OSA's Digital Library

Optics Letters

Optics Letters


  • Vol. 23, Iss. 14 — Jul. 15, 1998
  • pp: 1078–1080

Phase-shifted laser feedback interferometry

Ben Ovryn and James H. Andrews  »View Author Affiliations

Optics Letters, Vol. 23, Issue 14, pp. 1078-1080 (1998)

View Full Text Article

Acrobat PDF (1134 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We have introduced the techniques of phase-shifting interferometry into a laser feedback interference microscope based on a helium–neon laser. With moderate feedback, multiple reflections between the sample and the laser are shown to be negligible, and the interferometer responds sinusoidally with a well-characterized fringe modulation. One can obtain higher signal-to-noise ratios by determining the number of additional terms required for modeling the effect of multiple reflections on the phase and visibility measurements in the high-feedback regime. Changes in optical path length are determined with nanometer precision without phase averaging or lock-in detection.

© 1998 Optical Society of America

OCIS Codes
(110.0180) Imaging systems : Microscopy
(110.6880) Imaging systems : Three-dimensional image acquisition
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(180.3170) Microscopy : Interference microscopy

Ben Ovryn and James H. Andrews, "Phase-shifted laser feedback interferometry," Opt. Lett. 23, 1078-1080 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. G. Stephan and D. Hugon, Phys. Rev. Lett. 55, 703 (1985).
  2. A. Bearden, M. P. O’Neill, L. C. Osborne, and T. L. Wong, Opt. Lett. 18, 238 (1993).
  3. Th. H. Peek, P. T. Bolwijn, and C. Th. Alkemade, Am. J. Phys. 35, 820 (1967).
  4. G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, IEEE J. Quantum Electron. QE-20, 1163 (1984).
  5. J. Mork, B. Tromberg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
  6. R. Juskaitis, T. Wilson, and N. P. Rea, Opt. Commun. 109, 167 (1994).
  7. D. Sarid, V. Weissenberger, D. A. Iams, and J. T. Ingle, IEEE J. Quantum Electron. 25, 1968 (1989).
  8. K. Creath, in Progress in Optics XXVI, E. Wolf, ed. (North-Holland, Amsterdam, 1988), pp. 349–393.
  9. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
  10. E. B. Hooper, Jr., and G. Bekefi, J. Appl. Phys. 37, 4083 (1966) ; erratum, 38, 1998 (1967).
  11. A. Yariv, Quantum Electronics (Wiley, New York, 1989), pp. 192ff.
  12. D. Lenstra, M. van Vaalen, and B. Jaskorzynska, Physica C 125, 255 (1984).
  13. Preliminary calibration of the instrument reveals that the fringe visibility does not exceed 0.5; see B. Ovryn, J. H. Andrews, and S. Eppell, Proc. SPIE 2655, 153 (1996).
  14. J. E. Greivenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992) ; B. Ovryn and E. M. Haacke, Appl. Opt. 32, 147 (1993).
  15. In the absence of systematic errors, the signal-to-noise ratio of a phase measurement depends on environmental perturbations, errors in the phase shifts, and the error in the intensity measurements and is inversely proportional to the fringe visibility; see J. Schwider, in Progress in Optics XXVIII, E. Wolf, ed. (North-Holland, Amsterdam, 1990), pp. 272–343.
  16. P. Hariharan, B. F. Oreb, and T. Eiju, Appl. Opt. 26, 2504 (1987); P. Hariharan, Appl. Opt. 26, 2506 (1987). The phase, f=2kd, and the visibility m are determined by measurement of the intensities at each of five phase shifts Y in Eq. 1. Representing the measured intensities for the five phase shifts Y=-p, Y=-p/2, Y=0, Y=p/2, and Y=p as I1, I2, I3, I4, and I5, respectively, we calculated the quantities f and m : f=atan(a/b), m=3(a2+b2) 1/22(I1+I2+2I 3+I4+I5) where a=2I2-2I4 and b=2I3-I1-I5.
  17. The phase error with j=4 in Eq. 1 is tan(f)measured =]1-b2cos (2f)+b4cos(4f)]]1+b2cos(2f)+b4cos(4f) ] × tan(f)actual.
  18. Because there is no ambiguity in the direction of the change in OPL, the increased OPL indicates the presence of an etched trough in the silicon. This finding agrees with a topological scan by use of atomic-force microscopy, which indicates a mean step height of 76.2 nm for the sample shown in Fig. 2. A rms surface roughness of greater than 10 nm was measured within the narrow trough. The surface was smooth to less than 1 nm, however, outside the trough.

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited