OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 38, Iss. 28 — Oct. 1, 1999
  • pp: 6050–6054

n-Hindle-sphere arrangement with an exact ray trace for testing hyperboloid convex mirrors

María E. Percino-Zacarias and Alberto Cordero-Dávila  »View Author Affiliations

Applied Optics, Vol. 38, Issue 28, pp. 6050-6054 (1999)

View Full Text Article

Enhanced HTML    Acrobat PDF (587 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present calculations with an exact ray trace to determine the dimensions that define one or two Hindle spheres, since the paraxial theory is incongruent for convex hyperboloid mirrors with small f numbers. The equations are generalized to calculate the dimensions of n Hindle spheres, since in this way it is possible to reduce the dimensions of the spheres more. Actual calculations are done for the secondary mirrors of the Benemerita Universidad Autonoma de Puebla and Large Milimetric Telescopes; experimental results are shown for the latter.

© 1999 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(110.6770) Imaging systems : Telescopes
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(230.4040) Optical devices : Mirrors
(350.1260) Other areas of optics : Astronomical optics

Original Manuscript: March 5, 1999
Revised Manuscript: May 26, 1999
Published: October 1, 1999

María E. Percino-Zacarias and Alberto Cordero-Dávila, "n-Hindle-sphere arrangement with an exact ray trace for testing hyperboloid convex mirrors," Appl. Opt. 38, 6050-6054 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  2. R. Noble, D. Malacara, A. Cornejo, “Multistep Hindle test,” Appl. Opt. 13, 2476–2477 (1974). [CrossRef] [PubMed]
  3. I. S. Potyemin, A. S. Seregin, “New modification of Hindle scheme for interferometric testing of convex hyperbolical surfaces,” in Interferometry ’94: New Techniques and Analysis in Optical Measurements, M. Kujawinska, K. Patorski, eds., Proc. SPIE2340, 276–282 (1994).
  4. J. Hindle, “A new test for Cassegrainian and Gregorian secondary mirrors,” Mon. Not. R. Astron. Soc. 91, 592–595 (1931).
  5. A. Cordero-Dávila, E. Luna-Aguilar, S. Vázquez-Montiel, S. Zárate-Vázquez, M. E. Percino-Zacarias, “Ronchi test using a square grid,” Appl. Opt. 37, 672–675 (1998). [CrossRef]
  6. A. Cornejo, D. Malacara, “Ronchi test of aspherical surfaces, analysis, and accuracy,” Appl. Opt. 9, 1897–1901 (1970). [PubMed]
  7. Y. M. Liu, G. N. Lawrence, C. L. Koliopoulos, “Subaperture testing of aspheres with annular zones,” Appl. Opt. 27, 4504–4513 (1988). [CrossRef] [PubMed]
  8. M. Melozzi, L. Pezzati, A. Mazzoni, “Testing aspheric surfaces using multiple annular interferograms,” Opt. Eng. 32, 1073–1079 (1993). [CrossRef]

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited