A method and system for state tomography of three degrees of freedom classical non-separable states

Abstract

The application discloses a state tomography method and system for path-spin-orbit angular momentum-classical inseparable states. The method and system of the application comprise an amplitude measurement part and a phase identification part. The amplitude measurement part adopts each orthogonal basis projected to a Hilbert space by an optical stop, a circularly polarized analyzer, a spiral phase, etc., combines a surface array detector to receive a far-field diffraction light field distribution, and calculates a relative amplitude through a gray scale algorithm; the phase measurement part adopts a focusing lens to make different path beams in a to-be-measured light field interfere, inputs a two-dimensional distribution of a light field on an interference surface into a convolutional neural network built by the application, and directly obtains a phase difference between each path degree of freedom. Thus, complex coefficients of each orthogonal basis of the to-be-measured light field can be measured, a density matrix reconstruction is completed, and a state tomography result is obtained. The working principle of the application is completely developed according to the definition of classical inseparable state light fields of quantum-like states, the system structure is simple, the operation is simple, and the measurement precision is high.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of laser technology and optoelectronic technology, and relates to a method and system for state tomography of a three-degree-of-freedom classical non-separable state. BACKGROUND

[0002] Since Allen et al. discovered that a laser beam with a helical phase carries orbital angular momentum (OAM), research on OAM of a light beam has attracted extensive attention of scholars at home and abroad. OAM is a new degree of freedom of a light beam. Since its eigenvalue l can be any integer and OAM modes with different eigenvalues are orthogonal to each other, OAM constitutes an infinite-dimensional Hilbert space, making it possible to control a super-high-dimensional light field. This unique property makes OAM have great application prospects in many frontier fields. For example, in the field of optical communication, super-high-dimensional information coding and super-large-capacity information transmission can be realized by mixing multiple OAM modes to form mode division multiplexing; in the field of quantum technology, high-dimensional quantum superposition states, high-dimensional quantum entanglement preparation, and classical simulation of complex quantum states can be realized by using OAM.

[0003] Coupling OAM with other degrees of freedom of a light field can obtain a classical non-separable state (CNSS) light field. Since its expression has a similar mathematical form to that of a quantum state, it provides a solution for classical simulation of quantum processes such as quantum entanglement, quantum computing, and quantum walking, and is therefore also referred to as “classical entanglement” in some documents. At present, CNSS light fields are usually constructed in two coupled eigenfreedom degrees, among which spin angular momentum (SAM)-OAM coupled light fields are the most common, and the generation and manipulation technology is the most mature, having broad application prospects in laser processing, high-resolution imaging, and simulation of two-particle entangled states. However, SAM has only two orthogonal eigenstates, corresponding to macroscopic left-handed and right-handed circularly polarized states, which severely limits the ability of CNSS light fields to expand in dimension. Moreover, the actual generation of super-high-order OAM states is relatively difficult in technology, so the CNSS light fields that can be generated under the current technology cannot simulate high-dimensional quantum entanglement of multiple particles. Later, a method for generating a path-SAM-OAM three-degree-of-freedom CNSS light beam in the form of a Greenberger-Horne-Zeilinger (GHZ) state was proposed, and it is expected to realize classical simulation of three-particle maximum quantum entanglement based on this method. In the above process, in order to determine whether the generated CNSS light field has good “entanglement degree” and fidelity, it is necessary to perform state tomography analysis to calculate its density matrix. However, how to accurately realize state tomography of a path-SAM-OAM three-degree-of-freedom CNSS light field is still a blank at present. SUMMARY

[0004] Therefore, the application discloses a state tomography method and system for path-SAM-OAM three-dimensional classical inseparable state.

[0005] The state tomography method for path-SAM-OAM classical inseparable state of the application is composed of an amplitude measurement part based on a projection measurement principle and a phase identification part based on deep learning. The to-be-measured CNSS light field is divided into two paths by a beam splitter for amplitude measurement and phase measurement. The amplitude measurement part adopts an optical stop, a circular polarized analyzer and a spiral phase plate to project the to-be-measured CNSS light field into each orthogonal basis in Hilbert space, and combines a surface array detector to receive a far-field diffraction light field distribution, so that the relative amplitude in each basis complex coefficient is calculated through a gray scale algorithm. The phase measurement part adopts a focusing lens to make the light beams under different paths interfere, and inputs the two-dimensional distribution of the interference surface light field into the convolutional neural network built in the application to directly obtain the relative phase difference between paths, i.e., the relative phase of each basis complex coefficient. Thus, the basis complex coefficient of the to-be-measured inseparable state can be completely calculated, the density matrix reconstruction is completed, and the state tomography result is obtained.

[0006] The amplitude measurement part of the state tomography method for path-SAM-OAM three-dimensional classical inseparable state of the application is based on projection measurement. First, the complete Hilbert space is listed according to the degrees of freedom of the to-be-measured CNSS light field and corresponding eigenvalues. For all eigenbasis in the Hilbert space, projection is sequentially performed in three steps. First, the light field is projected into the measurement path degree of freedom through optical stop filtering. Second, the light field is projected into the SAM degree of freedom by making the required left-handed or right-handed polarization state transmit through a circular polarized analyzer. Third, the light field is projected into the OAM degree of freedom by making the l-order OAM mode degenerate into the 0-order OAM mode through a-l-order spiral phase plate, so that a central bright spot is formed on the far-field diffraction plane, and the OAM projection is realized. Finally, a gray scale pattern is collected, and the pixel size in the bright spot area is calculated by using a gray scale algorithm, so that the relative amplitude of each orthogonal basis can be inferred according to the proportional relationship.

[0007] The phase measurement part of the state tomography method for path-SAM-OAM three-dimensional classical inseparable state of the application is based on the double-OAM mode interference principle. A focusing lens is used to make different OAM modes on different paths interfere on an interference surface to produce a cross-shaped pattern related to the phase difference. Resnet50 is selected as a basic framework to extract the dislocation relationship of the cross-shaped head and tail stripes of the two-dimensional light field distribution after denoising, and the 3.6x10 4The group theory simulation picture is taken as a training set, an experimental picture is taken as a training set, after denoising preprocessing, data collection is carried out in the ResNet50 network, the adopted architecture has 48 convolution layers (Conv), 1 maximum pooling layer (MaxPool) and 1 average pooling layer (Average Pool), finally the above features are sent to the full connection layer to obtain the phase difference output in 0~2pi. According to the phase relationship between the paths, the relative phase of all bases in the Hilbert space can be measured.

[0008] The state tomography system based on the path-SAM-OAM classical inseparable state of the application has a collimator, a depolarization beam splitter prism, two diaphragms, two thin convex lenses, two circularly polarized analyzers, a liquid crystal spatial light modulator, two area array detectors and a host computer.

[0009] The collimator is used for collimating the to-be-measured light field and incident along the center of the system.

[0010] The depolarization beam splitter prism is arranged in the laser light path behind the collimator and is used for 1:1 beam splitting of the to-be-measured light field without changing the to-be-measured property, so as to respectively perform amplitude measurement and phase identification.

[0011] The first diaphragm is arranged in the laser light path in the reflection direction of the depolarization beam splitter prism and is used for projecting the light beam of a specific path in the amplitude measurement, so as to realize path freedom projection measurement.

[0012] The first circularly polarized analyzer is arranged behind the diaphragm and is used for projecting the light beam of a specific polarization state, so as to realize SAM freedom projection measurement and make the outgoing light into horizontal linear polarization to enter the rear liquid crystal spatial light modulator to realize pure phase modulation.

[0013] The liquid crystal spatial light modulator is arranged behind the first circularly polarized analyzer and is used for loading a spiral phase to realize OAM freedom projection measurement.

[0014] The first thin convex lens is arranged in the laser light path behind the liquid crystal spatial light modulator and is used for Fourier transform on the light field to obtain a far-field diffraction.

[0015] The first area array detector is arranged in the laser light path behind the first thin convex lens and the distance between the first area array detector and the first thin convex lens is the focal length f of the first thin convex lens, and the first area array detector is used for detecting and outputting the diffraction pattern of the to-be-measured light beam.

[0016] The second diaphragm is arranged in the laser light path in the transmission direction of the depolarization beam splitter prism and is used for selecting two different paths in the incident light field in the phase measurement, so as to realize double-beam interference.

[0017] The second circular polarized beam splitter is arranged in the laser light path behind the second diaphragm, and is used for projecting the polarization state of the whole incident light beam to horizontal polarization, so that the contrast of the subsequent interference pattern is improved.

