NL2010457C2 - Hartmann wavefront measuring instrument adapted for non-uniform light illumination. - Google Patents
Hartmann wavefront measuring instrument adapted for non-uniform light illumination. Download PDFInfo
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- NL2010457C2 NL2010457C2 NL2010457A NL2010457A NL2010457C2 NL 2010457 C2 NL2010457 C2 NL 2010457C2 NL 2010457 A NL2010457 A NL 2010457A NL 2010457 A NL2010457 A NL 2010457A NL 2010457 C2 NL2010457 C2 NL 2010457C2
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- 238000004364 calculation method Methods 0.000 abstract description 9
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J1/00—Photometry, e.g. photographic exposure meter
- G01J1/42—Photometry, e.g. photographic exposure meter using electric radiation detectors
- G01J1/4228—Photometry, e.g. photographic exposure meter using electric radiation detectors arrangements with two or more detectors, e.g. for sensitivity compensation
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J1/00—Photometry, e.g. photographic exposure meter
- G01J1/42—Photometry, e.g. photographic exposure meter using electric radiation detectors
- G01J1/4257—Photometry, e.g. photographic exposure meter using electric radiation detectors applied to monitoring the characteristics of a beam, e.g. laser beam, headlamp beam
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- Spectroscopy & Molecular Physics (AREA)
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- Testing Of Optical Devices Or Fibers (AREA)
- Photometry And Measurement Of Optical Pulse Characteristics (AREA)
Abstract
A Hartmann wavefront measuring instrument applicable to inhomogeneous light illumination includes a spectroscope, a light distribution measuring instrument, a reconstruction matrix calculator, a micro lens array, a CCD (charge coupled device) camera, a slope calculator and a wavefront reconstruction device. The light distribution measuring instrument firstly measures the emergent/incident wavefront light power density; the reconstruction device obtains the reconstruction matrix through calculations as per incident wavefront light power density and required reconstruction image aberration type; the slope calculator calculates and obtains a to-be-measured wavefront slope vector according to a spot array acquired by the CCD camera; and the wavefront reconstruction device calculates and obtains the to-be-measured wavefront according to the slope vector and the reconstruction matrix. According to the invention, the reconstruction matrix calculation method in the modal method wavefront reconstruction process adopted by the Hartmann sensor is improved, the wavefront slope calculation accuracy in the reconstruction matrix algorithm when the incident light intensity is uneven is improved, and the core solution is provided for high-precision recovery of the incident wavefront under the inhomogeneous light illumination condition.
Description
Title: HARTMANN WAVEFRONT MEASURING INSTRUMENT ADAPTED FOR
NON-UNIFORM LIGHT ILLUMINATION
Technical Field 5
[0001] The present disclosure relates to a Hartmann wavefront measuring instrument applicable to adaptive optics. In particular, the present disclosure relates to a Hartmann wavefront measuring instrument adapted for non-uniform light illumination.
10 Background
[0002] The Hartmann wavefront sensor was initially applied in astronomical adaptive optics because it can provide real-time measurement with suitable measurement accuracy. With development of technology, the Hartmann wavefront sensor has been 15 widely used as a precise wavefront measuring instrument in mirror surface type detection, laser parameter diagnosis, flow field CT reconstruction, human-eye aberration diagnosis, and optical path alignment, etc., due to its simple structure and principle. The Hartmann wavefront sensor generally comprises micro-lenses and a CCD camera. It performs wavefront measurement based on wavefront slope measurement.
20 [0003] In operation of the Hartmann wavefront sensor, an array of micro-lenses divides a wave surface to be measured into a plurality of sample units. The sample units are converged onto separate focuses by the respective high-quality lenses and received by the CCD camera, respectively. Wavefront slant within each sub-aperture will cause displacement of a corresponding light spot in x and y directions. The displacement of the 25 centroid of the light spot in the x and y directions reflects a wavefront slope of a corresponding sample unit in the two directions. In the Zernike modal wavefront reconstruction algorithm, Zernike coefficients of reconstructed wavefront are obtained by multiplying a wavefront slope vector with a reconstruction matrix. Thus, error of the reconstructed wavefront will decrease if the reconstruction matrix can be calculated 30 properly.
