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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 19 — Jul. 1, 2006
  • pp: 4554–4562

Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors

Bradley T. Kimbrough  »View Author Affiliations

Applied Optics, Vol. 45, Issue 19, pp. 4554-4562 (2006)

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In both temporal and spatial carrier phase shifting interferometry, the primary source of phase calculation error results from an error in the relative phase shift between sample points. In spatial carrier phase shifting interferometry, this phase shifting error is caused directly by the wavefront under test and is unavoidable. In order to minimize the phase shifting error, a pixelated spatial carrier phase shifting technique has been developed by 4D technologies. This new technique allows for the grouping of phase shifted pixels together around a single point in two dimensions, minimizing the phase shift change due to the spatial variation in the test wavefront. A formula for the phase calculation error in spatial carrier phase shifting interferometry is derived. The error associated with the use of linear N-point averaging algorithms is presented and compared with those of the pixelated spatial carrier technique.

© 2006 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Original Manuscript: October 27, 2005
Revised Manuscript: January 19, 2006
Manuscript Accepted: January 21, 2006

Bradley T. Kimbrough, "Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors," Appl. Opt. 45, 4554-4562 (2006)

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  1. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).
  2. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, 1992).
  3. J. Schwider, R. Burow, K. E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wave-front measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983). [CrossRef] [PubMed]
  4. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase shifting for nonsinusoidal waveforms with phase-shift errors," J. Opt. Soc. Am. A 12, 761-768 (1995). [CrossRef]
  5. K. G. Larkin and B. F. Oreb, "Design and assessment of symmetrical phase-shifting algorithms," J. Opt. Soc. Am. A 9, 1740-1748 (1992). [CrossRef]
  6. D. W. Phillion, "General methods for generating phase-shifting interferometry algorithms," Appl. Opt. 36, 8098-8115 (1997). [CrossRef]
  7. J. Schmit and K. Creath, "Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry," Appl. Opt. 34, 3610-3619 (1995). [CrossRef] [PubMed]
  8. M. Servin, D. Malacara, J. L. Marroquin, and F. J. Cuevas, "Complex linear filters for phase shifting with very low detuning sensitivity," J. Mod. Opt. 44, 1269-1278 (1997). [CrossRef]
  9. Y. Surrel, "Phase stepping: a new self-calibrating algorithm," Appl. Opt. 32, 3598-3600 (1993). [CrossRef] [PubMed]
  10. R. Jozwicki, M. Kujawinska, and L. A. Salbut, "New contra old wavefront measurement concepts for interferometric optical testing," Opt. Eng. 31, 422-433 (1992). [CrossRef]
  11. M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982). [CrossRef]
  12. D. M. Shough, O. Y. Kwon, and D. F. Leary, "High speed interferometric measurement of aerodynamic phenomena," in Propagation of High-Energy Laser Beams Through the Earth's Atmosphere, P. B. Ulrich and L. E. Wilson, eds., Proc. SPIE 1221, 394-403 (1990). [CrossRef]
  13. K. Creath and J. Schmit, "Errors in spatial phase-stepping techniques," in Interferometry '94: New Techniques and Analysis in Optical Measurements, M. Kujawinska and K. Patorski, eds., Proc. SPIE 2340, 170-176 (1994). [CrossRef]
  14. J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, "Pixelated phase-mask dynamic interferometer," in Interferometry XII: Techniques and Analysis, K. Creath and J. Schmit, eds., Proc. SPIE 5531, 304-314 (2004). [CrossRef]
  15. P. Hariharan, B. F. Oreb, and T. Eiji, "Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm," Appl. Opt. 26, 2504-2505 (1987). [CrossRef] [PubMed]
  16. P. de Groot, "Phase-shift calibration errors in interferometers with spherical Fizeau cavities," Appl. Opt. 34, 2856-2863 (1995). [CrossRef]
  17. J. D. Tobiason and K. W. Atherton, "Interferometer using integrated imaging array and high-density polarizer array," US Patent 6,850,329 (1 February 2005).
  18. J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, B. T. Kimbrough, and J. C. Wyant, "Pixelated phase-mask dynamic interferometers," in Fringe 2005 (Springer, 2005), pp. 640-647.

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