Abstract

When an optical surface or lens in an interferometer (Twyman–Green or Fizeau interferometer) is tested, the wave front at the pupil of the element being tested does not have the same shape as at the observation plane, because this shape changes along its propagation trajectory if the wave front is not flat or spherical. An imaging lens must then be used, as reported many times in the literature, to project the image of the pupil of the system being tested over the observation plane. This lens is especially necessary if the deviation of the wave front from sphericity is large, as in the case of testing paraboloidal or hyperboloidal surfaces. We show that the wave front at both positions does not need to have the same shape. The only condition is that the interferograms at both places be identical, which is a different condition. This leads to some considerations that should be taken into account in the optical design of such lenses.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Huang, “Propagation errors in precision Fizeau interferometry,” Appl. Opt. 32, 7016–7021 (1993).
    [CrossRef] [PubMed]
  2. T. Jozwick, “Influence of spherical aberration of an interferometric system on the measurement error in the case of a finite fringe,” Appl. Opt. 30, 3119–3132 (1991).
    [CrossRef]
  3. D. Malacara, C. Menchaca, “Imaging of the wavefront under test in interferometry,” in Southwest Conference on Optics ’85, R. S. McDowell, S. C. Stotlar, eds., Proc. Soc. Photo-Opt. Instrum. Eng.540, 34–40 (1985).
  4. D. Malacara, Optical Shop Testing (Wiley, New York, 1992), Chap. 2, p. 51.
  5. J. Dyson, “Unit magnification optical system without Seidel aberrations,” J. Opt. Soc. Am. 49, 713–716 (1959).
    [CrossRef]
  6. A. Offner, “A null corrector for paraboloidal mirrors,” Appl. Opt. 2, 153–156 (1963).
    [CrossRef]

1993 (1)

1991 (1)

1963 (1)

1959 (1)

Dyson, J.

Huang, C.

Jozwick, T.

Malacara, D.

D. Malacara, C. Menchaca, “Imaging of the wavefront under test in interferometry,” in Southwest Conference on Optics ’85, R. S. McDowell, S. C. Stotlar, eds., Proc. Soc. Photo-Opt. Instrum. Eng.540, 34–40 (1985).

D. Malacara, Optical Shop Testing (Wiley, New York, 1992), Chap. 2, p. 51.

Menchaca, C.

D. Malacara, C. Menchaca, “Imaging of the wavefront under test in interferometry,” in Southwest Conference on Optics ’85, R. S. McDowell, S. C. Stotlar, eds., Proc. Soc. Photo-Opt. Instrum. Eng.540, 34–40 (1985).

Offner, A.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Testing a concave surface in a Twyman–Green interferometer.

Fig. 2
Fig. 2

Complete optical system for imaging the surface being tested on the observation plane.

Fig. 3
Fig. 3

Testing a concave aspherical surface with a lens compensator and imaging lens.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

( W S ) = Δ W Δ S ,
m = T A Δ S .
T A = m Δ W ( W S ) ,
T A max = m Δ W max ( W y ) .
T A max = m σ 1 n .
T A max = σ 2 n ,
y = λ R σ 1 = m λ R σ 2 ,

Metrics