Ultra memory gradient iterative wavefront phase recovery method based on pyramid wavefront sensor

Abstract

The present application relates to a kind of super memory gradient iterative wavefront phase recovery method based on pyramid wavefront sensor.The pyramid wavefront sensor has the advantages of high sensitivity to the low-frequency component of the main influence of atmospheric turbulence, adjustable spatial sampling rate, and easy to adjust the detection dynamic range.In order to obtain high angular resolution and strong light collection ability, ground-based astronomical telescopes are in the trend of developing and building super large aperture, which leads to further increase the calculation load of distortion phase recovery, and the phase recovery algorithm needs to consider the real-time wavefront reconstruction and the quality of wavefront reconstruction simultaneously, which poses new challenges.Based on this, the present application proposes a super memory gradient iterative phase recovery method based on pyramid wavefront sensor, which can fully utilize multiple gradient information to calculate the next iteration point, while requiring less memory, and has certain advantages in solving large-scale phase recovery problems brought by large aperture telescopes in the future.

Description

Technical Field

[0001] This invention belongs to the field of wavefront sensing in optical technology, and specifically relates to a super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor. Background Technology

[0002] Large-aperture ground-based astronomical telescopes are the primary tools astronomers use to observe the universe, detect celestial information, and trace the evolution of spacetime. During ground-based observations, atmospheric turbulence causes fluctuations in the air's refractive index, resulting in irregular distortion of the light emitted by celestial bodies and blurred images. Adaptive optics systems can compensate for some of the wavefront distortion caused by atmospheric turbulence and restore the wavefront phase in real time, which is crucial for improving the clarity and resolution of telescope-observed images. The system mainly consists of three parts: wavefront sensing, wavefront control, and wavefront correction. Among these, the wavefront sensor is mainly used to detect the distorted phase information of the dynamically incident wavefront in real time; its accuracy is the foundation for the overall operation of the adaptive optics system.

[0003] In recent years, pyramidal wavefront sensors have gained favor among many international astronomical telescope research teams, and many telescope systems use them as the primary wavefront sensor. Compared with the classic Shaker-Hartmann wavefront sensor, the pyramidal wavefront sensor has advantages such as high sensitivity in detecting low-frequency components that are the main influence of atmospheric turbulence, adjustable sampling rate of the detection space, and easy adjustment of the detection dynamic range. The core of pyramidal wavefront sensing technology is a static or oscillating pyramidal optical element that splits the incident light into four sub-beams. These sub-beams propagate in different directions onto the detection plane, and wavefront aberration information can be calculated based on the intensity differences of the separated light spots on the detection plane.

[0004] As the aperture of telescopes increases, their light-gathering power and angular resolution continuously improve, allowing astronomers to observe increasingly distant celestial bodies and obtain richer image details. However, the application of extremely large aperture telescopes further increases the computational burden of phase restoration, posing new challenges to phase restoration algorithms that need to simultaneously consider the real-time performance and quality of wavefront reconstruction.

[0005] To address the aforementioned problems, this invention further extends the conjugate gradient linear iterative phase restoration algorithm, proposing a super-memory gradient iterative wavefront phase restoration method based on a pyramidal wavefront sensor. This algorithm fully utilizes multiple gradient information to calculate the next iteration point during the iteration process, exhibiting good global convergence. Furthermore, the algorithm does not require storing matrices during phase restoration, thus reducing memory requirements. This presents a significant advantage in addressing large-scale phase restoration problems arising from extremely large-aperture ground-based astronomical telescopes. Summary of the Invention

[0006] To overcome the shortcomings of existing wavefront reconstruction techniques, this invention provides a super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor.

[0007] The technical solution adopted in this invention is as follows:

[0008] A super-memory gradient iterative wavefront phase reconstruction method based on a pyramidal wavefront sensor is proposed, which achieves wavefront reconstruction through the following steps:

[0009] Step 1: Obtain the Zernike coefficients of each order from the simulation and the corresponding atmospheric turbulence images, where each Zernike coefficient is represented as A = [a1, a2, ..., a...]. n Atmospheric turbulence images are represented as follows:

[0010] Step 2: Input the distorted wavefront caused by atmospheric turbulence into the pyramidal wavefront sensor to acquire the sensor image data I. 00 I 01 I 10 I 11 Calculate the wavefront slope S in the x and y directions for each pixel. x S y ;

[0011] Step 3: Based on the simplified linear relationship between the wavefront slope measured by the sensor and the distorted wavefront S=Qφ, calculate the pyramidal wavefront sensor operator Q, and simultaneously obtain the normal equation Q. * Qφ=Q * S;

[0012] Step 4: Set the initial phase φ0, and the positive integer M. ρ is a constant factor, simplifying the linear error ε, the number of iterations k = 0, and constants δ and L0;

[0013] Step 5: Calculate the initial gradient g0 = S - Qφ0, G0 = Q * g0;

[0014] Step 6: Begin the iterative calculation process in Iterative phase φ k+1 =φ k +α k d k , where α k Let g be the step size, and g be the iterative gradient. k =S-Qφ k G k =Q * g k k = k + 1, and repeat the above iterative process;

[0015] Step 7: When the stopping condition ||G is met k When ||≤ε, exit the iteration and obtain the reconstructed wavefront.

