阅读说明：本技术 一种沙克哈特曼波前传感器的未配准偏差补偿方法 (Misregistration deviation compensation method of shack Hartmann wavefront sensor ) 是由 刘华锋 王岱崟 于 2021-08-26 设计创作，主要内容包括：本发明公开了一种沙克哈特曼波前传感器的未配准偏差补偿方法,通过理论建模,探明了这一未配准问题会引入误差至拓扑值探测中,并对该未配准偏差进行补偿,从而大幅提升拓扑值探测的精度,同时也证明了拓扑值探测方法的失效正是沙克哈特曼波前传感器中的未配准问题所导致的。此外,本发明提出相应的方法来补偿这一未配准偏差,实验结果表明,利用本发明补偿方法对沙克哈特曼波前传感器进行了补偿后,涡旋光束拓扑值探测的精度得到了显著的提升,从而验证了补偿沙克哈特曼波前传感器中未配准偏差的必要性以及本发明偏差补偿方法的有效性。(The invention discloses an misregistration deviation compensation method of a shack Hartmann wavefront sensor, which is used for proving that the misregistration problem can introduce errors into topological value detection through theoretical modeling and compensating the misregistration deviation, so that the accuracy of the topological value detection is greatly improved, and meanwhile, the failure of the topological value detection method is proved to be caused by the misregistration problem in the shack Hartmann wavefront sensor. In addition, the invention provides a corresponding method for compensating the misregistration deviation, and experimental results show that after the compensation method is used for compensating the shack Hartmann wavefront sensor, the precision of vortex beam topological value detection is remarkably improved, so that the necessity of compensating the misregistration deviation in the shack Hartmann wavefront sensor and the effectiveness of the deviation compensation method are verified.)

1. An misregistration offset compensation method for a shack Hartmann wavefront sensor, comprising the steps of:

(1) carrying out a pre-experiment of normal incidence parallel light to the shack Hartmann wavefront sensor to obtain a deflection angle delta between a lens array surface and an image sensor surface in the shack Hartmann wavefront sensor;

(2) incident vortex light beams are transmitted into a shack Hartmann wavefront sensor to obtain recorded images;

(3) calculating barycentric location coordinates (X) of image distribution_c,Y_c)；

(4) Solving an initial average phase slope distribution diagram based on the detection principle of the shack Hartmann wavefront sensor;

(5) calculating an average phase slope compensation value corresponding to each convergent light spot, and compensating the initial average phase slope distribution diagram by using the compensation value;

(6) and detecting the topological value of the vortex light beam according to the compensated initial average phase slope distribution diagram.

2. The misregistration deviation compensation method according to claim 1, characterized in that: the specific implementation process of the step (1) is as follows:

1.1, for a shack Hartmann wavefront sensor, acquiring convergent light spots of each row and each column in an image, and performing linear fitting by using a least square method to obtain a slope value psi of each row and each column;

wherein: (x)_k,y_k) The coordinate of the kth convergent light spot on a certain row or a certain column of the image, and N is the number of the convergent light spots on the row or the column;

1.2 applying an arctangent function to the slope value psi of each row and each column to obtain an included angle phi between each row and each column and a horizontal line;

1.3 calculating a deflection angle delta between a lens array surface and an image sensor surface in the shack Hartmann wavefront sensor according to the included angle phi through the following formula;

wherein:representing the angle between the p-th line in the image and the horizontal line,representing the angle between the q-th column and the horizontal in the image, K^LAnd K^CRespectively the number of rows and columns in the image.

3. The misregistration deviation compensation method according to claim 1, characterized in that: the barycentric position coordinates (X) of the image distribution are calculated in the step (3) by the following formula_c,Y_c)；

Wherein: and (xi, eta) is the coordinate of a certain point in the image distribution, and I (xi, eta) is the light intensity of the point corresponding to the coordinate (xi, eta).

4. The misregistration deviation compensation method according to claim 1, characterized in that: in the step (4), solving an initial average phase slope distribution diagram by the following formula;

wherein: (C)_x(i,j),C_y(i, j)) and (x (i, j), y (i, j)) are respectively the central coordinate of the ith row and jth column lens in the lens array and the corresponding convergent light spot coordinate, S_x(i, j) and S_y(i, j) are the components of the average phase slope in the horizontal direction and the vertical direction corresponding to the ith row and the jth column lens in the lens array respectively, f is the focal length of the lens, and lambda is the wavelength of the light beam.

5. The misregistration deviation compensation method according to claim 4, characterized in that: calculating an average phase slope compensation value corresponding to the converged light spot through the following formula in the step (5);

wherein: delta S_x(i, j) and Δ S_y(i, j) are the components of the average phase slope compensation value of the convergent light spot in the horizontal direction and the vertical direction at coordinates (x (i, j), y (i, j)) respectively.

