A method and system for measuring distorted phase based on phase space

Abstract

This invention discloses a method and system for measuring distorted phase based on phase space. The method includes: using a partially coherent beam carrying a distorted phase as the target beam, and spatially localizing it by loading a movable rectangular window onto its light source surface; performing a Fourier transform on the localized beam, and obtaining the Wigner distribution function based on the obtained spectral intensity distribution; determining the peak position of the Wigner distribution function, calculating its offset relative to the window position, and obtaining the distortion factor based on the linear relationship between the offset and the distortion factor, thereby obtaining the distorted phase. This invention eliminates the need for a reference beam, has a simple optical path structure, is easy to operate, avoids complex interferometric measurements and data processing, significantly improves measurement efficiency and accuracy, and is applicable to various partially coherent light sources with non-Gaussian distributions, thus broadening its application range.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical measurement technology, and in particular to a method and system for measuring twisted phase based on phase space. BACKGROUND

[0002] In the field of optical field modulation, phase, as one of the important parameters of optical field modulation, has attracted extensive attention of researchers. Common phase types include conventional phase, vortex phase and twisted phase. Twisted phase, as a special form of phase, is a function of spatial two-point position and cannot be split into the product of two independent one-dimensional coordinate parameters, which indicates that twisted phase only exists in partially coherent light. The size of the twisted phase is usually represented by a twist factor, which is limited by the non-negative positive condition of the cross-spectral density function, and is inversely proportional to the square of the coherent width of the beam cross section. Therefore, in fully coherent light (coherent width tends to infinity), the twist factor tends to zero, further confirming that the twisted phase is a special phase property of partially coherent light. Twisted phase also has chirality characteristics. The inherent asymmetry causes the beam to rotate along the optical axis during propagation and the divergence angle to expand, such as twisted Gaussian Schell-mode beams. Studies have shown that partially coherent light carrying twisted phase exhibits excellent anti-turbulence ability in free-space optical communication; as an illumination light source, it can break through the classical Rayleigh diffraction limit to some extent and improve the resolution of the imaging system; in addition, by modulating the correlation structure of the twisted partially coherent light, beam shaping and other applications can also be achieved.

[0003] However, the current methods for measuring twisted phase are limited, and mainly focus on the principle of interference. There are two main methods in the prior art: the first method is based on the generalized Hambury-Brown and Twyman interference principle, which introduces a reference light to interfere with the measured light beam to obtain the coherent structure distribution of the light beam, and then calculates the twist factor. This method can measure the twist factor, but it requires the introduction of a reference light path, which leads to a complex optical path structure and difficult experimental operation. In addition, it is limited by the Gaussian statistical theorem, which requires the measured light beam to satisfy the Gaussian distribution, greatly limiting the range of applicable light sources. The second method uses a double-hole mask to obtain the far-field diffraction intensity distribution, and analyzes the Fourier spectrum of the intensity distribution to obtain the twist factor. This method avoids the introduction of a reference light, but still requires Fourier transform processing of the intensity information, which increases the computational complexity and the difficulty of data processing, making it difficult to quickly and accurately measure the twisted phase.

[0004] In summary, the existing methods for measuring twisted phase generally have problems such as complex optical path, tedious operation, large amount of calculation, limited scope of application, etc. SUMMARY

[0005] To this end, the technical problem to be solved by the present application is to overcome the problems of the prior art, such as complex optical path, the need to introduce reference light, large amount of calculation, complicated operation and limited applicable light source type.

[0006] To solve the above technical problems, the present application provides a method for measuring the twisted phase based on phase space, comprising the following steps:

[0007] S1: generating a partially coherent light beam carrying a twisted phase as a target light beam, loading a movable rectangular window on the light source surface of the target light beam, and using the rectangular window to spatially localize the target light beam;

[0008] S2: Fourier transforming the target light beam after spatial localization by the rectangular window to obtain its spectral light intensity distribution, and obtaining the Wigner distribution function corresponding to the position of the loaded rectangular window based on the spectral light intensity distribution;

[0009] S3: determining the peak position of the Wigner distribution function, calculating the offset of the peak position relative to the position of the loaded rectangular window, obtaining the size of the twist factor based on the linear relationship between the offset and the twist factor, and obtaining the twisted phase.

[0010] In an embodiment of the present application, in step S2, the specific expression form of the Wigner distribution function is:

[0011] ,

[0012] wherein, is a position variable in phase space, is a direction variable in phase space, is a twist factor, , respectively represent the beam waist radius of the light spot in the x direction and the y direction of the light source surface, , the beam waist radius of the light spot in the x direction and the y direction, is a constant term, , the calculation formula of is:

[0013] ,

[0014] ,

[0015] wherein respectively represent , the transverse coherence width of the light spot in the x direction and the y direction.

[0016] In one embodiment of the present application, in step S3, the linear relationship between the offset and the distortion factor is:

[0017]

[0018] wherein, represents the displacement of the position of the rectangular window loading in the direction, represents the displacement of the peak of the Wigner distribution function in the direction, i.e. the peak offset.

[0019] In one embodiment of the present application, in step S1, the expression formula of the rectangular window is:

[0020]

[0021] wherein, is the position of the rectangular window loading, is the width of the rectangular window.

[0022] In one embodiment of the present application, in step S1, the width of the rectangular window is greater than the transverse coherence width of the partially coherent light beam and less than the beam waist width of the spot formed by the partially coherent light beam on the light source plane.

[0023] Based on the same inventive concept, the present application further provides a method for measuring distorted phase based on phase space, comprising the following steps:

[0024] Step 1: generating a partially coherent light beam by a light source;

[0025] Step 2: loading a distorted phase on the partially coherent light beam by a phase modulation module to generate a target light beam carrying the distorted phase;

[0026] Step 3: loading a movable rectangular window on the light source plane of the target light beam by a window loading module to spatially localize the target light beam;

[0027] Step 4: performing Fourier transform on the spatially localized target light beam by a Fourier transform module;

[0028] Step 5: obtaining the frequency spectrum intensity distribution of the Fourier transformed light beam by a detection module.

[0029] ​​​The processing module is connected with the detecting module, and is used for obtaining a Wigner distribution function corresponding to a position of the rectangular window based on the spectral light intensity distribution, determining a peak position of the Wigner distribution function, calculating an offset of the peak position relative to the position of the rectangular window, obtaining a size of a distortion factor based on a linear relationship between the offset and the distortion factor, and obtaining the distortion phase.

[0030] In an embodiment of the present application, the light source generating module comprises a laser, a polarization adjusting assembly and a beam expander; the polarization adjusting assembly comprises at least a linear polarizer and a half-wave plate, and is used for adjusting a polarization state of an outgoing light beam of the laser; and the beam expander is used for expanding and collimating the adjusted light beam.

[0031] In an embodiment of the present application, the phase modulating module is a first spatial light modulator, which receives the expanded and collimated light beam emitted by the light source generating module, and loads a plurality of random phase holograms to load the distortion phase on the light beam, so as to generate the target light beam carrying the distortion phase.

[0032] In an embodiment of the present application, the system for measuring the distortion phase based on the phase space further comprises a 4f system, which receives the modulated light beam emitted by the first spatial light modulator; and the window loading module is a second spatial light modulator, which is arranged at a back focal plane of a second lens of the 4f system, and is used for loading and movably controlling the rectangular window.

[0033] In an embodiment of the present application, the Fourier transform module comprises a third lens, which receives the light beam modulated by the window and performs Fourier transform; and the detecting module is a charge coupled device, which is arranged at a back focal plane of the third lens, and is used for recording the spectral light intensity distribution after the Fourier transform.

[0034] The above technical solution of the present application has the following advantages compared with the prior art:

[0035] The method and system described in this invention utilize a phase-space-based measurement principle, directly obtaining the Wigner distribution function of the target beam using a windowed Fourier transform. By analyzing the linear offset relationship between the peak position and the position of the applied rectangular window, the distortion factor is accurately and efficiently calculated, thus yielding the distortion phase. This method eliminates the need for a reference optical path, significantly simplifying the optical system structure and reducing the complexity and cost of experimental operations. Furthermore, it avoids complex post-processing calculations such as Fourier transforms, requiring only a simple measurement of the peak displacement for direct solution, greatly improving measurement efficiency and speed. In addition, this invention has no special requirements for the statistical characteristics of the light source, is applicable to partially coherent light with non-Gaussian distributions, expanding its application range and providing new technical means for optical imaging, beam manipulation, and information processing. Attached Figure Description

[0036] 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.

[0037] Figure 1 This is a flowchart illustrating the method for measuring distorted phase based on phase space provided in an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram of the system for measuring distorted phase based on phase space provided in an embodiment of the present invention;

[0039] Figure 3 This is a schematic diagram of a system for measuring distorted phase based on phase space, provided in an embodiment of the present invention.

[0040] Figure 4 This refers to the Wigner distribution function and its corresponding position when the rectangular window is theoretically in different locations, as shown in Experiment 1. A schematic diagram of one-dimensional distribution in the direction;

[0041] Figure 5 The Wigner distribution function and its corresponding values ​​for the rectangular window in different positions in Experiment 1 are shown below. A schematic diagram of one-dimensional distribution in the direction;

[0042] Figure 6 This is a schematic diagram showing the average values ​​of different torsion factors measured in Experiment 1;

[0043] Figure 7 This is a schematic diagram showing the simulation and experimental results of the Wigner distribution function under different distortion factors in Experiment 1.

[0044] The description of the drawings is as follows: 1, laser; 2, linear polarizer; 3, half-wave plate; 4, beam expander; 5, first spatial light modulator; 6, first beam splitter; 7, first lens; 8, single-hole filter; 9, second lens; 10, second beam splitter; 11, second spatial light modulator; 12, third lens; 13, charge-coupled device. DETAILED DESCRIPTION

[0045] The present application will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it.

[0046] Example 1:

[0047] As shown in the drawings, the present application provides a method for measuring twisted phase based on phase space, comprising the following steps: Figure 1 S1: generate a partially coherent light beam carrying twisted phase as a target light beam, load a movable rectangular window on the light source surface of the target light beam, and use the rectangular window to spatially localize the target light beam;

[0048] S2: Fourier transform the target light beam after spatial localization by the rectangular window to obtain its spectral light intensity distribution, and obtain the Wigner distribution function corresponding to the position of the loaded rectangular window based on the spectral light intensity distribution;

[0049] S3: determine the peak position of the Wigner distribution function, calculate the offset of the peak position relative to the position of the loaded rectangular window, which can be obtained by calculating the displacement of the peak of the Wigner distribution function, and based on the linear relationship between the offset and the twist factor, obtain the size of the twist factor, thereby obtaining the twisted phase.

[0050] The present application significantly simplifies the structure of the optical system by directly loading a movable rectangular window on the light source surface to spatially localize the target light beam, and enhances the applicability to partially coherent light beams; by Fourier transforming the spatially localized light beam and obtaining its spectral light intensity distribution, and then directly obtaining the Wigner distribution function, this process avoids complex interference measurement or multiple scanning, effectively reduces data acquisition and processing time, and improves measurement efficiency; by determining the peak position of the Wigner distribution function and calculating its offset relative to the window position, and using the explicit linear relationship between the offset and the twist factor, the twist factor can be accurately calculated, and then the twisted phase is obtained.

[0051]

[0052] ​Specifically, in step S1, a partially coherent beam carrying a twisted phase is generated as a target beam, typically in the form of a twisted Gaussian Schell-mode beam, and the cross-spectral density function of the target beam at the source plane can be expressed as

[0053]

[0054] wherein , represent two position coordinates of the source cross-section, , represent the position of the source plane , the beam waist radius of the spot in the , direction, , the transverse coherence width of the spot in the direction,

[0055] and

[0056]

[0057] wherein is the position of the rectangular window loading, is the width of the rectangular window.

[0058] The width of the rectangular window needs to be selected to be greater than the transverse coherence width of the partially coherent beam at the source plane and less than the beam waist width of the spot formed by the partially coherent beam at the source plane, so as to ensure the accuracy of subsequent measurement.

[0059] The target beam is spatially localized by the rectangular window, and the light field is constrained to a specific position .

[0060] Further, in step S2, the target beam after spatial localization by the rectangular window is subjected to Fourier transform to obtain a spectral light intensity distribution, which directly corresponds to the measurement value of the Wigner distribution function in the phase space.

[0061] The phase space is an abstract space used to completely describe the light field, and simultaneously contains spatial (spatial position) and directional (frequency) information, and its variables include position variable and directional variable , the position variable describes the specific position of the light field in the phase space, and the directional variable describes the propagation direction of the light field at the position. ​​

[0062] According to the definition of Wigner distribution function, the transformation relation between the cross-spectral density function and the Wigner distribution function is:

[0063] ,

[0064] where, is the Wigner distribution function in phase space, is the center of the two position vectors in the spatial domain, is the difference of the two position vectors in the spatial domain.

[0065] Substituting the cross-spectral density function into the transformation formula, the specific expression of the Wigner distribution function of the twisted Gaussian Schell-model in the phase space is:

[0066] ,

[0067] where, is a constant term, , The calculation formula of is:

[0068] ,

[0069] .

[0070] is the Wigner distribution of the twisted Gaussian Schell-model, which is also a distribution that can be measured in experiments. From the last two terms of the equation, it can be seen that the presence of the twist factor causes classical entanglement between the position variable and the direction variable, for example, and That is, the twist factor makes the Wigner distribution function cannot be separated into the product of the direction variable function and the position variable function; at the same time, the peak position of the Wigner distribution is related to the position variable and the size of the twist factor, that is, if the position variable and the Wigner distribution are known in experiments, the size of the twist factor can be measured.

[0071] A rectangular window is introduced at the light source plane to localize the spatial position at a certain point, and the Wigner distribution of the point is directly measured by using the Fourier transform property of the lens. The Wigner distribution measured at the back focal plane of the lens is actually the convolution of the Wigner distribution of the light source and the Wigner distribution of the window, and the specific expression is

[0072] ,

[0073] where represents the Wigner distribution actually measured at the back focal plane of the lens, represents the Wigner distribution of the added window, represents a convolution operation.

[0074] From the above, the size of the selected window is larger than the transverse coherence width of the light source and smaller than the beam waist width of the light spot, so The integral has little influence, and the measured Wigner distribution can be approximately regarded as the Wigner distribution of the light source, that is .

[0075] The loading position of the window, that is, the position variable of the Wigner function at this point The position of the window is continuously moved in the entire two-dimensional plane, that is, the entire four-dimensional Wigner distribution of the light source in space can be scanned.

[0076] Further, in step S3, the peak position of the Wigner distribution function is determined From the expression of the Wigner distribution function, it can be seen that the peak position is related to the position variable and the size of the twist factor. The existence of the twist factor causes the coupling (classical entanglement) between the position variable and the direction variable, resulting in the shift of the peak value of the Wigner distribution function. The shift amount of the peak position relative to the reference position is calculated. By changing the loading position of the rectangular window (for example, shifting in the direction), and respectively measuring the positions of the corresponding Wigner distribution peaks in the direction, the shift amount can be calculated. Specifically, the displacement of the window in the direction is , and the displacement of the peak of the corresponding Wigner distribution function in the direction is , that is, the peak shift amount. Based on the linear relationship between the shift amount and the twist factor:

[0077] ,

[0078] The size of the twist factor can be calculated, and after the size of the twist factor is obtained, the twist phase can be directly obtained through its mathematical expression. The essence of the twist phase is the phase term in the cross-spectral density function, and its specific form is: , wherein , respectively represent two position coordinates of the cross section of the light source, and are known items.

[0079] Embodiment two:

[0080] As Figure 2As shown, based on the same inventive concept as in Embodiment One, the present application provides a system for measuring a distorted phase based on a phase space, for implementing the method for measuring a distorted phase based on a phase space as described in Embodiment One, comprising the following modules:

[0081] a light source generation module for generating a partially coherent light beam;

[0082] a phase modulation module, optically connected with the light source generation module, for loading a distorted phase on the partially coherent light beam to generate a target light beam carrying the distorted phase;

[0083] a window loading module, arranged at a light source surface of the target light beam, for loading a movable rectangular window to spatially localize the target light beam;

[0084] a Fourier transform module for performing Fourier transform on the target light beam spatially localized by the window loading module;

[0085] a detection module for obtaining a frequency spectrum light intensity distribution after Fourier transform;

[0086] a processing module, connected with the detection module, for obtaining a Wigner distribution function corresponding to a position of the rectangular window loading based on the frequency spectrum light intensity distribution, determining a peak position of the Wigner distribution function, calculating an offset of the peak position relative to the position of the rectangular window loading, obtaining a size of a distortion factor based on a linear relationship between the offset and the distortion factor, and thus obtaining the distorted phase.

[0087] As shown, Figure 3 the light source generation module is used to generate a partially coherent light beam. Specifically, this module includes a laser 1, a wavelength of 532nm laser is used in the present application, for generating an initial linearly polarized laser beam; a polarization adjustment assembly, including a linear polarizer 2 and a half-wave plate 3, is arranged in the light path of the laser 1, for fine adjustment of the polarization state of the laser 1 output beam, so that its polarization direction is consistent with the preferred response direction of the subsequent spatial light modulator, thereby maximizing the modulation efficiency and suppressing stray light; a beam expander 4 is used to receive the polarized light beam after polarization adjustment and perform beam expansion and collimation processing, outputting an extended light beam with a distribution close to a plane wave, providing a uniform light field distribution for subsequent phase modulation.

[0088] The system for measuring a distorted phase based on a phase space further comprises a first beam splitter 6. It is arranged in the light path after the beam expander 4, for splitting the beam expanded and collimated into two paths: one is reflected light, and the other is transmitted light.

[0089] The light source generation module is the light field source of the whole system, and its core function is to generate and prepare the required partially coherent light beam. The laser 1 provides the initial laser with high spatial and temporal coherence. The polarization adjustment assembly adjusts the polarization state of the light beam by fine adjustment, so that it matches the liquid crystal orientation of the subsequent spatial light modulator, maximizes the modulation efficiency and suppresses unnecessary reflected and scattered light, ensures efficient use of light energy and signal-to-noise ratio of the system. The beam expander 4 expands the fine laser beam into a wide beam with good collimation, providing the necessary light field coverage for uniform phase modulation and spatial scanning. This module provides the initial light field for all subsequent operations.

[0090] Further, the phase modulation module is connected with the light source generation module in the optical path, and is used for loading a twisted phase on the partially coherent light beam to generate a target light beam carrying the twisted phase. Specifically, the module is a first spatial light modulator 5 which receives the reflected light split by the first beam splitter 6.

[0091] The first spatial light modulator 5 loads a plurality of (for example, 3000) random phase holograms generated by the pseudo-mode method to modulate the phase of the incident light beam, thereby loading the required twisted phase on the light beam to generate the target light beam carrying the twisted phase. A typical form of the target light beam is a twisted Gaussian Schell-mode light beam.

[0092] In the embodiment of the present application, the generated twisted Gaussian Schell-mode light beam has the following parameters: beam waist width , transverse coherence width , and the twist factor is the quantity to be measured. The present application selects the twist factor as , , , , and for measurement.

[0093] Based on the theory of partially coherent light, a series of random phase patterns generated by the pseudo-mode method are loaded for phase modulation by the first spatial light modulator 5. By controlling the statistical properties of these random phase patterns, the coherence structure (such as the coherence width) of the output light beam can be adjusted, and specific phase relationships can be introduced in the process, so that the required twisted phase can be accurately loaded.

[0094] Further, the system based on the measurement of the twisted phase in the phase space further comprises a 4f system for receiving the modulated light beam emitted by the first spatial light modulator 5 and performing filtering and transmission. Specifically, the 4f system is composed of two first lenses 7 and second lenses 9 with the same focal length (for example, f=250mm) in series.

[0095] A single pinhole filter 8 is placed at the back focal plane of the first lens 7, which is used to filter out the stray light and high order diffraction in the modulated light beam, and to retain the desired +1st order diffraction, to retain the desired diffraction order, and to ensure the quality of the light beam. The filtered light beam is transformed by the second lens 9, and the light source plane of the target light beam is accurately formed at the back focal plane of the second lens 9.

[0096] The first lens 7 Fourier transforms the complex light field modulated by the first spatial light modulator 5, and converts the spatial distribution information of the light field to the frequency spectrum plane. The single pinhole filter 8 located at the focal plane plays a spatial filtering role, filters out the high-order diffraction spots and optical noise caused by the pixel structure of the spatial light modulator, and only allows the pure +1st order diffraction light to pass, greatly improving the quality and signal-to-noise ratio of the outgoing light beam. The second lens 9 inversely Fourier transforms the filtered frequency spectrum, and the cleaned and modulated light field is reproduced at the back focal plane of the second lens 9, which is defined as the light source plane.

[0097] Further, the system based on phase space measurement and phase distortion further comprises a second beam splitter 10. The second beam splitter 10 is arranged after the 4f system, and is used to guide the formed target light beam to a subsequent measurement light path.

[0098] Further, the window loading module is arranged at the light source plane of the target light beam, and is used to load a movable rectangular window to spatially localize the target light beam. Specifically, the window loading module is a second spatial light modulator 11, which is arranged at the back focal plane of the second lens 9 of the 4f system, i.e., is accurately located at the light source plane of the target light beam, and receives the light beam guided by the second beam splitter 10. The second spatial light modulator 11 loads the rectangular window function, which is expressed as , wherein is the position of the rectangular window loading, is the width of the rectangular window.

[0099] By programming control of the hologram loaded on the second spatial light modulator 11, the two-dimensional position of the rectangular window on the light source plane can be movably controlled, i.e., the position is changed, so that the spatial localization scanning of different positions of the light beam is realized.

[0100] The window width needs to be selected according to the parameters of the target light beam, and needs to be greater than the transverse coherence width of the light beam and less than the waist width of the light spot (for example ), so as to ensure that the convolution approximation is established, so that the measurement is accurate.

[0101] The module is arranged at the light source side of the target light beam, and is used for loading and movably controlling a rectangular window to realize spatial localization of the light beam.

[0102] Further, the Fourier transform module is used for performing Fourier transform on the target light beam after the spatial localization by the window.

[0103] Specifically, the module comprises a third lens 12, and the focal length of the third lens 12 is selected as f=250mm. The third lens 12 receives the light beam emitted by the second spatial light modulator 11 and modulated by the rectangular window, and performs optical Fourier transform on the light beam.

[0104] The module performs optical transformation from the spatial domain to the frequency domain, and according to the Fourier optical principle, the front and back focal planes of a thin lens satisfy the Fourier transform relationship. The third lens 12 performs Fourier transform on the localized light field after the window interception by the second spatial light modulator 11, and maps the direction information of the light field to the spatial distribution.

[0105] Further, the detection module is used for acquiring the frequency spectrum light intensity distribution after the Fourier transform. Specifically, the module is a charge coupled device 13, and the charge coupled device 13 is arranged at the back focal plane of the third lens 12, that is, the Fourier spectrum plane. The charge coupled device 13 is used for accurately recording the two-dimensional frequency spectrum light intensity distribution formed after the Fourier transform, and the distribution directly corresponds to the measurement value of the Wigner distribution function in the phase space.

[0106] Optionally, the present application selects a CCD as the charge coupled device 13, and the high resolution, high dynamic range and linear response characteristics of the CCD camera ensure that the details and peak position of the distribution can be accurately captured, and the digital output can provide an accurate and reliable data source for the subsequent processing module.

[0107] The processing module is electrically connected with the detection module, and is used for receiving and processing the light intensity data recorded by the charge coupled device 13, including: based on the frequency spectrum light intensity distribution, the frequency spectrum light intensity distribution is directly identified as the Wigner distribution function corresponding to the current rectangular window loading position . The peak position of the Wigner distribution function is determined . The displacement of the peak value of the Wigner distribution corresponding to the window movement and the measurement is determined in the direction, that is, the peak offset. Based on the explicit linear relationship between the offset and the distortion factor , the size of the distortion factor is calculated.

[0108] Due to the mathematical form of the distorted phase Given that spatial coordinates are variables, the distortion factor can be measured. This is equivalent to completely determining the distorted phase.

[0109] Experiment 1:

[0110] To verify whether the experiment matches the theory, this invention first simulates the measurement process of the distortion factor, and the specific results are as follows: Figure 4 As shown, where Figure 4 (a) and Figure 4 (b) shows the Wigner distribution function of the distorted Gaussian Sher modulus at the rectangular window positions R=(0,0.2) and R=(0,0), respectively. Figure 4 (c) is for both in The distribution is one-dimensional along the direction. The distortion factor can be obtained from the peak offset.

[0111] like Figure 5 As shown in the figure, in the experiment, the magnitude of the distortion factor can be determined by observing the shift in the peak value of the Wigner distribution when the window position is changed. Figure 5 (a) and Figure 5 (b) The experimental distortion factor is respectively When the window position is R=(0,0.2) and R=(0,0), the Wigner distribution function of the distorted Gaussian Sher modulus is given. Figure 5 (c) is for both in The distribution is one-dimensional in the direction, and the average value is calculated for nine different locations. This is very close to the theoretical value of the distortion factor. For example... Figure 6 As shown, the average value (u_Average) of different distortion factors is measured. Ten sets of data are measured for each distortion factor, and it can be observed that the average value of each set of data is close to the theoretical value (u_Theory). The window scans across the entire two-dimensional plane, which can recover the four-dimensional Wigner distribution at all locations.

[0112] like Figure 7 As shown, the simulation and experimental results of the Wigner distribution function are compared under different distortion factors. Figure 7 (a) Figure 7 (b) and Figure 7 (c) represents the distortion factor, respectively , and Simulation results at that time, Figure 7 (d) Figure 7 (e) and Figure 7 (f) represents the distortion factor, respectively , and The experimental results at that time.

[0113] Contrast Figure 7 (a) and Figure 7 (b), or Figure 7 (b) and Figure 7 (c), the rotation phenomenon of the Wigner distribution function indicates that the twist factor causes the classical entanglement between the position variable and the direction variable.

[0114] Those skilled in the art will understand that embodiments of the present application can be provided as methods, systems, or computer program products. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0115] The present application is described in reference to the flowchart and / or block diagrams of the methods, apparatus (systems) and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagrams, and combinations of flows and / or blocks in the flowchart 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, create means for implementing the functions specified in the flowchart and / or block diagrams block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified by the flow or flows and / or block or blocks.

[0116] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions means which implement the function specified in the flowchart and / or block diagrams flow or flows and / or block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified by the flow or flows and / or block or blocks.

[0117] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagrams flow or flows and / or block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified by the flow or flows and / or block or blocks.

[0118] Obviously, the above embodiments are merely example for clearly illustrating, and are not limitation to the embodiments. For ordinary skilled in the art, other different forms of changes or variations can be made on the basis of the above description. Here, all the embodiments need not and can not be exhausted. The obvious changes or variations derived therefrom are still within the scope of the present invention.

