Abstract

While investigating the instrumental function of a Fabry–Perot interferometer [Appl. Opt. 34, 58 (1995)], we noticed some variation in finesse and contrast in the measured spectra when a 1.5-mm-diameter aperture was used at various spots within the standard 8-mm aperture. By comparing experimentally determined finesse versus contrast plots for many such spectra with calculated plots, we found spots on the plates that gave non-Airy-function line shapes over the entire order of interference, unlike the Airy line shape we determined previously by using the entire 8-mm aperture. We have reviewed several models that describe the effects of various types of surface defects, such as Gaussian-height distribution of roughness, curvature and tilt of plates, sinusoidal roughness, and asymmetrical roughness on the finesse and contrast. Our experimental results can be accounted for if we assume that the reflectivity is nonuniform over the Fabry–Perot plates and that there is some reasonable contribution that is due to Gaussian roughness, curvature, or tilt.

© 1996 Optical Society of America

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  1. R. W. Ditchburn, Light (Interscience, New York, 1964), Chap. 5.
  2. M. V. Klein, Optics (Wiley, New York, 1970), Chap. 5.
  3. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), Chap. 7, p. 328.
  4. E. D. Palik, H. Boukari, R. W. Gammon, “Line-shape studies for single- and triple-pass Fabry–Perot interferometer systems,” Appl. Opt. 34, 58–68 (1995).
    [CrossRef] [PubMed]
  5. H. Boukari, E. D. Palik, R. W. Gammon, “Closed-form expressions to fit data obtained with a multipass Fabry–Perot interferometer,” Appl. Opt. 34, 69–86 (1995).
    [CrossRef] [PubMed]
  6. E. A. Ballik, “The response of scanning Pabry–Perot interferometers to atomic transition profiles,” Appl. Opt. 5, 170–172 (1966).
    [CrossRef] [PubMed]
  7. H. W. Leidecker, J. T. LaMacchia, “Instrumental effects on Brillouin line shapes,” J. Acoust. Soc. Am. 43, 143–151 (1968).
    [CrossRef]
  8. S. M. Lindsay, S. Burgess, I. W. Shepherd, “Correction of Brillouin linewidths measured by multipass Pabry–Perot spectroscopy,” Appl. Opt. 16, 1404–1407 (1977).
    [CrossRef] [PubMed]
  9. J. M. Alvarez, J. A. Valles, “Determination of a Fabry– Perot multipass interferometer instrumental function,” Appl. Opt. 28, 2191–2193 (1989).
    [CrossRef] [PubMed]
  10. D. Zhechev, R. Zaprianova, I. Koleva, “On the Voigt analysis of interferograms by using Ballik's method,” Spectrosc. Lett. 14, 809–817 (1981).
    [CrossRef]
  11. G. Hernandez, “Analytical description of a Fabry–Perot photoelectric spectrometer,” Appl. Opt. 5, 1745–1748 (1966) and references therein.
    [CrossRef] [PubMed]
  12. P. K. Katti, K. Singh, “Fringe irradiance distribution in Fabry–Perot interferometer with a tilted mirror,” Optik 24, 347–354 (1967).
  13. J. G. Dil, N. C. J. A. van Hijningen, F. van Dorst, R. M. Aarts, “Tandem multipass Fabry–Perot interferometer for Brillouin scattering,” Appl. Opt. 20, 1374–1381 (1981).
    [CrossRef] [PubMed]
  14. D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chaps. 1 and 2.
  15. C. Roychoudhuri, “Multiple-beam interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 6.
  16. G. Koppelmann, K. Krebs, “Eine Registriermethode zur Vermessung des Reliefs höchstebener Oberflächen,” Optik 18, 349–357 (1961);“Zur Technologie des Pérot–Fabry Interferometers,” Optik 18, 358–373 (1961).
  17. I.J. Hodgkinson, “A method for mapping and determining the surface defects function of pairs of coated optical flats,” Appl. Opt. 8, 1373–1378 (1969).
    [CrossRef] [PubMed]
  18. T. L. Killeen, P. B. Hays, J. DeVos, “Parallelism maps for optically contacted etalons,” Appl. Opt. 20, 2616–2619 (1981).
    [CrossRef] [PubMed]
  19. G. J. Sloggett, “Fringe broadening in Fabry–Perot interferometers,” Appl. Opt. 23, 2427–2432 (1984).
    [CrossRef] [PubMed]
  20. V. N. Del Piano, A. F. Quesada, “Transmission characteristics of Pabry–Perot interferometers and a related electrooptic modulator,” Appl. Opt. 4, 1386–1390 (1965).
    [CrossRef]
  21. M.A. Khashan, “Analytical determination of linewidths using the Pabry–Perot spectrometer,” Physica 98C, 93–99 (1979).
  22. J. V. Ramsay, “Aberrations of Fabry–Perot interferometers when used as filters,” Appl. Opt. 8, 569–574 (1969).
    [CrossRef] [PubMed]
  23. V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrument contour of a nonideal Fabry–Perot interferometer: Part 2,” Opt. Spectrosc. 43, 460–462 (1977);Opt. Spektrosk. 43, 780–784 (1977).
  24. K. Krebs, A. Sauer, “Über die Intensittäsverteilung von Spektrallinien im Pérot–Fabry Interferometer,” Ann. Phys. 6, 359–368 (1953).
    [CrossRef]
  25. R. M. Hill, “Some fringe-broadening defects in a Fabry–Perot éalon,” Opt. Acta 10, 141–152 (1963).
    [CrossRef]
  26. T. N. Siraya, A. L. Etsina, I. S. Etsin, “Random defects in the medium and the mirrors in a Fabry–Perot interferometer,” Opt. Spectrosc. 45, 105–106 (1978)[Opt. Spektrosk. 45, 193–194 (1978).]
  27. P. A. Wilksch, “Instrument function of the Fabry–Perot spectrometer,” Appl. Opt. 24, 1502–1511 (1985).
    [CrossRef] [PubMed]
  28. G. S. Bhatnagar, K. Singh, B. N. Gupta, “Transmission profile of a Fabry–Perot interferometer suffering from asymmetric surface defects,” Nouv. Rev. Opt. 5, 237–240 (1974).
    [CrossRef]
  29. V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrumental profile of an ideal Fabry–Perot interferometer,” Opt. Spectrosc. 45, 87–89 (1978)[Opt. Spektrosk.45, 159–164 (1978).]
  30. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 4, p. 38.
  31. J. M. Bennett, Surface Finish and Its Measurement: Part A (Optical Society of America, Washington, D.C., 1992), Chap. IV.5, p. 376.
  32. G. Rasigni, F. Varnier, M. Rasigni, J. P. Palmari, A. Llebaria, “Autocovariance functions for polished optical surfaces,” J. Opt. Soc. Am. 73, 222–233 (1983).
    [CrossRef]
  33. C. Roychoudhuri, M. Hercher, “Stable multipass Fabry– Perot interferometer: design and analysis,” Appl. Opt. 16, 2514–2520 (1977).
    [CrossRef] [PubMed]
  34. C. Dufour, R. Picca, “Sur l'intérferomètre Fabry–Perot: importance des imperfections des surfaces,” Rev. Opt. 24, 19–34 (1945).
  35. J. M. Vaughan, The Fabry–Perot Interferometer, History, Theory, Practice, and Applications (Hilger, Bristol, 1989), Chap. 3, p. 124, Chap. 6, p. 239.
  36. G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, U.K.1986), Chap. 2, p. 25.
  37. R. Gupta, C. D. Prasad, “Instrumental broadening caused by the misalignment function in a Fabry–Perot étalon assembly,” Appl. Opt. 30, 373–375 (1991).
    [CrossRef] [PubMed]
  38. R. Chabbal, “Recherche des meilleures conditions d'utilisation d'un spectromètre photoélectrique Fabry–Perot,” J. Rech. CNRS 24, 138–186 (1953);“Finesse limite d'un Fabry–Perot interferometre formé de lames imparfaites,” J. Phys. Rad. 19, 295–300 (1958).
  39. J. M. Bennett, “Measurement of the rms roughness, autocovariance and other statistical properties of optical surfaces using a FECO scanning interferometer,” Appl. Opt. 15, 2705–2721 (1976).
    [CrossRef] [PubMed]
  40. L. N. Durvasula, R. W. Gammon, “Pressure-scanned three-pass Fabry–Perot interferometer,” Appl. Opt. 17, 3298–3303 (1978).
    [CrossRef] [PubMed]
  41. J. M. Vaughan, “Brillouin scattering in the nematic and isotropic phases of a liquid crystal,” Phys. Lett. A 58, 325–328 (1976).
    [CrossRef]
  42. S. M. Lindsay, I. W. Shepherd, “A high-contrast Fabry– Perot spectrometer,” J. Phys. E 10, 150–154 (1977).
    [CrossRef] [PubMed]
  43. J. R. Sandercock, “The design and use of a stabilized multipassed interferometer of high contrast ratio,” in Proceedings of the Second International Conference on Light Scattering in Solids, M. Balkanski, ed. (Flammarion, Paris, 1971), p. 9.
  44. J. G. Dil, E. M. Brody, “Brillouin scattering from isotropic metals,” Phys. Rev. B 14, 5218–5227 (1976).
    [CrossRef]
  45. T. L. Killeen, P. B. Hays, B. C. Kennedy, D. Rees, “Stable and rugged etalon for the Dynamics Explorer Fabry–Perot interferometer. 2: Performance,” Appl. Opt. 21, 3903–3912 (1982).
    [CrossRef] [PubMed]
  46. M. Čopič, M. Zgonik, “On multipass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
    [CrossRef]
  47. J. T. Trauger, “Broadband dielectric mirror coatings for Fabry–Perot spectroscopy,” Appl. Opt. 15, 2998–3005 (1976).
    [CrossRef] [PubMed]
  48. R. P. Netterfield, R. C. Schaeffer, W. G. Sainty, “Coating Fabry–Perot interferometer plates with broadband multilayer dielectric mirrors,” Appl. Opt. 19, 3010–3017 (1980).
    [CrossRef] [PubMed]
  49. C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).
  50. A. E. Ennos, “Stresses developed in optical film coatings,” Appl. Opt. 5, 51–61 (1966).
    [CrossRef] [PubMed]
  51. P. A. Greet, “Coating stress in Fabry–Perot étalons,” Appl. Opt. 25, 3328–3330 (1986).
    [CrossRef] [PubMed]
  52. E. D. Palik, J. W. Gibson, R. T. Holm, M. Hass, M. Braunstein, B. Garcia, “Infrared characterization of surfaces and coatings by internal-reflection spectroscopy,” Appl. Opt. 17, 1776–1785 (1978).
    [CrossRef] [PubMed]
  53. H. A. Macleod, “Structure-related optical properties of thin films,” J. Vac. Sci. Technol. A 4, 418–422 (1986).
    [CrossRef]
  54. I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
    [CrossRef]

1995

1991

1989

1986

P. A. Greet, “Coating stress in Fabry–Perot étalons,” Appl. Opt. 25, 3328–3330 (1986).
[CrossRef] [PubMed]

H. A. Macleod, “Structure-related optical properties of thin films,” J. Vac. Sci. Technol. A 4, 418–422 (1986).
[CrossRef]

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

1985

1984

1983

1982

1981

1980

1979

M.A. Khashan, “Analytical determination of linewidths using the Pabry–Perot spectrometer,” Physica 98C, 93–99 (1979).

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).

1978

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrumental profile of an ideal Fabry–Perot interferometer,” Opt. Spectrosc. 45, 87–89 (1978)[Opt. Spektrosk.45, 159–164 (1978).]

T. N. Siraya, A. L. Etsina, I. S. Etsin, “Random defects in the medium and the mirrors in a Fabry–Perot interferometer,” Opt. Spectrosc. 45, 105–106 (1978)[Opt. Spektrosk. 45, 193–194 (1978).]

E. D. Palik, J. W. Gibson, R. T. Holm, M. Hass, M. Braunstein, B. Garcia, “Infrared characterization of surfaces and coatings by internal-reflection spectroscopy,” Appl. Opt. 17, 1776–1785 (1978).
[CrossRef] [PubMed]

L. N. Durvasula, R. W. Gammon, “Pressure-scanned three-pass Fabry–Perot interferometer,” Appl. Opt. 17, 3298–3303 (1978).
[CrossRef] [PubMed]

1977

S. M. Lindsay, S. Burgess, I. W. Shepherd, “Correction of Brillouin linewidths measured by multipass Pabry–Perot spectroscopy,” Appl. Opt. 16, 1404–1407 (1977).
[CrossRef] [PubMed]

C. Roychoudhuri, M. Hercher, “Stable multipass Fabry– Perot interferometer: design and analysis,” Appl. Opt. 16, 2514–2520 (1977).
[CrossRef] [PubMed]

S. M. Lindsay, I. W. Shepherd, “A high-contrast Fabry– Perot spectrometer,” J. Phys. E 10, 150–154 (1977).
[CrossRef] [PubMed]

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrument contour of a nonideal Fabry–Perot interferometer: Part 2,” Opt. Spectrosc. 43, 460–462 (1977);Opt. Spektrosk. 43, 780–784 (1977).

1976

1974

G. S. Bhatnagar, K. Singh, B. N. Gupta, “Transmission profile of a Fabry–Perot interferometer suffering from asymmetric surface defects,” Nouv. Rev. Opt. 5, 237–240 (1974).
[CrossRef]

1969

1968

H. W. Leidecker, J. T. LaMacchia, “Instrumental effects on Brillouin line shapes,” J. Acoust. Soc. Am. 43, 143–151 (1968).
[CrossRef]

1967

P. K. Katti, K. Singh, “Fringe irradiance distribution in Fabry–Perot interferometer with a tilted mirror,” Optik 24, 347–354 (1967).

1966

1965

1963

R. M. Hill, “Some fringe-broadening defects in a Fabry–Perot éalon,” Opt. Acta 10, 141–152 (1963).
[CrossRef]

1961

G. Koppelmann, K. Krebs, “Eine Registriermethode zur Vermessung des Reliefs höchstebener Oberflächen,” Optik 18, 349–357 (1961);“Zur Technologie des Pérot–Fabry Interferometers,” Optik 18, 358–373 (1961).

1953

K. Krebs, A. Sauer, “Über die Intensittäsverteilung von Spektrallinien im Pérot–Fabry Interferometer,” Ann. Phys. 6, 359–368 (1953).
[CrossRef]

R. Chabbal, “Recherche des meilleures conditions d'utilisation d'un spectromètre photoélectrique Fabry–Perot,” J. Rech. CNRS 24, 138–186 (1953);“Finesse limite d'un Fabry–Perot interferometre formé de lames imparfaites,” J. Phys. Rad. 19, 295–300 (1958).

1945

C. Dufour, R. Picca, “Sur l'intérferomètre Fabry–Perot: importance des imperfections des surfaces,” Rev. Opt. 24, 19–34 (1945).

Aarts, R. M.

Alvarez, J. M.

Ballik, E. A.

Bennett, J. M.

J. M. Bennett, “Measurement of the rms roughness, autocovariance and other statistical properties of optical surfaces using a FECO scanning interferometer,” Appl. Opt. 15, 2705–2721 (1976).
[CrossRef] [PubMed]

J. M. Bennett, Surface Finish and Its Measurement: Part A (Optical Society of America, Washington, D.C., 1992), Chap. IV.5, p. 376.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 4, p. 38.

Bhatnagar, G. S.

G. S. Bhatnagar, K. Singh, B. N. Gupta, “Transmission profile of a Fabry–Perot interferometer suffering from asymmetric surface defects,” Nouv. Rev. Opt. 5, 237–240 (1974).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), Chap. 7, p. 328.

Boukari, H.

Braunstein, M.

Brody, E. M.

J. G. Dil, E. M. Brody, “Brillouin scattering from isotropic metals,” Phys. Rev. B 14, 5218–5227 (1976).
[CrossRef]

Burgess, S.

Carniglia, C. K.

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).

Chabbal, R.

R. Chabbal, “Recherche des meilleures conditions d'utilisation d'un spectromètre photoélectrique Fabry–Perot,” J. Rech. CNRS 24, 138–186 (1953);“Finesse limite d'un Fabry–Perot interferometre formé de lames imparfaites,” J. Phys. Rad. 19, 295–300 (1958).

Copic, M.

M. Čopič, M. Zgonik, “On multipass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
[CrossRef]

Del Piano, V. N.

DeVos, J.

Dil, J. G.

Ditchburn, R. W.

R. W. Ditchburn, Light (Interscience, New York, 1964), Chap. 5.

Dufour, C.

C. Dufour, R. Picca, “Sur l'intérferomètre Fabry–Perot: importance des imperfections des surfaces,” Rev. Opt. 24, 19–34 (1945).

Dunaev, V. V.

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrumental profile of an ideal Fabry–Perot interferometer,” Opt. Spectrosc. 45, 87–89 (1978)[Opt. Spektrosk.45, 159–164 (1978).]

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrument contour of a nonideal Fabry–Perot interferometer: Part 2,” Opt. Spectrosc. 43, 460–462 (1977);Opt. Spektrosk. 43, 780–784 (1977).

Durvasula, L. N.

Ennos, A. E.

Etsin, I. S.

T. N. Siraya, A. L. Etsina, I. S. Etsin, “Random defects in the medium and the mirrors in a Fabry–Perot interferometer,” Opt. Spectrosc. 45, 105–106 (1978)[Opt. Spektrosk. 45, 193–194 (1978).]

Etsina, A. L.

T. N. Siraya, A. L. Etsina, I. S. Etsin, “Random defects in the medium and the mirrors in a Fabry–Perot interferometer,” Opt. Spectrosc. 45, 105–106 (1978)[Opt. Spektrosk. 45, 193–194 (1978).]

Gammon, R. W.

Garcia, B.

Gibson, J. W.

Greet, P. A.

Gupta, B. N.

G. S. Bhatnagar, K. Singh, B. N. Gupta, “Transmission profile of a Fabry–Perot interferometer suffering from asymmetric surface defects,” Nouv. Rev. Opt. 5, 237–240 (1974).
[CrossRef]

Gupta, R.

Hass, M.

Hays, P. B.

Hercher, M.

Hernandez, G.

Hill, R. M.

R. M. Hill, “Some fringe-broadening defects in a Fabry–Perot éalon,” Opt. Acta 10, 141–152 (1963).
[CrossRef]

Hodgkinson, I. J.

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

Hodgkinson, I.J.

Holm, R. T.

Jacobson, M. R.

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

Katti, P. K.

P. K. Katti, K. Singh, “Fringe irradiance distribution in Fabry–Perot interferometer with a tilted mirror,” Optik 24, 347–354 (1967).

Kennedy, B. C.

Khashan, M.A.

M.A. Khashan, “Analytical determination of linewidths using the Pabry–Perot spectrometer,” Physica 98C, 93–99 (1979).

Killeen, T. L.

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 5.

Koleva, I.

D. Zhechev, R. Zaprianova, I. Koleva, “On the Voigt analysis of interferograms by using Ballik's method,” Spectrosc. Lett. 14, 809–817 (1981).
[CrossRef]

Koppelmann, G.