6. The misregistration deviation compensation method according to claim 5, characterized in that: compensating the initial average phase slope distribution diagram in the step (5) by the following formula;

S'_x(i,j)＝S_x(i,j)+ΔS_x(i,j)

S'_y(i,j)＝S_y(i,j)+ΔS_y(i,j)

wherein: s_x' (i, j) and S_y' (i, j) are components of the average phase slope in the horizontal direction and the vertical direction corresponding to the ith row and jth column lens in the compensated lens array, respectively.

7. The misregistration deviation compensation method according to claim 1, characterized in that: and (5) detecting the topological value of the vortex light beam by adopting an average brightest intensity ring method in the step (6).

Technical Field

The invention belongs to the technical field of wavefront detection, and particularly relates to an unregistered deviation compensation method of a shack Hartmann wavefront sensor.

Background

The shack Hartmann wavefront sensor is an important device in adaptive optics, and can be widely applied to the fields of astronomy, ophthalmology, microscopy and the like because the shack Hartmann wavefront sensor can conveniently and efficiently detect wavefront aberration. As shown in fig. 1, the shack hartmann wavefront sensor mainly comprises two parts, namely a lens array with equal size and equal focal length and an image sensor positioned on the back focal plane of the lens array; when the light wave propagates to the shack hartmann wavefront sensor, the lens array divides the incident wavefront into sub-wavefront beams of equal lens number, and each sub-wavefront is converged on the image sensor by the corresponding small lens. The core working principle of the shack Hartmann wavefront sensor is that the average phase slope of the sub-wavefront is directly determined by the position of an image spot of the sub-wavefront on the image sensor, namely the average phase slope of the sub-wavefront is proportional to the distance between the image spot and the focal point of the lens, and the proportionality coefficient is 2 pi/lambda f.

As a special light field, vortex light beams are similar to well-known vortex in typhoon and ocean, the wave front phase distribution of the vortex light beams is vortex, and the vortex light beams have many characteristics due to the special phase distribution and are widely applied to the fields of micro particle control, optical communication, optical measurement, remote sensing and the like. In many applications of vortex beams, the topological value, which is a key parameter of the vortex beams, is always closely related to the principles of the applications, and therefore, how to accurately detect the topological value of the vortex beams is a fundamental stone of the vortex beam related applications.

The topological value detection of vortex beams is one of important applications of the shack Hartmann wavefront sensor, and various scholars at home and abroad also provide various accurate and efficient vortex beam topological value detection methods based on the shack Hartmann wavefront sensor. However, as the application of the vortex beam is enriched, the application scenario of the vortex beam becomes more complex, and the topology value detection of the vortex beam also faces new requirements and challenges; the vortex light beam needs to work in a far-field state frequently, namely the using position of the vortex light beam is far away from the generating position, and in the state, the vortex light beam topological value detection method based on the shack Hartmann wavefront sensor cannot achieve accurate detection.

Therefore, the method has great research significance and application value for finding out the failure reason of the topological value detection method under the far-field condition and solving the related problems.

Disclosure of Invention

In view of the above, the present invention provides an misregistration offset compensation method for a shack hartmann wavefront sensor, which finds out through theoretical modeling that an error is introduced into the detection of a topological value by the misregistration problem, and compensates for the misregistration offset, thereby greatly improving the accuracy of the detection of the topological value, and simultaneously proves that the failure of the detection method of the topological value is caused by the misregistration problem in the shack hartmann wavefront sensor.

An misregistration offset compensation method for a shack Hartmann wavefront sensor, comprising the steps of:

(1) carrying out a pre-experiment of normal incidence parallel light to the shack Hartmann wavefront sensor to obtain a deflection angle delta between a lens array surface and an image sensor surface in the shack Hartmann wavefront sensor;

(2) incident vortex light beams are transmitted into a shack Hartmann wavefront sensor to obtain recorded images;

(3) calculating barycentric location coordinates (X) of image distribution_c,Y_c)；

(4) Solving an initial average phase slope distribution diagram based on the detection principle of the shack Hartmann wavefront sensor;

(5) calculating an average phase slope compensation value corresponding to each convergent light spot, and compensating the initial average phase slope distribution diagram by using the compensation value;

(6) and detecting the topological value of the vortex light beam according to the compensated initial average phase slope distribution diagram.

