OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 11638–11651

Phase errors in high line density CGH used for aspheric testing: beyond scalar approximation

S. Peterhänsel, C. Pruss, and W. Osten  »View Author Affiliations

Optics Express, Vol. 21, Issue 10, pp. 11638-11651 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1088 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



One common way to measure asphere and freeform surfaces is the interferometric Null test, where a computer generated hologram (CGH) is placed in the object path of the interferometer. If undetected phase errors are present in the CGH, the measurement will show systematic errors. Therefore the absolute phase of this element has to be known. This phase is often calculated using scalar diffraction theory. In this paper we discuss the limitations of this theory for the prediction of the absolute phase generated by different implementations of CGH. Furthermore, for regions where scalar approximation is no longer valid, rigorous simulations are performed to identify phase sensitive structure parameters and evaluate fabrication tolerances for typical gratings.

© 2013 OSA

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: February 27, 2013
Revised Manuscript: April 12, 2013
Manuscript Accepted: April 26, 2013
Published: May 6, 2013

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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. C. Wyant and V. P. Bennett, “Using computer generated holograms to test aspheric wavefronts,” omputer Generated Holograms to Test Aspheric Wavefronts,” Appl. Opt.112833–2839 (1972). [CrossRef] [PubMed]
  2. S. M. Arnold, “How to test an asphere with a computer-generated hologram,” Proc. SPIE1052191–197 (1989). [CrossRef]
  3. E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE4440 (2001). [CrossRef]
  4. J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng.50(2011).
  5. S. Reichelt, C. Pruss, and H. J. Tiziani, “Specification and characterization of CGHs for interferometrical optical testing,” Proc. SPIE4778 (2002). [CrossRef]
  6. Y.-C. Chang, P. Zhou, and J. H. Burge, “Analysis of phase sensitivity for binary computer-generated holograms,” Appl. Opt.454223–4234 (2006). [CrossRef] [PubMed]
  7. P. Zhou and J. H. Burge, “Fabrication error analysis and experimental demonstration for computer-generated holograms,” Appl. Opt.46657–663 (2007). [CrossRef] [PubMed]
  8. P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt.432063–2085 (1996). [CrossRef]
  9. W. Yu, K. Takahara, T. Konishi, T. Yotsuya, and Y. Ichioka, “Fabrication of multilevel phase computer-generated hologram elements based on effective medium theory,” Appl. Opt.393531–3536 (2000). [CrossRef]
  10. I. Richter, P.-C. Sun, F. Xu, and Yeshayahu Fainman, “Design considerations of form birefringent microstructures,” Appl. Opt.342421–2429 (1995). [CrossRef] [PubMed]
  11. N. Bokor, R. Shechter, N. Davidson, A. A. Friesem, and Erez Hasman, “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” Appl. Opt.402076–2080 (2001). [CrossRef]
  12. W. Iff, S. Glaubrecht, N. Lindlein, and J. Schwider, “Untersuchung der Abweichungen zwischen skalarer und rigoroser Rechnung an CGHs in Twyman-Green-Interferometern zur Linsenprüfung,” DGaO-Proceedings http://www.dgao-proceedings.de (2010).
  13. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics, (Wiley, 1978).
  14. Y. Sheng, D. Feng, and S. Larochelle, “Analysis and synthesis of circular diffractive lens with local linear grating model and rigorous coupled-wave theory,” J. Opt. Soc. Am. A141562–1568 (1997). [CrossRef]
  15. M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik - International Journal for Light and Electron Optics112 (2001). [CrossRef]
  16. L. Li and Gérard Granet, “Field singularities at lossless metal-dielectric right-angle edges and their ramifications to the numerical modeling of gratings,” J. Opt. Soc. Am. A28738–746 (2011). [CrossRef]
  17. L. Li, “Field singularities at lossless metaldielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings,” J. Opt. Soc. Am. A29593–604 (2012). [CrossRef]
  18. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, 1991).
  19. J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications, (Akademie Verlag, 1997).
  20. E. Popov, M. Nevière, B. Gralak, and G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A19 (2002). [CrossRef]
  21. P. Zhou and J. H. Burge, “Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors”Opt. Express1515410–15417 (2007). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited