Turbulence-robust angular rate measurement method and system based on partially coherent deep learning

Abstract

This invention relates to the field of angular velocity measurement technology, and discloses an anti-turbulent angular velocity measurement system and method based on partially coherent deep learning. The system includes: generating partially coherent light from an emitted laser and incident it onto a spatial light modulator; the emitted light then illuminates the surface of a rotating object through a turbulent environment; real-time acquisition of the light intensity image of the rotating object and its transmission to a partially coherent deep learning model to predict the turbulence phase expansion coefficient; generating a turbulence compensation phase based on the turbulence phase expansion coefficient and real-time loading it onto the spatial light modulator on the partially coherent light source surface to compensate the light source in real time; real-time acquisition of the compensated light intensity image of the rotating object; extraction of the light intensity time-domain signal to generate a corrected spectrum; extraction of the frequencies corresponding to the characteristic peaks in the corrected spectrum; and obtaining the rotational angular velocity of the rotating object according to the formula corresponding to the frequency and angular velocity. This invention enables high-precision angular velocity measurement of rotating objects in complex environments.

Description

Technical Field

[0001] This invention relates to the field of angular velocity measurement technology, and in particular to an anti-turbulent angular velocity measurement system and method based on partially coherent deep learning. Background Technology

[0002] The rotating Doppler effect is a phenomenon where the frequency shift of reflected or transmitted light occurs after a beam of light with an axially symmetrical phase or amplitude distribution interacts with a rotating object. This frequency shift is proportional to the object's angular velocity and offers significant advantages such as non-contact operation, high precision, and fast response. The discovery of the rotating Doppler effect has provided an effective and efficient method for non-contact measurement of the angular velocity of rotating objects. In 2013, Padgett's research team at the University of Glasgow in the UK pioneered the experimental measurement of angular velocity using the rotating Doppler frequency shift of optical vortices. The rotating Doppler effect angular velocity measurement technology based on optical vortices has since become a research hotspot in this field.

[0003] The coherence of a light source is one of the core characteristics of optical detection. Partially coherent light characterizes the correlation between different spatial positions of the light source. In the field of optical imaging, partially coherent light can suppress speckle effects and improve image quality; in the field of optical communication, it can suppress turbulence disturbances and improve the stability of communication systems. In 2021, the Anderson team at the University of Colorado used a projector to generate partially coherent petal-shaped beams to measure the rotational speed of an amplitude-type rotating object, experimentally verifying for the first time that the realization of the rotating Doppler effect does not depend on the complete coherence of the light source. Subsequent research further found that partially coherent light exhibits excellent properties such as anti-obstruction and support for off-axis measurement in rotating Doppler effect measurement, and also shows good robustness in weakly turbulent environments, making it a preferred detection light source for rotating Doppler velocimetry under complex transmission conditions. In existing technologies, methods for measuring rotational speed using the rotating Doppler effect can be mainly divided into the following categories according to the differences in light source characteristics and system implementation: The first method, based on the superposition of coherent light sources with conjugate orbital angular momentum (OAM) modes, is described in the paper: Lavery M, Speirits F, Barnett S, et al. (2013) “Detection of a spinning object using light's orbital angular momentum.” Science, 341(6145): 537. This method generates ± The classic method of rotating Doppler velocimetry is to use a topologically charged conjugate OAM superimposed petal beam to illuminate the rough surface of a rotating object, collect the beat frequency signal of the scattered light and perform a Fourier transform to extract the frequency shift features and invert the rotational speed of the object.

[0004] The second method is a quantum long-distance velocimetry method based on higher-order photonic orbital angular momentum, from the paper: Chen Lixiang, Zhang Yuanying. (2015). Research progress on preparation, control and sensing applications of higher-order photonic orbital angular momentum. Acta Physica Sinica, 64 (16):164210. This method transforms the polarization-orbit entanglement state of two photons into a higher-order OAM quantum entanglement state through polarization-orbit entanglement transformation technology. Utilizing the rotational symmetry of the higher-order OAM beam height, combined with the rotational Doppler effect, and with the aid of high-resolution spatial light modulators, multimode optical fibers and photodetectors, the frequency shift signal of the scattered light from the rotating object is detected. After Fourier transform processing, the frequency shift characteristics are extracted to invert the angular velocity of the object, realizing high-precision quantum-level rotational velocimetry over long distances.

[0005] The third method is a rotating Doppler velocities method based on spatially incoherent light sources, from the paper: Anderson A, Strong F, Heffernan B, et al. (2021) “Observation of the rotational Dopplershift with spatially incoherent light.” Optics Express, 29(3): 4058. This method uses a projector to generate an incoherent petal-shaped intensity pattern, which is imaged onto the rotating target. The time-domain signal of the reflected light is collected by a photodetector, and the rotating Doppler frequency shift is extracted by spectral analysis, thus breaking through the dependence of traditional schemes on coherent light sources.

[0006] However, these methods rely on precise optical axis alignment and cannot achieve off-axis measurements. Even slight optical axis misalignment can cause distortion in the velocity measurement signal, affecting the accuracy of frequency shift feature extraction. Furthermore, whether it is the partially coherent Doppler velocimetry technology that supports off-axis misalignment or the three methods mentioned above, they all lack effective atmospheric turbulence disturbance compensation and signal processing schemes. This leads to problems such as peak drift, signal broadening, and a sharp drop in signal-to-noise ratio in turbulent environments, making accurate measurements impossible. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide an anti-turbulent angular velocity measurement system and method based on partially coherent deep learning. It retains the advantage of partially coherent rotating Doppler measurement technology in supporting off-axis misalignment, and combines deep learning to accurately compensate for the distortion of partially coherent light sources under atmospheric turbulence disturbance and efficiently optimize the disturbed signal, so as to realize high-precision angular velocity measurement of rotating objects in complex environments.

