96 results about "Complex amplitude" patented technology

The invention provides a current transformer dielectric loss anti-interference measurement method based on a variable frequency power supply, and relates to the technical field of power detection, and the method comprises the steps: constructing an excitation channel, collecting a background response signal, recognizing a main interference frequency through combining a frequency tracking algorithm, and dynamically constructing a frequency deviation parameter; generating a pair of non-power-frequency excitation frequency control variable-frequency power supplies to output sine wave excitation signals; excitation voltage and response current signals are synchronously collected to form sampling signals, notch frequency is set according to frequency deviation parameters, main interference is filtered out, and first processing signals are obtained; performing weighting processing by constructing a window function matched with the frequency band characteristic to generate a second processing signal; the complex amplitude and phase information at the target frequency is extracted, the complex impedance is calculated based on the complex current method, the dielectric loss value of the current transformer is finally output, and the anti-interference capability and precision of measurement are effectively improved. According to the invention, the interference in the dielectric loss measurement of the current transformer can be processed, so that the measurement precision is improved.

The invention belongs to the technical field of optical calculation, and discloses an error-adaptive optical diffraction neural network in-situ training method, which comprises the following steps: based on the phase of each phase modulation layer, calculating the light field complex amplitude Uk of the input sample complex amplitude on the rear surface of each phase modulation layer and the light field complex amplitude Uo of the input sample complex amplitude on an output plane after forward propagation; calculating an error light field P based on Uo, carrying out three-dimensional central symmetry on a back propagation light path of the error light field P without changing the phase distribution of each phase modulation layer, and calculating the light field complex amplitude of the complex amplitude of the symmetrical error light field on the front surface of each phase modulation layer after forward propagation; the method comprises the steps of obtaining the light field complex amplitude Un + 1-k'of P back propagation to the rear surface of each phase modulation layer, calculating the gradient related to a loss function based on Uk and Un + 1-k 'so as to carry out updating, and carrying out the next round of training until a preset training round or loss convergence is reached. The method can adapt to errors existing in an optical system.

The invention discloses a real-time rendering method and system for physical simulation water surface waves, and the method comprises the following steps: constructing a generative adversarial network, obtaining a wave vector and an environment parameter variable of the waves, inputting the environment parameter variable into the pre-constructed generative adversarial network, and calculating the height of the waves through a Tessendorf method; calculating wave displacement through Fourier transform and inverse transform in a frequency domain based on the wave vector; calculating the velocity complex amplitude of the corresponding wave based on the wave vector, introducing a micro-scale vortex velocity field based on a particle system, and calculating the wave velocity based on the velocity complex amplitude and the micro-scale vortex field; and based on the wave height, the wave displacement and the wave speed, performing water surface wave rendering by adopting multi-cascade dynamic. According to the method, the physical rationality and visual authenticity of water surface wave simulation are improved, and water body physical simulation is promoted to develop from visual driving to the fusion direction of physical driving and data driving.

The invention relates to a high-resolution wavefront measurement method and device for a complex light field, electronic equipment and a storage medium, and the method comprises the steps: obtaining an observation image representing the to-be-measured wavefront intensity distribution based on to-be-measured light waves passing through a scattering sheet; obtaining initial complex amplitude space distribution corresponding to the wavefront to be measured based on the observation image; and inputting the initial complex amplitude space distribution and the observation image into a target function, taking the complex amplitude space distribution under the condition that the numerical value of the target function is minimum as the complex amplitude space distribution corresponding to the wavefront to be measured, and performing wavefront inversion by minimizing the target function to obtain the wavefront to be measured. The objective function comprises a data fidelity term, a spatial smoothness constraint term and a spatial spectrum bandwidth constraint term of the wavefront to be measured. And for a complex light field with strong aberration, turbulent flow or high-order singular points, the high-resolution wavefront is quickly reconstructed. Object information recording and imaging can be supported under the defocus condition, and the method is further suitable for application requirements of rapid and high-throughput detection and the like.

The invention provides a power distribution network resonance key element identification method and device based on harmonic monitoring data, and the method comprises the steps: collecting the harmonic voltage and branch harmonic current data of a key node through the deployment of an online harmonic monitoring device, converting a time domain signal to a frequency domain through band-pass filtering for a preset harmonic number set, and extracting a complex amplitude value, carrying out normalization processing to obtain standardized data; secondly, constructing a node admittance matrix in a frequency domain in combination with the newest power grid topology and equipment static parameters, identifying a feature root closest to zero and a corresponding resonant frequency thereof through eigenvalue decomposition, and obtaining a modal vector; tiny disturbance is applied to inductive reactance / capacitive reactance element parameters, and the sensitivity of the inductive reactance / capacitive reactance element parameters to modal admittance is calculated and normalized into dimensionless indexes; and screening and sorting according to the sensitivity threshold, and outputting a group of resonance key elements. The method does not need off-line simulation, has the advantages of high real-time performance, high engineering adaptability, low implementation cost and the like, and provides efficient technical support for active treatment of harmonic waves of the power distribution network.

The multi-phase metasurface holography method based on frequency and polarization decoupling belongs to the field of micro-nano holography. It includes the following steps: generating random phase holograms, multiplying them by a factor K to obtain n different K-fold phase holograms, calculating the mean square error of the output image and label, optimizing the phase of the random phase holograms using an adaptive moment estimation algorithm, multiplying the obtained basic phase by n factors K to obtain n optimized multi-phases, and matching the optimized multi-phases with frequency λ1 and a cross-circular polarization channel to obtain a phase φ; scanning the length and width of each nano-antenna column in the cross-circular polarization channel and the linear polarization channel with frequency λ2 to determine the complex amplitude modulation characteristics of the nano-antenna columns for different frequencies and polarizations, obtaining the corresponding phase distribution. This design of multi-phase metasurface holography based on frequency and polarization decoupling can improve energy conversion efficiency, and different combinations of polarization and frequency also enhance the flexibility of multi-phase holographic modulation.

This invention belongs to the field of coaxial holographic reconstruction and discloses a holographic reconstruction method based on a wavelet domain feature correlation complex-valued neural network. Specifically, the method involves: adding a phase term to the coaxial hologram A to construct a complex amplitude B, and performing an n-level discrete wavelet transform on it. The transformed result and the complex amplitude B are used as inputs to the complex-valued neural network, outputting the object field complex amplitude C. Next, noise suppression is applied to the object field complex amplitude C, and the suppressed complex amplitude D is used to simulate the forward propagation process of coaxial holography to generate a hologram E. Finally, the similarity between coaxial hologram A and hologram E is calculated, and a smoothing total variational constraint is applied to the phase of the complex amplitude D. Holographic reconstruction is achieved through a gradient descent optimization algorithm of the complex-valued neural network. This invention aims to utilize the inherent coupling relationship between the wavefront amplitude and phase terms in optical holography to construct a complex-valued feature correlation model to separate the target object from the background information, preserving target features while suppressing noise, thus achieving superior holographic reconstruction.

The application discloses a motor rotor dynamic balance test system and method, comprising: arranging an acceleration sensor and an encoder, collecting vibration, angular position signal and current signal; establishing a multi-resonance phase-locked loop, outputting a de-bouncing phase and an angular position sequence, forming a phase reference; angular domain resampling and sparse harmonic decomposition, extracting complex amplitude and generating observation and working condition data; complex value reversible flow model reverse mapping, combining constraint processing, outputting target counterweight instruction; target counterweight instruction injection virtual correction, calculating vibration decline rate, dynamically optimizing counterweight instruction; physical correction and recheck, archiving working condition label, counterweight instruction and recheck result after passing. The application realizes intelligent detection and correction of motor rotor dynamic balance by fusing multi-resonance phase-locked loop and complex value reversible flow model, and is free of test weight, high in precision and capable of multi-working condition.

The invention discloses a construction method of a non-acceleration PST Airy wave packet, and relates to the technical field of non-diffraction beams. The method comprises the following steps: defining Lorentz acceleration of a light beam in a PST domain; lorentz acceleration is applied to the light beam of the PST domain parabola-shaped frequency spectrum; superposing a cubic phase on the parabolic frequency spectrum of the PST domain; a non-acceleration PST Airy wave packet is generated by using a complex amplitude modulation method based on a spatial light modulator. Compared with a space-time light pulse scheme needing a pulse laser source, a 4f pulse shaping system and a complex field scanning device, the method achieves efficient generation of the wave packet through simplified configuration.

The invention discloses a motor rotor dynamic balance test system and method, and the method comprises the steps: arranging an acceleration sensor and an encoder, and collecting vibration and angular position signals and current signals; establishing a multi-resonance phase-locked loop, outputting a de-jitter phase and an angular position sequence, and forming a phase reference; carrying out angular domain resampling and sparse harmonic decomposition, extracting a complex amplitude and generating observation and working condition data; performing reverse mapping on the complex value countercurrent model, and outputting a target counterweight instruction in combination with constraint processing; virtual correction is injected into the target counterweight instruction, the vibration drop rate is calculated, and the counterweight instruction is dynamically optimized; and performing physical correction and reinspection, and archiving a working condition label, a counterweight instruction and a reinspection result after qualification. According to the method, the multi-resonance phase-locked loop and the complex value countercurrent model are fused, so that test-weight-free, high-precision and multi-working-condition intelligent detection and correction of dynamic balance of the motor rotor are realized.

The invention relates to the technical field of distortion correction, and discloses a laser imaging wavefront distortion correction system and method based on deep learning, and the system comprises a first module which collects three intensity images; the second module is used for estimating the Zernike coefficient and the amplitude of the target complex amplitude; the third module is used for constructing a loss function; a fourth module that calculates an actuator voltage; the fifth module is used for calculating the Stell ratio and the high-frequency lifting ratio in the modulation transfer function; and the sixth module is used for re-applying the voltage of the actuator when judging that the evaluation condition is not met. According to the method, a full-process correction mechanism is constructed by integrating deep learning and an optical physical rule, and initial correction is realized by stably solving the voltage of the actuator by utilizing Tagunov regularization, so that the high-frequency detail definition in imaging is improved, the correction accuracy, real-time performance and robustness are both considered, and the method is suitable for large-scale popularization and application. And the application suitability of the laser imaging technology in the high-precision field is greatly expanded.

The present invention belongs to the technical field related to projection light field control, and discloses a method and system for hybrid optimization of the amplitude and phase of a projection light field, wherein the method includes: calculating the actual generated projection light field based on the input light field; substituting the parameters of the target projection light field and the parameters of the actual generated projection light field into an objective function model to determine whether a preset threshold is met; the objective function model includes an amplitude objective function and a phase objective function, which are used to evaluate the accuracy of the amplitude and phase of the actual generated projection light field; if the preset threshold of the objective function model is not met, the input amplitude and input phase of the input light field are optimized and updated using a gradient method until the preset threshold of the objective function model is met or the number of optimizations reaches a preset number. The present invention achieves complex amplitude control of the light field with higher degrees of freedom by hybrid optimization of the amplitude and phase of the light field, while simultaneously controlling the amplitude and phase distribution of the generated light field.

