A Phase Image Coding Method and System Based on Random Vector Optical Complex Coherence Measurement

Abstract

This invention belongs to the field of image coding technology and relates to a phase image coding method and system based on random vector light complex coherence measurement: Phase information is loaded into the spatial distribution phase difference of the orthogonal complex electric field of an incoherent light source. According to the generalized van der Zernike theorem, a cross-spectral density matrix function of the partially coherent vector light field is constructed using a coding system. Based on mode decomposition theory and the cross-spectral density matrix function of the partially coherent vector light field, multiple orthogonal vector electric field mode bases are obtained to obtain partially coherent vector beams of multiple modes on the light source surface. Off-axis holography is used to measure each vector mode of the partially coherent vector beam from the interference light intensity, and the orthogonal polarization field of the partially coherent vector beam of each mode is constructed. Based on the orthogonal polarization field of the partially coherent vector beam, full-dimensional complex coherence information is obtained, and the phase information is recovered using a decoding system, thus realizing image coding and full-dimensional measurement of complex coherence based on vector partially coherent light.

Description

Technical Field

[0001] This invention relates to the field of image coding technology, and in particular to a phase image coding method and system based on random vector optical complex coherence measurement. Background Technology

[0002] Partially coherent optical fields refer to randomly structured light with reduced coherence. Studies have shown that by reducing the coherence length of the beam or precisely customizing the complex coherent structure of the partially coherent optical field, it is possible to effectively reduce or overcome speckle noise caused by high coherence, beam drift caused by atmospheric turbulence, beam flicker, and improve the self-repair capability of the beam spot after it is blocked by opaque obstacles. This has significant application advantages in realizing optical parallel computing, optical encryption, robust information transmission, free-space optical communication, and efficient beam shaping.

[0003] Encoding optical images using the coherent structure of a partially coherent light field refers to embedding image information into the coherent structure of the light field by controlling the spatial coherence distribution of the light field. This allows the light field to carry encrypted image information during propagation or interference. The core of this method is to use the physical properties of light field coherence as the encoding "key" or information carrier to achieve encrypted, hidden, or interference-resistant transmission of images.

[0004] In existing technologies, optical image encoding and encryption using coherent optical field structures are all performed by encoding and decoding images through scalar partially coherent optical fields. This is because scalar partially coherent light only needs to consider the amplitude and phase of the optical field. During encoding, it is only necessary to design the mapping relationship between the coherence of the optical field and the image pixels to encode the image information into the cross-spectral density function of the optical field, making the entire encoding and decoding process relatively simple. However, since the theoretical basis of scalar partially coherent beams is the scalar wave equation, which does not reflect the polarization properties of light (i.e., vector characteristics), this characteristic makes it impossible for scalar partially coherent optical fields to carry polarization-related information. Therefore, scalar partially coherent beams can only encode and decode images with pure amplitude, and cannot encode and decode images containing polarization information.

[0005] In summary, existing image encoding methods based on scalar partially coherent beams have the problem that they can only encode and decode pure amplitude images, but cannot encode and decode images containing polarization information. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the existing image encoding methods based on scalar partially coherent beams can only encode and decode pure amplitude images, but cannot encode and decode images containing polarization information.

[0007] To address the aforementioned technical problems, this invention provides a phase image encoding method based on random vector optical complex coherence measurement, comprising:

[0008] Image information is loaded into the spatial distribution phase difference of the orthogonal complex electric field of the incoherent light source. According to the generalized van der Zenik theorem, the spatial distribution phase difference is encoded into the cross correlation function of the partially coherent vector light field using an encoding system, and the cross spectral density matrix function of the partially coherent vector light field is constructed.

[0009] Based on mode decomposition theory, the cross spectral density matrix function of partially coherent vector light fields is decomposed to obtain multiple orthogonal vector electric field mode bases;

[0010] Based on multiple orthogonal vector electric field mode bases, partially coherent vector beams of multiple modes are obtained on the light source surface; the interference intensity of the partially coherent vector beams of each mode is measured using off-axis holography, thereby constructing the orthogonal polarization field of the partially coherent vector beams of each mode.

[0011] Based on the orthogonal polarization fields of partially coherent vector beams of all modes, the full-dimensional complex coherence information of the partially coherent vector light field is obtained, and the image information is recovered from the full-dimensional complex coherence information using a decoding system.

[0012] Preferably, the orthogonal complex electric field of the incoherent light source is expressed as:

[0013] ,

[0014] ,

[0015] in, Represents the spatial frequency domain coordinate position vector; This represents the polarization electric field component along the x-direction of an incoherent light source. This represents the polarization electric field component along the y-direction of an incoherent light source. The deterministic amplitude of the orthogonal complex electric field of an incoherent light source; This represents the spatial distribution phase difference that encodes image information;

[0016] The cross-spectral density matrix function of the partially coherent vector light field is expressed as:

[0017] ,

[0018] ,

[0019] in, The cross spectral density matrix function representing the partially coherent vector light field; , Represents any two points in a partially coherent vector light field; The anti-angle matrix element represents the polarization matrix of a completely incoherent light source; This indicates the process of constructing a partially coherent vector light field along... The complex conjugate of the system kernel function in the direction; This indicates the process of constructing a partially coherent vector light field along... The system kernel function in the direction; Indicates incoherent light source along Complex conjugate of polarization electric field components in the direction; Indicates incoherent light source along The polarization electric field component in the direction; Represents the Dirac function; , It represents the coordinates of any two points in the spatial domain.

[0020] Preferably, the cross-spectral density matrix function of the partially coherent vector light field is decomposed based on mode decomposition theory to obtain multiple orthogonal vector electric field mode bases, including:

[0021] Using the correlation between partially coherent vector beams of multiple modes in a partially coherent vector light field as a constraint, a constraint function is constructed for each mode to control the random complex screen function of the anti-diagonal element in the cross spectral density matrix;

[0022] Based on the constraint function of the random complex screen function under each mode, a random complex screen function is constructed to construct a partially coherent vector beam under each mode.

[0023] Based on the random complex screen functions of partially coherent vector beams in each mode, multiple orthogonal vector electric field mode bases are constructed.

[0024] Preferably, the mode decomposition theory is expressed as:

[0025] ,

[0026] in, The cross spectral density matrix function represents the partially coherent vector light field. ; , Represents any two points in a partially coherent vector light field; This represents the number of orthogonal vector electric field mode bases obtained from the decomposition; Indicates the first The weighting coefficients of an orthogonal vector electric field mode basis; , , , Indicates the first A basis of orthogonal instantaneous vector electric field modes, ; express Deterministic amplitude parameter; express Deterministic amplitude parameter; express A random complex screen function; express A random complex screen function;

[0027] ,

[0028] ,

[0029] in, Indicates the first Each mode along A complex screen function with random orientation; Indicates the first Each mode along A random complex screen function with a specific direction; This represents the system kernel function used to construct a partially coherent vector light field; This represents the first diagonal matrix element of the polarization matrix of a completely incoherent light source; The second diagonal matrix element represents the polarization matrix of a completely incoherent light source;

[0030] ,

[0031] ,

[0032] in, , Four independent Gaussian random numbers with zero mean and one variance; ; for The complex conjugate; Represents the anti-angular element of an incoherent matrix; , Represents the first and second diagonal elements of an incoherent matrix; Represents the imaginary unit;

[0033] The vector electric field mode basis of the nth partially coherent vector beam is represented as:

[0034] ,

[0035] in, 、 This represents the unit coordinate vector in the x and y directions of the Cartesian coordinate system.

