CN115183886A - Wavefront sensor based on defocused grating array - Google Patents

Abstract

The invention discloses a wavefront sensor based on a defocus grating array, which utilizes the defocus grating array to simultaneously realize the aperture division of the beam to be measured and the generation of ±1-order defocused light spots in the sub-apertures. The first-order defocus spot image can extract the wavefront slope information and high-order aberration mode coefficients in the sub-aperture, and realize high-resolution measurement of the wavefront in the sub-aperture. Compared with the traditional Shack-Hartmann wavefront sensor, the present invention can extract more detailed distribution information in the sub-aperture, so the wavefront can be recovered with higher accuracy under the same sub-aperture condition, or under the same recovery accuracy. The wavefront restoration is completed with a smaller number of sub-apertures, thus providing a new technical approach for the fields of low-light and high-precision wavefront detection.

Description

A wavefront sensor based on defocus grating array

technical field

The invention belongs to the technical field of wavefront detection, and in particular relates to a wavefront sensor based on a defocus grating array.

Background technique

Wavefront detection has always been one of the research hotspots in the optical field, and phase measurement is involved in many fields such as astronomical observation, optical detection, medical imaging, and adaptive optics. The existing mainstream phase measurement methods are mainly divided into three categories: interferometry, direct measurement and indirect measurement based on intensity distribution. Each type of method has its own unique advantages and is used in different occasions.

The defocus grating is essentially an off-axis Fresnel zone plate, which has the prism function of an ordinary grating, splits the incident wavefront on different diffraction orders of the grating, and has the lens function of the Fresnel zone plate at the same time. , introducing different lens effects at different diffraction orders. Finally, the input wavefront has a symmetrical distribution of ±1st-order diffraction optical axes, and has equal focal lengths, one positive and one negative, on the ±1st order.

The Shack-Hartmann wavefront sensor mainly divides and samples the wavefront through the microlens array. After passing through the microlens array, the sub-wavefront is focused on the photodetector to form a light spot array diagram. The measurement accuracy is related to the spatial sampling rate. There are inherent contradictions that limit the measurement performance of the Shack-Hartmann wavefront sensor. The curvature wavefront sensor calculates the normalized difference of the light intensity before and after the focusing lens, which is proportional to the wavefront curvature inside the pupil, but the curvature wavefront sensor cannot measure high-order information, which limits its development. Therefore, it is urgent to find a low-space sampling wavefront detection technology route with high detection accuracy and robustness.

Combining the characteristics of the defocus grating, the principle of the curvature wavefront sensor and the structure of the Hartmann wavefront sensor, a defocus grating array wavefront sensor is proposed. The defocus grating is introduced into a single sub-aperture to phase the incident wavefront. Modulation to obtain a ±1-order defocused spot on its focal plane, combined with the principle of the curvature wavefront sensor, to obtain the information of a single wavefront, and finally restore the wavefront according to the restoration matrix and the wavefront information in a single sub-aperture.

SUMMARY OF THE INVENTION

The technical problems to be solved by the present invention are: the inherent contradiction between the measurement accuracy of the Shack-Hartmann wavefront sensor and the spatial sampling rate, and the problem that the curvature wavefront sensor cannot detect the high-order information of the wavefront. Complete high-precision wavefront restoration under the condition of low spatial sampling, and restore higher-order wavefront aberration information with higher precision under the same sub-aperture condition.

The technical solution adopted by the present invention to solve the above technical problems is: a wavefront sensor based on a defocus grating array, the wavefront sensor adopts the defocus grating array to perform aperture division and phase modulation of the beam to be measured to form a ±1 order diffraction array, Then use the microlens array to focus the ±1-order diffraction array to form a ±1-order defocused spot array; the wavefront sensor mainly includes three parts: a defocus grating array, a microlens array and a photodetector;

The gratings in the defocus grating array are phase-type defocus gratings, which are used for aperture division of the beam to be measured to form a number of sub-apertures and phase modulation of the wavefront in the sub-aperture; let the wavefront before modulation of a single sub-aperture be φ _j (x, y), j is the sub-aperture number, and the phase shift function of the wavefront modulation in the sub-aperture is φ _m (x, y), then for the jth sub-aperture modulated wavefront φ' _j (x ,y) is:

