70 results about "Zernike polynomials" patented technology

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.

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 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 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 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 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.

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 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.

This invention discloses a method for extracting the wavefront tilt of astronomical optical interferometers. The method includes: acquiring an astronomical optical interferogram; preprocessing the interferogram using two-dimensional envelope detection normalization; performing anticosine phase unwrapping on the preprocessed interferogram to obtain the relative phase distribution of the wavefront; obtaining the tilt term coefficients through Zernike polynomial fitting and calculating the relative wavefront tilt. This invention can be applied to the extraction of the wavefront tilt of astronomical optical interferometers.

The application relates to a system aberration self-calibration method and device based on a double-interference common-optical-path measurement, wherein the method comprises the following steps: measuring an optical microstructure surface to be measured by using a double-interference common-optical-path measurement system to obtain phase distribution data and three-dimensional topographic height data; taking a Zernike polynomial as a base function to establish an aberration parameterization model of the double-interference common-optical-path measurement system; taking the phase distribution data as a reference, combining an analytical relationship between a laser interference channel and system aberration parameters, and inversely solving actual aberration coefficient sets of the double-interference common-optical-path measurement system in a current measurement state by using an optimization algorithm; reconstructing an aberration field corresponding to an entire measurement field by using the actual aberration coefficient sets of the double-interference common-optical-path measurement system and combining an analytical relationship between a white light interference channel and system aberration parameters, and point-by-point correcting the three-dimensional topographic height data by using the aberration field. The application can compensate system inherent aberration on line, self-reference and high precision.

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.

The application relates to the technical field of optical imaging, and discloses an optical lens splicing imaging method and system, the system comprising a calibration module, a preprocessing module, a registration module, a correction module and a fusion module; the registration module, the correction module and the fusion module are arranged, a mixed strategy of global mutual information guidance and local robust matching is used, registration error problems caused by sparse feature points in low-texture areas are solved, the registration precision is effectively improved, a global model based on a Zernike polynomial is used to compensate optical aberration of each sub-lens, the image quality of an edge area of a spliced image is effectively improved, a multi-resolution pyramid optimization mode is used to reduce the calculation complexity of global registration, real-time imaging requirements are met, and a splicing seam is effectively eliminated, and the overall smoothness of an image is significantly improved.

The invention provides a robustness support error separation method, electronic equipment and a storage medium, and relates to the technical field of support error separation, and the method comprises the steps: processing a physical reference mark in a non-clear aperture region of a to-be-detected optical element, recording the original coordinate of the physical reference mark in the coordinate system of the optical element to be detected; performing n times of interference measurement on the optical element to be detected; determining a 2D rotation matrix and a transverse translation vector corresponding to each measurement of the optical element to be detected; acquiring a preset measurement model; subtracting the interference surface data Mi measured at the ith time from the interference surface data Mi measured at the jth time; expanding Wtrue by adopting a Zernike polynomial, and constructing an overdetermined equation set in combination with Mi-Mj; carrying out reverse deduction to obtain a support error; the support error can be effectively separated.

This invention relates to an optimization method for progressive multifocal lenses. First, a portion of the progressive multifocal lens surface is replaced by a linear superposition of that area and a spherical surface. The spherical surface used is the one whose boundary is closest to the boundary of the replaced lens area, calculated using the least squares method. Then, Zernike polynomials are used to selectively fit the surface elevation of the replaced lens, further smoothing the progressive multifocal lens surface. This invention can control the optical power and astigmatic distribution in the astigmatic region of the progressive multifocal lens surface by changing the location and range of the region, thereby improving surface astigmatism and helping wearers obtain a better visual experience.

The application relates to a continuous surface fiber laser collimation beam combining device, belonging to the field of high-energy laser beam combining. The device comprises a fiber QBH interface backboard, a mechanical lens barrel and a continuous surface compound eye lens. The continuous surface compound eye lens is a free surface lens comprising a plurality of aspheric collimation units, and the collimation units are smoothly connected through an optimized Zernike polynomial fitting method. The collimation unit adopts a convex aspheric plano-convex lens structure, and the aperture amplification ratio is selected according to the relationship between the waist diameter multiple of a Gaussian beam and the in-circle energy ratio. The fiber QBH interface backboard comprises a plurality of QBH interfaces connected with fiber end caps, and the position of each interface corresponds to the object focal point of each collimation unit. The mechanical lens barrel is a hollow cylindrical structure, one end of which is connected with the fiber QBH interface backboard, and the other end is connected with the continuous surface compound eye lens. The application can realize higher laser energy transmission and obtain longer stable light emission time under the condition of ensuring the consistency and stability of the system outgoing optical axis.

The invention relates to the technical field of active optics, and particularly provides a time sequence filtering-based wave-front correction method for a patrol telescope, which comprises the following steps of: firstly, acquiring time sequence wave-front data of the telescope through a wave-front curvature sensor, decomposing the time sequence wave-front data in a spatial domain through a Zernike polynomial, forming a time sequence coefficient sequence by coefficients of each item of the Zernike polynomial in a time domain, and correcting the time sequence coefficient sequence according to the time sequence coefficient sequence; and carrying out frequency domain analysis on each time sequence coefficient sequence, calculating a power spectrum, identifying static aberration by using a Greenwood frequency as a threshold value, filtering dynamic aberration, and then carrying out wavefront correction. According to the method, Zernike polynomial decomposition and frequency domain filtering are combined, high-frequency disturbance introduced by atmospheric turbulence is effectively separated and filtered out, and low-frequency aberration wavefront correction is accurately achieved through active optics.

To provide vision quality assessment based on a machine learning model and wavefront analysis.SOLUTION: There is provided a system 10 and method for assessing vision quality of an eye E. A controller C includes a processor P and a tangible, non-transitory memory M in which instructions are recorded, and is configured to selectively execute at least one machine learning model 35, 36, 38. Execution of the instructions by the processor P causes the controller C to receive wavefront aberration data of an eye and express the wavefront aberration data as a collection of Zernike polynomials. The controller C is configured to obtain a plurality of input coefficients based on the collection of Zernike polynomials, which are fed to at least one machine learning model 35, 36, 38 trained to analyze the plurality of input coefficients. The machine learning model 35, 36, 38 generates at least one vision correction coefficient based in part on the plurality of input coefficients.SELECTED DRAWING: Figure 2

This invention relates to the field of optical system imaging, specifically to a method for constructing an optical system imaging quality prediction model that takes into account both surface shape error and pose error. The method employs Zernike polynomials to accurately fit the mirror surface shape error caused by bolt preload, and uses the finite element method to simulate the bolt tightening process of the optical system. Based on this, a joint simulation method for the assembly and imaging of a two-mirror optical system is proposed. Using Zernike polynomial fitting as the basic parameter, various mirror surface shape errors and assembly pose deviations are fully considered when using Zemax for optical path imaging simulation. Energy concentration is used as a quantitative evaluation index for imaging quality. An SVR surrogate model containing local and global hybrid kernel functions is established, and sensitivity analysis is performed on mirror surface shape and assembly pose parameters. An assembly dataset is obtained through joint assembly and imaging simulation, and the model is trained to obtain an imaging quality prediction model, enabling rapid and accurate prediction of imaging quality.

The invention discloses a large-aperture diffraction structure direct writing online calibration and error suppression system, which relates to the technical field of diffraction structure direct writing and comprises an error detection module, a compensation generation module, a dynamic execution module and a closed loop feedback module. The error detection module is provided with a workpiece carrying table and a wavefront sensor, obtains a residual light field, separates a tilt term, an out-of-focus term, an astigmatism term and a coma term caused by mechanical vibration of the carrying table through Zernike polynomial decomposition, and generates an error source feature vector. The compensation generation module generates geometric correction and an aberration compensation matrix through a reverse optical path tracing algorithm; the dynamic execution module feeds the correction amount and the compensation matrix back to the carrying table and the transmission-type spatial light modulator respectively, and pre-modulation and wavefront pre-shaping are completed; and the closed-loop feedback module scans the morphology through the confocal detection array and compares the morphology to generate an error distribution diagram for closed-loop input. According to the system, accurate error traceability and two-way synchronous pre-compensation are realized, and direct writing errors are effectively inhibited.