[0036] Preferably, a spatial modulator and a coaxial interference system are used to obtain a partially coherent vector beam of multiple modes on the light source surface based on multiple orthogonal vector electric field mode bases.

[0037] Preferably, measuring the interference intensity of the partially coherent vector beams of each mode using off-axis holography includes:

[0038] Using a linearly polarized uniform plane wave with a preset angle as a reference light, interference light is generated by interfering with partially coherent vector beams of various modes.

[0039] A polarization beam splitter is used to split the interference light into horizontally polarized light and vertically polarized light, and the intensity of the interference light is captured by the first detector and the second detector, respectively.

[0040] Preferably, the interference intensity of the partially coherent vector beam along the x-direction is expressed as:

[0041] ,

[0042] in, Indicates the first The interference intensity of partially coherent vector beams in each mode along the x-direction; This represents the amplitude of a uniformly polarized plane wave with a preset angle. Indicates the first Orthogonal vector electric field mode basis edges Instantaneous complex electric field in the direction; Represents the operation of the real part; Represents the Gaussian function; Represents the imaginary unit; Represents the light wave vector; Represents the x-coordinate in the Cartesian coordinate system; These represent the angles between the reference plane wave and the signal wave in the x and y directions, respectively.

[0043] The interference intensity of a partially coherent vector beam along the y-direction is expressed as:

[0044] ,

[0045] in, Indicates the first The interference intensity of partially coherent vector beams in each mode along the y-direction; Indicates the first Orthogonal vector electric field mode basis edges Instantaneous complex electric field in the direction.

[0046] Preferably, constructing the orthogonal polarization field of the partially coherent vector beams for each mode includes:

[0047] Fourier transform is performed on the interference intensity of the partially coherent vector beams of each mode along the x-direction to obtain the Fourier spectrum of the interference field component of the partially coherent vector beams of each mode along the x-direction; Fourier transform is performed on the interference intensity of the partially coherent vector beams of each mode along the y-direction to obtain the Fourier spectrum of the interference field component of the partially coherent vector beams of each mode along the y-direction.

[0048] From the Fourier spectrum of the interference field component of the partially coherent vector beam along the x-direction of each mode, extract the spectral components of the partially coherent vector beam along the x-direction of each mode; from the Fourier spectrum of the interference field component of the partially coherent vector beam along the y-direction of each mode, extract the spectral components of the partially coherent vector beam along the y-direction of each mode.

[0049] Inverse Fourier transforms are performed on the spectral components of the x-direction and y-direction components of the partially coherent vector beams of each mode to construct the instantaneous x-polarization field and instantaneous y-polarization field of the partially coherent vector beams of each mode.

[0050] This invention also provides a phase image coding system based on random vector optical complex coherence measurement. The system is used to implement the aforementioned phase image coding method based on random vector optical complex coherence measurement, and includes:

[0051] The beam modulation measurement module communicates with the host computer and is used to obtain partially coherent vector beams of multiple modes on the light source surface based on multiple orthogonal vector electric field modes; and to measure the interference intensity of the partially coherent vector beams of each mode using off-axis holography, thereby constructing the orthogonal polarization field of the partially coherent vector beams of each mode.

[0052] The host computer loads image information into the spatial distribution phase difference of the orthogonal complex electric field of the incoherent light source. According to the generalized van der Zernike theorem, the spatial distribution phase difference is encoded into the cross-correlation function of the partially coherent vector light field using an encoding system, thus constructing the cross-spectral density matrix function of the partially coherent vector light field. Based on mode decomposition theory, the cross-spectral density matrix function of the partially coherent vector light field is decomposed to obtain multiple orthogonal vector electric field mode bases. Based on the orthogonal polarization fields of the partially coherent vector beams of all modes, the full-dimensional complex coherence information of the partially coherent vector light field is obtained. The image information is then recovered from the full-dimensional complex coherence information using a decoding system.

[0053] Preferably, the beam modulation measurement module includes:

[0054] The beam modulation measurement module includes:

[0055] A laser is used to generate a laser beam.

[0056] Linear polarizers are used to modulate laser beams into horizontally linearly polarized light;

[0057] The first beam expander is located on the side of the linear polarizer away from the laser and is used to expand the horizontally linearly polarized light.

[0058] The first beam splitter is located on the side of the first beam expander away from the linear polarizer, and is used to split the expanded horizontal linear polarized light into first horizontal linear polarized light and second horizontal linear polarized light.

[0059] The second beam splitter has its incident surface facing the first horizontal linearly polarized light output surface of the first beam splitter. It is used to send the first horizontal linearly polarized light to the spatial light modulator and send the modulated first horizontal linearly polarized light returned by the spatial light modulator to the imaging system.

[0060] A spatial light modulator, whose incident surface faces the first exit surface of the second beam splitter, is used to modulate the first horizontally linearly polarized light based on multiple orthogonal vector electric field mode bases using the left and right half-screens, and reflects the first horizontally linearly polarized light after each modulation back to the second beam splitter.

[0061] Imaging systems, specifically including:

[0062] The first lens, whose incident surface is directly opposite the second exit surface of the second beam splitter, is used to focus each modulated first horizontally linearly polarized light.

[0063] A dual-aperture filter is used to filter the first horizontally linearly polarized light emitted from the first lens after focusing, so as to obtain the positive first-order light modulated by the left half screen of the spatial light modulator and the positive first-order light modulated by the right half screen of the spatial light modulator in each first horizontally linearly polarized light.

[0064] The first half-wave plate, whose incident light is directly aligned with the first light source aperture of the dual-aperture filter, is used to modulate each of the first positive first-order beams emitted from the dual-aperture filter into x-polarized light.

[0065] The second half-wave plate, whose incident light is directly aligned with the second light source aperture of the dual-aperture filter, is used to modulate each of the second positive first-order beams emitted from the dual-aperture filter into y-polarized light.

[0066] The second lens is used to focus the x-polarized and y-polarized light emitted from the first half-wave plate and the second half-wave plate.

[0067] A Ronchi grating, located at the focal plane of the second lens, is used to combine the focused x-polarized and y-polarized beams emitted from the second lens to form a partially coherent vector beam of multiple modes on the light source surface.

[0068] An attenuator, whose incident surface faces the second horizontally linearly polarized light exit surface of the first beam splitter, is used to modulate the second horizontally linearly polarized light.

[0069] The second beam expander, whose incident surface faces the exit surface of the attenuator, is used to expand the modulated second horizontally linearly polarized light to obtain a uniform plane wave.

[0070] A polarizer, with its incident surface facing the exit surface of the second beam expander, is used to modulate a uniform plane wave into linearly polarized light at a preset angle.

[0071] A plane mirror, positioned on the side of the polarizer away from the second beam expander, is used to change the direction of the optical path of linearly polarized light;

[0072] The third beam splitter has its first incident surface facing the exit surface of the imaging system and its second incident surface facing the exit surface of the plane mirror. It is used to interfere the linearly polarized light emitted from the plane mirror with the partially coherent vector beams of each mode obtained by the imaging system to generate multiple interference beams.

[0073] The third lens, whose incident surface faces the exit surface of the third beam splitter, is used to focus each interference beam onto the polarization beam splitter.

[0074] A polarization beam splitter, located at the focal plane of the third lens, is used to split the interference beams into x-polarized beams and y-polarized beams.

[0075] A charge-coupled device is used to capture the interference intensity of x-direction polarized light and y-direction polarized light of partially coherent vector beams of various modes, thereby obtaining the orthogonal polarization field of partially coherent vector beams of various modes.

[0076] The phase image encoding method based on random vector optical complex coherence measurement provided in this application has the following advantages:

[0077] First, this application utilizes a vector partially coherent beam as an information carrier. Leveraging the multi-degree-of-freedom characteristics of the vector partially coherent beam, it can encode information such as polarization of the image, thus overcoming the limitation of scalar partially coherent beams, which can only encode pure amplitude images. Because the parameters of the vector partially coherent beam are strongly coupled, when image information is loaded into the cross-spectral density matrix of the vector partially coherent beam, randomly encoding the image information to arbitrary parameters will lead to repeated encoding due to the coupling between parameters, resulting in information overlap and ultimately preventing the correct image information from being decoded. Therefore, this application loads the image information into the spatial distribution phase difference of the orthogonal complex electric field of an incoherent light source, thereby constructing a cross-spectral density matrix function of a partially coherent vector light field containing image information. This avoids repeated encoding of image information and overcomes interference from complex environments. Then, based on the pattern... The decomposition theory decomposes the cross-spectral density matrix function of the partially coherent vector light field to obtain multiple orthogonal vector electric field mode bases, thereby obtaining partially coherent vector beams of multiple modes on the light source surface. Furthermore, since the information encoding of the vector partially coherent beams has multidimensional coupling, and the image information and the vector coherence characteristics of the beam form a bound mapping, the full-dimensional coherence information of the vector partially coherent beams needs to be measured and inverted during decoding to fully recover the image information. Therefore, this application introduces off-axis holography to measure the interference intensity of the partially coherent vector beams of each mode, thereby obtaining the amplitude and phase information of the two orthogonal polarization fields of each mode's partially coherent vector beams. This allows the construction of the orthogonal polarization fields of each mode's partially coherent vector beams, ultimately obtaining the full-dimensional complex coherence information of the partially coherent vector light field. The image information can then be obtained by performing an inverse transform on the full-dimensional complex coherence information. This application provides, for the first time, an image encoding method based on vector partially coherent light, solving the problem that scalar partially coherent beams can only encode pure amplitude images, and also realizing full-dimensional measurement of the complex coherence of vector partially coherent beams. Attached Figure Description

[0078] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0079] Figure 1 A flowchart of the phase image encoding method based on random vector optical complex coherence measurement provided in this application;

[0080] Figure 2 A schematic diagram illustrating the principle of recovering instantaneous field components from the interference intensity of a partially coherent vector beam, provided for this application;

[0081] Figure 3 A schematic diagram of the beam modulation measurement module in the phase image coding system based on random vector optical complex coherence measurement provided in this application;

[0082] Figure 4 This is a schematic diagram illustrating the measurement results of the full-dimensional complex coherence information of a radially polarized Hermitian-Gaussian correlated Sher mode beam provided in an embodiment of this application; wherein, Figure 4 In (a), the spatial distribution of the four Stokes parameters of a partially radially polarized Hermitian-Gaussian correlated Sher mode beam is shown. Figure 4 (b) in the figure represents the spatial distribution of polarization degree of a partially radially polarized Hermitian-Gaussian correlated Sher mode beam. Figure 4 In the diagram, (c) represents the spatial distribution of the real part of the coherent structure of the radially polarized Hermitian-Gaussian correlated Sherman mode beam. Figure 4 In the diagram, (d) represents the spatial distribution of the imaginary part of the radially polarized Hermitian-Gaussian correlated Sher mode beam. Figure 4 In the figure, (e) represents the intensity correlation distribution of the radially polarized Hermitian-Gaussian correlated Sher mode beam;

[0083] Figure 5 This is a schematic diagram illustrating image encoding, measurement, and decoding using a partially coherent vector beam, as provided in an embodiment of this application; wherein, Figure 5 (a) in the image is the original phase image. Figure 5 In the diagram, (b) represents the real part of the coherent structure function measured during the phase image encoding process. Figure 5 In the figure, (c) represents the imaginary part of the coherent structure function measured during the phase image coding process. Figure 5 In the image, (d) represents the amplitude information of the decoded image. Figure 5 In the image, (e) represents the phase information of the decoded image;

[0084] Explanation of reference numerals in the accompanying drawings: 1. Laser; 2. Linear polarizer; 3. First beam expander; 4. First beam splitter; 5. Second beam splitter; 6. Spatial light modulator; 7. Imaging system; 71. First lens; 72. Two-aperture filter; 73. First half-wave plate; 74. Second half-wave plate; 75. Second lens; 76. Ronchi grating; 8. Attenuator; 9. Second beam expander; 10. Polarizer; 11. Plane mirror; 12. Third beam splitter; 13. Third lens; 14. Polarizing beam splitter; 15. Charge-coupled device. Detailed Implementation

[0085] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0086] Compared to scalar partially coherent beams, random vector beams (also known as vector partially coherent beams) possess a rich set of tunable degrees of freedom, such as light field intensity, polarization (including polarization state and degree of polarization), vector complex coherence, and higher-order intensity correlations. Currently, vector partially coherent beams are widely used in fields such as multi-particle capture and manipulation. Therefore, this application, for the first time, considers using vector partially coherent beams to encode images, leveraging the multi-degree-of-freedom characteristics of vector partially coherent beams to solve the problem that scalar partially coherent beams can only encode pure amplitude images.

[0087] However, determining which parameter in the vector coherent beam to encode image information for encrypted transmission and ensure eventual decoding and reconstruction is another challenge this application needs to overcome. This is because there is a strong coupling relationship between parameters such as the spatial distribution of polarization states, vector coherence, and complex amplitude of polarization components in the vector coherent beam. Therefore, some parameters cannot be independently controlled. If image information is encoded into these parameters, their coupling will lead to information overlap, resulting in the inability to uniquely recover the image during final decoding and causing decoding failure. For example, the phase of the x-polarization component and the phase of the y-polarization component are related through a cross-spectral density matrix. If image information is encoded into the phases of the x-polarization and y-polarization components, their coupling will cause information overlap, making separation impossible during final decoding. Furthermore, some parameters are extremely sensitive to external interference. For instance, the phase of the vector coherence fluctuates drastically with changes in optical path length. If image information is encoded into this parameter, even minor disturbances during beam propagation will completely erase the image information.

[0088] Furthermore, since the information encoding of the vector partially coherent beam has multidimensional coupling, and the image information and the vector coherence characteristics of the beam form a bound mapping, the full-dimensional coherence information of the vector partially coherent beam needs to be measured and inverted during decoding in order to fully recover the image information. However, the measurement of the vector partially coherent beam in the existing technology is mostly limited to the measurement of a single degree of freedom of the optical field. For example, the traditional Young's double-slit interference experiment and wavefront overlapping interference can only measure a single degree of freedom of the optical field and cannot realize the full-dimensional measurement of the complex coherence of the vector partially coherent beam. This is also a problem that needs to be solved in image encoding based on the vector partially coherent beam.

[0089] Please see Figure 1 , Figure 1 The flowchart shown is a phase image encoding method based on random vector optical complex coherence measurement provided in this application. The method specifically includes:

[0090] S10: Load the image information into the spatial distribution phase difference of the orthogonal complex electric field of the incoherent light source. According to the generalized van der Zernike theorem, use the coding system to encode the spatial distribution phase difference into the cross-correlation function of the partially coherent vector light field, and construct the cross-spectral density matrix function of the partially coherent vector light field.

[0091] Specifically, image information can include image phase information, complex amplitude information, polarization information, etc.

[0092] S20: Based on mode decomposition theory, the cross spectral density matrix function of partially coherent vector light fields is decomposed to obtain multiple orthogonal vector electric field mode bases.

[0093] S30: Based on multiple orthogonal vector electric field modes, partially coherent vector beams of multiple modes are obtained on the light source surface; the interference intensity of the partially coherent vector beams of each mode is measured using off-axis holography, thereby constructing the orthogonal polarization field of the partially coherent vector beams of each mode.

[0094] Specifically, by using a spatial modulator and a coaxial interference system, partially coherent vector beams of multiple modes are obtained on the light source surface based on multiple orthogonal vector electric field mode bases, thereby measuring the interference intensity of the partially coherent vector beams of each mode.

[0095] S40: Based on the orthogonal polarization fields of the partially coherent vector beams of all modes, the full-dimensional complex coherence information of the partially coherent vector light field is obtained, and the image information is recovered from the full-dimensional complex coherence information using the decoding system.

[0096] Specifically, the basic principle of step S10 is as follows:

[0097] In the spatial frequency domain, the statistical properties of partially coherent vector beams can be characterized by the cross-spectral density matrix, which represents any two points on a cross section. and The cross spectral density matrix between them can be expressed as:

[0098] ,

[0099] Among them, matrix elements , , Indicates along The electric field components along the direction and along The correlation function between the electric field components in the direction; for a quasi-monochromatic electric field, the cross spectral density matrix in the spatial frequency domain. Ignore angular frequency The impact.

[0100] Furthermore, according to the generalized van der Zernike theorem, the cross spectral density matrix function of any physically realizable partially coherent vector light field can be expressed as:

[0101] ,

[0102] ,

[0103] in, The cross spectral density matrix function representing the partially coherent vector light field; , Represents any two points in a partially coherent vector light field; The anti-angle matrix element represents the polarization matrix of a completely incoherent light source; This indicates the process of constructing a partially coherent vector light field along... The complex conjugate of the system kernel function in the direction; This indicates the process of constructing a partially coherent vector light field along... The system kernel function in the direction; Indicates incoherent light source along Complex conjugate of polarization electric field components in the direction; Indicates incoherent light source along The polarization electric field component in the direction; Represents the Dirac function; , It represents the coordinates of any two points in the spatial domain.

[0104] Based on the aforementioned generalized van der Zernike theorem, this application uses the polarization matrix of an incoherent light source as an information carrier and the system kernel function as an encoding protocol to load image information into the cross-spectral density matrix of a partially coherent vector beam. Then, all information of the cross-spectral density matrix of the partially coherent vector beam is measured, and finally, the image information can be decoded using a correct decoding system.

[0105] Then, due to the non-negative positive definite condition of the light source, i.e. , , It is possible to discover the anti-diagonal elements of an incoherent matrix. and Directly dependent on its diagonal element and If we directly use the diagonal elements of the incoherent matrix and As an information carrier, it can only encode information from two pure amplitude (non-negative) images. However, this application discovers that by designing the orthogonal complex electric field of an incoherent beam in the following form, and then utilizing the cross spectral density matrix function of the aforementioned partially coherent vector light field, the encoding and decoding of complex amplitude or phase images can be achieved. Specifically, the orthogonal complex electric field of the incoherent light source is expressed as:

[0106] ,

[0107] ,

[0108] in, Represents the spatial frequency domain coordinate position vector; This represents the polarization electric field component along the x-direction of an incoherent light source. This represents the polarization electric field component along the y-direction of an incoherent light source. The deterministic amplitude of the orthogonal complex electric field of an incoherent light source; This represents the spatial distribution phase difference that encodes image information.

[0109] Furthermore, encryption keys can be introduced into the system kernel function, such as fractional Fourier transform in a fractional Fourier transform system or a multi-key encryption system with multiple distortion factors superimposed on fractional Fourier transforms. To simplify the coding system, this application fixes the system kernel function to a kernel function with Fourier transform functionality, i.e. , The deterministic amplitude of a partially coherent vector beam is represented in some embodiments of this application. Fixed as Gaussian distribution, This represents the beam width of a Gaussian beam.

[0110] Furthermore, in order to facilitate the generation and measurement of partially coherent vector beams carrying phase information, this application utilizes mode decomposition theory to represent the cross spectral density matrix function of the partially coherent beam as an incoherent superposition of a series of coherent modes.

[0111] Specifically, the pattern decomposition theory is expressed as:

[0112] ,

[0113] in, The cross spectral density matrix function represents the partially coherent vector light field. ; , Represents any two points in a partially coherent vector light field; This represents the number of orthogonal vector electric field mode bases obtained from the decomposition; Indicates the first The weighting coefficients of an orthogonal vector electric field mode basis; , , , Indicates the first A basis of orthogonal instantaneous vector electric field modes, ; express Deterministic amplitude parameter; express Deterministic amplitude parameter; express A random complex screen function; express A random complex screen function.

