A method for extracting wavefront slope and curvature information based on Shack-Hartmann wavefront sensor

Abstract

The present invention discloses a method for extracting wavefront slope and curvature signals based on a Shack-Hartmann wavefront sensor. This method utilizes Fourier demodulation technology and the finite difference method to accurately obtain incident wavefront slope and curvature information, without any modulation devices, based on a conventional Shack-Hartmann wavefront sensor. Compared to conventional Shack-Hartmann wavefront sensors that only obtain wavefront slope information using a spatial centroid detection algorithm, the present invention simultaneously obtains wavefront slope and curvature information in the frequency domain, with fast calculation speed and simple processing. The present invention utilizes the traditional Shack-Hartmann wavefront sensor structure to improve light utilization, and the method exhibits strong noise immunity.

Description

Technical Field

[0001] The present invention belongs to the technical field of wavefront detection, and in particular relates to a method for extracting wavefront slope and curvature information based on a Shack-Hartmann wavefront sensor. Background Art

[0002] Phase measurement has long been a research hotspot in optics, affecting numerous fields, including astronomical observation, optical detection, medical imaging, and adaptive optics. Current mainstream phase measurement methods are categorized into three main types: interferometry, direct measurement, and indirect measurement based on intensity distribution. Each method has its own unique advantages and applications. Among them, the Shack-Hartmann wavefront sensor, with its fast measurement speed and high accuracy, has been widely used in various fields.

[0003] Traditional Shack-Hartmann wavefront sensors primarily segment and sample the wavefront through a microlens array, converging the sub-wavefronts onto the imaging CCD behind them. The wavefront within the sub-aperture is typically considered to contain only tilt aberrations. A centroid detection algorithm is then used based on geometric relationships to calculate the wavefront tilt and reconstruct the distorted wavefront. However, this assumption is subject to error; the local wavefront corresponding to the sub-aperture should strictly be a curved surface. Consequently, the wavefront slope information obtained by the centroid detection algorithm introduces some wavefront reconstruction errors, significantly reducing measurement accuracy.

[0004] Therefore, improving the detection performance of Shack-Hartmann wavefront sensors has been a hot topic of research. Some researchers have proposed using methods such as the GS algorithm and phase difference method to recover the wavefront based on the intensity distribution of the light spot. However, when the incident wavefront is significantly distorted and the signal-to-noise ratio of the detection signal is low, it is difficult to effectively obtain comprehensive wavefront information and thus reconstruct the wavefront. Therefore, a Shack-Hartmann wavefront detection technology with high detection accuracy and good robustness is currently needed. Summary of the Invention

[0005] The technical problems to be solved by the present invention are: to resolve the inherent contradiction that the Shack-Hartmann wavefront sensor can only detect the wavefront slope without a modulation device; to fully utilize the intensity distribution information of the spot array and combine it with Fourier demodulation technology and the finite difference method, so as to obtain the wavefront slope and curvature signals with high precision on the basis of the traditional Shack-Hartmann wavefront sensor, and to propose a method for extracting wavefront slope and curvature information based on the Shack-Hartmann wavefront sensor.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] A method for extracting wavefront slope and curvature information based on a Shack-Hartmann wavefront sensor. This method uses the intensity distribution of the light spot formed by the Shack-Hartmann wavefront sensor as input, combines Fourier demodulation technology with the finite difference method, and thus obtains the measured wavefront slope and curvature signals with high precision. The distorted wavefront is then reconstructed using a wavefront reconstruction algorithm. The method is specifically completed by the following steps:

[0008] Step 1: Record the image information of the light spot array of the wavefront to be measured, i.e., the far-field light intensity distribution I, through the Shack-Hartmann wavefront sensor and the photodetector CCD;

[0009] Step 2: Use discrete Fourier transform to perform Fourier transform on the spot array image information recorded in step 1 to obtain the spectrum distribution of the far-field light intensity distribution I represents the Fourier transform of I;

[0010] Step 3: Spectral distribution of the far-field light intensity distribution I obtained in step 2 The first-order spectra in the u and v directions are extracted using the set bandpass filter. and Then the extracted first-order spectrum in the u and v directions is moved to the center of the spectrum, and then the inverse Fourier transform is performed to obtain H 1，0 (x, y) and H 0，1 (x, y); u and v represent coordinates in the Fourier plane

[0011] Step 4: According to the law of energy conservation and the relationship between the first-order spectra in the u and v directions obtained in step 3 and the slope of the wavefront to be measured, the average slope of the subaperture in the x direction is obtained. Average slope in the (p, q) and y directions (p, q);

[0012]

[0013] Average slope The method to obtain (p, q) is:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] In the formula and They are I(x,y) and H (k,l) Fourier transform of (x,y), I(x,y) is the light intensity distribution, H (1，0，) (x, y) is the first harmonic information in the x direction; (x, y) is the coordinate system of the object plane, (u, v) is the coordinate system in the Fourier plane; (m, n) refers to the number of sampling points in the x and y directions, K is the order of the harmonic; k, l are the coordinate positions of the harmonics in the Fourier plane, is the first-order partial derivative of the wave surface in the x direction, which refers to the slope information, is the sampling interval, IMAGH 1，0 (x,y) is the pair H 1，0 (x, y) takes the imaginary part; (p,q) represents the slope of the (p,q) subaperture, represents the slope value of each point of the local wavefront in the (p,q) sub-aperture. The phase distribution of the wavefront to be measured is

[0021] Average slope The method to obtain (p, q) is:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] Where H (0，1) (x,y) is the first harmonic information in the y direction; is the first-order partial derivative of the wavefront to be measured in the y direction, which refers to the slope information, IMAGH 0，1 (x,y) is the pair H 0，1 (x, y) takes the imaginary part; (p,q) represents the slope of the (p,q) subaperture, Represents the slope value of each point of the local wavefront in the (p,q) sub-aperture;

[0029] Step 5: The average slope in the x direction obtained in step 4 Average slope in the (p, q) and y directions (p, q) uses the finite difference method to obtain the curvature signal of the wavefront to be measured in the x direction (the second-order partial derivative of the wavefront to be measured with respect to x) and the curvature signal of the wavefront to be measured in the y direction (the second-order partial derivative of the wavefront to be measured with respect to y), and then takes each sub-aperture as a unit to obtain the local curvature of the wavefront to be measured corresponding to the sub-aperture in the x direction. The local wavefront curvature to be measured corresponding to the (p, q) and y-direction sub-apertures (p,q)

[0030]

[0031]

[0032] In the formula is the second-order partial derivative of the wavefront to be measured in the x direction, is the wavefront curvature information, (m,n) is the discrete sampling point of the wavefront to be measured, (p,q) represents the wavefront curvature value to be measured at the sub-aperture (p,q), K1 and K2 represent the maximum and minimum values of curvature in the subaperture;

[0033]

[0034]

[0035] In the formula is the second-order partial derivative of the wavefront to be measured in the y direction, is the wavefront curvature information, (m,n) is the discrete sampling point of the wavefront to be measured, (p,q) represents the wavefront curvature value to be measured at the sub-aperture (p,q), K3 and K4 represent the maximum and minimum values of curvature in the subaperture;

[0036] Step 6: The average slope in the x direction obtained in step 4 Average slope in the (p, q) and y directions (p, q) and the curvature signal of the wavefront to be measured in the x direction and the curvature signal of the wavefront to be measured in the y direction obtained in step 5 are used to reconstruct the wavefront using the slope and curvature wavefront reconstruction algorithm, completing the extraction of the wavefront slope and curvature information based on the Shack-Hartmann wavefront sensor.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] (1) Compared with the traditional Shack-Hartmann wavefront sensor algorithm for obtaining the wavefront slope, the present invention can simultaneously obtain the distorted wavefront slope and curvature information with high precision without adding a modulation device, and can restore the distorted wavefront with high precision; the Fourier transform algorithm is used to process the obtained wavefront information, which has good noise resistance, simple operation, and improves the wavefront restoration rate; the invention only uses the traditional Shack-Hartmann sensor structure, which can improve the utilization rate of light energy and is expected to be used for wavefront detection in low light, high precision and other fields.

[0039] (2) The wavefront slope and curvature information can be obtained using a traditional Shack-Hartmann wavefront sensor, and the utilization rate of light can be increased without adding a modulation structure.

[0040] (3) The collected light intensity map can be Fourier transformed without constraints, and this algorithm has good noise resistance.

[0041] (4) It is relatively easy to extract the harmonics when operating in the frequency domain.

[0042] (5) With the support of theoretical formulas, it is easy to obtain the slope and curvature information of each sub-aperture of the wavefront, thereby reconstructing the wavefront with higher accuracy.

