An absolute calibration method for Hartmann sensor

Abstract

The present invention provides an absolute calibration method for a Hartmann sensor, which calculates the root mean square (RMS) of the measured wave surface fluctuation based on spherical wave data. 理论 , calculate the RMS value of the restored wavefront, and compare the RMS value of the restored wavefront with the RMS value of the measured wave surface fluctuation. 理论 The ratio of the Hartmann sensor is used to calibrate the proportional coefficient of the Hartmann sensor. When the displacement distance is small, the RMS value error rate of the spherical wavefront generated by the present invention is smaller, that is, the spherical wavefront generated by the present invention has higher accuracy and stability; when the distance is large, the error rate of the present invention and the existing calibration method will gradually become equal.

Description

Technical Field

[0001] The invention relates to the field of Shack-Hartmann wavefront sensors, and in particular to an absolute calibration method for a Hartmann sensor. Background Art

[0002] The Hartmann wavefront sensor is a detection device that uses a microlens array to divide and collect incident wavefront information. First, the wavefront to be measured is sampled to obtain a spot image; then a reasonable centroid algorithm is selected to obtain the centroid position of each sub-spot image, and the calibrated centroid position is subtracted therefrom to obtain the wavefront slope; finally, the wavefront restoration algorithm is used to restore the wavefront to be measured from the slope information to complete the wavefront detection.

[0003] Due to its ease of use and strong recovery capability, the Hartmann wavefront sensor has been applied to high-precision imaging, adaptive optics, atmospheric turbulence simulation, human eye imaging and other technical fields. In widespread application practice, the Hartmann wavefront sensor needs to be calibrated before use. The purpose of calibrating the Hartmann is, first, to eliminate the system errors caused by optical processing and equipment assembly; second, to measure the proportional coefficient of the restored wavefront to the actual measured wavefront.

[0004] The current Hartmann measurement error calibration methods include phase difference plate calibration method and spherical wave calibration method.

[0005] Among them, the phase difference plate calibration method needs to determine the error by comparing the phase difference of the phase difference plate detected by the phase difference detection device and the Shack-Hartmann wavefront sensor respectively. Therefore, the use of a phase difference detection device, usually an interferometer, is introduced, which also leads to the need to additionally calculate the error of the interferometer.

[0006] The spherical wave calibration uses the Hartmann wavefront sensor to directly detect the spherical wave emitted by the point light source, and after restoration, it is compared with the theoretically calculated spherical wave to obtain the proportional coefficient between the restored wavefront and the wavefront to be measured. However, this method can only produce a spherical wavefront with high curvature at a close distance, and cannot produce a plane wave or a spherical wavefront with low curvature. Therefore, the present invention aims to invent a method for calibrating the Hartmann wavefront sensor using a low-curvature spherical wavefront. Summary of the invention

[0007] The present invention provides an absolute calibration method for a Hartmann sensor, which mainly solves the technical problem that the existing Hartmann calibration method needs to introduce additional error factors, or uses a spherical wavefront with high curvature at a close distance, and cannot calibrate the Hartmann wavefront sensor with a plane wave or a spherical wavefront with low curvature, which will cause large errors in the calibration process.

[0008] In order to solve the above technical problems, the present invention provides an absolute calibration method of a Hartmann sensor, comprising:

[0009] S10. Calculate the RMS of the measured wave surface fluctuation based on the spherical wave data. 理论 ;

[0010] S20, calculating the RMS value of the restored wavefront, including:

[0011] S21, recording the spot image and spot position data formed on the receiver of the Hartmann wavefront sensor by spherical wavefronts with different wavefronts through experiments;

[0012] S22, according to the loaded spot image and spot position data, use the following formula (1) to calculate the spot centroid position (x) corresponding to the microlens with coordinates (n, m) on the Hartmann wavefront sensor i ,y i );

[0013]

[0014] The number of receiver pixels corresponding to the microlens is N*M, I nm is the pixel intensity at position (n, m) in a single microlens. The center position of the microlens corresponding to the pixel is set to (0, 0). The coordinate group (x i ,y i ) is the wavefront slope vector;

[0015] S23, using Zernike polynomials, as shown in the following formula (2), to fit the measured wavefront to obtain the RMS value of the restored wavefront;

[0016]

[0017] In the formula, a k are the Zernike polynomial coefficients;

[0018] S30, by calculating the RMS value of the restored wavefront and the root mean square RMS of the measured wave surface fluctuation 理论 The ratio of is used to realize the proportional coefficient calibration of the Hartmann wavefront sensor.

[0019] Furthermore, the spherical wave is generated by using an optical fiber to generate a point light source through a lens.

[0020] Furthermore, the spherical wave data includes the focal length f of the lens, the displacement d of the point light source relative to the lens focus, and the aperture r of the lens; and the root mean square RMS of the measured wave surface fluctuation is calculated based on the spherical wave data. 理论 include:

[0021] Through the following formula (3):

[0022]

[0023] In the formula, PV is the distance from the apex of the spherical wave to the light opening;

[0024] The distance PV from the apex of the spherical wave to the light opening is calculated by the following formula (4):

[0025]

[0026] Where R is the radius of the spherical wave;

[0027] The spherical wave radius R is calculated by the following formula (5):

[0028]

[0029] Optionally, the RMS value of the restored wavefront is the third-order polynomial coefficient of the Zernike polynomial.

[0030] The beneficial effects of the present invention are:

[0031] According to the present invention, a Hartmann sensor absolute calibration method is provided, comprising: S10, calculating the root mean square RMS of the measured wave surface fluctuation according to the spherical wave data; 理论 ; S20, calculating the RMS value of the restored wavefront, including: S21, experimentally recording the spot image and spot position data formed on the receiver of the Hartmann wavefront sensor by the spherical wavefront with different wavefront information; S22, according to the loaded spot image and spot position data, using the following formula (1) to calculate the spot centroid position (x) corresponding to the microlens with coordinates (n, m) on the Hartmann wavefront sensor i ,y i ); (1) The number of receiver pixels corresponding to the microlens is N*M, I nm is the pixel intensity at position (n, m) in a single microlens. The center position of the microlens corresponding to the pixel is set to (0, 0). The coordinate group (x i ,y i ) is the wavefront slope vector; S23, using the Zernike polynomial, as shown in the following formula (2), the measured wavefront is fitted to obtain the RMS value of the restored wavefront; (2) In the formula, a k is the Zernike polynomial coefficient; S30, by calculating the RMS value of the restored wavefront and the root mean square RMS of the measured wavefront fluctuation 理论 When the displacement distance is low, the theoretical error rate of the spherical wavefront radius generated by the present invention is smaller, that is, the spherical wavefront generated by the present invention has higher accuracy and stability; when the displacement distance is high, the error rate of the present invention and the existing calibration method will gradually become equal. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a schematic flow chart of an absolute calibration method for a Hartmann sensor according to Embodiment 1 of the present invention;

[0033] Figure 2 This is a schematic diagram of the calibration principle structure of the first embodiment of the present invention;

[0034] Figure 3 This is a schematic diagram of the calibration effect of the first embodiment of the present invention. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below through specific implementation methods in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0036] Embodiment 1:

[0037] This embodiment provides an absolute calibration method for a Hartmann sensor. Figure 1 , mainly including the following:

[0038] S10. Calculate the RMS of the measured wave surface fluctuation based on the spherical wave data. 理论 ;

[0039] Spherical waves are generated using optical fibers to generate point light sources through lenses.

[0040] The spherical wave data includes the focal length of the lens f, the displacement of the point light source relative to the lens focus d, and the aperture of the lens r; the root mean square RMS of the measured wave surface fluctuation is calculated based on the spherical wave data. 理论 Values ​​include:

[0041] Through the following formula (6):

[0042]

[0043] Where, RMS 理论 is the root mean square of the measured wave surface fluctuation, and PV is the distance from the apex of the spherical wave to the light opening; the distance PV from the apex of the spherical wave to the light opening is calculated by the following formula (7):

[0044]

[0045] Where R is the radius of the spherical wave;

[0046] The spherical wave radius R is calculated by the following formula (8):