[0008] To address the aforementioned technical problems, this invention provides an anti-turbulent angular velocity measurement system based on partially coherent deep learning, comprising a laser, a beam expander, a three-hole mask, a 4f system, a rotating frosted glass, a spatial light modulator, and a charge-coupled device. The laser is used to generate an outgoing laser beam. After being expanded and collimated by the beam expander, the outgoing laser beam is spatially modulated by the three-hole mask to form a specific spatial coherent structure. The specific spatial coherent structure is projected onto the rotating frosted glass by the 4f system. With the help of the random process of the rotating frosted glass and the Fourier transform process of the lens, a partially coherent light with a hexagonal lattice symmetric coherent structure is generated. After collimation, the coherent light is incident on the spatial light modulator. After passing through the turbulent environment, the emitted light source is transmitted through the 4f system and then illuminates the surface of the rotating object. After low-pass filtering by the 4f system, the light is imaged onto the charge-coupled device, thus completing the acquisition of the light intensity image of the rotating object's imaging surface. The acquired light intensity images are transmitted in real time to a partially coherent deep learning model to predict the turbulence phase expansion coefficient of the current turbulence and transmit it to a spatial light modulator. A turbulence compensation phase, conjugate with the distortion phase introduced by atmospheric turbulence, is generated based on the turbulence phase expansion coefficient. This turbulence compensation phase is used to compensate the light source in real time to obtain a compensated light source. The compensated light source is transmitted again along the original optical path and imaged onto the charge-coupled device, completing the acquisition of a single-frame compensated light intensity image of the rotating object's imaging surface. After acquiring a sequence of multiple frames of compensated light intensity images of the rotating object's imaging surface, the time-domain signal of the light intensity from the image sequence is extracted and subjected to a fast Fourier transform to generate a corrected spectrum. The frequencies corresponding to the characteristic peaks in the corrected spectrum are extracted, and the rotational angular velocity of the rotating object is obtained according to the formula corresponding to frequency and angular velocity.

[0009] This invention also provides an anti-turbulent angular velocity measurement method based on partially coherent deep learning, comprising: The emitted laser light is scattered to generate partially coherent light, which is then incident on a spatial light modulator. After passing through a turbulent environment, the emitted light source illuminates the surface of the rotating object. Real-time acquisition of rotating objects The light intensity image of the imaging surface is transmitted in real time to a partially coherent deep learning model to predict the turbulence phase expansion coefficient of the current turbulence. Based on the turbulence phase expansion coefficient, a turbulence compensation phase conjugate with the distortion phase introduced by atmospheric turbulence is generated and loaded in real time onto the spatial light modulator of the partially coherent light source surface to perform real-time compensation of the light source. Real-time acquisition of compensated rotating objects The light intensity image of the imaging surface is used to extract the light intensity time domain signal to generate a corrected spectrum. The frequency corresponding to the characteristic peak in the corrected spectrum is extracted, and the rotational angular velocity of the object is obtained according to the corresponding formula of frequency and angular velocity.

[0010] Furthermore, the step of generating partially coherent light from the emitted laser by scattering specifically involves the emitted laser passing through a three-hole mask and a rotating frosted glass to generate a partially coherent light source with a hexagonal lattice periodic coherent structure. The expression for the complex coherence of the partially coherent light source in polar coordinates is derived by Fourier transform of the spatial distribution of the light-transmitting mask with the vertices of an equilateral triangle at the center of the three holes. The coherent structure of the light-transmitting mask with the vertices of an equilateral triangle at the center of the three holes coincides with its own distribution every 60° rotation, exhibiting a hexagonal lattice periodicity.

[0011] Furthermore, the expression for the complex coherence of the partially coherent light source in polar coordinates is: , In the formula, Let be the complex coherence of the partially coherent light source, and exp be an exponential function. and Let be the two-dimensional position vector of any two points on the surface of the rotating object. , , for Radial polar diameter, for polar angle, for Radial polar diameter, for The polar angle; The center-to-center distance between two adjacent holes in a light-transmitting mask in which the vertices of an equilateral triangle are arranged at the center of the three holes; This represents the spatial coherence length of the corresponding beam. The incident light wavelength, This is the focal length of the Fourier lens.

[0012] Furthermore, the emitted light source illuminates the surface of the rotating object after passing through a turbulent environment, including: The random fluctuations in refractive index caused by atmospheric turbulence are equivalent to a spatial phase screen, and the spatial phase screen is applied to the beam propagation path. According to the theory of partially coherent light, a partially coherent light source is decomposed into a linear superposition of a series of pairwise orthogonal modes. The spatial second-order coherence characteristic of the light source is described as a cross-spectral density function at two different spatial points in the light source. The random spatial phase screen introduced by atmospheric turbulence acts on all modes, and the same random phase difference factor is added to each mode. The cross-spectral density function after turbulence perturbation is: , In the formula, The cross-spectral density function after being subjected to turbulent disturbance. The cross spectral density function is the function for the absence of turbulence. , Let be the two-dimensional position vector of any two points on the surface of the rotating object. The random phase difference factor introduced for turbulence, For the point Spatial phase screen at the location, For the point The spatial phase screen is located at , where e is the natural constant and i is the imaginary unit.

[0013] Furthermore, the spatial phase screen is: , In the formula, Radial coordinates, For the point Spatial phase screen at the location, For the first Zernike polynomial of order 1 For the first Turbulent phase expansion coefficients corresponding to the Zernike polynomial of order 1; Let be the order of the polynomial.

[0014] Furthermore, the cross-spectral density function under turbulent conditions is: , In the formula, The cross spectral density function is the function for the absence of turbulence. For the m-th mode, the light at the point Spatial distribution function at that location, To indicate complex conjugate, For the m-th mode, the light at the point Spatial distribution function at a location.

[0015] Furthermore, the quantitative relationship between the cross-spectral density function of two different spatial points in the light source and the complex coherence of the partially coherent light source is as follows: , In the formula, There is a quantitative relationship between the complex coherence of a partially coherent light source and its cross-spectral density function. For position The light intensity at that location, For position The light intensity at that location.

[0016] Furthermore, a turbulence-compensated phase, conjugate to the distortion phase introduced by atmospheric turbulence, is generated based on the turbulence phase expansion coefficient and applied in real time to a spatial light modulator on a partially coherent light source surface to compensate the light source in real time, including: Based on the turbulence phase expansion coefficients predicted by the partially coherent deep learning model, the predicted turbulence phase screen is obtained as follows: In the formula, For the predicted turbulent phase screen, For the predicted first Turbulent phase expansion coefficients corresponding to the Zernike polynomial of order 1; Based on the predicted turbulent phase screen, a conjugate compensated phase screen is constructed, and the compensated cross-spectral density function is obtained as follows: , In the formula, The compensated cross-spectral density function, , Let be the two-dimensional position vector of any two points on the surface of the rotating object. For the m-th pattern after compensation at point Spatial distribution function at that location, For the m-th pattern after compensation at point Spatial distribution function at that location, For the m-th model without turbulent disturbance at point... Spatial distribution function at that location, For the m-th model without turbulent disturbance at point... Spatial distribution function at that location, To indicate complex conjugate, , For residual phase error, For the point Spatial phase screen at the location, For the point The predicted turbulent phase screen at the location, where e is the natural constant and i is the imaginary unit.

[0017] Furthermore, the real-time acquisition of the compensated rotating object After obtaining the light intensity image of the imaging surface, a series of compensated rotating objects are obtained based on the detection surface. The light intensity image of the imaging surface is used to extract the light intensity time-domain signal and generate a corrected spectrum. The frequencies corresponding to the characteristic peaks in the corrected spectrum are then extracted as follows: , In the formula, The frequency corresponding to the characteristic peak. Let M be the angular velocity of the rotating object being measured, and M be the total intensity over one cycle. The number of cycles within.

[0018] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: This invention achieves high-precision restoration and compensation of distorted light sources by inverting the atmospheric turbulence phase in real time and completing closed-loop compensation through a partially coherent deep learning model; and by combining turbulence compensation technology with the rotating Doppler effect of partially coherent light, it achieves high-precision measurement of the angular velocity of rotating objects in complex turbulent environments. Attached Figure Description

[0019] 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: Figure 1 This is a flowchart of a method in a preferred embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram illustrating the principle of the anti-turbulent angular velocity measurement method based on partially coherent deep learning in a preferred embodiment of the present invention.

[0021] Figure 3 This is a comparison of the light intensity images of the rotating three-hole object before and after compensation in a simulation experiment when the atmospheric coherence length r = 0.5 mm under the corresponding turbulent environment.

[0022] Figure 4 This is a normalized spectrum of the probe light intensity of the rotating three-hole object under test in a simulation experiment, with an atmospheric coherence length r = 0.5 mm, before turbulence compensation.

[0023] Figure 5 This is the normalized spectrum of the probe light intensity of the rotating three-hole object under test in the corresponding turbulent environment when the atmospheric coherence length r=0.5mm in the simulation experiment.

[0024] Figure 6 This is a comparison of the light intensity images of the rotating three-hole object before and after compensation in a simulation experiment when the atmospheric coherence length r = 0.6 mm under the corresponding turbulent environment.

[0025] Figure 7 This is a normalized spectrum of the probe light intensity of the rotating three-hole object under test in a simulation experiment, with an atmospheric coherence length r = 0.6 mm, before turbulence compensation.

[0026] Figure 8 This is the normalized spectrum of the probe light intensity of the rotating three-hole object under test in the corresponding turbulent environment when the atmospheric coherence length r = 0.6 mm in the simulation experiment.

[0027] Figure 9This is a comparison of the light intensity images of the rotating three-hole object before and after compensation in a simulation experiment when the atmospheric coherence length r = 0.7 mm under the corresponding turbulent environment.

[0028] Figure 10 This is a normalized spectrum of the probe light intensity of the rotating three-hole object under test in a simulation experiment, with an atmospheric coherence length r = 0.7 mm, before turbulence compensation.

[0029] Figure 11 This is the normalized spectrum of the probe light intensity of the rotating three-hole object under test in the corresponding turbulent environment when the atmospheric coherence length r = 0.7 mm in the simulation experiment.

[0030] Figure 12 For simulation experiments, Comparison of light intensity images of the rotating object's imaging surface before and after time compensation.

[0031] Figure 13 For simulation experiments, Spectrum diagram before turbulence compensation.

[0032] Figure 14 For simulation experiments, Spectrum diagram after time-turbulence compensation.

[0033] Figure 15 For simulation experiments, Comparison of light intensity images of the rotating object's imaging surface before and after time compensation.

[0034] Figure 16 For simulation experiments, Spectrum diagram before turbulence compensation.

[0035] Figure 17 For simulation experiments, Spectrum diagram after time-turbulence compensation.

[0036] Figure 18 For simulation experiments, Comparison of light intensity images of the rotating object's imaging surface before and after time compensation.

[0037] Figure 19 For simulation experiments, Spectrum diagram before turbulence compensation.

[0038] Figure 20 For simulation experiments, Spectrum diagram after time-turbulence compensation.

[0039] Figure 21 This is a comparison of the light intensity images of the imaging surface of the rotating object before and after compensation in a simulation experiment, when the rotating object under test is a two-hole object.

[0040] Figure 22 This is the spectrum of the rotating object under test before turbulence compensation in the simulation experiment, when the rotating object is a two-hole object.

[0041] Figure 23 This is the spectrum diagram after turbulence compensation when the rotating object under test is a two-hole object in the simulation experiment.

[0042] Figure 24 This is a comparison of the light intensity images of the imaging surface of the rotating object before and after compensation in a simulation experiment, when the rotating object under test is a long strip.

[0043] Figure 25 This is the spectrum diagram before turbulence compensation when the rotating object under test is a long strip in the simulation experiment.

[0044] Figure 26 This is the spectrum diagram after turbulence compensation when the rotating object under test is a long strip in the simulation experiment.

[0045] Figure 27 This is a comparison of the light intensity images of the imaging surface of the rotating object before and after compensation in a simulation experiment, when the rotating object under test is a speckle body.

[0046] Figure 28 This is the spectrum diagram before turbulence compensation when the rotating object under test is a speckle body in the simulation experiment.

[0047] Figure 29 This is the turbulence compensation spectrum of the rotating object under test as a speckle body in the simulation experiment. Detailed Implementation

[0048] 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.

[0049] With the significant improvement in computing power and the introduction of trainable deep neural network models, deep learning-based artificial intelligence has been applied in cutting-edge optical fields such as computational imaging, mode decomposition, and micro / nano optical design due to its superior data processing capabilities. Artificial intelligence learns from large amounts of data to summarize and extract scene features, thereby establishing complex mapping relationships between inputs and outputs. This enables it to efficiently complete various complex computational tasks, providing a new and efficient technical means to solve various technical challenges in the field of optics. Therefore, this invention presents an anti-turbulent rotating Doppler velocimetry based on deep learning, referencing... Figure 1 and Figure 2 As shown, this invention discloses an anti-turbulent angular velocity measurement method based on partially coherent deep learning, comprising the following steps:

[0050] S1: The emitted laser light is scattered to generate partially coherent light, which is then incident on a spatial light modulator. After passing through a turbulent environment, the emitted light source illuminates the surface of the rotating object.

[0051] S1-1: The emitted laser passes through a three-hole mask and a rotating frosted glass to generate a partially coherent light source with a hexagonal lattice periodic coherent structure. The expression for the complex coherence of the partially coherent light source in polar coordinates is: , In the formula, For a partially coherent light source, exp represents the complex coherence, which quantitatively describes the degree of coherence between two points in the light field. exp is an exponential function. and Let be the position vector of two points on the object surface. for Radial polar diameter, for polar angle, for Radial polar diameter, for The polar angle; The distance between the centers of two adjacent holes in a light-transmitting mask in which the vertices of an equilateral triangle are arranged in a three-hole configuration is the side length of the equilateral triangle on the mask. This represents the spatial coherence length of the corresponding beam. The incident light wavelength, This is the focal length of the Fourier lens.

[0052] The expression for the complex coherence of a partially coherent light source in polar coordinates is derived by Fourier transform of the spatial distribution of a light-transmitting mask with equilateral triangle vertices at the center of the three apertures. The coherent structure of the light-transmitting mask with equilateral triangle vertices at the center of the three apertures coincides with its own distribution every 60° rotation, exhibiting a hexagonal lattice periodicity.

[0053] S1-2: Using the partially coherent light source described above to illuminate the rotating object under test (using an equilateral triangular three-hole mask as the rotating object), the light intensity on the detection surface can be obtained as follows: , In the formula, The two-dimensional position vector of the probe surface. To detect surface light intensity; It is a positive integer. , These are two-dimensional position vectors corresponding to the center positions of the j-th and k-th holes within the surface of the rotating object to be measured, respectively. The intensity factor is a constant. , Let this be the system's impulse response function; This means taking the real part of a complex number. Indicates the hole With Kong Between the spacing The complex coherence at the following level is the same as described above. The specific form of expression when the rotating object is a three-hole object; Connect the two points with the reference direction ( The angle between the positive direction of the axis; the first term corresponds to the incoherent superposition of the three Airy disks, and the second term is the pairwise interference term, whose weight is proportional to the real part of the complex coherence between the corresponding two points. Therefore, the light intensity distribution on the detector surface directly depends on the coherence characteristics between two points on the object. When the object rotates, Periodic changes occur, leading to The occurrence of periodic modulation leads to periodic modulation of the total light intensity on the detection surface.

[0054] In this embodiment, for a three-hole object, taking hole 1 and hole 2 as examples, the coordinates are respectively... , Let be the rotation angle of the entire equilateral triangular three-aperture mask to be tested about the rotation center. Therefore, the complex coherence between aperture 1 and aperture 2 can be obtained as follows: , In the formula, The complex coherence between aperture 1 and aperture 2, The line connecting hole 1 and hole 2 and the reference direction ( The angle between the positive axis and the axis. Let ,but Proportional to , This represents taking the real part of a complex number. It has been verified that... by For a period, similarly It also satisfies the aforementioned periodicity. Combining the expression for the light intensity of the detector surface, the total light intensity consists of two parts: the first term is the incoherent superposition of the three Airy disks, a constant value that does not change with the rotation angle; the second term is the coherent interference term of each pair of apertures, whose weight is proportional to the real part of the complex coherence of the corresponding aperture pair. Since the complex coherence of the three sets of aperture pairs is all proportional to the real part of the complex coherence of the corresponding aperture pair... With the smallest positive period, the total interference terms after linear superposition still maintain the periodicity of that angular domain, ultimately inducing periodic modulation of the total light intensity on the detector surface as the object rotates. The complex coherence is within one period. The number of loops within is The periodicity of this coherent structure is transmitted to the total light intensity at the detector surface, i.e. Therefore, ideally, by performing a Fourier transform on the total light intensity data collected over a period of time at different times, the characteristic frequency peaks can be obtained: , In the formula, The frequency corresponding to the characteristic peak. Let M be the angular velocity of the rotating object being measured, and M be the total intensity over one cycle. The number of cycles within. Ideally, the above process can achieve high-precision measurement of the target angular velocity.

[0055] S1-3: In actual atmospheric transmission environments, the light beam is inevitably affected by atmospheric turbulence. The random refractive index fluctuations caused by atmospheric turbulence will lead to wavefront distortion, which can be equivalent to introducing a random spatial phase screen along the beam propagation path. The spatial phase screen is: , In the formula, Radial coordinates, For spatial phase screen, For the first Zernike polynomial of order 1 For the first Turbulent phase expansion coefficients corresponding to the Zernike polynomial of order 1; Let be the order of the polynomial.

[0056] According to the theory of partially coherent light, a partially coherent light source can be decomposed into a linear superposition of a series of pairwise orthogonal modes. The spatial second-order coherence characteristic of the light source can be described as the cross-spectral density function (i.e., the cross-spectral density function in the absence of turbulence) at two different spatial points in the light source: , In the formula, Let be the cross-spectral density function of two different spatial points in the light source, used to quantitatively describe the spatial second-order coherence of the light field. The quantitative relationship between the cross-spectral density function and the complex coherence of a partially coherent light source in polar coordinates is as follows: , and Positions and The light intensity at that location (i.e., the cross spectral density function); , Let be the two-dimensional position vector of any two points on the surface of the rotating object. For the m-th mode, the light at the point Spatial distribution function at that location, To indicate complex conjugate, For the m-th mode, the light at the point Spatial distribution function at a location.

[0057] In this embodiment, the cross spectral density function is expressed in Fourier integral form as follows: , In the formula, It is a two-dimensional spatial frequency vector. It is a non-negative weight function. for and kernel function, for and The kernel function; , , It is the transmission function of the object surface; i is the imaginary unit; and Substitution A non-negative weighting function is constructed using a triangularly distributed Gaussian weighting function. The triangularly distributed Gaussian weighting function is defined by the side length formed by the centers of the three Gaussian light spots. The equilateral triangle has the following spatial frequency domain coordinates: , In the formula, , , The spatial frequency domain coordinates of the centers of the three Gaussian spots;

[0058] The constructed non-negative weight function is as follows: , In the formula, exp is an exponential function. Let the waist radius of a single Gaussian spot be . They are respectively The x and y coordinates.

[0059] The random spatial phase screen introduced by atmospheric turbulence acts on all models, adding the same random phase difference factor to each model. The cross-spectral density function after turbulence perturbation becomes: , In the formula, The cross-spectral density function after being subjected to turbulent disturbance. The cross spectral density function is the function for the absence of turbulence. Indicates complex conjugation. The random phase difference factor introduced by turbulence disrupts the translation invariance of the original coherent structure, causing the cross spectral density function and complex coherence to depend not only on the coordinate difference but also on the absolute position. This distorts the light intensity distribution on the detection surface, thus disrupting the periodic modulation of light intensity over time. Characteristic peaks in the spectrum broaden, shift, or even become completely submerged, severely affecting measurement accuracy and even causing the velocity measurement function to fail.

[0060] S2: After low-pass filtering, the camera captures images of the rotating object in real time. Light intensity image of the imaging surface. Enter the closed-loop adaptive turbulence compensation and compensation image acquisition process.

[0061] S3: Collect the rotating object The image of the light intensity of the imaging surface (i.e. the distorted image) is transmitted in real time to a partially coherent deep learning model to predict the turbulence phase expansion coefficient of the current turbulence.

[0062] Some coherent deep learning models utilize a ResNet-based regression network as input. The single-channel grayscale intensity image is used, and the output is the first 15 orders of turbulent phase expansion coefficients (excluding piston terms). The network consists of convolutional layers, residual blocks, and fully connected layers. Mean absolute error is used as the optimization objective, Adam is selected as the optimizer, and cosine annealing is used as the learning rate. Training data is generated through numerical simulation using the formula... A large number of turbulent phase screens are randomly generated and applied to an ideal partially coherent light source. Based on the theory of partially coherent optical transmission imaging, the distortion intensity image of the detector surface under turbulent disturbance is calculated. Simultaneously, the turbulent phase expansion coefficients used to generate these images are recorded as training labels. The dataset contains intensity images with different turbulence intensities and rotation angles to ensure the model learns the mapping relationship between turbulence features and image distortion. The training and validation sets contain 9600 and 2400 samples, respectively. After training to convergence, the model can predict the turbulent phase expansion coefficients relatively accurately from distorted images. In angular velocity measurement, intensity images of the detector surface affected by turbulence are acquired and input into the trained CNN to obtain the predicted turbulent phase expansion coefficients. The predicted turbulent phase expansion coefficients are denoted as... .

[0063] S4: Based on the turbulence phase expansion coefficient, a turbulence compensation phase conjugate with the distortion phase introduced by atmospheric turbulence is generated and loaded in real time onto the spatial light modulator of the partially coherent light source surface. The spatial light modulator uses the turbulence compensation phase to compensate the light source in real time, so that the camera acquisition plane can obtain the compensated light intensity of the rotating object.

[0064] To restore the original coherent structure, it is necessary to estimate and compensate for the turbulent phase screen from the distorted light intensity image. This invention uses a convolutional neural network (CNN) to predict the turbulent phase unfolding coefficient from a single-frame acquired image of the rotating object's imaging light intensity. ), to obtain the predicted turbulent phase screen In the formula, For the predicted turbulent phase screen, For the predicted first Turbulent phase expansion coefficients corresponding to the Zernike polynomial of order 1;

[0065] Based on this, a compensated phase screen conjugate to the turbulent phase screen is constructed, and the compensated cross-spectral density function is obtained as follows: , In the formula, The compensated cross-spectral density function, For the m-th pattern after compensation at point Spatial distribution function at that location, For the m-th model without turbulent disturbance at point... Spatial distribution function at that location, This represents the residual phase error. When the partially coherent deep learning model predicts accurately, the residual phase is close to zero, and the cross-spectral density of the compensated optical field is... Since there is a quantitative relationship between complex coherence and cross-spectral density, restoring the cross-spectral density to a turbulent-free state is equivalent to restoring the complex coherence to a turbulent-free state. The minimum rotational periodicity is also restored, at which point the compensated light source approximates the light source in the absence of turbulence.

[0066] By reintroducing the compensated light source into the imaging system, the compensated light intensity distribution on the detection surface is obtained. Its change over time will restore the original periodic modulation, and clear peaks will reappear in the spectrum, thus allowing for accurate calculation of the object's rotational angular velocity.

[0067] S5: Real-time acquisition of a series of compensated rotating objects The light intensity image of the imaging surface is used to extract the time-domain signal of the light intensity, which is then subjected to a Fast Fourier Transform to generate a corrected spectrum. The frequencies corresponding to the characteristic peaks in the corrected spectrum are then extracted as follows: , In the formula, The frequency corresponding to the characteristic peak. Let M be the angular velocity of the rotating object being measured, and M be the total intensity over one cycle. The number of cycles within.

[0068] S6: Obtain the rotational angular velocity of the rotating object based on the corresponding formulas for frequency and angular velocity.

[0069] This invention also discloses a deep learning-based anti-turbulence rotating Doppler velocimetry system, such as... Figure 2 As shown, it includes a laser, a beam expander, a three-hole mask, a 4f system, a rotating frosted glass, a spatial light modulator, and a charge-coupled device.

[0070] The laser is used to generate the emitted laser beam. After being expanded and collimated by a beam expander, the emitted laser beam is spatially modulated through a three-hole mask to form a specific spatial coherent structure. This specific spatial coherent structure is then processed by a 4f system (i.e., Figure 2Lens 1, lens 2, and mirror 1 are projected onto a rotating ground glass disk (RGGD). The random process of the rotating ground glass and the lenses (i.e.,...) are then utilized. Figure 2 The Fourier transform process of lens 3 in the middle generates partially coherent light with a hexagonal lattice symmetric coherent structure.

[0071] Some of the coherent light is collimated by a lens and then incident on the spatial light modulator. The outgoing light source passes through a turbulent environment and then through a 4f system (i.e., Figure 2 After transmission through lenses 4, aperture 1, and lens 5, the light is projected onto the surface of the rotating object, and then transmitted through the 4f system with built-in apertures (i.e., Figure 2 The mirror 2, lens 6, aperture 2, and lens 7 in the image are imaged onto the charge-coupled device (CCD) after low-pass filtering. Figure 2 (The CCD camera in the middle) completes one rotation of the object. Acquisition of light intensity images of the imaging surface.

[0072] After completing one light intensity image acquisition, the closed-loop adaptive turbulence compensation and compensated image acquisition process begins: the acquired light intensity image (i.e., the distorted image) of the rotating object's imaging surface is transmitted in real time to a partially coherent deep learning model to predict the turbulence phase expansion coefficient of the current turbulence and transmit it to the spatial light modulator of the partially coherent light source surface; based on the turbulence phase expansion coefficient, a turbulence compensation phase is generated in a short time and loaded into the spatial light modulator in real time to compensate the light source in real time, resulting in a compensated light source; the compensated light source is then transmitted again along the original optical path and finally imaged onto a charge-coupled device, completing a single frame of compensation for the rotating object under test. Acquisition of light intensity images of the imaging surface; repeat the above closed-loop process to complete the acquisition of a sequence of images after multi-frame compensation. After acquiring a sequence of light intensity images of the imaging surface of the rotating object after multi-frame compensation, extract the light intensity time-domain signal of the image sequence and perform a fast Fourier transform to generate a corrected spectrum; extract the frequency corresponding to the characteristic peak in the corrected spectrum, and obtain the rotational angular velocity of the rotating object according to the corresponding formula of frequency and angular velocity.

[0073] The present invention also discloses a device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a deep learning-based anti-turbulence rotating Doppler velocimetry method.

[0074] Compared with the prior art, the advantages of the present invention are: 1. This invention uses a partially coherent deep learning model to invert the atmospheric turbulence phase in real time and complete closed-loop compensation, thereby achieving high-precision restoration and compensation of distorted light sources.

[0075] 2. This invention combines turbulence compensation technology with the partially coherent optical rotating Doppler effect to achieve high-precision measurement of the angular velocity of rotating objects in complex turbulent environments.

[0076] 3. This invention has excellent generalization ability, and can effectively compensate and accurately measure different structural targets that have not participated in training, which can significantly reduce training costs.

[0077] To further demonstrate the beneficial effects of this invention, simulation experiments were conducted using this invention. The specific instruments used in the simulation experiments were: a Ventus laser with a wavelength of 532 nm and a power of 1.5 W; and a PDA100A2 photodetector (model 75.4). The device is manufactured by Thorlabs, Inc. (USA); the data acquisition card model is NI, USB-6366. After the photodetector receives the signal, it is connected to the data acquisition card. After being connected to a computer, the time-domain signal of the light intensity is recorded and saved using MATLAB software. Then, a fast Fourier transform is performed using MATLAB to obtain the spectrum.

[0078] (1) Measure the angular velocity of rotating objects under different turbulent conditions.

[0079] Experimental results of angular velocity measurement of rotating objects under different turbulent conditions are as follows: Figures 3-11 As shown, Figures 3-5 The images show a comparison of the light intensity before and after compensation for the rotating three-aperture object under turbulent conditions when the atmospheric coherence length r = 0.5 mm, the normalized spectrum of the probe light intensity before turbulence compensation, and the normalized spectrum of the probe light intensity after turbulence compensation. Figures 6-8 The images show a comparison of the light intensity before and after compensation for the rotating three-aperture object under turbulent conditions when the atmospheric coherence length r = 0.6 mm, the normalized spectrum of the probe light intensity before turbulence compensation, and the normalized spectrum of the probe light intensity after turbulence compensation. Figures 9-11 The images show a comparison of the light intensity before and after compensation for the rotating three-aperture object under turbulent conditions, with an atmospheric coherence length r = 0.7 mm. The images also include the normalized spectrum of the probe light intensity before turbulence compensation and the normalized spectrum of the probe light intensity after turbulence compensation. In all cases, the receiving aperture diameter of the turbulence phase screen is set to D = 5 mm. A smaller atmospheric coherence length r corresponds to stronger turbulence. The standard angular velocity of the rotating object is set to 0.3 r / s.

[0080] First, we analyze the measurement results before turbulence compensation. Affected by wavefront distortion caused by atmospheric turbulence, the light intensity image before compensation showed varying degrees of morphological distortion and spatial asymmetry. Correspondingly, in terms of frequency domain characteristics, the overall floor noise level of the spectrum before compensation was extremely high, the spectrum signal was chaotic, and the characteristic main peak corresponding to the rotational angular velocity was completely submerged in random clutter and background noise. It was impossible to effectively identify and extract the rotational Doppler frequency shift information through the spectrum peaks, and thus it was impossible to effectively measure the angular velocity of the rotating object.

[0081] After compensation using the deep learning-based turbulence compensation scheme proposed in this invention, the light intensity images under three turbulent conditions were effectively restored, and the distorted light source distribution was restored to a symmetrical coherent structure, laying the foundation for the stable extraction of the rotating Doppler frequency shift signal. Correspondingly, in the frequency domain characteristics, background clutter and floor noise were significantly suppressed in the compensated spectrum, and the characteristic main peak corresponding to the rotational angular velocity was sharp and prominent, clearly and accurately identifying the frequency corresponding to the main peak as 1.79688Hz. Based on the relationship between the rotating Doppler frequency shift and angular velocity... The angular velocity of the rotating object can be calculated as 1.79688 / 6≈0.2995 r / s, with a very small relative error of less than 0.2% compared to the preset angular velocity of 0.3 r / s, achieving high-precision angular velocity inversion.

[0082] (2) Perform compensation measurements at different angular velocities.

[0083] Measurements were performed on a rotating three-hole object with different rotational angular velocities under a fixed turbulent environment. The experimental results are as follows: Figures 12-20 As shown, Figures 12-14 for Comparison of light intensity images of a rotating object before and after time compensation, spectrum diagrams before and after turbulence compensation. Figures 15-17 for Comparison of light intensity images of a rotating object before and after time compensation, spectrum diagrams before and after turbulence compensation. Figures 18-20 for Comparison of light intensity images of rotating objects before and after time compensation, spectrum diagram before turbulence compensation, and spectrum diagram after turbulence compensation.

[0084] Under a fixed turbulent environment, all three sets of pre-compensated light sources exhibited significant wavefront distortion under different angular velocities. The corresponding pre-compensated spectra in the frequency domain showed high floor noise, with the characteristic peaks corresponding to the rotational angular velocities submerged in random clutter, making it impossible to accurately identify effective rotational Doppler frequency shift information. Traditional methods could not effectively measure different angular velocities. After compensation using a deep learning turbulence compensation scheme, all three sets of distorted light sources were effectively restored, with significant suppression of spectral background clutter and floor noise, allowing for accurate identification and extraction of frequency shift information. The frequencies corresponding to the characteristic peaks in the compensated spectra were read, and the angular velocities were calculated using formulas to be 0.1009 r / s, 0.2995 r / s, and 0.5990 r / s, respectively, with relative errors controlled within 0.2%.

[0085] (3) Perform turbulence compensation and angular velocity measurement for objects of different shapes.

[0086] Under a fixed turbulent environment, measurements were taken on rotating targets with different structures and a standard rotational angular velocity of 0.3 r / s to verify the generalization ability of this invention for test objects of different shapes. Experimental results are as follows: Figures 21-29 As shown, Figures 21-23 The image shows a comparison of light intensity before and after compensation when the rotating object under test is a two-hole object, along with the spectrum before and after turbulence compensation. Figures 24-26 The image shows a comparison of light intensity before and after compensation when the rotating object under test is a long strip. The image also shows the spectrum before and after turbulence compensation. Figures 27-29 The image shows a comparison of light intensity before and after compensation when the rotating object under test is a speckle body, as well as the spectrum before and after turbulence compensation.

[0087] Under a fixed turbulent environment, the light sources of three different structural objects exhibited certain distortions before compensation. The spectra before compensation all displayed high floor noise, with the main characteristic peak corresponding to the rotational angular velocity completely submerged in random clutter, making it impossible to accurately identify the effective rotational Doppler shift information. Furthermore, it was observed that as the symmetry of the object structure decreased, the clutter in the spectra before compensation significantly increased, further complicating signal extraction. After compensation using this deep learning turbulence compensation scheme, the distorted light sources of the three different structural objects were effectively restored. The background clutter and floor noise in the spectrum were significantly suppressed, and the main characteristic peak corresponding to the standard angular velocity was clearly distinguishable. The frequency corresponding to the main characteristic peak in the compensated spectra of the three different rotating objects was 1.79688 Hz. The calculated measured angular velocity was approximately 0.2995 r / s, with the relative error from the standard value of 0.3 r / s controlled within 0.2%, achieving high-precision angular velocity inversion.

[0088] Some coherent deep learning models were trained using datasets of three-hole objects, two-hole objects, and elongated objects, without specifically training on images before and after compensation for speckle with irregular structures. The models still effectively completed turbulence compensation and feature frequency shift extraction, fully demonstrating the excellent generalization and adaptability of this invention. As the symmetry of the object structure decreases, a small amount of residual clutter remains in the compensated spectrogram, but the signal-to-noise ratio of the main characteristic peak is still sufficient to support accurate angular velocity readings, without affecting the accuracy of the final measurement results. This verifies that this invention has a certain degree of universality for rotating objects with different structures.

[0089] 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.

[0090] 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.

[0091] 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.

[0092] 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 1The steps of the function specified in one or more boxes.

[0093] 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 turbulent angular velocity measurement system based on partially coherent deep learning, characterized in that, This includes lasers, beam expanders, three-hole masks, 4f systems, rotating frosted glass, spatial light modulators, and charge-coupled devices. The laser is used to generate an outgoing laser beam. After being expanded and collimated by the beam expander, the outgoing laser beam is spatially modulated by the three-hole mask to form a specific spatial coherent structure. The specific spatial coherent structure is projected onto the rotating frosted glass by the 4f system. With the help of the random process of the rotating frosted glass and the Fourier transform process of the lens, a partially coherent light with a hexagonal lattice symmetric coherent structure is generated. After collimation, the coherent light is incident on the spatial light modulator. After passing through the turbulent environment, the emitted light source is transmitted through the 4f system and then illuminates the surface of the rotating object. After low-pass filtering by the 4f system, the light is imaged onto the charge-coupled device, thus completing the acquisition of the light intensity image of the rotating object's imaging surface. The acquired light intensity images are transmitted in real time to a partially coherent deep learning model to predict the turbulence phase expansion coefficient of the current turbulence and then transmitted to the spatial light modulator. Based on the turbulence phase expansion coefficient, a turbulence compensation phase conjugate with the distortion phase introduced by atmospheric turbulence is generated. The turbulence compensation phase is used to compensate the light source in real time to obtain the compensated light source. The compensated light source is transmitted again along the original optical path and then imaged onto the charge-coupled device to complete the acquisition of the light intensity image of the rotating object imaging surface after single-frame compensation. After acquiring a multi-frame compensated image sequence of the light intensity of the rotating object's imaging surface, the light intensity time-domain signal of the image sequence is extracted and subjected to a fast Fourier transform to generate a corrected spectrum. The frequencies corresponding to the characteristic peaks in the corrected spectrum are extracted, and the rotational angular velocity of the rotating object is obtained according to the corresponding formula of frequency and angular velocity.

2. A method for measuring turbulent angular velocity based on partially coherent deep learning, characterized in that, include: The emitted laser light is scattered to generate partially coherent light, which is then incident on a spatial light modulator. After passing through a turbulent environment, the emitted light source illuminates the surface of the rotating object. Real-time acquisition of rotating objects The light intensity image of the imaging surface is transmitted in real time to a partially coherent deep learning model to predict the turbulence phase expansion coefficient of the current turbulence. Based on the turbulence phase expansion coefficient, a turbulence compensation phase conjugate with the distortion phase introduced by atmospheric turbulence is generated and loaded in real time onto the spatial light modulator of the partially coherent light source surface to perform real-time compensation of the light source. Real-time acquisition of compensated rotating objects The light intensity image of the imaging surface is used to extract the light intensity time domain signal to generate a corrected spectrum. The frequency corresponding to the characteristic peak in the corrected spectrum is extracted, and the rotational angular velocity of the object is obtained according to the corresponding formula of frequency and angular velocity.

3. The anti-turbulent angular velocity measurement method based on partially coherent deep learning according to claim 2, characterized in that: The process of generating partially coherent light from the emitted laser by scattering specifically involves the emitted laser passing through a three-hole mask and a rotating frosted glass to generate a partially coherent light source with a hexagonal lattice periodic coherent structure. The expression for the complex coherence of the partially coherent light source in polar coordinates is derived by Fourier transform of the spatial distribution of the light-transmitting mask with the vertices of an equilateral triangle at the center of the three holes. The coherent structure of the light-transmitting mask with the vertices of an equilateral triangle at the center of the three holes coincides with its own distribution every 60° rotation, exhibiting a hexagonal lattice periodicity.

4. The anti-turbulent angular velocity measurement method based on partially coherent deep learning according to claim 3, characterized in that: The expression for the complex coherence of the partially coherent light source in polar coordinates is: ， In the formula, Let be the complex coherence of the partially coherent light source, and exp be an exponential function. and Let be the two-dimensional position vector of any two points on the surface of the rotating object. , , for Radial polar diameter, for polar angle, for Radial polar diameter, for The polar angle; The center-to-center distance between two adjacent holes in a light-transmitting mask in which the vertices of an equilateral triangle are arranged at the center of the three holes; This represents the spatial coherence length of the corresponding beam. The incident light wavelength, This is the focal length of the Fourier lens.

5. The anti-turbulent angular velocity measurement method based on partially coherent deep learning according to claim 3, characterized in that: The emitted light source illuminates the surface of the rotating object after passing through a turbulent environment, including: The random fluctuations in refractive index caused by atmospheric turbulence are equivalent to a spatial phase screen, and the spatial phase screen is applied to the beam propagation path. According to the theory of partially coherent light, a partially coherent light source is decomposed into a linear superposition of a series of pairwise orthogonal modes. The spatial second-order coherence characteristic of the light source is described as a cross-spectral density function at two different spatial points in the light source. The random spatial phase screen introduced by atmospheric turbulence acts on all modes, and the same random phase difference factor is added to each mode. The cross-spectral density function after turbulence perturbation is: ， In the formula, The cross-spectral density function after being subjected to turbulent disturbance. The cross spectral density function is the function for the absence of turbulence. , Let be the two-dimensional position vector of any two points on the surface of the rotating object. The random phase difference factor introduced for turbulence, For the point Spatial phase screen at the location, For the point The spatial phase screen is located at a point, where e is the natural constant and i is the imaginary unit.

6. The anti-turbulent angular velocity measurement method based on partially coherent deep learning according to claim 5, characterized in that: The spatial phase screen is: ， In the formula, Radial coordinates, For the point Spatial phase screen at the location, For the first Zernike polynomial of order 1 For the first Turbulent phase expansion coefficients corresponding to the Zernike polynomial of order 1; Let be the order of the polynomial.

7. The anti-turbulent angular velocity measurement method based on partially coherent deep learning according to claim 5, characterized in that: The cross spectral density function under turbulent conditions is: ， In the formula, The cross spectral density function is the function for the absence of turbulence. For the m-th mode, the light at the point Spatial distribution function at that location, To indicate complex conjugate, For the m-th mode, the light at the point Spatial distribution function at a location.

8. The anti-turbulent angular velocity measurement method based on partially coherent deep learning according to claim 5, characterized in that: The quantitative relationship between the cross-spectral density function of two different spatial points in the light source and the complex coherence of the partially coherent light source is as follows: ， In the formula, The complex coherence of a partially coherent light source. For position The light intensity at that location, For position The light intensity at that location.

9. The anti-turbulent angular velocity measurement method based on partially coherent deep learning according to claim 2, characterized in that: Based on the turbulence phase expansion coefficient, a turbulence-compensated phase conjugate with the distortion phase introduced by atmospheric turbulence is generated and applied in real time to a spatial light modulator on a partially coherent light source surface to perform real-time compensation for the light source, including: Based on the turbulence phase expansion coefficients predicted by the partially coherent deep learning model, the predicted turbulence phase screen is obtained as follows: In the formula, For the predicted turbulent phase screen, For the predicted first Turbulent phase expansion coefficients corresponding to the Zernike polynomial of order Z; Based on the predicted turbulent phase screen, a conjugate compensated phase screen is constructed, and the compensated cross-spectral density function is obtained as follows: , In the formula, The compensated cross-spectral density function, , Let be the two-dimensional position vector of any two points on the surface of the rotating object. For the m-th pattern after compensation at point Spatial distribution function at that location, For the m-th pattern after compensation at point Spatial distribution function at that location, For the m-th model without turbulent disturbance at point... Spatial distribution function at that location, For the m-th model without turbulent disturbance at point... Spatial distribution function at that location, To indicate complex conjugate, , For residual phase error, For the point Spatial phase screen at the location, For the point The predicted turbulent phase screen at the location, where e is the natural constant and i is the imaginary unit.

10. The anti-turbulent angular velocity measurement method based on partially coherent deep learning according to claim 2, characterized in that: The real-time acquisition and compensation of the rotating object After obtaining the light intensity image of the imaging surface, a series of compensated rotating objects are obtained based on the detection surface. The light intensity image of the imaging surface is used to extract the light intensity time-domain signal and generate a corrected spectrum. The frequencies corresponding to the characteristic peaks in the corrected spectrum are then extracted as follows: ， In the formula, The frequency corresponding to the characteristic peak. Let M be the angular velocity of the rotating object being measured, and M be the total intensity over one cycle. The number of cycles within.

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