[0004] Conventional reconstruction matrix calculations for the Hartmann wavefront sensor are all based on an assumption that light intensity of the wavefront to be measured is in a uniform distribution. In such a case, the displacement of the centroid within a single 2 sub-aperture of the Hartmann wavefront sensor is proportional to an average slope of the wavefront within the sub-aperture (HARDY J W, Adaptive optics for astronomical telescope [M], Oxford University Press, 1998). However, in practice, light intensity of the wavefront to be measured is generally distributed non-uniformly. In such a case, the displacement of the 5 centroid within the single sub-aperture of the Hartmann wavefront sensor is relative to both the average slope of the wavefront within the sub-aperture and the distribution of the light intensity within the sub-aperture. As a result, the reconstructed wavefront will have a significant error if the reconstruction matrix is still calculated using the conventional method based on the average wavefront slope. This is disadvantageous for applications of the 10 Hartmann wavefront sensor in high-accuracy wavefront measurement.
[0005] In view of the foregoing problems, it has become an important research topic to improve the calculation method of the reconstruction matrix for the Hartmann wavefront sensor under non-uniform light illumination so as to improve reconstruction accuracy of the Hartmann wavefront sensor under the non-uniform light illumination.
15
Summary
[0006] In view of the foregoing problems of the prior art, the present disclosure provides, among others, a Hartmann wavefront measuring instrument adapted for 20 non-uniform light illumination to improve accuracy of wavefront reconstruction.
[0007] According to an aspect of the present disclosure, there is provided a Hartmann wavefront measuring instrument adapted for non-uniform light illumination. The Hartmann wavefront measuring instrument may comprise: a splitter, a light intensity distribution measuring instrument, a reconstruction matrix calculator, a micro-lens array, a 25 CCD camera, a slope calculator, and a wavefront reconstructor. The splitter can be configured to divide an incident wavefront into a portion for wavefront energy measurement and a portion for wavefront slope measurement. The light intensity distribution measuring instrument can be configured to receive the portion for wavefront energy measurement, and also to measure light power density of the incident wavefront and transfer light power 30 density data to the reconstruction matrix calculator. The reconstruction matrix calculator can be configured to calculate a reconstruction matrix from the light power density of the incident wavefront and a type of aberration to be reconstructed and transfer the reconstruction matrix to the wavefront reconstructor. The micro-lens array can be 3 configured to divide portion for the wavefront slope measurement, which, thus divided, generates a light spot array at the CCD camera. The CCD camera can be configured to collect an image of the light spot array and transfer the image to the slope calculator. The slope calculator can be configured to calculate a slope vector of the wavefront to be 5 measured and transfer the slope vector to the wavefront reconstructor. The wavefront reconstructor can be configured to reconstruct the wavefront to be measured from the slope vector and the reconstruction matrix.
[0008] The reconstruction matrix calculator may calculate the reconstruction matrix from the light power density of the incident wavefront and the type of the aberration to be 10 reconstructed by: (a) designating a number for each valid sub-aperture; (b) calculating a slope Zxk(m) in x direction and a slope Zyk(m) in y direction of a kth Zernike aberration at an mth aperture by: 15 ( ZAm)’i s.|f/(*,,)** jy l\lU,y)a'Z‘{*,y) dxdy
Zj*W= xjjl(x,y)Ady
20 S
where Zk(x,y) is a kth Zernike polynomial, I(x,y) is a light intensity distribution expression of the wavefront to be measured, which is measured by the light intensity distribution measuring instrument, and S is an area of the sub-aperture; (c) arranging, in case where the Hartmann wavefront sensor has M valid 25 sub-apertures in total and a number of Zernike aberrations to be reconstructed is K, the
Zxk(m) and Z k{m) calculated in step (b) as below to obtain a restoration matrix D: - zxfi) ζ,,ω ... ζ,,σΓ z„0) z„0) - z*0) Z„( 2) 2,,(2) ... Ζ„(2) 30 D- Z„<2) Z„<2) ... V(2) ;and ZJM) ... Ζλ(Μ) _Zyl(M) Zy2(M) ... ZyK(M)_ 4 (d) calculating an inverse matrix D+ of the restoration matrix D as the reconstruction matrix.
