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Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • 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)
http://dx.doi.org/10.1364/OL.23.001078


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Abstract

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

Citation
Ben Ovryn and James H. Andrews, "Phase-shifted laser feedback interferometry," Opt. Lett. 23, 1078-1080 (1998)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-23-14-1078


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References

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  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.

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