G. Koppelmann, K. Krebs, “Eine Registriermethode zur Vermessung des Reliefs höchstebener Oberflächen,” Optik 18, 349–357 (1961);“Zur Technologie des Pérot–Fabry Interferometers,” Optik 18, 358–373 (1961).

Krebs, K.

G. Koppelmann, K. Krebs, “Eine Registriermethode zur Vermessung des Reliefs höchstebener Oberflächen,” Optik 18, 349–357 (1961);“Zur Technologie des Pérot–Fabry Interferometers,” Optik 18, 358–373 (1961).

K. Krebs, A. Sauer, “Über die Intensittäsverteilung von Spektrallinien im Pérot–Fabry Interferometer,” Ann. Phys. 6, 359–368 (1953).
[CrossRef]

Kuchinskii, V. V.

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrumental profile of an ideal Fabry–Perot interferometer,” Opt. Spectrosc. 45, 87–89 (1978)[Opt. Spektrosk.45, 159–164 (1978).]

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrument contour of a nonideal Fabry–Perot interferometer: Part 2,” Opt. Spectrosc. 43, 460–462 (1977);Opt. Spektrosk. 43, 780–784 (1977).

LaMacchia, J. T.

H. W. Leidecker, J. T. LaMacchia, “Instrumental effects on Brillouin line shapes,” J. Acoust. Soc. Am. 43, 143–151 (1968).
[CrossRef]

Lee, C. C.

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

Leidecker, H. W.

H. W. Leidecker, J. T. LaMacchia, “Instrumental effects on Brillouin line shapes,” J. Acoust. Soc. Am. 43, 143–151 (1968).
[CrossRef]

Lindsay, S. M.

Llebaria, A.

Macleod, H. A.

H. A. Macleod, “Structure-related optical properties of thin films,” J. Vac. Sci. Technol. A 4, 418–422 (1986).
[CrossRef]

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chaps. 1 and 2.

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 4, p. 38.

Netterfield, R. P.

Palik, E. D.

Palmari, J. P.

Picca, R.

C. Dufour, R. Picca, “Sur l'intérferomètre Fabry–Perot: importance des imperfections des surfaces,” Rev. Opt. 24, 19–34 (1945).

Potoff, R. H.

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

Prasad, C. D.

Quesada, A. F.

Ramsay, J. V.

Rasigni, G.

Rasigni, M.

Rees, D.

Roychoudhuri, C.

C. Roychoudhuri, M. Hercher, “Stable multipass Fabry– Perot interferometer: design and analysis,” Appl. Opt. 16, 2514–2520 (1977).
[CrossRef] [PubMed]

C. Roychoudhuri, “Multiple-beam interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 6.

Sainty, W. G.

Sandercock, J. R.

J. R. Sandercock, “The design and use of a stabilized multipassed interferometer of high contrast ratio,” in Proceedings of the Second International Conference on Light Scattering in Solids, M. Balkanski, ed. (Flammarion, Paris, 1971), p. 9.

Sauer, A.

K. Krebs, A. Sauer, “Über die Intensittäsverteilung von Spektrallinien im Pérot–Fabry Interferometer,” Ann. Phys. 6, 359–368 (1953).
[CrossRef]

Schaeffer, R. C.

Shepherd, I. W.

Sikkens, M.

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

Singh, K.

G. S. Bhatnagar, K. Singh, B. N. Gupta, “Transmission profile of a Fabry–Perot interferometer suffering from asymmetric surface defects,” Nouv. Rev. Opt. 5, 237–240 (1974).
[CrossRef]

P. K. Katti, K. Singh, “Fringe irradiance distribution in Fabry–Perot interferometer with a tilted mirror,” Optik 24, 347–354 (1967).

Siraya, T. N.

T. N. Siraya, A. L. Etsina, I. S. Etsin, “Random defects in the medium and the mirrors in a Fabry–Perot interferometer,” Opt. Spectrosc. 45, 105–106 (1978)[Opt. Spektrosk. 45, 193–194 (1978).]

Sloggett, G. J.

Sprague, R.

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

Trauger, J. T.

Valles, J. A.

van Dorst, F.

van Hijningen, N. C. J. A.

Varnier, F.

Vaughan, J. M.

J. M. Vaughan, “Brillouin scattering in the nematic and isotropic phases of a liquid crystal,” Phys. Lett. A 58, 325–328 (1976).
[CrossRef]

J. M. Vaughan, The Fabry–Perot Interferometer, History, Theory, Practice, and Applications (Hilger, Bristol, 1989), Chap. 3, p. 124, Chap. 6, p. 239.

Wilksch, P. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), Chap. 7, p. 328.

Zaprianova, R.

D. Zhechev, R. Zaprianova, I. Koleva, “On the Voigt analysis of interferograms by using Ballik's method,” Spectrosc. Lett. 14, 809–817 (1981).
[CrossRef]

Zgonik, M.

M. Čopič, M. Zgonik, “On multipass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
[CrossRef]

Zhechev, D.

D. Zhechev, R. Zaprianova, I. Koleva, “On the Voigt analysis of interferograms by using Ballik's method,” Spectrosc. Lett. 14, 809–817 (1981).
[CrossRef]

Zhiglinskii, A. G.

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrumental profile of an ideal Fabry–Perot interferometer,” Opt. Spectrosc. 45, 87–89 (1978)[Opt. Spektrosk.45, 159–164 (1978).]

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrument contour of a nonideal Fabry–Perot interferometer: Part 2,” Opt. Spectrosc. 43, 460–462 (1977);Opt. Spektrosk. 43, 780–784 (1977).

Ann. Phys.

K. Krebs, A. Sauer, “Über die Intensittäsverteilung von Spektrallinien im Pérot–Fabry Interferometer,” Ann. Phys. 6, 359–368 (1953).
[CrossRef]

Appl. Opt.

V. N. Del Piano, A. F. Quesada, “Transmission characteristics of Pabry–Perot interferometers and a related electrooptic modulator,” Appl. Opt. 4, 1386–1390 (1965).
[CrossRef]

A. E. Ennos, “Stresses developed in optical film coatings,” Appl. Opt. 5, 51–61 (1966).
[CrossRef] [PubMed]

G. Hernandez, “Analytical description of a Fabry–Perot photoelectric spectrometer,” Appl. Opt. 5, 1745–1748 (1966) and references therein.
[CrossRef] [PubMed]

J. V. Ramsay, “Aberrations of Fabry–Perot interferometers when used as filters,” Appl. Opt. 8, 569–574 (1969).
[CrossRef] [PubMed]

I.J. Hodgkinson, “A method for mapping and determining the surface defects function of pairs of coated optical flats,” Appl. Opt. 8, 1373–1378 (1969).
[CrossRef] [PubMed]

J. M. Bennett, “Measurement of the rms roughness, autocovariance and other statistical properties of optical surfaces using a FECO scanning interferometer,” Appl. Opt. 15, 2705–2721 (1976).
[CrossRef] [PubMed]

J. T. Trauger, “Broadband dielectric mirror coatings for Fabry–Perot spectroscopy,” Appl. Opt. 15, 2998–3005 (1976).
[CrossRef] [PubMed]

S. M. Lindsay, S. Burgess, I. W. Shepherd, “Correction of Brillouin linewidths measured by multipass Pabry–Perot spectroscopy,” Appl. Opt. 16, 1404–1407 (1977).
[CrossRef] [PubMed]

C. Roychoudhuri, M. Hercher, “Stable multipass Fabry– Perot interferometer: design and analysis,” Appl. Opt. 16, 2514–2520 (1977).
[CrossRef] [PubMed]

E. D. Palik, J. W. Gibson, R. T. Holm, M. Hass, M. Braunstein, B. Garcia, “Infrared characterization of surfaces and coatings by internal-reflection spectroscopy,” Appl. Opt. 17, 1776–1785 (1978).
[CrossRef] [PubMed]

L. N. Durvasula, R. W. Gammon, “Pressure-scanned three-pass Fabry–Perot interferometer,” Appl. Opt. 17, 3298–3303 (1978).
[CrossRef] [PubMed]

R. P. Netterfield, R. C. Schaeffer, W. G. Sainty, “Coating Fabry–Perot interferometer plates with broadband multilayer dielectric mirrors,” Appl. Opt. 19, 3010–3017 (1980).
[CrossRef] [PubMed]

J. G. Dil, N. C. J. A. van Hijningen, F. van Dorst, R. M. Aarts, “Tandem multipass Fabry–Perot interferometer for Brillouin scattering,” Appl. Opt. 20, 1374–1381 (1981).
[CrossRef] [PubMed]

T. L. Killeen, P. B. Hays, J. DeVos, “Parallelism maps for optically contacted etalons,” Appl. Opt. 20, 2616–2619 (1981).
[CrossRef] [PubMed]

T. L. Killeen, P. B. Hays, B. C. Kennedy, D. Rees, “Stable and rugged etalon for the Dynamics Explorer Fabry–Perot interferometer. 2: Performance,” Appl. Opt. 21, 3903–3912 (1982).
[CrossRef] [PubMed]

G. J. Sloggett, “Fringe broadening in Fabry–Perot interferometers,” Appl. Opt. 23, 2427–2432 (1984).
[CrossRef] [PubMed]

P. A. Wilksch, “Instrument function of the Fabry–Perot spectrometer,” Appl. Opt. 24, 1502–1511 (1985).
[CrossRef] [PubMed]

E. D. Palik, H. Boukari, R. W. Gammon, “Line-shape studies for single- and triple-pass Fabry–Perot interferometer systems,” Appl. Opt. 34, 58–68 (1995).
[CrossRef] [PubMed]

H. Boukari, E. D. Palik, R. W. Gammon, “Closed-form expressions to fit data obtained with a multipass Fabry–Perot interferometer,” Appl. Opt. 34, 69–86 (1995).
[CrossRef] [PubMed]

E. A. Ballik, “The response of scanning Pabry–Perot interferometers to atomic transition profiles,” Appl. Opt. 5, 170–172 (1966).
[CrossRef] [PubMed]

P. A. Greet, “Coating stress in Fabry–Perot étalons,” Appl. Opt. 25, 3328–3330 (1986).
[CrossRef] [PubMed]

R. Gupta, C. D. Prasad, “Instrumental broadening caused by the misalignment function in a Fabry–Perot étalon assembly,” Appl. Opt. 30, 373–375 (1991).
[CrossRef] [PubMed]

J. M. Alvarez, J. A. Valles, “Determination of a Fabry– Perot multipass interferometer instrumental function,” Appl. Opt. 28, 2191–2193 (1989).
[CrossRef] [PubMed]

J. Acoust. Soc. Am.

H. W. Leidecker, J. T. LaMacchia, “Instrumental effects on Brillouin line shapes,” J. Acoust. Soc. Am. 43, 143–151 (1968).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. E

S. M. Lindsay, I. W. Shepherd, “A high-contrast Fabry– Perot spectrometer,” J. Phys. E 10, 150–154 (1977).
[CrossRef] [PubMed]

J. Rech. CNRS

R. Chabbal, “Recherche des meilleures conditions d'utilisation d'un spectromètre photoélectrique Fabry–Perot,” J. Rech. CNRS 24, 138–186 (1953);“Finesse limite d'un Fabry–Perot interferometre formé de lames imparfaites,” J. Phys. Rad. 19, 295–300 (1958).

J. Vac. Sci. Technol. A

H. A. Macleod, “Structure-related optical properties of thin films,” J. Vac. Sci. Technol. A 4, 418–422 (1986).
[CrossRef]

Nouv. Rev. Opt.

G. S. Bhatnagar, K. Singh, B. N. Gupta, “Transmission profile of a Fabry–Perot interferometer suffering from asymmetric surface defects,” Nouv. Rev. Opt. 5, 237–240 (1974).
[CrossRef]

Opt. Acta

R. M. Hill, “Some fringe-broadening defects in a Fabry–Perot éalon,” Opt. Acta 10, 141–152 (1963).
[CrossRef]

Opt. Commun.

M. Čopič, M. Zgonik, “On multipass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
[CrossRef]

Opt. Eng.

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).

Opt. Spectrosc.

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrument contour of a nonideal Fabry–Perot interferometer: Part 2,” Opt. Spectrosc. 43, 460–462 (1977);Opt. Spektrosk. 43, 780–784 (1977).

T. N. Siraya, A. L. Etsina, I. S. Etsin, “Random defects in the medium and the mirrors in a Fabry–Perot interferometer,” Opt. Spectrosc. 45, 105–106 (1978)[Opt. Spektrosk. 45, 193–194 (1978).]

V. V. Dunaev, A. G. Zhiglinskii, V. V. Kuchinskii, “Instrumental profile of an ideal Fabry–Perot interferometer,” Opt. Spectrosc. 45, 87–89 (1978)[Opt. Spektrosk.45, 159–164 (1978).]

Optik

G. Koppelmann, K. Krebs, “Eine Registriermethode zur Vermessung des Reliefs höchstebener Oberflächen,” Optik 18, 349–357 (1961);“Zur Technologie des Pérot–Fabry Interferometers,” Optik 18, 358–373 (1961).

P. K. Katti, K. Singh, “Fringe irradiance distribution in Fabry–Perot interferometer with a tilted mirror,” Optik 24, 347–354 (1967).

Phys. Lett. A

J. M. Vaughan, “Brillouin scattering in the nematic and isotropic phases of a liquid crystal,” Phys. Lett. A 58, 325–328 (1976).
[CrossRef]

Phys. Rev. B

J. G. Dil, E. M. Brody, “Brillouin scattering from isotropic metals,” Phys. Rev. B 14, 5218–5227 (1976).
[CrossRef]

Physica

M.A. Khashan, “Analytical determination of linewidths using the Pabry–Perot spectrometer,” Physica 98C, 93–99 (1979).

Rev. Opt.

C. Dufour, R. Picca, “Sur l'intérferomètre Fabry–Perot: importance des imperfections des surfaces,” Rev. Opt. 24, 19–34 (1945).

Spectrosc. Lett.

D. Zhechev, R. Zaprianova, I. Koleva, “On the Voigt analysis of interferograms by using Ballik's method,” Spectrosc. Lett. 14, 809–817 (1981).
[CrossRef]

Thin Solid Films

I. J. Hodgkinson, M. R. Jacobson, H. A. Macleod, R. H. Potoff, M. Sikkens, R. Sprague, C. C. Lee, “Water penetration fronts in thin films deposited at oblique incidence,” Thin Solid Films 138, 289–296 (1986).
[CrossRef]

Other

J. R. Sandercock, “The design and use of a stabilized multipassed interferometer of high contrast ratio,” in Proceedings of the Second International Conference on Light Scattering in Solids, M. Balkanski, ed. (Flammarion, Paris, 1971), p. 9.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chaps. 1 and 2.

C. Roychoudhuri, “Multiple-beam interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 6.

R. W. Ditchburn, Light (Interscience, New York, 1964), Chap. 5.

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 5.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), Chap. 7, p. 328.

J. M. Vaughan, The Fabry–Perot Interferometer, History, Theory, Practice, and Applications (Hilger, Bristol, 1989), Chap. 3, p. 124, Chap. 6, p. 239.

G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, U.K.1986), Chap. 2, p. 25.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 4, p. 38.

J. M. Bennett, Surface Finish and Its Measurement: Part A (Optical Society of America, Washington, D.C., 1992), Chap. IV.5, p. 376.

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Figures (4)

Fig. 1
Fig. 1

(a) Calculated finesse ℱ as a function of the defect parameter m in λ/m for mL , mG , mC , and mT , which correspond to Lorentzian roughness, Gaussian roughness, curvature, and tilt (R = 0.94); (b) Calculated contrast C as a function of the defect parameter m; (c) Calculated maximum and minimum intensities, I max and I min, as functions of the defect parameter m.

Fig. 2
Fig. 2

(a) Calculated contrast C plotted as a function of calculated finesse ℱ for an Airy function with a range of values of R from 0.94 to 0.30. If defects of Gaussian roughness are introduced for various values of parameter λ/mG , the grid shown is obtained. For curvature defects only, some values of mC , are shown and a corresponding grid can be inferred. (b) Measured contrast is plotted as a function of measured finesse. Similar points indicate data derived from 1-pass spectra taken the same day but at different 1.5-mm-diameter spots on the plates. To give some estimate of the variations of R and curvature or Gaussian roughness over the plates, we show C versus ℱ curves derived for ideal FP plates (solid curve) and FP plates with defects (dashed curve).

Fig. 3
Fig. 3

Experimental 1-pass spectrum fitted over one order of interference (FSR) with the defect model discussed in the text, mG = mT = mC = 20,000, R = 0.910. From the calculated fit we find ℱ = 33.3, C = 453. The two sets of data points are from spectra obtained with (●) and without (○) the filters, which emphasize the maximum and the minimum, respectively. Count-rate statistics (normalized) are indicated by a few vertical bars at that level of count rate. (b) Experimental 1-pass spectrum taken at a different spot from that of (a) is fitted with mG = mT = 20,000, R = 0.919 but with mC = 120. From the calculated fit we find ℱ = 31.6 and C = 502. (c) Experimental 1-pass spectrum fitted with mG = mT = 20,000, R = 0.937, and mC = 100. From the calculated fit we find ℱ = 34.7, C = 732.

Fig. 4
Fig. 4

(a) Calculated 1-pass contrast C 1 is plotted as a function of calculated finesse ℱ1 for 0.84 ≤ R ≤ 0.93 (solid curve). When curvature is added at R = 0.91, for example, the contrast and the finesse are degraded, as shown by the dashed curve. The experimental data listed in Table 1 are plotted: our experimental 1-pass datum point (Δ), the 1-pass experimental (or inferred) data points of Durvasula and Gammon40 (●), Vaughan41 (□), Lindsay and Shepherd42 (∇), our measured datum point for a second interferometer (○). (b) Calculated 3-pass contrast C 3 is plotted as a function of calculated finesse ℱ3 (solid curve). When curvature is added at R = 0.91, the contrast and the finesse are degraded, as shown by the dashed curve. Experimental 3-pass data points listed in Table 1 are plotted; the data points are identified in the caption of (a). (c) Calculated 5-pass contrast C 5 is plotted as a function of calculated finesse ℱ5 (solid curve). When curvature is added at R = 0.91, the contrast and the finesse are degraded, as shown by the dashed curve. Experimental 5-pass data points listed in Table 1 are plotted: Sandercock43 (□) and Dil and Brody44 (Δ), (∇).

Tables (1)

Tables Icon

Table 1 Comparison of 1-, 3- and 5-Pass Measured Values of ℱ and C with Calculated Values Determined from Measured or Inferred R a

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

I ( ν ) = [ 1 A / ( 1 R ) ] 2 1 + F sin 2 ( π ν / Δ ) ,
I ( ν ) = ( 1 2 π ) ( 1 + 2 k [ R k exp ( 4 π k / m L ) ] × { exp [ ( 2.35 π k / m G ln 2 ) 2 ] } [ sin ( 2 π k / m C ) ( 2 π k / m C ) ] × [ sin ( 2 π k / m T ) ( 2 π k / m T ) ] cos ( 2 π k ν / Δ ) ) ,
1 T 2 = 1 R 2 + 1 S 2 .
n = 1 / ( 2 1 / n 1 ) 1 / 2 ,
C n = C 1 n .

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