera, etc., the reference wave is diffracted by the holographic fringe pattern, as shown in Fig. 3 (a), so that the three-dimensional object used in the generation is optically or numerically restored at a certain distance (e.g., distance d2). However, at a different distance (e.g., distance d1) from the location where the three-dimensional object is located, a defocused image that is not in focus is restored.

[0083] The Fourier spectra for the holographic fringe pattern and the numerically reconstructed image at distances 0, d1, and d2 are shown in Fig. 3(b). Since the Fourier spectrum represents the spatial frequency distribution of various harmonic waves for the corresponding image, the Fourier spectra of the holographic fringe pattern and the reconstructed images have different distributions depending on the distance.

[0084] Finally, the angular spectrum shown in (c) of Fig. 3 represents the distribution of incident angles of various plane waves for the corresponding image. Since the angular spectrum is a linear and distance-invariant system, the angular spectra of the holographic fringe pattern and the restored images at each distance have the same distribution. This is because the absolute value of the angular spectrum at distance 0 is the same as the absolute value of the angular spectrum at distance d, as shown in Equation 9 below.

[0085] [Formula 9]

[0086]

[0087] Equation 9 can imply the following meaning. A reference wave incident on a holographic fringe pattern is diffracted and propagated, and the propagation direction information of the diffracted wavefront can be expressed as an angular spectrum. In addition, since the propagation direction information does not change while propagating in the z-axis direction, it has the same angular spectrum regardless of the distance.

[0088] Figure 4 is a flowchart of a conventional objective quality assessment method using a holographic fringe pattern or a numerically restored image thereof. To evaluate the degree of quality degradation after compressing and restoring a holographic fringe pattern, PSNR has been used conventionally, and the holographic fringe pattern or the numerically restored image has been independently separated and used as a target for calculating PSNR. However, although these two images contain the same information, they produce different PSNR results because their focal points differ depending on the restoration distance. Using the Fourier spectrum of the holographic fringe pattern or the numerically restored image as an evaluation target may also not be suitable as a target for objective quality assessment for the same reason.

[0089] However, since the angular spectrum has distance invariant characteristics, it can be considered suitable for objective quality evaluation of holographic fringe patterns and numerically restored images.

[0090] FIG. 5 is a flowchart provided to explain an objective quality evaluation method for a holographic fringe pattern using an angular spectrum according to one embodiment of the present invention.

[0091] As shown, first, the original holographic fringe pattern H is used as a reference. ref(x,y) and the Target holographic fringe pattern H with information loss or pattern damage to be compared tar (x,y) is input (S110, S115).

[0092] The fringe pattern can be composed of amplitude-only, phase-only or complex amplitude, and in the case of amplitude-only or phase-only, it is converted to complex amplitude with amplitude and phase (S120, S125).

[0093] Angular spectrum A according to Equation 9 below for the transformed complex amplitude ref (f X ,f Y ) and A tar (f X ,f Y ) is calculated (S130, S135).

[0094] [Formula 10]

[0095]

[0096] The absolute value of the next generated Angular spectrum is taken (S140, S145), and as the final step, the PSNR value is calculated according to the following equation 10 (S150).

[0097] [Formula 11]

[0098]

[0099] Here, MAX is the maximum value of the holographic fringe pattern, and MSE is the Mean Squared Error. The absolute value |A| for the complex amplitude A = α+jβ is is produced by. Through this process, an objective quality evaluation is performed between the original holographic fringe pattern and the target holographic fringe pattern.

[0100] FIG. 6 is a flowchart provided to explain an objective quality evaluation method for a holographic fringe pattern using an angular spectrum according to another embodiment of the present invention.

[0101] The proposed objective quality assessment method is based on the original holographic fringe pattern H ref The holographic fringe pattern H is the target holographic fringe pattern that is restored (S213) after compression of (x,y). tar This is when input is (x,y).

[0102] Since steps S210 to S250 are substantially the same as steps S110 to S150 illustrated in FIG. 5, detailed descriptions of these steps are omitted.

[0103]

[0104] 4. Experimental Results

[0105] The results of an experiment conducted according to an objective quality assessment method according to embodiments of the present invention are shown in Fig. 7. First, three types of 3D objects were used: a single point, five points, and the 1,453 points that constitute the airplane shown in Fig. 2. The reference holographic fringe pattern was generated using the Rayleigh-Sommerfeld integral shown in Equation 1 and converted to an 8-bit gray-scale image. The target holographic fringe pattern was artificially degraded by adjusting the bit count to 4, 3, 2, and 1 bit. For example, a 1-bit holographic fringe pattern becomes a binary pattern. Through this process, five holographic fringe patterns, including the reference, were prepared for each object. The generated holographic fringe patterns were numerically restored using Equation 8. In addition, the absolute value of the angular spectrum for each generated holographic fringe pattern was obtained using Equations 10 and 11.

[0106] PSNR was calculated using the target images and reference images prepared through this process.

[0107] As shown in Fig. 7, although the holographic fringe pattern and the numerically reconstructed image contain the same information, the distributions of the calculated PSNR values ​​are different. The PSNR of the holographic fringe pattern shows a relatively lower value than that of the numerically reconstructed image. The numerically reconstructed image shows a relatively high value, and it can be seen that the value decreases as the number of points increases. However, the PSNR for the absolute value of the angular spectrum shows a relatively suitable PSNR distribution. The PSNR value decreases as the number of bits decreases, and a similar distribution is shown even when the number of points increases. Furthermore, since the absolute values ​​of the angular spectrum for the holographic fringe pattern and the numerically reconstructed image are the same, there is no need to calculate the PSNR independently. This experiment demonstrates that methods for calculating PSNR for the holographic fringe pattern and the numerically reconstructed image show different distributions depending on various factors, such as the number of points, making stable quality assessment difficult. The method according to the embodiment of the present invention shows that it can produce stable quality assessment results without being affected by changes in various factors, such as changes in the number of points.

[0108]

[0109] 5. Objective Hologram Quality Evaluation System

[0110] FIG. 8 is a diagram illustrating the configuration of an objective quality assessment system for a holographic fringe pattern using an angular spectrum according to another embodiment of the present invention. As illustrated, the quality assessment system according to an embodiment of the present invention can be implemented as a computing system comprising a communication unit (310), an output unit (320), a processor (330), an input unit (340), and a storage unit (350).

[0111] The communication unit (310) is a communication means for communicating with external devices and accessing external networks. The output unit (320) outputs the computational results of the processor (330), and the input unit (340) transmits user commands to the processor (330). The storage unit (350) provides the storage space necessary for the computation of the processor (330).

[0112] The processor (330) performs an objective quality evaluation of a holographic fringe pattern using an angular spectrum as presented in the aforementioned FIGS. 5 and 6, and outputs the evaluation result through the output unit (320) or transmits it through the communication unit (310).

[0113]

[0114] 6. Variations

[0115] So far, we have described in detail, using preferred embodiments, a method for objectively evaluating the quality of holographic fringe patterns and restored images using angular spectrum and PSNR.

[0116] Conventional hologram quality assessment methods have used PSNR to numerically assess the quality of holographic fringe patterns or numerically reconstructed images. However, the PSNR values ​​of holographic fringe patterns and their numerically reconstructed images differ, and the focus-defocus ranges vary depending on the restoration location, resulting in different PSNR values. These characteristics mean that PSNR, which has been used as an objective quality assessment of images, is unsuitable for hologram quality assessment.

[0117] In embodiments of the present invention, an angular spectrum for a holographic fringe pattern is calculated, and PSNR is calculated based on this. Since the angular spectrum takes a complex amplitude as input, it can be applied to amplitude-only or phase-only holographic fringe patterns. Furthermore, since it is a distance-invariant system, it has the same characteristics regardless of distance. Therefore, the PSNR value is the same not only at the holographic fringe pattern location but also at any arbitrary distance, even for a diffraction wavefront.

[0118] Although there has been no suitable method for objective quality evaluation of existing holographic fringe patterns, the present invention can provide a method for conducting objective quality evaluation, and it is expected that it can be utilized in various holographic content application fields in the future.

[0119] Meanwhile, in the above embodiment, the PSNR value was calculated based on the absolute value of the angular spectrum of the original holographic fringe pattern and the target holographic fringe pattern, i.e., the amplitude of the angular spectrum. Here, the amplitude of the angular spectrum can be replaced with the phase of the angular spectrum, and the technical idea of ​​the present invention can be applied to this case as well.

[0120] It goes without saying that the technical idea of ​​the present invention can also be applied to a computer-readable recording medium containing a computer program that performs the functions of the device and method according to the present embodiment. In addition, the technical idea of ​​various embodiments of the present invention can be implemented in the form of computer-readable code recorded on a computer-readable recording medium. The computer-readable recording medium can be any data storage device that can be read by a computer and store data. For example, the computer-readable recording medium can be a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, an optical disk, a hard disk drive, etc. In addition, the computer-readable code or program stored on the computer-readable recording medium can be transmitted through a network connected between computers.

[0121] Although the preferred embodiments of the present invention have been illustrated and described above, the present invention is not limited to the specific embodiments described above, and various modifications may be made by a person skilled in the art to which the invention pertains without departing from the gist of the present invention as claimed in the claims. Furthermore, such modifications should not be understood individually from the technical idea or prospect of the present invention.

Claims

1. Step of receiving the original holographic fringe pattern; A step of receiving a target holographic fringe pattern to be compared; A step of calculating the angular spectrum of the input original holographic fringe pattern and the target holographic fringe pattern, respectively; An objective quality assessment method, characterized by including a step of calculating a quality value of a target holographic fringe pattern from the produced angular spectra.

2. In claim 1, The target holographic fringe pattern is, An objective quality assessment method characterized by a holographic fringe pattern in which loss occurs due to bit number adjustment from an original holographic fringe pattern.

3. In claim 2, The target holographic fringe pattern is, An objective quality assessment method characterized by a holographic fringe pattern that has suffered loss by restoring an original holographic fringe pattern after compression.

4. In claim 2, The quality values ​​of the target holographic fringe pattern are: An objective quality assessment method characterized in that the same value appears regardless of the location calculated from the holographic fringe pattern in the direction of the numerical restoration image.

5. In claim 1, An objective quality assessment method, characterized in that it further includes a step of converting an input holographic fringe pattern into a holographic fringe pattern composed of complex amplitudes if the input holographic fringe pattern is not a holographic fringe pattern composed of complex amplitudes having amplitude and phase.

6. In claim 5, If the holographic fringe pattern is not a holographic fringe pattern composed of complex amplitudes, An objective quality assessment method characterized in that the holographic fringe pattern is composed of amplitude only or a holographic fringe pattern composed of phase only.

7. In claim 1, The calculation steps are: An objective quality assessment method characterized by calculating the quality value of a target holographic fringe pattern by taking the absolute value of each of the produced angular spectra and calculating the PSNR value.

8. In claim 8 The output stage is, Using the formula below, each Angular spectrum is calculated, A ref (f X ,f Y ) is the Angular spectrum of the original holographic fringe pattern. A tar (f X ,f Y ) is the Angular spectrum of the target holographic fringe pattern. H ref (x,y) is the original holographic fringe pattern, H tar (x,y) is the target holographic fringe pattern, f X Wow f Y An objective quality assessment method characterized by spatial frequency.

9. In claim 8, The calculation steps are: The PSNR value is calculated using the following formula: MAX is the maximum value of the holographic fringe pattern, The absolute value |A| for the complex amplitude A = α+jβ is is produced by, NM is an objective quality assessment method characterized by the number of vertical × horizontal pixels.

10. A processor that receives an original holographic fringe pattern and a target holographic fringe pattern to be compared, calculates angular spectra of the input original holographic fringe pattern and the target holographic fringe pattern, and calculates a quality value of the target holographic fringe pattern from the calculated angular spectra; and An objective quality assessment system characterized by including a storage unit providing storage space required by a processor.

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