CN-121994151-A - Aspheric adaptive annular sub-aperture splicing measurement method and system

CN121994151ACN 121994151 ACN121994151 ACN 121994151ACN-121994151-A

Abstract

The invention discloses an aspheric self-adaptive annular sub-aperture splicing measurement method and system, and belongs to the technical field of optical precision measurement. The method comprises the steps of obtaining aspheric surface type parameters and setting axial displacement delta, constructing a matching criterion function to ensure that interference fringe density accords with a Nyquist sampling limit of a detector, automatically solving the tangential point position of a sub-aperture and a reference spherical wave parameter based on an inversion model, adaptively dividing annular sub-apertures and meeting a 25% overlapping rate threshold, carrying out interferometry on all the sub-apertures and collecting phase data, correcting system errors through a global least square stitching model, and reconstructing a full-caliber surface shape. The invention realizes automation and high precision of aspheric surface detection, avoids manual preset tangent points, remarkably improves measurement efficiency and splicing quality, and is suitable for high-precision measurement of high-steepness and large-caliber aspheric elements.

Inventors

LI BING
Hu Zhenchuan
ZHAO ZHUO
Geng Leqi
LI GUANGKAI
LU JIACHENG

Assignees

西安交通大学

Dates

Publication Date: 20260508
Application Date: 20260227

Claims (10)

1. The aspheric adaptive annular sub-aperture splicing measurement method is characterized by comprising the following steps of: S1, acquiring surface type parameters of an aspheric surface to be measured, wherein the surface type parameters comprise caliber, vertex curvature radius, quadratic term constant and high-order term coefficient, and simultaneously setting axial displacement of a reference spherical wavefront relative to the aspheric surface ; S2, based on the surface type parameter and the axial displacement Combining the geometrical approaching degree of the aspheric surface type function and the reference spherical wave front in a local area to construct a matching criterion function, wherein the matching criterion function is used for restricting the optical path difference change rate between the aspheric surface and the reference spherical wave front, so that the optical path difference change rate accords with the Nyquist sampling frequency limit of an interferometer detector, and the interference fringe density is ensured to be in the resolvable range of the detector; S3, searching candidate radial positions or radial intervals according to the calculation result of the matching criterion function, and adaptively determining the radial positions and coverage areas of at least one annular sub-aperture, wherein the division of the annular sub-apertures is required to meet a preset overlapping rate threshold of 25%; S4, respectively carrying out interferometry on the aspheric surface areas corresponding to the annular sub-apertures according to the determined radial positions and coverage areas, and acquiring and obtaining surface shape phase data and optical path difference data of the sub-apertures; S5, correcting and fusion splicing are carried out on the measurement data of all the sub-apertures through a global sub-aperture splicing model by utilizing the data of the overlapping area among the sub-apertures, the global sub-aperture splicing model builds an overlapping area residual error objective function based on a least square method and solves an adjustment coefficient, and finally, an aspheric full-caliber surface shape measurement result is obtained.
2. The method for measuring the stitching of the aspherical surface adaptive annular sub-aperture according to claim 1, wherein in the step S2, when a matching criterion function is constructed, an inversion model of the characteristic parameters of the sub-aperture is also constructed, and the inversion model uses the axial displacement of the aspherical mirror to be measured For input quantity, calculating the position of the sub-aperture tangential point by back-pushing Corresponding to the radius of curvature of the reference spherical wavefront 。
3. The aspheric adaptive annular sub-aperture stitching measurement method according to claim 2, wherein the inverse model of the sub-aperture characteristic parameters comprises a geometrically tangent mathematical model, the mathematical model introduces an axial sagittal height consistency constraint and a tangential slope consistency constraint, which together form a nonlinear equation set, and the unknown number of the nonlinear equation set is [ ] , ) The known input is 。
4. The method of claim 3, wherein the axial sagittal curvature uniformity constraint is that the aspheric surface is at the tangent point The axial sagittal height at the point is equal to the centre of sphere being offset along the optical axis The reference sphere behind is at the tangent point The tangential slope consistency constraint is that the aspheric surface is at the tangent point The tangential slope at the point of tangency is equal to that of the reference sphere Tangential slope at (a).
5. The method of claim 3, wherein the inverse model of the sub-aperture characteristic parameters further comprises a two-dimensional coarse positioning strategy, wherein the two-dimensional coarse positioning strategy is to divide grids in a reasonable interval and enumerate grid point combinations, and each group is , ) Calculating a combined residual error function, and finding out the minimum residual error point as a coarse positioning initial value , ) The traversing interval of the grid is ∈[0, /2]、 ∈[0.8 ,1.2 The method of the present invention, wherein, Is of an aspheric caliber, Is the radius of curvature of the vertex of the aspherical surface.
6. The method of claim 5, wherein the inverse model of the sub-aperture characteristic parameters further comprises a nonlinear least squares fine positioning strategy, wherein the fine positioning strategy uses a Levenberg-Marquardt nonlinear least square method to solve the nonlinear equation set finely based on the coarse positioning initial value to obtain the current Corresponding sub-aperture tangential point positions Radius of curvature of matching reference sphere And deducing the reference sphere center position and sphere wave radius.
7. The method for measuring the split joint of the aspherical self-adaptive annular sub-aperture according to claim 1, wherein in the step S3, when the boundary range of the sub-aperture is calculated and determined, a criterion formula is substituted from the tangent point to the two radial sides point by point, the point which does not satisfy the criterion formula is calculated as a preliminary boundary point, the sub-aperture range corresponding to the preliminary boundary point is subjected to overlap ratio verification, and if the preset overlap ratio threshold of 25% is not satisfied, the axial displacement is adjusted And re-executing step S2 until both the nyquist sampling frequency limit constraint and the overlap ratio threshold are satisfied.
8. The method for splicing and measuring the aspherical self-adaptive annular sub-aperture according to claim 1, wherein in step S4, phase shift interferometry is adopted to collect interferograms corresponding to each annular sub-aperture, and surface shape phase data and optical path difference data of each sub-aperture are obtained through data processing steps of phase extraction and phase unwrapping.
9. The method according to claim 1, wherein in step S5, the adjustment coefficients are used to correct translational and oblique systematic errors in the sub-aperture measurement process, and the optimal adjustment coefficients of the sub-apertures are obtained by solving the equation set by performing bias guide on each adjustment coefficient in the residual objective function of the overlapping region and making the partial derivative zero.
10. An aspheric adaptive annular sub-aperture stitching measurement system, comprising: the parameter module is used for acquiring the surface type parameters of the aspheric surface to be measured, wherein the surface type parameters comprise caliber, vertex curvature radius, quadratic term constant and higher-order term coefficient, and meanwhile, the axial displacement delta of the reference spherical wavefront relative to the aspheric surface is set; The criterion module is used for constructing a matching criterion function based on the surface type parameter and the axial displacement delta and combining the geometrical approaching degree of the aspherical surface type function and the reference spherical wave front in a local area, wherein the matching criterion function is used for restraining the optical path difference change rate between the aspherical surface and the reference spherical wave front so as to enable the optical path difference change rate to be in accordance with the Nyquist sampling frequency limit of the interferometer detector and ensure that the interference fringe density is in the resolvable range of the detector; The dividing module is used for searching candidate radial positions or radial intervals according to the calculation result of the matching criterion function, and adaptively determining the radial position and coverage of at least one annular sub-aperture, wherein the dividing of the annular sub-apertures is required to meet a preset overlapping rate threshold of 25%; The measuring module is used for respectively carrying out interferometry on the aspheric surface areas corresponding to the annular sub-apertures according to the determined radial positions and coverage areas, and acquiring the surface shape phase data and the optical path difference data of the sub-apertures; and the splicing module is used for correcting and fusion splicing the measurement data of all the sub-apertures through a global sub-aperture splicing model by utilizing the data of the overlapping area between the sub-apertures, wherein the global sub-aperture splicing model is used for constructing an overlapping area residual error objective function based on a least square method and solving an adjustment coefficient, and finally, an aspheric full-caliber surface shape measurement result is obtained.

Description

Aspheric adaptive annular sub-aperture splicing measurement method and system Technical Field The invention belongs to the technical field of optical precision measurement, and particularly relates to an aspheric self-adaptive annular sub-aperture splicing measurement method and system. Background With the development of modern optical systems toward high performance, light weight and miniaturization, aspheric (Aspheric Surface) optical elements have become a key component in the core due to their excellent aberration correction capability and freedom. The method is widely applied to national strategy-level high-end equipment such as aerospace remote sensing, large-caliber astronomical observation, high-energy laser systems, extreme Ultraviolet (EUV) lithography machines and the like. These "high-rise" application scenarios place extremely high demands on the surface shape accuracy of the aspheric element, often on the order of nanometers or even sub-nanometers. In the field of optical manufacturing, the processing precision depends on the detection precision, so that the realization of high-precision and nondestructive detection of the aspheric surface shape is a precondition for ensuring the performance of an optical system. Among the numerous detection means, the laser interferometry technique is known as the "gold standard" of optical precision detection by virtue of its non-contact, high precision and high spatial resolution. However, with increasing aspheric aperture and increasing steepness (STEEPNESS), conventional full aperture interferometry presents a significant challenge. Because the standard reference spherical wave emitted by the interferometer cannot be well matched with the aspheric surface to be detected in the full caliber range, the interference fringe density is increased sharply due to the overlarge wavefront deviation of the standard reference spherical wave and the aspheric surface to be detected. Once the fringe density exceeds the resolution limit (nyquist frequency) of the interferometer detector (e.g., CCD), valid phase data cannot be acquired, resulting in measurement failure. While zero-compensation detection (Null Test) can solve this problem, it requires custom expensive compensators (e.g., CGH), is poorly versatile and has a long period. In order to solve the problem of generalized measurement of large-caliber high-gradient aspheric surfaces on the premise of not depending on a special compensator, a sub-aperture splicing interference detection technology is generated. The key idea of the technology is that the technology is 'integrated into zero' and is divided into a plurality of partial subareas (sub-apertures) by dividing the aspheric surface to be detected, so that the wavefront deviation in each subarea is in the measurable range of an interferometer, and after data are respectively acquired, the sub-aperture data are accurately 'stitched' into a full-caliber surface shape through a mathematical algorithm. The technology not only expands the dynamic measurement range of the universal interferometer, but also obviously reduces the detection cost, and is an important research direction facing to high-order aspheric surface flexible measurement at present. In 1981 Kim proposed a measurement method based on sub-aperture stitching for the first time at university of arizona in the united states. However, since there is no overlap between sub-apertures, the splice accuracy is low. In the initial stitching measurement algorithm, the stitching algorithm is based on Zernike surface fitting, and the Zernike polynomial expression of the full aperture surface shape can be obtained by fitting the surface shape data of each sub aperture. Describing the surface shape by using the Zernike polynomials has a certain limitation, and for some local irregular surface shapes, the Zernike polynomials cannot be accurately expressed. To solve this problem, stuhlinger proposed a discrete phase measurement method in 1986. The measuring method adopts a large number of discrete phase points to represent the shape of the sub-aperture surface, and proposes the idea of overlapping areas. Because of the limitation of the positioning precision of the early mechanical structure, the measurement precision is not ideal, but the idea of eliminating the overlapping area provides a new idea for the subsequent sub-aperture splicing measurement. In 2015 Sj, edahl and Bozenko, a splicing method of iterative splicing is proposed. And (3) obtaining optimal estimated values of six parameters by utilizing singular value decomposition in each iteration, updating data in the overlapping area after each calculation to obtain a group of new data, and repeatedly optimizing by taking the group of new data as an objective function until the algorithm converges to a given threshold parameter. In 2020, chen et al propose a method for analyzing a spliced cylindricity interferometry error based on Bayesian statistical analysi