[0114] Furthermore, and Each of the base edges representing orthogonal vector electric field modes and A series of discrete modes in the direction, namely the instantaneous complex electric field of the partially coherent vector beam in each mode, means that as long as a sufficient set of discrete modes is measured, the complete cross-spectral density information of the partially coherent vector beam can be reconstructed, including the intensity, polarization state and degree of polarization of the partially coherent vector beam, the second-order complex coherent structure and higher-order intensity correlations.

[0115] However, when decomposing the cross spectral density matrix function of a partially coherent vector light field into multiple orthogonal vector electric field mode bases, it is necessary to first accurately generate the random complex screen function that constructs the partially coherent vector beams under each mode, thereby constructing multiple orthogonal vector electric field mode bases.

[0116] Specifically, in step S20, the cross-spectral density matrix function of the partially coherent vector light field is decomposed based on mode decomposition theory to obtain multiple orthogonal vector electric field mode bases, including:

[0117] S200: Using the correlation between partially coherent vector beams of multiple modes in a partially coherent vector light field as constraints, construct constraint functions for controlling the random complex screen functions of the anti-diagonal elements in the cross spectral density matrix under each mode.

[0118] S201: Based on the constraint function of the random complex screen function in each mode, construct a random complex screen function for constructing a partially coherent vector beam in each mode.

[0119] S202: Construct multiple orthogonal vector electric field mode bases based on the random complex screen functions of partially coherent vector beams in each mode.

[0120] Specifically, , , , Indicates the first A basis of orthogonal instantaneous vector electric field modes, ; express Deterministic amplitude parameter; express Deterministic amplitude parameter; express A random complex screen function; express A random complex screen function;

[0121] ,

[0122] ,

[0123] in, Indicates the first Each mode along A random complex screen function with a specific direction; Indicates the first Each mode along A random complex screen function with a specific direction; This represents the system kernel function used to construct a partially coherent vector light field; This represents the first diagonal matrix element of the polarization matrix of a completely incoherent light source; The second diagonal matrix element represents the polarization matrix of a completely incoherent light source;

[0124] ,

[0125] ,

[0126] in, , Four independent Gaussian random numbers with zero mean and one variance; ; for The complex conjugate; Represents the anti-angular element of an incoherent matrix; , Represents the first and second diagonal elements of an incoherent matrix; Represents the imaginary unit;

[0127] The vector electric field mode basis of the nth partially coherent vector beam is represented as:

[0128] ,

[0129] in, , This represents the unit coordinate vector in the x and y directions of the Cartesian coordinate system.

[0130] Furthermore, in actual experiments, only the intensity information of the light beam can be measured, and the instantaneous electric field components cannot be measured. Therefore, this application introduces off-axis holography technology to achieve simultaneous measurement of a series of instantaneous electric field components through a series of interference light intensities.

[0131] The specific principle of off-axis holography is as follows: On the z=0 plane, a beam of uniformly polarized plane wave with a preset angle is introduced into the instantaneous light field to be measured. As a reference light It represents the amplitude of a linearly polarized uniform plane wave at a preset angle, and then detects the instantaneous intensity in the x and y directions.

[0132] Specifically, in the embodiments of this application, measuring the interference intensity of the partially coherent vector beams of each mode using off-axis holography includes:

[0133] Using a linearly polarized uniform plane wave with a preset angle as a reference light, interference light is generated by interfering with partially coherent vector beams of various modes.

[0134] A polarization beam splitter is used to split the interference light into horizontally polarized light and vertically polarized light, and the intensity of the interference light is captured by the first detector and the second detector, respectively.

[0135] For example, the preset angle can be 45°.

[0136] Specifically, the interference intensity of a partially coherent vector beam along the x-direction is expressed as:

[0137] ,

[0138] in, Indicates the first The interference intensity of partially coherent vector beams in each mode along the x-direction; This represents the amplitude of a uniformly polarized plane wave with a preset angle. Indicates the first Orthogonal vector electric field mode basis edges Instantaneous complex electric field in the direction; Represents the operation of the real part; Represents the Gaussian function; Represents the imaginary unit; Represents the light wave vector; Represents the x-coordinate in the Cartesian coordinate system; These represent the angles between the reference plane wave and the signal wave in the x and y directions, respectively.

[0139] The interference intensity of a partially coherent vector beam along the y-direction is expressed as:

[0140] ,

[0141] in, Indicates the first The interference intensity of partially coherent vector beams in each mode along the y-direction; Indicates the first Orthogonal vector electric field mode basis edges Instantaneous complex electric field in the direction.

[0142] Furthermore, based on the interference intensity of the partially coherent vector beams of each mode, the orthogonal polarization fields of the partially coherent vector beams of each mode are constructed as follows:

[0143] Fourier transform is performed on the interference intensity of the partially coherent vector beams of each mode along the x-direction to obtain the Fourier spectrum of the interference field component of the partially coherent vector beams of each mode along the x-direction; Fourier transform is performed on the interference intensity of the partially coherent vector beams of each mode along the y-direction to obtain the Fourier spectrum of the interference field component of the partially coherent vector beams of each mode along the y-direction.

[0144] From the Fourier spectrum of the interference field component of the partially coherent vector beam along the x-direction of each mode, the spectral components of the partially coherent vector beam along the x-direction of each mode are extracted; from the Fourier spectrum of the interference field component of the partially coherent vector beam along the y-direction of each mode, the spectral components of the partially coherent vector beam along the y-direction of each mode are extracted.

[0145] Inverse Fourier transforms are performed on the spectral components of the x-direction and y-direction components of the partially coherent vector beams of each mode to construct the instantaneous x-polarization field and instantaneous y-polarization field of the partially coherent vector beams of each mode.

[0146] For example, taking the field component in the x-direction as an example, such as Figure 2 The figure shows the instantaneous interference light intensity in the x-direction. The Fourier spectrum of the interference light intensity can be obtained, and it can be observed that the Fourier spectrum of the interference light intensity is divided into three parts. The rectangularly labeled part is the Fourier spectrum of the instantaneous field. By shifting it back to the center of a zero-value matrix and finally performing an inverse Fourier transform, the instantaneous x-polarization field can be obtained. Repeating this step will yield a series of instantaneous x-polarization fields. and instantaneous y-polarization field .

[0147] Based on the phase image encoding method based on random vector light complex coherence measurement provided in the above embodiments, this application also provides a phase image encoding system based on random vector light complex coherence measurement to implement the above method, which specifically includes a beam modulation measurement module and a host computer.

[0148] The beam modulation measurement module communicates with the host computer to obtain partially coherent vector beams of multiple modes on the light source surface based on multiple orthogonal vector electric field modes; and uses off-axis holography to measure the interference intensity of the partially coherent vector beams of each mode, thereby constructing the orthogonal polarization field of the partially coherent vector beams of each mode.

