Journal of the European Optical Society - Rapid publications, Vol 9 (2014)
Error correction of a phase-only computer-generated hologram for an aspheric surface
Abstract
When applying phase-only computer-generated hologram (CGH) as a standard model of optical measurement in computer-generated holography for aspheric surface testing, it has the advantage of simplifying optical path configuration and improving the diffraction efficiency of the incoming light. However, errors always exists during the encoding process of fabricating multiphase level CGHs and this kind of errors will be amplified level by level in the measurement. According to the analysis of the encoding error, the error of CGH increases linearly when its quantified period increases. For example, if the quantified period is 32, the maximum of encoding error is 16.46 which can lead wave-front aberration 0.085λ of a secondary parabolic surface with 512 x 512 sampling pixels. In this article, an optimization method based on deviation of minimum boundary value has been used to eliminate the encoding error of CGH. In the experiment, we use a liquid crystal spatial light modulator to generate CGHs and measure residuals of reconstructed wave-front of a secondary parabolic surface. The measurement results show that average decrease of the RMS values of the residuals is 0.07λ when their periods range from 3 to 6, which indicates the optimization method is effective.
© The Authors. All rights reserved. [DOI: 10.2971/jeos.2014.14039]
Citation Details
Cite this articleReferences
H. Liu, Z. W. Lu, F. Y. Li, and Q. Sun, ”Design of a novel hologram for full measurement of large and deep convex aspheric surfaces,” Opt. Express 15, 3120–3126 (2007).
E. Garbusi, and W. G. Osten, ”Analytical study of disturbing diffraction orders in in-line computer generated holograms for aspheric testing,” Opt. Commun. 283, 2651–2656 (2010).
X. M. Hong, P. J. Gou, and J. F. Ren, ”Two Computer-generated Holograms for Testing Convex Aspheric Surface,” Proc. SPIE 8192, 1–8 (2011).
M. Kino, and M. Kurita, ”Interferometric testing for off-axis aspherical mirrors with computer-generated holograms,” Appl. Optics 51, 4291–4297 (2012).
A.G. Poleshchuk, R. K. Nasyrov, and J. M. Asfour, ”Combined computer-generated hologram for testing steep aspheric surfaces,” Opt. Express 17, 5420–5425 (2009).
S. Reichelt, C. Pruss, and H. J. Tiziani, ”Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Optics 42, 4468–4479 (2003).
V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, ”Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A 24, 3500–3507 (2007).
S. Peterhänsel, C. Pruss, and W. Osten, ”Phase errors in high line density CGH used for aspheric testing: beyond scalar approximation,” Opt. Express 21, 11638–11651 (2013).
Y. Tang, X. Y. Su, Y. K. Liu, and H. L. Jing, ”3D shape measurement of the aspheric mirror by advanced phase measuring deflectometry,” Opt. Express 16, 1590–1596 (2008).
W. R. Cai, P. Zhou, C. Y. Zhao, and J. H. Burge, ”Analysis of wavefront errors introduced by encoding computer-generated holograms,” Appl. Optics 52, 8324–8331 (2013).
F. Z. Li, J. L. Zhao, R. G. Li, B. Z. Zhang, L. G. Zheng, and X. J.Zhang, ”Design and Fabrication of CGH for aspheric surface testing and its experimental comparison with null lens,” Proc. SPIE 7656, 1–6 (2010).
H. S. Yang, J. B. Song, I.W. Lee, and Y. W. Lee, ”Testing of steep convex aspheric surface with a Hartmann sensor by using a CGH,” Opt. Express 14, 3247–3254 (2006).