[0047]

[0048] S20, calculating the RMS value of the restored wavefront, including:

[0049] S21, recording the spot image and spot position data formed on the receiver of the Hartmann wavefront sensor by spherical wavefronts with different wavefronts through experiments;

[0050] S22, according to the loaded spot image and spot position data, the spot centroid position (x) corresponding to the microlens with coordinates (n, m) on the Hartmann wavefront sensor is calculated using the following formula (9): i ,y i );

[0051]

[0052] The number of receiver pixels corresponding to the microlens is N*M, I nm is the pixel intensity at position (n, m) in a single microlens. The center position of the microlens corresponding to the pixel is set to (0, 0). The coordinate group (x i ,y i ) is the wavefront slope vector;

[0053] S23, using Zernike polynomials, as shown in the following formula (10), to fit the measured wavefront to obtain the RMS value of the restored wavefront;

[0054]

[0055] In the formula, a k are the Zernike polynomial coefficients;

[0056] S30, by calculating the RMS value of the restored wavefront and the theoretical root mean square value RMS of the measured wave surface fluctuation 理论 The ratio of is used to realize the proportional coefficient calibration of the Hartmann wavefront sensor.

[0057] Figure 2 This is the calibration principle of the present invention. In the figure, f is the focal length, d is the displacement of the light source relative to the focus, R is the radius of the spherical wave, r is the aperture, and PV is the distance from the vertex of the spherical wave to the aperture. A point light source is generated using an optical fiber, and a wavefront to be processed by the Hartmann wavefront sensor is generated through a lens. When the point light source is placed at the focal position of the lens, according to the principle of geometric optics, as shown in formula (11), the point light source wavefront will form a plane wavefront after passing through the lens, which is equivalent to the light source being incident from infinity.

[0058]

[0059] Formula (11) is the principle of lens imaging, where f is the focal length of the lens, v is the image distance on the left side of the lens, and u is the object distance on the right side of the lens. Since the optical path is reversible, it can be considered that the point light source is at the image distance v = d + f, then the wavefront of the point light source after passing through the lens is equivalent to the spherical wavefront propagating from the point light source at the object distance position u = R to the lens, and the radius of the spherical wavefront is the same as the object distance R. R can be calculated by formula (11), and then the PV value is calculated using R and the aperture r.

[0060]

[0061]

[0062] According to the spherical wave undulation root mean square RMS 理论 The proportional relationship with the PV value is:

[0063]

[0064] The spot images and spot position data formed by low-curvature spherical wavefronts with different wavefronts on the receiver of the Hartmann wavefront sensor are experimentally recorded.

[0065] According to the loaded spot image and spot position and formula (15), the coordinates on the Hartmann wavefront sensor are calculated as (x i ,y i ) is the centroid position of the light spot corresponding to the microlens.

[0066]

[0067] The number of receiver pixels corresponding to the microlens is N*M, I nm is the pixel intensity at position (n, m) in a single microlens. The center position of the microlens corresponding to the pixel can be set to (0, 0), then the coordinate group (x i ,y i ) is the wavefront slope vector.

[0068] After obtaining the wavefront slope vector, the RMS value of the restored wavefront can be obtained by fitting the measured wavefront using the Zernike polynomial as shown in equation (16), where a k is the Zernike polynomial coefficient. The proportional coefficient of the Hartmann wavefront sensor is obtained by comparing the restored wavefront with the measured wavefront theoretical value.

[0069]

[0070] The Zernike polynomial and the slope of the corresponding position of the microlens have the following relationship:

[0071]

[0072] Where Z xk and Z yk is the average phase difference slope in the x and y directions, expressed as:

[0073]

[0074] Where S is the normalized area corresponding to the microlens.

