A surface shape anti-vibration measurement method for large-aperture high-resolution phase-shifting interferometer

Abstract

A method for surface shape measurement of large aperture high resolution phase shifting interferometer is provided. The method decouples the vibration offset estimation from the high resolution wavefront reconstruction, and only uses a single set of high resolution interferogram images collected in the vibration environment to complete the vibration resistant phase reconstruction. The method includes: collecting high resolution interferogram images in the vibration environment and performing noise suppression and contrast compensation preprocessing; downsampling the preprocessed images, and iteratively estimating the vibration offset of each frame of interferogram image in the low resolution domain; using the vibration offset as a known parameter, performing a linear least squares fitting on the full resolution preprocessed image to reconstruct the measured wavefront phase distribution. The method shortens the calculation time by 8-10 times while ensuring the accuracy of the phase reconstruction, does not need to collect low resolution data and modify the hardware, and is suitable for phase shifting interferometers with an aperture of ≥Φ100mm and a resolution of ≥1000×1000 pixels.

Description

Technical Field

[0001] This invention belongs to the field of optical interferometry technology, specifically relating to a method for measuring the surface shape vibration resistance of a large-aperture, high-resolution phase-shifting interferometer. It is suitable for detecting the high-resolution surface shape and transmission wavefront error of large-aperture optical elements under vibration environment conditions. Background Technology

[0002] Phase-shifting interferometry (PSI) is a technique that acquires multiple interferometric images by applying a precisely controllable phase shift in a reference optical path, and then deduces the phase distribution of the wavefront under test from the interferograms. It is one of the most accurate and spatially resolution optical measurement methods currently available.

[0003] However, PSI technology is extremely sensitive to vibration. In large-aperture interferometric systems, environmental vibrations and air disturbances can cause overall translational and tilting of the interference fringes, resulting in phase shift errors and fringe tilt errors, which severely damage traditional phase shifting algorithms. To compensate for these errors, various random phase shifting algorithms based on least-squares iteration have been proposed, which can simultaneously estimate the wavefront phase and phase shift errors.

[0004] Among them, TIA estimates the wavefront phase, x / y fringe tilt, and frame-by-frame phase shift through iterative estimation. This method can achieve high vibration resistance under small aperture and low resolution conditions (Liu et al., Opt. Express (2013)). However, when processing full-resolution data, this algorithm requires multiple iterations, and the computational load is proportional to the square of the number of pixels. When the resolution reaches 2048×2048 pixels and the number of interferometric image frames is more than ten, the single solution time can reach hundreds of seconds or even longer, which is difficult to meet the requirements of large aperture and high-resolution online detection.

[0005] On the other hand, to improve vibration resistance, some studies have embedded intra-frame and inter-frame contrast compensation during the TIA iteration process to suppress the influence of non-uniformity of interferometric image contrast on iteration convergence (Liu et al., J. Opt. (2017)). Although this method can improve measurement accuracy, it further increases the computational burden of each iteration, resulting in a longer overall computation time, thus limiting the application of the TIA algorithm on large-aperture interferometers with apertures of Φ100mm and above, especially those with apertures of Φ400mm to Φ600mm.

[0006] In addition, a related patent (CN106840418B) discloses a phase-shifting interferometry vibration reduction method that combines camera pixel combination with MTIA, but this method requires the separate acquisition of two sets of data, one high-resolution and one low-resolution, resulting in many system hardware constraints and a complex measurement process.

[0007] Therefore, there is an urgent need for a vibration-resistant measurement method that can quickly and accurately recover the high-resolution wavefront phase under vibration conditions to meet the needs of online inspection of large-aperture optical components. Summary of the Invention

[0008] The purpose of this invention is to address the problems of high sensitivity to environmental vibration and large computational load of anti-vibration algorithm iteration in existing large-aperture high-resolution phase-shifting interferometry. It provides a surface vibration measurement method for large-aperture high-resolution phase-shifting interferometers. By decoupling the iterative estimation process of vibration offset from the high-resolution wavefront phase reconstruction process, and completing the iterative calculation in the low-resolution image domain after downsampling, the high-resolution wavefront phase can still be recovered with low computational cost and high computational speed even in complex vibration environments.

[0009] To achieve the above objectives, the technical solution of the present invention is as follows:

[0010] A method for measuring the vibration resistance of a surface shape in a large-aperture, high-resolution phase-shifting interferometer includes the following steps:

[0011] Step 1. High-resolution interferometric image acquisition: Using a phase-shifting interferometer, acquire multiple frames of high-resolution interferometric images of the optical element under test according to a predetermined phase-shifting sequence under vibration conditions;

[0012] Step 2. Image preprocessing: Noise suppression and contrast compensation are performed on the multi-frame high-resolution interferometric images to obtain a preprocessed high-resolution interferometric image sequence, and the preprocessed high-resolution interferometric image sequence is used as the unified input for subsequent low-resolution vibration offset iterative estimation and high-resolution wavefront phase reconstruction;

[0013] Step 3. Iterative estimation of low-resolution vibration offset: Based on the same set of preprocessed high-resolution interferometric image sequences, downsampling is performed to obtain low-resolution interferometric image data for vibration offset estimation. The low-resolution interferometric image data is obtained by transforming the high-resolution interferometric image sequence. On the low-resolution interferometric image data, the vibration offset of each frame of the interferometric image during the interferometry process is estimated by an iterative algorithm. The vibration offset includes the phase shift offset of each frame of the interferometric image relative to the first frame, the linear tilt phase shift parameter in the x-direction, and the linear tilt phase shift parameter in the y-direction.

[0014] Step 4. High-resolution wavefront phase reconstruction: Substitute the vibration offset estimated in Step 3 as a known parameter into the phase-shifting interferometry model, directly establish a linear least squares equation set for the preprocessed high-resolution interferometric image sequence, and obtain the full-resolution wavefront phase distribution of the optical element under test by solving the equation through a linear fitting.

[0015] Furthermore, the noise suppression and contrast compensation processing in step 2 specifically includes: first, performing two-dimensional median filtering on each frame of high-resolution interferometric image to suppress random noise and speckle noise, and then performing grayscale histogram equalization processing on the filtered image to compensate for the contrast difference of interference fringes within and between frames. The contrast compensation is completed once in the preprocessing stage, and contrast compensation is not repeated in subsequent iterations.

[0016] Furthermore, the low-resolution interferometric image data in step 3 is obtained by downsampling a set of preprocessed high-resolution interferometric images. Specifically, the preprocessed high-resolution interferometric images are first sampled by integer multiples in the row and column directions according to preset row and column sampling factors, reducing the number of pixels to 1 / N of the original number, where N is an integer greater than 1. This avoids the need for additional low-resolution interferometric image data acquisition.

[0017] Furthermore, the extraction factor of the downsampling process is adaptively adjusted according to the interferometer's camera resolution, environmental vibration frequency, and interference fringe density to ensure that the interference fringe width in the downsampled low-resolution image contains at least 3-5 pixels, so as to retain the fringe tilt and translation information caused by vibration while reducing the computational load.

[0018] Furthermore, the method for estimating the vibration offset using an iterative algorithm in step 3 includes: fitting each frame of the interferometric image using a least squares iterative algorithm in the low-resolution image domain, iteratively solving the phase shift offset, x-direction linear tilt phase shift parameter, and y-direction linear tilt phase shift parameter of each frame of the interferometric image relative to the first frame, and using the overall phase shift offset and the linear tilt phase shift parameters in each direction as the vibration offset characterizing the environmental vibration.

[0019] Furthermore, the specific process of obtaining the full-resolution wavefront phase distribution through a single linear fitting in step 4 is as follows: taking the vibration offset of each frame estimated in step 3 as known parameters, for each pixel (x,y) in the preprocessed full-resolution interferometric image sequence, establish a system of linear equations about the background light intensity A(x,y), the modulation amplitude cosine term B(x,y)cos[φ(x,y)], and the modulation amplitude sine term B(x,y)sin[φ(x,y)]. Solve the equations using the linear least squares method to obtain the phase value φ(x,y) of the pixel, and then obtain the continuous wavefront phase distribution through the unwrapping algorithm.

[0020] Furthermore, the effective aperture of the phase-shifting interferometer is ≥ Φ100mm, and the pixel resolution of the high-resolution interferometric image is not less than 1000×1000 pixels.

[0021] Compared with the prior art, the technical effects of the present invention are as follows:

[0022] ① By performing iterative estimation of vibration offset on low-resolution interferometric image data, the most time-consuming iterative process is moved from the high-resolution domain to the low-resolution domain. Under typical high-resolution interferometric image conditions of 2048×2048 pixels, the overall calculation time can be shortened by about 8 to 10 times compared with the traditional TIA method.

[0023] ② Since the high-resolution stage uses a first least squares fitting and the vibration offset is accurately estimated by the low-resolution iteration, this method can control the phase recovery error within about 1 to 3% of the variance of the surface topography in both simulation and experiment, which meets the requirements of large-diameter precision detection.

[0024] ③ This method can effectively process interferograms acquired under conditions of vibration displacement amplitude of 0.4mm to 2mm and vibration frequency of about 20Hz, and accurately restore their phase data. It is suitable for laboratories or production sites with obvious environmental vibrations and can realize stable vibration resistance measurement of optical components with aperture ≥ Φ100mm.

[0025] ④ Contrast compensation, downsampling, iterative estimation, and high-resolution fitting can all be implemented on a general-purpose CPU platform through software algorithms. There is no need to change the optical path structure of the existing phase-shifting interferometer; deployment can be achieved simply by upgrading the software. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the surface vibration resistance measurement method for a large-aperture, high-resolution phase-shifting interferometer according to the present invention.

[0027] Figure 2 This is a schematic diagram of the interference image frame acquired during measurement using a small-aperture (Φ100mm) phase-shifting interferometer according to Embodiment 1 of the present invention;

[0028] Figure 3 This is a schematic diagram of the results of measuring the vibration phase shift by the spatial offset of the interference fringes in a small-aperture (Φ100mm) phase-shifting interference experiment according to Embodiment 1 of the present invention. Among them, (a) is the total offset curve of each frame of interference fringes relative to the first frame, and (b) is the residual offset curve of each direction caused by vibration after removing the preset phase shift change trend.

[0029] Figure 4 The image shows a comparison of the high-resolution phase inversion results in a small-aperture phase-shifting interferometry experiment according to Embodiment 1 of the present invention. In the image, (a) is the wavefront phase distribution map calculated using the traditional three-step least squares iterative algorithm (TIA), (b) is the wavefront phase distribution map calculated using the algorithm proposed in this invention, and (c) is the residual distribution map obtained by subtracting (a) and (b) pixel by pixel.

[0030] Figure 5This is a schematic diagram of an interference image frame acquired during measurement using a large-aperture (Φ600mm) phase-shifting interferometer in Embodiment 2 of the present invention.

[0031] Figure 6 This is a schematic diagram of the results of measuring the vibration phase shift by the spatial offset of the interference fringes in a large-aperture phase-shifting interference experiment according to Embodiment 2 of the present invention. Among them, (a) is the total offset curve of each frame of interference fringes relative to the first frame, and (b) is the residual offset curve of each direction caused by vibration after removing the preset phase shift change trend.

[0032] Figure 7 The image shows a comparison of the high-resolution phase inversion results in a large-aperture phase-shifting interferometry experiment according to Embodiment 2 of the present invention. Among them, (a) is the wavefront phase distribution map calculated by the traditional three-step least squares iterative algorithm (TIA), (b) is the wavefront phase distribution map calculated by the algorithm proposed in this invention, and (c) is the residual distribution map obtained by subtracting (a) and (b) pixel by pixel. Detailed Implementation

[0033] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. The embodiments described herein are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0034] Example 1: Vibration resistance measurement verification on a small-aperture (Φ100mm) phase-shifting interferometer

[0035] Step 1: High-resolution interferometric image acquisition

[0036] This embodiment employs a small-aperture Fizeau-type phase-shifting interferometer with a laser wavelength of 632.8 nm and an effective aperture of Φ100 mm. The device under test is a standard planar optical element. Measurements are performed under laboratory conditions with normal environmental vibrations. The interferometer's camera continuously acquires 100 high-resolution interferometric images according to a preset phase-shifting sequence, with a total phase shift of 2π. Thirteen images are uniformly selected from this dataset, ensuring that the nominal phase shifts between adjacent frames are approximately equal. The resolution of each recorded single-frame interferometric image is 2048 × 2048 pixels. Figure 2 A typical measured interferometric image is shown, in which the interference fringes are clear, but may have slight shifts due to vibration.

[0037] Step 2: Image Preprocessing

[0038] The 13 high-resolution interferometric images acquired were preprocessed. First, a 3×3 two-dimensional median filter window was applied to each frame for convolution to suppress random noise and speckle noise from the CCD camera. Then, global grayscale histogram equalization was performed on the filtered images. This operation enhances image contrast and compensates for inconsistencies in intra- and inter-frame interference fringe contrast caused by light source fluctuations or environmental changes, providing high-quality and uniform input data for subsequent processing. The preprocessed image sequence was used as the unified input for all subsequent steps.

[0039] Step 3: Low-resolution vibration offset estimation

[0040] The preprocessed high-resolution image is downsampled. Specifically, integer sampling is performed in both the row and column directions of the image, using a factor of 4, meaning one pixel is selected from every 4×4 pixel block. This compresses the original 2048×2048 pixel image into a low-resolution 512×512 pixel image dataset, reducing the total number of pixels to 1 / 16 of the original.

[0041] In the low-resolution image domain, the least squares iterative (TIA) algorithm is performed. This algorithm iteratively minimizes the residual between the actual interferogram and the model-estimated interferogram. After the iteration converges, the vibration offset parameters of each frame of the image are obtained with accurate estimation in the low-resolution domain. Figure 3 The results estimated in this embodiment are shown, where (a) is the total offset of the interference fringes in each frame relative to the first frame, and (b) is the residual offset in each direction caused by vibration after removing the nominal linear phase shift trend. Figure 3 Phase jitter caused by vibration can be clearly observed in (b).

[0042] Step 4: High-resolution wavefront phase reconstruction

[0043] The vibration offset estimated in step 3 is used as a known parameter and substituted into the original phase-shifting interferometry measurement model. At this point, for the original 2048×2048 pixel full-resolution preprocessed image, a system of linear least squares equations containing actual phase shift and vibration offset correction terms is established.

[0044] At each pixel (x, y), for 13 frames of interferogram, the light intensity value is linearly related to the unknown quantity to be determined. Since the vibration offset has been determined, by independently solving a system of three linear equations for each pixel, the full-resolution sum and complex modulation field can be obtained at once, and then the phase can be wrapped. Finally, the continuous wavefront phase distribution can be obtained through the unwrapping algorithm.

[0045] To verify the accuracy of this invention, the classic TIA algorithm was used to directly solve the phase of the original high-resolution image (without downsampling and the separation estimation step described in this invention) as a comparison benchmark. Figure 4 The comparison results are shown, where (a) is the wavefront phase map calculated by the TIA algorithm, (b) is the wavefront phase map calculated by the algorithm proposed in this invention, and (c) is the residual map obtained by subtracting the two pixel by pixel. Calculations show that the root mean square (RMS) value of the residual map is only about 1% of the surface topography variance obtained by the TIA algorithm. The results demonstrate that this invention improves computational efficiency by nearly an order of magnitude while maintaining phase restoration accuracy highly consistent with traditional iterative algorithms, with minimal error.

[0046] Example 2: Vibration Measurement Application on a Large-Aperture (Φ600mm) Phase-Shifting Interferometer

[0047] Step 1: High-resolution interferometric image acquisition

[0048] This embodiment employs a large-aperture Fizeau-type phase-shifting interferometer with a laser wavelength of 632.8 nm and an effective aperture of Φ600 mm. The test piece is a planar optical element measuring 400 mm × 400 mm. The measurement environment is a typical optical workshop with environmental vibrations of approximately 20 Hz and an amplitude of approximately 1 mm. 100 frames of images were acquired according to a preset phase-shifting sequence, resulting in a total phase shift of 2π. Thirteen frames with approximately equal phase shift intervals were selected for analysis. Due to limitations in camera target size, the resolution of each recorded interferometric image is 1000 × 1000 pixels. Figure 5 A typical interferometric image acquired using this large-aperture system is shown. The fringe density is moderate, but due to vibration, the fringes may dynamically shift at the moment of image acquisition.

[0049] Step 2: Image Preprocessing

[0050] Thirteen frames of 1000×1000 pixel high-resolution images were preprocessed. A 5×5 two-dimensional median filter was used to suppress noise, and gray-level histogram equalization was performed to enhance stripe contrast, ensuring that subsequent processing was not affected by light intensity fluctuations.

[0051] Step 3: Low-resolution vibration offset estimation

[0052] The preprocessed image is downsampled. Considering that the original resolution is lower than that of Example 1, this example uses a row and column downsampling factor of 2 times to compress the image to 500×500 pixels. The TIA algorithm is executed in the low-resolution domain to iteratively estimate the vibration offset of each frame of the interferometric image. Since the number of pixels is reduced to 1 / 4 of the original, the speed of iterative solution is significantly improved. The goal of downsampling is to maximize the reduction of data dimensionality while preserving the information on fringe tilt and translation caused by vibration. Generally, it should be ensured that the width of the interference fringes still occupies at least 3-5 pixels in the downsampled image to avoid spatial aliasing. The downsampling factor should be selected according to the resolution of the interferometric image and the spatial distribution characteristics of the fringes to retain the fringe spatial offset information required for vibration parameter estimation while reducing the computational load. For cases with dense fringes, a smaller downsampling factor is preferable. Conversely, a larger downsampling factor can be selected.

[0053] Figure 6 The vibration offset estimated in this embodiment is shown in (a) as the total offset of the interference fringes in each frame relative to the first frame, and (b) as the residual offset caused by vibration after removing the nominal phase shift. Figure 6 In (b), the vibration characteristics of approximately 1 mm amplitude and approximately 20 Hz frequency can be clearly seen, which is consistent with the actual vibration conditions of the measured environment.

[0054] Step 4: High-resolution wavefront phase reconstruction

[0055] The vibration offset accurately estimated in step 3 is used as a known parameter and substituted into the original phase-shifting interferometry model. For the preprocessed interferometric image at full resolution (1000×1000 pixels), a system of linear least square equations is established pixel by pixel to solve for the high-resolution wavefront phase distribution in one step.

[0056] Similarly, the results of this invention are compared with the results of directly performing TIA iterative calculations on high-resolution images. Figure 7 The comparison results are shown, where (a) is the result calculated by the TIA algorithm, (b) is the result calculated by the algorithm of this invention, and (c) is the difference between the two. The calculations show that the difference between the two remains controlled at approximately 1% of the surface variance. Furthermore, in terms of computation time, the method of this invention (downsampling iteration + high-resolution single-step fitting) is approximately 8 times faster than directly performing TIA iteration on a 1000×1000 pixel image. This embodiment fully demonstrates that this invention can effectively cope with actual environmental vibrations in large-aperture interferometry, significantly improving the efficiency of vibration-resistant measurements while maintaining nanometer-level measurement accuracy, thus meeting the needs of online and rapid detection of large-aperture optical components.

[0057] In summary, this invention cleverly decouples the vibration estimation and high-resolution reconstruction processes, and completes the most computationally intensive iterative part in the low-resolution domain, achieving high-precision and high-efficiency measurement of large-aperture high-resolution phase-shifting interferometry in complex vibration environments. This method is simple to implement in software, requires no hardware modifications, and has extremely high industrial application value.

Claims

1. A method for measuring the vibration resistance of a surface shape in a large-aperture, high-resolution phase-shifting interferometer, characterized in that, Includes the following steps: Step 1. High-resolution interferometric image acquisition: Using a phase-shifting interferometer, acquire multiple frames of high-resolution interferometric images of the optical element under test according to a predetermined phase-shifting sequence under vibration conditions; Step 2. Image preprocessing: Noise suppression and contrast compensation are performed on the multi-frame high-resolution interferometric images to obtain a preprocessed high-resolution interferometric image sequence, and the preprocessed high-resolution interferometric image sequence is used as the unified input for subsequent low-resolution vibration offset iterative estimation and high-resolution wavefront phase reconstruction; Step 3. Iterative estimation of low-resolution vibration offset: Based on the same set of preprocessed high-resolution interferometric image sequences, downsampling is performed to obtain low-resolution interferometric image data for vibration offset estimation. The low-resolution interferometric image data is obtained by transforming the high-resolution interferometric image sequence. On the low-resolution interferometric image data, the vibration offset of each frame of the interferometric image during the interferometry process is estimated by an iterative algorithm. The vibration offset includes the phase shift offset of each frame of the interferometric image relative to the first frame, the linear tilt phase shift parameter in the x-direction, and the linear tilt phase shift parameter in the y-direction. Step 4. High-resolution wavefront phase reconstruction: Substitute the vibration offset estimated in Step 3 as a known parameter into the phase-shifting interferometry model, directly establish a linear least squares equation set for the preprocessed high-resolution interferometric image sequence, and obtain the full-resolution wavefront phase distribution of the optical element under test by solving the equation through a linear fitting.

2. The method for measuring surface vibration resistance of a large-aperture, high-resolution phase-shifting interferometer according to claim 1, characterized in that, The noise suppression and contrast compensation processing in step 2 specifically includes: first, performing two-dimensional median filtering on each frame of high-resolution interferometric image to suppress random noise and speckle noise; then, performing grayscale histogram equalization processing on the filtered image to compensate for the contrast difference of interference fringes within and between frames. The contrast compensation is completed once in the preprocessing stage and is not repeated in subsequent iterations.

3. The method for measuring surface vibration resistance of a large-aperture, high-resolution phase-shifting interferometer according to claim 1, characterized in that, The low-resolution interferometric image data in step 3 is obtained by downsampling a set of preprocessed high-resolution interferometric images. Specifically, the preprocessed high-resolution interferometric images are first sampled in the row and column directions according to preset row and column sampling factors, so that the number of pixels is reduced to 1 / N of the original number, where N is an integer greater than 1.

4. The method for measuring surface vibration resistance of a large-aperture, high-resolution phase-shifting interferometer according to claim 3, characterized in that, The extraction factor of the downsampling process is adaptively adjusted according to the interferometer's camera resolution, environmental vibration frequency, and interference fringe density to ensure that the interference fringe width in the downsampled low-resolution image contains at least 3-5 pixels, so as to retain the fringe tilt and translation information caused by vibration while reducing the computational load.

5. The surface vibration measurement method for a large-aperture, high-resolution phase-shifting interferometer according to claim 1, characterized in that the method for estimating the vibration offset through an iterative algorithm in step 3 includes: In the low-resolution image domain, the least squares iterative algorithm is used to fit each frame of the interferometric image. The phase shift offset, x-direction linear tilt phase shift parameter and y-direction linear tilt phase shift parameter of each frame of the interferometric image relative to the first frame are iteratively solved. The overall phase shift offset and the linear tilt phase shift parameters in each direction are used as vibration offsets to characterize environmental vibration.

6. The method for measuring surface vibration resistance of a large-aperture, high-resolution phase-shifting interferometer according to claim 1, characterized in that, The specific process of obtaining the full-resolution wavefront phase distribution through a single linear fitting in step 4 is as follows: taking the vibration offset of each frame estimated in step 3 as known parameters, for each pixel (x,y) in the preprocessed full-resolution interferometric image sequence, establish a system of linear equations about the background light intensity A(x,y), the modulation amplitude cosine term B(x,y)cos[φ(x,y)], and the modulation amplitude sine term B(x,y)sin[φ(x,y)]. Solve the equations using the linear least squares method to obtain the phase value φ(x,y) of the pixel, and then obtain the continuous wavefront phase distribution through the unwrapping algorithm.

7. The method for measuring surface vibration resistance of a large-aperture, high-resolution phase-shifting interferometer according to claim 1, characterized in that, The effective aperture of the phase-shifting interferometer is ≥ Φ100mm, and the pixel resolution of the high-resolution interferometric image is not less than 1000×1000 pixels.

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