Astronomical light interference wave front tilt extraction method

Abstract

This invention discloses a method for extracting the wavefront tilt of astronomical optical interferometers. The method includes: acquiring an astronomical optical interferogram; preprocessing the interferogram using two-dimensional envelope detection normalization; performing anticosine phase unwrapping on the preprocessed interferogram to obtain the relative phase distribution of the wavefront; obtaining the tilt term coefficients through Zernike polynomial fitting and calculating the relative wavefront tilt. This invention can be applied to the extraction of the wavefront tilt of astronomical optical interferometers.

Description

Technical Field

[0001] This invention relates to the technical fields of high-resolution astronomical imaging, optical detection, and stellar interferometers, specifically a method for extracting the tilt of the wavefront in astronomical optical interferometry. Background Technology

[0002] Astronomical optical interferometry is a crucial method for exploring the angular diameters and related properties of celestial objects such as stars. Measuring and compensating for the phase error of two interferometric beams is fundamental for high-resolution detection. Atmospheric turbulence causes relative tilting between beams received by different sub-telescopes, adding a carrier frequency during beam combining and severely affecting fringe visibility. To meet observational requirements, it is essential to measure and correct the tip / tilt error of the starlight wavefront. Many operational astronomical optical interferometers internationally possess corresponding wavefront tilt measurement and correction devices. High-precision adaptive optics systems can measure and correct higher-order wavefront distortions. However, most astronomical optical interferometers only consider lower-order wavefront distortions, employing special optical path designs where the wavefront tilt is obtained from the relative offset of the center of mass during observation; some use measurement methods based on four-quadrant detectors. Summary of the Invention

[0003] This invention proposes a method for extracting the wavefront tilt of astronomical optical interferometers to solve the problem of limited observation resolution of astronomical optical interferometers, and can realize the extraction of tilt amount.

[0004] The technical solution to achieve the objective of this invention is as follows: a method for extracting the wavefront tilt of astronomical optical interferometry, comprising the following steps:

[0005] Step 1: Acquire several synchronous phase-shifting interferograms Where a(x,y) represents the background of the interferogram, and b(x,y) represents the modulation scheme of the interferogram. This represents the relative phase distribution of the two interference wavefronts.

[0006] Step 2: Preprocess the interferogram obtained in Step 1 using two-dimensional envelope detection normalization to remove the background and normalize the modulation index, thus obtaining the preprocessed interferogram.

[0007] Step 3: Unwrap the preprocessed interferogram with an anticosine phase to obtain the relative phase distribution of the interference wavefront.

[0008] Step 4: Fit the relative phase distribution of the interference wavefront obtained in Step 3 using a Zernike polynomial to obtain the second coefficient a2 and the third coefficient a3 of the Zernike polynomial.

[0009] Step 5: Calculate the tilt θ in the x and y directions of the wavefront using the coefficients of the second and third terms of the Zernike polynomial obtained in Step 4.x =2a² / a, θ y =2a3 / a, where a represents the pupil radius, and the results of multiple synchronous phase-shifting interferograms are averaged to improve the test accuracy.

[0010] Compared with the prior art, the significant advantages of this invention are:

[0011] (1) This invention eliminates the need for extracting the tilt amount using multiple phase-shifting interferograms. It can detect the relative tilt amount of the wavefront using only a single interferogram, avoiding calculation errors caused by phase inaccuracy and interferogram mismatch, and greatly simplifying the test optical path. In a synchronous phase-shifting system, the detection accuracy can be improved by solving each interferogram separately and averaging the results.

[0012] (2) Under existing conditions, the present invention can extract the wavefront tilt amount, and under certain conditions, it can measure higher-order terms of other wavefront distortions for more complex telescope systems. Attached Figure Description

[0013] Figure 1 This is a flowchart of a method for extracting the tilt of astronomical optical interference wavefront according to the present invention.

[0014] Figure 2 This is an application case of this method in the indoor verification system for phase detection of an astronomical optical interferometer, where (a) to (d) are four unregistered interferograms obtained by synchronous phase shifting. Detailed Implementation

[0015] This invention discloses a method for extracting wavefront tilt in astronomical optical interferometry to address the problem of wavefront tilt affecting the observation resolution of astronomical optical interferometers. The invention removes background from the interferogram and regularizes it through two-dimensional envelope detection normalization; it then performs anticosine phase unwrapping on the preprocessed interferogram to obtain the relative phase distribution of the wavefront, and obtains the tilt term coefficients through Zernike polynomial fitting to calculate the relative wavefront tilt.

[0016] The present invention will now be described in further detail with reference to the accompanying drawings.

[0017] Combination Figure 1 The specific steps of the astronomical optical interference wavefront tilt extraction method described in this invention are as follows:

[0018] Step 1: Collect several synchronous phase-shifting interferograms Where a(x,y) represents the background of the interferogram, and b(x,y) represents the modulation scheme of the interferogram. This represents the relative phase distribution of the two interference wavefronts.

[0019] Step 2: A two-dimensional envelope detection normalization method is proposed for the first time. This method is used to preprocess the interferogram obtained in Step 1, removing the background and normalizing the modulation depth, resulting in the preprocessed interferogram, as shown below:

[0020] Step 2-1: Extract the interferogram from Step 1 in one dimension by row or column to obtain the position and value of the maximum and minimum values ​​of the corresponding row or column; to avoid losing the modulation information of the interferogram, the extraction direction should not be completely parallel to the interference fringes.

[0021] Step 2-2: For the obtained maxima and minima, perform interpolation and two-dimensional envelope fitting according to their positions to obtain the fitted envelope surface I. max (x,y)=IF{ODE max [I0]},I min (x,y)=IF{ODE min [I0]};where ODE max [] denotes a one-dimensional maximum extraction function, ODE min [] represents a one-dimensional minimum extraction function, and IF{} represents a two-dimensional interpolation envelope fitting function.

[0022] Steps 2-3: Interpolation fitting value I from the maximum value at the same pixel location max The interpolated fit value I of the minimum value min And the measured value I0, through The background a(x,y) of I0 is removed and the modulation b(x,y) is normalized to obtain the preprocessed interferogram.

[0023] Step 3: The phase unwrapping algorithm must target the wrapped phases distributed between [-π, π] rad. Typically, this requires performing a sine-cosine transform on the preprocessed interferogram and then using the arctangent to extract the wrapped phases. This process is complex and prone to partial phase flipping, significantly impacting unwrapping. If an inverse cosine transform is directly applied to the preprocessed interferogram, the method described in this invention can be used to obtain the wrapped phases distributed between [-π, π] rad. Then, the phase unwrapping algorithm can be applied to obtain the relative phase distribution of the interference wavefront, as detailed below:

[0024] Step 3-1: Perform an inverse cosine transform on the preprocessed interferogram to obtain the first enclosed phase distributed in the range [0, π] rad. I1(x,y) is the preprocessed interferogram.

[0025] Step 3-2: Phase of the first package Inverting the phase yields a second wrap-around phase distributed between [-π, 0] rad.

[0026] Step 3-3: Phase of the first package Second package phase Binarization and watershed segmentation transform are applied separately, and their differences are compared to obtain the consistent region A1 and inconsistent region A2 of the two results. The key to whether the watershed segmentation transform is correct lies in the first wrapping phase during binarization. The threshold ξ1 and the second wrap phase The threshold ξ2 is selected such that ξ1 takes the value [2.6, 3.1] rad and ξ2 takes the value [-0.5, -0.1] rad, as follows:

[0027] Step 3-3-1: Set an empirical threshold ξ1', and adjust the first wrapping phase under the empirical threshold ξ1'. Binarization and watershed segmentation transformation are performed to obtain the region segmentation step map B1. It is then determined whether the number of segmented regions and their boundary positions are in phase with the first wrapper in step 3-1. If the number and position of the wave crests are consistent, let ξ1 = ξ1' and proceed to step 3-3-2; otherwise, proceed to step 3-3-3.

[0028] Step 3-3-2: Set an empirical threshold ξ2', and adjust the second wrapping phase under the empirical threshold ξ2'. Binarization and watershed segmentation transformation are performed to obtain the region segmentation step map B2. It is then determined whether the number of segmented regions and their boundary positions are in phase with the second wrapping phase in step 3-2. If the number and position of the wave crests are consistent, let ξ2 = ξ2' and proceed to step 3-3-4; otherwise, proceed to step 3-3-3.

[0029] Step 3-3-3: If the number and boundary positions of the segmented regions are inconsistent with the number and position of the phase wrapping peaks, it is necessary to determine whether ξ1' or ξ2' needs to be decreased or increased by the size of the set-1 region in binarization; if the segmented regions overlap due to the set-1 region being too large, then ξ1' or ξ2' needs to be increased; if the set-1 region is too small and the phase wrapping peaks at the image edge are not recognized to participate in the region segmentation, then ξ1' or ξ2' needs to be decreased until the requirements are met.

[0030] Step 3-3-4: Compare B1 and B2. Mark the consistent area as A1 and the inconsistent area as A2.

[0031] It should be noted that initially, in order to facilitate subsequent condition judgment and value adjustment, ξ1' and ξ2' are taken as the midpoint of the value range, let ξ1' = 2.8 rad and ξ2' = -0.3 rad. If the judgment requirements of step 3-3-1 or step 3-3-2 are not met, ξ1' and ξ2' will both decrease or increase by a change of 0.1 rad.

[0032] Steps 3-4: Extract the phase of the first package Extract the second package phase from the value corresponding to region A1. The values ​​corresponding to region A2 are then extracted and concatenated to obtain the third wrap-around phase distributed between [-π, π] rad.

[0033] Steps 3-5: Phase of the third package The relative phase distribution of the interference wavefront is obtained by applying the phase unwrapping algorithm.

[0034] Step 4: Fit the relative phase distribution of the interference wavefront obtained in Step 3 using a Zernike polynomial to obtain the second coefficient a2 and the third coefficient a3 of the Zernike polynomial.

[0035] Step 5: Calculate the tilt θ in the x and y directions of the wavefront using the coefficients of the second and third terms of the Zernike polynomial obtained in Step 4. x =2a² / a, θ y =2a3 / a, where a represents the pupil radius, and the results of multiple synchronous phase-shifting interferograms are averaged to improve the test accuracy.

[0036] Combination Figure 2 This invention can be used to detect the wavefront tilt of astronomical optical interferometers. The detection results are shown in Table 1.

[0037] Table 1. Results of Wavefront Tilt Measurement

[0038]

[0039] This invention proposes a method for extracting wavefront tilt in astronomical optical interferometry. By using two-dimensional envelope detection normalization, anticosine phase unwrapping, and Zernike polynomial fitting, the wavefront tilt can be extracted from the interferogram, which can be applied to the detection of wavefront tilt in astronomical optical interferometers.

Claims

1. A method for extracting the tilt of the wavefront in astronomical optical interference, characterized in that, The steps are as follows: Step 1: Acquire several synchronous phase-shifting interferograms Where a(x,y) represents the background of the interferogram, and b(x,y) represents the modulation scheme of the interferogram. This represents the relative phase distribution of the two interference wavefronts; Step 2: Preprocess the interferogram obtained in Step 1 using two-dimensional envelope detection normalization to remove the background and normalize the modulation index, thus obtaining the preprocessed interferogram. Step 3: Unwrap the preprocessed interferogram with an anticosine phase to obtain the relative phase distribution of the interference wavefront; Step 4: Fit the relative phase distribution of the interference wavefront obtained in Step 3 using a Zernike polynomial to obtain the second coefficient a2 and the third coefficient a3 of the Zernike polynomial. Step 5: Calculate the tilt θ in the x and y directions of the wavefront using the coefficients of the second and third terms of the Zernike polynomial obtained in Step 4. x =2a² / a, θ y =2a3 / a, where a represents the pupil radius, and the results of multiple synchronous phase-shifting interferograms are averaged to improve the test accuracy.

2. The method for extracting the wavefront tilt of astronomical optical interference according to claim 1, characterized in that, In step 2, the interferogram obtained in step 1 is preprocessed using two-dimensional envelope detection normalization to remove the background and normalize the modulation index, resulting in the preprocessed interferogram, as shown below: Step 2-1: Extract the interferogram from Step 1 in one dimension by row or column to obtain the position and value of the maximum and minimum values ​​of the corresponding row or column; to avoid losing the modulation information of the interferogram, the extraction direction should not be completely parallel to the interference fringes; Step 2-2: For the obtained maxima and minima, perform interpolation and two-dimensional envelope fitting according to their positions to obtain the fitted envelope surface I. max (x,y)=IF{ODE max [I0]},I min (x,y)=IF{ODE min [I0]};where ODE max [] denotes a one-dimensional maximum extraction function, ODE min [] denotes a one-dimensional minimum extraction function, and IF{} denotes a two-dimensional interpolation envelope fitting function; Steps 2-3: Interpolation fitting value I from the maximum value at the same pixel location max The interpolated fitting value I of the minimum value min And the measured value I0, through The background a(x,y) of I0 is removed and the modulation b(x,y) is normalized to obtain the preprocessed interferogram.

3. The method for extracting the wavefront tilt of astronomical optical interference according to claim 2, characterized in that, In step 3, the preprocessed interferogram is unwrapped using an anticosine phase to obtain the relative phase distribution of the interference wavefront, as follows: Step 3-1: Perform an inverse cosine transform on the preprocessed interferogram to obtain the first enclosed phase distributed in the range [0, π] rad. I1(x,y) is the preprocessed interferogram; Step 3-2: Phase of the first package Inverting the phase yields a second wrap-around phase distributed between [-π, 0] rad. Step 3-3: Phase of the first package Second package phase Binarization and watershed segmentation transformation are applied respectively, and the differences between the two are compared to obtain the consistent region A1 and the inconsistent region A2 of the two results; Steps 3-4: Extract the phase of the first package Extract the second package phase from the value corresponding to region A1. The values ​​corresponding to region A2 are then extracted and concatenated to obtain the third wrap-around phase distributed between [-π, π] rad. Steps 3-5: Phase of the third package The relative phase distribution of the interference wavefront is obtained by applying the phase unwrapping algorithm.

4. The method for extracting the wavefront tilt of astronomical optical interference according to claim 3, characterized in that, In step 3-3, the first package phase Second package phase Binarization and watershed segmentation transformation are applied respectively, and their differences are compared to obtain the consistent region A1 and inconsistent region A2 of the two results, as follows: During binarization, let the first wrap phase be... The threshold is ξ1, and the second wrap phase The threshold is ξ2, where ξ1 takes values ​​of [2.6, 3.1] rad and ξ2 takes values ​​of [-0.5, -0.1] rad. The specific determination method is as follows: Step 3-3-1: Set an empirical threshold ξ1', and adjust the first wrapping phase under the empirical threshold ξ1'. Binarization and watershed segmentation transformation are performed to obtain the region segmentation step map B1. It is then determined whether the number of segmented regions and their boundary positions are in phase with the first wrapper in step 3-1. If the number and position of the wave crests are consistent, let ξ1 = ξ1' and proceed to step 3-3-2; otherwise, proceed to step 3-3-3. Step 3-3-2: Set an empirical threshold ξ2', and adjust the second wrapping phase under the empirical threshold ξ2'. Binarization and watershed segmentation transformation are performed to obtain the region segmentation step map B2. It is then determined whether the number of segmented regions and their boundary positions are in phase with the second wrapping phase in step 3-2. If the number and position of the wave crests are consistent, let ξ2 = ξ2' and proceed to step 3-3-4; otherwise, proceed to step 3-3-3. Step 3-3-3: If the number of segments and their boundary positions are inconsistent with the number and position of the phase-wrapped peaks, it is necessary to determine whether ξ1' or ξ2' needs to be reduced or increased by the size of the set-1 region in binarization; if the segmented regions overlap due to the set-1 region being too large, then ξ1' or ξ2' needs to be increased. If the phase wrapping peaks at the image edge are not identified and participate in region segmentation because the set area is too small, then ξ1' or ξ2' needs to be reduced until the requirements are met. Step 3-3-4: Compare B1 and B2. Mark the consistent area as A1 and the inconsistent area as A2.

5. The method for extracting the wavefront tilt of astronomical optical interference according to claim 4, characterized in that, Let ξ1' = 2.8 rad and ξ2' = -0.3 rad. If the judgment requirements of step 3-3-1 or step 3-3-2 are not met, ξ1' and ξ2' will both decrease or increase by a change of 0.1 rad.

6. A method for extracting the wavefront tilt of astronomical optical interference according to any one of claims 1 to 5, characterized in that, It can be used to extract wavefront tilt from astronomical optical interferometers.

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