[0009] According to the present disclosure, the Hartmann wavefront sensor may include the light intensity distribution measuring instrument and the reconstruction matrix 5 calculator therein. The light intensity distribution measuring instrument is configured to measure the light intensity distribution of the wavefront to be measured, and the reconstruction matrix calculator is configured to calculate the reconstruction matrix from the light intensity distribution of the incident wavefront and the type of the aberration to be reconstructed. In this way, errors of calculating the reconstruction matrix by the 10 conventional reconstruction matrix calculation method caused by not taking into consideration the influence of the light intensity can be corrected. As a result, the accuracy of wavefront reconstruction can be improved.
[0010] The present disclosure can provide the following advantages, for example.
(1) A conventional Hartmann wavefront sensor based on modal 15 reconstruction algorithm calculates the reconstruction matrix by calculating the slope distribution of the wavefront within individual sub-apertures based on the average slope method. The average slope method adopts a premise that the light intensity of the wavefront to be measured is in a uniform distribution. However, in practice, the light intensity of the wavefront to be measured may have a non-uniform distribution and thus the 20 slope of the wavefront within a single sub-aperture may be different from the average slope. As a result, the reconstructed wavefront by multiplying the reconstruction matrix calculated using the conventional reconstruction matrix algorithm with the slope vector of the wavefront to be measured has a significant error. According to the present disclosure, the reconstruction matrix is calculated by taking into consideration both the light intensity 25 distribution of the wavefront and the phase distribution of the wavefront, so as to correct the calculation error of the reconstruction matrix in the conventional reconstruction matrix calculation method due to not taking into consideration the influence of the light intensity and thus improve the accuracy of wavefront reconstruction.
(2) In case where the Hartmann wavefront sensor is used for measuring the 30 wavefront having a non-uniform light intensity distribution, the sensor operates in a way similar to the conventional Hartmann wavefront sensor except that the algorithm of calculating the reconstruction matrix needs to be modified. Therefore, costs for deploying the present technology can be low.
5
Brief Description of Drawings
[0011] Fig. 1 is a schematic view of a Hartmann wavefront sensor according to an embodiment of the present disclosure;
[0012] Fig.2 is a schematic view of arrangement and numbering of sub-apertures 5 according to an embodiment;
[0013] Fig. 3 is a diagram showing power density of incident light according to an embodiment;
[0014] Fig.4 is a light spot array image under non-uniform light illumination according to an embodiment; 10 [0015] Fig.5 is a schematic view of a wavefront to be measured according to an embodiment; and
[0016] Fig.6 is a plot showing errors of reconstructed wavefront by a conventional reconstruction matrix algorithm and errors of reconstructed wavefront by a reconstruction matrix algorithm according to the present disclosure.
15 [0017] 1 splitter 2 light intensity distribution measuring instrument 3 reconstruction matrix calculator 4 micro-lens array 20 5 CCD camera 6 slope calculator 7 wavefront reconstructor 8 wavefront to be measured 9 portion for wavefront energy measurement 25 10 portion for wavefront slope measurement
Detailed Description of Embodiments
[0018] According to an embodiment of the present disclosure, a Hartmann 30 wavefront sensor may have a 10x10 sub-aperture array. Fig.2 shows an example of the arrangement and numbering of the sub-apertures, wherein only valid ones of the sub-apertures are shown. Here, the first twenty-five Zernike aberrations need to be reconstructed. A wavefront 8 to be measured may have a light intensity in Gaussian 6 distribution as shown in Fig.3. The wavefront 8 to be measured may have aberration such
as out-of-focus aberration with an out-of-focus amount of as shown in Fig.5. A CCD
camera 5 may have a full measuring range of 4095ADU (12-bit). A mean square root of noise of the CCD camera can be 20ADU. A single sub-aperture of the CCD camera 5 may 5 have a size of 1 mm x 1 mm.
[0019] Expressions of Zernike polynomials used in this embodiment where the aberrations to be reconstructed are out-of-focus aberrations as stated above can be as below: Ζπμλ (?,&) = λ/2(/ϊ + Ι)< (λ) cos(jm - 0)} 10 _ f..............0 A 0 0) = ι/2(Η + 1)Λί - Θ) , Zk(rfB) = p(n+\)R»(r).........................................i = 0 (1) = 16 y2_(-iy(tt-ir)! ^!LCö + ö)/2-i]![(ö-è)/2-4’J! b<^a,a- \ b\=even where k is an order of the polynomials, r and □ are a radial position and an angular position of the polynomials in a polar coordinate system, respectively, and a and b are a radial frequency and an angular frequency of the polynomials, respectively.
[0020] As shown in Fig. 1, the incident wavefront 8 can be divided into a portion 9 20 for wavefront energy measurement and a portion 10 for wavefront slope measurement via a splitter 1. The portion 9 for wavefront energy measurement enters a light intensity distribution measuring instrument 2. The portion 10 for wavefront slope measurement is divided via a micro-lens array 4 and then generates an array of light spots at the CCD camera 5.
25 [0021] According to the present disclosure, the wavefront 8 to be measured can be reconstructed by the following process.
1) The light intensity distribution measuring instrument 2 measures light power density (for example, one as shown in Fig.3) of the wavefront 8 to be measured to obtain a light power density expression I(x,y) .
30 2) A reconstruction matrix calculator 3 calculates a slope in x direction and a slope in y direction for each of the 1st to the 25th Zernike aberrations in each sub-aperture in order in accordance with the numbering shown in Fig.3. Here, the slope Zxk(m) in the x 7 direction and the slope Zyk(m) in the y direction of the kth Zernike aberration at the mth aperture can be calculated based on the light power density of the incident wavefront 8 and the type of aberrations to be reconstructed (out-of-focus aberrations in this example) as follows: 5 \\l{x,y)dZk^y^-dx<fy ^ ^ s' (2) 10 ljr{x,y)^*^’y-cbafy ZV,.I>H) = -ft-— S- jy(x,y')tbidy
L S
15 where Zk(pc,y) is a kth Zernike polynomial as expressed above for the out-of-focus aberrations, I(x,y) is a light intensity distribution expression of the wavefront 8 to be measured, and S is an area of the sub-aperture.
3) The reconstruction matrix calculator 3 arranges the results obtained in 2) as below to obtain a restoration matrix D: 20 "^P> Z*<1) ... Z,3S<1)·
Zyl(l) 1) ... Z^i 1)
Zal(2) Ζ^(2) ... Zx25(2) D= Zyi (2} Zy2(2) ... ZySS (2) ^2) 25 ...........
(76) Zx2(76) .....Zm(76) Z..C76) 2,,(76) ... ZrfJ( 76)_
Then, the reconstruction matrix calculator 3 calculates an inverse matrix D+ of the restoration matrix D to obtain the reconstruction matrix D+.
30 4) A slope calculator 6 calculates centroids of for the array of light spots (as
shown in Fig.4) collected by a CCD camera 5 by, e.g. a method as disclosed by CN Application No. 201210071732.0, entitled “A HARTMANN WAVEFRONT SENSOR
8 ADOPTING TIME-DIVISION EXPOSURE.” For example, the centroid of the light spot at a sub-aperture m can be calculated as:
L,M LJM
Zw (4) Zw xc(™) = Jh—— (4) Z X &<j v v where xc(m) and yc(m) represent the positions of the centroid of the light spot at the
X V
sub-aperture m in x and y directions, respectively; represent the positions of a pixel in x and y directions; ^ is a gray value at the pixel within a 10 sub-aperture; and L,M represent the sizes of the sub-aperture in x and y directions in unit of pixel.
5) The array of centroids thus calculated is converted to a slope vector G by: (s).
15 where and ' ^ * are slopes of the wavefront to be measured at the sub-aperture m in the x direction and the y direction, respectively, and f is a focal length of a single micro-lens in the micro-lens array 4. Then the array of slopes is arranged as below to obtain the slope vector G of the wavefront 8 to be measured: 2Q ¢ = [G, (1), Gy (1), G, (2), Gy (2).....Gx (76), G, ¢76)]' (6).
6) A wavefront reconstructor 7 calculates a Zernike vector A of a reconstructed wavefront from the reconstruction matrix D+ and the slope vector G by the following equation so as to obtain the reconstructed wavefront: A = D+G ¢7).
25 (7).