Claims

1. A method for measuring a distorted phase based on a phase space, characterized by, The method comprises the following steps: S1: generating a partially coherent light beam carrying a distorted phase as a target light beam, loading a movable rectangular window on a light source surface of the target light beam, and spatially localizing the target light beam by using the rectangular window, wherein the rectangular window has an expression formula of: ， wherein a position for the rectangular window to be loaded, a width of the rectangular window; S2: performing Fourier transform on the target light beam after spatial localization by the rectangular window to obtain a spectral light intensity distribution, and obtaining a Wigner distribution function corresponding to a position of the rectangular window based on the spectral light intensity distribution, wherein the Wigner distribution function has a specific expression form of: ， wherein, is a position variable in phase space, is a direction variable in phase space, is a twist factor, , represent the light source plane , is the beam waist radius of the spot in the direction, is a constant term, , The calculation formula of is: ， ， wherein , respectively represent , lateral coherence width of the light spot in the direction S3: determining the peak position of the Wigner distribution function, calculating the offset of the peak position relative to the position of the rectangular window loading, which can be obtained by calculating the displacement of the peak of the Wigner distribution function, obtaining the size of the distortion factor based on the linear relationship between the offset and the distortion factor, thereby obtaining the distortion phase, wherein the linear relationship between the offset and the distortion factor is: ， wherein a displacement of the position of the rectangular window loading in direction, a displacement of the peak of the Wigner distribution function in direction, i.e. a peak shift.

2. The method for measuring a twist phase based on a phase space according to claim 1, characterized by: In step S1, the width of the rectangular window is greater than the transverse coherence width of the partially coherent light beam and less than the beam waist width of a light spot formed by the partially coherent light beam on the light source surface.

3. A system for measuring a distorted phase based on a phase space for implementing the method of measuring a distorted phase based on a phase space according to any one of claims 1 to 2, characterized in that The system comprises the following modules: A light source generation module for generating a partially coherent light beam; A phase modulation module connected in an optical path of the light source generation module for loading a distorted phase on the partially coherent light beam to generate a target light beam carrying the distorted phase; A window loading module arranged on a light source surface of the target light beam for loading a movable rectangular window to spatially localize the target light beam; A Fourier transform module for performing Fourier transform on the target light beam after spatial localization by the window loading module; A detection module for obtaining a spectral light intensity distribution after Fourier transform; A processing module connected with the detection module for obtaining a Wigner distribution function corresponding to a position of the rectangular window based on the spectral light intensity distribution, determining a peak position of the Wigner distribution function, calculating an offset of the peak position relative to the position of the rectangular window, obtaining a size of a distortion factor based on a linear relationship between the offset and the distortion factor, and thus obtaining the distorted phase.

4. The system for measuring twist phase based on phase space according to claim 3, characterized in that: The light source generation module comprises a laser, a polarization adjustment assembly, and a beam expander; the polarization adjustment assembly at least includes a linear polarizer and a half-wave plate for adjusting a polarization state of an outgoing light beam of the laser, and the beam expander is used for expanding and collimating the adjusted light beam.

5. The system for measuring twist phase based on phase space according to claim 3, characterized in that: The phase modulation module is a first spatial light modulator which receives the expanded and collimated light beam emitted by the light source generation module, and loads a plurality of random phase holograms to load a distorted phase on the light beam, thereby generating the target light beam carrying the distorted phase.

6. The system for measuring twist phase based on phase space according to claim 3, characterized in that: The system for measuring a distorted phase based on a phase space further comprises a 4f system which receives the modulated light beam emitted by the first spatial light modulator; the window loading module is a second spatial light modulator arranged at a back focal plane of a second lens of the 4f system for loading and movably controlling the rectangular window.

7. The system for measuring twist phase based on phase space according to claim 3, characterized in that: The Fourier transform module comprises a third lens which receives the light beam modulated by the window and performs Fourier transform; and the detection module is a charge coupled device arranged at a back focal plane of the third lens for recording the spectral light intensity distribution after Fourier transform.

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