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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 30 — Oct. 20, 2012
  • pp: 7308–7313

Self-referenced technique for the determination of meridional figure errors of a toroidal mirror with a Sagnac interferometer

Sanjib Chatterjee and Y. Pavan Kumar  »View Author Affiliations

Applied Optics, Vol. 51, Issue 30, pp. 7308-7313 (2012)

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A simple, self-referenced technique for the determination of meridional surface slope errors of toroidal mirrors (TMs) used in synchrotron radiation is presented. An expanded, collimated, linearly polarized laser beam is allowed to fall on a TM, and the reflected toric wavefront from the TM is allowed to enter a Sagnac interferometer based lateral shearing interferometer setup, which duplicates the beam into identical wavefront components having orthogonal linear polarizations, i.e., p and s polarizations, and introduces appropriate lateral shear between the identical pair of wavefronts along the meridional direction. The laterally sheared identical wavefronts interfere when brought to the same state of polarization. The optical path difference (OPD) variation along the direction of the lateral shear in the interference field is a map of the slope variation. Polarization phase shifting interferometery has been applied to find the OPD variation and thus the slope distribution and errors. Results obtained for a TM of moderately long average radius of curvature along the central meridional section and a relatively shorter radius of curvature along the sagittal section are presented and compared with that obtained with a long trace profiler.

© 2012 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: June 22, 2012
Revised Manuscript: September 14, 2012
Manuscript Accepted: September 14, 2012
Published: October 16, 2012

Sanjib Chatterjee and Y. Pavan Kumar, "Self-referenced technique for the determination of meridional figure errors of a toroidal mirror with a Sagnac interferometer," Appl. Opt. 51, 7308-7313 (2012)

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  1. A. Freund, “Mirrors for synchrotron beamlines,” in Handbook of Optics III, M. Bass, J. M. Enoch, E. W. V. Stryland, and W. L. Wolfe, eds. (McGraw-Hill, 2001), pp. 26.3–26.8.
  2. R. A. Paquin and M. R. Howells, “Mirror materials for synchrotron radiation optics,” Proc. SPIE 3152, 2–6 (1997). [CrossRef]
  3. P. Z. Takacs, S. Qian, and J. Colbert, “Design of a long-trace profiler,” Proc. SPIE 749, 59–64 (1987).
  4. G. Ludbrook, S. Alcock, and K. J. S. Sawhney, “A Fizeau interferometer system with double-pass and stitching for characterizing the figure error of large (>1  m) synchrotron optics,” Proc. SPIE 7389, 738939 (2009). [CrossRef]
  5. S. Morozumi, “Toric-wavefront testing holographic interferometry for concave grating,” Appl. Opt. 23, 3082–3090 (1984). [CrossRef]
  6. T. M. Jeong, M. Menon, and G. Yoon, “Measurement of wave-front aberration in soft contact lens by use of a Shack-Hartmann wave-front sensor,” Appl. Opt. 44, 4523–4527 (2005). [CrossRef]
  7. M. Strojnik, G. Paez, and M. Mantravadi, “Lateral shear interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 122–184.
  8. M. V. R. K. Murty, “The use of a single plane parallel plate as a lateral shearing interferometer with a visible gas laser source,” Appl. Opt. 3, 531–534 (1964). [CrossRef]
  9. Y. H. Lo, A. R. D. Somervell, and T. H. Barnes, “Wavefront measurement with a phase-shifting, lateral-shearing Sagnac interferometer operating in broadband light,” Opt. Laser Eng. 43, 33–42 (2005). [CrossRef]
  10. M. P. Kothiyal and C. Delisle, “Shearing interferometer for phase shifting interferometry with polarization phase shifter,” Appl. Opt. 24, 4439–444 (1985). [CrossRef]
  11. S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Technol. 39, 268–274 (2007). [CrossRef]
  12. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometery: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987). [CrossRef]
  13. K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1988), Vol. 26, pp. 349–393.
  14. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998), pp. 248–255.

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