[0018] The second thin convex lens is arranged in the laser light path behind the second circular polarized beam splitter, and is used for focusing the two path light beams and causing interference on the back focal plane.

[0019] The second area array detector is arranged at the intersection of the back focal plane of the second thin convex lens and the laser light path, so that the two-dimensional light field distribution on the interference plane is obtained.

[0020] The host computer is used for analyzing the diffraction and interference patterns captured by the two area array detectors, and calculating the final complex coefficient and density matrix.

[0021] The present application has the following beneficial effects:

[0022] (1) The state tomography method for path-SAM-OAM three-dimensional classical inseparable state disclosed by the present application is completely based on the definition of state tomography, and can perform entangled state tomography on any path-SAM-OAM inseparable state to determine the fidelity of classical GHZ-like state.

[0023] (2) The state tomography device for path-SAM-OAM three-dimensional classical inseparable state disclosed by the present application has a simple structure, is conducive to system integration, and is suitable for engineering scenarios. DETAILED DESCRIPTION

[0024] Figure 1(a) is the amplitude measurement principle in the state tomography method for path-SAM-OAM three-dimensional classical inseparable state of the present application.

[0025] Figure 1(b) is the phase measurement principle in the state tomography method for path-SAM-OAM three-dimensional classical inseparable state of the present application.

[0026] Figure 1(c) is a state tomography system for path-SAM-OAM three-dimensional classical inseparable state of the present application. Figure 2 Figure 1(c) is a state tomography system for path-SAM-OAM three-dimensional classical inseparable state of the present application, wherein 1 is a collimator, 2 is a depolarization beam splitter prism, 3 is a first diaphragm, 4 is a first circular polarized beam splitter, 5 is a liquid crystal spatial light modulator, 6 is a first thin convex lens, 7 is a first area array detector, 8 is a second diaphragm, 9 is a second circular polarized beam splitter, 10 is a second thin convex lens, 11 is a second area array detector, and 12 is a host computer.

[0027] Figure 1(c) is a state tomography system for path-SAM-OAM three-dimensional classical inseparable state of the present application. Figure 3 Figure 1(c) is a state tomography system for path-SAM-OAM three-dimensional classical inseparable state of the present application. Figure 1(c) is a state tomography system for path-SAM-OAM three-dimensional classical inseparable state of the present application.

[0028] attached Figure 4 is a virtual part density matrix in the experimental result of the state tomography method and system for path-SAM-OAM three-dimensional classical inseparable state of the CNSS optical field state of the GHZ-like state. DETAILED DESCRIPTION

[0029] The application will be described in detail below with reference to the accompanying drawings and embodiments.

[0030] A state tomography method for path-SAM-OAM three-dimensional classical inseparable state of the application, the applicable premise is that the eigenvalues of each degree of freedom in the measured CNSS optical field are known and can form a complete Hilbert space. Under this premise, the eigenvalues of the path degree of freedom are determined by the number of paths in the optical field, and the eigenstate is represented as |n>, wherein n represents the nth path; the SAM degree of freedom has only two eigenvalues, corresponding to the macroscopic left-handed and right-handed circular polarization states, represented as |L> and |R>, wherein L and R correspond to left-handed and right-handed circles; the eigenvalues of the OAM degree of freedom are determined by the topological charge l, and the eigenstate is represented as |l m >l m m represents the mth topological charge value. Thus, the three-dimensional inseparable state has n x 2 x m = 2mn eigenbases, forming a 2mn-dimensional Hilbert space, represented as H 2mn ∈{|1>|L>|l1>,|1>|L>|l2>,......|n>|R>|l m >} The superposition state of the corresponding inseparable optical field can be represented as In the formula, |P k >|S k >|l k >∈H 2mn is the kth basis of the Hilbert space, |P k > represents the path eigenstate in the kth basis, |S k > represents the spin angular momentum eigenstate in the kth basis, |l k > represents the orbital angular momentum eigenstate in the kth basis, and α k represents the weight of the kth basis, satisfying In classical optics, the values are A k and are the amplitudes and phases of the classical optical field corresponding to the basis. Thus, the reconstructed density matrix ρ = |ψ><ψ| can be calculated.

