Astronomical light interference wavefront tilt extraction method

Abstract

The invention discloses an astronomical light interference wavefront tilt extraction method. The method comprises the following steps: acquiring an astronomical light interference pattern; preprocessing the interferogram by using two-dimensional envelope detection normalization; performing anti-cosine phase unwrapping on the preprocessed interferogram to obtain wavefront relative phase distribution; the tilt term coefficient is obtained through Zernike polynomial fitting, and the relative wavefront tilt amount is obtained through calculation. The method can be applied to extraction of the wavefront tilt amount of the astronomical light interference telescope.

Description

Technical Field

[0001] The invention relates to the technical fields of celestial body high-resolution imaging, optical detection, stellar light interferometer, etc., and specifically to a method for extracting astronomical light interference wavefront tilt. Background Art

[0002] Astronomical light interferometry is an important way to explore the angular diameter of stars and other celestial bodies and their related characteristics. The measurement and compensation of the common phase error of two interfering light beams is the basis for high-resolution detection. Atmospheric turbulence will cause relative tilt between the light beams received by different sub-telescopes, and the carrier frequency will be added when the beams are combined, which will seriously affect the visibility of the fringe. In order to meet the observation needs, the Tip / Tilt error of the starlight wavefront must be measured and corrected. At present, many astronomical light interferometry telescopes that have been put into use internationally have corresponding wavefront tilt measurement and correction devices, and high-precision adaptive optical systems can measure and correct high-order wavefront distortions. However, most astronomical light interferometry telescopes only consider low-order wavefront distortions and adopt a special optical path design. During observation, the tilt of the wavefront can be obtained from the relative offset of the center of mass position; some use a measurement method based on a four-quadrant detector. Summary of the invention

[0003] The present invention proposes an astronomical light interference wavefront tilt extraction method to solve the problem of limited observation resolution of astronomical light interference telescopes, and can realize the extraction of tilt amount.

[0004] The technical solution to achieve the purpose of the present invention is: a method for extracting astronomical light interference wavefront tilt, the steps are as follows:

[0005] Step 1: Collect several synchronous phase-shifting interferograms Among them, a(x,y) represents the interference pattern background, b(x,y) represents the interference pattern modulation, Represents the relative phase distribution of the two interfering wavefronts.

[0006] Step 2: Use two-dimensional envelope detection normalization to preprocess the interference pattern obtained in step 1, remove the background in the interference pattern and normalize the modulation degree to obtain the preprocessed interference pattern.

[0007] Step 3: Perform arccosine phase unwrapping on the preprocessed interference pattern to obtain the relative phase distribution of the interference wavefront.

[0008] Step 4: Perform Zernike polynomial fitting on the relative phase distribution of the interference wavefront obtained in step 3 to obtain the second coefficient a2 and the third coefficient a3 of the Zernike polynomial.

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

[0010] Compared with the prior art, the present invention has the following significant advantages:

[0011] (1) The present invention does not need to extract the tilt amount through multiple phase-shifting interferograms, but can detect the relative tilt of the wavefront through a single interferogram, thus avoiding the calculation error caused by inaccurate phase shifting and interferogram mismatch, and can greatly simplify the test optical path. In the synchronous phase-shifting system, the detection accuracy can be improved by solving and averaging separately.

[0012] (2) The present invention can realize the extraction of wavefront tilt under existing conditions, and for more complex telescope systems, it can measure other high-order terms of wavefront distortion under certain conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The present invention is a flow chart of a method for extracting astronomical light interference wavefront tilt.

[0014] Figure 2 This is an application example of the method in the indoor verification system of phase detection of astronomical optical interferometer telescope, where (a) to (d) are four unaligned interference patterns obtained by synchronous phase shifting. DETAILED DESCRIPTION

[0015] The invention discloses a method for extracting wavefront tilt of astronomical light interference to solve the problem that the resolution of astronomical light interferometer telescope observation is affected by wavefront tilt. The invention removes the background in the interference pattern and regularizes the interference pattern through two-dimensional envelope detection normalization; performs arccosine phase unwrapping on the pre-processed interference pattern to obtain the relative phase distribution of the wavefront, obtains the tilt term coefficient through Zernike polynomial fitting, and calculates the relative wavefront tilt.

[0016] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0017] Combination Figure 1 The astronomical light interference wavefront tilt extraction method of the present invention comprises the following specific steps:

[0018] Step 1: Collect several synchronous phase-shifting interferograms Among them, a(x,y) represents the interference pattern background, b(x,y) represents the interference pattern modulation, Represents the relative phase distribution of the two interfering wavefronts.

[0019] Step 2: A two-dimensional envelope detection normalization method is proposed for the first time. The interference pattern obtained in step 1 is preprocessed using the two-dimensional envelope detection normalization method. The background in the interference pattern is removed and the modulation degree is normalized to obtain the preprocessed interference pattern. The details are as follows:

[0020] Step 2-1: Extract the interference pattern in 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 interference pattern, the extraction direction needs to be non-completely parallel to the interference fringes.

[0021] Step 2-2: For the obtained maximum and minimum values, interpolation and two-dimensional envelope surface fitting are performed 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 [] represents 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] Step 2-3: Interpolation fitting value I from the maximum value at the same pixel position max , the interpolation fitting value of the minimum value I min And the measured value I0, through Remove the background a(x, y) of I0 and normalize the modulation b(x, y) to obtain the preprocessed interference pattern

[0023] Step 3: The phase unwrapping algorithm must be targeted at the wrapped phase distributed between [-π,π]rad. It is usually necessary to perform a sine-cosine transform on the preprocessed interference pattern, and then use the inverse tangent to extract the wrapped phase. The steps are complicated and prone to the problem of overall flipping of some wrapped phases, which has a huge impact on the unwrapping. If the preprocessed interference pattern is directly subjected to an inverse cosine transform, it is only necessary to use the method mentioned in the present invention to obtain the to-be-solved wrapped phase distributed between [-π,π]rad, and then apply the phase unwrapping algorithm to obtain the relative phase distribution of the interference wavefront, as follows:

[0024] Step 3-1: Perform an inverse cosine transform on the preprocessed interferogram to obtain the first package phase distributed between [0,π]rad I1(x,y) is the interference pattern after preprocessing.

[0025] Step 3-2: Phase the first package Take the inversion and get the second wrapped phase distributed between [-π, 0] rad

[0026] Step 3-3: Phase the first package and the second wrapping phase Apply binarization and watershed segmentation transformation respectively, compare the differences between the two, and obtain the consistent area A1 and inconsistent area A2 of the two results. The key to whether the watershed segmentation transformation is correct lies in the first parcel phase during binarization. The threshold ξ1 and the second wrapping phase The selection of the threshold ξ2, the value of ξ1 is [2.6, 3.1] rad, and the value of ξ2 is [-0.5, -0.1] rad, as follows:

[0027] Step 3-3-1: Set the empirical threshold ξ1', and perform the first package phase Perform binarization and watershed segmentation transformation to obtain the regional segmentation step map B1, and determine whether the number and boundary position of the segmented regions are consistent with the first wrapped phase in step 3-1. The number and position of the wrapped wave peaks are consistent. If they are consistent, set ξ1=ξ1' and proceed to step 3-3-2. If they are inconsistent, proceed to step 3-3-3.

[0028] Step 3-3-2: Set the empirical threshold ξ2', and perform the second package phase Perform binarization and watershed segmentation transformation to obtain the regional segmentation step map B2, and determine whether the number and boundary position of the segmented regions are consistent with the second wrapping phase in step 3-2. The number and position of the wrapped wave peaks are consistent. If they are consistent, set ξ2=ξ2' and proceed to step 3-3-4. If they are inconsistent, 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 positions of the phase wrapping peaks, it is necessary to determine whether ξ1' or ξ2' needs to be reduced or increased based on the size of the set-1 region in the binarization; if the segmented regions overlap due to the set-1 region being too large, it is necessary to increase ξ1' or ξ2'; if the phase wrapping peaks at the edge of the image are not identified and involved in the region segmentation due to the set-1 region being too small, it is necessary to reduce ξ1' or ξ2' 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' take the median value of the value range, and let ξ1'=2.8rad, ξ2'=-0.3rad. If it does not meet the judgment requirements of step 3-3-1 or step 3-3-2, ξ1' and ξ2' are both reduced or increased by a change of 0.1rad.

[0032] Step 3-4: Extract the first wrapped phase The value corresponding to the A1 region in the second wrapping phase is extracted The values ​​corresponding to the A2 region are then concatenated to obtain the third wrapped phase distributed between [-π,π]rad

[0033] Step 3-5: Phase 3 wrapping Apply the phase unwrapping algorithm to obtain the relative phase distribution of the interference wavefront

[0034] Step 4: Perform Zernike polynomial fitting on the relative phase distribution of the interference wavefront obtained in step 3 to obtain the second coefficient a2 and the third coefficient a3 of the Zernike polynomial.

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

[0036] Combination Figure 2 The present invention can be used to detect the wavefront tilt of an astronomical optical interferometer telescope. The detection results are shown in Table 1:

[0037] Table 1 Wavefront tilt detection results

[0038]

[0039] The present invention proposes a method for extracting wavefront tilt of astronomical light interferometry. The wavefront tilt can be extracted from the interference pattern through two-dimensional envelope detection normalization, arccosine phase unwrapping and Zernike polynomial fitting. The method can be applied to the detection of wavefront tilt of astronomical light interferometry telescopes.

Claims

1. A method for extracting astronomical light interference wavefront tilt, characterized in that: Here are the steps: Step 1: Collect several synchronous phase-shifting interferograms Among them, a(x,y) represents the interference pattern background, b(x,y) represents the interference pattern modulation, represents the relative phase distribution of the two interfering wavefronts; Step 2: Preprocess the interference pattern obtained in step 1 by using two-dimensional envelope detection normalization, remove the background in the interference pattern and normalize the modulation degree to obtain the preprocessed interference pattern; Step 3: Perform arccosine phase unwrapping on the preprocessed interference pattern to obtain the relative phase distribution of the interference wavefront; Step 4: Perform Zernike polynomial fitting on the relative phase distribution of the interference wavefront obtained in step 3 to obtain the second coefficient a2 and the third coefficient a3 of the Zernike polynomial; Step 5: Calculate the wavefront inclination θ in the x and y directions using the second and third coefficients of the Zernike polynomial obtained in step 4. x =2a2 / a,θ y =2a3 / a, a represents the pupil radius, and the results of multiple synchronous phase-shifting interference patterns are averaged to improve the test accuracy.

2. The method for extracting astronomical light interference wavefront tilt according to claim 1, characterized in that: In step 2, the interference pattern obtained in step 1 is preprocessed by using two-dimensional envelope detection normalization to remove the background in the interference pattern and normalize the modulation degree to obtain the preprocessed interference pattern, as follows: Step 2-1: Extract the interference pattern in 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; in order to avoid losing the modulation information of the interference pattern, the extraction direction needs to be not completely parallel to the interference fringes; Step 2-2: For the obtained maximum and minimum values, interpolation and two-dimensional envelope surface fitting are performed 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 [] represents one-dimensional maximum extraction function, ODE min [] represents a one-dimensional minimum extraction function, IF{} represents a two-dimensional interpolation envelope fitting function; Step 2-3: Interpolation fitting value I from the maximum value at the same pixel position max , the interpolation fitting value of the minimum value I min And the measured value I0, through Remove the background a(x, y) of I0 and normalize the modulation b(x, y) to obtain the preprocessed interference pattern 3. The method for extracting astronomical light interference wavefront tilt according to claim 2, characterized in that: In step 3, the preprocessed interference pattern is subjected to arccosine phase unwrapping 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 package phase distributed between [0,π]rad I1(x,y) is the interference pattern after preprocessing; Step 3-2: Phase the first package Take the inversion and get the second wrapped phase distributed between [-π, 0] rad Step 3-3: Phase the first package and the second wrapping phase Apply binarization and watershed segmentation transformation respectively, compare the differences between the two, and obtain the consistent area A1 and inconsistent area A2 of the two results; Step 3-4: Extract the first wrapped phase The value corresponding to the A1 region in the second wrapping phase is extracted The values ​​corresponding to the A2 region are then concatenated to obtain the third wrapped phase distributed between [-π,π]rad Step 3-5: Phase 3 Apply the phase unwrapping algorithm to obtain the relative phase distribution of the interference wavefront 4. The method for extracting astronomical light interference wavefront tilt according to claim 3, characterized in that: In step 3-3, for the first package phase and the second wrapping phase Apply binarization and watershed segmentation transformation respectively, compare the differences between the two, and obtain the consistent area A1 and inconsistent area A2 of the two results, as follows: When binarizing, let the first wrapped phase The threshold is ξ1, and the second wrapping phase The threshold is ξ2, the value of ξ1 is [2.6, 3.1] rad, and the value of ξ2 is [-0.5, -0.1] rad. The specific judgment method is as follows: Step 3-3-1: Set the empirical threshold ξ1', and perform the first package phase Perform binarization and watershed segmentation transformation to obtain the regional segmentation step map B1, and determine whether the number and boundary position of the segmented regions are consistent with the first wrapped phase in step 3-1. The number and position of the wrapped wave peaks are consistent. If they are consistent, set ξ1 = ξ1' and proceed to step 3-3-2. If they are inconsistent, proceed to step 3-3-3. Step 3-3-2: Set the empirical threshold ξ2', and perform the second package phase Perform binarization and watershed segmentation transformation to obtain the regional segmentation step map B2, and determine whether the number and boundary position of the segmented regions are consistent with the second wrapping phase in step 3-2. The number and position of the wrapped wave peaks are consistent. If they are consistent, set ξ2 = ξ2' and proceed to step 3-3-4. If they are inconsistent, proceed to step 3-3-3. Step 3-3-3: If the number and boundary positions of the segmented regions are inconsistent with the number and positions of the phase wrap peaks, it is necessary to determine whether ξ1' or ξ2' needs to be reduced or increased by the size of the 1 region in the binarization; if the segmented regions overlap due to the 1 region being too large, it is necessary to increase ξ1' or ξ2'; If the phase wrapping peak at the edge of the image is not identified and used for regional segmentation because the area set to 1 is too small, then ξ1' or ξ2' needs to be reduced until the requirement is 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 astronomical light interference wavefront tilt according to claim 4, characterized in that: Assume ξ1'=2.8rad, ξ2'=-0.3rad. If the judgment requirements of step 3-3-1 or step 3-3-2 are not met, ξ1' and ξ2' are both reduced or increased by a change of 0.1rad.

6. The method for extracting astronomical light interference wavefront tilt according to any one of claims 1 to 5, characterized in that: It can be used to extract the wavefront tilt of astronomical optical interferometer telescope.

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