An optical system adjustment sensitivity visual analysis method based on mechanical equivalent space

Abstract

The application discloses an optical system adjustment sensitivity visualization analysis method based on mechanical equivalent space, which comprises the following steps: firstly, acquiring wavefront aberration data of an optical system in a preset tolerance interval; secondly, extracting angle tilt misadjustment of an optical element, and mapping the angle tilt misadjustment to an equivalent physical linear displacement at an effective light passing edge based on spatial geometric correlation, so as to eliminate dimensional barriers of a multi-dimensional space and establish an equivalent evaluation system; further, constructing a cross-coupling evaluation model based on the calculated mechanical equivalent sensitivity, quantifying dimensional interference, and directly identifying high-sensitive aberration sources of the system; and finally, outputting a closed-loop adjustment sequence plan based on high-sensitivity priority. The application realizes quantitative dimension reduction decoupling of the optical system under multi-element misadjustment, and provides solid theoretical support and methodological guidance for stable and monotonic convergence of an automatic closed-loop adjustment process.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided assembly and adjustment of optical systems and optomechanical system engineering technology, specifically relating to a visualization analysis method for the assembly and adjustment sensitivity of optical systems based on mechanical equivalent space. Background Technology

[0002] With the continuous development of modern optical technology, the imaging quality requirements of various high-end optical systems (such as deep ultraviolet lithography objectives, large-aperture space remote sensing cameras, multi-band multiplexing common aperture systems, and complex off-axis reflection systems) are approaching the diffraction limit. These high-performance optical systems are typically characterized by complex structures, multiple degrees of freedom, and strong nonlinearity. In the actual assembly and integration process, optical components inevitably experience multi-dimensional rigid body displacement misalignments (such as translational eccentricity along each axis and angular tilt around each axis), which greatly increases the difficulty of closed-loop assembly and aberration compensation.

[0003] Traditional assembly and adjustment processes often rely on engineers' experience and trial-and-error, with conventional strategies employing mechanical, sequential adjustments (e.g., translation followed by tilt), tentatively addressing multiple degrees of freedom of misalignment for each component. This method lacks rigorous mathematical support, easily leading to low efficiency and a high risk of getting trapped in local optima. In complex optical systems, different rigidity misalignments have fundamentally different impacts on the final wavefront aberration error amplification gain, contribution, or sensitivity. If the assembly and adjustment sequence is poorly planned, prioritizing the correction of low-sensitivity degrees of freedom, even minute mechanical errors can instantly disrupt the previously converged state through high-order nonlinear coupling within the system when compensating for high-sensitivity degrees of freedom, causing repeated oscillations or even divergence in the assembly and adjustment process. Therefore, determining a scientific and reasonable assembly and adjustment priority is a core prerequisite for ensuring closed-loop convergence in advanced optical systems.

[0004] Currently, in optical engineering applications, the sensitivity matrix method, which guides assembly and adjustment strategies, faces two unresolved core contradictions:

[0005] First, the dimension barrier. Translational misalignment (usually measured in millimeters) and tilt misalignment (usually measured in angles or radians) in optical systems have fundamentally different physical dimensions, making direct horizontal comparison impossible in mathematical terms. Simply comparing the absolute values ​​of conventional sensitivity coefficients leads to a loss of physical meaning and fails to accurately reflect the actual destructive force of different types of misalignment on the optical system.

[0006] Second, there is a contradiction between local and global perspectives. Traditional linear sensitivity analysis often focuses only on the first-order slope (instantaneous sensitivity) near the current nominal design point, while neglecting the total wavefront aberration accumulated due to higher-order nonlinear coupling over the entire mechanical tolerance stroke (e.g., within the clearance of a real precision adjustment mechanism in the positive and negative tolerance zones). This local analysis method makes it difficult to establish the main controlling factors of system wavefront stability from a macroscopic statistical perspective.

