CN117824851A - Hartmann wavefront sensor mode restoration method for screening sub-aperture data - Google Patents
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Abstract
The invention discloses a Hartmann wavefront sensor mode restoration method for screening sub-aperture data, which is characterized in that a linear fitting method is adopted to correct a reconstruction matrix according to the detection characteristic of the Hartmann wavefront sensor by utilizing the centroid deviation of sub-light spots based on the arrangement design of the sub-apertures of the Hartmann wavefront sensor, and the sub-aperture data is screened according to the deviation of actual data compared with fitting data. The method breaks through the classical processing mode that all sub-apertures participate in detection in the conventional method, corrects the reconstruction matrix through the linear fitting method, selects sub-aperture data with higher fitting degree to participate in wavefront restoration, realizes the transformation and optimization of the mode restoration matrix, improves the wavefront detection precision, has the characteristics of simplicity in realization, strong universality and the like, provides a new thought for the design optimization of the sub-apertures of the Hartmann wavefront sensor and the further improvement of the precision of the mode restoration algorithm, and can be directly applied to various existing Hartmann wavefront sensors.
Description
Technical Field
The invention belongs to the technical field of optical information measurement, and particularly relates to a Hartmann wavefront sensor mode restoration method for screening sub-aperture data.
Background
The shearing interferometer is widely applied because of high measurement precision, but has the defects of high environmental requirement, low measurement speed, high price and the like. In contrast, the Hartmann wavefront sensor is used as a high-efficiency light beam wavefront distortion measuring instrument, and has a simple structure, a high measuring speed and high environmental adaptability, so that the Hartmann wavefront sensor is widely applied to various fields and scenes with high requirements on wavefront measurement instantaneity, such as optical detection, adaptive optics, ophthalmic medicine, laser wavefront diagnosis, laser communication and the like.
The typical Hartmann wavefront sensor currently mainly adopts a shack-Hartmann wavefront sensor structure, which is a well-known improved structure proposed by R.V. shack et al in 1971, see "Lenticular Hartmann Screen" [ Platt B.C and R.V. shack ] [ J ]. Opt.Sci.Newsl.5,15-16,1971]. The shack-Hartmann wavefront sensor mainly adopts a micro-lens array to divide and sample the wavefront of the light wave to form a plurality of sub-apertures, the micro-lens array can divide the incident light wave and focus the divided light wave on an array type photoelectric detector (such as a common CCD or CMOS camera), a light spot array corresponding to the sub-apertures one by one is formed on the target surface of the array type photoelectric detector, and the position change of the light spot contains information corresponding to the front slope in the sub-apertures. The array type photoelectric detector collects the formed light spot array image, and the required wave-front phase measurement data can be obtained through calculation processing according to the offset change of the mass center positions of all the sub light spots. The division and focusing of the microlens array greatly improve the light energy utilization rate of the Hartmann wavefront sensor and the signal-to-noise ratio of the light spot array image, so that the method is used up to now.
In the Hartmann wavefront sensor, the directly obtained data is the position offset information of each sub-light spot, and the spatial distribution of the wavefront distortion can be reconstructed only by adopting a specific recovery algorithm, namely the Hartmann wavefront sensor wavefront recovery algorithm. The most commonly used methods for wavefront rehabilitation of Hartmann wavefront sensors are mainly two of the area method (see "Wave-front estimation from Wave-front slope measurements", W.H. southwell. [ J ]. JOSA 70 (8), 998-1006, 1980) and the mode method (see "Wave-front reconstruction using a Shack-Hartmann sensor", R.G. Lane and M.Tallon. [ J ]. Appl. Opt.31 (32), 6902-6908, 1992). The mode method mainly utilizes a mode coefficient restoration matrix constructed in advance through a least square mathematical principle, and calculates an aberration mode coefficient by using spot centroid data of an actual light beam to be measured and the mode coefficient restoration matrix. Hartmann wavefront sensors typically employ high aperture arrays to increase the number and frequency of samples to the wavefront slope, thereby improving the wavefront measurement accuracy. For the mode restoration algorithm, the high-density array number can provide more sufficient information, and the accuracy and stability of mode coefficient calculation are improved. Therefore, in the information processing modes of the two wavefront reconstruction algorithms, all the sub-aperture data are used as effective information to participate in the wavefront reconstruction calculation.
However, in the construction process of the Hartmann wavefront sensor mode coefficient restoration matrix, the basic principle that each order aberration mode coefficient is input into the Hartmann wavefront sensor to obtain sub-facula centroid offset data under unit coefficient is mainly adopted. This method is premised on a linear response of centroid shifts of each spot to aberration mode coefficient changes. In an actual Hartmann wavefront sensor device, however, the linearity of the sub-aperture with respect to aberration mode coefficient variation is not completely uniform. This means that the reconstruction matrix may be subject to errors due to low linearity, which may affect the final resolution of the aberration mode coefficients. Therefore, the linear fitting method is adopted to correct the restoration matrix, and then the sub-aperture and the data thereof are optimized according to the fitting degree, so that the wavefront measurement precision can be improved, the size of the sub-aperture data volume used for the wavefront reconstruction calculation can be effectively controlled, and the method has great practical significance for improving the resolving speed of the wavefront mode coefficient.
Disclosure of Invention
In order to solve the technical problems, the method for constructing a restoration matrix by breaking sub-spot centroid offset data obtained by inputting unit coefficient each order aberration mode in a conventional method and processing sub-aperture information by taking all effective sub-aperture data into wavefront reconstruction calculation is broken, under the condition that the number of sub-apertures and the spot centroid offset data are ensured to be sufficient, the invention provides a Hartmann wavefront sensor mode restoration method for screening sub-aperture data.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a Hartmann wavefront sensor mode restoration method for screening sub-aperture data adopts a linear fitting method to correct a reconstruction matrix according to the detection characteristic that the Hartmann wavefront sensor utilizes the centroid deviation of sub-light spots, and the method for screening sub-aperture data according to the deviation of actual data compared with fitting data realizes aberration mode restoration by the following steps:
step 1: setting coefficient vector C to be n a The number N of effective sub-apertures is determined according to the design and arrangement of the sub-apertures of the Hartmann wavefront sensor, wherein the number of the sub-apertures is formed by arranging the coefficients from small to large sa Calibrating the centroid zero point of the Hartmann wavefront sensor, and setting the number of aberration modes to be measured as N z ；
Step 2: calculating offset data of the spot centroid of each sub-aperture of the Hartmann wavefront sensor in the x and y directions under the condition that 1 st-order aberration modes with different coefficients are used as input wave fronts, and forming a spot centroid offset data matrix D of each sub-aperture under the 1 st-order aberration modes to be measured with different coefficients (1) The dimension of the matrix is 2N sa ×n a The linear fitting method is adopted to fit the data that the light spot centroid offset of each sub-aperture is in linear distribution along with the coefficient change, and a fitting slope vector k is obtained (1) Vector length of 2N sa The method comprises the steps of carrying out a first treatment on the surface of the Will fit the slope vector k (1) Multiplying the transposed C' of the coefficient vector to obtain sub-aperture facula centroid offset data of different coefficient aberration modes of reference and forming a matrix D idea (1) The dimension of the matrix is 2N sa ×n a ；
Step 3: calculation D (1) Medium data compared with D idea (1) Absolute value data matrix M of percentage of data deviation (1) Dimension of 2N sa ×n a The method comprises the steps of carrying out a first treatment on the surface of the Summing the absolute values of the deviation percentages corresponding to each sub-aperture to obtain a linear fitting deviation vector m of each sub-aperture when the first-order mode aberration is input (1) Length N sa ；
Step 4: for the 2 nd to the N th z Repeatedly executing the step 2 and the step 3 in each order aberration mode to be detected to obtain a linear distribution interval fitting slope vector of each sub-aperture centroid along with coefficient change when each order mode aberration is inputAnd a linear fitting deviation vector +.>Each vector has a length of N sa ；
Step 5: will beAdding to obtain a linear fitting deviation vector m of each sub-aperture to each order mode aberration, wherein the length is N sa ；
Step 6: will beAdding to obtain a linear fitting deviation vector m of each sub-aperture to each order mode aberration;
step 7: reconstructing a sub-aperture facula centroid offset data matrix D under each order of aberration by using the sub-aperture screened in the step 6 and the fitting slope corresponding to the step 2 and the step 4, wherein the dimension of the matrix is 2N '' sa ×N Z The inverse matrix of the calculated D is a corresponding optimized aberration mode coefficient restoration matrix R, and the dimension of the matrix is N Z ×2N' sa ；
Step 8: the Hartmann wavefront sensor obtains the light spot in the screened sub-aperture after the actual light beam to be measured is divided and focused by the sub-apertureCentroid offset data vector G, vector length N' sa The aberration mode coefficient vector A=R.G of each order in the wave front of the light beam to be detected can be calculated; according to the solved aberration mode coefficient vector A of each order, the vector length is N Z The wave front distribution to be measured can be restored by using a classical aberration mode reconstruction method, and the wave front sensing measurement is completed.
Further, the number n of coefficient samples selected by the aberration mode in the step 2 a The method can be used for uniformly setting all the order aberration modes, and the aberration value is within the dynamic range of the Hartmann wavefront sensor.
Further, the i-th order aberration mode to be measured in the step 2 and the step 4 is used as a sub-aperture facula centroid offset data matrix D under the condition of aberration input (i) Has the form:
in the method, in the process of the invention,under the condition that the first mode coefficient in the coefficient taking vector C of the ith order aberration mode to be measured respectively forms input aberration, the centroid shift of the sub-light spot corresponding to the kth sub-aperture in the x direction and the centroid shift of the sub-light spot in the y direction are respectively represented, and the l value is 1 to->Is an integer of from 1 to N sa Integer of>I.e. the number of coefficient samples selected in the coefficient value range of the ith order aberration mode to be measured, N sa For Hartmann wavefront sensor effective sub-aperture number, the sub-aperture facula centroid offset data matrix D (i) Dimension is->
Further, the ith order aberration pattern to be measured in the step 2 is used as the sub-aperture spot centroid offset data matrix D of each order of different coefficient aberration patterns to be referenced under the aberration input condition idea (i) Has the form:
D idea (i) ＝k (i) C T ，
wherein k is (i) The fitting slope vector of the linear distribution interval of each sub-aperture centroid along with the coefficient change in the ith order aberration mode to be measured in the step 2 and the step 3 is represented, and the length is N sa ，C T Transpose of coefficient vector C, D idea (i) The dimension is
Further, the i-th order aberration mode to be measured in the step 3 is used as an absolute value data matrix M of the percentage of the data offset under the aberration input condition (i) The method comprises the following steps:
wherein D is (i) (i, j) represents matrix D (i) Elements of row j, D idea (i) (m, n) represents matrix D idea (i) The elements in the m-th row and N-th column have values of 1 to N sa The integers of j and n are 1 toInteger of N sa For the number of sub-apertures, M (i) Is +.>
Further, the i-th order aberration mode to be measured in the step 3 and the step 4 is used as the offset percentage and the vector m of each sub-aperture under the aberration input condition (i) The method comprises the following steps:
matrix in matrixIs of dimension N sa ×2N sa Vector->Length ofVector M has length N sa 。
Further, the linear fitting degree vector m of each sub-aperture to each order mode aberration in the step 5 has the following form:
in N z For the number of aberration modes to be measured, the length of the vector m is N sa 。
Further, the sub-aperture spot centroid offset data matrix D of each order aberration mode regenerated in the step 6 has the following form:
in the method, in the process of the invention,the sub-pore size selected in the step 6 is k (i) The corresponding fitting slope is composed of a length of 2N' sa I takes on a value of 1 to N z Integer of N' sa For the number of sub-apertures selected in step 6, the dimension of matrix D is 2N' sa ×N Z 。
Further, the spot centroid offset data vector G in the step 8 is a one-dimensional matrix vector, and has the form:
[G x (1),G y (1),G x (2),G y (2),…,G x (N' sa ),G y (N' sa )] T ，
wherein G is x (m)、G y And (m) respectively represents the centroid shift of the sub-light spot in the x direction and the centroid shift of the sub-light spot in the y direction corresponding to the mth sub-aperture under the actual light beam input condition to be detected.
Compared with the prior art, the invention has the beneficial effects that:
the method breaks through the classical processing mode that all the bright and effective sub-apertures participate in detection in the conventional method, corrects the reconstruction matrix through the linear fitting method, selects sub-aperture data with higher fitting degree to participate in wavefront restoration, realizes the transformation and optimization of the mode restoration matrix, improves the wavefront detection precision, does not need to change hardware, has the characteristics of simplicity in realization, strong universality and the like, provides a new thought for the optimization of the sub-aperture design of the Hartmann wavefront sensor and the further improvement of the precision of the mode restoration algorithm, and can be directly applied to various existing Hartmann wavefront sensors.
Drawings
FIG. 1 is a flow chart of a Hartmann wavefront sensor mode restoration method for filtering sub-aperture data according to the present invention;
fig. 2 is a schematic diagram of a hartmann wavefront sensor according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a Hatmann wavefront sensor sub-aperture arrangement according to an embodiment of the present invention, wherein the blue box identifies sub-apertures that have been obtained through screening;
FIG. 4 is a diagram of a wavefront distortion profile to be measured as input in an embodiment of the present invention;
FIG. 5 is a graph of comparing the mode coefficient calculation result obtained by the method according to the present invention with the conventional mode coefficient calculation result;
fig. 6 (a), fig. 6 (b) is a comparison of a wavefront restoration residual error using the method proposed by the present invention and a wavefront restoration residual error using the conventional method in the embodiment of the present invention, where fig. 6 (a) is an error of the classical mode restoration algorithm; fig. 6 (b) shows the error of the restored wavefront after the restoration matrix is corrected according to the present invention.
Detailed Description
The invention is further described below with reference to the drawings and examples.
As shown in fig. 2, in the present embodiment, the hartmann wavefront sensor is mainly composed of a microlens array 1 and a CCD detector 2. The effective microlens array number of the microlens array 1 is 16×16, the microlens size is 396.8 μm, the focal length is 42.3mm, and the detection wavelength is 635nm; the effective pixel number of the CCD detector 2 is 992×992. Thus, an example is a typical Hartmann wavefront sensor with an array number of 16 x 16 and a detection wavelength of 635 nm.
As shown in fig. 1, a method for recovering a Hartmann wavefront sensor mode for screening sub-aperture data according to the present invention includes the steps of:
step 1: setting the range of the Zernike aberration modes to [ -1,1]The coefficients of the 41 different input modes of (a) are-1, -0.95, …, -0.05, 0, 0.05, 0.1, …, 0.95, 1 respectively, so as to form coefficient vectors C of Zernike aberration modes, calibrating centroid zero points of each sub-aperture of the Hartmann wavefront sensor by using plane waves as inputs according to the design arrangement of the sub-apertures of the Hartmann wavefront sensor in the embodiment shown in FIG. 3, and setting the number N of aberration modes to be measured Z The aberration mode is a Zernike aberration mode, namely the mode method of the Hartmann wavefront sensor is used for recovering and measuring the Zernike aberration of the first 35 th order.
Step 2: calculating offset data of the spot centroid of each sub-aperture of the Hartmann wavefront sensor in the x and y directions under the condition that the first-order Zernike aberration modes take different coefficients as input wave fronts, and forming a sub-aperture spot centroid offset data matrix D under the condition that the 1 st-order Zernike aberration modes with different coefficients are taken as input wave fronts (1) The matrix dimension is 376 multiplied by 41, and a linear fitting method is adopted to fit the interval in which the light spot centroid offset data of each sub-aperture is in linear distribution, so as to obtain a fitting slope vector k (1) Each vector has a length 376, wherein the number of effective sub-apertures of the Hartmann wavefront sensor is 188; will fit the slope vector k (1) Transpose C with coefficient vector T Multiplying to obtain sub-aperture spot centroid offset data of different coefficient aberration modes of reference and forming matrix D idea (1) The matrix dimension is 376×41;
step 3: calculation D (1) Medium data compared with D idea (1) Absolute value data matrix M of percentage amount of data offset (1) The dimension of the matrix is 376 multiplied by 41, and the absolute value of the deviation percentage corresponding to each sub-aperture is summed to obtain a linear fitting deviation vector m of each sub-aperture when the first-order mode aberration is input (1) The length of the vector is 188;
step 4: repeatedly executing the step 2 and the step 3 for each order of aberration modes to be measured from the 2 nd order to the 35 th order to obtain a linear distribution interval fitting slope vector of each sub-aperture centroid along with coefficient change when each order mode aberration is inputAnd a linear fitting deviation vector +.>Each vector has a length of 188;
step 5: let m (1) ～m (35) Adding to obtain a linear fitting deviation vector m of each sub-aperture to each order mode aberration, wherein the length of the vector is 188;
step 6: sorting the data sizes in m, selecting the first 47 shift reference centroid data percentages and the smaller sub-aperture centroid shift data, and marking the selected sub-apertures in figure 3 by using gray frames;
step 7: reconstructing a sub-aperture facula centroid offset data matrix D under each order of aberration by using the sub-aperture screened in the step 6 and the fitting slope corresponding to the step 2 and the step 3, wherein the dimension of D is 94 multiplied by 35, the inverse matrix of D' is calculated and is a corresponding optimized aberration mode coefficient recovery matrix R, and the dimension of R is 35 multiplied by 94;
step 8: the wave front distortion to be measured of the input test consists of a first 35-order declivated Zernike aberration mode, the aberration mode coefficient is randomly generated and distributed to meet the Kelmogorov turbulence spectrum, and the aberration space distribution is shown in figure 4. The PV value of the input aberration reached 4.728 μm and the RMS value was 0.897 μm. After the Hartmann wavefront sensor obtains the wavefront distortion to be measured, the sub-aperture is divided and focused, the centroid of the facula in the sub-aperture shifts by a data vector G, and the 35-order Zernike aberration mode coefficient in the wavefront distortion to be measured, namely a mode coefficient vector A=R.G, is calculated by utilizing an aberration mode coefficient restoration matrix R. Comparing the 35-order declivity Zernike aberration mode coefficient error calculated by the invention with the coefficient error calculated by the traditional method adopting all sub-aperture calculation, the result shown in the histogram in figure 5 can be obtained. Wherein the abscissa represents the mode order, the ordinate represents the difference between the calculated mode coefficient and the input value, namely the coefficient calculation error, the black columnar data is the mode coefficient calculation error of the traditional method, and the white columnar data is the mode coefficient calculation error of the method provided by the invention. As is apparent from fig. 5, the aberration mode coefficient calculation error of the proposed method is controlled to be smaller as a whole. From the result, the advantage of the method in the aberration mode coefficient resolving precision can be primarily seen.
And according to the solved 35-order Zernike aberration mode coefficient A, recovering the wavefront distribution to be measured by using a classical aberration mode reconstruction method, and completing the wavefront sensing measurement.
Fig. 6 (a), fig. 6 (b) show the wavefront restoration residual error using the method according to the present invention and the wavefront restoration residual error result using the conventional method in the embodiment of the present invention. FIG. 6 (a) is the error of the classical mode recovery algorithm; fig. 6 (b) shows the error of the restored wavefront after the restoration matrix is corrected according to the present invention. In the case of an input aberration PV value of 7.446 λ and an RMS value of 1.413 λ, the error PV value of 0.0823 and an RMS value of 0.006945 λ, which are about 0.49% of the input value, are obtained by the method of the present invention. The error PV value of the wave front restoration result obtained by the classical mode restoration algorithm is 0.801 lambda, the RMS value is 0.051 lambda and the error is about 3.6% of the input value. This means that the method provided by the invention improves 86% of restoration accuracy compared with the traditional method under the condition that only 25% of sub-aperture data are adopted to participate in wavefront restoration. This has practical use value for optimizing Hartmann wavefront sensor to improve wavefront restoration accuracy.
While the invention has been described with respect to specific embodiments thereof, it will be appreciated that the invention is not limited thereto, but rather encompasses modifications and substitutions within the scope of the present invention as will be appreciated by those skilled in the art.
Claims (9)
1. A Hartmann wavefront sensor mode restoration method for screening sub-aperture data is characterized in that: according to the Hartmann wavefront sensor sub-aperture arrangement design, starting from the Hartmann wavefront sensor by utilizing the detection characteristic of sub-facula centroid offset, correcting a reconstruction matrix by adopting a linear fitting method, and screening sub-aperture data according to the offset of actual data compared with fitting data, wherein the method comprises the following steps:
step 1: setting coefficient vector C to be n a The number N of effective sub-apertures is determined according to the design and arrangement of the sub-apertures of the Hartmann wavefront sensor, wherein the number of the sub-apertures is formed by arranging the coefficients from small to large sa Calibrating the centroid zero point of the Hartmann wavefront sensor, and setting the number of aberration modes to be measured as N z ；
Step 2: calculating offset data of the spot centroid of each sub-aperture of the Hartmann wavefront sensor in the x and y directions under the condition that 1 st-order aberration modes with different coefficients are used as input wave fronts, and forming a spot centroid offset data matrix D of each sub-aperture under the 1 st-order aberration modes to be measured with different coefficients (1) The dimension of the matrix is 2N sa ×n a The linear fitting method is adopted to fit the data that the light spot centroid offset of each sub-aperture is in linear distribution along with the coefficient change, and a fitting slope vector k is obtained (1) Vector length of 2N sa The method comprises the steps of carrying out a first treatment on the surface of the Will fit the slope vector k (1) Multiplying the transposed C' of the coefficient vector to obtain sub-aperture facula centroid offset data of different coefficient aberration modes of reference and forming a matrix D idea (1) The dimension of the matrix is 2N sa ×n a ；
Step 3: calculation D (1) Medium data compared with D idea (1) Absolute value data matrix M of percentage of data deviation (1) Dimension of 2N sa ×n a The method comprises the steps of carrying out a first treatment on the surface of the Summing the absolute values of the deviation percentages corresponding to each sub-aperture to obtain a linear fitting deviation vector m of each sub-aperture when the first-order mode aberration is input (1) Length N sa ；
Step 4: for the 2 nd to the N th z Repeatedly executing the step 2 and the step 3 in each order aberration mode to be detected to obtain a linear distribution interval fitting slope vector of each sub-aperture centroid along with coefficient change when each order mode aberration is inputAnd a linear fitting deviation vector +.>Each vector has a length of N sa ；
Step 5: will beAdding to obtain a linear fitting deviation vector m of each sub-aperture to each order mode aberration, wherein the length is N sa ；
Step 6: will beAdding to obtain a linear fitting deviation vector m of each sub-aperture to each order mode aberration;
step 7: reconstructing a sub-aperture facula centroid offset data matrix D under each order of aberration by using the sub-aperture screened in the step 6 and the fitting slope corresponding to the step 2 and the step 4, wherein the dimension of the matrix is 2N '' sa ×N Z The inverse matrix of the calculated D is a corresponding optimized aberration mode coefficient restoration matrix R, and the dimension of the matrix is N Z ×2N′ sa ；
Step 8: hartmann wavefront sensor obtains actual beam path to be measuredAfter sub-aperture segmentation and focusing, the centroid of the light spot in the screened sub-aperture shifts by a data vector G, and the vector length is N '' sa The aberration mode coefficient vector A=R.G of each order in the wave front of the light beam to be detected can be calculated; according to the solved aberration mode coefficient vector A of each order, the vector length is N Z And (3) recovering the distribution of the wavefront to be measured by using a classical aberration mode reconstruction method to finish the wavefront sensing measurement.
2. The method for recovering a Hartmann wavefront sensor mode for filtering sub-aperture data as recited in claim 1, wherein: the number n of coefficient samples selected by the aberration mode in the step 2 a The method is characterized in that the method is uniformly set for all the order aberration modes, and the aberration value is within the dynamic range of the Hartmann wavefront sensor.
3. The method for recovering a Hartmann wavefront sensor mode for filtering sub-aperture data as recited in claim 1, wherein: the ith order aberration mode to be measured in the step 2 and the step 4 is used as a sub-aperture facula centroid offset data matrix D under the condition of aberration input (i) Has the following form:
in the method, in the process of the invention,under the condition that the first mode coefficient in the coefficient taking vector C of the ith order aberration mode to be measured respectively forms input aberration, the centroid shift of the sub-light spot corresponding to the kth sub-aperture in the x direction and the centroid shift of the sub-light spot in the y direction are respectively represented, and the l value is 1 to->Is an integer of from 1 to N sa Integer of>I.e. the number of coefficient samples selected in the coefficient value range of the ith order aberration mode to be measured, N sa For Hartmann wavefront sensor effective sub-aperture number, the sub-aperture facula centroid offset data matrix D (i) Dimension is->
4. The method for recovering a Hartmann wavefront sensor mode for filtering sub-aperture data as recited in claim 1, wherein: the ith order aberration mode to be measured in the step 2 is used as a sub-aperture facula centroid offset data matrix D of each order of different coefficient aberration modes which are referenced under the aberration input condition idea (i) Has the following form:
D idea (i) ＝k (i) C T ，
wherein k is (i) The fitting slope vector of the linear distribution interval of each sub-aperture centroid along with the coefficient change in the ith order aberration mode to be measured in the step 2 and the step 3 is represented, and the length is N sa ，C T Transpose of coefficient vector C, D idea (i) The dimension is
5. The method for recovering a Hartmann wavefront sensor mode for filtering sub-aperture data as recited in claim 1, wherein: the i-th order aberration mode to be measured in the step 3 is taken as an absolute value data matrix M of the percentage of the data offset under the aberration input condition (i) Has the following form:
wherein D is (i) (i，j) Representation matrix D (i) Elements of row j, D idea (i) (m, n) represents matrix D idea (i) The elements in the m-th row and N-th column have values of 1 to N sa The integers of j and n are 1 toInteger of N sa For the number of sub-apertures, M (i) Is +.>
6. The method for recovering a Hartmann wavefront sensor mode for filtering sub-aperture data as recited in claim 1, wherein: the ith order aberration mode to be measured in the step 3 and the step 4 is used as the offset percentage and the vector m of each sub-aperture under the aberration input condition (i) Has the following form:
matrix in matrixIs of dimension N sa ×2N sa Vector->Length of->Vector M has length N sa 。
7. The method for recovering a Hartmann wavefront sensor mode for filtering sub-aperture data as recited in claim 1, wherein: the linear fitting degree vector m of each sub-aperture to each order mode aberration in the step 5 has the following form:
wherein N is z For the number of aberration modes to be measured, the length of the vector m is N sa 。
8. The method for recovering a Hartmann wavefront sensor mode for filtering sub-aperture data as recited in claim 1, wherein: the sub-aperture spot centroid offset data matrix D of each order aberration mode regenerated in the step 6 has the following form:
in the method, in the process of the invention,the sub-pore size selected in the step 6 is k (i) The corresponding fitting slope is composed of a length of 2N' sa I takes on a value of 1 to N z Integer of N' sa For the number of sub-apertures selected in step 6, the dimension of matrix D is 2N' sa ×N Z 。
9. The method for recovering a Hartmann wavefront sensor mode for filtering sub-aperture data as recited in claim 1, wherein: the spot centroid offset data vector G in the step 8 is a one-dimensional matrix vector, and has the following form:
[G x (1)，G y (1)，G x (2)，G y (2)，...，G x (N′ sa )，G y (N′ sa )] T ，
wherein G is x (m)、G y (m) respectively represents the centroid shift and the y direction of the sub-light spot corresponding to the mth sub-aperture in the x direction under the input condition of the actual light beam to be detectedIs shifted by the centroid of (a).
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