[0031] A state tomography method for path-SAM-OAM classical inseparable state of the application, as shown in FIG. 1, includes a kth basis |P k >|Sk >|l k > amplitude A k and phase Measurement, the incident light field is equally divided into two parts by a beam splitter to realize measurement. Among them, Fig. 1(a) shows the flow of the amplitude measurement part. First, by means of diaphragm filtering, projection to the measurement path, the process is represented as <P k |; second, by means of a polarization detection element, only the polarization state S k is transmitted to the measured spin angular momentum; third, by means of a-l k order spiral phase plate, the l k order OAM beam can be degraded, and in the far-field diffraction plane, it is represented as a central bright spot, realizing the projection of orbital angular momentum, represented as <l k |; finally, the gray scale pattern is collected by a surface array detector, and the gray scale algorithm is used to calculate only the pixel size in the bright spot area, and according to the principle of not including other side lobes, the relative amplitude of the basis can be inferred according to the proportional relationship. According to this process, the relative amplitude of each basis in the Hilbert space is measured in turn.

[0032] For the phase measurement part, the phase measurement part involved is based on the inseparable state principle and the double vortex interference principle to measure the phase difference between states Since each basis has different orbital angular momentum in different paths, a focusing lens can be used to make each basis, i.e. the light beams with different orbital angular momentum in different paths, interfere non-coaxially in the interference plane to produce a fork pattern related to the phase difference, as shown in Fig. 1(b). A surface array detector is placed in the interference plane to receive the two-dimensional light field distribution of the experimental interference fringes to be measured. The convolutional neural network ResNet50 is selected as the basic framework to extract the denoised two-dimensional light field distribution to identify the dislocation relationship of the fork-shaped head and tail fringes, and then the phase relationship is obtained. The identification process is divided into four steps of data acquisition, preprocessing, feature extraction and linear regression. First, 3.6x10 4 different phase differences, different OAM and different position offsets are simulated to train, and through binarization, opening operation, superposition mask preprocessing, the training data and the test data are better matched. Next, the ResNet50 is used to extract the image features, the input surface of the network is the processed interference light field pattern, the architecture adopted has 48 convolutional layers (Conv), 1 maximum pooling layer (MaxPool) and 1 average pooling layer (Average Pool), and finally the above features are sent to the fully connected layer to obtain the phase difference output within 0~2pi. The verification results show that the regression mean square error (MSE) of the data set is 6.32x10 -3 , indicating that the measurement accuracy of the phase recognition based on the convolutional neural network is high, and can meet the measurement requirements. According to this method, the phase difference between the bases of different paths can be obtained The eigenbase of one path can be selected as a reference phase, and the phases of other paths can be calculated by relative relationship, so that all relative phases of each base in Hilbert space can be measured

[0033] The state tomography system based on path-SAM-OAM classical inseparable state of the application is shown in the figure. Figure 2 The collimator is used for collimating the to-be-measured light field and is incident along the center of the system; the depolarization beam splitting prism is arranged in the laser light path behind the collimator and is used for 1:1 beam splitting of the to-be-measured light field without changing the to-be-measured property, so as to respectively perform amplitude measurement and phase identification; the first diaphragm is arranged in the laser light path in the reflection direction of the depolarization beam splitting prism and is used for projecting the light beam of a specific path, so as to realize path freedom degree projection measurement; the first circularly polarized analyzer is arranged behind the diaphragm and is used for projecting the light beam of a specific polarization state, so as to realize SAM freedom degree projection measurement and make the outgoing light into horizontal linear polarization to enter the liquid crystal spatial light modulator behind to realize pure phase modulation; the liquid crystal spatial light modulator is arranged behind the first circularly polarized analyzer and is used for loading a spiral phase, so as to realize OAM freedom degree projection measurement; the first thin convex lens is arranged in the laser light path behind the liquid crystal spatial light modulator and is used for performing Fourier transform on the light field to obtain a far-field diffraction; the first area array detector is arranged in the laser light path behind the first thin convex lens and is located at a distance of the focal length f of the first thin convex lens from the first thin convex lens, and is used for detecting and outputting a diffraction pattern of the to-be-measured light beam; the second diaphragm is arranged in the laser light path in the transmission direction of the depolarization beam splitting prism and is used for selecting two different paths in the incident light field to realize double-beam interference in phase measurement; the second circularly polarized analyzer is arranged in the laser light path behind the second diaphragm and is used for projecting the polarization state of all incident light beams to horizontal polarization, so as to improve the contrast of a subsequent interference pattern; the second thin convex lens is arranged in the laser light path behind the second circularly polarized analyzer and is used for focusing the light beams of the two paths and causing interference on the back focal plane; the second area array detector is arranged at the intersection of the back focal plane of the second thin convex lens and the laser light path, so as to obtain a two-dimensional light field distribution on the interference plane. The host computer is used for analyzing the diffraction and interference patterns captured by the two area array detectors and calculating the final complex coefficient and density matrix.

[0034] The actual system of the state tomography method and system for path-SAM-OAM three-freedom-degree classical inseparable state of the application will be briefly introduced below in combination with a specific embodiment.

[0035] Embodiment: The GHZ-like state |ψ0> = α1|1>|L>|l = 3> + α8|2>|R>|l = -3> is tomographically analyzed by using the application. The eigenbasis belongs to the three degrees of freedom eight-dimensional Hilbert space composed of the double paths (|1>, |2>), the SAMs (|L>, |R>), and the OAMs (|l = 3>, |l = -3>).

[0036] In this embodiment, the GHZ-like state generated in the experiment is tomographically analyzed by using the state tomography method and system of the path-SAM-OAM classical inseparable state according to the application. In the amplitude measurement, each basis H8 ∈ {|1>|L>|l = 3>, |1>|L>|l = -3>, |1>|R>|l = 3>, |1>|R>|l = -3>, |2>|L>|l = 3>, |2>|L>|l = -3>, |2>|R>|l = 3>, |2>|R>|l = -3>} in the Hilbert space needs to be projected. Taking |1>|L>|l = 3> as an example, the first diaphragm in the system is selected to be 1-path transparent to realize 1-path projection. Then, the first circularly polarized analyzer is rotated to project the incident light to the left circularly polarized state, and the transmitted light is converted into horizontally polarized light to be incident on the liquid crystal spatial light modulator. The liquid crystal spatial light modulator is loaded with an inverse phase, that is, a l = -3-order spiral phase to diffract the incident light. After the transmitted light passes through the first rear thin convex lens, the far-field distribution pattern is received on the rear focal plane. The pixel values in the bright spot region are calculated by the host computer center, and the side lobes should not be included. Finally, the pixel values corresponding to each basis are proportional to the intensity of each basis, and the relative amplitude of each basis can be known. In the phase measurement, the second diaphragm makes the two paths pass through at the same time. After passing through the second focusing lens, the interference pattern is received by the second area array detector, input into the ResNet50 built, and the phase relationship of the 1-path and the 2-path is directly output. The phase of the 1-path beam is selected as the reference phase, and then the phase of each of the eight bases can be obtained. Figure 3 The real part density matrix of |ψ0> measured in the experiment is Figure 4 The imaginary part density matrix of |ψ0> measured in the experiment is shown in the upper part of the dashed box, and the difference between the measured and theoretical density matrices is shown in the lower part. The fidelity calculated from this is 93.79%, which proves the effectiveness of the application.

[0037] In summary, the above is only a preferred example of the application, and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application should be included in the protection scope of the application.

Claims

1. A state tomography method for the path-spin angular momentum-orbital angular momentum classical inseparable state, consisting of an amplitude measurement part based on the projection measurement principle and a phase recognition part based on deep learning. The classical inseparable state light field to be measured is divided into two paths by a beam splitter for amplitude measurement and phase measurement respectively: the amplitude measurement part uses an aperture, a circular polarization analyzer, and a spiral phase plate diffraction to project the classical inseparable state light field to be measured onto each orthogonal basis in the Hilbert space, and combines the far-field diffraction light field distribution received by the area array detector to calculate the relative amplitude in the complex coefficients of each basis through a grayscale algorithm; the phase measurement part uses a focusing lens to interfere the light beams under different paths, and inputs the two-dimensional distribution of the interference surface light field into the constructed convolutional neural network to directly obtain the relative phase difference between the paths, that is, the relative phase of the complex coefficients of each basis. At this point, the complex coefficients of each basis of the inseparable state to be measured can be completely calculated, the density matrix reconstruction is completed, and the state tomography result is obtained.

