A method and device for aspheric wavefront recovery based on TIE

Abstract

This invention discloses a wavefront reconstruction method and apparatus for aspherical surfaces based on TIE (Transient Image Estimation), relating to the fields of optical measurement and wavefront reconstruction technology. It addresses the shortcomings of existing aspherical detection technologies, such as system complexity, low efficiency, and difficulty in simultaneously meeting the core requirements of high precision, high fidelity, and engineering adaptability for aspherical detection. The method includes: obtaining the shear overlap region and its wavefront gradient based on the small shear assumption and shear amount; obtaining the full-aperture reconstructed gradient field based on the minimum distance from pixels in the non-overlapping region to the boundary of the shear overlap region, the preliminary full-aperture gradient distribution, and the smoothed gradient data of the overlapping region; obtaining the full-aperture wavefront phase distribution based on the wavefront phase estimation of the nth iteration, the optimized full-aperture intensity axial derivative, the Poisson equation, and the adaptive step size; converting the full-aperture wavefront phase distribution into optical surface shape deviation to obtain the wavefront reconstruction result of the aspherical surface under test.

Description

Technical Field

[0001] This invention relates to the field of optical measurement and wavefront recovery technology, and more specifically to a method and apparatus for aspherical wavefront recovery based on TIE. Background Technology

[0002] As a core component of modern high-end optical systems, the surface accuracy of aspherical optical elements directly determines the performance limits of the system. With the increasing demands of optical technology applications in various fields, the industry has set higher standards for aspherical inspection technology, requiring not only nanometer-level high precision but also high efficiency, low cost, and good engineering adaptability to suit practical application scenarios such as rapid inspection and online inspection.

[0003] Currently, high-precision detection technologies for aspherical surfaces are mainly divided into two categories: interferometry and non-interferometry. In interferometry, while zero-position interferometry and sub-aperture stitching techniques can achieve nanometer-level precision, the system structure is complex, calibration is difficult, and environmental stability requirements are extremely high, making it difficult to meet the needs of rapid, online detection. Sub-aperture stitching technology also suffers from cumbersome measurement processes and difficulty in controlling stitching errors. In non-interferometry, point scanning detection is inefficient and carries the risk of damaging the component surface, while digital holography is extremely sensitive to environmental vibrations, making its engineering application difficult.

[0004] In addition, the Transport of Intensity Equation (TIE), as a phase retrieval method based on the physical laws of light intensity propagation, has advantages such as simple optical path, no need for a reference surface, and low requirements for environmental vibration and light source coherence. It has great potential in low-cost, engineering-oriented detection. However, when applied to aspherical surface detection, because the light intensity of aspherical surfaces changes only slightly along the axial direction, the axial derivative of the light intensity calculated by discrete pixel difference is easily affected by noise, quantization errors, and other disturbances, leading to a significant decrease in wavefront reconstruction accuracy or even failure. Although traditional shearing interferometry can provide high-precision wavefront gradient information, it is usually based on Zernike polynomial fitting to reconstruct the wavefront phase distribution. This method is essentially a global fitting process based on a low-order aberration model, which smooths out local distortions and high-frequency details in the wavefront, causing wavefront reconstruction distortion and failing to meet the detail fidelity requirements of high-precision detection.

[0005] In summary, existing aspherical surface inspection technologies either suffer from bottlenecks in engineering applications such as system complexity, poor environmental adaptability, and low efficiency, or have inherent defects in terms of accuracy or detail fidelity, making it difficult to simultaneously meet the core requirements of aspherical surface inspection for high precision, high fidelity, and engineering adaptability. Summary of the Invention

[0006] This invention provides a TIE-based method and apparatus for aspherical wavefront recovery, which addresses the shortcomings of existing aspherical detection technologies, such as system complexity, low efficiency, and difficulty in simultaneously meeting the core requirements of aspherical detection for high precision, high fidelity, and engineering adaptability.

[0007] This invention provides a TIE-based aspherical wavefront recovery method, comprising:

[0008] Based on the intensity transmission equation (TIE) detection system including the shearer, four phase-shifted shear interferograms and continuously distributed shear phase differences are acquired. According to the small shear amount assumption and shear amount, the shear overlap region and the wavefront gradient of the shear overlap region are obtained. Based on the continuous smoothness of the aspherical wavefront, the edge gradient of the shear overlap region is used as the boundary, and the gradient is filled by local trend extrapolation to obtain the preliminary gradient distribution of the full aperture. Based on the minimum distance from the pixels included in the non-overlapping region to the boundary of the shear overlap region, the preliminary gradient distribution of the full aperture, and the smooth gradient data of the overlapping region, the full aperture reconstructed gradient field is obtained.

[0009] Based on the reconstructed gradient field, full-aperture wavefront curvature, and TIE, the optimized full-aperture intensity axial guide is obtained. The TIE is transformed into a Poisson equation, and the wavefront phase estimate for the nth iteration is obtained through a fast Fourier transform. Based on the wavefront phase estimate for the nth iteration, the optimized full-aperture intensity axial guide, the Poisson equation, and the adaptive step size, the phase correction for the nth iteration and the wavefront phase estimate for the (n+1)th iteration are obtained. When the iteration conditions are obtained, the wavefront phase estimate for the (n+1)th iteration is determined as the full-aperture wavefront phase distribution.

[0010] The full-aperture wavefront phase distribution is converted into an optical wavefront distribution to obtain the wavefront reconstruction result of the aspherical surface under test.

[0011] This invention provides a TIE-based aspherical wavefront recovery device, comprising:

[0012] The first obtaining unit is used to acquire four phase-shifted shear interferograms and a continuously distributed shear phase difference based on the intensity transmission equation (TIE) detection system including the shearer. Based on the small shear assumption and the shear amount, it obtains the shear overlap region and the wavefront gradient of the shear overlap region. Based on the continuous smoothness of the aspherical wavefront, using the edge gradient of the shear overlap region as the boundary, it fills the gap through local trend extrapolation to obtain the preliminary gradient distribution of the full aperture. Based on the minimum distance from the pixels included in the non-overlapping region to the boundary of the shear overlap region, the preliminary gradient distribution of the full aperture, and the smooth gradient data of the overlapping region, it obtains the reconstructed gradient field of the full aperture.

[0013] The determining unit is used to obtain the optimized full-aperture intensity axial guide number based on the reconstructed full-aperture gradient field, full-aperture wavefront curvature, and TIE; to convert the TIE into a Poisson equation, and to obtain the wavefront phase estimate of the nth iteration through a fast Fourier transform; based on the wavefront phase estimate of the nth iteration, the optimized full-aperture intensity axial guide number, the Poisson equation, and the adaptive step size, to obtain the phase correction amount of the nth iteration and the wavefront phase estimate of the (n+1)th iteration; when the iteration conditions are obtained, the wavefront phase estimate of the (n+1)th iteration is determined as the full-aperture wavefront phase distribution;

[0014] The second obtaining unit is used to convert the full aperture wavefront phase distribution into an optical wavefront distribution to obtain the wavefront reconstruction result of the aspherical surface under test.

[0015] This invention provides a computer device including a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs any of the above-described aspherical wavefront recovery methods based on TIE.

[0016] This invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform any of the above-described aspherical wavefront recovery methods based on TIE.

[0017] This invention provides a method and apparatus for aspherical wavefront reconstruction based on TIE. The method extracts noise-insensitive wavefront gradients through a four-step phase-shift shearing interferometry and employs a direct reconstruction method independent of fitting, avoiding the high-frequency information smoothing loss problem caused by traditional Zernike polynomial fitting. This achieves high-fidelity reconstruction of aspherical wavefronts (including high-frequency details). Furthermore, based on the small shearing assumption, a first-order difference approximation is used to calculate the gradient, combined with an edge extension method constrained by the Poisson equation, effectively suppressing gradient extrapolation errors in non-interference regions, thus improving computational efficiency while enhancing overall performance. The invention improves the reconstruction accuracy of the full aperture gradient field. It only requires simultaneous acquisition of four-step phase-shift shearing interferograms, eliminating the need for forward and backward detector movement. This completely eliminates acquisition errors caused by stage accuracy, assembly and adjustment errors, and environmental vibrations, significantly enhancing system stability and ease of operation. While retaining the simplicity of the original TIE optical path, the system only adds a shearing module, resulting in low cost, easy integration, and suitability for engineering applications. The improved maximum assumption method combined with an adaptive step-size mechanism enhances the fitting ability and convergence efficiency for complex curvature wavefronts of aspherical surfaces, while maintaining the inherent advantages of TIE in high-frequency information recovery. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1A This is a schematic diagram of a TIE-based aspherical wavefront recovery method provided in an embodiment of the present invention;

[0020] Figure 1B A schematic diagram of a TIE detection system including a shearer provided in an embodiment of the present invention;

[0021] Figure 2A This is a schematic diagram of a four-axis phase-shift shearing interference in the x-direction provided in an embodiment of the present invention;

[0022] Figure 2B This is a schematic diagram of a 4-axis phase-shift shearing interference in the y-direction provided in an embodiment of the present invention;

[0023] Figure 3A The embodiments of the present invention provide and Figure 2A A schematic diagram of the unwrapping phase in the corresponding x-direction;

[0024] Figure 3B The embodiments of the present invention provide and Figure 2B A schematic diagram of the unwrapping phase in the corresponding y-direction;

[0025] Figure 4A The embodiments of the present invention provide and Figure 3A A schematic diagram of the phase gradient in the x-direction;

[0026] Figure 4B The embodiments of the present invention provide and Figure 3B A schematic diagram of the phase gradient in the y-direction;

[0027] Figure 5 This is a schematic diagram of the axial derivative obtained based on the method provided in the embodiments of the present invention;

[0028] Figure 6A This is a schematic diagram of the wavefront to be tested provided in an embodiment of the present invention;

[0029] Figure 6B This is a schematic diagram of wavefront reconstruction obtained based on the method provided in the embodiments of the present invention;

[0030] Figure 6C Provided for embodiments of the present invention Figure 6A The wavefront diagram to be measured shown is... Figure 6B The diagram shows the residual of the reconstructed wavefront;

[0031] Figure 7 This is a schematic diagram of an aspherical wavefront recovery device based on TIE provided in an embodiment of the present invention. Detailed Implementation

[0032] 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 embodiments of the present invention, and not all embodiments. 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.

[0033] Figure 1A This is a schematic diagram of a TIE-based aspherical wavefront recovery method provided in an embodiment of the present invention; Figure 1B The diagram below illustrates the structure of a TIE detection system including a shearer, as provided in an embodiment of the present invention. The following, using Figures 1 and 2 as examples, details a TIE-based aspherical wavefront recovery method provided in this embodiment. As shown in Figure 1, the method includes the following steps:

[0034] Step 101: Based on the TIE detection system including the shearer, four phase-shifted shear interferograms and continuously distributed shear phase differences are acquired. According to the small shear amount assumption and the shear amount, the shear overlap region and the wavefront gradient of the shear overlap region are obtained. Based on the continuous smoothness of the aspherical wavefront, the edge gradient of the shear overlap region is used as the boundary, and the gradient is filled by extrapolation of local trends to obtain the preliminary gradient distribution of the full aperture. Based on the minimum distance from the pixels included in the non-overlapping region to the boundary of the shear overlap region, the preliminary gradient distribution of the full aperture, and the smooth gradient data of the overlapping region, the full aperture reconstructed gradient field is obtained.

[0035] Step 102: Based on the reconstructed full-aperture gradient field, full-aperture wavefront curvature, and TIE, obtain the optimized full-aperture intensity axial derivative; convert the TIE into a Poisson equation, and obtain the wavefront phase estimate for the nth iteration through a fast Fourier transform; based on the wavefront phase estimate for the nth iteration, the optimized full-aperture intensity axial derivative, the Poisson equation, and the adaptive step size, obtain the phase correction for the nth iteration and the wavefront phase estimate for the (n+1)th iteration; when the iteration conditions are obtained, determine the wavefront phase estimate for the (n+1)th iteration as the full-aperture wavefront phase distribution;

[0036] In step 103, the full aperture wavefront phase distribution is converted into an optical wavefront distribution to obtain the wavefront reconstruction result of the aspherical surface under test.

[0037] Before introducing the aspherical wavefront recovery method based on TIE provided in the embodiments of the present invention, we will first introduce the system for acquiring the phase-shift shearing interferogram in the present invention, such as... Figure 1B As shown, the TIE detection system mainly includes: a light source and collimation module, a module for acquiring the aspherical surface under test and the wavefront, a polarization control optical path module, and a detection module.

[0038] Specifically, the light source and collimation module mainly includes a light source unit, collimation, and calibration. The light source unit uses a He-Ne linearly polarized laser 1 as the light source. The output linearly polarized light passes through an attenuator 2, a quarter-wave plate 3, and a microscope objective 4 before being focused onto a pinhole filter 5. The pinhole filter is used to filter out high-frequency stray light and improve the spatial coherence of the beam. Further, the beam filtered by the pinhole filter is reflected by a beam splitter prism 6 and enters the collimation objective system 7, where it is collimated into parallel light. A partial compensation mirror 8 is used to pre-compensate for the system's own wavefront error, ensuring that the wavefront of the beam incident on the surface under test is as close as possible to an ideal plane wave.

[0039] Furthermore, the aspherical surface 9 under test in the wavefront acquisition module reflects the incident parallel light. The reflected light, carrying information about the surface morphology or wavefront distortion, is collected by the collimating objective 7 and then re-enters the beam splitter 6. At this time, the beam splitter guides part of the transmitted light to the plane mirror 10, which then enters the shearing interference detection branch.

[0040] Furthermore, the polarization-controlled optical path module includes a parallel polarization beam splitter 11. When reflected light carrying surface topography or wavefront distortion information is incident, light with different polarization directions (such as s-polarization and p-polarization) will generate a small lateral displacement (shearing amount s), thereby forming two misaligned wavefronts and interfering with each other. Furthermore, the parallel polarization beam splitter also integrates polarization control elements such as a polarizer and a quarter-wave plate. By synchronously adjusting the polarization state (such as 0°, 45°, 90°, 135°), multiple shearing interferograms with different phases are obtained, thereby eliminating background noise and phase blurring in the interferograms and improving wavefront reconstruction accuracy.

[0041] It should be noted that in this system, the core of the shearer is to utilize the polarization-dependent deflection characteristics of the parallel polarization beam splitter, and through the control of polarized light, allow the same set of optical elements to simultaneously achieve wavefront shearing and phase shifting functions.

[0042] Furthermore, the imaging objective 12 in the detection module focuses the shearing interference fringes onto the separate focal plane polarization detection system 12, which can simultaneously acquire interference images of different polarization states and combine them with multiple interference patterns obtained by synchronous phase shifting (such as four synchronous phase shift shearing interference patterns).

[0043] In step 101, a light intensity distribution map is acquired at the focal plane based on a traditional TIE detection system. The intensity distribution of the wavefront to be measured is shown as the intensity distribution of the light on the focusing surface. Then, keeping the optical path and detector positions unchanged, the shearer is placed into the optical path, i.e., the TIE detection system including the shearer provided in Figure 2 of this embodiment. Four phase-shifted shearing interferograms of the wavefront are simultaneously acquired using a polarization camera, with the phase shifts being sequentially... , , , , respectively denoted as , , , (x-direction shearing) and , , , (Y-direction shearing), as follows: Figure 2A , 2B As shown, all acquired images have undergone preprocessing such as registration and normalization to ensure data consistency and the reliability of subsequent processing.

[0044] In this embodiment of the invention, for transverse shear interference, let the original wavefront be... After introducing a shear quantity s in the x-direction, a shear wavefront is formed as follows: The corresponding interference intensity distribution can be expressed by the following formula:

[0045]

[0046] (1-1)

[0047] After introducing a shear amount s in the y-direction, a shear wavefront is formed as follows: The corresponding interference intensity distribution can be expressed by the following formula:

[0048]

[0049] (1-2)

[0050] in, , These represent the shear phase difference in the x and y directions, respectively. Indicates the phase shift. Indicates the amount of shear.

[0051] Furthermore, using the standard four-step phase shift formula, the shear phase difference in the x and y directions can be demodulated from the interferogram:

[0052] (2-1) (2-2)

[0053] In practical applications, the phase difference in the demodulated x and y directions is sheared. , By performing phase unwrapping, the continuous sheared phase difference in the x and y directions can be obtained. and , respectively Figure 3A , 3B As shown.

[0054] In this embodiment of the invention, based on the small shearing assumption, the continuous shearing phase difference in the x and y directions is transformed into a wavefront gradient through a first-order difference approximation, as shown below:

[0055] (3-1)

[0056] (3-2)

[0057] in, Indicates the shear overlap region The wavefront gradient of the direction, Indicates the shear overlap region The wavefront gradient of the direction, This indicates the continuous shearing phase difference in the x-direction after unwrapping. This represents the continuous shear phase difference in the y-direction after unwrapping.

[0058] To reconstruct the gradient field within the complete aperture and suppress the influence of non-interference regions at the edges, this embodiment of the invention introduces a periodic extension and weighted fusion method.

[0059] Specifically, periodic extension utilizes the continuous smoothness of aspherical wavefronts to fill gradient gaps in non-overlapping regions, obtaining a preliminary full-aperture gradient. Due to the small shearing amount and short extension distance, the error introduced by periodic extension is very limited and its impact on the final wavefront reconstruction result is negligible. It employs local linear trend extrapolation, using the gradient at the edge of the overlapping region as the boundary, fitting a linear equation to extrapolate the gradient in the non-overlapping region, thus obtaining a preliminary full-aperture gradient distribution. Since transverse shearing interferometry can only acquire gradient information in the sheared overlapping region, gradient gaps exist in the non-overlapping region. By using the continuous smoothness of the aspherical wavefront to extrapolate and fill these gaps, full-aperture gradient coverage is achieved for the first time. This avoids the loss of high-frequency details in traditional shearing interferometry low-pass filtering, preserving detailed information in high-gradient regions such as the aspherical edge.

[0060] Furthermore, to reduce edge errors, weights that decay with the distance to the aperture edge are constructed to provide a weighting basis for subsequent gradient fusion. The weight values ​​range from [0,1], with a value of 1 in the overlapping region and decreasing with distance in the non-interference region. The exponential weighting function is shown below:

[0061] (4)

[0062] in, This represents the weight distribution across the entire pore size. Indicates the overlapping region of the cut. This represents the minimum distance between the pixels included in the non-overlapping region and the boundary of the clipping overlapping region. This represents the smoothing coefficient.

[0063] It should be noted that, in this embodiment of the invention, Gaussian filtering is performed on the wavefront gradient in the shear overlap region to obtain smooth gradient data of the shear overlap region, which can effectively suppress environmental noise in the phase-shift interferogram.

[0064] By fusing the extended gradient and the smoothed gradient, edge errors are suppressed and high-frequency details are preserved. The full-aperture reconstructed gradient field can be obtained by weighted fusion, as expressed by the following formula:

[0065] (5)

[0066] in, This represents the full aperture reconstruction gradient field. This represents the initial gradient distribution across the entire pore size. This represents the smoothed gradient data of the sheared overlapping region. This method effectively reduces the continuation error in the non-interfering region while preserving high-precision gradient information in the overlapping region, achieving robust reconstruction of the full aperture gradient field. The reconstructed full aperture gradient fields are shown below. Figure 4A , 4B As shown.

[0067] In the above method, Gaussian filtering of the wavefront gradient in the shearing overlap region can effectively suppress environmental noise in the phase-shifted interferogram. By fusing the extrapolated gradient and the smoothed gradient with exponential weights, the weight of the non-overlapping region decreases with distance from the boundary, avoiding the extrapolation error from spreading to the overlapping region and improving the signal-to-noise ratio of the reconstructed full-aperture gradient field.

[0068] For example, suppose the diameter of the aspherical surface to be measured is... (circular aperture) (Pixel array 800×800, pixel size 10μm); shear lateral shearing amount Pixel (corresponding to physical clipping amount) (Satisfying small shearing amounts); Polarization camera: acquires 4 phase-shifted shearing interferograms each in the x and y directions, with phase shifts of 0°, 90°, 180°, and 270° respectively, denoted as... (x direction) (y-direction); Light intensity distribution on the focal plane (800×800 pixel matrix, registration and normalization preprocessing completed, light intensity range [0,1]).

[0069] Step 201: To introduce the four-step phase-shifting interferometric phase difference demodulation, four phase-shifting shearing interferograms are used to obtain a continuously distributed shearing phase difference through the four-step phase-shifting formula; according to formula (2-1), the demodulated shearing phase difference in the x-direction is... .

[0070] In the example, a typical pixel is selected: pixel coordinates are selected. (Aperture center) (Within the overlapping area of ​​the aperture edge), the light intensity values ​​(normalized) of the four interferograms are shown in the table below:

[0071] Pixel coordinates 0.85 0.5 0.15 0.50 0.70 0.30 0.30 0.70

[0072] Substitute the above data into formula (2-1) to calculate:

[0073] For the aperture center coordinate point (400, 400): molecule: ; Denominator: ; .

[0074] For the coordinates (100, 100) within the overlapping region of the aperture edge: numerator: ; Denominator: =0.70−0.30=0.40; .

[0075] Similarly, for the four interferograms in the y-direction Performing the same calculation yields... .

[0076] Step 202: Demodulated , The value range is [−π,π] (wrapped phase), and the continuous phase difference distribution needs to be obtained by unwrapping.

[0077] In this example, the "path tracing method" is used to unwrap the image: the unwrap reasoning logic is that the aspherical wavefront is continuous and smooth, and the phase difference change between adjacent pixels should be less than π (satisfying the "continuity assumption"); starting from the aperture center (400,400), the image is traversed pixel by pixel along the horizontal and vertical directions. If the phase difference between adjacent pixels jumps by more than π, then 2π (or 2π minus) is added as a correction to ensure phase continuity.

[0078] Example of unpacking result: For After unwrapping, the aperture center (400, 400) remains at 0 rad, the edge pixel (100, 100) remains at π / 4 rad, and the phase difference between adjacent pixels is less than 0.1 rad (continuous distribution).

[0079] for After unwrapping, the aperture center (400, 400) has a value of 0.2 rad, and the edge pixel (100, 100) has a value of 0.3 rad, with no phase jump.

[0080] Step 203: Calculation of wavefront gradient under small shear:

[0081] According to formulas (3-1) and (3-2), the shear amount Pixels (small cropping amount, meeting the accuracy requirements of first-order difference approximation).

[0082] Example of wavefront gradient calculation: For the aperture center point pixel (400, 400): , For the pixel with coordinates (100, 100) within the overlapping area of ​​the aperture edge: , .

[0083] In the example, the shear overlap region is defined as the original wavefront during shearing in the x-direction. With shear wavefront Overlapping areas for: , (The first 8 columns of pixels are removed horizontally, totaling 792×800 pixels); when cropping in the y-direction, the overlapping area... for: , (The first 8 rows of pixels were removed vertically, resulting in a total of 800×792 pixels).

[0084] Final effective overlapping area : , (In an 800×800 pixel array, the 8-pixel ring area at the edge is removed, and the core overlapping area is 784×784 pixels).

[0085] Only It contains valid gradient values, and the non-overlapping regions (x<8 or x>792, y<8 or y>792) are blank (no gradient data).

[0086] Step 204: Based on the "continuous smoothness and gradual curvature" characteristics of aspherical wavefronts, "local gradient trend extension" is adopted: for pixels in non-overlapping regions... Calculate its nearest distance to the boundary of the overlapping region. And direction; along this direction, select the gradient values ​​of 5 consecutive pixels from the boundary of the overlapping region inward, and fit a linear trend ( Based on this trend, extrapolate the gradient values ​​of non-overlapping regions; extension priority: first extend the blank in the x direction (x<8 or x>792), then extend the blank in the y direction (y<8 or y>792).

[0087] Specific example of extension calculation (taking the non-overlapping region on the left boundary in the x-direction as an example):

[0088] Non-overlapping region on the left boundary in the x-direction: , (Total 8×784 pixels), needs to be extended based on the gradient value of the left boundary (x=8) of the overlapping region.

[0089] Select y=400 (horizontal midline), and the gradient value at x=8 on the left boundary of the overlapping region: , .

[0090] Select 5 pixel gradient values ​​from x=8 to 12 inwards and fit the gradient trend in the x-direction:

[0091] x (pixels) 8 9 10 11 12 0.01 0.012 0.014 0.016 0.018

[0092] Fitting linear equations: ( =1.0, completely linear), extended to x=0~7 Value: x=7 =0.002×7−0.006=0.008rad / pixel; x=6: =0.002×6−0.006=0.006rad / pixel; ...; x=0: =0.002×0−0.006=−0.006rad / pixel.

[0093] Gradient extension in the y-direction ( ): The left boundary of the overlapping region is at x=8, y=400. x=9~12 All values ​​are 0.02 rad / pixel (the gradient in the y-direction remains unchanged in this column), therefore, the extension to x=0~7 and y=400... .

[0094] Through the above extension, the blank gradient values ​​in the non-overlapping areas were filled, resulting in a preliminary gradient distribution of the full aperture of 800×800 pixels. Its characteristics are as follows:

[0095] Overlapping area ( ): Retains the high-precision gradient of the original calculation without distortion; Non-overlapping region (x<8 or x>792, y<8 or y>792): The gradient value transitions smoothly along the boundary of the overlapping region without abrupt changes; Overall distribution: The gradient in the x-direction gradually increases from -0.006 rad / pixel at the left boundary (x=0) to 0.03 rad / pixel at the right boundary (x=799), and the gradient in the y-direction is generally stable at 0.02~0.04 rad / pixel, which conforms to the gradient distribution law of "small curvature at the center and large curvature at the edge" of the aspherical wavefront.

[0096] In this embodiment of the invention, the high-precision wavefront gradient information within the complete circular aperture obtained in step 101 can be used to optimize the calculation of the key parameter in the TIE—the intensity axial derivative. Since the traditional TIE method directly calculates the derivative using the finite difference method, it is susceptible to noise interference. Therefore, in this embodiment of the invention, reconstruction of the physical equation can significantly improve the calculation accuracy and noise resistance.

[0097] In step 102, the optimized full-aperture light intensity axial guide number is obtained based on the full-aperture reconstructed gradient field, full-aperture wavefront curvature, and TIE.

[0098] Specifically, based on the reconstructed full-aperture gradient field, the wavefront curvature is calculated by directly taking the partial derivatives of the gradient components:

[0099] (6-1)

[0100] (6-2)

[0101] Right now:

[0102] (6-3)

[0103] Under the paraxial approximation, TIE can be expressed as:

[0104] (6-4)

[0105] Expanding the divergence operator yields:

[0106] (6-5)

[0107] The calculated , and Substituting into the TIE expansion formula, we can deduce the optimized full-aperture light intensity axial guide number:

[0108] (6-3)

[0109] in, Indicates the full aperture wavefront curvature. This represents the second-order partial derivative of the wavefront gradient in the x-direction. Let represent the second partial derivative of the wavefront gradient in the y-direction. Indicates wave number, Indicates the light intensity distribution on the focal plane. This represents the optimized full-aperture light intensity axial guide number. This represents the light intensity gradient at the focal plane. This represents the wavefront gradient field.

[0110] Traditional TIE (Transient Intensity Estimation) calculates the full-aperture axial guide number using finite difference multi-plane intensity calculations, which is susceptible to noise interference leading to wavefront reconstruction failure. The optimized TIE, however, uses the full-aperture gradient field and wavefront curvature to inversely derive the full-aperture axial guide number, directly relating it to wavefront physical properties. This reduces the calculation error of the axial guide number and makes it suitable for detection scenarios where the axial intensity variation on aspherical surfaces is minimal. The optimized full-aperture axial guide number is shown below. Figure 5 As shown.

[0111] For example, three typical pixels are selected, and calculations are performed based on preceding parameters (using uniform physical units):

[0112] 1. Pixel (400, 400) (Extreme Light Intensity Point): Known , , , .

[0113] calculate: , (The negative sign indicates that the light intensity decreases along the positive z-axis).

[0114] 2. Pixel (100, 100) (edge ​​of overlapping region): Known , , , .

[0115] calculate: , , .

[0116] 3. Pixel (0, 400) (edge ​​of non-overlapping region): Known , , , .

[0117] Calculate: Dot product term = 0.1 × 0.48 = 0.048, right-hand side term = 0.20 × 3 + 0.048 = 0.648. .

[0118] The axial guide of the light intensity of the three pixels is continuously distributed without abrupt changes, which conforms to the physical laws of light intensity transmission.

[0119] In this embodiment of the invention, by utilizing the optimized intensity axial derivative with strong noise resistance, combined with the improved maximum assumption method and its adaptive step-size iteration mechanism, the TIE can be solved with high precision and stability, and the aspherical wavefront phase can be reconstructed.

[0120] The TIE is transformed into a Poisson equation. Through a Fast Fourier Transform, the wavefront phase estimate for the nth iteration is obtained. Based on the wavefront phase estimate for the nth iteration, the optimized full-aperture intensity axial guide, the Poisson equation, and the adaptive step size, the phase correction for the nth iteration and the wavefront phase estimate for the (n+1)th iteration are obtained. It should be noted that n here is a positive integer greater than zero.

[0121] Given the light intensity of the focal plane and the optimized full aperture light intensity axial guide number The TIE problem can then be expressed as an elliptic partial differential equation as shown below:

[0122] (7-1)

[0123] In this embodiment of the invention, during each iteration, based on the maximum intensity assumption, the TIE expressed as an elliptic partial differential equation is converted into a Poisson equation, specifically:

[0124] (7-2)

[0125] in, Denotes the divergence operator, Indicates the light intensity distribution on the focal plane. Represents the wavefront gradient field. This represents the phase distribution of the aspherical wavefront. Indicates wave number, This represents the optimized full-aperture light intensity axial guide number. This represents the wavefront phase estimate in the nth iteration. Indicates the first The residual derivative value of the next iteration. This indicates the maximum light intensity.

[0126] The above method uses the maximum intensity assumption to transform the TIE into a Poisson equation, which is solved by fast Fourier transform. The single iteration speed is twice as fast as the traditional multigrid method.

[0127] Furthermore, a Fast Fourier Transform is performed on the source term of the nth iteration to obtain the wavefront phase estimate of the nth iteration. .

[0128] Obtain the wavefront phase estimate of the nth iteration Substituting back into TIE yields the theoretical derivative residual for the nth iteration, as shown below:

[0129] (7-3)

[0130] Furthermore, by using the theoretical derivative residual from the nth iteration as a new source term to solve the Poisson equation again, we can obtain the phase correction for the nth iteration as shown below. :

[0131] (7-4)

[0132] During the iteration process, the wavefront error is continuously compensated by the phase correction amount. Even if the aspheric surface under test has a large curvature (such as a high-order aspheric surface), it can approximate the true wavefront through multiple iterations, thus solving the limitation that traditional TIE is only applicable to weakly distorted wavefronts.

[0133] In this embodiment of the invention, based on the phase correction amount and adaptive step size of the nth iteration, the wavefront phase estimate of the (n+1)th iteration can be obtained as follows:

[0134] (7-5)

[0135] in, This represents the theoretical derivative residual of the nth iteration. Denotes the divergence operator, Indicates the light intensity distribution on the focal plane. This represents the wavefront gradient field in the nth iteration. This represents the wavefront phase estimate in the nth iteration. This represents the optimized full-aperture light intensity axial guide number. Represents the Laplace operator. Indicates the maximum light intensity. This represents the phase correction amount in the nth iteration. This represents the wavefront phase estimate in the (n+1)th iteration. This represents the adaptive step size for the nth iteration.

[0136] In this embodiment of the invention, the adaptive step size is dynamically adjusted using the Armijo criterion to avoid iterative divergence. When the convergence condition is met, the relative error of the wavefront phase estimation is ≤ Far superior to traditional TIE Magnitude.

[0137] This ensures stable convergence of the iteration. The criterion requires the updated objective function value... Satisfy the following formula:

[0138] (7-6)

[0139] in, Represents small positive numbers (usually taken as...) ), Indicates the first The adaptive step size of the next iteration Indicates the first The phase correction amount for the next iteration. In practical applications, if the updated objective function value does not meet the requirements, then a decay factor is used. Reduce step size: Until the conditions are met.

[0140] In this embodiment of the invention, the objective is solved iteratively by continuously refining the wavefront phase estimate through adaptive step-size iterations until the iteration conditions are met. The convergence conditions for the wavefront phase estimation iteration include any one of the following: the norm of the wavefront phase estimate in the (n+1)th iteration is below a threshold; the maximum number of iterations is reached; or the rate of decrease of the objective function value approaches zero.

[0141] When the iteration condition is met, the wavefront phase estimate of the (n+1)th iteration is output, which is close enough to the true wavefront phase of the aspherical surface under test, and therefore can be determined as the full aperture wavefront phase distribution.

[0142] For example, if the initial phase in the initial conditions (Full aperture), initial step size The optimized full-aperture light intensity axial guide output from the above steps is used as the initial source term. Key iteration steps are recorded below:

[0143] 1. 0th iteration (n=0): Source term (400, 400)); FFT solution yields = , = residual Solve for the correction amount Verify that the Armijo criterion is satisfied and update the phase. .

[0144] 2. 10th iteration (n=10): Phase estimation , residual (Decrease by 90%); Step size adjusted to After the update .

[0145] 3. 35th iteration (convergence): Phase correction norm Final phase: (Benchmark) , Objective function (The value is much smaller than the initial value of 0.8), and the iteration terminates.

[0146] In step 103, the full aperture wavefront phase distribution is converted into an optical wavefront distribution, thus obtaining the wavefront reconstruction result of the aspherical surface under test.

[0147] Specifically, the full aperture wavefront phase distribution Directly corresponds to the phase distortion information of the optical wavefront, combined with the wavelength of the incident light wave Establish a quantitative relationship between phase distribution and optical wavefront physical quantities:

[0148] (8)

[0149] in, It represents the optical wavefront distribution of the aspherical surface under test, with the unit being length (such as nm or μm). Its physical meaning is the deviation of the actual wavefront from the ideal plane wave.

[0150] Substituting the full-aperture wavefront phase distribution into the above formula generates a two-dimensional pseudo-color image of the optical wavefront distribution. The spatial distribution characteristics of the wavefront deviation are visually displayed using color gradients. Key indicators such as peak-to-valley (PV) and root mean square (RMS) values ​​are extracted to evaluate the wavefront quality of the aspherical surface under test.

[0151] For example, the final phase distribution This refers to the recovered aspherical wavefront phase. The target wavefront is as follows: Figure 6A As shown, the wavefront peak-to-trough value is 11.5659λ, and the root mean square value is 3.3633λ. The wavefront recovered by the method provided in this embodiment of the invention is as follows: Figure 6B As shown, the peak-to-trough value of the recovered wavefront is 11.5608λ, and the root mean square value is 3.3631λ. Figure 6C The residual plot between the recovered wavefront and the target wavefront is provided by the method of this embodiment of the invention. The peak-to-valley value of the residual wavefront is 5.4948E-03λ, the relative error of the peak-to-valley value is 0.0475%, and the root mean square value is 6.9895E-04λ, the relative error of the root mean square value is 0.0208%.

[0152] In summary, this invention provides a TIE-based aspherical wavefront reconstruction method. This method achieves full aperture gradient field coverage through local trend extrapolation and weighted fusion, eliminating the blind zone of non-overlapping regions in shear interference. It combines wavefront gradient field back-calculation to optimize the intensity axial derivative, replacing the traditional, easily interfered multi-plane intensity difference method. Furthermore, it incorporates synchronous phase-shift anti-interference technology and an adaptive step-size iterative algorithm, ultimately achieving nanometer-scale wavefront reconstruction (residual ≤15nm). The phase estimation accuracy is on the order of magnitude, and the aberration analysis error is one order of magnitude better than similar technologies. The detection process does not require reference wavefront calibration and sub-aperture stitching, and the iteration time is shortened by solving the Poisson equation through fast Fourier transform. This solution is suitable for high curvature and large-diameter aspherical components and can still work stably in harsh environments such as workshop-level vibration and air turbulence, breaking through the limitation of traditional TIEs that are only applicable to weakly distorted wavefronts. The output surface deviation and Zernike aberration analysis results meet ISO standards and can be directly connected to existing optical assembly and adjustment software without secondary data conversion, which greatly reduces the threshold for engineering applications and maintenance costs. It solves the problems of existing aspherical detection technologies, such as system complexity, low efficiency, and difficulty in simultaneously meeting the core requirements of aspherical detection for high precision, high fidelity, and engineering adaptability.

[0153] Based on the same inventive concept, this invention provides a TIE-based aspherical wavefront recovery device. Since the principle of this device in solving the technical problem is similar to that of a TIE-based aspherical wavefront recovery method, the implementation of this device can refer to the implementation of the method, and the repeated parts will not be described again.

[0154] like Figure 7 As shown, the device includes a first obtaining unit 701, a determining unit 702, and a second obtaining unit 703.

[0155] The first obtaining unit 701 is used to acquire four phase-shifted shear interferograms and a continuously distributed shear phase difference based on the intensity transmission equation (TIE) detection system including the shearer. According to the small shear amount assumption and the shear amount, the shear overlap region and the wavefront gradient of the shear overlap region are obtained. Based on the continuous smoothness of the aspherical wavefront, the edge gradient of the shear overlap region is used as the boundary, and the gradient is filled by extrapolation of local trends to obtain the preliminary gradient distribution of the full aperture. Based on the minimum distance from the pixels included in the non-overlapping region to the boundary of the shear overlap region, the preliminary gradient distribution of the full aperture, and the smooth gradient data of the overlapping region, the full aperture reconstructed gradient field is obtained.

[0156] The determining unit 702 is used to obtain the optimized full-aperture intensity axial guide number based on the reconstructed full-aperture gradient field, full-aperture wavefront curvature, and TIE; to convert the TIE into a Poisson equation, and to obtain the wavefront phase estimate of the nth iteration through a fast Fourier transform; based on the wavefront phase estimate of the nth iteration, the optimized full-aperture intensity axial guide number, the Poisson equation, and the adaptive step size, to obtain the phase correction amount of the nth iteration and the wavefront phase estimate of the (n+1)th iteration; when the iteration conditions are obtained, the wavefront phase estimate of the (n+1)th iteration is determined as the full-aperture wavefront phase distribution;

[0157] The second obtaining unit 703 is used to convert the full aperture wavefront phase distribution into an optical wavefront distribution, that is, to obtain the wavefront reconstruction result of the aspherical surface under test.

[0158] It should be understood that the units included in the above-described TIE-based aspherical wavefront recovery device are merely a logical division based on the functions implemented by the device. In practical applications, the units can be superimposed or split. Furthermore, the functions implemented by the TIE-based aspherical wavefront recovery device provided in this embodiment correspond one-to-one with the TIE-based aspherical wavefront recovery method provided in the above-described embodiment. The more detailed processing flow implemented by this device has been described in detail in the first embodiment of the method described above, and will not be described in detail here.

[0159] Another embodiment of the present invention provides a computer device, the computer device including: a processor and a scene database; the scene database is used to store computer program code, the computer program code including computer instructions; when the processor executes the computer instructions, the electronic device performs various steps of the TIE-based aspherical wavefront recovery method shown in the above method embodiment.

[0160] Another embodiment of the present invention provides a computer-readable storage medium storing computer instructions that, when executed on a computer device, cause the computer device to perform the various steps of the TIE-based aspherical wavefront recovery method shown in the above method embodiment.

[0161] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A TIE-based aspheric wavefront recovery method, characterized in that, include: Based on the intensity transmission equation (TIE) detection system including the shearer, four phase-shifted shear interferograms and continuously distributed shear phase differences are acquired. According to the small shear amount assumption and shear amount, the shear overlap region and the wavefront gradient of the shear overlap region are obtained. Based on the continuous smoothness of the aspherical wavefront, the edge gradient of the shear overlap region is used as the boundary, and the gradient is filled by local trend extrapolation to obtain the preliminary gradient distribution of the full aperture. Based on the minimum distance from the pixels included in the non-overlapping region to the boundary of the shear overlap region, the preliminary gradient distribution of the full aperture, and the smooth gradient data of the overlapping region, the full aperture reconstructed gradient field is obtained. Based on the reconstructed full-aperture gradient field, full-aperture wavefront curvature, and TIE, the optimized full-aperture intensity axial guide is obtained. The TIE is transformed into a Poisson equation, and the wavefront phase estimate for the nth iteration is obtained through a fast Fourier transform. Based on the wavefront phase estimate for the nth iteration, the optimized full-aperture intensity axial guide, the Poisson equation, and the adaptive step size, the phase correction for the nth iteration and the wavefront phase estimate for the (n+1)th iteration are obtained. When the iteration condition is met, the wavefront phase estimate for the (n+1)th iteration is determined as the full-aperture wavefront phase distribution. The full-aperture wavefront phase distribution is converted into an optical wavefront distribution to obtain the wavefront reconstruction result of the aspherical surface under test.

2. The method of claim 1, wherein, Based on the continuous smoothness of the aspherical wavefront, and using the edge gradient of the shear overlap region as the boundary, the preliminary gradient distribution of the entire aperture is obtained by extrapolating and filling through local trends. Specifically, this includes: Based on the range of the cut-overlapping region, determine the non-overlapping blank regions that need to be extended in four directions; based on each non-overlapping blank region, take the gradient of a first set number of consecutive pixels adjacent to the non-overlapping blank region as the fitting benchmark, and obtain the linear relationship between gradient value and pixel coordinates based on the least squares method. The preliminary gradient distribution of the full aperture is obtained based on the pixel coordinates of the non-overlapping blank areas and the linear relationship.

3. The method of claim 1, wherein, The process of obtaining the full-aperture reconstructed gradient field based on the minimum distance from the pixels in the non-overlapping region to the boundary of the clipping overlapping region, the preliminary gradient distribution of the full aperture, and the smoothed gradient data of the overlapping region specifically includes: Based on the shearing overlap region and the preliminary gradient distribution of the full aperture, each pixel is determined to be either a pixel included in the shearing overlap region or a pixel included in the non-overlapping region. Determine the minimum distance between the pixels included in the non-overlapping region and the boundary of the clipping overlapping region, as well as the full aperture weight distribution; The full aperture reconstructed gradient field is obtained based on the full aperture weight distribution, the full aperture preliminary gradient distribution, and the smoothed gradient data of the overlapping region.

4. The method as described in claim 3, characterized in that, The full aperture weight distribution is expressed by the following formula: The full-aperture reconstructed gradient field is expressed by the following formula: in, This represents the weight distribution across the entire pore size. Indicates the overlapping region of the cut. This represents the minimum distance between the pixels included in the non-overlapping region and the boundary of the clipping overlapping region. This represents the full aperture reconstruction gradient field. This represents the initial gradient distribution across the entire pore size. This represents the smoothed gradient data representing the overlapping regions of the shearing process. This represents the smoothing coefficient.

5. The method of claim 1, wherein, The process of transforming the TIE into a Poisson equation and obtaining the wavefront phase estimate for the nth iteration through a fast Fourier transform specifically includes: Based on the maximum intensity assumption, the TIE, which is based on the elliptic partial differential equation, is transformed into the Poisson equation. Based on the wavenumber, maximum light intensity, the axial derivative of the full aperture light intensity, and the Poisson equation, the source term for the nth iteration is obtained; Perform a fast Fourier transform on the source term of the nth iteration to obtain the wavefront phase estimate of the nth iteration; The TIE based on elliptic partial differential equations is expressed by the following formula: The Poisson equation is expressed by the following formula: in, Denotes the divergence operator, Indicates the light intensity distribution on the focal plane. Represents the wavefront gradient field. This represents the phase distribution of the aspherical wavefront. Indicates wave number, This represents the optimized full-aperture light intensity axial guide number. This represents the wavefront phase estimate in the nth iteration. Indicates the first The residual derivative value of the next iteration. This indicates the maximum light intensity.

6. The method of claim 1, wherein, Based on the wavefront phase estimate from the nth iteration and the measured axial derivative of the light intensity, the following deviation between the current phase estimate and the true wavefront is obtained: Based on the deviation between the current phase estimate and the true wavefront and the Poisson equation, the phase correction for the nth iteration is obtained as follows: Based on the phase correction amount and adaptive step size of the nth iteration, the wavefront phase estimate of the (n+1)th iteration is obtained as shown below: in, This represents the theoretical derivative residual of the nth iteration. Denotes the divergence operator, Indicates the light intensity distribution on the focal plane. This represents the wavefront gradient field in the nth iteration. This represents the wavefront phase estimate in the nth iteration. This represents the axial derivative of the measured light intensity. Represents the Laplace operator. Indicates the maximum light intensity. This represents the phase correction amount in the nth iteration. This represents the wavefront phase estimate in the (n+1)th iteration. This represents the adaptive step size for the nth iteration.

7. The method of claim 1, wherein, The iteration condition includes any one of the following: The norm of the wavefront phase estimate in the (n+1)th iteration is below a threshold; or Reaching the maximum number of iterations; or The rate of decrease of the objective function value approaches zero.

8. The method as described in claim 1, characterized in that, The optimized full-aperture optical intensity axial guide number is expressed by the following formula: in, Indicates wave number, Indicates the light intensity distribution on the focal plane. This represents the optimized axial guide number of the full aperture light intensity. Indicates the full aperture wavefront curvature. This represents the light intensity gradient at the focal plane. Represents the wavefront gradient field. Represents the Laplace operator. This represents the second-order partial derivative of the wavefront gradient in the x-direction. This represents the second-order partial derivative of the wavefront gradient in the y-direction. Indicates the shear overlap region The wavefront gradient of the direction, Indicates the shear overlap region The wavefront gradient of the direction, This indicates the continuous shearing phase difference in the x-direction after unwrapping. This represents the continuous shear phase difference in the y-direction after unwrapping. Indicates the amount of shearing.

9. A TIE-based aspherical wavefront recovery device, characterized in that, include: The first obtaining unit is used to acquire four phase-shifted shear interferograms and a continuously distributed shear phase difference based on the intensity transmission equation (TIE) detection system including the shearer. Based on the small shear assumption and the shear amount, it obtains the shear overlap region and the wavefront gradient of the shear overlap region. Based on the continuous smoothness of the aspherical wavefront, using the edge gradient of the shear overlap region as the boundary, it fills the gap through local trend extrapolation to obtain the preliminary gradient distribution of the full aperture. Based on the minimum distance from the pixels included in the non-overlapping region to the boundary of the shear overlap region, the preliminary gradient distribution of the full aperture, and the smooth gradient data of the overlapping region, it obtains the reconstructed gradient field of the full aperture. The determining unit is used to obtain the optimized full-aperture intensity axial guide number based on the reconstructed full-aperture gradient field, full-aperture wavefront curvature, and TIE; to convert the TIE into a Poisson equation, and to obtain the wavefront phase estimate of the nth iteration through a fast Fourier transform; based on the wavefront phase estimate of the nth iteration, the optimized full-aperture intensity axial guide number, the Poisson equation, and the adaptive step size, to obtain the phase correction amount of the nth iteration and the wavefront phase estimate of the (n+1)th iteration; when the iteration conditions are obtained, the wavefront phase estimate of the (n+1)th iteration is determined as the full-aperture wavefront phase distribution; The second obtaining unit is used to convert the full aperture wavefront phase distribution into an optical wavefront distribution to obtain the wavefront reconstruction result of the aspherical surface under test.

10. A computer device, comprising: The computer device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform the TIE-based aspherical wavefront recovery method as described in any one of claims 1-8.

Images