[0149] The host computer loads image information into the spatial distribution phase difference of the orthogonal complex electric field of the incoherent light source. According to the generalized van der Zernike theorem, the spatial distribution phase difference is encoded into the cross-correlation function of the partially coherent vector light field using an encoding system, thus constructing the cross-spectral density matrix function of the partially coherent vector light field. Based on mode decomposition theory, the cross-spectral density matrix function of the partially coherent vector light field is decomposed to obtain multiple orthogonal vector electric field mode bases. Based on the orthogonal polarization fields of the partially coherent vector beams of all modes, the full-dimensional complex coherence information of the partially coherent vector light field is obtained. The image information is then recovered from the full-dimensional complex coherence information using a decoding system.

[0150] Furthermore, such as Figure 3 The diagram shows the structure of the beam modulation measurement module, which specifically includes a laser 1, a linear polarizer 2, a first beam expander 3, a first beam splitter 4, a second beam splitter 5, a spatial light modulator 6, an imaging system 7, an attenuator 8, a second beam expander 9, a polarizer 10, a plane mirror 11, a third beam splitter 12, a third lens 13, a polarization beam splitter 14, and a charge-coupled device 15.

[0151] Laser 1 is used to generate a laser beam. For example, the laser is an Nd:YAG laser, and the wavelength of the laser beam is 532 nm.

[0152] Linear polarizer 2 is used to modulate the laser beam into horizontally linearly polarized light.

[0153] The first beam expander 3 is positioned on the side of the linear polarizer 2 away from the laser 1, and is used to expand the horizontally linearly polarized light beam.

[0154] The first beam splitter 4 is located on the side of the first beam expander 3 away from the linear polarizer 2, and is used to split the expanded horizontally linearly polarized light into first horizontally linearly polarized light and second horizontally linearly polarized light.

[0155] The incident surface of the second beam splitter 5 is directly opposite the first horizontally linearly polarized light output surface of the first beam splitter 4, and is used to send the first horizontally linearly polarized light to the spatial light modulator 6, and send the modulated first horizontally linearly polarized light returned by the spatial light modulator 6 to the imaging system 7.

[0156] The incident surface of the spatial light modulator 6 is directly opposite the first exit surface of the second beam splitter 5. It is used to modulate the first horizontally linearly polarized light based on multiple orthogonal vector electric field mode bases using the left and right half screens, and reflect the first horizontally linearly polarized light after each modulation back to the second beam splitter 5.

[0157] Specifically, the left and right halves of the spatial light modulator 6 are based on orthogonal vector electric field mode base edges. direction and along The instantaneous complex electric field in each direction independently controls the electric field in the x-direction and the electric field in the y-direction.

[0158] The imaging system 7 specifically includes a first lens 71, a dual-aperture filter 72, a first half-wave plate 73, a second half-wave plate 74, a second lens 75, and a Ronchi grating 76.

[0159] The incident surface of the first lens 71 is directly opposite the second exit surface of the second beam splitter 5, and is used to focus each modulated first horizontally polarized light.

[0160] The dual-aperture filter 72 is used to filter the first horizontal linearly polarized light emitted from the first lens 71 after focusing, so as to obtain the positive first-order light modulated by the left half screen of the spatial light modulator 6 and the positive first-order light modulated by the right half screen of the spatial light modulator 6 in each first horizontal linearly polarized light.

[0161] The incident light from the first half-wave plate 73 is aligned with the first light source aperture of the dual-aperture filter 72, and is used to modulate each of the first positive first-order beams emitted from the dual-aperture filter 72 into x-polarized light.

[0162] The incident light from the second half-wave plate 74 is aligned with the second light source aperture of the dual-aperture filter 72, and is used to modulate each of the second positive first-order beams emitted from the dual-aperture filter 72 into y-polarized light.

[0163] The second lens 75 is used to focus the x-polarized light and y-polarized light emitted from the first half-wave plate 73 and the second half-wave plate 74.

[0164] The Ronchi grating 76 is located at the focal plane of the second lens 75 and is used to combine the focused x-polarized light and y-polarized light emitted from the second lens 75 to form a partially coherent vector beam of multiple modes on the light source surface.

[0165] For example, the focal length of the first lens 71 The focal length of the second lens 75 It can be 250mm.

[0166] The incident surface of the attenuator 8 is directly opposite the exit surface of the second horizontally linearly polarized light of the first beam splitter 4, and is used to modulate the second horizontally linearly polarized light.

[0167] The incident surface of the second beam expander 9 is directly opposite the exit surface of the attenuator 8, and is used to expand the modulated second horizontally linearly polarized light to obtain a uniform plane wave.

[0168] The incident surface of the polarizer 10 is directly opposite the exit surface of the second beam expander 9, and is used to modulate the uniform plane wave into linearly polarized light at a preset angle.

[0169] The plane mirror 11 is positioned on the side of the polarizer 10 away from the second beam expander 9, and is used to change the optical path direction of linearly polarized light.

[0170] The first incident surface of the third beam splitter 12 faces the exit surface of the imaging system 7, and its second incident surface faces the exit surface of the plane mirror 11. It is used to interfere with the partially coherent vector beams of each mode obtained by the imaging system 7 with the linearly polarized light emitted from the plane mirror 11 to generate multiple interference beams.

[0171] The incident surface of the third lens 13 is directly opposite the exit surface of the third beam splitter 12, and is used to focus each interference beam onto the polarization beam splitter 14.

[0172] For example, the focal length of the third lens 13 It can be 250mm.

[0173] The polarization beam splitter 14 is located at the focal plane of the third lens 13 and is used to split each interference beam into x-polarized light and y-polarized light.

[0174] The charge-coupled device 15 is used to capture the interference intensity of x-polarized light and y-polarized light, thereby obtaining the orthogonal polarization field of the partially coherent vector beams of each mode.

[0175] Specifically, the distance between the third lens 13 and the third beam splitter 12 is The distance between the third lens 13 and the charge-coupled device 15 is 2. .

[0176] Specifically, in some embodiments, two charge-coupled devices 15 can be used to simultaneously capture the interference light intensity of x-polarized light and y-polarized light.

[0177] The effectiveness of the above method and system is verified through a specific example below:

[0178] This embodiment takes a radially polarized Hermitian-Gaussian correlated Sherman mode beam as an example. For a radially polarized Hermitian-Gaussian correlated Sherman mode beam, its deterministic amplitude... , and coherent structure function They are represented as follows:

[0179] ,

[0180] ,

[0181] ,

[0182] in, , Representing Hermitian polynomials and The order of; , It is a constant; Represents coherent structure function The lateral coherence length.

[0183] In this embodiment, , , , .

[0184] Then, the letter "A" was selected as a typical phase diagram, and the phase information was encoded into a partially coherent vector beam to realize phase image encoding, measurement and decoding using a partially coherent vector beam as the information carrier.

[0185] like Figure 4 The diagram shown is a schematic representation of the measurement results of the full-dimensional complex coherence information of a radially polarized Hermitian-Gaussian correlated Sher mode beam provided in an embodiment of this application; wherein, Figure 4 In (a), the spatial distribution of the four Stokes parameters of a partially radially polarized Hermitian-Gaussian correlated Sher mode beam is shown. Figure 4 (b) in the figure represents the spatial distribution of polarization degree of a partially radially polarized Hermitian-Gaussian correlated Sher mode beam. Figure 4 In the diagram, (c) represents the spatial distribution of the real part of the coherent structure of the radially polarized Hermitian-Gaussian correlated Sherman mode beam. Figure 4 In the diagram, (d) represents the spatial distribution of the imaginary part of the radially polarized Hermitian-Gaussian correlated Sher mode beam. Figure 4 In the equation (e), the intensity correlation distribution of the radially polarized Hermetic Gaussian correlated Sher mode beam is given.

[0186] like Figure 5 The diagram shown is a schematic representation of image encoding, measurement, and decoding using a partially coherent vector beam according to an embodiment of this application; wherein, Figure 5 (a) in the image is the original phase image. Figure 5 In the diagram, (b) represents the real part of the coherent structure function measured during the phase image encoding process. Figure 5 In the figure, (c) represents the imaginary part of the coherent structure function measured during the phase image coding process. Figure 5 In the image, (d) represents the amplitude information of the decoded image. Figure 5 In the image, (e) represents the phase information of the decoded image.

[0187] from Figure 5 As can be seen, the original phase image is the letter "A". After encoding based on partially coherent vector beams, the final decoded image phase information is "A". This indicates that the application provides a method that uses partially coherent vector beams as information carriers to achieve encoding, measurement and high-quality decoding of complex-valued images or phase images, overcoming the limitation that traditional partially coherent light can only achieve encoding and encryption of pure amplitude images.

[0188] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0189] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0190] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0191] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0192] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A phase image encoding method based on random vector optical complex coherence measurement, characterized in that, include: Image information is loaded into the spatial distribution phase difference of the orthogonal complex electric field of the incoherent light source. According to the generalized van der Zenik theorem, the spatial distribution phase difference is encoded into the cross correlation function of the partially coherent vector light field using an encoding system, and the cross spectral density matrix function of the partially coherent vector light field is constructed. Based on mode decomposition theory, the cross spectral density matrix function of partially coherent vector light fields is decomposed to obtain multiple orthogonal vector electric field mode bases; Based on multiple orthogonal vector electric field mode bases, partially coherent vector beams of multiple modes are obtained on the light source surface; the interference intensity of the partially coherent vector beams of each mode is measured using off-axis holography, thereby constructing the orthogonal polarization field of the partially coherent vector beams of each mode. Based on the orthogonal polarization fields of partially coherent vector beams of all modes, the full-dimensional complex coherence information of the partially coherent vector light field is obtained, and the image information is recovered from the full-dimensional complex coherence information using a decoding system.

2. The phase image encoding method based on random vector optical complex coherence measurement according to claim 1, characterized in that, The orthogonal complex electric field of an incoherent light source is expressed as: ， ， in, Represents the spatial frequency domain coordinate position vector; This represents the polarization electric field component along the x-direction of an incoherent light source. This represents the polarization electric field component along the y-direction of an incoherent light source. The deterministic amplitude of the orthogonal complex electric field of an incoherent light source; This represents the spatial distribution phase difference that encodes image information; The cross-spectral density matrix function of the partially coherent vector light field is expressed as: ， ， in, The cross spectral density matrix function representing the partially coherent vector light field; , Represents any two points in a partially coherent vector light field; The anti-angle matrix element represents the polarization matrix of a completely incoherent light source; This indicates the process of constructing a partially coherent vector light field along... The complex conjugate of the system kernel function in the direction; This indicates the process of constructing a partially coherent vector light field along... The system kernel function in the direction; Indicates incoherent light source along Complex conjugate of polarization electric field components in the direction; Indicates incoherent light source along The polarization electric field component in the direction; Represents the Dirac function; , It represents the coordinates of any two points in the spatial domain.

3. The phase image encoding method based on random vector optical complex coherence measurement according to claim 1, characterized in that, Based on mode decomposition theory, the cross-spectral density matrix function of the partially coherent vector light field is decomposed to obtain multiple orthogonal vector electric field mode bases, including: Using the correlation between partially coherent vector beams of multiple modes in a partially coherent vector light field as a constraint, a constraint function is constructed for each mode to control the random complex screen function of the anti-diagonal element in the cross spectral density matrix function; Based on the constraint function of the random complex screen function under each mode, a random complex screen function is constructed to construct a partially coherent vector beam under each mode. Based on the random complex screen functions of partially coherent vector beams in each mode, multiple orthogonal vector electric field mode bases are constructed.

4. The phase image encoding method based on random vector optical complex coherence measurement according to claim 3, characterized in that, The pattern decomposition theory is expressed as: ， in, The cross spectral density matrix function represents the partially coherent vector light field. , , , These represent the x and y coordinates in the Cartesian coordinate system, respectively. , Represents any two points in a partially coherent vector light field; This represents the number of orthogonal vector electric field mode bases obtained from the decomposition; Indicates the first The weighting coefficients of an orthogonal vector electric field mode basis; , , , Indicates the first A basis of orthogonal instantaneous vector electric field modes, ; express Deterministic amplitude parameter; express Deterministic amplitude parameter; express A random complex screen function; express A random complex screen function; ， ， in, Indicates the first Each mode along A complex screen function with random orientation; Indicates the first Each mode along A complex screen function with random orientation; This represents the system kernel function used to construct a partially coherent vector light field; This represents the first diagonal matrix element of the polarization matrix of a completely incoherent light source; The second diagonal matrix element represents the polarization matrix of a completely incoherent light source; ， ， Among them, among them, , Four independent Gaussian random numbers with zero mean and one variance; ; for The complex conjugate; Represents the anti-angular element of an incoherent matrix; , Represents the first and second diagonal elements of an incoherent matrix; Represents the imaginary unit; The vector electric field mode basis of the nth partially coherent vector beam is represented as: ， in, , This represents the unit coordinate vector in the x and y directions of the Cartesian coordinate system.

5. The phase image encoding method based on random vector optical complex coherence measurement according to claim 1, characterized in that, By using a spatial modulator and a coaxial interference system, partially coherent vector beams of multiple modes are obtained on the light source surface based on multiple orthogonal vector electric field mode bases.

6. The phase image encoding method based on random vector optical complex coherence measurement according to claim 1, characterized in that, The measurement of interference intensity of partially coherent vector beams in various modes using off-axis holography includes: Using a linearly polarized uniform plane wave with a preset angle as a reference light, interference light is generated by interfering with partially coherent vector beams of various modes. A polarization beam splitter is used to split the interference light into horizontally polarized light and vertically polarized light, and the intensity of the interference light is captured by the first detector and the second detector, respectively.

