[논문]Improved Iterative Method for Wavefront Reconstruction from Derivatives in Grid Geometry

Nguyen, Vu-Hai-Linh; Rhee, Hyug-Gyo; Ghim, Young-Sik

doi:10.3807/copp.2022.6.1.001

Improved Iterative Method for Wavefront Reconstruction from Derivatives in Grid Geometry 원문보기

Current optics and photonics, v.6 no.1, 2022년, pp.1 - 9

Nguyen, Vu-Hai-Linh (Department of Science of measurement, University of Science and Technology) , Rhee, Hyug-Gyo (Department of Science of measurement, University of Science and Technology) , Ghim, Young-Sik (Department of Science of measurement, University of Science and Technology)

Abstract ▼ AI-Helper

This paper proposes a robust, simple zonal wavefront-estimation method in a grid sampling model. More slopes are added to the integral equation of the algorithm to improve the accuracy and convergence rate of this approach, especially for higher-order optical aberrations. The Taylor theorem is applied to clarify the mathematical description of the remaining error in the proposed method. Several numerical simulations are conducted to ensure the performance and improvement in comparison to the Southwell and previous algorithm. An experiment is also conducted according to deflectometry output and the results are verified using a reference measured with a stylus system.

주제어

표/그림 (9)

그림 FIG. 1. Grid sampling geometry for the zonal wavefront-reconstruction method. In this geometry, the phase values coincide with the vertical and horizontal slopes at each grid point.
그림 FIG. 2. Domain divided: each set of nine grid points is sorted into four groups. There are four phase points in each group.
그림 FIG. 3. Comparison of relative error levels of the algorithms. The simulated wavefront aberrations are Zernike polynomials, from 2^nd term to 36^th term.
그림 FIG. 4. The random Gaussian rough surface for the simulation.
그림 FIG. 5. Residual error between the ideal and the reconstructed surface, by (a) Southwell [11], (b) Phuc [18], (c) Pathak [17], and (d) proposed algorithms.
그림 FIG. 6. Convergence rates of the algorithms for the first 36 Zernike terms.
그림 FIG. 7. Comparison of the error-propagation rates of four algorithms. N is the size of the grid in one dimension (that is, from 10 to 100).
그림 FIG. 8. Concept of defelectometry, and its output. The sinusoidal fringe patterns are projected onto the sample, and the slope data can be obtained from the image information taken by the camera.
그림 FIG. 9. 3D surface profile map: (a) reconstructed using the proposed method, (b) measured by a commercial stylus, and (c) comparison result of the A-A’ line profiles by the two methods.

참고문헌 (24)

J. H. Lee, S. E. Lee, and Y. J. Kong, "Performance prediction of a laser-guide star adaptive optics system for a 1.6 m telescope," Curr. Opt. Photonics 2, 269-279 (2018).

원문보기 상세보기
J. H. Lee, S. Shin, G. N. Park, H.-G. Rhee, and H.-S. Yang, "Atmospheric turbulence simulator for adaptive optics evaluation on an optical test bench," Curr. Opt. Photonics 1, 107-112 (2017).

원문보기 상세보기
K. Ahn, S.-H. Lee, I.-K. Park, and H.-S. Yang, "Simulation of a laser tomography adaptive optics with Rayleigh laser guide stars for the satellite imaging system," Curr. Opt. Photonics 5, 101-113 (2021).

원문보기 상세보기
Y.-S. Ghim, H.-G. Rhee, A. Davies, H.-S. Yang, and Y.-W. Lee, "3D surface mapping of freeform optics using wavelength scanning lateral shearing interferometry," Opt. Express 22, 5098-5105 (2014).

상세보기
M. T. Nguyen, Y.-S. Ghim, and H.-G. Rhee, "Single-shot deflectometry for dynamic 3D surface profile measurement by modified spatial-carrier frequency phase-shifting method," Sci. Rep. 9, 3157 (2019).

상세보기
M. P. Rimmer, "Method for evaluating lateral shearing interferograms," Appl. Opt. 13, 623-629 (1974).

상세보기
J. Herrmann, "Least-squares wave front errors of minimum norm," J. Opt. Soc. Am. 70, 28-35 (1980).

상세보기
E. P. Wallner, "Optimal wave-front correction using slope measurements," J. Opt. Soc. Am. 73, 1771-1776 (1983).

상세보기
L. Huang and A. Asundi, "Improvement of least-squares integration method with iterative compensations in fringe reflectometry," Appl. Opt. 51, 7459-7465 (2012).

상세보기
K. R. Freischlad and C. L. Koliopoulos, "Modal estimation of a wave front from difference measurements using the discrete Fourier transform," J. Opt. Soc. Am. A 3, 1852-1861 (1986).

상세보기
W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 998-1006 (1980).

상세보기
R. Cubalchini, "Modal wave-front estimation from phase derivative measurements," J. Opt. Soc. Am. 69, 972-977 (1979).

상세보기
R. H. Hudgin, "Wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. 67, 375-378 (1977).

상세보기
D. L. Fried, "Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements," J. Opt. Soc. Am. 67, 370-375 (1977).

상세보기
W. Zou and J. P. Rolland, "Quantifications of error propagation in slope-based wavefront estimations," J. Opt. Soc. Am. A 23, 2629-2638 (2006).

상세보기
G. Li, Y. Li, K. Liu, X. Ma, and H. Wang, "Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry," J. Opt. Soc. Am. A 30, 1448-1459 (2013).

상세보기
B. Pathak and B. R. Boruah, "Improved wavefront reconstruction algorithm for Shack-Hartmann type wavefront sensors," J. Opt. 16, 055403 (2014).
P. H. Phuc, N. T. Manh, H.-G. Rhee, Y.-S. Ghim, H.-S. Yang, and Y.-W. Lee, "Improved wavefront reconstruction algorithm from slope measurements," J. Korean Phys. Soc. 70, 469-474 (2017).

상세보기
Y. Saad and H. A. van der Vorst, "Iterative solution of linear systems in the 20th century," J. Comput. Appl. Math. 123, 1-33 (2000).

상세보기
C. Canuto and A. Tabacco, "Taylor expansions and applications BT," in Mathematical Analysis I, C. Canuto and A. Tabacco, Eds., 2nd ed. (Springer International Publishing, Charm, Germany. 2015), pp. 225-257.
B. Pathak and B. R. Boruah, "Improvement in error propagation in the Shack-Hartmann-type zonal wavefront sensors," J. Opt. Soc. Am. A 34, 2194-2202 (2017).

상세보기
R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976).

상세보기
V. Lakshminarayanan and A. Fleck, "Zernike polynomials: a guide," J. Mod. Opt. 58, 545-561 (2011).

상세보기
M. T. Nguyen, P. Kang, Y.-S. Ghim, and H.-G. Rhee, "Nonlinearity response correction in phase-shifting deflectometry," Meas. Sci. Technol. 29, 045012 (2018).

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