123 results about "Zernike polynomials" patented technology

The invention discloses an online monitoring method and system for the light transmittance of an optical lens, and relates to the technical field of precise optical detection. The objective of the invention is to solve the problem of large light transmittance calculation error caused by halo scattering noise interference, low optical path calibration precision of a complex curved lens, a measurement blind area of a large-aperture lens and environmental disturbance of a high-reflection / high-light-transmittance lens in the prior art. According to the scheme, a three-dimensional curved surface model is constructed based on Gray code structured light projection and ICP registration, a dynamic partition scanning instruction set is generated through an improved genetic algorithm, and multi-wavelength polarized light is driven to scan and collect multi-dimensional data; specular reflection and scattering noise are suppressed by combining an improved Stokes vector algorithm and an attention mechanism U-Net network, and the data precision of the complex curved surface is improved by adopting Bayesian optimization and Zernike polynomial weighted fusion; constructing a double-loop coupling optimization architecture to realize closed-loop adaptive optimization; according to the invention, the anti-interference capability, the complex lens adaptability and the full-aperture detection precision are obviously improved.

The invention discloses a wafer polishing laser interference closed-loop pressure control method, and relates to the technical field of semiconductor manufacturing, and the method comprises the following steps: S1, triggering an automatic measurement program after a ceramic plate and a wafer are overturned; s2, driving a laser interference measuring head to perform non-contact scanning on T2 / T4 point positions of the wafer through a six-axis mechanical arm positioning system to obtain thickness distribution data; s3, fitting the thickness distribution data by adopting a Zernike polynomial to generate a three-dimensional distribution diagram, and calculating a pressure correction amount based on a process dynamic model and a pressure prediction model constructed by a support vector machine regression algorithm; s4, detecting a data outlier in real time through an exception handling module, and triggering an equipment protection strategy when the deviation exceeds a set threshold value; and S5, a pressure control instruction is transmitted to the polishing head through the PROFINET bus by means of the PLC. Through non-contact laser interference measurement, the laser interference technology is applied to thickness detection of the polished wafer for the first time, the single measurement time is shorter than 20 seconds, and the detection efficiency is remarkably improved.

The invention discloses an optical performance-oriented key geometric error identification method for a large aspheric element multi-axis numerical control machine tool. According to the method, a tool setting point is used as a key node to establish a surface shape error model, geometric errors and surface shape errors of a machine tool are accurately associated, multi-error coupling analysis is simplified, and targeted compensation, online monitoring and real-time correction are achieved. On the basis, a machine tool space error model is constructed in combination with a multi-body system theory, a mapping relation between a surface shape error and wavefront aberration is established by utilizing a ray tracing theory, the wavefront aberration is fitted through a Zernike polynomial, and the contribution degree of each geometric error to the aberration is quantified by means of principal component analysis, so that a key geometric error is identified and compensation is implemented. According to the method, the machining error and the final optical performance are directly associated, and the machining precision and the performance quality of the large aspheric element can be improved. The method is suitable for the manufacturing field of large complex optical elements machined by a multi-axis numerical control machine tool.

The invention relates to a multi-spectral wavefront aberration restoration method and system based on double roof prisms, and the method comprises the following steps: taking a sub-pupil image as the input of a classification model, obtaining classification feature data, and carrying out the data expansion of the classification feature data, the sub pupil image is obtained by inputting incident wavefront aberration into a simulation light path of the double-ridge prism wavefront sensor, the double-ridge prism wavefront sensor comprises two groups of double-ridge prisms, each group of double-ridge prisms comprises two ridge prisms which are vertically and oppositely arranged, the characteristics of the ridge prisms are equal, and the characteristics of the double-ridge prisms are equal. The two groups of double-roof prisms are made of a material combination for eliminating chromatic aberration; splicing the sub pupil images and the classification feature data after data expansion to serve as input of a regression model, and obtaining a Zernike coefficient matrix corresponding to incident wavefront aberration; and according to the Zernike coefficient matrix corresponding to the incident wavefront aberration and the Zernike polynomial, obtaining a recovered wavefront aberration. Compared with the prior art, the method has the advantage that the wavefront aberration recovery accuracy is improved.

The invention discloses an underwater vortex optical communication anti-turbulence method based on a photoelectric hybrid deep neural network, and the method comprises the steps: carrying out the all-optical information compression at a front end through the diffraction deep neural network through the fusion of a diffraction deep neural network and a convolutional neural network, and transmitting the processed information to a rear end of the convolutional neural network, a model task is completed through training, a predicted coefficient of a Zernike polynomial is output, prediction and compensation of ocean turbulence are achieved, and the mode purity of vortex beams is improved. The front-end diffraction deep neural network is utilized to effectively improve the problem that the rear-end convolutional neural network is difficult to process massive information, the photoelectric hybrid deep neural network model is high in integration, high in operation speed and accurate in light field signal processing, the power overhead for achieving turbulence resistance through the machine learning technology is saved, operation is easy, implementation is easy, and the method is suitable for popularization and application. The method has a wide application prospect in the aspects of vortex beam underwater communication and the like.

The invention relates to an aspheric wavefront detection device and method based on multi-direction orthogonal lateral shear interference. The device is composed of a laser, a linear polarizer, a light splitting element, a reflector array, a two-dimensional orthogonal grating array, a light splitting system, a polarization phase shifting element and a CMOS camera. The method comprises the following steps: firstly, an antisymmetric continuation method is included, secondly, dynamic phase recovery and distortion compensation are adopted, Zernike polynomial local fitting is introduced, and self-adaptive compensation is carried out on high-order aberration (such as coma aberration and trefoil aberration) of an aspheric surface edge region. According to the method, the multi-direction orthogonal lateral shearing interferogram can be obtained through single measurement, and a high-precision, high-efficiency and high-robustness solution is provided for precise detection of the aspheric optical element through cooperation of an algorithm and hardware. The method is suitable for high-precision phase recovery in the fields of optical detection, microscopic imaging and the like, and is suitable for high-precision dynamic detection of complex optical elements such as off-axis aspheric surfaces, free-form surfaces and the like.

The invention relates to the technical field of coupling alignment of single-mode optical fibers, in particular to an optical fiber coupling alignment method and system based on wavefront aberration and a sensitivity matrix. The system comprises an optical measurement module, a processing and control module and a multi-axis precision adjustment platform, and the alignment method comprises the steps that firstly, an interference fringe image is obtained and processed through an interference light path, continuous wavefront is recovered through Fourier transform and phase unwrapping, and a Zernike coefficient for quantizing wavefront distortion is obtained through Zernike polynomial fitting. A sensitivity matrix representing the linear relation between the degree-of-freedom adjustment amount and Zernike coefficient changes is established and serves as a physical guide item to introduce a speed updating formula of a particle swarm optimization algorithm, an SG-PSO algorithm is formed, a particle swarm is guided to conduct directional intelligent search and rapidly output the optimal adjustment amount, and finally a multi-axis precision adjustment platform is driven to complete alignment. According to the method, optimization of wavefront sensing and physical model guiding is effectively fused, and the convergence speed, the alignment precision and the global search capability are remarkably improved.

The invention relates to the technical field of optical imaging, and discloses an optical lens splicing imaging method and system, and the system comprises a calibration module, a preprocessing module, a registration module, a correction module, and a fusion module. Through the arrangement of the registration module, the correction module and the fusion module, the problem of registration errors caused by sparse feature points of a low-texture region can be solved through a mixed strategy of global mutual information guidance and local robust matching, the registration precision is effectively improved, the optical aberration of each sub-lens is compensated through a global model based on a Zernike polynomial, and the registration precision is improved. The image quality of the marginal area of the spliced image is effectively improved, a multi-resolution pyramid optimization mode is adopted, the calculation complexity of global registration is reduced, the real-time imaging requirement is met, meanwhile, splicing seams are effectively eliminated, and the overall smoothness of the image is remarkably improved.

The invention relates to the technical field of image processing, and discloses a laser holographic aberration compensation system and method based on deep learning, and the system comprises a first module which determines a phase-to-gray lookup table; the second module is used for calculating to obtain stacking strength; the third module is used for obtaining a Zernike polynomial coefficient through a convolutional neural network regression device; the fourth module is used for calculating to obtain predicted intensity and an aberration estimator; the fifth module is used for outputting two grey-scale maps; and the sixth module outputs two phase diagrams. According to the method, self-supervised training data is constructed through three-plane intensity collection, and an angular spectrum method physical model and Zernike polynomial coefficient low-dimensional representation are combined, so that a convolutional neural network regression device can stably learn aberration mapping, and compensation precision and generalization ability are both considered; double-phase two-frame time division coding is adopted, the output characteristics of a phase type spatial light modulator can be adapted, and cooperative control of aberration compensation and target complex field reproduction is achieved.

A single-frame speckle deflection measurement method based on subarea wavefront correction belongs to the technical field of optical measurement, and comprises the following steps: based on a monocular deflection measurement system, projecting a standard speckle image to a to-be-measured mirror surface from a screen, and collecting a single-frame deformed speckle image reflected by the to-be-measured mirror surface; processing the reflected image by using a Zernike polynomial projection distortion correction method based on a mark point, and correcting the projection distortion of the reflected image caused by a non-orthogonal light path; obtaining sub-pixel mapping of the reflection image and the standard image based on a sub-region wavefront fitting correction and iterative registration algorithm; and based on system calibration and camera calibration, establishing a spatial incident light model and a spatial reflected light model, obtaining surface gradient distribution of the to-be-measured mirror surface, and reconstructing a three-dimensional shape of the to-be-measured mirror surface. According to the method, a reference plane is not needed, high-reflection surface shape measurement of only collecting a single-frame image can be achieved, the dynamic range and precision of speckle deflection measurement are improved through subarea wavefront correction, and the surface reconstruction precision can reach hundreds of nanometers.

The invention belongs to the technical field of short-wave communication channel modeling, and discloses a short-wave channel modeling method and system based on signal wavefront recovery, and the method comprises the steps: projecting standard plane waves to an antenna array from different angles through a cooperative target radiation source, collecting antenna array signals in different directions under the condition of no disturbance, and storing the signals as calibration data; calculating the time delay of each antenna before receiving the wavefront relative to the center of the antenna array, calculating the relative time delay of the time delay and the calibration data, and multiplying the relative time delay by the wavelength to realize the time domain-space domain conversion of wavefront distortion to obtain wavefront slope distribution; and calculating the size of a Zernike polynomial coefficient of each order based on wavefront slope distribution, analyzing specific components of aberration contained in signal wavefront, and performing wavefront fitting reconstruction so as to complete short-wave channel modeling. According to the method, the Zernike polynomial is adopted to fit the wavefront disturbance quantity, the influence of the ionized layer on the wavefront of the short-wave signal is quantified in real time, and a high-precision channel model is constructed.

The invention relates to an optical component, in particular a mirror, comprising: at least one heating structure (25, 25a) that can be subjected to an electric current, in particular a resistance heating structure, for introducing heat into a material of the optical component. In one aspect of the invention, the heating structure (25a) and a further, adjacent heating structure (25b) have interlocking edge structures (30a, 30b), wherein a heating power density (1a) of the edge structures (30a) of the heating structure (25a) on a side (32b) of the edge structures (30a) of the heating structure (25a) facing the further heating structure (25b) is lower than on a side (32a) of the edge structures (30a) of the heating structure (25a) facing away from the further heating structure (25b).In another aspect of the invention, the at least one heating structure (25) extends substantially over the entire optical surface (27) of the optical component and has a locally varying electrical resistance (Ra(x,y)) which preferably approximates a basis function extending substantially over the entire optical surface (27), in particular a Zernike polynomial.

The invention discloses a method for obtaining human eye wavefront aberration and a human eye aberration measuring device, and relates to the technical field of optical instruments.The method for obtaining the human eye wavefront aberration is applied to a Hartmann sensor and comprises the steps that an actual slope matrix is obtained through calculation according to a wavefront light spot diagram obtained by the Hartmann sensor; multiplying the generalized inverse matrix of the standard slope matrix by the actual slope matrix to obtain a Zernike coefficient matrix; subtracting the actual slope matrix from the product of the standard slope matrix and the Zernike coefficient matrix to obtain a residual matrix; and updating the Zernike coefficient matrix according to the residual matrix until the residual matrix of the updated Zernike coefficient matrix is smaller than or equal to a preset value. Wherein the standard slope matrix is a matrix formed by wavefront slope of Zernike polynomial full-term superposition. According to the technical scheme provided by the invention, the accuracy of obtaining the wavefront aberration of the human eye can be improved.

The invention relates to a dynamic light beam shaping system and method based on a spatial light modulator. The system comprises a laser light source module, a beam expanding collimation light path, a light beam modulator, a focusing optical assembly, a detection and feedback module and a control and optimization module. According to the method, the uniformity of the output flat-topped beam can be corrected by virtue of a random parallel gradient descent (SPGD) algorithm and combining a Zernike polynomial as a control variable. Meanwhile, a composite performance index comprehensively considering energy distribution and shape features is constructed, the correction process of the flat-topped beam is accelerated by adopting a mode of gradually improving Zernike polynomial orders in multiple stages, the convergence trend of the performance index is used as a judgment basis of stage switching, stage independent variable dimension expansion is implemented, and the correction precision of the flat-topped beam is improved. And the convergence speed is obviously improved. Besides, adaptive selection of disturbance amplitude and learning rate parameters in the SPGD algorithm is realized by using noise estimation and a local linearity index, and the robustness of the system to noise and environmental disturbance is enhanced.

The invention relates to a rapid tilt compensation method based on a Zernike polynomial. The method comprises the following steps: acquiring a two-dimensional image matrix output by a digital holographic microscope; the two-dimensional image matrix is preprocessed; the preprocessed image intensity matrix is projected to a Zernike polynomial base # imgabs0 #, Zernike fitting is achieved, and a Zernike model of a related sample to be detected is obtained; calculating tilt term coefficients alpha x and alpha y of a first-order polynomial in the Zernike model; and calculating out-of-focus aberration # imgabs1 #, performing tilt compensation on the preprocessed image intensity matrix by adopting tilt term coefficients alpha x and alpha y, and outputting the compensated image intensity matrix. The invention further discloses the corresponding electronic equipment. According to the method, the shot image can be quickly and effectively compensated and corrected, and the robustness and the calculation speed are considerable.

The invention relates to an SAR photoelectric processor phase error compensation method based on a Zernike polynomial, and the method comprises the steps: obtaining an SAR photoelectric processor to be subjected to phase error compensation, and employing the Zernike polynomial to express the modulation phase of a spatial light modulator in the SAR photoelectric processor; respectively calculating two-dimensional frequency domain phases of an ideal SAR echo signal and a non-ideal SAR echo signal of the SAR photoelectric processor, determining a focusing phase error, fitting the focusing phase error by adopting a Zernike polynomial, and evaluating focusing phase error (parameter) estimation performance; a plurality of Zernike coefficients are randomly generated for a Zernike polynomial, optimization of the Zernike coefficients is carried out by adopting a genetic algorithm, and the quality of the SAR image is used as a fitness value of the genetic algorithm until the Zernike coefficients meeting optimization conditions of the genetic algorithm are obtained and used for prediction of a modulation phase. Compared with the prior art, the two-dimensional frequency domain phase error can be effectively corrected, and a theoretical foundation is laid for an automatic focusing algorithm special for SAR optical processing.

The invention relates to the technical field of myopia prevention and control lens manufacturing, and discloses a multi-focus out-of-focus myopia prevention and control lens based on a micro-lens array, the multi-focus out-of-focus myopia prevention and control lens comprises a peripheral area and a central area, the central area is used for correcting refraction, and the central area is located in the middle of the peripheral area. The peripheral area uses a Zernike polynomial to construct a dynamic defocusing model, the defocusing amount can be dynamically adjusted, the dynamic defocusing model obtains eyeball movement information through a feedback system, the frequency of real-time adjustment of the defocusing amount along with eyeball movement is larger than or equal to 10 Hz, and the defocusing amount of the peripheral area is changed in a gradient mode from + 2.00 D to + 4.00 D. A dynamic defocusing model is constructed by using a Zernike polynomial, and the model obtains eyeball movement information through a feedback system, so that the problem that the prevention and control effect is reduced due to the fact that the defocusing amount of the peripheral area of a traditional multi-focus defocusing myopia prevention and control lens is mostly fixed and the focus cannot be overlapped with the retina in real time when the eyeball moves is solved.

The invention discloses a novel method for measuring the surface shape of a large-aperture film mirror surface, and the method comprises the steps: obtaining a reflected deformed fringe image based on a four-step phase shift method, and obtaining the wrapped phase distribution of the image after modulation; performing labeling processing on the level of the wrapped phase distribution by using a Gray code to obtain unpacked phase distribution; a camera is used for collecting a film mirror image, center coordinate and radius labeling is carried out on the image, center coordinate symmetry operation is carried out on unpacking phase distribution, and phase change is obtained; obtaining the relation between the phase change and the gradient, obtaining the coefficient matrix of the first 36 constant terms of the zernike polynomial by using the least square method, further obtaining the surface shape data of the thin film mirror surface, and outputting the current surface shape data of the thin film mirror surface when the difference value of the current and later surface shape data of the thin film mirror surface reaches a convergence threshold value, thereby completing the measurement of the surface shape of the thin film mirror surface. According to the invention, the problems of large stripe deformation and discontinuous phase caused by overlarge mirror gradient are solved, and the limitation of film mirror measurement is solved.

The present application relates to the technical field of optical interferometry, and particularly relates to a high-precision phase demodulation method based on a PhaseUnet++ network.The method comprises the following steps:1. Zernike polynomials are used to generate training data and test data for network training;2. a neural network PhaseUnet++ is established and trained;3. normalized cosine interferograms I cos and auxiliary diagrams I sac are input into the trained network, and normalized sinusoidal interferograms I sin are output;4. the wrapped phase distribution is obtained by using an arctangent function, and the unwrapped phase distribution φ(x,y) is obtained by using a phase unwrapping algorithm.The present application has high precision, can process interferograms of different sizes, has strong noise resistance, can realize phase measurement of dynamic samples, has high reconstruction result precision, simple steps, wide application range, and great application prospect in the field of optical interferometry research.

The application discloses a wafer polishing laser interference closed-loop pressure control method, and relates to the technical field of semiconductor manufacturing, and comprises the following steps: S1: a ceramic plate is triggered to automatically measure a program after being turned over with a wafer; S2: a laser interference measurement head is driven by a six-axis mechanical arm positioning system to non-contact scan T2 / T4 points of the wafer, and thickness distribution data is acquired; S3: a Zernike polynomial is adopted to fit the thickness distribution data to generate a three-dimensional distribution graph, and a pressure correction amount is calculated based on a pressure prediction model constructed by a process kinetics model and a support vector machine regression algorithm; S4: an abnormal processing module is used to detect data outliers in real time, and a device protection strategy is triggered when a deviation exceeds a set threshold; and S5: a pressure control instruction is transmitted to a polishing head by a PLC controller through a PROFINET bus. By means of non-contact laser interference measurement, the laser interference technology is applied to wafer thickness detection after polishing for the first time, and single measurement time is less than 20 seconds, so that the detection efficiency is significantly improved.

The present application relates to the field of optical interferometry, and aims at the phase distortion problem in off-axis interferometric quantitative phase imaging, and provides an interferometric microscopic phase distortion elimination method based on PACUNeXt3+ network. The method comprises the following steps: 1. using Zernike polynomials and test target pictures to simulate and generate a data set; 2. establishing and training a PACUNeXt3+ neural network model; 3. inputting the interference graph I or of the sample to be measured into the trained neural network, and outputting the background interference graph I' r corresponding to the sample without sample information; 4. using the two interference graphs I or and I' r to reconstruct the sample phase distribution φ o (x, y) without phase distortion. The present application has high precision and speed, can eliminate the secondary or high-order phase distortion in interferometric quantitative phase imaging, and has great application prospect in the field of phase imaging.

This invention relates to the fields of optical interferometry and artificial intelligence image processing, specifically to a high-precision phase extraction method for orthogonal transverse shearing interferograms based on generative multimodal AI. This method integrates the spatial texture of the interferogram with the constraints of the orthogonal shearing mathematical model through a multimodal feature fusion module, constructing a hybrid architecture of Generative Adversarial Network (GAN) and U-Net with a physical prior loss function. This achieves an end-to-end nonlinear mapping from the interferogram to the wrapped phase, and combines differential Zernike polynomial (DZF) to complete high-precision reconstruction of the absolute phase. Experimental results show that in low signal-to-noise ratio orthogonal transverse shearing interferograms, the proposed method reduces the root mean square error (RMSE) of phase extraction by 42.7% compared to the traditional DZF method, and improves the spatial resolution to λ / 100, providing an efficient and high-precision phase extraction scheme for optical wavefront detection.

The invention discloses an under-sampling interference fringe wrapped phase demodulation method, and relates to the technical field of optical detection, the invention relates to an under-sampling interference fringe pattern wrapped phase demodulation method, according to an original to-be-demodulated wrapped phase, the phase gradient distribution of the original to-be-demodulated wrapped phase in x and y directions is calculated: gradx, grady; according to the method, the characteristic that phase data to be demodulated are continuous and derivable is utilized, and the method of mode Zernike polynomial fitting and residual least square fitting is combined to complete demodulation of the under-sampled fringe pattern wrapped phase data. According to the method, the problem that the dynamic range is limited in the interference measurement process can be solved without changing the hardware conditions of the interferometer, such as changing the wavelength of a light source or increasing the resolution of a detector, and particularly, the method has a good application effect on large deviation errors caused by the edge effect of the surface of an optical element in the initial stage of optical processing.

The invention discloses a beta distribution-based composite aberration construction method, which relates to the technical field of laser optics and comprises the following steps of: constructing a non-ideal laser initial light field; generating a Zernike polynomial weight coefficient based on a beta distribution model; substituting the weight coefficient into the phase expression to form a composite aberration mode, and substituting the composite aberration mode into the non-ideal laser initial light field to obtain a non-ideal laser initial light field with composite aberration; repeating the steps, generating N groups of different weight coefficient combinations corresponding to N composite aberration scenes, simulating transmission evolution of laser in atmospheric turbulence by adopting a multi-layer phase screen method for each group of aberrations, and performing simulation calculation; a simulation result change rule is observed by changing parameters of the beta distribution model, and a parameter-light spot quality mapping relation is established. According to the method, the beta distribution model is introduced, a brand new technical path is provided for flexible construction and high-precision simulation of the composite aberration, and the reliability and efficiency of laser optical system design can be effectively improved.

The present application relates to the technical field of semiconductor lithography, and particularly relates to a high-precision overlay compensation method, comprising: using Zernike polynomials to calculate global overlay error of a wafer to obtain field-by-field compensation model parameters; using a compensation formula based on the field-by-field compensation model parameters to calculate to obtain actual wafer overlay compensation parameters; comparing the actual wafer overlay compensation parameters and the field-by-field compensation model parameters of the actual wafer to obtain a comparison result. The comparison result is judged, if the comparison result is within a preset range, the comparison result is applied to production process for compensation, if the comparison result is not within the preset range, the problem is explored and diagnosed, by using the Zernike polynomial model and the field-by-field compensation model of the reference wafer, the overlay error of the wafer of any batch and any machine is quickly compensated, thereby solving the problem of low efficiency of the existing compensation method.