Further, the specific implementation process of the step (1) is as follows:

1.1, for a shack Hartmann wavefront sensor, acquiring convergent light spots of each row and each column in an image, and performing linear fitting by using a least square method to obtain a slope value psi of each row and each column;

wherein: (x)_k,y_k) The coordinate of the kth convergent light spot on a certain row or a certain column of the image, and N is the number of the convergent light spots on the row or the column;

1.2 applying an arctangent function to the slope value psi of each row and each column to obtain an included angle phi between each row and each column and a horizontal line;

1.3 calculating a deflection angle delta between a lens array surface and an image sensor surface in the shack Hartmann wavefront sensor according to the included angle phi through the following formula;

wherein:representing the angle between the p-th line in the image and the horizontal line,representing the angle between the q-th column and the horizontal in the image, K^LAnd K^CRespectively the number of rows and columns in the image.

Further, the barycentric position coordinates (X) of the image distribution are calculated in the step (3) by the following formula_c,Y_c)；

Wherein: and (xi, eta) is the coordinate of a certain point in the image distribution, and I (xi, eta) is the light intensity of the point corresponding to the coordinate (xi, eta).

Further, in the step (4), the initial average phase slope distribution diagram is solved through the following formula;

wherein: (C)_x(i,j),C_y(i, j)) and (x (i, j), y (i, j)) are respectively the central coordinate of the ith row and jth column lens in the lens array and the corresponding convergent light spot coordinate, S_x(i, j) and S_y(i, j) are the components of the average phase slope in the horizontal direction and the vertical direction corresponding to the ith row and the jth column lens in the lens array respectively, f is the focal length of the lens, and lambda is the wavelength of the light beam.

Further, in the step (5), an average phase slope compensation value corresponding to the converged light spot is calculated through the following formula;

wherein: delta S_x(i, j) and Δ S_y(i, j) are the components of the average phase slope compensation value of the convergent light spot in the horizontal direction and the vertical direction at coordinates (x (i, j), y (i, j)) respectively.

Further, the initial average phase slope distribution map is compensated in the step (5) by the following formula;

S'_x(i,j)＝S_x(i,j)+ΔS_x(i,j)

S'_y(i,j)＝S_y(i,j)+ΔS_y(i,j)

wherein: s_x' (i, j) and S_y' (i, j) are components of the average phase slope in the horizontal direction and the vertical direction corresponding to the ith row and jth column lens in the compensated lens array, respectively.

Further, in the step (6), the topological value of the vortex beam is detected by using an average brightest intensity ring method.

The invention points out and verifies that the non-registration deviation exists in the shack Hartmann wavefront sensor, and provides a detection error caused by the non-registration deviation under the application scene of vortex beam topology value detection in a theoretical modeling mode. In addition, the invention provides a corresponding method for compensating the misregistration deviation, and experimental results show that after the compensation method is used for compensating the shack Hartmann wavefront sensor, the precision of vortex beam topological value detection is remarkably improved, so that the necessity of compensating the misregistration deviation in the shack Hartmann wavefront sensor and the effectiveness of the deviation compensation method are verified.

Drawings

Fig. 1 is a schematic diagram of a system principle of a shack hartmann wavefront sensor.

Fig. 2 is a schematic diagram illustrating the misregistration problem of the shack hartmann wavefront sensor, where a black dot is a central point of each sub-region of the image sensor surface after region segmentation, and a gray dot is a projection point of the central point of the sub-lens in the lens array on the image sensor surface.

Fig. 3 is a schematic diagram illustrating experimental demonstration of the misregistration problem of the shack-hartmann wavefront sensor, in which the left large image is an image recorded by incident parallel light to the shack-hartmann wavefront sensor, and the right four small images are enlarged images of the area surrounded by the gray square in the corresponding direction of the left large image.

FIG. 4 is a schematic diagram of a solution model of vortex beam topological values.

FIG. 5 is a simplified vortex beam topology value solution model diagram.

Fig. 6 is a diagram illustrating a topology value deviation caused by an misregistration problem.

Fig. 7 is a flowchart illustrating steps of the misregistration offset compensation method according to the present invention.

Detailed Description

In order to more specifically describe the present invention, the following detailed description is provided for the technical solution of the present invention with reference to the accompanying drawings and the specific embodiments.

As shown in fig. 2, the misregistration problem of the shack hartmann wavefront sensor means that a deflection angle exists between the lens array plane and the image sensor plane; to verify the existence of this misregistration problem, we performed experiments on parallel-light normal-incidence shack hartmann wavefront sensors. Fig. 3 is an image recorded by the shack hartmann wavefront sensor, and ideally, the convergence points of the lens array should be distributed on the horizontal and vertical lines shown by the solid lines in the figure, however, due to the existence of the deflection angle, the convergence points of the same row and column are distributed on both sides of the horizontal and vertical lines: the upper enlarged view has the convergence point to the left of the solid line, and the lower enlarged view has the convergence point to the right of the solid line; the convergence point is lower than the solid line in the left enlarged view, and upper than the solid line in the right enlarged view. That is, a counterclockwise deflection angle exists between the lens array plane and the image sensor plane, thereby proving the misregistration problem in the shack Hartmann wavefront sensor.

