OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 18, Iss. 9 — Sep. 1, 2001
  • pp: 2146–2152

Wave-front measurement errors from restricted concentric subdomains

Kenneth A. Goldberg and Kevin Geary  »View Author Affiliations


JOSA A, Vol. 18, Issue 9, pp. 2146-2152 (2001)
http://dx.doi.org/10.1364/JOSAA.18.002146


View Full Text Article

Enhanced HTML    Acrobat PDF (200 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In interferometry and optical testing, system wave-front measurements that are analyzed on a restricted subdomain of the full pupil can include predictable systematic errors. In nearly all cases, the measured rms wave-front error and the magnitudes of the individual aberration polynomial coefficients underestimate the wave-front error magnitudes present in the full-pupil domain. We present an analytic method to determine the relationships between the coefficients of aberration polynomials defined on the full-pupil domain and those defined on a restricted concentric subdomain. In this way, systematic wave-front measurement errors introduced by subregion selection are investigated. Using vector and matrix representations for the wave-front aberration coefficients, we generalize the method to the study of arbitrary input wave fronts and subdomain sizes. While wave-front measurements on a restricted subdomain are insufficient for predicting the wave front of the full-pupil domain, studying the relationship between known full-pupil wave fronts and subdomain wave fronts allows us to set subdomain size limits for arbitrary measurement fidelity.

© 2001 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(220.1010) Optical design and fabrication : Aberrations (global)
(220.4840) Optical design and fabrication : Testing

History
Original Manuscript: December 21, 2000
Manuscript Accepted: February 21, 2001
Published: September 1, 2001

Citation
Kenneth A. Goldberg and Kevin Geary, "Wave-front measurement errors from restricted concentric subdomains," J. Opt. Soc. Am. A 18, 2146-2152 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-9-2146


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. J. Fischer, J. T. O’Bryan, R. Lopez, H. P. Stahl, “Vector formulation for interferogram surface fitting,” Appl. Opt. 32, 4738–4743 (1993). [CrossRef] [PubMed]
  2. J. Y. Wang, D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1518 (1980). [CrossRef] [PubMed]
  3. M. Carpio, D. Malacara, “Closed Cartesian representation of the Zernike polynomials,” Opt. Commun. 110, 514–516 (1994). [CrossRef]
  4. S. D. Conte, C. de Boor, Elementary Numerical Analysis: An Algorithmic Approach, 3rd ed. (McGraw-Hill, New York, 1980), Chap. 6.
  5. P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, Boston, 1992), p. 126.
  6. C. R. Hayslett, W. H. Swantner, “Wave-front derivation by three computer programs,” Appl. Opt. 19, 161–163 (1980). [CrossRef]
  7. V. N. Mahajan, “Zernike circle polynomials and optical aberrations of systems with circular pupils,” Appl. Opt. 33, 8121–8124 (1994). [CrossRef] [PubMed]
  8. J. S. Loomis, FRINGE User’s Manual (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1976).
  9. “FRINGE Zernikes,” in Code V Reference Manual, R. C. Juergens, ed. (Optical Research Associates, Pasadena, Calif., 1998), Vol. 1, version 8.30, pp. 2A-595–2A-596.
  10. “Fitting interferograms using Zernike polynomials,” in FAST! V/AI Operations Manual (Phase Shift Technology, Tucson, Ariz., 1990), pp. 2-3–2-5.
  11. J. Spanier, K. B. Oldham, “The unit-step and related functions,” in An Atlas of Functions (Hemisphere, Washington, D.C., 1987), Chap. 8, pp. 63–69.

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.

Figures

Fig. 1
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited