CN-121977475-A - High-precision transient interference surface shape measurement method

CN121977475ACN 121977475 ACN121977475 ACN 121977475ACN-121977475-A

Abstract

The invention provides a high-precision transient interference surface shape measurement method, which relates to the technical field of surface shape measurement, and in the method, multiple calibration processing is carried out, and carrier inclination amount combination corresponding to each calibration processing and Zernike coefficients of measured wave fronts are obtained; the method comprises the steps of obtaining a carrier inclination amount combination and a Zernike coefficient based on multiple calibration processing, obtaining a correction parameter matrix, carrying out carrier interferometry on an optical element to be tested, obtaining initial surface shape data and carrier offset combination corresponding to the optical element to be tested, reconstructing a return error based on the correction parameter matrix and the carrier offset combination corresponding to the optical element to be tested, deducting the return error from the initial surface shape data to obtain target surface shape data corresponding to the optical element to be tested, and completing phase calculation and high-precision error correction only by a single frame interference fringe image, thereby remarkably improving the surface shape measurement precision, being lower in cost, simple in process and high in universality.

Inventors

SU RONG
XUN HUI
WEN RONGXIAN
CHEN CHENG

Assignees

中国科学院上海光学精密机械研究所

Dates

Publication Date: 20260505
Application Date: 20260210

Claims (6)

1. The high-precision transient interference surface shape measuring method is characterized by comprising the following steps of: the calibration step comprises the steps of carrying out m times of carrier interferometry on the same test optical element under different inclined postures based on a target laser interferometer, synchronously collecting a single-frame interference fringe image and an exit pupil plane target image each time of measurement, calculating and fitting a Zernike coefficient list C i from the single-frame interference fringe image, and extracting a carrier offset combination B i representing a space carrier state from the exit pupil plane target image so as to construct a calibration data set { (B i ,C i ) |i=1, 2. Modeling, namely establishing a polynomial function model of each Zernike coefficient about carrier offset based on the calibration data set, and solving a global model parameter matrix E through mathematical fitting; setting column intensities corresponding to constant items in the model parameter matrix E to zero so as to obtain a correction parameter matrix G of physical constraint, wherein the correction parameter matrix G represents the mapping relation of systematic return errors of the target laser interferometer along with carrier offset changes; The method comprises the steps of carrying out carrier interference measurement on an optical element to be measured by using the target laser interferometer, and synchronously collecting a single-frame interference fringe image and an exit pupil plane target image, thereby obtaining initial surface shape data containing return errors and a current carrier offset combination H; and the compensation step is to calculate the Zernike representation of the return error in the current state based on the correction parameter matrix G and the current carrier offset combination H, further reconstruct the return error surface shape of the space domain, and subtract the return error surface shape from the initial surface shape data to obtain compensated target surface shape data.
2. The method of claim 1, wherein the test optical element is an arbitrary profile optical element that is used only as a tool for generating different carrier states during the calibration step.
3. The method for measuring a high-precision transient interferometry surface shape according to claim 1, wherein the modeling step specifically comprises: Constructing a matrix equation D i = E × F i , wherein D i is a column vector formed by a Zernike coefficient list C i measured at the ith time, F i is a column vector formed by a carrier offset combination B i measured at the ith time and a power term; and solving the model parameter matrix E by a least square method based on all m measured { D i , F i } data pairs.
4. A method of high precision transient interferometry surface shape measurement according to claim 1 or 3, wherein the compensating step specifically comprises: constructing a column vector K in the same form as F i according to the current carrier offset combination H; Calculating a Zernike coefficient vector R=G×K of a return error, wherein G is a correction parameter matrix obtained by zeroing a constant term column of E; And reconstructing a return error surface shape of the space domain by using the Zernike coefficient vector R and a standard Zernike polynomial.
5. The method of claim 1, wherein the carrier offset combination B i =(α i ,β i ) is a difference between pixel coordinates of a centroid of a reference spot and a test spot extracted from the exit pupil plane target image in x-axis and y-axis directions, and the Zernike coefficients list C i =(C i1 ,C i2 ,…,C ij ,…,C in , wherein C ij is a j-th Zernike coefficient in the Zernike coefficients list C i .
6. The high-precision transient interference surface shape measurement system is characterized by comprising a laser interferometer, a first optical fiber, a second optical fiber, a third optical fiber and a fourth optical fiber, wherein the laser interferometer is configured to synchronously acquire carrier interference fringe images and pupil plane light spot images; An adjusting device for carrying and changing the inclined posture of the test optical element or the optical element to be tested relative to the reference plane of the laser interferometer; A data processing and control unit programmed to perform the method according to any one of claims 1 to 5.

Description

High-precision transient interference surface shape measurement method Technical Field The invention relates to the technical field of precise optical interferometry, in particular to a high-precision transient interference surface shape measurement method which is particularly suitable for high-precision and rapid measurement of the surface shape of an optical element in unstable environments such as vibration, air disturbance and the like. Background The optical interferometry technique is widely used for optical element surface topography detection, precision machining error evaluation and in-situ adjustment due to its advantages of non-contact, high precision and high resolution. The traditional phase-shifting interferometer relies on a multi-frame phase-shifting sequence to carry out phase solution, has high measurement accuracy, but has extremely high requirement on environmental stability, and is difficult to apply to production sites with larger vibration or air disturbance. To overcome the long time and environmental sensitivity problems of multi-frame phase-shift Interferometry, carrier interference (CARRIER FRINGE Interferometry) techniques have been developed. By introducing a tiny inclination angle between the reference surface and the measured surface, single-frame coding of the space carrier fringes is realized, so that transient (single-frame) surface shape measurement can be realized through algorithms such as Fourier transform and the like. However, in carrier interferometry, the system can produce a return error (Retrace Error) due to the non-co-propagation of the reference light and the test light in space. This error is particularly noticeable in the presence of a tilted carrier, and can lead to distortion of low order aberrations (e.g., spherical aberration, coma, astigmatism, etc.), thus limiting the absolute accuracy of the measurement. The existing return error correction method mainly comprises a ray tracing method, a reverse optimization method and a multi-frame compensation method based on experience calibration. These methods often rely on accurate modeling of the internal optical path of the interferometer, or require high quality standard mirrors for calibration, are complex to apply and difficult to implement in a production environment. The method of eliminating the return error of Fizeau interferometer (CN 110332883B) uses the "multi-frame averaging method". It requires multiple physical adjustments (at least 4 measurements) in specific directions (positive and negative) through the adjusting frame, and the return error is counteracted by averaging four measurements, which cannot be done dynamically/in real time. Therefore, a method capable of realizing high-precision surface shape measurement under a single frame condition and simultaneously effectively compensating return errors caused by inclined carriers is needed, so that real-time, high-precision and low-cost transient interferometry is realized. Disclosure of Invention The invention aims to solve the problem of reduced measurement precision caused by return errors due to non-common-path propagation in the conventional carrier interferometry, and provides a high-precision transient interferometry surface shape measurement method which can realize high-precision surface shape recovery under the transient (single-frame) measurement condition. Specifically, the invention aims to solve the following technical problems: (1) The return error in the traditional carrier interference systematically changes along with the change of the inclined carrier vector, and unified mathematical modeling is lacked; (2) The existing correction method depends on internal optical path parameters or high-precision standard components, and has no universality; (3) The existing correction method needs a plurality of measurement or iteration methods and does not have real-time performance; In order to achieve the above purpose, the present invention provides a high-precision transient interference surface shape measurement method, which comprises the following steps: S1, calibrating, namely, based on a target laser interferometer, carrying out m times of carrier interferometry on the same test optical element under different inclined postures, synchronously acquiring a single-frame interference fringe image and an exit pupil plane target image each time of measurement, resolving and fitting a Zernike coefficient list C i from the single-frame interference fringe image, extracting a carrier offset combination B i representing a space carrier state from the exit pupil plane target image, thereby constructing a calibration data set (B i,Ci) i=1, 2, and m, wherein alpha i,βi is the pixel coordinate difference value of the centroid of a reference spot extracted from the exit pupil plane target image and a test spot in the x-axis and y-axis directions, the Zernike coefficient list C i=(Ci1,Ci2,…,Cij,…,Cin is the j Zernike coefficient in the Zernike co