[0022] Conventional wavefront reconstruction process does not take into consideration influence of the light power distribution of the wavefront 8 to be measured on the position of the centroids of the array of light spots at the CCD camera 5. Thus, it does not include measuring the light power distribution of the wavefront 8 to be measured as 30 described in step 1). Further, in step 2), the slopes in the x direction and the y direction within the mth sub-aperture are calculated by: i 9 |ζ'-Μ=-ε-^- j b ¢6), 5 ίν, iz •‘(”)--S- Z' (m) Z' (m) where xkK ’ and yky ’ are the slopes in the x direction and the y direction within the mth sub-aperture, respectively, and S is the area of the sub-aperture.
7' (m\ 7' (m)
[0023] After the ’ and yk ’are obtained, the conventional wavefront 10 reconstruction process is analogous to the wavefront reconstruction process according to the present disclosure.
[0024] Fig.6 is a plot showing errors of reconstructed wavefront for 100 times of reconstruction of the wavefront 8 to be measured by the conventional reconstruction method and the reconstruction method described herein, respectively. Fluctuations of the 15 errors are mainly due to the noise of the CCD camera 5. As shown in Fig.6, the error of the reconstructed wavefront calculated by the conventional reconstruction matrix algorithm is 0.18Z% jhe error 0f the reconstructed wavefront calculated by the reconstruction matrix algorithm described herein is 0.11λ% Thus, the technology of the present disclosure improves the accuracy of the wavefront reconstruction.
20 [0025] In summary, in case where the wavefront 8 to be measured has a light intensity in a non-uniform distribution, the present disclosure calculates the reconstruction matrix by taking into consideration the light intensity distribution of the wavefront and the phase distribution of the wavefront, which corrects the errors in calculating the reconstruction matrix by the conventional reconstruction matrix calculation method due to 25 not taking into consideration the influence of the light intensity and improves the accuracy of the wavefront reconstruction.
30
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| CN201210072934.7A CN102589720B (en) | 2012-03-19 | 2012-03-19 | Hartmann wavefront measuring instrument suitable for non-uniform light illumination |
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| CN105842848A (en) * | 2016-06-15 | 2016-08-10 | 中国科学院长春光学精密机械与物理研究所 | Hartmann wavefront detector electron multiplication gain self-adaptive control method |
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| CN104239740B (en) * | 2014-09-26 | 2018-04-13 | 中国科学院光电技术研究所 | Mode wavefront restoration method based on Hartmann wavefront sensor |
| CN106644059B (en) * | 2016-09-14 | 2018-07-31 | 苏州大学 | A kind of measurement method of the double connected function of light beam |
| CN106441084B (en) * | 2016-11-21 | 2019-02-01 | 深圳大学 | Wavefront sensor, wavefront sensing methods and system based on micro- hologram array |
| CN108151888B (en) * | 2017-11-22 | 2019-09-27 | 中国科学院长春光学精密机械与物理研究所 | A method of for scanning the error decoupling of Hartmann's detection device |
| CN109029719B (en) * | 2018-06-25 | 2020-12-25 | 南京理工大学 | Ultraviolet light energy distribution detection system based on shack Hartmann method and detection method thereof |
| CN116659686B (en) * | 2023-04-27 | 2024-06-28 | 西安工业大学 | Wavefront reconstruction method and device |
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| US5777719A (en) * | 1996-12-23 | 1998-07-07 | University Of Rochester | Method and apparatus for improving vision and the resolution of retinal images |
| US6199986B1 (en) * | 1999-10-21 | 2001-03-13 | University Of Rochester | Rapid, automatic measurement of the eye's wave aberration |
| CN100573065C (en) * | 2006-08-07 | 2009-12-23 | 中国科学院光电技术研究所 | Wavefront measurement method based on linear phase inversion |
| JP2009162614A (en) * | 2008-01-07 | 2009-07-23 | Mitsubishi Electric Corp | Optical wavefront measuring apparatus |
| JP5452032B2 (en) * | 2009-02-13 | 2014-03-26 | 株式会社日立製作所 | Wavefront aberration measuring method and apparatus |
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| CN105842848A (en) * | 2016-06-15 | 2016-08-10 | 中国科学院长春光学精密机械与物理研究所 | Hartmann wavefront detector electron multiplication gain self-adaptive control method |
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