[0043] (6) The present invention discloses a method for extracting wavefront slope and curvature signals based on a Shack-Hartmann wavefront sensor. The method of the present invention uses Fourier demodulation technology and finite difference method to obtain incident wavefront slope and curvature information more accurately on the basis of the traditional Shack-Hartmann wavefront sensor without adding any modulation device. Compared with the traditional Shack-Hartmann wavefront sensor that only obtains wavefront slope information using the spatial centroid detection algorithm, the present invention obtains wavefront slope and curvature information simultaneously in the frequency domain, and has fast calculation speed and simple processing. The present invention uses the traditional Shack-Hartmann wavefront sensor structure to improve the utilization rate of light, and the method has strong anti-noise ability. The present invention provides a new technical approach for the fields of weak light, high-precision wavefront detection, and provides a new idea for future high-precision wavefront reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Flowchart of the method for extracting wavefront slope and curvature information based on the Shack-Hartmann wavefront sensor in the present invention;

[0045] Figure 2 Schematic diagram of the structure of the Shack-Hartmann wavefront sensor with incident distorted wavefront in the embodiment;

[0046] Figure 3 is a spot array diagram of the spherical aberration wavefront to be measured in the embodiment;

[0047] Figure 4is a Fourier transform spectrum diagram of the spot array of the spherical aberration wavefront to be measured in the embodiment;

[0048] Figure 5 is the original wavefront image containing a single aberration of spherical aberration;

[0049] Figure 6 is the restored wavefront diagram of the spherical aberration wavefront to be measured in the present invention;

[0050] Figure 7 This is the surface reconstruction error diagram of the present invention. DETAILED DESCRIPTION

[0051] In order to make the purpose and technical solutions of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0052] Figure 1 The flowchart of the method for extracting wavefront slope and curvature signals based on the Shack-Hartmann wavefront sensor of the present invention is shown in FIG. In actual operation, the traditional Shack-Hartmann wavefront sensor is still used, and its optical structure is as follows: Figure 2 A CCD detector is placed at the rear focal plane of the microlens array. The microlens array is arranged in a 40*40 pattern, with a sampling point of 51*51 in a single microlens. The aperture size of a single lens is 500 μm, and the focal length is 37 mm.

[0053] In the specific implementation, for the input wavefront represented by the Zernike polynomial, the light intensity distribution diagram is first obtained through the microlens array, and then the spectrum diagram of its light intensity is obtained through the discrete Fourier transform. Due to the fence effect produced by the discrete Fourier transform operation, this will introduce a certain wavefront tilt in the harmonic extraction due to the misalignment between the theoretical carrier frequency and the actual frequency. Therefore, in order to eliminate this effect and obtain wavefront information more accurately, actual simulation experiments can be used to eliminate this part of the influence.

[0054] Then, through a bandpass filter, the first-order spectra in the u and v directions are obtained, and they are moved to the center of the spectrum plane respectively. According to the algorithm steps combining Fourier demodulation and the finite difference method, the wavefront slope and curvature information in the x and y directions are obtained, and then the slope and curvature information of the local wavefront corresponding to each sub-aperture is obtained.

[0055] Finally, the slope and curvature mixed wavefront reconstruction algorithm is used to reconstruct the distorted wavefront, and the final output restored wavefront is as follows Figure 7As shown in the figure, the PV is 0.0181 rad, and the relative reconstruction error of the wavefront is 0.0142, less than 5%. Therefore, the wavefront can be well restored. The method of the present invention also has good noise immunity. When the noise level of Gaussian white noise is less than 10%, the simulation results show that the measurement repeatability is also good, and the relative reconstruction error is less than 2%.

[0056] Example

[0057] A method for extracting wavefront slope and curvature information based on Shack-Hartmann wavefront sensor, such as Figure 1 As shown, the method is specifically completed by the following steps:

[0058] Step 1: The distorted surface wave is incident on the Shack-Hartmann wavefront sensor, as shown in Figure 2 As shown, the Shack-Hartmann wavefront sensor and the photodetector CCD record the image information of the light spot array of the wavefront to be measured, and the spherical aberration wavefront is incident on the Shack-Hartmann wavefront sensor to obtain the light spot array image of the spherical aberration wavefront to be measured as shown in FIG. Figure 3 As shown, that is, the far-field light intensity distribution I;

[0059] Step 2: Use discrete Fourier transform to perform Fourier transform on the spot array image information recorded in step 1 to obtain the spectrum distribution of the far-field light intensity distribution I like Figure 4 As shown, Represents the Fourier transform of I; Step 3: Spectrum distribution of the far-field light intensity distribution I obtained in step 2 The first-order spectra in the u and v directions are extracted using the set bandpass filter. and Then the extracted first-order spectrum in the u and v directions is moved to the center of the spectrum, and then the inverse Fourier transform is performed to obtain H 1，0 (x, y) and H 0，1 (x, y); u and v represent coordinates in the Fourier plane;

[0060] Step 4: According to the law of energy conservation and the relationship between the first-order spectra in the u and v directions obtained in step 3 and the slope of the wavefront to be measured, the average slope of the subaperture in the x direction is obtained. Average slope in the (p, q) and y directions (p, q);

[0061]

[0062] Average slope The method to obtain (p, q) is:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] In the formula and They are I(x,y) and H (k,l) Fourier transform of (x,y), I(x,y) is the light intensity distribution, H (1，0，) (x, y) is the first harmonic information in the x direction; (x, y) is the coordinate system of the object plane, (u, v) is the coordinate system in the Fourier plane; (m, n) refers to the number of sampling points in the x and y directions, K is the order of the harmonic; k, l are the coordinate positions of the harmonics in the Fourier plane, is the first-order partial derivative of the wave surface in the x direction, which refers to the slope information, is the sampling interval, IMAGH 1，0 (x,y) is the pair H 1，0 (x, y) takes the imaginary part; (p,q) represents the slope of the (p,q) subaperture, represents the slope value of each point of the local wavefront in the (p,q) sub-aperture. The phase distribution of the wavefront to be measured is

[0070] Average slope The method to obtain (p, q) is:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] Where H (0，1) (x,y) is the first harmonic information in the y direction; is the first-order partial derivative of the wavefront to be measured in the y direction, which refers to the slope information, IMAGH 0，1 (x,y) is the pair H0，1 (x, y) takes the imaginary part; (p,q) represents the slope of the (p,q) subaperture, Represents the slope value of each point of the local wavefront in the (p,q) sub-aperture;

[0078] Step 5: The average slope in the x direction obtained in step 4 Average slope in the (p, q) and y directions (p, q) uses the finite difference method to obtain the curvature signal of the wavefront to be measured in the x direction (the second-order partial derivative of the wavefront to be measured with respect to x) and the curvature signal of the wavefront to be measured in the y direction (the second-order partial derivative of the wavefront to be measured with respect to y), and then takes each sub-aperture as a unit to obtain the local curvature of the wavefront to be measured corresponding to the sub-aperture in the x direction. The local wavefront curvature to be measured corresponding to the (p, q) and y-direction sub-apertures (p,q)

[0079]

[0080]

[0081] In the formula is the second-order partial derivative of the wavefront to be measured in the x direction, is the wavefront curvature information, (m,n) is the discrete sampling point of the wavefront to be measured, (p,q) represents the wavefront curvature value to be measured at the sub-aperture (p,q), K1 and K2 represent the maximum and minimum values of curvature in the subaperture;

[0082]

[0083]

[0084] In the formula is the second-order partial derivative of the wavefront to be measured in the y direction, is the wavefront curvature information, (m,n) is the discrete sampling point of the wavefront to be measured, (p,q) represents the wavefront curvature value to be measured at the sub-aperture (p,q), K3 and K4 represent the maximum and minimum values of curvature in the subaperture;

[0085] Step 6: The average slope in the x direction obtained in step 4 Average slope in the (p, q) and y directions (p, q) and the curvature signal of the wavefront to be measured in the x direction and the curvature signal of the wavefront to be measured in the y direction obtained in step 5 are used to reconstruct the wavefront using the slope and curvature wavefront reconstruction algorithm, completing the extraction of the wavefront slope and curvature information based on the Shack-Hartmann wavefront sensor.

[0086] The wavefront slope and curvature information extracted by the above method are used to reconstruct the wavefront to obtain the restored wavefront diagram of the spherical aberration wavefront to be measured, as shown in Figure 6 As shown, the original wavefront diagram containing spherical aberration is as follows Figure 5 As shown, Figure 6 and Figure 5 By comparison, we can get the surface reconstruction error diagram as shown in the figure below: Figure 7 As shown, according to Figure 7 It can be seen that the PV is 0.0181 rad and the relative reconstruction error of the wavefront is 0.0142, which is less than 5%.

[0087] Therefore, the wavefront can be restored better, and the method of the present invention has good noise resistance. When the noise level is less than 10% of Gaussian white noise, 10 simulations are performed at each noise level. The simulation results show that the measurement repeatability is also good, and the relative reconstruction error is less than 2%.

Claims

1. A method for extracting wavefront slope and curvature information based on a Shack-Hartmann wavefront sensor, characterized by the steps of include: Step 1: Record the image information of the light spot array of the wavefront to be measured, i.e., the far-field light intensity distribution I; Step 2: Perform Fourier transform on the spot array image information recorded in step 1 to obtain the spectrum distribution of the far-field light intensity distribution I Step 3: Spectral distribution of the far-field light intensity distribution I obtained in step 2 Extract the first-order spectrum in the u and v directions and Move to the center of the spectrum and perform inverse Fourier transform to get H 1，0 (x, y) and H 0，1 (x, y); Step 4: Obtain the wavefront slope of each point in the (p,q) sub-aperture in the x-direction of the sub-aperture and the wavefront slope of each point within the y-direction (p,q) subaperture Step 5: Obtain the local wavefront curvature to be measured corresponding to the sub-aperture in the x-direction The local wavefront curvature to be measured corresponding to the y-direction sub-aperture In step 5, the wavefront slope in the x direction obtained in step 4 is and the wavefront slope in the y direction The finite difference method is used to obtain the curvature signal of the wavefront to be measured in the x direction and the curvature signal of the wavefront to be measured in the y direction, and then the local curvature of the wavefront to be measured corresponding to the sub-aperture in the x direction is obtained with each sub-aperture as a unit. The local wavefront curvature to be measured corresponding to the y-direction sub-aperture In the formula is the second-order partial derivative of the wavefront to be measured in the x direction, is the wavefront curvature information, (m,n) is the discrete sampling point of the wavefront to be measured, is the sampling interval, represents the wavefront curvature value to be measured at the sub-aperture (p, q), K1 and K2 represent the maximum and minimum curvature values in the sub-aperture respectively; In the formula is the second-order partial derivative of the wavefront to be measured in the y direction, which is the wavefront curvature information. K3 and K4 represent the maximum and minimum values of the curvature in the sub-aperture, respectively. In step 4, the slope of the subaperture in the x direction is obtained based on the energy conservation and the relationship between the first-order spectra in the u and v directions obtained in step 3 and the slope of the wavefront to be measured. and the slope in the y direction Wavefront slope The method to obtain is: In the formula and They are I(x,y) and H (k，l) Fourier transform of (x,y), I(x,y) is the light intensity distribution, H (1，0，) (x, y) is the first harmonic information in the x direction; (x, y) is the coordinate system of the object plane, (u, v) is the coordinate system in the Fourier plane; K is the order of the harmonic; k, l are the coordinate positions of the harmonic in the Fourier plane, is the first-order partial derivative of the wave in the x direction, which refers to the slope information, IMAGH (1,0) (x,y) is the pair H (1,0) (x,y) takes the imaginary part; represents the slope value of each point of the local wavefront in the (p,q) sub-aperture. The phase distribution of the wavefront to be measured is Wavefront slope The method to obtain is: Where H (0，1) (x,y) is the first harmonic information in the y direction; It is the first-order partial derivative of the wavefront to be measured in the y direction, which refers to the slope information; The wavefront slope in the x direction obtained in step 4 is and the wavefront slope in the y direction The curvature signal of the wavefront to be measured in the x direction and the curvature signal of the wavefront to be measured in the y direction obtained in step 5 are used to reconstruct the wavefront using the slope and curvature wavefront reconstruction algorithm.

2. The method for extracting wavefront slope and curvature information based on a Shack-Hartmann wavefront sensor according to claim 1, characterized in that: In the step 1, the light spot array image information of the wavefront to be measured, ie, the far-field light intensity distribution I, is recorded by a Shack-Hartmann wavefront sensor and a photodetector CCD.

3. The method for extracting wavefront slope and curvature information based on a Shack-Hartmann wavefront sensor according to claim 1 or 2, characterized in that: In step 2, the light spot array image information recorded in step 1 is Fourier transformed using discrete Fourier transform to obtain the spectrum distribution of the far-field light intensity distribution I. represents the Fourier transform of I.

4. The method for extracting wavefront slope and curvature information based on a Shack-Hartmann wavefront sensor according to claim 1 or 2, characterized in that: In the step 3, the spectrum of the far-field light intensity distribution I obtained in step 2 is distributed as follows: The first-order spectra in the u and v directions are extracted using the set bandpass filter. and Then the extracted first-order spectra in the u and v directions are moved to the center of the spectrum, and then the first-order spectra are and Perform inverse Fourier transform to get H (1,0) (x,y) and H (0,1) (x,y); u and v represent coordinates in the Fourier plane.

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