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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 7 — Mar. 1, 2011
  • pp: 981–991

Mirror tilt immunity interferometry with a cat’s eye retroreflector

Fabián E. Peña-Arellano and Clive C. Speake  »View Author Affiliations

Applied Optics, Vol. 50, Issue 7, pp. 981-991 (2011)

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This paper describes the behavior of a cat’s eye retroreflector, which is incorporated in a novel way in a double-pass homodyne polarization interferometer. The amount of mirror tilt immunity a cat’s eye provides is calculated within the paraxial approximation using 4 × 4 A B C D matrices. It is found that there is a position of the target mirror in which the tilt immunity is at a maximum. A real cat’s eye, which is affected by aberrations, is optimized and examined using Zemax software for optical design. The maximum amount of mirror tilt immunity is numerically calculated and written in terms of defocus and spherical aberration. Finally, for the purposes of comparison, the amplitude of the Lissajous pattern as the target mirror tilts is calculated for both an interferometer with an integrated cat’s eye and an interferometer with a cube corner.

© 2011 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: October 5, 2010
Revised Manuscript: December 28, 2010
Manuscript Accepted: December 28, 2010
Published: February 18, 2011

Fabián E. Peña-Arellano and Clive C. Speake, "Mirror tilt immunity interferometry with a cat’s eye retroreflector," Appl. Opt. 50, 981-991 (2011)

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  1. E. R. Peck, “Theory of the corner-cube interferometer,” J. Opt. Soc. Am. 38, 1015–1024 (1948). [CrossRef] [PubMed]
  2. P. Hariharan and D. Sen, “The separation of symmetrical and asymmetrical wave-front aberrations in the Twyman interferometer,” Proc. Phys. Soc. London 77, 328–334 (1961). [CrossRef]
  3. S. J. Bennett, “A double-passed Michelson interferometer,” Opt. Commun. 4, 428–430 (1972). [CrossRef]
  4. M. J. Downs and K W. Raine, “An unmodulated bi-directional fringe counting interferometer system for measuring displacements,” Precis. Eng. 1, 85–88 (1979). [CrossRef]
  5. M. J. Downs and J. W. Nunn, “Verification of the sub-nanometric capability of an NPL differential plane mirror interferometer with a capacitance probe,” Meas. Sci. Technol. 9, 1437–1440 (1998). [CrossRef]
  6. P. de Groot, “Jones matrix analysis of high-precision displacement measuring interferometers,” in ODIMAP II (Pavia, 1999), pp. 9–14.
  7. H. J. Büchner and G. Jäger, “A novel plane mirror interferometer without using corner cube reflectors,” Meas. Sci. Technol. 17, 746–752 (2006). [CrossRef]
  8. J. J. Snyder, “Paraxial ray analysis of a cat’s-eye retroreflector,” Appl. Opt. 14, 1825–1828 (1975). [CrossRef] [PubMed]
  9. M. L. Biermann, W. S. Rabinovich, R. Mahon, and G. C. Gilbreath, “Design and analysis of a diffraction-limited cat’s-eye retroreflector,” Opt. Eng. 41, 1655–1660 (2002). [CrossRef]
  10. S. E. Segre and V. Zanza, “Mueller calculus of polarization change in the cube-corner retroreflector,” J. Opt. Soc. Am. A 20, 1804–1811 (2003). [CrossRef]
  11. J. Dyson, Interferometry as a Measuring Tool (The Machinery Publishing Company, 1970).
  12. F. Petrů and O. Čip, “Problems regarding linearity of data of a laser interferometer with a single-frequency laser,” Precis. Eng. 23, 39–50 (1999). [CrossRef]
  13. G. D. Hammond, A. Pulido Patón, C. C. Speake, and C. Trenkel, “Novel torsion balance based on a spherical superconducting suspension,” Rev. Sci. Instrum. 75, 955–961(2004). [CrossRef]
  14. G. D. Hammond, C. C. Speake, A. J. Matthews, E. Rocco, and F. E. Peña-Arellano, “Development of a second generation torsion balance based on a spherical superconducting suspension,” Rev. Sci. Instrum. 79, 025103 (2008). [CrossRef] [PubMed]
  15. F. E. Peña-Arellano, C. C. Speake, H. Panjwani, and L. Carbone “An interferometer for measuring angular motion,” in preparation.
  16. E. R. Peck and S. W. Obetz, “Wavelength or length measurement by reversible fringe counting,” J. Opt. Soc. Am. 43, 505–509 (1953). [CrossRef] [PubMed]
  17. P. L. M. Heydemann, “Determination and correction of quadrature fringe measurements errors in interferometers,” Appl. Opt. 20, 3382–3384 (1981). [CrossRef] [PubMed]
  18. K. W. Raine and M. J. Downs, “Beam-splitter coatings for producing phase quadrature interferometer outputs,” J. Mod. Opt. 25, 549–558 (1978). [CrossRef]
  19. V. Greco, C. Iemmi, S. Ledesma, G. Molesini, and F. Quercioli, “Multiphase homodyne interferometry: analysis of some error sources,” Appl. Opt. 34, 2207–2213 (1995). [CrossRef] [PubMed]
  20. M. A. Zumberge, J. Berger, M. A. Dzieciuch, and R. L. Parker, “Resolving quadrature fringes in real time,” Appl. Opt. 43, 771–775 (2004). [CrossRef] [PubMed]
  21. F. E. Peña-Arellano, “Characterization of polarization homodyne interferometers,” Ph.D. dissertation (University of Birmingham, 2008).
  22. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993). [CrossRef]
  23. F. Pedrotti and L. Pedrotti, Introduction to Optics (Prentice-Hall, 1996).
  24. S. Wang and L. Ronchi, “Principles and design of optical arrays,” Prog. Opt. 25, 279–310 (1988). [CrossRef]
  25. C. C. Speake and S. M. Aston, “An interferometric sensor for satellite drag-free control,” Class. Quant. Grav. 22, S269–S277 (2005). [CrossRef]
  26. F. E. Peña-Arellano, C. C. Speake, and S. M. Aston are preparing a manuscript to be called “Experimental realization of an interferometer with mirror tilt immunity.”
  27. C. C. Speake, S. M. Aston, F. E. Peña-Arellano, and T. P. E. Copland, “Improved interferometer,” International patent, pub. no. WO 2009/010750 A1 (22 January 2009).

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