OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 10, Iss. 4 — Apr. 1, 1971
  • pp: 929–934

Establishing an Optical Flatness Standard

G. Schulz, J. Schwider, C. Hiller, and B. Kicker  »View Author Affiliations

Applied Optics, Vol. 10, Issue 4, pp. 929-934 (1971)

View Full Text Article

Enhanced HTML    Acrobat PDF (711 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Methods proposed by the authors to establish a flatness standard without using a liquid mirror are proved in practice and extended. The extension is performed by a development of methods for the determination and compensation of random and systematic measuring errors by means of condition equations which must be satisfied by the measured sums of deviations from absolute planeness. Linear errors of these sums of deviations which can lead to ambiguities and errors of planeness deviations can be discovered and completely eliminated. Also nonlinear errors, for example, as a result of temperature differences or of mechanical stress, can be recognized without repeating the interference photography procedure. The deviations from absolute planeness of three fused silica plates were determined along seven diameters (angular distance 2π/14) with an accuracy of λ/500 (mean square error). This was performed by evaluating two sets of four different interference photographs, each with contour plane distances of λ/50 (from fringe to fringe).

© 1971 Optical Society of America

Original Manuscript: July 21, 1970
Published: April 1, 1971

G. Schulz, J. Schwider, C. Hiller, and B. Kicker, "Establishing an Optical Flatness Standard," Appl. Opt. 10, 929-934 (1971)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Schulz, J. Schwider, Appl. Opt. 6, 1077 (1967). [CrossRef] [PubMed]
  2. G. Schulz, Opt. Acta 14, 375 (1967). [CrossRef]
  3. J. Schwider, Opt. Acta 14, 389 (1967). [CrossRef]
  4. J. Schwider, Opt. Acta 15, 351 (1968). [CrossRef]
  5. Rayleigh, Nature 48, 212 (1893).
  6. H. Barrell, R. Marriner, Brit. Sci. News 2, 130 (1949).
  7. E. Einsporn, Feingerätetechnik 4, 539 (1955);Feingerätetechnik 10, 67 (1961).
  8. R. Bünnagel, Z. Angew. Phys. 8, 342 (1956); Opt. Acta 3, 81 (1956); Z. Instrumentenk. 73, 214 (1965).
  9. O. Schönrock, Z. Instrumentenk. 25, 148 (1905); Z. Instrumentenk. 28, 180 (1908).
  10. O. Schönrock, Z. Instrumentenk. 59, 31 (1939).
  11. E. Emerson, J. Res. Nat. Bur. Stand. 49, 336 (1952).
  12. J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, Opt. Acta 13, 103 (1966). [CrossRef]
  13. J. Schwider, thesis (Humboldt-University of Berlin, 1966).
  14. G. Dew, J. Sci. Instrum. 43, 809 (1966). [CrossRef]
  15. T. Sakurai, K. Shishido, Sci. Rep. Res. Inst. Tohoku Univ. AI, No. 1 (1949).
  16. J. B. Saunders, J. Res. Nat. Bur. Stand. 47, 148 (1951). [CrossRef]
  17. D. R. Herriott, J. Opt. Soc. Amer. 51, 1142 (1961). [CrossRef]
  18. As an approximation this plane is to contain the three reference points fixed by steps 1 and 2. However, this is not exactly so, since the measured values in some of these points need not be faultless. Therefore small deviations may arise between the reference points of the steps 1 and 2 and the discussed reference plane.

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