The invention discloses a head-mounted display optical system based on a free-form surface. The head-mounted display optical system sequentially comprises a digital image source, a relay lens group and optical goggles from a light source side, light rays are emitted by the digital image source, refracted by the relay lens group and finally reflected by the optical goggles to enter pupils of a user; according to the invention, an off-axis structure is adopted, and the whole relay lens group can freely shift and rotate in the spatial position relative to the reflecting surface of the optical goggles, so that the phase difference is eliminated, and the imaging quality is improved. The relay lens group comprises four groups of five pieces, and the optical axes of the four groups of lenses are consistent, so that the complexity of processing and adjustment is greatly reduced. The optical goggles adopt a Zernike polynomial free-form surface type, the phase difference caused by off-axis eccentricity is further controlled, and the projection imaging quality is further improved.

The application discloses a real-time single-frame wavefront measurement method and device, relates to the technical field of optical measurement and imaging, and comprises the following steps: S1, performing an experiment on a to-be-measured wavefront according to a displacement stage of a shearing interference structure, and acquiring a single-frame interference image containing multiple shearing interference fringes in an arbitrary direction; S2, using a method combining a two-dimensional variational mode decomposition algorithm and a four-step phase-shifting technique to quickly extract phase distribution information; and S3, simultaneously using a differential Zernike polynomial as a base function to reconstruct the wavefront according to the extracted phase distribution information. The method allows collecting a single interference image containing multiple shearing interference fringes in an arbitrary direction in one measurement, can improve the measurement efficiency, and can widen the application potential of the shearing interference method in wavefront analysis.

The application discloses a fast tilt compensation method based on Zernike polynomials, which comprises the following steps: obtaining a two-dimensional image matrix output by a digital holographic microscope; pre-processing the two-dimensional image matrix; projecting the pre-processed image intensity matrix onto a Zernike polynomial base, realizing Zernike fitting, and obtaining a Zernike model about a sample to be measured; calculating tilt term coefficients alpha x , alpha y of a first-order polynomial in the Zernike model; calculating defocus aberration by using the tilt term coefficients alpha x , alpha y ; performing tilt compensation on the pre-processed image intensity matrix, and outputting a compensated image intensity matrix. Further, corresponding electronic equipment is disclosed. The application can quickly and effectively compensate and correct a photographed image, and is quite considerable in robustness and calculation speed.

This invention discloses a system error calibration method for a phase-shifting point diffraction interferometer based on mask rotation. The proposed method requires a simple hardware structure and, compared to traditional point diffraction interferometer calibration methods, does not add any additional optical modules, enabling sub-nanometer-level system error calibration. The proposed method precisely controls the mask rotation angle by rotating alignment marks, making the diffraction error caused by pinhole diffraction a variable before and after rotation. Furthermore, it utilizes the orthogonality and parity-even symmetry properties of Zernike polynomials in the unit circle domain to calibrate the pinhole diffraction error. Compared to conventional mask replacement methods and rotating the optical system under test methods, this method further reduces system error; and compared to methods that involve multiple pinhole rotations and averaging, it reduces operational complexity.

This invention relates to the field of optical inspection technology, and in particular provides a method and apparatus for sub-aperture stitching inspection of large-aperture optical elements. The method includes the following steps: S1, setting up an inspection system, including an electrically controlled rotary table, a display screen, and a camera; S2, establishing a mirror coordinate system with the center of the mirror surface under test as the origin; S3, rotating the mirror under test and transforming the coordinates of sampling points within each sub-aperture to the world coordinate system; S4, ray tracing to calculate the local slope data of the sampling points; S5, uniformly transforming the slope data of each sub-aperture to the mirror coordinate system, and constructing a full-aperture slope field based on a slope stitching fusion method; S6, constructing an overdetermined linear least squares equation system based on Zernike polynomials to obtain the full-aperture reconstructed surface shape of the mirror surface under test. This invention acquires sub-aperture data through rotational scanning and uses a slope stitching fusion method to achieve full-aperture surface shape reconstruction and high-precision complete inspection of the surface of large-aperture optical elements.