OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 31 — Nov. 1, 2007
  • pp: 7670–7678

Precise determination of the zero-gravity surface figure of a mirror without gravity-sag modeling

Eric E. Bloemhof, Jonathan C. Lam, V. Alfonso Feria, and Zensheu Chang  »View Author Affiliations

Applied Optics, Vol. 46, Issue 31, pp. 7670-7678 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (1730 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The zero-gravity surface figure of optics used in spaceborne astronomical instruments must be known to high accuracy, but earthbound metrology is typically corrupted by gravity sag. Generally, inference of the zero-gravity surface figure from a measurement made under normal gravity requires finite-element analysis (FEA), and for accurate results the mount forces must be well characterized. We describe how to infer the zero-gravity surface figure very precisely using the alternative classical technique of averaging pairs of measurements made with the direction of gravity reversed. We show that mount forces as well as gravity must be reversed between the two measurements and discuss how the St. Venant principle determines when a reversed mount force may be considered to be applied at the same place in the two orientations. Our approach requires no finite-element modeling and no detailed knowledge of mount forces other than the fact that they reverse and are applied at the same point in each orientation. If mount schemes are suitably chosen, zero-gravity optical surfaces may be inferred much more simply and more accurately than with FEA.

© 2007 Optical Society of America

OCIS Codes
(000.2780) General : Gravity
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.4840) Optical design and fabrication : Testing

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: June 29, 2007
Manuscript Accepted: August 10, 2007
Published: October 25, 2007

Eric E. Bloemhof, Jonathan C. Lam, V. Alfonso Feria, and Zensheu Chang, "Precise determination of the zero-gravity surface figure of a mirror without gravity-sag modeling," Appl. Opt. 46, 7670-7678 (2007)

Sort:  Year  |  Journal  |  Reset  


  1. M. Shao, "Science overview and status of the SIM project," Proc. SPIE 5491, 328-333 (2004). [CrossRef]
  2. R. A. Laskin, "Successful completion of SIM-PlanetQuest technology," Proc. SPIE 6268, 626823 (2006). [CrossRef]
  3. D. Korsch, Reflective Optics (Academic, 1991).
  4. R. Goullioud, "Results from the TOM3 testbed: thermal deformation of optics at the picometer level," presented at the IEEE Aerospace Conference, Big Sky, Montana (IEEE, 2006).
  5. V. A. Feria, J. C. Lam, and D. Van Buren, "M1 mirror print-thru investigation and performance on the thermo-opto-mechanical testbed for the Space Interferometry Mission," Proc. SPIE 6273, 62731C (2006). [CrossRef]
  6. Z. Chen, Finite Element Methods and Their Applications (Springer-Verlag, 2005).
  7. D. W. Nicholson, Finite Element Analysis: Thermomechanics of Solids (CRC, 2003). [CrossRef]
  8. R. Richards, Jr., Principles of Solid Mechanics (CRC, 2001).

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