Next, we demonstrate through theoretical modeling that this misregistration problem introduces errors into the detected topological values of the vortex beam.

In an ideal case, that is, when there is no deflection angle between the lens array surface and the image sensor surface of the shack Hartmann wavefront sensor, the topological value solution model of the vortex beam can be shown in FIG. 4, where the origin of the coordinate axes is the projection point of the central point of the lens array surface on the image sensor surface, (x)₀,y₀) The central point of the far field distribution of the vortex beam on the image sensor surface. We first demonstrated that moving the lens array face of a shack hartmann wavefront sensor in the horizontal or vertical direction does not affect the solution of the vortex beam topology values.

For any point (x, y) on the far field distribution of the vortex beam, the phase gradient is:

wherein: n is the topological value and R is the radius of the distribution.

The displacement of this point along the tangential direction is small:

l_x＝-R sinθ·dθ

l_y＝R cosθ·dθ

the topological value TC can be solved based on the above two formulas:

that is, it is proved that when there is a horizontal or vertical offset between the lens array surface and the image sensor surface of the shack hartmann wavefront sensor, the solution of the topological value does not change. Therefore, the topological value solution model of the vortex beam can be simplified to the case where the projected point of the central point of the lens array plane coincides with the central point of the far field distribution of the vortex beam as shown in fig. 5.

Based on the above demonstration and simplification, we further explore the situation that a deflection angle exists between the lens array surface and the image sensor surface of the shack hartmann wavefront sensor. As shown in fig. 6, due to the deflection angle between the two surfaces, the projection point of the lens center point (black point) will not coincide with the center point (gray point) of the far-field distribution of the vortex beam on the image sensor, resulting in a change in the detected phase slope. Specifically, when the deflection angle is δ, the positional displacement amount of the (x, y) point is:

Δx＝R(cos(α+δ)-cosα)

Δy＝R(sin(α+δ)-sinα)

accordingly, the amount of change in phase slope is:

wherein: f and L are the focal length and diameter of the lens, respectively, and λ is the wavelength of the light beam.

Further, the change Δ TC of the vortex beam topology value is:

the above derivation verifies that the misregistration problem of the shack hartmann wavefront sensor introduces errors into the detection of the topological values.

Therefore, the invention provides a method for compensating for misregistration deviation, which comprises the following specific steps as shown in fig. 7:

s1, firstly, carrying out a preliminary experiment, comprising the following steps:

s1.1, the parallel light is normally incident into the shack Hartmann wavefront sensor, and the recorded image is obtained.

S1.2, linearly fitting convergence points of each row and column in the obtained image by using a least square method to obtain a slope value psi:

s1.3, converting the slope value of each row and column into an included angle value phi between the slope value and a horizontal line by using an arc tangent function:

Φ＝arctan(Ψ)

s1.4, performing statistical averaging on all the obtained phi to obtain the size of the deflection angle delta of the shack Hartmann wavefront sensor according to the following formula:

and S2, injecting the vortex light beam into the shack Hartmann wavefront sensor, and obtaining the recorded image.

S3, determining the gravity center position (X) of the distribution in the obtained image by using the following formula_c,Y_c)：

S4, solving an initial average phase slope distribution diagram based on the detection principle of the shack Hartmann wavefront sensor:

s5, calculating the corresponding average phase slope compensation value of each facula:

and compensating the initial average phase slope map:

S'_x(i,j)＝S_x(i,j)+ΔS_x(i,j)

S'_y(i,j)＝S_y(i,j)+ΔS_y(i,j)

s6, detecting the topological value of the vortex light beam by using a proper method such as an average brightest intensity ring method.

In order to verify that the method can effectively compensate the misregistration deviation of the shack Hartmann wavefront sensor, the following experiments are carried out: under two conditions of application and non-application of the compensation method, the average brightest intensity ring method is used for detecting the topological value of the far-field vortex light beam with the topological value range of +/-20, and experimental results show that the compensation method can obviously improve the performance of detecting the topological value. More specifically, when the absolute value of the topological value is greater than 10, the topological value detection accuracy of the far-field vortex light beam by the average brightest intensity loop method is improved from 0% to 100% by the compensation method; the experimental result fully verifies the effectiveness of the compensation method, and simultaneously verifies that the misregistration problem of the shack Hartmann wavefront sensor is the symptom that the topological value detection method fails under the far field condition.

The previous description of the specific embodiments is provided to enable any person skilled in the art to make or use the present invention. It will be readily apparent to those skilled in the art that various modifications to the specific embodiments described above may be made, and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art should make improvements and modifications to the present invention based on the disclosure of the present invention within the protection scope of the present invention.