The present invention provides a method and device for combined quantitative distribution analysis of wavefronts and image quality assessment of a three-mirror zoom system. The method comprises: obtaining aberration changes caused by changes in pupil position during zooming based on the relationship between primary aberration coefficients and diaphragm position, and evaluating the optimal diaphragm position of the three-mirror zoom system based on the aberration changes; fitting the wavefront shape of the exit pupil in the three-mirror zoom system using Zernike polynomials, and evaluating the oscillation of the wavefront shape based on the fitting results; analyzing the pupil wavefront before and after the diaphragm position change, calculating the pupil wavefront deformation caused by the diaphragm movement, and achieving full-focal-range image quality assessment of the three-mirror zoom system. The present invention can analyze the exit pupil wavefront shape and the aberration coefficients and wavefront changes caused by pupil changes for a three-mirror zoom system with variable focal length at all focal lengths, providing a theoretical basis for subsequent directional optimization design of optical systems.

A method for compensating for grating defocusing errors in grating shearing interferometry systems involves replacing the coefficients of the Z4 and Z9 Zernike polynomials of the fitted wavefront measured after the image-plane grating has defocused with the corresponding coefficients when the image-plane grating is located at the focal plane. This refits the wavefront to achieve algorithmic compensation for the system error. Simultaneously, the method calculates the actual defocus distance of the image-plane grating, enabling mechanical compensation by adjusting the grating to the imaging focal plane. This method eliminates the defocusing error introduced by image-plane grating defocusing, improving the accuracy of grating shearing interferometry detection optical systems.

The off-focus holographic measurement method of the planet zoom-based radio telescope of the application carries out off-focus observation on a planet as a source, obtains an actual observed beam pattern of the planet through deconvolution, establishes a theoretical far-field model of the planet, compares the theoretical far-field model of the planet with the actually observed beam pattern to calculate a redundancy value, continuously updates coefficients of Zernike polynomials through minimization of the redundancy value and iteration until an optimal phase model is determined, and determines a phase error on an aperture plane according to the phase model. The off-focus holographic measurement method of the application introduces a planet as a radio source, not only improves measurement accuracy and stability, but also enhances real-time measurement effect and multi-frequency calibration capability, significantly improves calibration accuracy and overall performance of the Tianma radio telescope, and solves many limitations of traditional surface measurement methods, such as slow measurement speed, need of additional hardware devices, great influence of weather, limited application range and the like.

The invention discloses a method and a system for improving the signal-to-noise ratio of a dark field scattering signal of a semiconductor wafer. The method comprises the following steps: S1, acquiring an original dark field signal of a bare wafer or a coated wafer; s2, preprocessing the original dark field signal data, including zero equalization of the data and removal of outlier signals in the original data; s3, performing Zernike polynomial fitting on the preprocessed dark field data to obtain a low-frequency background noise signal of the dark field data; and S4, subtracting the low-frequency background noise signal fitted by the Zernike polynomial from the dark field original data to obtain residual data. After the fitted background noise is removed, the signal intensity of the original defect is basically kept unchanged, but the signal-to-noise ratio can be remarkably improved, and the defect detection sensitivity and accuracy can be improved.

The invention provides an interference measurement method, device and equipment for eliminating wavefront errors of low-temperature window glass and a storage medium, relates to the technical field of interference measurement, and aims to solve the problem that the interference measurement precision is reduced due to additional wavefront errors introduced by thermal deformation of window glass in a low-temperature environment. The method comprises the following steps: enabling a low-temperature vacuum cavity to stably run until the wavefront error of window glass is stable, carrying out in-situ, X-direction translation, Y-direction translation and four times of interference measurement after rotation on a to-be-measured piece in the cavity, calculating differential wavefront data, expressing the surface shape of the to-be-measured piece by using a Zernike polynomial, substituting the surface shape into the differential data, solving a coefficient fitting surface shape by using a least square method, and calculating the wavefront error of the to-be-measured piece. And window wavefront error elimination is realized. The collimator and the six-dimensional adjusting frame are matched to control inclination errors, simulation and experiments verify that the residual error root-mean-square error is low, and the low-temperature interference measurement precision and reliability can be effectively improved.