Aspheric self-adaptive annular sub-aperture splicing measurement method and aspheric self-adaptive annular sub-aperture splicing measurement system

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 following steps: acquiring an aspheric surface profile parameter and setting an axial displacement delta; constructing a matching criterion function, and ensuring that the interference fringe density accords with the Nyquist sampling limit of the detector; automatically solving a sub-aperture tangency point position and a reference spherical wave parameter based on an inversion model; adaptively dividing the annular sub-aperture and satisfying a 25% overlapping ratio threshold value; performing interference measurement on each sub-aperture and acquiring phase data; and correcting system errors through a global least square splicing model, and reconstructing a full-aperture surface shape. According to the invention, automation and high precision of aspheric surface detection are realized, manual presetting of tangency points is avoided, the measurement efficiency and the splicing quality are significantly improved, and the method is suitable for high-precision measurement of high-gradient and large-aperture aspheric surface elements.

Description

Technical Field

[0001] This invention belongs to the field of optical precision measurement technology, specifically relating to an aspherical adaptive annular sub-aperture splicing measurement method and system. Background Technology

[0002] As modern optical systems evolve towards high performance, lightweight design, and miniaturization, aspheric surface optical elements have become core components due to their superior aberration correction capabilities and degrees of freedom. They are widely used in national strategic high-end equipment such as aerospace remote sensing, large-aperture astronomical observation, high-energy laser systems, and extreme ultraviolet (EUV) lithography machines. These high-end applications place extremely high demands on the surface accuracy of aspheric elements, often reaching nanometer or even sub-nanometer levels. In the field of optical manufacturing, "processing accuracy depends on inspection accuracy." Therefore, achieving high-precision, non-destructive testing of aspheric surface shapes is a prerequisite for ensuring the performance of optical systems.

[0003] Among numerous detection methods, laser interferometry is widely recognized as the "gold standard" for optical precision testing due to its non-contact, high precision, and high spatial resolution. However, with the increase in aspherical aperture and steepness, traditional full-aperture interferometry faces severe challenges. Because the standard reference spherical wave emitted by the interferometer cannot achieve a good match with the aspherical surface under test across the entire aperture range, excessive wavefront deviation leads to a sharp increase in interference fringe density. Once the fringe density exceeds the resolution limit (Nyquist frequency) of the interferometer detector (such as a CCD), effective phase data cannot be obtained, resulting in measurement failure. Although the null test can solve this problem, it requires a custom-made, expensive compensator (such as a CGH), has poor versatility, and a long development cycle.

[0004] To address the challenge of universal measurement of large-aperture, high-steep aspherical surfaces without relying on dedicated compensators, sub-aperture stitching interferometry has emerged. The core idea of ​​this technique is "divide and conquer": by dividing the aspherical surface under test into several local sub-regions (sub-apertures), the wavefront deviation within each sub-region is kept within the measurable range of the interferometer. Data is collected separately for each sub-aperture, and then mathematical algorithms are used to precisely "stitch" these sub-aperture data into the full-aperture surface shape. This technique not only expands the dynamic measurement range of general-purpose interferometers but also significantly reduces testing costs, making it an important research direction for flexible measurement of high-order aspherical surfaces.

[0005] In 1981, Kim first proposed a measurement method based on sub-aperture stitching at the University of Arizona. However, the stitching accuracy was low due to the non-overlapping nature of the sub-apertures. The initial stitching measurement algorithm was based on Zernike surface fitting; by fitting the surface shape data of each sub-aperture, a Zernike polynomial expression for the entire aperture surface shape could be obtained. However, using Zernike polynomials to describe surface shapes has limitations; for some locally irregular surfaces, Zernike polynomials cannot accurately represent them. To address this issue, in 1986, Stuhlinger proposed the discrete phase measurement method. This method uses a large number of discrete phase points to represent the sub-aperture surface shape and introduces the concept of overlapping regions. Due to limitations in the positioning accuracy of early mechanical structures, the measurement accuracy was not ideal, but the idea of ​​eliminating overlapping regions provided a new approach for subsequent sub-aperture stitching measurements. In 2015, Sjöedahl and Bozenko proposed an iterative stitching method. In each iteration, singular value decomposition is used to obtain the optimal estimates of the six parameters. After each calculation, the data in the overlapping area is updated to obtain a new set of data. This new set of data is then used as the objective function to repeatedly optimize until the algorithm converges to the given threshold parameters. In 2020, Chen et al. proposed an error analysis method for spliced ​​cylindricity interferometry measurement based on Bayesian statistical analysis, realizing the surface splicing of the measured cylindrical optical element. In 2021, Wang et al. used sub-aperture interferometry to splice the inner and outer surfaces of a transparent spherical shell. Compared with traditional roundness measurement, this measurement method can accurately measure the surface morphology and thickness of the spherical shell through full aperture coverage.

[0006] Although sub-aperture stitching technology has made some progress, in practical applications, there are still significant shortcomings in sub-aperture partitioning strategies for aspherical surfaces (especially highly steep rotationally symmetric aspherical surfaces), mainly in the following two aspects: 1. Limitations of Circular Sub-Aperture Splicing: Traditional circular sub-aperture division typically employs a two-dimensional grid scanning method (Lattice layout). While this method is highly versatile, it neglects the geometric features of rotationally symmetric aspherical surfaces. This necessitates complex mechanical movements along the X and Y axes, results in a large number of sub-apertures, and excessive overlap between adjacent sub-apertures, easily amplifying accumulated splicing errors and leading to low measurement efficiency.

[0007] 2. Shortcomings of traditional annular sub-aperture splicing: For rotationally symmetric aspherical surfaces, although existing annular sub-aperture division methods utilize axial movement (along the Z-axis) to match the curvature of different annular zones, their division strategies are often rather rigid.

[0008] 1) Lack of adaptability: Existing methods mostly use fixed step size or empirical trial and error to determine the axial movement position. However, the curvature of aspherical surfaces changes nonlinearly with radial position. Fixed step size is very likely to cause excessively dense interference fringes (exceeding the Nyquist sampling limit) in regions with drastic curvature changes, making measurement impossible, or to oversample in gentle regions, reducing efficiency.

[0009] 2) Complex operation: In order to avoid excessively dense fringes, operators often need to repeatedly fine-tune the moving distance and observe the interferogram. There is a lack of a mathematical model that can automatically invert the optimal measurement position based on the surface equation and the resolution limit of the detector.

[0010] In summary, the main drawback of existing technologies is that they cannot automatically plan the optimal sub-aperture distribution based on the aspherical steepness without human intervention, making it difficult to achieve both "measurement coverage" and "detection efficiency".

[0011] For widely used rotationally symmetric aspherical optical elements, the annular sub-aperture partitioning strategy has inherent geometric advantages. Compared to traditional grid-like circular sub-aperture scanning, annular partitioning only requires controlling the movement of the device under test or interferometer along the optical axis, avoiding complex two-dimensional lateral mechanical scanning, thereby significantly reducing motion errors.

[0012] However, existing ring partitioning algorithms mostly employ rigid equal-width segmentation or fixed-step movement, ignoring the nonlinear curvature variation characteristics of aspherical surfaces. The adaptive ring sub-aperture partitioning method proposed in this invention can automatically adjust the distribution density of sub-apertures according to the changes in the local slope of the aspherical surface—automatically densifying the rings where curvature changes drastically and automatically widening the range where curvature changes gently.

[0013] like Figure 1 As shown in (a), the geometric positional relationship between the reference spherical wavefront and the aspherical wavefront is dynamically adjusted by the relative axial movement between the interferometer and the surface under test. Here, 'matching' does not mean that the two wavefronts completely coincide, but rather a specific state that satisfies the imaging sampling law of the CCD detector.

[0014] Specifically, according to the Nyquist Sampling Theorem, the resolution of interference fringes by an interferometer CCD detector is limited by its pixel pitch. To prevent aliasing or loss of contrast in the interference fringes, the spatial frequency of the fringes projected onto the CCD must be lower than the detector's cutoff frequency (i.e., each fringe period is sampled by at least two pixels). Summary of the Invention

[0015] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing an aspherical adaptive ring sub-aperture splicing measurement method and system. Given the displacement (vertex offset Δ) of the aspherical surface to be measured, the corresponding sub-aperture tangent point position and the radius of curvature of the reference spherical wavefront are automatically determined, thereby realizing adaptive sub-aperture division and high-precision splicing. It is particularly suitable for the precision measurement of high-order aspherical optical elements and solves the technical problems of traditional methods, such as sub-aperture division relying on manual experience, poor flexibility, and accumulation of splicing errors.

[0016] The present invention adopts the following technical solution: A method for measuring the splicing of aspherical adaptive annular sub-apertures includes the following steps: S1. Obtain the surface profile parameters of the aspherical surface to be measured. The surface profile parameters include the aperture, vertex radius of curvature, quadratic constant, and higher-order coefficients. Simultaneously, set the axial displacement of the reference spherical wavefront relative to the aspherical surface. ; S2, Based on the surface parameters and axial displacement By combining the geometric similarity between the aspherical surface shape function and the reference spherical wavefront in a local region, a matching criterion function is constructed. The matching criterion function is used to constrain the rate of change of optical path difference between the aspherical surface and the reference spherical wavefront, so that it conforms to the Nyquist sampling frequency limit of the interferometer detector, and ensures that the interference fringe density is within the resolvable range of the detector. S3. Based on the calculation result of the matching criterion function, search for candidate radial positions or radial intervals, and adaptively determine the radial position and coverage of at least one annular sub-aperture. The division of the annular sub-aperture must meet a preset overlap rate threshold of 25%. S4. According to the determined radial position and coverage range, perform interferometry on the aspherical region corresponding to each annular sub-aperture, and collect and obtain the surface phase data and optical path difference data of each sub-aperture. S5. Using the overlapping area data between each sub-aperture, the measurement data of all sub-apertures are corrected and fused by the global sub-aperture stitching model. The global sub-aperture stitching model is based on the least squares method to construct the objective function of the overlapping area residual and solve the adjustment coefficient, and finally obtains the full-aperture surface shape measurement results of the aspherical surface.

[0017] Preferably, in step S2, when constructing the matching criterion function, an inversion model of the sub-aperture characteristic parameters is also constructed, wherein the inversion model uses the axial displacement of the aspherical mirror under test. Using the input quantity, the position of the sub-aperture tangent point is calculated by reverse calculation. and the corresponding reference spherical wavefront radius of curvature .

[0018] Preferably, the inversion model of the sub-aperture characteristic parameters includes a geometrically tangent mathematical model. This mathematical model introduces axial sag consistency constraints and tangential slope consistency constraints, which together form a nonlinear equation system. The unknowns of this nonlinear equation system are (…). , Given the input is .

[0019] Preferably, the axial sagittal consistency constraint is a non-spherical surface at the tangent point. The axial sagitta at that point is equal to the offset of the sphere's center along the optical axis. The reference sphere at the point of tangency The sag at the point; the tangential slope consistency constraint is that the aspherical surface at the tangent point The slope of the tangent at the point of tangency is equal to that at the reference sphere at the point of tangency. The slope of the tangent at that point.

[0020] Preferably, the inversion model of the sub-aperture characteristic parameters further includes a two-dimensional coarse positioning strategy. This strategy involves dividing the area into grids within a reasonable range and enumerating grid point combinations. For each group (… , Calculate the joint residual function and find the point with the smallest residual as the initial value for coarse localization. , The traversal interval of the grid is... ∈[0, / 2]、 ∈[0.8 1.2 ],in, It is an aspherical aperture. Let be the radius of curvature of the vertex of the aspherical surface.

[0021] Preferably, the inversion model of the sub-aperture characteristic parameters further includes a nonlinear least squares fine positioning strategy. This fine positioning strategy, based on the initial coarse positioning values, uses the Levenberg-Marquardt nonlinear least squares method to finely solve the nonlinear equations, obtaining the current... Corresponding sub-aperture tangent point position and the radius of curvature of the matching reference sphere And the reference sphere center position and spherical wave radius are derived.

[0022] Preferably, in step S3, when calculating and determining the boundary range of the sub-aperture, the criteria formula is substituted point by point from the tangent point toward both radial sides. Points that do not meet the criteria formula are taken as preliminary boundary points. Then, the overlap rate of the sub-aperture range corresponding to the preliminary boundary points is checked. If the preset overlap rate threshold of 25% is not met, the axial displacement is adjusted. Then repeat step S2 until both the Nyquist sampling frequency limit constraint and the overlap rate threshold are satisfied.

[0023] Preferably, in step S4, the phase-shifting interferometry method is used to acquire the interferograms corresponding to each annular sub-aperture. Through the data processing steps of phase extraction and phase unpacking, the surface phase data and optical path difference data of each sub-aperture are obtained.

[0024] Preferably, in step S5, the adjustment coefficient is used to correct translation and tilt systematic errors in the sub-aperture measurement process. The optimal adjustment coefficient for each sub-aperture is obtained by taking the partial derivative of each adjustment coefficient in the objective function of the residual in the overlapping region and setting the partial derivative to zero, and solving the equation system.

[0025] Secondly, embodiments of the present invention provide an aspherical adaptive annular sub-aperture splicing measurement system, comprising: The parameter module is used to obtain the surface parameters of the aspherical surface to be measured. The surface parameters include the aperture, vertex radius of curvature, quadratic constant and higher-order coefficients. At the same time, the axial displacement Δ of the reference spherical wavefront relative to the aspherical surface is set. The criterion module is used to construct a matching criterion function based on the surface parameters and axial displacement Δ, combined with the geometric similarity between the aspherical surface function and the reference spherical wavefront in a local region. The matching criterion function is used to constrain the rate of change of optical path difference between the aspherical surface and the reference spherical wavefront, so that it conforms to the Nyquist sampling frequency limit of the interferometer detector, and ensures that the interference fringe density is within the resolvable range of the detector. The segmentation module is used to search for candidate radial positions or radial intervals based on the calculation results of the matching criterion function, and adaptively determine the radial position and coverage of at least one annular sub-aperture. The segmentation of the annular sub-aperture must meet a preset overlap rate threshold of 25%. The measurement module is used to perform interferometric measurements on the aspherical regions corresponding to each annular sub-aperture according to the determined radial position and coverage range, and to collect and acquire the surface phase data and optical path difference data of each sub-aperture. The stitching module is used to utilize the overlapping area data between each sub-aperture, and to correct and fuse the measurement data of all sub-apertures through a global sub-aperture stitching model. The global sub-aperture stitching model is based on the least squares method to construct the objective function of the overlapping area residual and solve the adjustment coefficient, and finally obtains the full-aperture surface shape measurement results of the aspherical surface.

[0026] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described aspherical adaptive annular sub-aperture splicing measurement method.

[0027] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described aspherical adaptive annular sub-aperture splicing measurement method.

[0028] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described aspherical adaptive annular sub-aperture splicing measurement method.

[0029] In a sixth aspect, embodiments of the present invention provide an electronic device, including a computer program, which, when executed by the electronic device, implements the steps of the above-described aspherical adaptive annular sub-aperture splicing measurement method.

[0030] Compared with the prior art, the present invention has at least the following beneficial effects: An adaptive annular sub-aperture stitching measurement method for aspherical surfaces uses axial displacement Δ as the core driving variable. Combining the geometric characteristics of the aspherical surface with the detector sampling limit, a matching criterion function is constructed to achieve adaptive sub-aperture division. This method automates and intelligently integrates the measurement process, avoiding the reliance on manual experience to set sub-aperture positions in traditional methods. By introducing a 25% overlap threshold, it balances measurement accuracy and efficiency. The global least-squares stitching model effectively suppresses systematic errors and improves the accuracy of full-aperture surface reconstruction. It achieves automated sub-aperture division and high-precision stitching, balancing measurement coverage and efficiency without manual intervention. This solves the pain point of sacrificing both efficiency and accuracy in high-steep aspherical surface measurements and is applicable to the detection of various high-order aspherical components.

[0031] Furthermore, the system achieves automatic solution of key parameters, eliminating the need for operators to rely on trial and error based on experience, significantly reducing operational complexity. The inversion model and matching criterion function work together to ensure adaptive matching between sub-aperture division and aspherical curvature changes, maintaining fringe density compliance even in regions with drastic curvature variations. This enhances the method's versatility and adaptability, laying a parametric foundation for subsequent accurate annular zoning.

[0032] Furthermore, the optimal matching of the reference sphere and aspherical surface is achieved geometrically. Dual constraints ensure spatial coincidence and consistency of normal directions, minimizing interference fringe density in the tangent region and maximizing data acquisition quality. This decouples the core conditions for aspherical surface matching, improving the accuracy and stability of parameter inversion and avoiding matching deviations caused by a single constraint, thus providing rigorous theoretical support for subsequent determination of sub-aperture ranges.

[0033] Furthermore, the ambiguity of the constraints is eliminated, making the solution process quantifiable and reproducible, and avoiding inversion errors caused by unclear constraint definitions. This provides a clear objective function for subsequent coarse and fine positioning, improving the efficiency and accuracy of parameter solving and ensuring the reliability of the core parameters of the sub-aperture.

[0034] Furthermore, it effectively avoids the problem of getting trapped in local optima by directly iteratively solving. The grid interval setting fully covers the reasonable range of parameters, ensuring that no optimal solution region is missed, and it can be executed in parallel, resulting in high computational efficiency. Compared with direct solving without initial values, it provides near-global optimal initial values ​​for fine localization, significantly reducing the number of iterations and convergence difficulty in subsequent fine optimization, and improving the robustness of the inversion model. It is especially suitable for solving parameters of complex surfaces such as high-order aspherical surfaces.

[0035] Furthermore, combining the advantages of gradient descent and Gauss-Newton methods, this approach achieves fast convergence and strong stability, enabling rapid iteration to obtain optimal parameters. Fine positioning further optimizes the tangent point location and the reference sphere radius, significantly reducing parameter errors and providing high-precision parameter support for sub-aperture range division. Simultaneously, a coupled mode of coarse positioning for range locking and fine positioning for accurate solution is achieved, balancing solution efficiency and accuracy to ensure that the inversion results meet the parameter requirements for nanometer-scale measurements.

[0036] Furthermore, the adaptive determination of the sub-aperture range was achieved, ensuring that each ring band could satisfy the sampling theorem; the convergence and accuracy of the splicing algorithm were guaranteed through overlap rate verification; if the overlap rate did not meet the requirements, Δ was automatically adjusted and re-divided, forming a closed-loop optimization mechanism, which improved the robustness of the method.

[0037] Furthermore, it ensures the accuracy and integrity of the measurement data; the phase-shifting interferometry method has the characteristics of high resolution and strong anti-interference ability, and is suitable for high-precision aspherical detection; the data processing flow is standardized, which facilitates seamless integration with subsequent stitching modules.

[0038] Furthermore, unified correction and fusion of multi-aperture data were achieved; by minimizing the residuals in the overlapping area, splicing accumulation error was effectively suppressed; the solution process has a clear mathematical form, is easy to implement and integrate, and provides a reliable guarantee for full-aperture surface reconstruction.

[0039] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0040] In summary, this invention achieves automation and high precision in aspherical surface measurement through adaptive annular sub-aperture division and global least squares stitching; it eliminates the need for manual pre-setting of tangent points, making sub-aperture division intelligent and efficient; the 25% overlap threshold balances accuracy and efficiency; the inversion model and geometric constraints ensure matching accuracy; and the stitching model effectively suppresses errors, making it suitable for high-steepness aspherical surface detection.

[0041] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0042] Figure 1 The image shows a stitched diagram of the annular sub-aperture, where (a) represents the detection principle, (b) represents the annular sub-aperture, and (c) represents the interference diagram. Figure 2 This is a geometric diagram of aspherical measurement. Figure 3 The images show the interference pattern with and without distortion (left and right). Figure 4 The remaining sub-aperture geometry diagram; Figure 5 This is a schematic diagram illustrating the principle of the coarse-fine coupled inversion strategy. Figure 6 Diagram showing the division of the ring zone; Figure 7 This is a flowchart of the method of the present invention; Figure 8 This is a diagram of the experimental environment for this invention; Figure 9 This is a diagram illustrating the experimental steps of the present invention; Figure 10 The image shows the phase extraction results for each sub-aperture ring. Figure 11 This is the stitched image; Figure 12 This is a diagram showing the phase extraction results of each sub-aperture ring in a traditional splicing method. Figure 13 The figures are interferograms and results of a single measurement, where (a) is the interferogram of a single measurement of the full aperture, and (b) is the result of the surface reconstruction of a single measurement of the full aperture. Figure 14 The images show the ZYGO measurement interferogram and the processed results, where (a) is the original interferogram acquired by the ZYGO interferometer, and (b) is the surface shape processing result of the ZYGO measurement data. Figure 15 A schematic diagram of a computer device provided in an embodiment of the present invention; Figure 16 This is a block diagram of a chip provided according to an embodiment of the present invention.

[0043] Among them, 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0046] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0047] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0048] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0049] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0050] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0051] This invention provides an adaptive annular sub-aperture stitching measurement method for aspherical surfaces. The method uses the axial displacement Δ of the aspherical surface under test (i.e., the physical scanning distance of the vertex of the measured element along the optical axis relative to the wavefront focus of the reference sphere) as the driving variable, and inverts the optimal sub-aperture parameters based on the Nyquist sampling limit of the interferometer detector. The method includes: establishing a coupling model between the aspherical surface shape and the reference wavefront; automatically calculating the tangent point position and the radius of the reference sphere that satisfy the null interference condition using Δ as input; gradually generating annular sub-aperture measurement regions while ensuring that the overlapping area of ​​the sub-apertures meets a set threshold (overlapping area greater than 20%); and finally, employing a stitching strategy based on least squares and weighted averaging to achieve global stitching and seamless connection between the sub-apertures. Simulation and experimental results show that, compared with the traditional fixed step size method, this method does not require preset tangent points and is suitable for flexible measurement of various types of aspherical workpieces. It improves the automation level of sub-aperture generation and the accuracy and efficiency of the measurement process. The rationality of sub-aperture planning is significantly improved, and the residual RMS of the spliced ​​surface and the full-aperture measurement results is better than 3nm. It effectively solves the problem that the sub-aperture division in the measurement of high-steep aspherical surfaces depends on experience and the accuracy is difficult to guarantee.

[0052] The adjustment process described in this invention is essentially about finding an optimal set of axial relative positions and an effective reference spherical wave radius, so that the deviation of the normal direction between the reference wavefront and the aspherical wavefront is minimized within the annular region. This ensures that the rate of change of the optical path difference (i.e., the fringe density) formed by the two is strictly controlled within the resolution limit of the CCD, thereby ensuring that clear and accurate phase data can be acquired.

[0053] In the splicing inspection of annular sub-apertures, the overlap ratio between adjacent annular bands is a key parameter affecting the final splicing quality.

[0054] Based on error propagation theory and numerical simulation analysis, it is shown that there is a significant nonlinear coupling relationship between overlap rate and splicing accuracy and efficiency: when the overlap area is too small (e.g., less than 15%), there are insufficient effective data points for calculating splicing coefficients (tilt, translation, etc.), which leads to a sharp increase in the condition number of the global splicing matrix. The algorithm is prone to falling into ill-conditioned mode, resulting in a significant decrease or even divergence in splicing accuracy. When the overlap area is too large (e.g., greater than 40%), although the robustness is improved slightly due to data redundancy, the number of sub-apertures required to cover the full aperture increases exponentially, which significantly reduces measurement efficiency and introduces more accumulated errors.

[0055] Simulation results show that when the overlap area is set at around 25%, the stitching algorithm achieves the optimal balance between convergence stability and measurement efficiency. Based on this optimization principle, this invention sets the overlap rate threshold to 25% in path planning. A typical schematic diagram of annular sub-aperture division is shown below. Figure 1 As shown in (b), the corresponding interference fringe simulation pattern is as follows: Figure 1 As shown in (c).

[0056] In studying the problem of toroidal sub-aperture partitioning, we use a common quadratic surface as an example to illustrate the derivation process of the toroidal sub-aperture partitioning model. The partitioning process for other higher-order surfaces is similar; only the surface equations need to be replaced. Next, we introduce the principle and flow of traditional toroidal sub-aperture splicing. Figure 2 The diagram shows the geometric relationship of aspherical surface measurement. Let the radius of curvature at the vertex of a certain quadratic aspherical surface be... Its meridian equation is: (1) in, For vertex curvature, ; It is the constant of the quadratic term of the aspherical surface; Let A be the surface elevation, and B be the coefficients of higher-order terms.

[0057] Using radius When a vertex-referenced spherical wave is used to measure the surface shape of an aspherical surface, the optical path difference generated at any point on the aspherical surface is: (2) Let the coordinates of two adjacent points at a certain point on an aspherical surface be respectively , The difference in optical path difference between the two adjacent points is then... (3) Assume the maximum resolution that the CCD can use during measurement is If the diameter of the aspherical surface is D, then the diameter of two adjacent points is... , Spacing between The corresponding pixel spacing is Then the difference in optical path difference corresponding to a unit pixel spacing is: (4) Based on the preceding analysis, if the wavelength of the light source is The condition for no interference image distortion is: (5) Substituting equations (2), (3), and (4) into equation (5) yields: (6) This can be further expressed as: (7) The boundary value of the sub-aperture can be obtained by solving equation (7), thereby determining the range of the sub-aperture.

[0058] The derivation of the above sub-aperture boundary division formula is based on radius. The vertex is derived from a spherical wave reference. This boundary is used as the boundary range of the reference sub-aperture. The principle for dividing the remaining sub-apertures is as follows: The equation of the meridian of an aspherical surface is: The coordinates of the tangent point between the reference spherical wave and the aspherical surface of a certain sub-aperture are: The slope of the normal at the point of tangency is: (8) The equation of the normal is: (9) make The coordinates of the sphere's center can be obtained as follows: Then the radius of the spherical wavefront is the distance between the center of the sphere and the point of tangency, that is, the radius of the reference spherical wavefront is: (10) The vertex offset is: (11) The division formula is: (12) The sub-apertures can be obtained using the above division formula.

[0059] This invention proposes a method that uses the relative axial displacement Δ of the aspherical surface under test along the optical axis as the core driving variable, and adaptively inverts the characteristic position of the sub-aperture measurement area and the corresponding reference spherical wavefront parameters based on the matching state between the aspherical surface and the reference spherical wavefront.

[0060] Here, It does not refer to some uncontrollable alignment error, but rather to the physical distance that the vertex of the aspherical surface under test moves relative to the focal point of the reference spherical wave in the optical axis direction during sub-aperture scanning.

[0061] In actual measuring devices, This corresponds to the controlled stroke of a high-precision displacement stage. From a geometric optics perspective, as Δ changes continuously, the tangent position (i.e., the zero-position interference region) between the reference spherical wavefront and the aspherical surface shifts from the vertex to the edge of the aspherical surface. Therefore, It is a crucial bridge connecting mechanical motion and wavefront matching; this invention achieves this by changing... This input is used to dynamically find the optimal sub-aperture tangent point that meets the detector resolution requirements.

[0062] In a preferred embodiment, the characteristic position can be selected as the location where the aspherical and reference spherical wavefronts have the best matching degree in a local region. This position can be represented as a geometric tangent point or an approximate tangent point, and the corresponding radius of curvature of the reference spherical wavefront can be determined simultaneously. This method does not require manual specification of the tangent point position and has the advantages of strong adaptability and high linkage accuracy.

[0063] Please see Figure 7 The present invention provides a method for measuring the splicing of aspherical adaptive annular sub-apertures, comprising the following steps: S1. Obtain the surface profile parameters of the aspherical surface to be measured, and set the axial displacement of the reference spherical wavefront relative to the aspherical surface. ; First, obtain the basic surface parameters of the aspherical surface to be tested, including the aperture. D Vertex radius of curvature The design parameters include the quadratic constant k and the coefficients of higher-order terms A / B, and the axial displacement of the reference spherical wavefront relative to the aspherical surface is also set. , It serves as the core input for subsequent inversion calculations of sub-aperture feature parameters.

[0064] S2. Under the condition of a given axial displacement Δ, a matching criterion function is constructed based on the geometric similarity between the aspherical surface shape function and the reference spherical wavefront in the local region. The matching relationship is specifically defined as follows: the rate of change of the optical path difference between the aspherical surface and the reference spherical wavefront satisfies the Nyquist sampling frequency limit constraint of the interferometer detector to ensure that the interference fringe density is within the resolvable range of the detector. For the reference sub-aperture, its tangent point is at the vertex of the center of curvature of the aspherical surface. By solving the above equation (7), the range of the reference sub-aperture can be determined under the premise of satisfying the Nyquist sampling theorem, and the relevant data of the reference sub-aperture can be obtained. For the sub-aperture after axial displacement, its tangent point position and the radius of the spherical reference wavefront are unknowns. This step achieves the determination of the range of the reference sub-aperture by constructing an inversion model based on the axial displacement. Using this as input, the position of the sub-aperture tangent point is calculated in reverse. 0 and the corresponding reference spherical wavefront radius of curvature R The purpose of this inversion model is to consist of the following three main parts: 1. Establish a geometric tangency mathematical model To achieve precise alignment between the reference spherical wavefront and the aspherical surface under test at the optimal fitting position, this invention establishes a mathematical model based on geometric tangency. This model requires that the two surfaces align precisely at the tangency point. At point 0, not only do the spatial coordinates coincide, but the normal directions are also collinear. Specifically, the following two core constraints are introduced: 1) Axial sagittal consistency constraint (position matching): (13) That is, the height of the aspherical surface at the tangent point is equal to the height of the cross-section of the reference sphere (centered at a point Δ outside the optical axis). This formula constrains the geometric relationship between the two in the optical axis direction (Z-axis). For aspherical surfaces in radial position The axial sagitta at point 0; the right side of the equation is the sagitta of the reference sphere with radius R and its center offset Δ along the optical axis. This constraint ensures that the reference sphere and the aspherical surface are at the tangent point. Spatial contact is achieved at 0 points.

[0065] 2) Tangential slope consistency constraint (normal matching): (14) This formula constrains the relationship between the first derivatives of the two surfaces. Specifically, the slope of the tangent line to the aspherical surface at the point of tangency must be equal to the slope of the tangent line to the reference sphere. This constraint ensures that the wavefront of the reference sphere and the normal direction of the aspherical surface are aligned at the point of tangency, thus minimizing the interference fringe density in that region.

[0066] Together, they form a system of nonlinear equations, with the unknowns being ( 0, R Given that the input is Δ.

[0067] 2. Two-dimensional coarse positioning strategy: Mesh traversal Δ → ( 0, R The initial solution space of ) To avoid getting stuck in local extrema when directly iterating through nonlinear equations, a two-dimensional coarse search strategy is proposed. This strategy divides the system into grids within a reasonable range and enumerates combinations to efficiently obtain the initial values ​​for the optimal solution. The specific steps are as follows: 1) Determine the grid traversal interval: 0∈[0, D / 2], where, D It is an aspherical aperture; ∈[0.8 R 0, 1.2 R 0], covering the possible range of changes in the curvature of the reference sphere; 2) Enumerate the grid point combinations, for each group ( , R Calculate the joint residual function: (15) 3) Find the point with the smallest residual as the initial value for coarse positioning. 0, R ).

[0068] This step can be executed in parallel efficiently and has good convergence, ensuring that the optimal region is not missed.

[0069] 3. Nonlinear least squares precise localization: using the coarse solution as the initial value for joint inverse solution. After obtaining the coarse location results, the Levenberg-Marquardt nonlinear least squares method was used to solve the equations in detail: (16) By iteratively converging, the position of the sub-aperture tangent point corresponding to the current Δ can be obtained. 0, Matching reference sphere curvature half R Furthermore, based on geometric relationships, it can be directly deduced that: Reference center position : (17) spherical wave radius : (18) This step uses Δ as input to inversely deduce the aperture tangent point and reference sphere parameters, eliminating the need for manual setting; it simultaneously decouples the aspherical matching conditions by combining constraints, ensuring both positional and directional continuity and improving splicing accuracy; and employs a joint strategy of two-dimensional coarse positioning and nonlinear fine optimization to avoid local convergence traps, balancing computational efficiency and robustness.

[0070] Under certain implementation conditions, the positional constraint and the normal constraint can be satisfied simultaneously, thus forming a strict geometric tangent point; under other implementation conditions, the feature position that satisfies the optimal matching degree can be determined by minimizing the joint residual corresponding to the constraint conditions. A schematic diagram is shown below. Figure 5 As shown.

[0071] S3. By searching for candidate radial positions or radial intervals, the radial position and coverage of at least one annular sub-aperture are adaptively determined based on the calculation results of the criterion function. In step S1, the characteristic location (tangent point) of the sub-aperture measurement area is determined. 0) and the corresponding reference spherical wavefront parameters (radius of curvature) R Center position of the ball After that, this step involves dividing the annular sub-aperture's zonal range. The core of this step is to adaptively determine the radial position and coverage area of ​​the sub-aperture under the dual constraints of the Nyquist sampling theorem and the overlap rate threshold. The specific steps are as follows: S301, Set overlap rate threshold By selecting 25% as the optimal overlap rate threshold, the system can minimize the number of sub-apertures while ensuring the convergence stability of the global least squares stitching algorithm, thereby optimizing the measurement efficiency.

[0072] S302, Determine the sub-aperture boundary criteria Based on the Nyquist sampling theorem, the criterion formula for determining the boundary range of the sub-aperture is expressed as follows: (19) S303, Solving for preliminary boundary points The tangent point is obtained from the previous step. 1, z1) and the radius of curvature of the spherical wavefront R Then, calculate from the tangent point outwards, substituting each point into formula (12) for calculation, that is... (20) When a point does not satisfy the above equation, it proves that the boundary points on both sides have appeared, i.e. ( 2, z2), ( 3, z3), to preliminarily determine the radial coverage range of the sub-aperture.

[0073] S304. Overlap Rate Verification and Parameter Correction The overlap rate of the initially determined sub-aperture range is checked to determine whether the proportion of its overlap area with adjacent sub-apertures meets the 25% threshold requirement. If the calculated area does not meet the overlap requirement, it proves that the current axial displacement Δ (vertex offset) does not meet the actual measurement requirements. After adaptively adjusting Δ, return to S1 to re-invert the characteristic parameters, and repeat the annular zone division process in this step until the sub-aperture range simultaneously meets the Nyquist sampling constraint and the 25% overlap rate constraint. At this point, the final radial position and coverage area of ​​the sub-aperture are determined. S305, Iterative division of full-aperture sub-apertures Following the steps described above, adjust the axial displacement Δ sequentially to complete the division of all annular sub-apertures within the full diameter range of the aspherical surface. The division logic for each sub-aperture is consistent and will not be elaborated further here.

[0074] S4. Perform interferometric measurements on the aspherical regions corresponding to the annular sub-apertures to obtain measurement data for each sub-aperture; Based on the axial displacement Δ, radial position, and coverage area corresponding to each annular sub-aperture determined in step S2, the aspherical surface under test or the interferometer is sequentially moved to the target position along the optical axis using a high-precision six-degree-of-freedom electromechanical positioning platform, and laser interferometry is performed on each annular sub-aperture region.

[0075] During the measurement process, phase-shifting interferometry (PSI) is used to acquire interferograms. Through data processing steps such as phase extraction and phase unpacking, measurement data such as surface phase data and optical path difference data corresponding to each sub-aperture are obtained to ensure that the interference fringe density in each sub-aperture region does not exceed the Nyquist sampling limit of the detector. The acquired interferograms are clear and distortion-free, and the measurement data are valid and accurate.

[0076] S5. Based on the overlapping area between sub-apertures, a unified splicing model is used to correct and splice the measurement data of each sub-aperture to obtain the full-aperture measurement results of the aspherical surface.

[0077] This invention employs a global sub-aperture stitching strategy. Based on the overlapping area data between each sub-aperture, a unified stitching model is established. Systematic error correction and global stitching are performed on the measurement data of each sub-aperture to finally obtain the full-aperture surface shape measurement results of the aspherical surface. The specific stitching process is as follows: S401, Set basic splicing parameters Suppose the aspherical surface to be measured has a total aperture divided into 3 sections. M Each sub-aperture, the overlapping area between adjacent sub-apertures is M 1; the first sub-aperture (center reference sub-aperture) is selected as the splicing reference, and its phase distribution is as follows: 1(x,y), the first The phase distribution of each aperture is as follows i(x,y), the first The adjustment factor for the individual aperture relative to the reference aperture is: , , , (Used to correct systematic errors such as translation and tilt).

[0078] S402. Establish phase matching relationship The matching relationship between the phase distribution of each sub-aperture and the phase distribution of the reference sub-aperture is as follows: (twenty one) S403. Constructing the least squares objective function The least squares objective function is constructed with the goal of minimizing the phase residual within the overlapping region: (twenty two) in, For the first Number of phase data points in each overlapping region.

[0079] S404, Solving for adjustment coefficients For each adjustment coefficient , , , By taking the partial derivatives and setting them all to zero, the optimal adjustment coefficients for each sub-aperture can be obtained by solving the following system of equations: (twenty three) S405, Global Stitching and Surface Reconstruction Substituting the obtained adjustment coefficients into the phase matching formula, the measurement data of all sub-apertures are systematically corrected, the phase data of each sub-aperture are unified into the coordinate system of the reference sub-aperture, and the seamless splicing of the full-aperture sub-apertures is completed by data fusion of the overlapping areas. Finally, the full-aperture surface shape distribution result of the aspherical surface to be measured is reconstructed.

[0080] In another embodiment of the present invention, an aspherical adaptive ring sub-aperture splicing measurement system is provided. This system can be used to implement the above-mentioned aspherical adaptive ring sub-aperture splicing measurement method. Specifically, the aspherical adaptive ring sub-aperture splicing measurement system includes a parameter module, a criterion module, a division module, a measurement module, and a splicing module.

[0081] The parameter module is used to obtain the surface shape parameters of the aspherical surface to be measured. The surface shape parameters include the aperture, vertex radius of curvature, quadratic constant and higher-order coefficients. At the same time, the axial displacement Δ of the reference spherical wavefront relative to the aspherical surface is set. The criterion module is used to construct a matching criterion function based on the surface parameters and axial displacement Δ, combined with the geometric similarity between the aspherical surface function and the reference spherical wavefront in a local region. The matching criterion function is used to constrain the rate of change of optical path difference between the aspherical surface and the reference spherical wavefront, so that it conforms to the Nyquist sampling frequency limit of the interferometer detector, and ensures that the interference fringe density is within the resolvable range of the detector. The segmentation module is used to search for candidate radial positions or radial intervals based on the calculation results of the matching criterion function, and adaptively determine the radial position and coverage of at least one annular sub-aperture. The segmentation of the annular sub-aperture must meet a preset overlap rate threshold of 25%. The measurement module is used to perform interferometric measurements on the aspherical regions corresponding to each annular sub-aperture according to the determined radial position and coverage range, and to collect and acquire the surface phase data and optical path difference data of each sub-aperture. The stitching module is used to utilize the overlapping area data between each sub-aperture, and to correct and fuse the measurement data of all sub-apertures through a global sub-aperture stitching model. The global sub-aperture stitching model is based on the least squares method to construct the objective function of the overlapping area residual and solve the adjustment coefficient, and finally obtains the full-aperture surface shape measurement results of the aspherical surface.

[0082] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or function. The processor described in this embodiment can be used for the operation of an aspherical adaptive ring sub-aperture stitching measurement method, including: Obtain the surface profile parameters of the aspherical surface to be tested, including the aperture, vertex radius of curvature, quadratic constant, and higher-order coefficients. Simultaneously, set the axial displacement of the reference spherical wavefront relative to the aspherical surface. Based on the surface parameters and axial displacement By combining the geometric similarity between the aspherical surface shape function and the reference spherical wavefront in a local region, a matching criterion function is constructed. This matching criterion function is used to constrain the rate of change of optical path difference between the aspherical surface and the reference spherical wavefront, ensuring that it conforms to the Nyquist sampling frequency limit of the interferometer detector and that the interference fringe density is within the resolvable range of the detector. Based on the calculation results of the matching criterion function, candidate radial positions or radial intervals are searched, and the radial position and coverage of at least one annular sub-aperture are adaptively determined. The division of the annular sub-aperture must meet a preset overlap rate threshold of 25%. According to the determined radial position and coverage, interferometry is performed on the aspherical region corresponding to each annular sub-aperture, and the surface shape phase data and optical path difference data of each sub-aperture are collected and acquired. Using the overlapping region data between each sub-aperture, the measurement data of all sub-apertures are corrected and fused by a global sub-aperture stitching model. The global sub-aperture stitching model is based on the least squares method to construct the objective function of the overlapping region residual and solve the adjustment coefficient, finally obtaining the full-aperture surface shape measurement results of the aspherical surface.

[0083] Please see Figure 15 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the aspherical adaptive annular sub-aperture stitching measurement method of this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the aspherical adaptive annular sub-aperture stitching measurement system of this embodiment. To avoid repetition, these details are not elaborated here.

[0084] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 15 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0085] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0086] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0087] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0088] Please see Figure 16 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0089] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 7 The steps are shown in the figure.

[0090] Storage unit 620 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include a read-only memory (ROM) 6203.

[0091] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0092] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0093] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0094] Example 3 This invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0095] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0096] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0097] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the aspherical adaptive annular sub-aperture stitching measurement method in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps: Obtain the surface profile parameters of the aspherical surface to be tested, including the aperture, vertex radius of curvature, quadratic constant, and higher-order coefficients. Simultaneously, set the axial displacement of the reference spherical wavefront relative to the aspherical surface. Based on the surface parameters and axial displacement By combining the geometric similarity between the aspherical surface shape function and the reference spherical wavefront in a local region, a matching criterion function is constructed. This matching criterion function is used to constrain the rate of change of optical path difference between the aspherical surface and the reference spherical wavefront, ensuring that it conforms to the Nyquist sampling frequency limit of the interferometer detector and that the interference fringe density is within the resolvable range of the detector. Based on the calculation results of the matching criterion function, candidate radial positions or radial intervals are searched, and the radial position and coverage of at least one annular sub-aperture are adaptively determined. The division of the annular sub-aperture must meet a preset overlap rate threshold of 25%. According to the determined radial position and coverage, interferometry is performed on the aspherical region corresponding to each annular sub-aperture, and the surface shape phase data and optical path difference data of each sub-aperture are collected and acquired. Using the overlapping region data between each sub-aperture, the measurement data of all sub-apertures are corrected and fused by a global sub-aperture stitching model. The global sub-aperture stitching model is based on the least squares method to construct the objective function of the overlapping region residual and solve the adjustment coefficient, finally obtaining the full-aperture surface shape measurement results of the aspherical surface.

[0098] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0099] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0100] To fully verify the effectiveness of the adaptive annular sub-aperture division and stitching algorithm proposed in this invention in high-precision aspherical surface detection, this study built a high-end optical testing platform based on point diffraction interferometry (PDI) and carried out experimental verification.

[0101] Using higher-order aspherical surfaces as the experimental object, different partitioning results were compared. The parameters of the higher-order aspherical surfaces are as follows: Table 1 Design parameters for higher-order aspherical surfaces

[0102] Experimental setup such as Figure 8 and Figure 9 As shown, the entire optical path is placed on an active vibration isolation optical platform, and the laboratory ambient temperature is controlled at 20℃±0.1℃. The core hardware configuration is as follows: (1) Difrotec Point Diffraction Laser Interferometer: The point diffraction interferometer developed by Difrotec features a large aperture (≥700mm) and high precision (≤0.6nm RMS). The absolute measurement accuracy (Peak-to-valley) is ±0.6nm (λ / 1000), the resolution (Peak-to-valley) is 0.05nm (λ / 12000), the wavefront repeatability (RMS) is <0.23nm (λ / 2800), the numerical aperture (NA) is 0.55 (f#0.91), and data acquisition uses phase-shifting interferometry (PSI). (2) Zaber 6-DOF electromechanical positioning platform: provides six-dimensional positioning of the component under test in space. Precision positioning. The optical axis (Z-axis) has a 75mm focusing range for precisely adjusting the distance between the interferometer and the workpiece under test. Automated control is achieved by connecting to a computer and running Zaber software. The platform is equipped with a dedicated knob for manual control of the slider movement. Knob functions include: turning counterclockwise to zero, adjusting the direction and speed of movement, and pressing the knob to stop movement.

[0103] 1. Optimized annular sub-aperture division and splicing results The radius of curvature of the detected high-order aspherical surface is 96 mm, and the aperture is 31 mm. With the CCD pixel size set to 400×400 and λ=633 nm, based on the introduced adaptive annular sub-aperture division method, the final division results are shown in Table 2. Only three sub-aperture rings are needed to achieve full aperture coverage, and the overlap ratio of each sub-aperture is close to the optimal threshold of 25%, highly consistent with the set value.

[0104] Table 2 Results of Optimized Sub-aperture Division

[0105] Using the central sub-aperture (sub-aperture 1) as the splicing reference, deviation adjustment errors are introduced in ring 2 and ring 3 to simulate systematic errors in actual measurements. The adjustment error coefficients are shown in Table 3.

[0106] Table 3. Adjustment error coefficients for each sub-aperture

[0107] The global least squares stitching model of this invention eliminates the wavefront bias between each annulus, completing data fusion and stitching. The phase extraction results of each sub-aperture annulus are as follows: Figure 10 As shown, the final full-caliber splicing result is as follows: Figure 11 As shown.

[0108] 2. Results of traditional splicing and full-caliber measurement To verify the accuracy of the splicing algorithm, a comparative measurement was performed using the traditional fixed-step-size annular sub-aperture division method. The division results are shown in Table 4. The proportion of overlapping areas of each sub-aperture deviates from the optimal threshold of 25%.

[0109] Table 4 Results of Traditional Sub-Aperture Classification

[0110] The phase extraction results of each sub-aperture annular zone using the traditional method are as follows: Figure 12 As shown. Simultaneously, by adjusting the position of the mirror under test, a single interferometric measurement of the entire aperture of the experimental object was achieved. The interferogram and measurement results are shown below. Figure 13 As shown in Table 5, the optimized stitching results, the traditional stitching results, and the full-caliber single measurement results were compared.

[0111] Table 5 Comparison Results

[0112] Both of the above results were obtained on D7, using Zernike Fringe polynomials for aberration elimination.

[0113] In addition, this invention was also validated on ZYGO, where the raw data from ZYGO measurements were processed in the same way. Compared with a single full-caliber measurement, the stitching residuals were optimized. PV=6.887nm RMS=0.784nm, traditional splicing residual PV=11.325nm With an RMS of 1.682 nm, the splicing restoration accuracy of the method of this invention is significantly better than that of the traditional method.

[0114] To further verify the engineering applicability of the method of this invention, a commercial ZYGO interferometer was used to measure the same experimental object. The raw data from the ZYGO measurement underwent the same aberration elimination and data processing. The ZYGO measurement range is 29.5 mm. The interferogram and processing results are as follows. Figure 14 As shown, the measurement results are PV value 1134.9nm and RMS value 298.3386nm.

[0115] Comparing the optimized stitching results of this invention, the traditional stitching results, and the ZYGO measurement results, the optimized stitching residual of this invention is: PV=20.416nm RMS=8.1744nm, traditional splicing residual PV=24.854nm With an RMS of 9.0724 nm, the measurement results obtained by the method of this invention are more consistent with those of commercial high-end interferometers, and it effectively solves the technical problem that full-aperture imaging cannot be performed in a single operation in high-steep aspherical regions.

[0116] Experimental conclusions The optimized stitching results of this invention are highly consistent with the results of full-aperture single measurement and ZYGO commercial interferometer measurement, and the stitching accuracy is significantly better than the traditional fixed step size method, fully verifying the effectiveness, high accuracy and engineering applicability of the method of this invention: 1. This invention achieves fully automatic solution of sub-aperture characteristic parameters by constructing an inversion model with axial displacement Δ as the core. It abandons the manual preset tangent point method of traditional methods, greatly improves the automation and adaptability of aspherical detection, and only requires 3 sub-apertures to achieve full aperture coverage of the experimental object, significantly improving measurement efficiency. 2. The 25% overlap threshold achieves the optimal balance between stitching accuracy and measurement efficiency. Combined with the global least squares stitching model, it effectively reduces the cumulative stitching error and improves the convergence stability of the stitching algorithm. 3. The method of the present invention does not require a customized compensator. It can achieve high-precision measurement of steep aspherical surfaces using only a general interferometer and a high-precision displacement stage, which greatly reduces the detection cost and simplifies the operation process, solving the technical pain points of traditional methods that are complicated to operate and rely on human experience.

[0117] In summary, the aspherical adaptive ring sub-aperture splicing measurement method and system of the present invention effectively simplifies the sub-aperture planning process and reduces redundant measurement times while ensuring nanometer-level measurement accuracy. It provides an efficient, reliable, and universal solution for the detection of high-precision, high-steep aspherical optical components and can be widely applied in the field of aspherical component detection in high-end optical equipment such as aerospace, astronomical observation, and lithography machines.

[0118] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0119] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0120] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0121] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0122] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0123] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0124] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random-access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0125] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0126] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0127] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0128] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for measuring the splicing of aspherical adaptive annular sub-apertures, characterized in that, Includes the following steps: S1. Obtain the surface profile parameters of the aspherical surface to be measured. The surface profile parameters include the aperture, vertex radius of curvature, quadratic constant, and higher-order coefficients. Simultaneously, set the axial displacement of the reference spherical wavefront relative to the aspherical surface. ; S2, Based on the surface parameters and axial displacement By combining the geometric similarity between the aspherical surface shape function and the reference spherical wavefront in a local region, a matching criterion function is constructed. The matching criterion function is used to constrain the rate of change of optical path difference between the aspherical surface and the reference spherical wavefront, so that it conforms to the Nyquist sampling frequency limit of the interferometer detector, and ensures that the interference fringe density is within the resolvable range of the detector. S3. Based on the calculation result of the matching criterion function, search for candidate radial positions or radial intervals, and adaptively determine the radial position and coverage of at least one annular sub-aperture. The division of the annular sub-aperture must meet a preset overlap rate threshold of 25%. S4. According to the determined radial position and coverage range, perform interferometry on the aspherical region corresponding to each annular sub-aperture, and collect and obtain the surface phase data and optical path difference data of each sub-aperture. S5. Using the overlapping area data between each sub-aperture, the measurement data of all sub-apertures are corrected and fused by the global sub-aperture stitching model. The global sub-aperture stitching model is based on the least squares method to construct the objective function of the overlapping area residual and solve the adjustment coefficient, and finally obtains the full-aperture surface shape measurement results of the aspherical surface.

2. The aspherical adaptive annular sub-aperture splicing measurement method according to claim 1, characterized in that, In step S2, when constructing the matching criterion function, an inversion model of the sub-aperture characteristic parameters is also constructed. The inversion model uses the axial displacement of the aspherical mirror under test. Using the input quantity, the position of the sub-aperture tangent point is calculated by reverse calculation. and the corresponding reference spherical wavefront radius of curvature .

3. The aspherical adaptive annular sub-aperture splicing measurement method according to claim 2, characterized in that, The inversion model for the sub-aperture characteristic parameters includes a geometrically tangent mathematical model. This mathematical model incorporates axial sag consistency constraints and tangential slope consistency constraints, which together form a nonlinear equation system. The unknowns of this nonlinear equation system are (…). , Given the input is .

4. The aspherical adaptive annular sub-aperture splicing measurement method according to claim 3, characterized in that, The axial sagittal consistency constraint is that the aspherical surface at the tangent point... The axial sagitta at that point is equal to the offset of the sphere's center along the optical axis. The reference sphere at the point of tangency The sag at the point; the tangential slope consistency constraint is that the aspherical surface at the tangent point The slope of the tangent at the point of tangency is equal to the slope of the reference sphere at the point of tangency. The slope of the tangent at that point.

5. The aspherical adaptive annular sub-aperture splicing measurement method according to claim 3, characterized in that, The inversion model for the sub-aperture characteristic parameters also includes a two-dimensional coarse positioning strategy. This strategy involves dividing the area into grids within a reasonable range and enumerating grid point combinations. For each group (… , Calculate the joint residual function and find the point with the smallest residual as the initial value for coarse localization. , The traversal interval of the grid is... ∈[0, / 2]、 ∈[0.8 1.2 ],in, It is an aspherical aperture. Let be the radius of curvature of the vertex of the aspherical surface.

6. The aspherical adaptive annular sub-aperture splicing measurement method according to claim 5, characterized in that, The inversion model for the sub-aperture characteristic parameters also includes a nonlinear least squares fine-localization strategy. This strategy, based on the initial coarse-localization values, uses the Levenberg-Marquardt nonlinear least squares method to finely solve the nonlinear equations, obtaining the current... Corresponding sub-aperture tangent point position and the radius of curvature of the matching reference sphere And the reference sphere center position and spherical wave radius are derived.

7. The aspherical adaptive annular sub-aperture splicing measurement method according to claim 1, characterized in that, In step S3, when calculating and determining the boundary range of the sub-aperture, the criteria formula is substituted point by point from the tangent point to both radially sides. Points that do not meet the criteria formula are taken as preliminary boundary points. Then, the overlap rate of the sub-aperture range corresponding to the preliminary boundary points is checked. If the preset overlap rate threshold of 25% is not met, the axial displacement is adjusted. Then repeat step S2 until both the Nyquist sampling frequency limit constraint and the overlap rate threshold are satisfied.

8. The aspherical adaptive annular sub-aperture splicing measurement method according to claim 1, characterized in that, In step S4, the phase-shifting interferometry method is used to acquire the interferograms corresponding to each annular sub-aperture. Through the data processing steps of phase extraction and phase unpacking, the surface phase data and optical path difference data of each sub-aperture are obtained.

9. The aspherical adaptive annular sub-aperture splicing measurement method according to claim 1, characterized in that, In step S5, the adjustment coefficient is used to correct translation and tilt systematic errors in the sub-aperture measurement process. The optimal adjustment coefficient for each sub-aperture is obtained by taking the partial derivative of each adjustment coefficient in the objective function of the residual in the overlapping area and setting the partial derivative to zero, and solving the equation system.

10. An aspherical adaptive annular sub-aperture splicing measurement system, characterized in that, include: The parameter module is used to obtain the surface parameters of the aspherical surface to be measured. The surface parameters include the aperture, vertex radius of curvature, quadratic constant and higher-order coefficients. At the same time, the axial displacement Δ of the reference spherical wavefront relative to the aspherical surface is set. The criterion module is used to construct a matching criterion function based on the surface parameters and axial displacement Δ, combined with the geometric similarity between the aspherical surface function and the reference spherical wavefront in a local region. The matching criterion function is used to constrain the rate of change of optical path difference between the aspherical surface and the reference spherical wavefront, so that it conforms to the Nyquist sampling frequency limit of the interferometer detector, and ensures that the interference fringe density is within the resolvable range of the detector. The segmentation module is used to search for candidate radial positions or radial intervals based on the calculation results of the matching criterion function, and adaptively determine the radial position and coverage of at least one annular sub-aperture. The segmentation of the annular sub-aperture must meet a preset overlap rate threshold of 25%. The measurement module is used to perform interferometric measurements on the aspherical regions corresponding to each annular sub-aperture according to the determined radial position and coverage range, and to collect and acquire the surface phase data and optical path difference data of each sub-aperture. The stitching module is used to utilize the overlapping area data between each sub-aperture, and to correct and fuse the measurement data of all sub-apertures through a global sub-aperture stitching model. The global sub-aperture stitching model is based on the least squares method to construct the objective function of the overlapping area residual and solve the adjustment coefficient, and finally obtains the full-aperture surface shape measurement results of the aspherical surface.

Images