[0016] Furthermore, the method for obtaining simulated atmospheric turbulence data is as follows: Based on Kolmogorov's statistical turbulence theory, the telescope pupil diameter D, Fried parameter r0, and Zernike order n are set. Corresponding Zernike coefficients of various orders are generated from different turbulence intensities (D / r0). This forms a simulated atmospheric turbulence screen.

[0017] Furthermore, the wavefront sensor employs a pyramidal wavefront sensor, where incident light generates four sub-pupil images I after passing through the pyramid. 00 I 01 I 10 I 11 Wavefront slope S x S y The calculation formula is:

[0018]

[0019]

[0020] The expression for I0 is: I0 is the average light intensity on the detector plane;

[0021] Then, the wavefront slope S x S y Normalize the slopes so that the RMS value of all slopes is 1.

[0022] Furthermore, the pyramidal wavefront sensor operator is represented as follows: in n, c, l represent the three cases of the pyramidal wavefront sensor: no modulation, circular modulation, and linear modulation, respectively. χ Ω (x,y) represents the telescope aperture mask, k n (x) = 1, k c (x)=J0(α λ x), k l (x)=sinc(α λ x), Modulation parameters r is the modulation radius, λ is the wavelength, and D is the diameter of the telescope pupil.

[0023] Furthermore, α k Using a fixed step size formula in

[0024] Furthermore, during the phase restoration process, solutions are calculated separately for the x and y directions, and the final reconstructed wavefront is the average of the solutions in both directions.

[0025] The advantages of this invention compared to the prior art are:

[0026] (1) The wavefront sensor of the present invention adopts a quadrangular pyramidal wavefront sensor. Compared with the traditional Shake-Hartmann wavefront sensor, the pyramidal wavefront sensor has the advantages of high sensitivity, real-time adjustment of sampling in the pupil plane, easy continuous adaptation of dynamic range, and suitability for weak light detection applications.

[0027] (2) This invention proposes a super-memory gradient iterative wavefront phase restoration method based on a pyramidal wavefront sensor. The super-memory gradient linear iterative algorithm is used to quickly calculate the phase using the current point gradient and the gradient information of several previous points, and finally realizes the distortion wavefront phase restoration.

[0028] (3) The phase restoration algorithm of this invention is a further extension of the conjugate gradient linear iterative algorithm, which makes full use of multiple gradient information to calculate the next iteration point and has good global convergence. In addition, no matrix storage is required during the solution process, thus reducing memory requirements. This gives it an advantage in dealing with large-scale phase restoration problems caused by extremely large aperture ground-based astronomical telescopes in the future. Attached Figure Description

[0029] Figure 1 This is a classic optical path propagation diagram of a pyramidal wavefront sensor, where 1 is a laser, 2 is distortion turbulence, 3 is a focusing lens, 4 is a pyramidal lens, 5 is an imaging lens, and 6 is a CCD camera.

[0030] Figure 2 This is a flowchart of the super-memory gradient iterative wavefront phase restoration method based on a pyramidal wavefront sensor according to the present invention.

[0031] Figure 3 This is the pseudocode for the super-memory gradient iterative phase recovery algorithm. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0033] This invention relates to an optical system for wavefront sensing based on a pyramidal wavefront sensor, such as... Figure 1As shown, the system includes a laser 1, a focusing lens 3, a pyramidal lens 4, an imaging lens 5, and a CCD camera 6. In this embodiment, the laser wavelength of the laser 1 is 650 nm, the resolution of the distorted turbulence 2 plane is 160×160, the resolution of the pyramidal wavefront sensor imaging at the CCD is 200×200, the pixel size is 10 μm, and the phase restoration algorithm adopts the super-memory gradient linear iterative algorithm.

[0034] Figure 2 This is a flowchart illustrating the workflow of a super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor. Figure 3 The pseudocode for the super-memory gradient iterative phase recovery algorithm is as follows:

[0035] Step 1: Set the turbulence intensity D / r0 = 10, and obtain the corresponding first 65 Zernike coefficients (excluding the 0th-order piston term) and the simulated atmospheric turbulence image. The Zernike coefficients are represented as A = [a1, a2, ..., a...]. 65 Atmospheric turbulence distortion wavefront is represented as

[0036] Step 2: Input the distorted wavefront corresponding to the simulated atmospheric turbulence into the pyramidal wavefront sensor to acquire the sensor image data I. 00 I 01 I 10 I 11 Secondly, the wavefront slope S in the x and y directions corresponding to each pixel is calculated. x S y Wavefront slope S x S y The calculation formula is:

[0037]

[0038]

[0039] The expression for I0 is: I0 is the average light intensity on the detector plane;

[0040] Then, the wavefront slope S x S y Normalize the slopes so that the RMS value of all slopes is 1.

[0041] Step 3: Based on the simplified linear relationship between the wavefront slope and the distorted wavefront measured by the sensor, S = Qφ, this case uses an unmodulated pyramidal wavefront sensor, and the operator is expressed as follows: in k n (x)=1, χ Ω(x,y) represents the telescope aperture mask, and the normal equation Q is obtained simultaneously. * Qφ=Q * S;

[0042] Step 4: Set the initial phase φ0 = 0, positive integer M = 4, ρ = 0.001, and simplified linear error ε = 1 × 10⁻⁶. -4 The iteration number k = 0, the constant δ = 0.001, and L0 = 1 × 10 -4 ;

[0043] Step 5: Calculate the initial gradient g0 = S - Qφ0, G0 = Q * g0;

[0044] Step 6: Begin the iterative calculation process in Iterative phase φ k+1 =φ k +α k d k The calculation is performed using the fixed step size formula. Iterative gradient g k =S-Qφ k G k =Q * g k k = k + 1, and repeat the above iterative process.

[0045] Step 7: When the stopping condition ||G is met k When ||≤ε, exit the iteration. The iteration is then performed to solve for φ in the x and y directions respectively. x φ y The final reconstructed wavefront is the average of the solutions in the two directions.

[0046] The above description represents a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All design schemes that fall within the scope of the present invention's concept are within the scope of protection of the present invention.

Claims

1. A super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor, characterized in that, This method achieves wavefront reconstruction through the following steps: Step 1: Obtain the simulated Zernike coefficients of each order and the corresponding atmospheric turbulence images, where the Zernike coefficients of each order are represented as follows: Atmospheric turbulence images are represented as ; Step 2: Input the distorted wavefront caused by atmospheric turbulence into the pyramidal wavefront sensor to acquire the sensor image data. Calculate the corresponding value of each pixel. , directional wavefront slope , ; Step 3: Calculate the simplified linear relationship between the wavefront slope and the distorted wavefront based on sensor measurements. Calculate the operator of the pyramidal wavefront sensor At the same time, the normal equation is obtained. ; The pyramidal wavefront sensor operator is represented as follows ,in , These represent three cases for the pyramidal wavefront sensor: no modulation, circular modulation, and linear modulation. For telescope aperture mask, , , , modulation parameters , For the modulation radius, For wavelength, The diameter of the telescope's pupil; Step 4: Set the initial phase , positive integer , , As a constant factor, simplifying linear error Number of iterations ,constant , ; Step 5: Calculate the initial gradient , ; Step 6: Begin the iterative calculation process ,in Iterative phase ,in Step size, iterative gradient , , Repeat the above iterative process; Step 7: When the stopping condition is met When exiting the iteration, we obtain , Obtain the reconstructed wavefront .

2. The super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor according to claim 1, characterized in that, The method for obtaining simulated atmospheric turbulence data is as follows: based on Kolmogorov's statistical turbulence theory, the telescope pupil diameter is set. Fried parameters Zernike order Due to different turbulence intensities Generate the corresponding Zernike coefficients of each order, by Create a simulated atmospheric turbulence screen.

3. The super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor according to claim 1, characterized in that, The wavefront sensor uses a pyramidal wavefront sensor, where incident light generates four sub-pupil images after passing through the pyramid. wavefront slope , The calculation formula is: in, The expression is: , The average light intensity on the detector plane; Then, the wavefront slope , Normalize the slopes so that the RMS value of all slopes is 1.

4. The super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor according to claim 1, characterized in that, Using a fixed step size formula ,in .

5. The super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor according to claim 1, characterized in that, The linear operator of the pyramidal wavefront sensor is obtained under approximate conditions, and there is a certain approximation error during the reconstruction process. Therefore, it is necessary to set a stopping condition. When the stopping condition is met When that happens, exit the iteration.

6. The super-memory gradient iterative wavefront phase recovery method based on a pyramidal wavefront sensor according to claim 1, characterized in that, During the phase restoration process, respectively targeting , The solution is obtained by considering the directions, and the final reconstructed wavefront is the average of the solutions from the two directions. .

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