Non-iterative optimization off-axis amplitude hologram generation method

Abstract

The invention provides a non-iterative optimization off-axis amplitude hologram generation method. Performing off-line optimization and storing the initial phase; reading the stored optimized initial phase, the specific target intensity distribution of the combined object plane and the complex amplitude distribution of the resultant plane; the object plane complex amplitude is propagated to a holographic surface through a band-limited angular spectrum method; and encoding the complex amplitude of the holographic surface into an off-axis amplitude hologram by using off-axis reference light. According to the method, an initial phase is generated and stored in an off-line optimization mode, the initial phase can be directly read and utilized when the hologram is coded, the calculation time of the hologram is not increased, non-iterative optimization of the off-axis amplitude hologram is achieved, conjugate image noise and speckle noise can be eliminated through frequency domain filtering during reconstruction, and the reconstruction efficiency is improved. And the quality of the reconstructed image can be further improved through time multiplexing.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of non-iterative optimization off-axis amplitude hologram generation method, belong to display technical field. BACKGROUND

[0002] Holographic three-dimensional display can record and reproduce the amplitude and phase information of object, provide the complete depth cues necessary for human eye three-dimensional visual perception, show outstanding potential in military sand table, education medical treatment, manufacturing design, intelligent navigation etc., be regarded as ultimate three-dimensional display technology.In recent years, with the development of computer holography, can be simulated hologram recording process by computer, and load the computed hologram by the help of refreshable spatial light modulator, realize the dynamic reconstruction of real or virtual three-dimensional scene.However, current commercial spatial light modulator usually only supports pure amplitude or pure phase modulation, so the computed hologram needs to be encoded as amplitude type or phase type accordingly.

[0003] Amplitude type computed hologram is often disturbed by multiple speckle noise in reconstruction process, seriously affect reconstruction quality.This problem mainly comes from the following three aspects: first, amplitude encoding process inevitably causes partial phase information loss, leading to incomplete wavefront reconstruction;Second, amplitude type computed hologram is mathematically represented as non-negative real number matrix, its frequency spectrum has Hermite symmetry, thereby introducing zero-order diffraction term and conjugate image noise in reconstruction;In addition, to achieve depth focusing effect, random phase is usually introduced in the computed hologram wavefront distribution, which leads to a large number of random noise in holographic reconstruction image.

[0004] In order to effectively suppress speckle noise in amplitude hologram, iterative algorithm is widely used to optimize hologram.For example, Gerchberg-Saxton (GS) algorithm solves the optimal hologram by iteratively applying amplitude constraints between hologram plane and imaging plane;And stochastic gradient descent (SGD) method models the hologram as a differentiable optimization variable, searches for the optimal solution along the gradient direction by minimizing the difference between the reconstructed image and the target image.Although this kind of iterative algorithm performs significantly in speckle suppression, its calculation efficiency is low, and it is difficult to meet the demand of real-time processing.

[0005] In view of the above, the present application aims to provide a kind of non-iterative optimization off-axis amplitude hologram generation method to solve one or more technical problems described above. SUMMARY

[0006] In order to solve one or more technical problems in the prior art, according to one aspect of the present application, a non-iterative optimization off-axis amplitude hologram generation method is provided, characterized in that it comprises the following steps:

[0007] Offline optimization and storage of initial phase;

[0008] reading the stored optimized initial phase, combining the specific target intensity distribution of the object plane, generating the complex amplitude distribution of the object plane;

[0009] propagating the complex amplitude of the object plane to the holographic plane by band-limited angular spectrum method;

[0010] encoding the complex amplitude of the holographic plane into off-axis amplitude hologram by off-axis reference light.

[0011] According to another aspect of the present application, the specific steps of the off-line optimization and storage of the initial phase are: (1) using a window target as the amplitude distribution, combining the initial random phase, generating the complex amplitude distribution of the object plane; (2) propagating the complex amplitude of the object plane to the holographic plane by angular spectrum; (3) performing frequency domain bandwidth limitation on the complex amplitude of the holographic plane; (4) encoding the bandwidth complex amplitude of the holographic plane into amplitude hologram, obtaining the reconstructed amplitude distribution of the amplitude hologram; (5) taking the difference between the reconstructed amplitude distribution and the initial window target as the loss function, using the gradient descent method to iteratively update the initial phase, and storing the optimized initial phase.

[0012] According to another aspect of the present application, the specific process of performing frequency domain bandwidth limitation on the complex amplitude of the holographic plane in the specific steps of the off-line optimization and storage of the initial phase is: transforming the complex amplitude of the holographic plane into frequency domain by Fourier transform, multiplying it by a spectrum limitation function, and then inversely Fourier transforming it into spatial domain. Preferably, the aperture of the spectrum limitation function is less than or equal to half of the spectral bandwidth of the complex amplitude of the holographic plane.

[0013] According to another aspect of the present application, the complex amplitude of the holographic plane can be encoded into on-axis amplitude hologram; alternatively, the complex amplitude of the holographic plane can also be encoded into off-axis amplitude hologram.

[0014] According to another aspect of the present application, the process of storing the optimized initial phase needs to record the optimization parameters, which include but are not limited to the propagation distance, the wavelength of light, the size of the object plane, the size of the holographic plane, the size of the window target, the aperture size of the spectrum limitation function, and the reference angle of the off-axis reference light; when the optimization parameters are the same, the optimization batch needs to be recorded.

[0015] According to another aspect of the present application, the process of off-line optimization and storage of the initial phase can be performed multiple times off-line, and multiple optimized initial phases can be batch-generated and stored for different optimization parameters.

[0016] According to another aspect of the present application, the specific target intensity distribution of the object plane can be a two-dimensional target or a three-dimensional target, including monochromatic and color targets, and the optimization parameters corresponding to the read optimized initial phase need to match the optimization parameters of the final off-axis amplitude hologram.

[0017] According to another aspect of the present invention, the specific target intensity distribution on the object plane is a three-dimensional target, and the three-dimensional target can be layered according to depth, and the intensity distribution of each depth layer is combined with the optimized initial phase of the corresponding depth; for a color target, the wavelength parameter of each color component must match the wavelength parameter of the optimized initial phase.

[0018] According to another aspect of the present invention, the spectra of the reconstructed image and the conjugate image in the off-axis amplitude hologram are separated according to the angle of the off-axis reference light. The reconstruction process requires off-axis reference light and is filtered in the frequency domain.

[0019] According to another aspect of the present invention, in the encoding of the off-axis amplitude hologram, optimized initial phases with the same parameters from multiple batches can be read simultaneously in batches, and after encoding the off-axis amplitude holograms respectively, time multiplexing is used to further reduce the speckle noise of the reconstruction.

[0020] Compared with the prior art, the present invention has one or more of the following technical effects:

[0021] First, the method uses an offline optimization approach to generate and store the initial phase, which can be directly read and used when encoding the hologram without increasing the computation time of the hologram, thus achieving non-iterative optimization of the off-axis amplitude hologram.

[0022] Secondly, this method can generate high-quality off-axis amplitude holograms. During reconstruction, frequency domain filtering can eliminate conjugate image noise and suppress speckle noise, resulting in a reconstructed image with a depth focusing effect.

[0023] Third, this method can generate multiple optimized initial phases for off-axis amplitude hologram encoding, and further improve the quality of the reconstructed image by reusing the hologram. Attached Figure Description

[0024] To understand the details of the above-described features of the present invention, a more detailed description of the invention, briefly summarized above, can be obtained by referring to the embodiments. The accompanying drawings relate to preferred embodiments of the invention and are described below:

[0025] Figure 1 This is a flowchart of a non-iterative optimization method for generating off-axis amplitude holograms according to a first preferred embodiment of the present invention;

[0026] Figure 2 This is a schematic diagram of a non-iterative optimization method for generating off-axis amplitude holograms according to a first preferred embodiment of the present invention;

[0027] Figure 3 (a) is a schematic diagram of the spectrum limiting function used for offline optimization according to the first preferred embodiment of the present invention;

[0028] Figure 3(b) is a schematic diagram of the spectrum of the complex amplitude of the holographic surface during offline optimization according to the first preferred embodiment of the present invention;

[0029] Figure 4 (a) is a schematic diagram of the spectrum of an off-axis amplitude hologram according to a first preferred embodiment of the present invention;

[0030] Figure 5 This is a schematic diagram of a non-iterative optimization method for generating off-axis amplitude holograms according to a second preferred embodiment of the present invention;

[0031] Figure 6 This is a schematic diagram of a non-iterative optimization method for generating three-dimensional off-axis amplitude holograms according to a third preferred embodiment of the present invention. Specific Implementation

[0032] Various embodiments will now be described in detail, one or more examples of which are illustrated in the figures. The examples are provided for illustrative purposes and are not intended to be limiting. For example, features illustrated or described as part of one embodiment can be used in or combined with any other embodiment to produce yet another embodiment. The invention is intended to include such modifications and variations.

[0033] In the following description of the accompanying drawings, the same reference numerals indicate the same or similar structures. Generally, only the differences between individual embodiments will be described. Unless otherwise expressly indicated, the description of parts or aspects of one embodiment can also be applied to corresponding parts or aspects of another embodiment.

[0034] Example 1

[0035] See Figure 1 It illustrates a non-iterative optimization method for generating off-axis amplitude holograms, characterized by the following steps:

[0036] 101. Optimize offline and store the initial phase;

[0037] 11. Read the optimized initial phase from the storage, 12. Combine the specific target intensity distribution on the object plane to generate the complex amplitude distribution on the object plane;

[0038] 13. The complex amplitude of the object plane is propagated to the holographic surface using the band-limited angle spectrum method;

[0039] 14. Using an off-axis reference beam, the complex amplitude of the holographic surface is encoded into an off-axis amplitude hologram.

[0040] According to a preferred embodiment of the present invention, steps 11, 12, 13, and 14 belong to the encoding process of the 102 off-axis amplitude hologram.

[0041] According to a preferred embodiment of the present invention, the specific steps of step 101, which involves offline optimization and storage of the initial phase, are as follows: (1) 01 Using a window target as the amplitude distribution, and combining it with the initial random phase, a complex amplitude distribution of the object plane is generated; (2) 02 The complex amplitude of the object plane is propagated to the holographic surface through the angular spectrum; (3) 03 The complex amplitude of the holographic surface is subjected to frequency domain bandwidth limitation; (4) 04 The bandwidth complex amplitude of the holographic surface is encoded into an amplitude hologram, and the reconstructed amplitude distribution of the amplitude hologram is obtained; (5) 05 The difference between the reconstructed amplitude distribution and the initial window target is used as the loss function, and the initial phase is iteratively updated using the gradient descent method, and the optimized initial phase is stored.

[0042] According to a preferred embodiment of the present invention, in the specific steps of offline optimization and storage of the initial phase in step 101, the specific process of frequency domain bandwidth limiting of the complex amplitude of the holographic surface 03 is as follows: the complex amplitude of the holographic surface is Fourier transformed to the frequency domain, multiplied by the spectral limiting function, and then inversely Fourier transformed to the spatial domain. The aperture of the spectral limiting function must be less than or equal to half of the spectral bandwidth of the complex amplitude of the holographic surface. The spectral limiting function is as follows: Figure 3 As shown in (a), the complex amplitude spectrum of the holographic surface is as follows: Figure 4 As shown in (a).

[0043] According to a preferred embodiment of the present invention, in the specific steps of offline optimization and storage of the initial phase in step 101, the complex amplitude of the holographic surface can be encoded as a coaxial amplitude hologram; optionally, the complex amplitude of the holographic surface can also be encoded as an off-axis amplitude hologram.

[0044] According to a preferred embodiment of the present invention, the process of storing the optimized initial phase in step 101 requires recording optimization parameters, including but not limited to propagation distance, light wavelength, object plane size, holographic surface size, window target size, aperture size of the spectral limiting function, and reference angle of the off-axis reference light; when the optimization parameters are the same, the optimization batch needs to be recorded.

[0045] According to a preferred embodiment of the present invention, the process of offline optimization and storage of the initial phase in step 101 can be performed offline multiple times, and multiple optimized initial phases can be generated and stored in batches for different optimization parameters.

[0046] According to a preferred embodiment of the present invention, the target intensity distribution on the object plane in step 12 can be a two-dimensional target or a three-dimensional target, including monochrome and color targets, and the optimization parameters corresponding to the initial phase should match the optimization parameters of the final off-axis amplitude hologram.

[0047] According to a preferred embodiment of the present invention, the specific target intensity distribution on the object plane in step 12 is a three-dimensional target. The three-dimensional target can be layered according to depth, and the intensity distribution of each depth layer is combined with the optimized initial phase of the corresponding depth. For a colored target, the wavelength parameter of each color component must match the wavelength parameter of the optimized initial phase.

[0048] According to a preferred embodiment of the present invention, the spectra of the reconstructed image and the conjugate image in the off-axis amplitude hologram encoded in step 14 are separated according to the off-axis reference light angle. The reconstruction process requires off-axis reference light and is simultaneously filtered in the frequency domain. The spectrum of the off-axis amplitude hologram is as follows: Figure 4 As shown in (b), the filtering function used in the frequency domain for off-axis amplitude hologram reconstruction is as follows: Figure 3 As shown in (b).

[0049] According to a preferred embodiment of the present invention, in the encoding of the off-axis amplitude hologram in step 14, optimized initial phases with the same parameters from multiple batches can be read simultaneously. After encoding the off-axis amplitude holograms respectively, time multiplexing is used to further reduce the speckle noise of the reconstruction.

[0050] According to another preferred embodiment of the present invention, the working principle of the present invention will be further described in detail below.

[0051] Figure 2 This is a schematic diagram of a non-iterative optimization off-axis amplitude hologram generation method according to a first preferred embodiment of the present invention. The process of generating a non-iterative optimization off-axis amplitude hologram consists of two parts: (1) offline optimization and storage of the initial phase; (2) non-iterative optimization encoding of the off-axis amplitude hologram.

[0052] In offline optimization and storage of the initial phase, a window target is used as the initial amplitude distribution. Combined with the initial random phase to generate a complex amplitude distribution, it can be expressed as:

[0053]

[0054] Where A0 is the target amplitude of the window. The initial random phase is used. The initial complex amplitude propagates to the holographic surface through the angular spectrum.

[0055] A H =FFT -1 [FFT(A)·H AS ]

[0056] Where A H For the complex amplitude distribution of the holographic surface, FFT and FFT -1 Representing the Fast Fourier Transform and Inverse Fourier Transform, the angular spectral transfer function can be expressed as:

[0057]

[0058] By applying frequency domain bandwidth limitation to the complex amplitude of the holographic surface, the spectrum of the complex amplitude can be concentrated within a central range, such as... Figure 4 As shown in (a). The spectrum limiting function is as follows. Figure 3 As shown in (a), it can be represented as:

[0059]

[0060] After encoding the complex amplitude of the holographic surface into an amplitude-type hologram, angular spectrum propagation reconstruction is performed. The reconstructed amplitude distribution is compared with the original window target amplitude. The mean squared error (MSE) is used as the loss function, and the gradient is backpropagated to the initial random phase. The initial random phase is then updated using the gradient descent (SGD) method.

[0061]

[0062] After multiple rounds of optimization, the iteration ends when the loss function reaches the predetermined target, and the optimized initial phase is stored locally.

[0063] In non-iterative optimization of off-axis amplitude hologram encoding, the stored optimized initial phase is read and combined with the specific target intensity distribution on the object plane to generate the complex amplitude distribution on the object plane. This complex distribution is then propagated to the holographic surface. The off-axis amplitude hologram is encoded using an off-axis reference light, and the carrier frequency of the off-axis reference light is:

[0064]

[0065] The reconstructed image and conjugate image of the off-axis amplitude hologram will be separated in the frequency domain, and their spectrum is as follows: Figure 4 As shown in (b). To avoid frequency aliasing between the conjugate and reconstructed images, the off-axis reference optical carrier frequency should satisfy the following relationship:

[0066]

[0067] An off-axis reference light is required during reconstruction, and filtering is performed in the frequency domain. The filtering function is as follows: Figure 3 As shown in (b).

[0068] Figure 5 This is a schematic diagram of a non-iterative optimization off-axis amplitude hologram generation method according to a second preferred embodiment of the present invention. Using the same offline optimization method, multiple band-limited optimized initial phases are generated and stored in batches. Combined with the target intensity distribution on the object plane, multiple off-axis holograms can be encoded for time-multiplexed reconstruction, thereby further suppressing speckle noise in the reconstructed image.

[0069] Figure 6This is a schematic diagram of a non-iterative optimization method for generating three-dimensional off-axis amplitude holograms according to a third preferred embodiment of the present invention. For a three-dimensional scene, the scene is layered according to depth information to obtain intensity distributions 201 for different depth layers. For the depth value of each depth layer, the initial phase 202 of the corresponding depth parameters is optimized offline and stored, and then combined with the intensity distribution 201 of each layer. The complex amplitude distributions of all depth layers on the holographic plane are calculated, superimposed, and the complex amplitude distribution of the holographic plane of the three-dimensional scene is generated. Finally, it is encoded into an off-axis amplitude hologram using an off-axis reference light. Similarly, multiple off-axis amplitude holograms can be batch-encoded and then time-multiplexed for reconstruction.

[0070] Compared with the prior art, the present invention has one or more of the following technical effects:

[0071] First, the method uses an offline optimization approach to generate and store the initial phase, which can be directly read and used when encoding the hologram without increasing the computation time of the hologram, thus achieving non-iterative optimization of the off-axis amplitude hologram.

[0072] Secondly, this method can generate high-quality off-axis amplitude holograms. During reconstruction, frequency domain filtering can eliminate conjugate image noise and suppress speckle noise, resulting in a reconstructed image with a depth focusing effect.

[0073] Third, this method can generate multiple optimized initial phases for off-axis amplitude hologram encoding, and further improve the quality of the reconstructed image by reusing the hologram.

[0074] While the foregoing describes embodiments of the present invention, other further embodiments may be devised without departing from the basic scope of the present invention, the scope of which is defined by the claims.

[0075] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Technical features in these embodiments that do not contradict each other can be combined with each other. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A non-iterative optimization method for generating off-axis amplitude holograms, characterized in that... Includes the following steps: Optimize and store the initial phase offline; Read the optimized initial phase from the storage, combine it with the specific target intensity distribution on the object plane, and generate the complex amplitude distribution on the object plane; The complex amplitude of the object plane is propagated to the holographic surface using the band-limited angle spectrum method; Using an off-axis reference beam, the complex amplitude of the holographic surface is encoded into an off-axis amplitude hologram.

2. The non-iterative optimization method for generating off-axis amplitude holograms according to claim 1, characterized in that... The specific steps for offline optimization and storage of the initial phase are as follows: (1) Using the window target as the amplitude distribution, combined with the initial random phase, the complex amplitude distribution of the object plane is generated; (2) The complex amplitude of the object plane is propagated to the holographic surface through the angular spectrum; (3) The complex amplitude of the holographic surface is subject to frequency domain bandwidth limitation; (4) The bandwidth complex amplitude of the holographic surface is encoded into an amplitude hologram, and the reconstructed amplitude distribution of the amplitude hologram is obtained; (5) The difference between the reconstructed amplitude distribution and the initial window target is used as the loss function, the initial phase is iteratively updated using the gradient descent method, and the optimized initial phase is stored.

3. The non-iterative optimization method for generating off-axis amplitude holograms according to claim 1, characterized in that... In the specific steps of offline optimization and initial phase storage, the process of frequency domain bandwidth limiting of the complex amplitude of the holographic surface is as follows: the complex amplitude of the holographic surface is Fourier transformed to the frequency domain, multiplied by the spectral limiting function, and then inversely Fourier transformed to the spatial domain. Preferably, the aperture of the spectral limiting function should be less than or equal to half of the spectral bandwidth of the complex amplitude of the holographic surface.

4. The non-iterative optimization method for generating off-axis amplitude holograms according to any one of claims 1-3, characterized in that... In the specific steps of offline optimization and storage of the initial phase, the complex amplitude of the holographic surface can be encoded as a coaxial amplitude hologram; optionally, the complex amplitude of the holographic surface can also be encoded as an off-axis amplitude hologram.

5. The non-iterative optimization method for generating off-axis amplitude holograms according to any one of claims 1-3, characterized in that... The process of storing and optimizing the initial phase requires recording optimization parameters, including but not limited to propagation distance, light wavelength, object plane size, holographic surface size, window target size, aperture size of the spectral constraint function, and reference angle of the off-axis reference light; when the optimization parameters are the same, the optimization batch needs to be recorded.

6. The non-iterative optimization method for generating off-axis amplitude holograms according to any one of claims 1-3, characterized in that... The offline optimization and initial phase storage process can be executed offline multiple times, generating and storing multiple optimized initial phases in batches for different optimization parameters.

7. The non-iterative optimization method for generating off-axis amplitude holograms according to any one of claims 1-3, characterized in that... The specific target intensity distribution on the object plane can be a two-dimensional or three-dimensional target, including monochrome and color targets. The optimization parameters corresponding to the initial phase should match the optimization parameters of the final off-axis amplitude hologram.

8. The non-iterative optimization method for generating off-axis amplitude holograms according to any one of claims 1-7, characterized in that... The specific target intensity distribution on the object plane is a three-dimensional target. The three-dimensional target can be layered according to depth, and the intensity distribution of each depth layer is combined with the optimized initial phase of the corresponding depth. For color targets, the wavelength parameters of each color component must match the wavelength parameters of the optimized initial phase.

9. The non-iterative optimization method for generating off-axis amplitude holograms according to any one of claims 1-7, characterized in that... The spectra of the reconstructed image and the conjugate image in the off-axis amplitude hologram are separated according to the angle of the off-axis reference light. The reconstruction process requires off-axis reference light and is also filtered in the frequency domain.

10. The non-iterative optimization method for generating off-axis amplitude holograms according to any one of claims 1-7, characterized in that... In the encoding of the off-axis amplitude hologram, optimized initial phases with the same parameters from multiple batches can be read simultaneously. After encoding the off-axis amplitude holograms separately, time multiplexing is used to further reduce speckle noise in the reconstruction.

Images