2. The method as claimed in claim 1, wherein the amplitude measurement part involved is based on projection measurement. First, a complete Hilbert space is listed according to the degree of freedom of the classical inseparable state light field to be measured and the corresponding eigenvalues. For all eigenvalue bases in the Hilbert space, projection is performed in sequence, which is divided into three steps: first, through aperture filtering, projection can be performed to the measurement path degree of freedom; second, through a circular polarization analyzer, the required left-handed or right-handed polarization state is transmitted, and projection can be performed to the spin angular momentum degree of freedom; third, through a -1 order spiral phase plate, the 1st order orbital angular momentum mode can be degenerated to the 0th order orbital angular momentum mode, which appears as a central bright spot on the far-field diffraction surface, realizing orbital angular momentum projection; finally, a grayscale pattern is collected, and a grayscale algorithm is used to calculate only the pixel size in the bright spot area, with the principle of excluding other light field side lobes. The relative amplitude of each orthogonal basis can be inferred based on the proportional relationship.

3. The method according to claim 1, wherein the phase measurement part is based on the principle of dual orbital angular momentum mode interference, using a focusing lens to cause different orbital angular momentum modes on different paths to interfere non-coaxially on the interference surface, generating a fork pattern related to the phase difference, and placing a planar array detector on the interference surface to receive the two-dimensional light field distribution of the interference fringes; selecting the convolutional neural network ResNet50 as the basic framework to extract the denoised two-dimensional light field distribution, identify the dislocation relationship between the head and tail of the fork fringes, and then obtain the phase relationship; the recognition process is divided into four steps: data acquisition, preprocessing, feature extraction, and linear regression; collecting 3.6×10 4 A set of interference patterns with different phase differences, different orbital angular momentum and different position offsets are trained, and after binarization, opening operation and superposition mask preprocessing, they are input into the ResNet50 network; the ResNet50 network architecture adopted has 48 convolutional layers (Conv), 1 maximum pooling layer (MaxPool) and 1 average pooling layer (Average Pool), and finally the above features are sent to the fully connected layer to obtain the phase difference output within 0~2pi. According to the phase relationship between the paths, all relative phases of each basis in the Hilbert space can be measured.

4. A state tomography system based on the classical inseparable state of path-spin angular momentum-orbital angular momentum, characterized in that: The device comprises a collimator, a depolarizing beam splitter, a first aperture, a second aperture, a first thin convex lens, a second thin convex lens, a first circular polarization analyzer, a second circular polarization analyzer, a liquid crystal spatial light modulator, a first area array detector, a second area array detector and a host, wherein: The collimator is used to collimate the light field to be measured and make it incident along the center of the system; The depolarizing beam splitter is placed in the laser light path after the collimator, and is used to split the light field to be measured in a 1:1 ratio without changing the properties to be measured, and perform amplitude measurement and phase identification respectively; The first aperture is placed in the laser light path in the reflection direction of the depolarizing beam splitter prism, and is used to project a light beam of a specific path in amplitude measurement, thereby realizing path freedom projection measurement; The first circular polarization analyzer is placed behind the first aperture and is used to project a light beam with a specific polarization state to achieve projection measurement of the spin angular momentum degree of freedom, and convert the output light into horizontal linear polarization to enter the liquid crystal spatial light modulator behind it to achieve pure phase modulation; The liquid crystal spatial light modulator is placed after the first circular polarization analyzer and is used to load the spiral phase to achieve orbital angular momentum degree of freedom projection measurement; The first thin convex lens is placed in the laser light path behind the liquid crystal spatial light modulator to perform Fourier transform on the light field to obtain far-field diffraction; The first area array detector is placed in the laser light path behind the first thin convex lens, and the distance between the first area array detector and the first thin convex lens is the focal length f of the first thin convex lens, and is used to detect and output the diffraction pattern of the light beam to be measured; The second aperture is placed in the transmission direction of the depolarization beam splitter prism in the laser light path, and is used to select two different paths in the incident light field in phase measurement to achieve double-beam interference; The second circular polarization analyzer is placed in the laser light path behind the second aperture and is used to project the polarization state of the entire incident light beam to horizontal polarization to improve the contrast of the subsequent interference pattern; The second thin convex lens is placed in the laser light path behind the second circular polarization analyzer, and is used to focus the two path light beams and cause interference on the back focal plane; The second array detector is placed at the intersection of the back focal plane of the second thin convex lens and the laser light path to obtain a two-dimensional light field distribution on the interference surface; The host is used to analyze the diffraction and interference patterns captured by the two area array detectors and calculate the final complex coefficients and density matrix.

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