_φ'j (x,y)＝ _φj (x,y)+ _φm (x,y)

Among them, x, y are the coordinates of the defocus grating;

The microlens array is located behind the defocusing grating array and corresponds to the defocusing grating array one-to-one. The microlens array focuses the light beam modulated by the defocusing grating array, forming ±1 on the focal plane. stage defocused spot array;

The photodetector is located at the focal plane of the microlens array, and detects ±1-order defocus spot image data within each sub-aperture, and the de-focus spot image data is used to calculate higher-order orders in the sub-aperture using the curvature wavefront restoration method Aberration information and reconstruction of full aperture high-resolution wavefronts.

Further, the defocus grating array is greater than or equal to 2×2.

Further, the curvature wavefront restoration method is an eigenfunction wavefront restoration method based on two ±1-order defocused light spot images, including all methods for extracting wavefront information based on ±1-order defocused light spots.

Further, the photodetector may be a CCD, CMOS, or other array type detectors.

Compared with the prior art, the present invention has the following advantages:

In the present invention, the input wavefront is modulated by the defocus grating, and the modulated wavefront can obtain the information of the positive and negative focal planes on the focal plane of the microlens array. Combined with the wavefront recovery algorithm of the curvature wavefront sensor, a single sub-aperture can be obtained. Corresponding to the high-order information of the wavefront to improve the wavefront restoration accuracy; compared with the traditional Shack-Hartmann wavefront sensor restoration method, the present invention can restore the wavefront with higher accuracy under the same sub-aperture condition, and the sparse sub-aperture Under the condition of aperture, higher-order distorted wavefronts can be recovered with higher precision, and it is expected to be used for wavefront detection in the fields of weak light and high precision.

Description of drawings

FIG. 1 is a schematic structural diagram of a 2×2 defocus grating array wavefront sensor according to an embodiment of the present invention;

FIG. 2 is a phase diagram of a 2×2 defocus grating array according to an embodiment of the present invention;

Fig. 3 is the light intensity diagram of the wavefront to be measured and the focal plane in Embodiment 1 of the present invention, wherein (a) is the wavefront diagram to be measured, and (b) is the light intensity diagram of the focal plane;

4 is a wavefront restoration result according to Embodiment 1 of the present invention, wherein (a) is a restored wavefront graph according to Embodiment 1 of the present invention, and (b) is a residual graph of wavefront restoration according to Embodiment 1 of the present invention;

Fig. 5 is the restoration result of the traditional Shack-Hartmann wavefront sensor restoration algorithm, wherein (a) is the wavefront image restored by the mode method, and (b) is the residual image of the mode method wavefront restoration.

Detailed ways

In order to make the purpose and technical solution of the present invention clearer, the present invention will be further described in detail below with reference to the specific embodiment 1 and the accompanying drawings.

The present invention is a defocus grating array wavefront sensor. In the first embodiment, a 2×2 defocus grating array wavefront sensor is used. Its optical structure is shown in FIG. 1. The defocus grating performs phase modulation on the input wavefront. The defocus grating array 1 is located in front of the microlens array 2 , and the CCD 3 is located at the focal plane of the microlens array 2 . Among them, the defocus grating array and the microlens array are arranged in 2×2, the focal length of the microlens array is 50mm, the size of a single sub-aperture is 1200μm, and the wavelength of the light wave is 632.8nm.

The specific implementation is divided into two parts, as follows:

1. The modulation effect of the defocus grating on the incident wavefront is expressed as:

The defocus grating is a binary phase modulation plate, and the phase shift function φ'(x, y) satisfies the following relationship:

Among them, x, y are the coordinates of the defocused grating, and x ₀ is the offset of the defocused grating.

In the first embodiment, the wavefront to be measured includes the first 16 eigenfunction aberrations, the pupil is a rectangle with a length a and a width b, and the analytical expression of the eigenfunction on the rectangular area is:

其中m,n＝0、1、2、3…The corresponding eigenvalues are

where m,n=0, 1, 2, 3...

Then the input wavefront can be represented by the eigenfunction as:

Among them, Wi represents the phase difference of the eigenfunction of the _ith order, a _i is the coefficient of the eigenfunction of the ith order, and the wavefront is represented by the eigenfunction of the L order in total.

The phase of the wavefront to be measured is modulated by the defocus grating, and after passing through the microlens array, positive and negative defocus light intensity images are formed on the CCD of its focal plane. The phase of the defocus grating array is shown in Figure 2. The measured wavefront is shown in Fig. 3(a), and the positive and negative defocused light intensity images formed on the CCD on the focal plane are shown in Fig. 3(b).

Let the wavefront before the modulation of the jth sub-aperture be φ _j (x, y), and the phase shift function of the modulation of the wave front in the sub-aperture is φ _m (x, y), then the wavefront after modulation of the jth sub-aperture is _φ'j (x,y) is:

_φ'j (x,y)＝ _φj (x,y)+ _φm (x,y)

2. The wavefront recovery process of the wavefront detector based on the defocus grating array is as follows:

Step 1: Solve for the wavefront information

The input wavefront can be represented by the eigenfunction as:

Wherein, Wi represents the phase difference of the eigenfunction of the _ith order, a _ij is the coefficient of the eigenfunction of the ith order, and the wavefront is represented by the eigenfunction of the kth order in total.

After the modulated wavefront, the light intensity information I ₊ , I- of the positive and negative defocal planes with a transmission distance of δz can be obtained on the focal plane of a single sub-aperture. Define S(x,y) as:

Among them, k is the wave vector, and I ₀ is the near-field light intensity information.

Then, according to the wavefront recovery algorithm of the curvature wavefront sensor, the wavefront information in a single sub-aperture can be recovered. The specific method is as follows:

Among them, Wi is the eigenfunction basis of the _ith order, c _i =∫ _σ Wi ₍ x,y)dσ is the normalization coefficient of the eigenfunction basis of the ith order, and λ _i corresponds to the basis of the eigenfunction basis eigenvalue.

From this, the coefficient of each order eigenfunction can be obtained, and then the wavefront information in a single sub-aperture can be obtained.

Step 2: Solve the coefficient vector for the subaperture

将各个子孔径的系数按列排列为一个列向量A，则A矩阵的转置矩阵

计算得到的子孔径的系数向量A将用于步骤4中的全口径波前重构。According to the method in step 1, the wavefront information in each sub-aperture can be solved, and the wavefront information in a single sub-aperture can be expressed as a _i,j , where i is the order information, j is the sub-aperture number, then the jth The wavefront information in the sub-apertures is expressed as

Arrange the coefficients of each sub-aperture into a column vector A, then the transpose matrix of the A matrix

The calculated coefficient vector A of the sub-aperture will be used for the full-aperture wavefront reconstruction in step 4.

Step 3: Solve the full aperture recovery matrix

To solve the restoration matrix of the eigenfunction of the full aperture, the number of effective sub-apertures is j, then j=1, 2, 3...n. As above, denote the wavefront information of each sub-aperture as A _j . The full aperture wavefront is represented by the eigenfunctions of order m in total, and the information A _i of each wavefront corresponding to the eigenfunctions of different orders m is represented as A _i,j , i=1, 2, 3 ...m, then the full aperture restoration matrix D composed of A _{i, j} is:

Here, j corresponds to the effective sub-aperture number j=1, 2, 3...n in the wavefront detector of the defocus grating array, and i corresponds to the order number i=1, 2, 3...m of the eigenfunction. Each matrix element contains a column vector A _j of coefficients of the eigenfunction of the wavefront, and D is a matrix of 6×i rows and j columns.

Convert the full aperture restoration matrix D into a pseudo-inverse matrix D ⁺ , and store the data of the pseudo-inverse matrix D ⁺ into the computer system for wavefront restoration. Will be used for full aperture wavefront reconstruction in step 4.

Step 4: Full Aperture Wavefront Reconstruction

The full-aperture wavefront φ ₀ (x, y) is expressed as a linear superposition pattern of coefficients of various order eigenfunctions calculated from the full-aperture restoration matrix:

Among them, a' _i is the coefficient of each eigenfunction obtained by calculation, i=1, 2, 3...m.

When the wavefront detector of the defocus grating array detects the full-aperture wavefront φ ₀ (x, y), according to the coefficient vector calculated by the restoration algorithm of the curvature wavefront sensor in step 2 and the restoration matrix calculated in step 3 The pseudo-inverse matrix D ⁺ of D satisfies the following relation:

a' _i =D ⁺ ·A

The calculation of the wavefront restoration can calculate and reconstruct the full-aperture wavefront information φ ₀ (x, y) according to the above mathematical relationship.

The final output restored wavefront is shown in Figure 4 (a) (RMS=2.6344rad, PV=10.4121rad), and the wavefront restoration residual is shown in Figure 4 (b) (RMS=0.0308rad, PV=0.1161rad) As shown, the RMS value and PV value are respectively 1.17% and 1.12% of the input wavefront, which can restore the wavefront well. In order to highlight the advantages of the present invention, in the first embodiment, under the same conditions, the model method is used The input wavefront is restored, and the restoration result is shown in Figure 5, where (a) is the wavefront restored by the mode method (RMS=0.4434rad, PV=1.9403rad), (b) is the residual error of the mode method restoration (RMS =2.5154rad, PV=8.5746rad), the RMS value and the PV value are respectively 567.3% and 441.92% of the input wavefront, and the distorted wavefront cannot be effectively restored. The above results fully prove that the present invention can restore the wavefront with high precision under the condition of 2×2 sub-apertures, and the wavefront restoration accuracy is hardly affected by the number of sub-apertures.

The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited to this, any person familiar with the technology can understand the transformation or replacement that comes to mind within the technical scope disclosed by the present invention, All should be included within the scope of the present invention.

Claims (4)

1. A wave front sensor based on an out-of-focus grating array is characterized in that: the wavefront sensor adopts an out-of-focus grating array to perform aperture segmentation and phase modulation on a light beam to be detected to form a +/-1-level diffraction array, and then utilizes a micro-lens array to focus the +/-1-level diffraction array to form a +/-1-level out-of-focus light spot array; the wavefront sensor mainly comprises three parts, namely a defocusing grating array, a micro-lens array and a photoelectric detector;

the gratings in the defocusing grating array are phase-type defocusing gratings and are used for carrying out aperture segmentation on the light beam to be detected so as to form a plurality of sub apertures and carrying out phase modulation on wavefront in the sub apertures; let the wavefront before single subaperture modulation be phi _j (x, y), j is the sub-aperture number, and the phase shift function for the wavefront modulation within the sub-aperture is φ _m (x, y), wavefront φ 'after modulating the jth sub-aperture' _j (x, y) is:

φ′ _j (x,y)＝φ _j (x,y)+φ _m (x,y)，

wherein x and y are coordinates of the defocused grating;

the micro lens array is positioned behind the defocusing grating array and corresponds to the defocusing grating array one by one, and focuses the light beams modulated by the defocusing grating array to form a +/-1-level defocusing light spot array on a focal plane of the micro lens array;

the photoelectric detector is positioned on the focal plane of the micro-lens array and is used for detecting +/-1-level defocusing spot image data in each sub-aperture, and the defocusing spot image data is used for calculating high-order aberration information in the sub-apertures and reconstructing full-aperture high-resolution wavefront by using a curvature wavefront restoration method.

2. The wavefront sensor based on an out-of-focus grating array of claim 1, wherein: the defocused grating array is larger than or equal to 2 x 2.

3. The wavefront sensor based on an out-of-focus grating array of claim 1, wherein: the curvature wave front restoration method is an eigen function wave front restoration method based on two +/-1-level defocused light spot images, and comprises all methods for extracting wave front information based on +/-1-level defocused light spots.

4. The wavefront sensor based on an out-of-focus grating array of claim 1, wherein: the photodetector may be a CCD, CMOS, or other array type detector.

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