The invention belongs to the technical field of high-precision morphology measurement, and discloses an automatic refocusing large-measurement-range nano-morphology measurement method, which comprises the following steps of: 1, acquiring a spectral interference signal of a sample by using an OCT (Optical Coherence Tomography) system, and performing one-dimensional inverse Fourier transform on the signal in a wavenumber domain to obtain an airspace complex amplitude signal; step 2, selecting a surface complex amplitude signal according to the maximum signal intensity based on the airspace complex amplitude signal; step 3, calculating average low-frequency intensity based on the surface complex amplitude signal to obtain an actual defocusing distance; 4, performing refocusing calculation based on the surface complex amplitude signal and the actual out-of-focus distance to obtain a refocusing surface signal; and step 5, based on the refocusing surface signal, calculating and outputting a morphology height difference. According to the method, the effective measurement range of OCT nano-morphology detection can be expanded, the morphology detection capability of a non-flat surface is optimized, side lobe artifacts caused by defocusing are inhibited, the method is realized based on numerical calculation, and the system complexity and cost are reduced.

The invention discloses an Airy beam generation method and device. The method comprises the following steps: S1, determining a working frequency and constructing the device; s2, establishing a corresponding relationship between the geometric parameters of the leaky wave unit and the leaky wave phase and amplitude; s3, solving one-dimensional Airy beam complex amplitude distribution; s4, reversely solving unit geometric parameters to realize target complex amplitude regulation and control; and S5, constructing the metasurface complex amplitude regulation and control device based on the one-way electromagnetic mode. According to the invention, the size of the metal block and the thickness of the air dielectric layer are independently regulated and controlled, so that complex amplitude regulation and control of transmission waves in a free space are realized; the metasurface device is simple and convenient in structural design, high in efficiency, easy to integrate and reconfigurable, can replace a spatial light modulator through a one-way waveguide phase regulation and control function, reduces the system cost, improves the integration level, and is suitable for on-chip integrated efficient free space wavefront control application.

The invention discloses a four-focus long-focal-depth broadband achromatic superlens design based on an improved weighted GS algorithm, and belongs to the field of micro-nano optics. The super lens comprises a silicon dioxide substrate and a titanium dioxide cylindrical nano column array. In the initial iteration stage of the GS algorithm, focusing and axicon superposition phases are adopted to construct a complex amplitude field, and a dynamic amplitude weighted feedback mechanism is introduced. According to the design, four off-axis focuses with highly uniform energy are realized on a target focal plane, and focal length drift caused by broadband dispersion is covered by using an expanded super-long focal depth. Simulation shows that within the range of 640-740 nm, the average focal depth of the device reaches 6.33 microns, the focus intensity deviation is smaller than 5%, the average focusing efficiency is 62.47%, and broadband achromatic focusing is effectively achieved. The method has a wide application prospect in the fields of parallel laser processing, high-throughput imaging and the like.

The present invention discloses an efficient and differentiable method for simulating optical system degradation. The method involves first processing the optical system's entrance pupil in computer optical simulation software, sampling the entrance pupil and then processing it to obtain sampling grid points. Coherent complex amplitude and conjugate product processing are then performed on the sampling grid points to obtain a point spread function (PSF). Backward gradient propagation is then performed on the parameters in the PSF to obtain the optimized gradients of the parameters in the PSF. Finally, degradation processing is performed on the optical system based on the optimized gradients. The present invention accurately simulates image quality degradation in optical systems using the PSF and implements gradient backpropagation with low computational overhead. The method is widely applicable to optical-numerical joint optimization tasks in general optical systems.

This invention proposes a low-noise holographic 3D display method based on a fractional Fourier transform algorithm. The method includes the following steps: First, setting the signal and noise intervals of the recorded object to obtain a preprocessed image RD(X,Y); Second, superimposing the image RD(X,Y) with a quadratic phase generator to produce a corresponding complex amplitude distribution D0(X,Y) on the object plane; then, performing a fractional Fourier transform based on the complex amplitude distribution D0(X,Y) on the object plane to obtain a complex amplitude distribution D1(X,Y) on the holographic plane; extracting the phase information of D1(X,Y) and... The complex amplitude distribution D2(X,Y) of the object plane is obtained through fractional-order inverse Fourier transform. A double constraint of amplitude and second-order phase is applied to the signal interval of D2(X,Y) to obtain the complex amplitude distribution D3(X,Y) of the object plane, completing the first iteration. The complex amplitude distribution D3(X,Y) is then used to replace D0(X,Y) to start the next loop, continuing until the phase converges to the optimal solution. In the third step, the phase distribution of the optimal solution is extracted to generate a pure phase hologram. By superimposing pure phase holograms of different depths, the final pure phase hologram of the 3D object is obtained. Low-noise holographic 3D display is achieved by illuminating the pure phase hologram of the 3D object with coherent light.

The application relates to a kind of optical device parameter measurement methods based on mathematical physics combination, medium and system, to optoelectronic test technical field, it includes: the physical field simulation model of optical device is established and obtains port electromagnetic field distribution;Utilize waveguide mode orthogonality to the port electromagnetic field is carried out surface integration, obtains the frequency domain complex amplitude of each port;According to the frequency domain complex amplitude, calculate scattering matrix, extract optical device parameter.The optical device parameter measurement method provided by the application can reflect the physical characteristics of the optical device, and can be accurately fitted and optimized through mathematical algorithm, thereby improving the accuracy and efficiency of parameter extraction.

The application discloses a mode purity measurement method of a few-mode ring core fiber based on principal component prior information. First, all spatial modes supported by the few-mode ring core fiber to be measured are calculated to determine the highest order; second, a nonlinear equation set connecting the fiber output intensity mode spot and the complex amplitude of each spatial mode is listed, and an algorithm for solving the equation set by using the principal component order prior information is designed, so that the recovery of the complex amplitude of each mode and the measurement of the principal component mode purity are realized. Then, an optical device for detecting the fiber exit mode field is built. For the fiber near-field intensity mode spot at any time, the prior information of the principal component order is obtained through an interference pattern or the shape of the intensity mode spot, and the measurement of the mode purity can be realized by applying the above-mentioned algorithm. The application can accurately recover the mode purity of the few-mode ring core fiber from the fiber output near-field intensity mode spot only, and has strong applicability.

The application provides a line spectrum estimation method for a two-dimensional blind source compressed signal. The blind source is reflected in that the number of effective signal sources is unknown, the azimuth angle is unknown, and the signal complex amplitude is also unknown. Signal data is obtained by a sensor and then compressed and added with noise to obtain detection data. According to the detection data, an approximate message passing method on a factor graph is used to respectively estimate the activated factor sequence and the approximate posterior probability of the signal complex amplitude, the signal angle value is obtained by using a positioning module, and then the estimation value of the signal source number and the signal complex amplitude is obtained according to the signal source number and the approximate posterior probability of the signal complex amplitude. Compared with the prior art, the advantages of the present application are as follows: first, compared with BIG-AMP, the algorithm has the advantage of not needing the prior distribution of the signal azimuth angle; second, compared with ESPRIT, the algorithm has the advantage of also providing an estimation of the signal complex amplitude; and third, compared with the AMP+ESPRIT algorithm, the algorithm has the advantage of allowing the signal source number to be unknown.

The application discloses a two-dimensional direction of arrival estimation method based on L-array prior waveform signal source, comprising the following steps: solving the two-dimensional direction of arrival angle of the prior waveform based on a first convex optimization function to solve the underdetermined equation insoluble problem generated when solving the two-dimensional direction of arrival angle according to an estimated angle vector model, and obtaining an initial estimated value of the two-dimensional direction of arrival angle; solving the two-dimensional direction of arrival angle of the prior waveform based on a second convex optimization function to solve the off-lattice phenomenon generated when executing the above step, and obtaining an optimal estimated value of the two-dimensional direction of arrival angle; determining the complex amplitude estimated value of each group of two-dimensional direction of arrival angle according to the optimal estimated value; and matching the prior waveform corresponding to the two-dimensional direction of arrival angle according to the complex amplitude estimated value, and obtaining the optimal estimated value of the two-dimensional direction of arrival angle of each prior waveform. The application has a smaller calculation complexity and can be applied to a scene with a higher real-time requirement.

The invention provides a design method for a diffraction optical element with a large diffraction angle, and the method comprises the steps: firstly, calculating a transmission complex amplitude needed for achieving a diffraction pattern in a far field according to a target diffraction pattern and related parameters; and gradually reducing the diffraction propagation distance through iteration by taking the transmission complex amplitude of the element as an initial parameter until the transmission complex amplitude of the element meeting the requirement is obtained and is output as a result. The method is suitable for the design of a diffractive optical element working under the conditions of a large diffraction angle and a limited propagation distance; compared with an existing design method for a small diffraction angle, the design method has the advantage that the designable diffraction angle range is obviously increased. Meanwhile, the calculation complexity is effectively optimized, and the method is suitable for design of large-size diffractive optical elements in finite time. Besides, correction processing on the transmission complex amplitude of the element is added in the design process, so that the working robustness of the designed element can be effectively improved, and the designed element can stably work under the condition that a certain machining error exists.

The application relates to a UAV array dynamic angle of arrival estimation method and system, which comprises the following steps: S1, acquiring array snapshot data after reference channel auxiliary synchronization and waveform compensation; S2, establishing a parameterized space-time coupling phase model in a short coherence processing interval; S3, based on the array snapshot data, obtaining a single-channel input sequence through beam forming, and estimating a radial parameter pair by using time domain atom matching filtering; S4, based on the radial parameter pair, performing common time phase compensation on the array snapshot data to obtain a compensated snapshot matrix; S5, performing two-dimensional correlation calculation by using a space-time steering atom to estimate an angle parameter pair; S6, constructing a complete space-time dictionary atom, and estimating a complex amplitude by using a least square criterion; and S7, performing successive interference cancellation to update a residual error. Compared with the prior art, the application has the advantages of keeping low signal-to-noise ratio coherence gain and significantly reducing calculation complexity.

The invention proposes a polarization Fourier 3D hologram calculation method, and the method comprises the following four steps: 1, dividing a 3D object into a 3D object I corresponding to a left-hand circular polarization state and a 3D object II corresponding to a right-hand circular polarization state, and introducing a phase difference to represent the polarization state; 2, superposing random phases to obtain initial complex amplitude distribution of an object plane, obtaining holographic surface complex amplitude distribution based on fractional Fourier transform, obtaining holographic surface phase distribution after applying first constraint, obtaining complex amplitude distribution of the object plane through fractional Fourier inverse transform and second constraint, and obtaining holographic surface phase distribution after applying second constraint; the initial complex amplitude distribution is replaced for circulation until the phase converges; 3, respectively exporting final phase distribution corresponding to the left-handed circular polarization state and the right-handed circular polarization state to obtain a left-handed polarization state sub-hologram and a right-handed polarization state sub-hologram; and step 4, sampling the two sub-holograms line by line to obtain a final polarization Fourier 3D hologram.

Provided is a method for generating a high-quality amplitude-type computer-generated hologram. Selecting target light field intensity distribution of the object plane, and generating an initial phase; generating complex amplitude distribution of the object plane according to the intensity distribution and the initial phase of the object plane; performing single side band angular spectrum iteration on the complex amplitude distribution of the object plane to obtain diffraction complex amplitude distribution of a holographic surface; and coding the complex amplitude distribution of the holographic surface into an amplitude-type computer-generated hologram, and generating an optimized high-quality amplitude-type computer-generated hologram. The single side band angular spectrum propagation adopted by the method reduces the calculation data volume and complexity, can generate a high-quality amplitude type calculation hologram, suppresses conjugate image noise and speckle noise in wavefront reconstruction, and is stable in convergence and wide in application range.

The invention discloses an information encryption method and system based on incoherent topological structure light. The method comprises the following steps: determining a target topological structure serving as an encryption key and a statistical coherence parameter representing to-be-encrypted information; constructing a cross spectral density function of a light source surface based on the two, and coding coherent singular point distribution of a corresponding target topological structure in the complex coherence degree; generating a complex amplitude hologram according to the function, generating a partially coherent topological structure light field through modulation of a spatial light modulator, and performing interference with reference light to obtain a light field image; performing coordinate transformation and frequency domain filtering on the image, and extracting a complex coherence degree function and counting far-field intensity distribution corresponding to coherence parameters; and finally, authentication is completed by verifying the consistency of the reconstructed topological structure and the target topological structure, and transmitted information is decoded based on intensity distribution. According to the invention, high-capacity and high-security optical information encryption is realized through two-degree-of-freedom independent coding of a topological structure and statistical coherence.

The invention discloses a mode selection analysis method and system for a satellite-ground laser communication mode diversity technology, a product and an element manufacturing method, belongs to the technical field of space laser communication, and solves the problem that the prior art directly selects first several modes as a group of fixed orthogonal mode bases due to experience; therefore, the technical problem that the stability of a communication link is reduced due to the fact that the optimal performance cannot be kept in a dynamically changing channel is solved. The method comprises the steps of 1, constructing a dynamic turbulence data set; 2, performing dynamic mode decomposition on complex amplitude distribution of the degraded light spots in the dynamic turbulence data set to obtain instantaneous power proportions of the degraded light spots in different modes; and 3, carrying out statistical analysis on the instantaneous power proportions of the degraded light spots in different modes, and screening out an optimal fixed mode combination in combination with the target turbulence intensity. The invention is used for realizing efficient optical signal transmission.

In a digital holographic wrapped phase aberration compensation method based on deep learning, a random Zernike polynomial coefficient and a corresponding wrapped phase map are generated by a computer and are respectively treated as a learning label and a network to train a neural network model. A digital holographic optical setup is built to record a hologram of a sample to be measured, the wrapped phase map is inputted into the trained neural network model after numerical reconstruction, and the Zernike polynomial coefficient is outputted to reconstruct a phase aberration distribution and to compensate complex amplitude in a spatial domain. Phase filtering and unwrapping are performed on the compensated wrapped phase map, and Zernike polynomial fitting based on background segmentation is performed on the unwrapped phase to compensate for residual aberration.

This invention discloses a method and system for phase measurement of metalenses in a refractive-meta-hybrid system. By constructing a reference complex amplitude distribution corresponding to the modulation characteristics of the refractive optical unit, the phase modulation introduced by the refractive optical unit can be decoupled based on the reference complex amplitude distribution after phase inversion. When the physical parameters of the refractive optical unit are set to be equivalent to free space or air, the reference complex amplitude distribution is the light field distribution directly propagated from the illumination source to the surface of the metalens. To address factors such as light source power fluctuations, exposure differences, and non-ideal illumination beam profiles, the measurement amplitude distribution corresponding to the measurement intensity distribution of the defocus plane is normalized and corrected using an energy ratio coefficient. Furthermore, by fusing the reference amplitude distribution with a hybrid weighting factor and the return amplitude distribution corresponding to the return complex amplitude distribution of the exit surface, the stability of the iterative inversion process can be improved and the inversion bias introduced by amplitude mismatch can be reduced.

This invention provides a wavefront phase recovery method, an atmospheric channel estimation method, and an apparatus for atmospheric laser communication systems. The method includes: acquiring multiple sets of deflection measurement amplitude data corresponding to a target distorted beam; obtaining a first complex amplitude corresponding to each set of deflection measurement amplitude data based on a non-convex initialization prediction algorithm; iteratively operating on each set of first complex amplitudes using a gradient descent-based non-convex optimization algorithm to obtain a reconstructed complex amplitude that meets the target recovery conditions; and determining the wavefront phase information of the target distorted beam based on the reconstructed complex amplitude. This invention can obtain the globally optimal wavefront phase information when using a gradient descent-based non-convex optimization algorithm for wavefront phase recovery, thereby improving the accuracy of phase recovery.