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Applied Optics

Applied Optics


  • Vol. 34, Iss. 32 — Nov. 10, 1995
  • pp: 7474–7485

Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances

Chris S. Anderson  »View Author Affiliations

Applied Optics, Vol. 34, Issue 32, pp. 7474-7485 (1995)

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Common-path interferometers have been used to perform phase visualization for over 40 years. A number of techniques have been proposed, including dark central ground, phase contrast (π/2 and π), and field-absorption interferometers. The merits of the interferometers have been judged ad hoc by either tests with a small number of phase objects or by computer simulation. Three standardized criteria, which consolidate the work of others, are proposed to evaluate common-path interferometers: fringe visibility, fringe irradiance, and fringe accuracy. The interferometers can be described as one generic class of Fourier-plane filters and can be analyzed for all input conditions. Closed-form expressions are obtained for visibility and irradiance under the forced condition that little inaccuracy is tolerated. This analysis finds that the π-phase-contrast interferometer is a good choice if the optical phase disturbance is at least 2π; for smaller disturbances, the π/2 filter selected by Zernike is near optimum. It is shown mathematically that the resulting fringe visibility is highly object dependent, and good results are not ensured. By allowing the optical beam to be 50% larger than the phase object, the interferometer performs well under all conditions. With this approach and a combination π-phase/field-absorption filter, interference fringe visibility is greater than 0.8 for all phase objects.

© 1995 Optical Society of America

Original Manuscript: March 6, 1995
Revised Manuscript: July 6, 1995
Published: November 10, 1995

Chris S. Anderson, "Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances," Appl. Opt. 34, 7474-7485 (1995)

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  1. R. Anderson, J. Milton, C. Anderson, “Common path interferometers for flow visualization: a review,” AIAA 95-0481 (American Institute of Aeronautics and Astronautics, New York, 1995).
  2. R. C. Anderson, S. Lewis, “Flow visualization by dark central ground interferometer,” Appl. Opt. 24, 3687 (1985). [CrossRef] [PubMed]
  3. R. C. Anderson, J. E. Milton, “A large aperture inexpensive interferometer for routine flow measurements,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 394–399. [CrossRef]
  4. L. Carr, M. Chandrasekhara, S. Ahmed, N. Brock, “A study of dynamic stall using real time interferometry,” AIAA 91-0007 (American Institute of Aeronautics and Astronautics, New York, 1991).
  5. L. Carr, M. Chandrasekhara, N. Brock, “A quantitative study of unsteady compressible flow on an oscillating airfoil,” AIAA-91-1683 (American Institute of Aeronautics and Astronautics, New York, 1991).
  6. M. Taylor, “Phase contrast flow visualization,” M.S. thesis (College of Engineering, University of Florida, Gainesville, Fla., 1980).
  7. S. F. Erdmann, “Ein neues, sehr einfaches Interferometer zum Erhalt quantitativ auswertbarer Strömungsbilder,” Appl. Sci. Res. Sect. B 2, 1–50 (1951).
  8. R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, 351–356 (1975).
  9. R. N. Smartt, “Special applications of the point-diffraction interferometer,” in Interferometry, G. W. Hopkins, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 192, 35–40 (1979).
  10. F. Zernike, “Phase contrast, a new method for the microscopic observation of transparent objects Part I,” Physica 9, 686–698 (1942; F. Zernike, “Phase contrast, a new method for the microscopic observation of transparent objects Part II,” Physica 9, 974–986 (1942). [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chaps. 5–7.

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