[0007] In summary, existing assembly and adjustment evaluation systems struggle to intuitively and accurately identify truly high-sensitivity aberration sources in complex systems on a unified physical scale. Overcoming the dimensional barriers between translation and tilt, transforming instantaneous local sensitivity into a comprehensive physical assessment across the entire path, quantifying the actual destructive power of each misalignment degree of freedom on the system's wavefront, and using this as a basis to plan an assembly and adjustment sequence that effectively decouples and avoids iterative oscillations, are key common technical problems that urgently need to be solved in the manufacturing and assembly of various high-end optical instruments. Summary of the Invention

[0008] The purpose of this invention is to solve the above-mentioned problems and provide a method for visual analysis of optical system assembly sensitivity based on mechanical equivalent space. This method can solve the problem of dimensional obstruction in existing assembly and adjustment techniques where translation and tilt misalignment cannot be directly compared laterally. It overcomes the defect of traditional local linear sensitivity ignoring full-stroke nonlinear coupling, avoids the problem of small mechanical errors caused by unreasonable assembly and adjustment priorities instantly destroying the converged state through high-order nonlinear coupling, causing repeated oscillations or even divergence.

[0009] To solve the above-mentioned technical problems, the technical solution of the present invention is: a method for visual analysis of the assembly sensitivity of an optical system based on mechanical equivalent space, comprising the following steps:

[0010] S1. Acquire wavefront aberration data: Acquire wavefront aberration change data of each misalignment degree of freedom under individual or coupled perturbation within the preset tolerance range of the optical system;

[0011] S2. Calculate the mechanical equivalent sensitivity: Map the angular tilt misalignment in each degree of misalignment to the equivalent physical line displacement of the optical element edge, and establish an evaluation system with unified dimensions; and divide the wavefront aberration change data by the corresponding translational misalignment or equivalent physical line displacement to obtain the mechanical equivalent sensitivity of each degree of misalignment.

[0012] S3. Construct a cross-coupling evaluation model: Based on the mechanical equivalent sensitivity, quantify the degree of cross-coupling between multidimensional misalignment degrees of freedom and specific aberration indices, and identify the highly sensitive misalignment degrees of freedom of the system.

[0013] S4. Output assembly and adjustment sequence planning: Based on the identified high-sensitivity misalignment degrees of freedom, the closed-loop iterative assembly and adjustment sequence is output according to the priority of compensating high-sensitivity degrees of freedom first and then low-sensitivity degrees of freedom.

[0014] Furthermore, in step S1, a pose matrix satisfying a random distribution is generated within the preset tolerance range through joint simulation using optical design software and numerical calculation software, and the corresponding wavefront coefficients and / or Zernike polynomial coefficients are extracted in batches to construct a model training dataset.

[0015] Furthermore, the calculation method for mapping the angular tilt misalignment to the equivalent physical line displacement includes: obtaining the angular tilt rotation axis of the optical element and determining its effective light-transmitting edge position; based on the structural dimensions and spatial geometric relationships of the optical element, calculating the maximum actual physical line displacement generated at its effective light-transmitting edge under a given angular tilt misalignment; defining the maximum actual physical line displacement as the equivalent physical line displacement to achieve dimensional unification between the tilt misalignment and the translation misalignment.

[0016] Furthermore, S3 further includes: generating single-degree-of-freedom scanning data based on the mechanical equivalent sensitivity, establishing a reference circle in polar coordinates, using the wavefront aberration change value after normalization of the stroke as the outward expansion vector, and drawing a continuous envelope radar map; identifying highly sensitive misalignment degrees of freedom by comparing the area of ​​the envelope line corresponding to each misalignment degree of freedom deviating from the reference circle, and judging the linearity of the misalignment response by the symmetry of the envelope line.

[0017] Furthermore, S3 further includes: calculating the mechanical equivalent sensitivity of each misalignment degree of freedom to different orders of aberrations, constructing a misalignment-aberration cross-coupling sensitivity matrix, and mapping it to a high-contrast heatmap; based on the color block features in the heatmap, locking the main influencing misalignment degree of freedom of a specific aberration, and achieving targeted quantitative decoupling.

[0018] The beneficial effects of this invention are:

[0019] 1. The present invention provides a visualization analysis method for the assembly and adjustment sensitivity of an optical system based on mechanical equivalent space, which completely breaks through the dimensional barrier and establishes a unified mechanical action scale: it innovatively transforms the angle into edge displacement, removes the interference of the absolute dimension of translation and tilt misalignment, establishes an equivalent evaluation system based on the destructive force of unified mechanical execution action, and gives real physical meaning to the lateral comparison of different degrees of freedom.

[0020] 2. This invention moves from instantaneous local to full-stroke global, improving the system's disturbance rejection capability: it converts instantaneous sensitivity into full-stroke integral contribution. By evaluating the "total energy" of the component's full-stroke motion within the mechanical tolerance clearance on the system's wavefront disruption, it accurately identifies the main controlling factors of system stability, statistically avoiding state divergence caused by local optima.

[0021] 3. This invention achieves intuitive quantitative dimensionality reduction and decoupling: By constructing a cross-coupling sensitivity matrix and a heatmap, it not only reveals the natural physical orthogonality of in-plane and out-of-plane misalignments in the system, but also mathematically reduces the ill-conditioned nature of the inversion solution of the multivariate coupled equation system. The highlighted features of the heatmap enable the control algorithm to quickly identify the main influencing variables of the anomalous wavefront, achieving targeted compensation.

[0022] 4. This invention ensures monotonic convergence of closed-loop assembly and adjustment: Based on the high-sensitivity priority assembly and adjustment sequence planned by this method, a decoupling path is established from the underlying logic of optical physics, avoiding the repeated trial and error costs brought about by traditional experience-based trial and error, and greatly improving the automated assembly and adjustment efficiency and batch assembly yield of complex optical systems. Attached Figure Description

[0023] Figure 1 This is a radar chart comparison of different misalignment quantities contributing to aberrations (Z4-Z9) in a visualization analysis method for optical system assembly and adjustment sensitivity based on mechanical equivalent space, as described in this invention.

[0024] Figure 2 This is a heatmap of the cross-coupling sensitivity matrix of the contribution of different misalignment amounts to aberrations (Z4-Z9) in this invention. Detailed Implementation

[0025] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0026] like Figure 1 and Figure 2 As shown, the present invention provides a visualization analysis method for the assembly sensitivity of an optical system based on mechanical equivalent space, comprising the following steps:

[0027] S1. Acquire wavefront aberration data: Full-range data acquisition based on optical and numerical co-simulation. Acquire wavefront aberration changes of each misaligned degree of freedom under individual or coupled perturbations within a preset tolerance range.

[0028] In step S1, a pose matrix that satisfies a random distribution is generated within the preset tolerance range by joint simulation using optical design software and numerical calculation software, and the corresponding wavefront coefficients and / or Zernike polynomial coefficients are extracted in batches to construct a model training dataset.

[0029] In this embodiment, to obtain the actual evolution law of the optical system within a preset tolerance range, a joint simulation interaction is performed using optical design software (such as Zemax) and numerical calculation software (such as MATLAB). The specific implementation steps are as follows:

[0030] S11. Nominal Model Establishment: Establish the nominal design file of the target optical system in the optical design software, and set the evaluation field of view, working wavelength, and effective aperture D of the system.

[0031] S12. Tolerance Range Setting: In the numerical calculation software, based on the initial tolerance allocation of the system, set the maximum clearance range for each rigid body degree of freedom. For example, set the translational misalignment tolerance to ±1mm and the angular tilt misalignment tolerance to ±0.25°.

[0032] S13, Random Pose Injection: In the numerical calculation software, multiple sets (e.g., 101 sets) of rigid body pose perturbation matrices that satisfy the above tolerance distribution are generated by the Monte Carlo random function, and then written in batches into the coordinate break surface in the optical design software.

[0033] S14. Aberration Data Extraction: For each group of pose perturbations, the Zernike Fringe wavefront analysis function of the optical design software is called to extract the wavefront peak-valley values ​​(PV), wavefront root mean square values ​​(RMS), and Zernike wavefront coefficients of each order (such as Z4-Z9) in batches to construct the underlying aberration dataset for training the assembly model.

[0034] S2. Calculate the mechanical equivalent sensitivity: Map the angular tilt misalignment in each degree of misalignment to the equivalent physical line displacement of the optical element edge, and establish an evaluation system with unified dimensions. Divide the wavefront aberration change data by the corresponding translational misalignment or equivalent physical line displacement to obtain the mechanical equivalent sensitivity of each degree of misalignment.

[0035] In step S2, the calculation method for mapping the angular tilt misalignment to an equivalent physical linear displacement includes: obtaining the angular tilt rotation axis of the optical element and determining its effective light-transmitting edge position. Based on the structural dimensions and spatial geometric relationships of the optical element, calculating the maximum actual physical linear displacement generated at its effective light-transmitting edge under a given angular tilt misalignment. This maximum actual physical linear displacement is defined as the equivalent physical linear displacement to achieve dimensional unification between the tilt misalignment and the translational misalignment.

[0036] In this embodiment, the mechanical equivalence sensitivity is calculated based on the dimensional unification of spatial geometric correlation.

[0037] To eliminate the dimensional barriers of multidimensional space and establish an equivalent evaluation system based on a unified mechanical motion scale, this step strictly maps angular tilt misalignment to the equivalent physical line displacement of the optical element edge. The specific calculation logic steps are as follows:

[0038] S21. Obtain the angle tilt rotation axis of the optical element in the adjustment mechanism, and determine the specific position of its effective light-transmitting edge.

[0039] S22. Based on spatial geometric correlation, calculate the maximum actual physical linear displacement generated at the edge. Assuming the effective aperture of the optical system is D, and the tilt misalignment at a given angle is θ, the approximate calculation method for the edge equivalent physical linear displacement Δz can be expressed as: Δz≈D / 2·tan(θ).

[0040] S23. Calculation and verification of the example: Taking a secondary mirror of an off-axis system as an example, its effective half-aperture R sub =35mm. When a tilt of 0.25° occurs, its equivalent mechanical edge displacement is approximately Δz=35×tan(0.25°)≈0.153mm.

[0041] S24. Divide the wavefront aberration changes (e.g., RMS) extracted from each degree of freedom in S1 by their corresponding physical translation or the equivalent physical linear displacement calculated above (e.g., 0.153 mm) to obtain the absolute mechanical equivalent sensitivity in a uniform dimension (e.g., λ / mm). This converts the instantaneous sensitivity into a full-stroke integral contribution, truly reflecting the absolute destructive force of the mechanical action on the system's wavefront.

[0042] S3. Construct a cross-coupling evaluation model: Based on the mechanical equivalent sensitivity, quantify the degree of cross-coupling between multidimensional misalignment degrees of freedom and specific aberration indices, and identify the highly sensitive misalignment degrees of freedom of the system.

[0043] Step S3 further includes: generating single-degree-of-freedom scanning data based on the mechanical equivalent sensitivity; establishing a reference circle in polar coordinates; using the wavefront aberration change value after normalization of the stroke as the outward expansion vector; and drawing a continuous envelope radar map. By comparing the area of ​​the envelope corresponding to each misalignment degree of freedom deviating from the reference circle, highly sensitive misalignment degrees of freedom are identified, and the linearity of the misalignment response is determined by the symmetry of the envelope.

[0044] Step S3 further includes: calculating the mechanical equivalent sensitivity of each misalignment degree of freedom to aberrations of different orders, constructing a misalignment-aberration cross-coupling sensitivity matrix, and mapping it to a high-contrast heatmap. Based on the color patch features in the heatmap, the main influencing misalignment degrees of freedom of a specific aberration is identified, achieving targeted quantitative decoupling.

[0045] In step S3, with the center of the polar coordinate system as the zero point, a fixed radius is set as the reference circle to represent the ideal zero-aberration state. The aberration change value after normalization of the travel is used as the outward expansion radius vector to draw a continuous envelope radar map that is connected end to end. If the envelope line is perfectly symmetrical, it indicates that the mismatch response has good linearity. If it is obviously distorted, it indicates the presence of high-order nonlinear coupling, and the number of closed-loop iterations needs to be increased.

[0046] Specifically as follows:

[0047] Based on the mechanical equivalent sensitivity calculated by S2, in order to further remove absolute dimension interference and intuitively identify the high-sensitivity aberration sources of the system, this step constructs two visualization evaluation models:

[0048] Construction and Analysis of Continuous Envelope Radar Chart: A continuous envelope radar chart based on the reference circle area method is introduced. With the center of the polar coordinate axis as the zero point, a fixed radius R0 is set as the reference circle (representing the ideal zero-aberration state). The aberration changes generated by each degree of freedom within its normalized stroke are used as the outward expansion vectors, and the ends are connected to form a closed envelope.

[0049] Sensitivity determination: The further the envelope deviates from the reference circle and the larger the area it encloses, the greater the impact of the misalignment on the system stability, i.e., the higher the equivalent sensitivity.

[0050] Linearity determination: If the envelope is perfectly symmetrical (such as a centrally symmetrical figure-eight or peanut-shaped structure), it indicates that the mismatch response has good linearity or quadratic symmetry; if it is obviously distorted, it suggests that there is high-order nonlinear coupling in the system.

[0051] Construction of misalignment-abnormality cross-coupled heatmap: The equivalent sensitivity values ​​of multidimensional misalignment degrees of freedom and specific micro aberrations (Z4-Z9) are transformed into a high-contrast cross-coupled matrix heatmap.

[0052] Orthogonal decoupling feature extraction: By analyzing the color block distribution of the heatmap matrix, the odd and even symmetry patterns of the system are extracted. For example, in-plane misalignments (such as tilting around the X-axis Tx and eccentricity along the Y-axis Dy) only significantly excite symmetry and meridional aberrations (such as Z4, Z5, Z8, Z9); while out-of-plane misalignments (such as tilting around the Y-axis Ty and eccentricity along the X-axis Dx) dominate oblique astigmatism and lateral coma (Z6, Z7). This verifies the physical orthogonality of targeted compensation for specific aberrations by specific misalignments.

[0053] S4. Output assembly and adjustment sequence planning: Based on high-sensitivity priority targeted closed-loop control, according to the identified high-sensitivity misalignment degrees of freedom, the output closed-loop iterative assembly and adjustment sequence is determined by prioritizing compensation of high-sensitivity degrees of freedom followed by compensation of low-sensitivity degrees of freedom.

[0054] The optical system is an off-axis reflective optical system. The specific assembly and adjustment sequence is planned as follows: first, correct the tilt misalignment degree of freedom, and then correct the translation misalignment degree of freedom. Furthermore, the out-of-plane misalignment degree of freedom is used first to compensate for oblique astigmatism and lateral coma, while the in-plane misalignment degree of freedom is used to compensate for symmetry aberration and meridional aberration.

[0055] By combining the S3 evaluation model, the control algorithm quickly identifies the main influencing factors of the imbalance and outputs the final iterative assembly sequence, avoiding state divergence in traditional assembly. The specific planning criteria are as follows:

[0056] High-sensitivity priority compensation: By comparing the radar map area with the extreme values ​​of the heat map, if the equivalent sensitivity of the system exhibiting tilt misalignment is much greater than that of translation misalignment (i.e., the optical lever amplification effect is significant), then the tilt degree of freedom must be corrected first. Based on the data from the example, the output system assembly priority is: Tx>Ty>Dz>Dy>Dx.

[0057] Targeted decoupling compensation: Dimensionality reduction and decoupling are achieved based on the characteristics of heatmap color patches. For example, when a large-scale defocus aberration (Z4) is measured, since the axial spacing (Dz) exhibits an independent high equivalent sensitivity peak, Dz can be preferentially decoupled and compensated as an independent targeted variable without worrying about crosstalk effects. Through the above strategy, the stable monotonic convergence of the closed-loop iterative assembly is ensured.

[0058] This invention provides a visualization analysis method for the assembly and adjustment sensitivity of optical systems based on mechanical equivalent space. Traditional assembly and adjustment processes often rely on empirical trial and error, with the conventional assembly and adjustment sequence being XY translation first, then XY tilt, and finally Z translation, adjusting multiple misalignment amounts each time. This method lacks rigorous mathematical support, is prone to getting trapped in local optima, and under the dimensional barrier, translation misalignment (mm) and tilt misalignment (deg) cannot be directly compared laterally.

[0059] This invention addresses the problem of inconsistent dimensions in multidimensional misalignment during assembly and adjustment, where traditional linear sensitivity fails to reflect global nonlinear coupling, easily leading to iterative oscillations. This method first acquires wavefront aberration data of the optical system within a preset tolerance range. Second, it extracts the angular tilt misalignment of optical elements and maps it to the equivalent physical line displacement at the effective light-passing edge based on spatial geometric correlation, thereby eliminating the dimensional barriers of multidimensional space and establishing an equivalent evaluation system. Furthermore, based on the calculated mechanical equivalent sensitivity, a cross-coupling evaluation model is constructed to quantitatively remove dimensional interference and intuitively identify high-sensitivity aberration sources in the system. Finally, it outputs a closed-loop assembly and adjustment sequence plan based on high sensitivity priority. This invention achieves quantitative dimensionality reduction and decoupling under multidimensional misalignment of the optical system, providing solid theoretical support and methodological guidance for the stable and monotonically convergent automated closed-loop assembly and adjustment process.

[0060] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A visualization analysis method for the assembly sensitivity of an optical system based on mechanical equivalent space, characterized in that, Includes the following steps: S1. Acquire wavefront aberration data: Acquire wavefront aberration change data of each misalignment degree of freedom under individual or coupled perturbation within the preset tolerance range of the optical system; S2. Calculate the mechanical equivalent sensitivity: Map the angular tilt misalignment in each degree of misalignment to the equivalent physical line displacement of the optical element edge, and establish an evaluation system with unified dimensions; and divide the wavefront aberration change data by the corresponding translational misalignment or equivalent physical line displacement to obtain the mechanical equivalent sensitivity of each degree of misalignment. S3. Construct a cross-coupling evaluation model: Based on the mechanical equivalent sensitivity, quantify the degree of cross-coupling between multidimensional misalignment degrees of freedom and specific aberration indices, and identify the highly sensitive misalignment degrees of freedom of the system. S4. Output assembly and adjustment sequence planning: Based on the identified high-sensitivity misalignment degrees of freedom, the closed-loop iterative assembly and adjustment sequence is output according to the priority of compensating high-sensitivity degrees of freedom first and then low-sensitivity degrees of freedom.

2. The method according to claim 1, characterized in that, In step S1, a pose matrix that satisfies a random distribution is generated within the preset tolerance range through joint simulation using optical design software and numerical calculation software. The corresponding wavefront coefficients and / or Zernike polynomial coefficients are extracted in batches to construct a model training dataset.

3. The method according to claim 1, characterized in that, In step S2, the calculation method for mapping the angular tilt misalignment to the equivalent physical line displacement includes: obtaining the angular tilt rotation axis of the optical element and determining its effective light-transmitting edge position; based on the structural dimensions and spatial geometric relationships of the optical element, calculating the maximum actual physical line displacement generated at its effective light-transmitting edge under a given angular tilt misalignment; defining the maximum actual physical line displacement as the equivalent physical line displacement to achieve dimensional unification between the tilt misalignment and the translation misalignment.

4. The method according to claim 1 or 3, characterized in that, S3 further includes: generating single-degree-of-freedom scanning data based on the mechanical equivalent sensitivity, establishing a reference circle in polar coordinates, using the wavefront aberration change value after normalization of the stroke as the outward expansion vector, and drawing a continuous envelope radar map; identifying highly sensitive misalignment degrees of freedom by comparing the area of ​​the envelope line corresponding to each misalignment degree of freedom deviating from the reference circle, and judging the linearity of the misalignment response by the symmetry of the envelope line.

5. The method according to claim 1, characterized in that, S3 further includes: calculating the mechanical equivalent sensitivity of each misalignment degree of freedom to aberrations of different orders, constructing a misalignment-aberration cross-coupling sensitivity matrix, and mapping it to a high-contrast heatmap; based on the color block features in the heatmap, locking the main influencing misalignment degree of freedom of a specific aberration, and achieving targeted quantitative decoupling.

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