18 results about "Zernike polynomials" patented technology

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.

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.

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.

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.

The application provides an optical element surface shape regulation and control method based on a KAN neural network, and relates to the technical field of optical element surface shape regulation and control. The method comprises the following steps: establishing an APDL parameterized finite element model of an optical element and a corresponding multi-point support system; performing finite element simulation through an APDL batch processing mode, obtaining corresponding optical surface deformation data, fitting to obtain Zernike polynomial coefficients, and constructing a sample data set; building a KAN neural network model, training the model by using the sample data set, and establishing a nonlinear mapping relationship from support force input to Zernike coefficient output; constructing an optimization objective function; and performing reverse optimization on the input support force by using a gradient optimization algorithm to obtain an optimal support force distribution for realizing target Zernike term adjustment. The application provides a high-precision, strong-decoupling and low-cost method for active surface shape correction of a high-precision optical system.

This invention relates to the field of optical design, and more particularly to a method for obtaining polarization aberrations in an optical system. The method includes: S1: Tracing N rays using a three-dimensional polarization ray tracing algorithm to extract the corresponding biaxial attenuation-related Jones matrices and phase delay-related Jones matrices; S2: Fitting the Jones matrices and the Jones matrices using N directional Zernike polynomials to obtain the components of biaxial attenuation and phase delay, and reconstructing the biaxial attenuation and phase delay to obtain the polarization aberration distribution across the entire pupil of the optical system. This invention requires only a small number of rays to accurately obtain the polarization aberrations across the entire pupil, significantly reducing computational complexity. It also overcomes the limitations of existing simplified methods on the optical system structure, making it applicable to various complex optical systems.

The application provides a free-form surface-based imaging spectrometer telescope system, which comprises six optical lenses in sequence in the light incidence direction, namely a concave lens, a concave lens, a convex lens, a convex lens, a convex lens and a concave lens; the focal length of the lens is 7.6 mm, the F number is 2.0, the working wavelength range is 400 nm-700 nm, the visible light wavelength range is 400 nm-700 nm, the field of view angle is 47.5°, and the total optical length of the system is 100 mm; the free-form surface optical system is designed as an image-side telecentric optical path structure and can be used as a telescope lens of a free-form surface imaging spectrometer; the free-form surface technology represented by Zernike polynomials is adopted in the design process of the optical system, one of the six lenses is a free-form surface lens, all aberrations are corrected in the optimization process, and finally the lens has the advantages of excellent image quality, large relative aperture, large field of view angle and image-side telecentricity.

A laser system parameter measurement system and method, storage medium, and electronic device are disclosed. The method includes the following steps: S1, zero-point calibration of the detection system: when the incident light is an ideal flat-top light, the focal point of the beam focused by the lens array is located on the center line of the lens. The centroid coordinates of the focal point output by the detector corresponding to each sub-lens are recorded as (X0, Y0), and used as the reference centroid; S2, the laser system under test emits light, and the centroid coordinates of the focal spot output by the detector corresponding to each sub-lens are recorded as (X0, Y0). i ,Y i S3, which is the actual measured centroid; S4, obtain the wavefront average slope (Gx) within each sub-lens region. i ,Gy i S4: The wavefront reconstruction matrix is ​​determined by the number of sub-lenses and the order of the restored Zernike polynomial, and then the average slope of the wavefront (Gx) is used. i ,Gy i The wavefront can be reconstructed using the Zernike mode method. This invention solves the problem of atmospheric disturbance in the original laser intensity measurement method, and allows for direct measurement at the laser system exit, ensuring the accuracy of beam parameter measurement.

This invention discloses a computationally adaptive aberration correction imaging method for deep tissue based on upconversion nanoparticle guide stars. A near-infrared fluorescence imaging system is constructed using rare-earth upconversion nanoparticles as guide stars. Fluorescence distortion images of deep tissue samples are acquired through near-infrared excitation, and imaging aberrations are parameterized based on Zernike polynomials. Aberration coefficients are reconstructed using a deep learning model incorporating physical prior constraints. Digital wavefront compensation is performed based on the reconstructed aberration information to achieve deep tissue aberration correction and obtain high-resolution imaging results. This invention eliminates the need for complex optical hardware such as wavefront sensors or deformable mirrors, and can stably achieve aberration estimation and compensation even in 360 μm deep tissue conditions. Compared with traditional aberration correction methods, the correction effect is improved by more than 30%, enabling rapid image correction and high-precision positioning. It solves the problems of weak guide star signals, low aberration correction efficiency, and high system cost in deep tissue imaging, and is applicable to deep tissue optical imaging in fields such as clinical diagnosis, biological cell observation, and drug development.

This invention relates to a precision optical system testing device and method, specifically to a three-dimensional optical axis consistency testing system and method based on multi-pose interferometry, addressing the problems of existing optical axis testing technologies such as environmental sensitivity, dimensional limitations, low efficiency, and low accuracy. The multi-pose adjustment module of this invention includes a parallel Stewart platform, enabling automatic adjustment of the pitch and yaw angles of the optical system under test mounted on it; the interferometry module is a Fizeau laser interferometer, uniformly distributed in a ring around the exit pupil center of the optical system under test, capable of simultaneously acquiring phase-shifting interferograms under multiple poses, providing three-dimensional wavefront data; the data processing module extracts the wavefront phase through a four-step phase-shifting algorithm, constructs a three-dimensional mathematical model using Zernike polynomials, unifies the multi-pose data through coordinate transformation, and finally outputs a three-dimensional optical axis consistency testing report.

The application discloses a method for analyzing thermal blooming aberration with different truncation factors based on Zernike polynomials, and belongs to the technical field of high-energy laser atmospheric transmission and thermal blooming correction. Firstly, a thermal blooming wavefront phase distribution of a Gaussian beam after atmospheric transmission is acquired, and normalization processing is performed; then, mode decomposition is performed on the normalized wavefront by using Zernike polynomials, and Zernike coefficients of each order under different truncation factors are extracted; further, the evolution law of the structure characteristics and aberration components of the thermal blooming wavefront distortion with the truncation factor is quantitatively analyzed; based on a point spread function, a Strehl ratio is calculated, and a source energy transmittance is introduced to construct a target light intensity evaluation index, and the optimal truncation factor balancing the transmission efficiency and aberration suppression is determined through extreme value optimization; finally, the optimal truncation factor is converted into a hardware control instruction to drive a variable beam expander telescope or a dynamic diaphragm to perform physical adjustment. The application can effectively improve the peak target light intensity of the system under typical thermal blooming conditions.

The application discloses a non-iterative design method of a non-uniform continuous distribution composite pupil function, solves the problem that the design method of an existing pupil function is relatively complex, including expansion of the pupil function, matrix calculation and a calculation process of solving a high-resolution gain expression, the non-uniform continuous distribution composite pupil function is composed of a Sonine polynomial, a Zernike polynomial and a Fourier-Bessel series, numerical mapping relationships between the Sonine polynomial, the Zernike polynomial, the Fourier-Bessel series and an imaging complex amplitude distribution at a radial focal plane are respectively constructed, coefficients of the Sonine polynomial, the Zernike polynomial and the Fourier-Bessel series are solved, a function formula of the composite pupil function is finally determined, and the mapping relationship is relatively simple and operable.

An information processing apparatus includes: an acquisition unit that acquires measured film thickness data of a plurality of measurement points on a substrate surface with a film formed thereon by a substrate processing apparatus; a prediction model generation unit that generates a prediction model by regressing the measured film thickness data using Zernike polynomials; a prediction unit that predicts film thickness data of a plurality of prediction points on the substrate surface using the prediction model, and outputs the predicted film thickness data; and a display control unit that displays the predicted film thickness data on an output device.

The present application relates to the field of active optics, and specifically provides a time series filtering-based wavefront correction method for a survey telescope, which obtains time series wavefront data of the telescope through a wavefront curvature sensor, decomposes the time series wavefront data in a spatial domain through Zernike polynomials, forms a time series coefficient sequence for each term of the Zernike polynomials in a time domain, performs frequency domain analysis on each time series coefficient sequence, calculates a power spectrum, uses a Greenwood frequency as a threshold to identify static aberrations, and performs wavefront correction after filtering out dynamic aberrations. The present application effectively separates and filters out high-frequency disturbances introduced by atmospheric turbulence by combining Zernike polynomial decomposition and frequency domain filtering, and accurately realizes low-frequency aberration wavefront correction through active optics.

A method for extending a working range of an imaging system having an optical axis and an aperture stop includes imparting a wavefront aberration on an optical beam, propagating through the aperture stop, that is representable as an expansion of orthonormal circular Zernike polynomials having non-zero coefficients A11, A22, and A37. A working-range-extending phase plate imparts a wavefront aberration on an optical beam, propagating therethrough, that is representable as an expansion of orthonormal circular Zernike polynomials having non-zero coefficients A11, A22, and A37.

This invention discloses a method, apparatus, storage medium, and computer device for determining the budget range of aberrations, applied to a photolithography system. The method includes: acquiring multiple target Zernike terms, wherein each target Zernike term is a Zernike term from multiple Zernike polynomials whose causal correlation with the exposure results of the photolithography system based on the Zernike polynomial satisfies a first preset condition; performing a deterministic fitting selection on the Zernike polynomial to determine the target second-order coupling term, and obtaining the corresponding higher-order coupling term based on the target Zernike term; establishing an analytical model based on the target Zernike term, the target second-order coupling term, and the higher-order coupling term, and fitting the analytical model based on random experiments to obtain a fitted model; and obtaining the budget range of aberrations based on a predetermined exposure result range through the fitted model. This method improves the efficiency of obtaining the aberration budget range.

The present application relates to a kind of complete phase reconstruction methods based on Shack-Hartmann wavefront sensor, belong to laser communication, imaging and adaptive optics field.The present application obtains light intensity information and phase gradient information using Shack-Hartmann wavefront sensor;Phase singularity position is detected by calculating the ratio of second moment beam width and diffraction limit point diameter;Phase singularity rotation direction is judged using phase gradient loop summation;Complex plane is established with the center of detection surface as origin and the implicit phase is reconstructed by complex logarithm operation;Complete wavefront phase is obtained by combining the implicit phase with the continuous phase fitted by Zernike polynomial.The present application aims to solve the fundamental defect that existing Shack-Hartmann wavefront sensor cannot measure vortex phase when measuring wavefront containing phase singularity, and can realize the accurate reconstruction of complete wavefront phase information containing implicit phase.