[0075] Assume the slope wavefront vector is G = (G x (i),G y (i))=(x i ,y i ), it is clear that G and Zernike polynomials have the following relationship:

[0076]

[0077] In short:

[0078] G=DA n (20)

[0079] Where D is Z in formula (19) xk and Z yk The matrix is ​​composed of k = 1 to n. n is the Zernike polynomial coefficient, which is the wavefront information we need to calculate. By applying the inverse matrix of D obtained by singular value decomposition method to G, we can calculate A n . Then A n Substituting into formula (16) we can get the restored wavefront. At this time, the coefficient of the third-order Zernike polynomial is the RMS value of the fitted restoration. By comparing the restored RMS with the RMS given by formula (14), 理论 The calibration coefficient of the Hartmann wavefront sensor can be obtained.

[0080] Compared with the current method of calibrating Hartmann using a fiber point light source to emit a high curvature spherical wavefront, the present invention has higher accuracy at close range. Substituting equation (13) into equation (14), taking the derivative of equation (14) with respect to displacement d can obtain equation (21):

[0081]

[0082] At the same time, the difference between the generation of the traditional spherical wavefront and the present invention is that the displacement d of the traditional spherical wavefront is the same as the wavefront R. Therefore, R can be directly used for derivation to obtain:

[0083]

[0084] The above two equations are the changes in the RMS value when d has an error. Use f=2000mm, d ranging from 1mm to 15mm, and r as 2mm as input to calculate the above two equations. The calculation results of the ratio change are shown as follows Figure 3 Since the wavefront curvature radius of the present invention is small, the RMS 理论 The change value and RMS 理论 The change in ratio obtained as a comparison itself is more convincing.

[0085] Obviously, if Figure 3 As shown, when the displacement distance is small, the RMS of the spherical wavefront generated by the present invention is 理论 The error rate is smaller, that is, the spherical wavefront generated by the present invention has higher accuracy and stability. When the displacement distance is high, the error rate of the present invention and the existing calibration method will gradually equalize, but in actual use, the point light source at a farther position will introduce alignment errors, so high accuracy at close range is more important.

[0086] Obviously, those skilled in the art should understand that the modules or steps of the present invention described above can be implemented by a general-purpose computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a computer storage medium (ROM / RAM, magnetic disk, optical disk) and executed by the computing device, and in some cases, the steps shown or described can be executed in a different order than that here, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Therefore, the present invention is not limited to any specific combination of hardware and software.

[0087] The above contents are further detailed descriptions of the present invention in combination with specific implementation methods, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. An absolute calibration method for a Hartmann sensor, characterized in that: include: S10. Calculate the RMS of the measured wave surface fluctuation based on the spherical wave data. 理论 , the spherical wave is generated by using an optical fiber to generate a point light source through a lens; S20, calculating the RMS value of the restored wavefront, including: S21, recording the spot image and spot position data formed on the receiver of the Hartmann sensor by spherical wavefronts with different wavefronts through experiments; S22, according to the loaded spot image and spot position data, use the following formula (1) to calculate the spot centroid position (x) corresponding to the microlens with coordinates (n, m) on the Hartmann sensor i ,y i ); The number of receiver pixels corresponding to the microlens is N*M, I nm is the pixel intensity at position (n, m) in a single microlens. The center position of the microlens corresponding to the pixel is set to (0, 0). The coordinate group (x i ,y i ) is the wavefront slope vector; S23, using Zernike polynomials, as shown in the following formula (2), to fit the measured wavefront to obtain the RMS value of the restored wavefront; In the formula, a k are Zernike polynomial coefficients; S30, by calculating the RMS value of the restored wavefront and the root mean square RMS of the measured wave surface fluctuation 理论 The ratio of is used to calibrate the proportional coefficient of the Hartmann sensor; The spherical wave data includes the focal length f of the lens, the displacement d of the point light source relative to the lens focus, and the aperture r of the lens; the root mean square RMS of the measured wave surface fluctuation is calculated based on the spherical wave data. 理论 include: Through the following formula (3): In the formula, PV is the distance from the apex of the spherical wave to the light opening; The distance PV from the apex of the spherical wave to the light opening is calculated by the following formula (4): Where R is the radius of the spherical wave; The spherical wave radius R is calculated by the following formula (5):

2. The absolute calibration method of the Hartmann sensor according to claim 1, characterized in that: The RMS value of the restored wavefront is the third-order polynomial coefficient of the Zernike polynomial.

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