7. The phase image encoding method based on random vector optical complex coherence measurement according to claim 6, characterized in that, The interference intensity of a partially coherent vector beam along the x-direction is expressed as: ， in, Indicates the first The interference intensity of partially coherent vector beams in each mode along the x-direction; This represents the amplitude of a uniformly polarized plane wave with a preset angle. Indicates the first Orthogonal vector electric field mode basis edges Instantaneous complex electric field in the direction; Represents the operation of the real part; Represents the Gaussian function; Represents the imaginary unit; Represents the light wave vector; Represents the x-coordinate in the Cartesian coordinate system; Represents the y-coordinate in the Cartesian coordinate system; These represent the angles between the reference plane wave and the signal wave in the x and y directions, respectively. The interference intensity of a partially coherent vector beam along the y-direction is expressed as: ， in, Indicates the first The interference intensity of partially coherent vector beams in each mode along the y-direction; Indicates the first Orthogonal vector electric field mode basis edges Instantaneous complex electric field in the direction.

8. The phase image encoding method based on random vector optical complex coherence measurement according to claim 1, characterized in that, The orthogonal polarization fields for constructing partially coherent vector beams for each mode include: Fourier transform is performed on the interference intensity of the partially coherent vector beams of each mode along the x-direction to obtain the Fourier spectrum of the interference field component of the partially coherent vector beams of each mode along the x-direction; Fourier transform is performed on the interference intensity of the partially coherent vector beams of each mode along the y-direction to obtain the Fourier spectrum of the interference field component of the partially coherent vector beams of each mode along the y-direction. From the Fourier spectrum of the interference field component of the partially coherent vector beam along the x-direction of each mode, extract the spectral components of the partially coherent vector beam along the x-direction of each mode; from the Fourier spectrum of the interference field component of the partially coherent vector beam along the y-direction of each mode, extract the spectral components of the partially coherent vector beam along the y-direction of each mode. Inverse Fourier transforms are performed on the spectral components of the x-direction and y-direction components of the partially coherent vector beams of each mode to construct the instantaneous x-polarization field and instantaneous y-polarization field of the partially coherent vector beams of each mode.

9. A phase image coding system based on random vector optical complex coherence measurement, characterized in that, The system is used to implement the phase image encoding method based on random vector optical complex coherence measurement as described in any one of claims 1 to 8, comprising: The beam modulation measurement module communicates with the host computer and is used to obtain partially coherent vector beams of multiple modes on the light source surface based on multiple orthogonal vector electric field modes; and to measure the interference intensity of the partially coherent vector beams of each mode using off-axis holography, thereby constructing the orthogonal polarization field of the partially coherent vector beams of each mode. The host computer loads image information into the spatial distribution phase difference of the orthogonal complex electric field of the incoherent light source. According to the generalized van der Zernike theorem, the spatial distribution phase difference is encoded into the cross-correlation function of the partially coherent vector light field using an encoding system, thus constructing the cross-spectral density matrix function of the partially coherent vector light field. Based on mode decomposition theory, the cross-spectral density matrix function of the partially coherent vector light field is decomposed to obtain multiple orthogonal vector electric field mode bases. Based on the orthogonal polarization fields of the partially coherent vector beams of all modes, the full-dimensional complex coherence information of the partially coherent vector light field is obtained. The image information is then recovered from the full-dimensional complex coherence information using a decoding system.

10. The phase image coding system based on random vector optical complex coherence measurement according to claim 9, characterized in that, The beam modulation measurement module includes: A laser is used to generate a laser beam. Linear polarizers are used to modulate laser beams into horizontally linearly polarized light; The first beam expander is located on the side of the linear polarizer away from the laser and is used to expand the horizontally linearly polarized light. The first beam splitter is located on the side of the first beam expander away from the linear polarizer, and is used to split the expanded horizontal linear polarized light into first horizontal linear polarized light and second horizontal linear polarized light. The second beam splitter has its incident surface facing the first horizontal linearly polarized light output surface of the first beam splitter. It is used to send the first horizontal linearly polarized light to the spatial light modulator and send the modulated first horizontal linearly polarized light returned by the spatial light modulator to the imaging system. A spatial light modulator, whose incident surface faces the first exit surface of the second beam splitter, is used to modulate the first horizontally linearly polarized light based on multiple orthogonal vector electric field mode bases using the left and right half-screens, and reflects the first horizontally linearly polarized light after each modulation back to the second beam splitter. Imaging systems, specifically including: The first lens, whose incident surface is directly opposite the second exit surface of the second beam splitter, is used to focus each modulated first horizontally linearly polarized light. A dual-aperture filter is used to filter the first horizontally linearly polarized light emitted from the first lens after focusing, so as to obtain the positive first-order light modulated by the left half screen of the spatial light modulator and the positive first-order light modulated by the right half screen of the spatial light modulator in each first horizontally linearly polarized light. The first half-wave plate, whose incident light is directly aligned with the first light source aperture of the dual-aperture filter, is used to modulate each of the first positive first-order beams emitted from the dual-aperture filter into x-polarized light. The second half-wave plate, whose incident light is directly aligned with the second light source aperture of the dual-aperture filter, is used to modulate each of the second positive first-order beams emitted from the dual-aperture filter into y-polarized light. The second lens is used to focus the x-polarized and y-polarized light emitted from the first half-wave plate and the second half-wave plate. A Ronchi grating, located at the focal plane of the second lens, is used to combine the focused x-polarized and y-polarized beams emitted from the second lens to form a partially coherent vector beam of multiple modes on the light source surface. An attenuator, whose incident surface faces the second horizontally linearly polarized light exit surface of the first beam splitter, is used to modulate the second horizontally linearly polarized light. The second beam expander, whose incident surface faces the exit surface of the attenuator, is used to expand the modulated second horizontally linearly polarized light to obtain a uniform plane wave. A polarizer, with its incident surface facing the exit surface of the second beam expander, is used to modulate a uniform plane wave into linearly polarized light at a preset angle. A plane mirror, positioned on the side of the polarizer away from the second beam expander, is used to change the direction of the optical path of linearly polarized light; The third beam splitter has its first incident surface facing the exit surface of the imaging system and its second incident surface facing the exit surface of the plane mirror. It is used to interfere the linearly polarized light emitted from the plane mirror with the partially coherent vector beams of each mode obtained by the imaging system to generate multiple interference beams. The third lens, whose incident surface faces the exit surface of the third beam splitter, is used to focus each interference beam onto the polarization beam splitter. A polarization beam splitter, located at the focal plane of the third lens, is used to split the interference beams into x-polarized beams and y-polarized beams. A charge-coupled device is used to capture the interference intensity of x-direction polarized light and y-direction polarized light of partially coherent vector beams of various modes, thereby obtaining the orthogonal polarization field of partially coherent vector beams of various modes.

Images