CN109060122B - Two-step phase recovery method, equipment and system based on single intensity measurement - Google Patents
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Abstract
The invention discloses a two-step phase recovery method based on single intensity measurement,An apparatus and system for initializing the amplitude and phase of a 2D complex light field to obtain an initialized spatial amplitude A1And an initialization phase
According to the initialized spatial amplitude A1And an initialization phase
Synthesizing complex amplitudes g (x, y); performing cyclic iteration of Fourier transformation and inverse Fourier transformation on the complex amplitude g (x, y) to obtain an amplitude estimation value of a complex optical field in a spatial domain on a 2D coded aperture plane; and processing the amplitude information of the spatial domain and the frequency domain amplitude information obtained by measurement based on a dual-intensity phase recovery algorithm, and recovering the phase of the complex optical field in the spatial domain on the 2D coded aperture plane. The invention obviously improves the quality of the reconstruction phase and the reconstruction power.
Description
Technical Field
The invention relates to the technical field of optical imaging, in particular to a two-step phase recovery method, equipment and a system based on single intensity measurement.
Background
Phase recovery, which is the recovery of lost phase information from recorded intensity measurements combined with known a priori knowledge, has played a very important role in the imaging field, such as: x-ray crystallography, optics, astronomical imaging, microscopy, and biomedicine, among others.
Gerchberg and Saxton originally proposed the phase recovery algorithm for alternate projections-the GS algorithm (Gerchberg-Saxton algorithm). The algorithm is primarily to use the intensity data in the spatial and fourier domains to recover the phase of the light field. Subsequently, Fienup demonstrated that the GS algorithm had significant Error-reducing properties, and proposed an Error Reduction (ER) algorithm and a Hybrid Input-Output (HIO) algorithm. Currently, the ER algorithm and the HIO algorithm are considered to be the most effective methods in the field of phase recovery. Since the above algorithm only aims at the forward transformation system, no one is concerned about any linear transformation system. Therefore, Yang Guzhen and the origin of consideration put forward the amplitude phase detection theory in any linear transformation system, i.e. Yang-Gu algorithm (Y-G algorithm for short). In 2015, guo et al optimized the iterative algorithm and proposed two improved GS iterative phase recovery algorithms-the spatial phase perturbation Gerchberg-Saxton algorithm and the combined GS hybrid input output algorithm. For both improved algorithms, the squared value of the squared error value drops rapidly to an acceptable value, and the lost phase can be successfully recovered in the spatial and fourier domains, meaning that both algorithms can jump out of local minima and converge to a global minimum.
The earliest proposed GS algorithm was an intensity measurement for two planes, but in some cases the intensity of two planes could not be measured. Therefore, the relevant scholars propose a GS algorithm based on single intensity measurement, and incorporate some a priori knowledge to recover the phase. The phase recovery method of single intensity measurement has the problems of poor reconstruction quality and low success rate.
Disclosure of Invention
The invention aims to provide a two-step phase recovery method based on single intensity measurement so as to improve the phase reconstruction quality.
To achieve the above object, the present invention employs a two-step phase recovery method based on single intensity measurement for processing intensity information of a 2D complex light field captured by an image sensor disposed at a back focal plane of a lens whose front focal plane is disposed with a 2D coded aperture M, the method comprising:
initializing the amplitude and phase of the 2D complex light field to obtain an initialized spatial amplitude A1And an initialization phase
According to the initialized spatial amplitude A1And an initialization phase
Synthesizing complex amplitudes g (x, y);
performing cyclic iteration of Fourier transformation and inverse Fourier transformation on the complex amplitude g (x, y) to obtain an amplitude estimation value of a complex optical field in a spatial domain on a 2D coded aperture plane;
and processing the amplitude information of the spatial domain and the frequency domain amplitude information obtained by measurement based on a dual-intensity phase recovery algorithm, and recovering the phase of the complex optical field in the spatial domain on the 2D coded aperture plane.
Further, the performing a cyclic iteration of fourier transform and inverse fourier transform on the complex amplitude g (x, y) to obtain amplitude information of a spatial domain includes:
s101, carrying out Fourier transform on the complex amplitude G (x, y) to obtain complex amplitude G (xi, eta) of a frequency domain;
s102, recording the frequency domain amplitude A in the frequency domain2Replacing the amplitude of the frequency domain complex amplitude G (xi, eta) to obtain a synthesized frequency domain complex amplitude G' (xi, eta);
s103, performing inverse Fourier transform on the frequency domain complex amplitude G '(xi, eta) to obtain a spatial domain complex amplitude G' (x, y);
s104, in the space domain, performing dot product operation on the complex amplitude g ' (x, y) of the space domain and the coding aperture M, and updating the complex amplitude g ' (x, y) of the space domain to obtain g ' (x, y);
s105, repeatedly executing the steps S101 to S104 on the updated spatial domain complex amplitude g '(x, y) until the updated spatial domain complex amplitude g' (x, y) converges;
and S106, when the updated spatial domain complex amplitude g '(x, y) converges, converging according to the updated spatial domain complex amplitude g' (x, y), and obtaining the amplitude estimation value of the complex optical field on the 2D coding aperture plane in the spatial domain.
Further, the processing the amplitude information of the spatial domain and the measured frequency domain amplitude information based on a dual intensity phase recovery algorithm to recover the phase of the complex optical field in the spatial domain on the 2D coded aperture plane includes:
s201, utilizing the amplitude estimation value of the complex optical field in the space domain on the 2D coding aperture plane and the initialization phase
Composite complex amplitude g1(x,y)；
S202, for complex amplitude g1(x, y) Fourier transform to obtain complex amplitude G in frequency domain1(ξ,η)；
S203, frequency domain amplitude A to be recorded in frequency domain2Instead of the frequency domain complex amplitude G1(xi, eta) to obtain a synthesized frequency domain complex amplitude G1′(ξ,η)；
S204, the complex amplitude G of the frequency domain1' (xi, eta) is subjected to inverse Fourier transform to obtain complex amplitude g of a spatial domain1′(x,y)；
S205, in the space domain, replacing the complex amplitude g of the space domain with the amplitude estimation value of the complex optical field of the 2D coding aperture plane in the space domain1' (x, y) to obtain an iteratively updated spatial domain complex amplitude g1”(x,y)；
S206, the space domain complex amplitude g after the iterative update1"(x, y) repeatedly executing steps S202-S205 until the iteratively updated spatial domain complex amplitude g1The phase of "(x, y) converges to obtain the phase of the complex optical field in the space domain on the 2D coded aperture plane.
Further, the initialized spatial amplitude A1For full 1 amplitude, the initialization phase
For uniformly randomizing the phase and having a phase interval of [0, π/2]。
In another aspect, there is provided a two-step phase recovery apparatus based on single intensity measurement, comprising: the device comprises an acquisition module, an initialization module, a synthesis module, a spatial domain intensity estimation module and a dual-intensity phase recovery module;
the acquisition module is used for capturing the intensity information of the complex light field by the image sensor;
the initialization module is used for initializing the amplitude and the phase of the 2D complex light field to obtain an initialized spatial amplitude A1And an initialization phase
The synthesis module is used for synthesizing the spatial amplitude A according to the initialization1And an initialization phase
Synthesizing complex amplitudes g (x, y);
the spatial domain intensity estimation module is used for performing cyclic iteration of Fourier transform and inverse Fourier transform on the complex amplitude g (x, y) to obtain an amplitude estimation value of a complex optical field in a spatial domain on a 2D coded aperture plane;
and the dual-intensity phase recovery module is used for processing the amplitude information of the spatial domain and the frequency domain amplitude information obtained by measurement based on a dual-intensity phase recovery algorithm and recovering the phase of the complex optical field in the spatial domain on the 2D coded aperture plane.
Further, the spatial domain intensity estimation module is configured to perform the following steps:
s101, carrying out Fourier transform on the complex amplitude G (x, y) to obtain complex amplitude G (xi, eta) of a frequency domain;
s102, recording the frequency domain amplitude A in the frequency domain2Replacing the amplitude of the frequency domain complex amplitude G (xi, eta) to obtain a synthesized frequency domain complex amplitude G' (xi, eta);
s103, performing inverse Fourier transform on the frequency domain complex amplitude G '(xi, eta) to obtain a spatial domain complex amplitude G' (x, y);
s104, in the space domain, performing dot product operation on the complex amplitude g ' (x, y) of the space domain and the coding aperture M, and updating the complex amplitude g ' (x, y) of the space domain to obtain g ' (x, y);
s105, repeatedly executing the steps S101 to S104 on the updated spatial domain complex amplitude g '(x, y) until the updated spatial domain complex amplitude g' (x, y) converges;
and S106, when the updated spatial domain complex amplitude g '(x, y) converges, converging according to the updated spatial domain complex amplitude g' (x, y), and obtaining the amplitude estimation value of the complex optical field on the 2D coding aperture plane in the spatial domain.
Further, the dual intensity phase recovery module is configured to perform the following steps:
s201, utilizing the amplitude estimation value of the complex optical field in the space domain on the 2D coding aperture plane and the initialization phase
Composite complex amplitude g1(x,y)；
S202, for complex amplitude g1(x, y) Fourier transform to obtain complex amplitude G in frequency domain1(ξ,η)；
S203, frequency domain amplitude A to be recorded in frequency domain2Instead of the frequency domain complex amplitude G1(xi, eta) to obtain a synthesized frequency domain complex amplitude G1′(ξ,η)；
S204, the complex amplitude G of the frequency domain1' (xi, eta) is subjected to inverse Fourier transform to obtain complex amplitude g of a spatial domain1′(x,y)；
S205, in the space domain, replacing the complex amplitude g of the space domain with the amplitude estimation value of the complex optical field of the 2D coding aperture plane in the space domain1' (x, y) to obtain an iteratively updated spatial domain complex amplitude g1”(x,y)；
S206, the space domain complex amplitude g after the iterative update1"(x, y) repeatedly executing steps S202-S205 until the iteratively updated spatial domain complex amplitude g1The phase of "(x, y) converges to obtain the phase of the complex optical field in the space domain on the 2D coded aperture plane.
Further, the initialized spatial amplitude A1For full 1 amplitude, the initialization phase
For uniformly randomizing the phase and having a phase interval of [0, π/2]。
On the other hand, a two-step phase recovery system based on single intensity measurement is provided, and comprises a 2D complex optical field, a CCD image sensor, a Fourier lens, a 2D coded aperture M and the two-step phase recovery device;
the 2D coded aperture M and the CCD image sensor are respectively arranged on a front focal plane and a rear focal plane of the Fourier lens, the 2D complex light field is placed in front of the coded aperture M, and the longitudinal section of the 2D complex light field, the section of the 2D coded aperture M, the mirror surface of the Fourier lens and the plane of the CCD image sensor are positioned on the same light path, and the output end of the CCD image sensor is connected with a computer.
Compared with the prior art, the invention has the following technical effects: for single intensity measurement, namely frequency domain intensity, firstly restoring amplitude information of a complex optical field on a 2D coded aperture plane in a spatial domain, and then restoring the phase of the complex optical field on the 2D coded aperture plane in the spatial domain by using the frequency domain intensity obtained through measurement and the spatial domain intensity obtained through restoration. The method can effectively obtain the spatial domain amplitude and the frequency domain amplitude of the complex light field on the 2D coding aperture plane, and overcomes the defect that the dual-intensity measurement of the spatial domain and the frequency domain is difficult to obtain in some application occasions in the traditional method. Meanwhile, the quality and the reconstruction power of the reconstruction phase can be obviously improved.
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The following detailed description of embodiments of the invention refers to the accompanying drawings in which:
FIG. 1 is a schematic flow diagram of a two-step phase recovery method based on single intensity measurements;
FIG. 2 is a schematic flow chart of the TSPR algorithm;
FIG. 3 is a schematic diagram of the optical setup of a 2D complex optical field imaging process;
FIG. 4 is a schematic diagram of a two-step phase recovery device based on a single intensity measurement;
FIG. 5 is a schematic diagram of a two-step phase recovery system based on a single intensity measurement;
FIG. 6 is a graph of the effect of a single phase recovery test;
FIG. 7 is a graph of amplitude and phase as a function of iteration number;
FIG. 8 is a graphical illustration of phase reconstruction success rate as a function of sampling rate;
FIG. 9 is a schematic diagram of 3 coded apertures at a sampling rate of 0.3;
FIG. 10 is a comparison of reconstruction performance for different coded apertures;
fig. 11 is a comparative schematic of phase reconstruction performance under different algorithms.
Detailed Description
To further illustrate the features of the present invention, refer to the following detailed description of the invention and the accompanying drawings. The drawings are for reference and illustration purposes only and are not intended to limit the scope of the present disclosure.
As shown in fig. 1 to 2, the present embodiment discloses a two-step phase recovery method based on single intensity measurement, which is used for processing intensity information of a 2D complex light field captured by an image sensor, the image sensor is arranged at a back focal plane of a lens, and a front focal plane of the lens is provided with a 2D coded aperture M, and the method comprises the following steps:
s1, initializing the amplitude and the phase of the 2D complex light field to obtain an initialized space amplitude A1And an initialization phase
S2, according to the initialized space amplitude A1And an initialization phase
Synthesizing complex amplitudes g (x, y);
s3, carrying out cyclic iteration of Fourier transform and inverse Fourier transform on the complex amplitude g (x, y) to obtain an amplitude estimation value of the complex optical field in the space domain on the 2D coded aperture plane;
and S4, processing the amplitude information of the spatial domain obtained in the previous step and the frequency domain amplitude information obtained by measurement based on a dual-intensity phase recovery algorithm, and recovering the phase of the complex optical field in the spatial domain on the 2D coding aperture plane.
Note that the coded aperture and CCD are placed at the front and back focal planes of the lens, respectively, as shown in fig. 3. Firstly, the complex light field u (x, y) is filtered by the coding aperture M to obtain the complex light field uM(x, y), imaging through a Fourier lens, and finally recording the intensity on a CCD plane. The specific expression is as follows:
the main purpose of the solution of the embodiment is to measure I from the recorded intensityCCDIn which the phase information of the complex light field is recovered.
In this embodiment, a Two-Step Phase recovery (TSPR) algorithm based on Single Intensity measurement is adopted to recover the Phase of the complex optical field in the spatial domain on the 2D coding aperture plane, and first, a Single Intensity Phase Recovery (SIPR) algorithm is used to recover the amplitude information of the spatial domain, and then, according to the measured Intensity of the complex optical field in the frequency domain and the Intensity of the spatial domain, a dual Intensity Phase recovery (TIPR) algorithm is used to recover the Phase of the complex optical field in the spatial domain on the 2D coding aperture plane. In practical applications, measuring intensity information requires sophisticated optical measurement equipment. Sometimes it is desirable to obtain both intensity information simultaneously, but the optical detection device may not be able to meet the conditions. The method well overcomes the defect that dual-intensity measurement of a space domain and a frequency domain is difficult to obtain in some occasions, and effectively improves the quality of the reconstruction phase and the reconstruction power.
Further, the above-mentioned cyclic iteration of fourier transform and inverse fourier transform on the complex amplitude g (x, y) to obtain the amplitude estimation value of the complex optical field in the spatial domain on the 2D coded aperture plane specifically includes the following steps:
s101, Fourier transform is carried out on the complex amplitude G (x, y) to obtain the complex amplitude G (xi, eta) of a frequency domain,
s102, recording the frequency domain amplitude A in the frequency domain2A synthesized frequency-domain complex amplitude G '(xi, eta) is obtained instead of the amplitude of the frequency-domain complex amplitude G (xi, eta), where G' (xi, eta) ═ A2- { j ψ (ξ, η) }, ψ (ξ, η) is the phase of the frequency-domain complex amplitude G' (ξ, η);
s103, performing inverse Fourier transform on the frequency domain complex amplitude G '(xi, eta) to obtain a spatial domain complex amplitude G' (x, y), wherein,
s104, performing a dot product operation on the complex amplitude g ' (x, y) of the spatial domain and the coding aperture M in the spatial domain, and updating the complex amplitude g ' (x, y) of the spatial domain to obtain g "(x, y) ═ g ' (x, y) · M;
s105, repeatedly executing the steps S101 to S104 on the updated spatial domain complex amplitude g '(x, y) until the updated spatial domain complex amplitude g' (x, y) converges;
s106, when the updated space domain complex amplitude g '(x, y) converges, obtaining the amplitude estimation value | g of the complex light field in the space domain on the 2D coding aperture plane according to the updated space domain complex amplitude g' (x, y) convergesest(x,y)|＝|g”(x,y)|。
Further, based on a dual intensity phase recovery algorithm, processing the amplitude information of the spatial domain and the measured frequency domain amplitude information, and recovering the phase of the complex optical field in the spatial domain on the 2D coded aperture plane, including:
s201, utilizing the amplitude estimation value of the complex optical field in the space domain on the 2D coding aperture plane and the initialization phase
Composite complex amplitude g1(x,y)；
S202, for complex amplitude g1(x, y) Fourier transform to obtain complex amplitude G in frequency domain1(xi, η), wherein
S203, recording the frequency domain amplitude A in the frequency domain2Complex amplitude G instead of frequency domain1(xi, eta) to obtain a synthesized frequency domain complex amplitude G1' (xi, eta), wherein G1′(ξ,η)＝A2·{jψ1(ξ,η)}，ψ1(xi, eta) is the frequency domain complex amplitude G1' (xi, η) phase;
s204, the complex amplitude G of the frequency domain1' (xi, eta) is subjected to inverse Fourier transform to obtain complex amplitude g of a spatial domain1' (x, y) wherein
S205, in the space domain, replacing the complex amplitude g of the space domain with the amplitude estimation value of the complex optical field of the 2D coding aperture plane in the space domain1' (x, y) to obtain an iteratively updated spatial domain complex amplitude g1”(x,y)，
Wherein
For the complex amplitude g of the spatial domain1' (x, y) phase;
s206, the space domain complex amplitude g after the iterative update1"(x, y) repeatedly executing steps S202-S205 until the iteratively updated spatial domain complex amplitude g1The phase of "(x, y) converges to obtain the phase of the complex optical field in the space domain on the 2D coded aperture plane.
Further, the spatial amplitude A is initialized1For full 1 amplitude, the initialization phase
For uniformly randomizing the phase and having a phase interval of [0, π/2]。
As shown in fig. 4, the present embodiment discloses a two-step phase recovery apparatus based on single intensity measurement, comprising: the device comprises an acquisition module, an initialization module, a synthesis module, a spatial domain intensity estimation module and a dual-intensity phase recovery module;
the acquisition module is used for capturing the intensity information of the complex light field by the image sensor;
the initialization module is used for initializing the amplitude and the phase of the 2D complex light field to obtain an initialized spatial domain amplitude A1And an initialization phase
The synthesis module is used for synthesizing the spatial amplitude A according to the initialization1And an initialization phase
Synthesizing complex amplitudes g (x, y);
the spatial domain intensity estimation module is used for performing cyclic iteration of Fourier transform and inverse Fourier transform on the complex amplitude g (x, y) to obtain an amplitude estimation value of a complex optical field in a spatial domain on a 2D coded aperture plane;
and the dual-intensity phase recovery module is used for processing the amplitude information of the spatial domain and the frequency domain amplitude information obtained by measurement based on a dual-intensity phase recovery algorithm and recovering the phase of the complex optical field in the spatial domain on the 2D coded aperture plane.
In this embodiment, each module in the two-step phase recovery device based on single intensity measurement is used to implement each step in the two-step phase recovery method based on single intensity measurement, and details are not repeated here. The two-step phase recovery device may be a computer or the like.
As shown in fig. 5, the present embodiment discloses a two-step phase recovery system based on single intensity measurement, comprising a 2D complex light field, a CCD image sensor, a fourier lens, a 2D coded aperture M, and a two-step phase recovery device according to any of claims 5 to 8;
the 2D coded aperture M and the CCD image sensor are respectively arranged on a front focal plane and a rear focal plane of the Fourier lens, the 2D complex light field is placed in front of the 2D coded aperture M, the longitudinal section of the 2D complex light field, the section of the 2D coded aperture M, the mirror surface of the Fourier lens and the plane of the CCD image sensor are located on the same light path, and the output end of the CCD image sensor is connected with the two-step phase recovery device (such as a computer).
It should be noted that the present embodiment performs a single phase recovery experiment, so as to verify the effectiveness of the TSPR method through the single phase recovery experiment. Two gray-scale maps ("Lena" and "Cameraman" are 256 × 256 pixels) were used in the experiment. These two images are dot-multiplied with the code aperture (256 × 256 pixels) to obtain their amplitude and phase, respectively. The complex amplitude (256 × 256 pixels) is then synthesized from the amplitude and phase. The complex amplitude is filtered by the coding aperture to obtain a new complex amplitude. And finally, carrying out a phase recovery experiment. Where the code apertures are mask patterns with 0/1 randomly distributed locations, 0 indicates no light passing, 1 indicates light passing, and the probability of occurrence of the {0,1} values is 1/2. The sampling rate in this section of experiment was 0.4 and the phase recovery results are shown in fig. 6. Fig. 6(a) is 0/1 randomly distributed code apertures and a sampling rate of 0.4. Fig. 6(b) - (c) are the amplitude and phase of the complex light field after the coded aperture. Fig. 6(d) is the amplitude recorded in the frequency domain. Fig. 6(e) - (f) are amplitude and phase recovered using the SIPR algorithm, with SNR of 343.04dB and 19.85dB, respectively, as an objective metric, by Signal-to-Noise Ratio (SNR). Fig. 6(g) - (h) are amplitude and phase recovered using the TSPR algorithm with SNR of 343.04dB and 45.58dB, respectively. Comparing fig. 6(f) - (h), it is easy to find that the SNR of the reconstructed phase by the TSPR algorithm in the present scheme is significantly improved.
Fig. 7 is a graph of amplitude and phase as a function of iteration number for a single phase recovery experiment using the TSPR algorithm. From this figure, it can be seen that in the first step SIPR algorithm, the amplitude of the complex optical field in the spatial domain at the 2D coded aperture plane can be well recovered, but the phase recovery result is poor. As the number of iterations increases, the signal-to-noise ratio (SNR) of the phase can only reach around 19 dB. However, in the second step TIPR algorithm, the SNR of the recovered phase is as high as 45dB, and the phase is recovered with high quality, which is not successfully recovered compared to the SIPR method. The TSPR method provided by the scheme utilizes the amplitude estimated in the SIPR step and combines the known frequency domain amplitude, and then utilizes the TSPR method to successfully recover the lost phase, namely the combination of the SIPR and the TIPR.
Figure 8 is a graph of reconstructed power in amplitude and phase versus sampling rate for a single reconstruction experiment using the SIPR algorithm. The coding aperture adopts a uniform random sampling mode, the sampling rate of the coding aperture is used as a variable parameter in an experiment, and the sampling rate is gradually increased from 0.1 to 0.7, and is increased by 0.05 each time. And when a reconstruction experiment is carried out by adopting the SIPR method, calculating the SNR of the reconstructed amplitude and the original amplitude and the SNR of the reconstructed phase and the original phase. The reconstruction experiment was run independently 500 times, and the SNR for each reconstruction was counted. The SNR threshold is 25dB, i.e. if the SNR for reconstructing amplitude or phase is greater than 25dB, the reconstruction is considered successful. The reconstruction success rate of the reconstruction amplitude and the reconstruction phase are calculated, and the reconstruction effect graph is shown as 8. As can be seen from the experimental results in the figure, the SIPR method has a high success rate of reconstructing the amplitude, but a low success rate of reconstructing the phase, because the SIPR algorithm recovers the phase only from a single intensity measurement recorded in the frequency domain. Therefore, the TSPR method is proposed in this embodiment to solve the problems of poor reconstruction quality and low success rate of the phase recovery method for single intensity measurement.
Fig. 9 shows 3 code apertures at a sampling rate of 0.3, namely Uniform Random (UR) sampling, Radial Line (RL) sampling, and Variable Density (VD) sampling patterns. The different coded apertures in this embodiment mean that the 0/1 locations are randomly distributed, and the distribution of the complex light field in fig. 3 is changed by multiplying the complex light field.
In order to test the influence of different coded apertures on the method and the SIPR algorithm, the present embodiment adopts three coded apertures, and takes the sampling rate of the coded apertures as a variable parameter in an experiment, and the sampling rate is set in the range of 0.01 to 0.7. And respectively reconstructing each coded aperture by adopting a TSPR method, and calculating the SNR of the reconstructed phase and the original phase. Each group of the same parameter reconstruction experiments independently run for 500 times, and the reconstruction SNR of each time is counted. The SNR threshold is 25dB, i.e. if the SNR of the reconstruction phase is greater than 25dB, the reconstruction is considered successful. The reconstruction power of the reconstruction phase is calculated, and the reconstruction effect of different code apertures is shown in fig. 10. As can be seen from the figure, the TSPR algorithm proposed by the present embodiment is superior to the conventional SIPR method. The TSPR method aims at the coded aperture of the uniform random sampling mode, has the best reconstruction effect and has very good stability.
Figure 11 is a graph that tests the performance of the TSPR method, the TIPR algorithm and the SIPR algorithm as the sampling rate increases under a coded aperture of a uniform random sampling pattern. The sampling rate of the coded aperture is 0.1 to 0.7 and the step size is set to 0.05. And counting the reconstructed SNR of each time. The SNR threshold is 25dB, i.e. if the SNR of the reconstruction phase is greater than 25dB, the reconstruction is considered successful. The reconstruction success rate of the reconstruction phase is calculated, and the comparison of the reconstruction effects of different algorithms is shown in fig. 8. As can be seen from the experimental results of fig. 8, the best reconstruction effect is obtained by the TIPR algorithm when the phase recovery is performed under different sampling rate conditions for different algorithms. The reason is that the TIPR method knows the most information, i.e. the intensity information of two planes. The TSPR method is the second to be effective, the SIPR method is the worst. The difference between the TSPR method and the SIPR method is that the TSPR method uses the idea of the TIPR method for reference. The amplitude in the spatial domain is first estimated using the SIPR method and then the phase is recovered using the TIPR method. In summary, the TSPR method is superior to the SIPR method.
For single intensity measurement, namely frequency domain intensity, the embodiment recovers the amplitude information of the complex optical field in the spatial domain on the 2D coded aperture plane, and then recovers the phase of the complex optical field in the spatial domain on the 2D coded aperture plane by using the frequency domain intensity (namely the square of the amplitude) obtained by the measurement and the recovered spatial domain intensity, so as to significantly improve the quality of the reconstruction phase and the reconstruction power.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (5)
1. A two-step phase retrieval method based on single intensity measurement for processing intensity information of a 2D complex light field captured by an image sensor arranged at a back focal plane of a lens, a front focal plane of the lens being arranged with a 2D coded aperture M, the method comprising:
initializing the amplitude and phase of the 2D complex light field to obtain an initialized spatial amplitude A1And an initialization phase
According to the initialized spatial amplitude A1And an initialization phase
Synthesizing complex amplitudes g (x, y);
performing cyclic iteration of Fourier transformation and inverse Fourier transformation on the complex amplitude g (x, y) to obtain an amplitude estimation value of a complex optical field in a spatial domain on a 2D coded aperture plane;
based on a dual-intensity phase recovery algorithm, processing the amplitude information of the spatial domain and the frequency domain amplitude information obtained by measurement, and recovering the phase of the complex optical field in the spatial domain on the 2D coded aperture plane;
the iterative iteration of fourier transform and inverse fourier transform is performed on the complex amplitude g (x, y) to obtain the amplitude estimation value of the complex optical field in the spatial domain on the 2D coded aperture plane, and the method comprises the following steps:
s101, carrying out Fourier transform on the complex amplitude G (x, y) to obtain complex amplitude G (xi, eta) of a frequency domain;
s102, recording the frequency domain amplitude A in the frequency domain2Replacing the amplitude of the frequency domain complex amplitude G (xi, eta) to obtain a synthesized frequency domain complex amplitude G' (xi, eta);
s103, performing inverse Fourier transform on the frequency domain complex amplitude G '(xi, eta) to obtain a spatial domain complex amplitude G' (x, y);
s104, in the space domain, performing dot product operation on the complex amplitude g ' (x, y) of the space domain and the coding aperture M, and updating the complex amplitude g ' (x, y) of the space domain to obtain g ' (x, y);
s105, repeatedly executing the steps S101 to S104 on the updated spatial domain complex amplitude g '(x, y) until the updated spatial domain complex amplitude g' (x, y) converges;
s106, when the updated spatial domain complex amplitude g '(x, y) is converged, obtaining an amplitude estimation value of the complex optical field on the 2D coding aperture plane in the spatial domain according to the updated spatial domain complex amplitude g' (x, y) convergence;
the method for recovering the phase of the complex optical field in the space domain on the 2D coded aperture plane based on the dual-intensity phase recovery algorithm by processing the amplitude information of the space domain and the frequency domain amplitude information obtained by measurement comprises the following steps:
s201, utilizing the amplitude estimation value of the complex optical field in the space domain on the 2D coding aperture plane and the initialization phase
Composite complex amplitude g1(x,y)；
S202, repeatingAmplitude g1(x, y) Fourier transform to obtain complex amplitude G in frequency domain1(ξ,η)；
S203, frequency domain amplitude A to be recorded in frequency domain2Instead of the frequency domain complex amplitude G1(xi, eta) to obtain a synthesized frequency domain complex amplitude G1′(x,y)；
S204, the complex amplitude G of the frequency domain1' (x, y) is inverse Fourier transformed to obtain complex amplitude g in the spatial domain1′(x,y)；
S205, in the space domain, replacing the complex amplitude g of the space domain with the amplitude estimation value of the complex optical field of the 2D coding aperture plane in the space domain1' (x, y) to obtain an iteratively updated spatial domain complex amplitude g1″(x,y)；
S206, the updated space domain complex amplitude g1Repeatedly executing the steps S202 to S205 until the iteratively updated spatial domain complex amplitude g1And (x, y) converging the phase to obtain the phase of the complex optical field in the space domain on the 2D coding aperture plane.
2. Two-step phase recovery method based on single intensity measurement according to claim 1, characterized in that said initialization spatial amplitude a1For amplitudes with elements all being 1, the initialization phase
For uniformly randomizing the phase and having a phase interval of [0, π/2]。
3. A two-step phase recovery device based on single intensity measurements, comprising: the device comprises an acquisition module, an initialization module, a synthesis module, a spatial domain intensity estimation module and a dual-intensity phase recovery module;
the acquisition module is used for acquiring intensity information of a complex light field captured by an image sensor, the image sensor is arranged on the back focal plane of the lens, and the front focal plane of the lens is provided with a 2D coding aperture M;
the initialization module is used for initializing the amplitude and the phase of the 2D complex light field to obtain initializationSpatial amplitude A1And an initialization phase
The synthesis module is used for synthesizing the spatial amplitude A according to the initialization1And an initialization phase
Synthesizing complex amplitudes g (x, y);
the spatial domain intensity estimation module is used for performing cyclic iteration of Fourier transform and inverse Fourier transform on the complex amplitude g (x, y) to obtain an amplitude estimation value of a complex optical field in a spatial domain on a 2D coded aperture plane;
the dual-intensity phase recovery module is used for processing the amplitude information of the spatial domain and the frequency domain amplitude information obtained by measurement based on a dual-intensity phase recovery algorithm and recovering the phase of the complex optical field on the 2D coded aperture plane in the spatial domain;
the spatial domain intensity estimation module is used for executing the following steps:
s101, carrying out Fourier transform on the complex amplitude G (x, y) to obtain complex amplitude G (xi, eta) of a frequency domain;
s102, recording the frequency domain amplitude A in the frequency domain2Replacing the amplitude of the frequency domain complex amplitude G (xi, eta) to obtain a synthesized frequency domain complex amplitude G' (xi, eta);
s103, performing inverse Fourier transform on the frequency domain complex amplitude G '(xi, eta) to obtain a spatial domain complex amplitude G' (x, y);
s104, performing dot product operation on the complex amplitude g ' (x, y) of the spatial domain and the 2D coding aperture in the spatial domain, and updating the complex amplitude g ' (x, y) of the spatial domain to obtain g ' (x, y);
s105, repeatedly executing the steps S101 to S104 on the updated spatial domain complex amplitude g '(x, y) until the updated spatial domain complex amplitude g' (x, y) converges;
s106, when the updated spatial domain complex amplitude g '(x, y) is converged, obtaining an amplitude estimation value of the complex optical field on the 2D coding aperture plane in the spatial domain according to the updated spatial domain complex amplitude g' (x, y) convergence;
the dual intensity phase recovery module is configured to perform the following steps:
s201, utilizing the amplitude estimation value of the complex optical field in the space domain on the 2D coding aperture plane and the initialization phase
Composite complex amplitude g1(x,y)；
S202, for complex amplitude g1(x, y) Fourier transform to obtain complex amplitude G in frequency domain1(ξ,η)；
S203, frequency domain amplitude A to be recorded in frequency domain2Instead of the frequency domain complex amplitude G1(xi, eta) to obtain a synthesized frequency domain complex amplitude G1′(ξ,η)；
S204, the complex amplitude G of the frequency domain1' (xi, eta) is subjected to inverse Fourier transform to obtain complex amplitude g of a spatial domain1′(x,y)；
S205, in the space domain, replacing the complex amplitude g of the space domain with the amplitude estimation value of the complex optical field of the 2D coding aperture plane in the space domain1' (x, y) to obtain an iteratively updated spatial domain complex amplitude g1″(x,y)；
S206, the space domain complex amplitude g after the iterative update1Repeatedly executing the steps S202 to S205 until the iteratively updated spatial domain complex amplitude g1And (x, y) converging the phase to obtain the phase of the complex optical field in the space domain on the 2D coding aperture plane.
4. A two-step phase recovery device based on a single intensity measurement as claimed in claim 3, characterized in that said initialization spatial amplitude a1For amplitudes with elements all being 1, the initialization phase
For uniformly randomizing the phase and having a phase interval of [0, π/2]。
5. A two-step phase recovery system based on single intensity measurement, comprising a 2D complex light field, a CCD image sensor, a Fourier lens, a 2D coded aperture M and a two-step phase recovery device according to any one of claims 3 to 4;
the 2D coded aperture M and the CCD image sensor are respectively arranged on a front focal plane and a rear focal plane of the Fourier lens, the 2D complex light field is placed in front of the 2D coded aperture M, the longitudinal section of the 2D complex light field, the section of the 2D coded aperture M, the mirror surface of the Fourier lens and the plane of the CCD image sensor are located on the same light path, and the output end of the CCD image sensor is connected with the two-step phase recovery device.
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| CN112486003B (en) * | 2020-12-24 | 2021-12-07 | 四川大学 | Phase hologram generation method based on self-adaptive weight feedback GS algorithm |
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