Abstract

A scanning spectrometer may be described either by its transmission as a function of an actual spectral variable (e.g., wavelength) or by its response to a monochromatic source as a function of an instrumental scanning parameter. The distinction between these two descriptions has not always been recognized in previous developments of the theory of the parallel-plate Fabry-Perot spectrometer, and errors and ambiguities have often resulted. An outline and review of the theory is presented, including the effects of etalon surface irregularities and the finite solid angle of radiation admitted through the etalon. The order of interference is used as the argument of the functions involved, careful attention being given to the definitions and physical meanings of all functions and quantities. Optimization of the operating parameters of a spectrometer is considered very briefly.

© 1985 Optical Society of America

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    [CrossRef]
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).
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  4. P. Jacquinot, C. Dufour, “Optical Conditions in the Use of Photo-Electric Cells in Spectrographs and Interferometers,” J. Rech. CNRS 6, 91 (1948).
  5. R. J. Chabbal, “Recherche des Meilleures Conditions d'Utilisation d'un Spectromètre Fabry-Perot,” J. Rech. CNRS 24, 138 (1953).English translation, “Research on the Best Conditions for Using a Fabry-Perot Photo-Electric Spectrometer,” AERE Lib. Trans., 778Harwell (1958).
  6. K. Krebs, A. Sauer, “Über die Intensitätsverteilung von Spektrallinien im Pérot-Fabry-Interferometer,” Ann. Phys. 6, 359 (1953).
    [CrossRef]
  7. F. Bayer-Helms, “Analyse von Linienprofilen. I. Grundlagen und Messeinrichtungen,” Z. Angew.Phys. 15, 330 (1963).
  8. E. A. Ballik, “The Response of Scanning Fabry-Perot Interferometers to Atomic Transition Profiles,” Appl. Opt. 5, 170 (1966).
    [CrossRef] [PubMed]
  9. P. Jacquinot, “Luminosity of Spectrometers with Prisms, Gratings, or Fabry-Perot Etalons,” J. Opt.Soc. Am. 44, 761 (1954).
    [CrossRef]
  10. P. Jacquinot, “New Developments in Interference Spectroscopy,” Rep. Prog. Phys. 23, 267 (1960).
    [CrossRef]
  11. R. M. Hill, “Some Fringe-Broadening Defects in a Fabry-Perot Etalon,” Opt. Acta 10, 141 (1963).
    [CrossRef]
  12. J. O. Stoner, “PEPSIOS Purely Interferometric High-resolution Scanning Spectrometer. III. Calculation of Interferometer Characteristics by a Method of Optical Transients,” J. Opt.Soc. Am. 56, 370 (1966).
    [CrossRef]
  13. J. V. Ramsay, “Aberrations of Fabry-Perot Interferometers when Used as Filters,” Appl. Opt. 8, 569 (1969).
    [CrossRef] [PubMed]
  14. 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 (1974).
    [CrossRef]
  15. G. Hernandez, “Analytical Description of a Fabry-Perot Photoelectric Spectrometer,” Appl. Opt. 5, 1745 (1966).
    [CrossRef] [PubMed]
  16. D. Goorvitch, “Galatry Profile Convolved with the Fabry-Perot Instrument Function,” Appl. Opt. 16, 1732 (1977).
    [CrossRef] [PubMed]
  17. P. Connes, “L'étalon de Fabry-Perot Sphérique,” J. Phys.Radium 19, 262 (1958).
    [CrossRef]
  18. J. R. Johnson, “A High Resolution Scanning Confocal Interferometer,” Appl. Opt. 7, 1061 (1968).
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  19. M. Hercher, “The Spherical Mirror Fabry-Perot Interferometer,” Appl. Opt. 7, 951 (1968).
    [CrossRef] [PubMed]
  20. A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453 (1961).
  21. H. K. V. Lotsch, “The Fabry-Perot Interferometer with a Large Fresnel Number,” Ann. Phys. 16, 7 (1965).
    [CrossRef]
  22. H. Ogura, Y. Yoshida, J. Ikenoue, “Theory of Deformed Fabry-Perot Resonator,” J. Phys. Soc. Jpn. 20, 598 (1965).
    [CrossRef]
  23. R. Yamada, “On the Plane Fabry-Perot Interferometer,” Jpn. J. Appl. Phys. 6, 904 (1967).
    [CrossRef]
  24. Y. Yoshida, H. Ogura, J. Ikenoue, “Fabry-Perot Resonator with Slightly Tilted Mirrors,” Jpn. J. Appl. Phys. 8, 285 (1969).
    [CrossRef]
  25. H. Neuhaus, “Zur Theorie der Vielstrahlinterferometer einschliesslich Betrachtungen über das theoretische Auflösungsvermögen des Pérot-Fabryschen Etalons,” Ark. Fys. 31, 91 (1966);H. Neuhaus, P. Nylén, “Zur Apparatfunktion des Fabry-Pérotschen Interferometers,” Ark. Fys. 37, 59 (1968);H. Neuhaus, P. Nylén, “Die Apparatfunktion eines aus Fabry-Pérotschen Etalons zusammengesetzten Systems bei endlicher Apertur. Teil III,” Ark. Fys. 40, 405 (1970).
  26. H. Neuhaus, P. Nylén, “The Theoretical Instrument Function of a Fabry-Perot Etalon with Finite Aperture,” Opt. Acta 18, 637 (1971).
    [CrossRef]
  27. Y. A. Ananev, “The Maximum Attainable Resolution of a Real Fabry-Perot Etalon,” Opt. Spectrosc. 20, 89 (1966).
  28. R. Chabbal, “Finesse Limite d'un Fabry-Perot Formé de Lames Imparfaites,” J. Phys. Radium 19, 295 (1958).
    [CrossRef]
  29. F. L. Roesler, W. Traub, “Precision Mapping of Pairs of Uncoated Optical Flats,” Appl. Opt. 5, 463 (1966).
    [CrossRef] [PubMed]
  30. J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen. I,” Opt. Acta 13, 103 (1966).
    [CrossRef]
  31. H. T. Duong, S. Gerstenkorn, J. M. Helbert, “Cartes des Lames d'un Fabry-Perot,” J. Phys. Paris 28, 266 (1967).
    [CrossRef]
  32. W. Primak, “The Determination of the Absolute Contours of Optical Flats,” Appl. Opt. 6, 1917 (1967).
    [CrossRef] [PubMed]
  33. I. J. Hodgkinson, “A Method for Mapping and Determining the Surface Defects Function of Pairs of Coated Optical Flats,” Appl. Opt. 8, 1373 (1969).
    [CrossRef] [PubMed]
  34. C. F. Bruce, F. P. Sharples, “Relative Flatness Measurement of Uncoated Optical Flats,” Appl. Opt. 14, 3082 (1975).
    [CrossRef] [PubMed]
  35. V. N. Del Piano, A. F. Quesada, “Transmission Characteristics of Fabry-Perot Interferometers and a Related Electrooptic Modulator,” Appl. Opt. 4, 1386 (1965).
    [CrossRef]
  36. K. Singh, G. S. Bhatnagar, “Sparrow Limit of Spectral Resolution in the Reflection Echelon and the Fabry-Perot Interferometer Having Surface Imperfections,” Appl. Opt. 9, 2326 (1970).
    [CrossRef] [PubMed]
  37. G. J. Sloggett, “Fringe Broadening in Fabry-Perot Interferometers,” Appl. Opt. 23, 2427 (1984).
    [CrossRef] [PubMed]
  38. C. F. Bruce, “On Automatic Parallelism Control in a Scanning Fabry-Perot Interferometer,” Appl. Opt. 5, 1447 (1966).
    [CrossRef] [PubMed]
  39. J. R. Sandercock, “Simple Stabilization Scheme for Maintenance of Mirror Alignment in a Scanning Fabry-Perot Interferometer,” J. Phys. E 9, 566 (1976).
    [CrossRef]
  40. G. Hernandez, “Analytical Description of a Fabry-Perot Spectrometer. 3: Off-Axis Behavior and Interference Filters,” Appl. Opt. 13, 2654 (1974).
    [CrossRef] [PubMed]
  41. C. F. Bruce, “Aperture Correction in Fabry-Perot Interferometer Measurements,” Rev. Sci. Instrum. 37, 349 (1966).
    [CrossRef]
  42. P. S. Nylén, “Scanning Aperture Correction in Fabry-Perot Interferometry,” Optik 37, 123 (1973);P. S. Nylén, “On the Scanning Fabry-Perot Interferometer,” Phys. Scr. 8, 81 (1973).
    [CrossRef]
  43. H. Dupoisot, R. Prat, S. Slansky, “Luminous Flux Amplification in Fabry-Perot Spectrometry,” Appl. Opt. 17, 3930 (1978).
    [CrossRef] [PubMed]
  44. H. Dupoisot, R. Prat, “High Resolvance Interference Spectrometry with a High Factor of Merit in the Visible Spectrum,” Appl. Opt. 18, 85 (1979).
    [CrossRef] [PubMed]
  45. C. Roychoudhuri, M. Hercher, “Stable Multipass Fabry-Perot Interferometer: Design and Analysis,” Appl. Opt. 16, 2514 (1977).
    [CrossRef] [PubMed]
  46. R. E. Loughhead, R. J. Bray, N. Brown, “Instrumental Profile of a Triple Fabry-Perot Interferometer for use in Solar Spectroscopy,” Appl. Opt. 17, 415 (1978).
    [CrossRef] [PubMed]
  47. G. Hernandez, “Analytical Description of a Fabry-Perot Spectrometer. 5: Optimization for Minimum Uncertainties in the Determination of Doppler Widths and Shifts,” Appl. Opt. 18, 3826 (1979).
    [PubMed]
  48. G. Hernandez, “Analytical Description of a Fabry-Perot Spectrometer. 3: Off-Axis Behavior and Interference Filters: Erratum,” Appl. Opt. 18, 3364 (1979).
    [CrossRef] [PubMed]
  49. A. H. Vaughan, “Astronomical Fabry-Perot Interference Spectroscopy,” Ann. Rev. Astron. Astrophys. 5, 139 (1967).
    [CrossRef]

1984 (1)

1979 (3)

1978 (2)

1977 (2)

1976 (1)

J. R. Sandercock, “Simple Stabilization Scheme for Maintenance of Mirror Alignment in a Scanning Fabry-Perot Interferometer,” J. Phys. E 9, 566 (1976).
[CrossRef]

1975 (1)

1974 (2)

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 (1974).
[CrossRef]

G. Hernandez, “Analytical Description of a Fabry-Perot Spectrometer. 3: Off-Axis Behavior and Interference Filters,” Appl. Opt. 13, 2654 (1974).
[CrossRef] [PubMed]

1973 (1)

P. S. Nylén, “Scanning Aperture Correction in Fabry-Perot Interferometry,” Optik 37, 123 (1973);P. S. Nylén, “On the Scanning Fabry-Perot Interferometer,” Phys. Scr. 8, 81 (1973).
[CrossRef]

1971 (1)

H. Neuhaus, P. Nylén, “The Theoretical Instrument Function of a Fabry-Perot Etalon with Finite Aperture,” Opt. Acta 18, 637 (1971).
[CrossRef]

1970 (1)

1969 (3)

1968 (2)

1967 (4)

R. Yamada, “On the Plane Fabry-Perot Interferometer,” Jpn. J. Appl. Phys. 6, 904 (1967).
[CrossRef]

H. T. Duong, S. Gerstenkorn, J. M. Helbert, “Cartes des Lames d'un Fabry-Perot,” J. Phys. Paris 28, 266 (1967).
[CrossRef]

W. Primak, “The Determination of the Absolute Contours of Optical Flats,” Appl. Opt. 6, 1917 (1967).
[CrossRef] [PubMed]

A. H. Vaughan, “Astronomical Fabry-Perot Interference Spectroscopy,” Ann. Rev. Astron. Astrophys. 5, 139 (1967).
[CrossRef]

1966 (9)

C. F. Bruce, “Aperture Correction in Fabry-Perot Interferometer Measurements,” Rev. Sci. Instrum. 37, 349 (1966).
[CrossRef]

C. F. Bruce, “On Automatic Parallelism Control in a Scanning Fabry-Perot Interferometer,” Appl. Opt. 5, 1447 (1966).
[CrossRef] [PubMed]

F. L. Roesler, W. Traub, “Precision Mapping of Pairs of Uncoated Optical Flats,” Appl. Opt. 5, 463 (1966).
[CrossRef] [PubMed]

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen. I,” Opt. Acta 13, 103 (1966).
[CrossRef]

H. Neuhaus, “Zur Theorie der Vielstrahlinterferometer einschliesslich Betrachtungen über das theoretische Auflösungsvermögen des Pérot-Fabryschen Etalons,” Ark. Fys. 31, 91 (1966);H. Neuhaus, P. Nylén, “Zur Apparatfunktion des Fabry-Pérotschen Interferometers,” Ark. Fys. 37, 59 (1968);H. Neuhaus, P. Nylén, “Die Apparatfunktion eines aus Fabry-Pérotschen Etalons zusammengesetzten Systems bei endlicher Apertur. Teil III,” Ark. Fys. 40, 405 (1970).

Y. A. Ananev, “The Maximum Attainable Resolution of a Real Fabry-Perot Etalon,” Opt. Spectrosc. 20, 89 (1966).

G. Hernandez, “Analytical Description of a Fabry-Perot Photoelectric Spectrometer,” Appl. Opt. 5, 1745 (1966).
[CrossRef] [PubMed]

J. O. Stoner, “PEPSIOS Purely Interferometric High-resolution Scanning Spectrometer. III. Calculation of Interferometer Characteristics by a Method of Optical Transients,” J. Opt.Soc. Am. 56, 370 (1966).
[CrossRef]

E. A. Ballik, “The Response of Scanning Fabry-Perot Interferometers to Atomic Transition Profiles,” Appl. Opt. 5, 170 (1966).
[CrossRef] [PubMed]

1965 (3)

H. K. V. Lotsch, “The Fabry-Perot Interferometer with a Large Fresnel Number,” Ann. Phys. 16, 7 (1965).
[CrossRef]

H. Ogura, Y. Yoshida, J. Ikenoue, “Theory of Deformed Fabry-Perot Resonator,” J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

V. N. Del Piano, A. F. Quesada, “Transmission Characteristics of Fabry-Perot Interferometers and a Related Electrooptic Modulator,” Appl. Opt. 4, 1386 (1965).
[CrossRef]

1963 (2)

F. Bayer-Helms, “Analyse von Linienprofilen. I. Grundlagen und Messeinrichtungen,” Z. Angew.Phys. 15, 330 (1963).

R. M. Hill, “Some Fringe-Broadening Defects in a Fabry-Perot Etalon,” Opt. Acta 10, 141 (1963).
[CrossRef]

1961 (1)

A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453 (1961).

1960 (1)

P. Jacquinot, “New Developments in Interference Spectroscopy,” Rep. Prog. Phys. 23, 267 (1960).
[CrossRef]

1958 (3)

S. G. Rautian, “Real Spectral Apparatus,” Sov. Phys. Usp. 66, 245 (1958).
[CrossRef]

P. Connes, “L'étalon de Fabry-Perot Sphérique,” J. Phys.Radium 19, 262 (1958).
[CrossRef]

R. Chabbal, “Finesse Limite d'un Fabry-Perot Formé de Lames Imparfaites,” J. Phys. Radium 19, 295 (1958).
[CrossRef]

1954 (1)

P. Jacquinot, “Luminosity of Spectrometers with Prisms, Gratings, or Fabry-Perot Etalons,” J. Opt.Soc. Am. 44, 761 (1954).
[CrossRef]

1953 (2)

R. J. Chabbal, “Recherche des Meilleures Conditions d'Utilisation d'un Spectromètre Fabry-Perot,” J. Rech. CNRS 24, 138 (1953).English translation, “Research on the Best Conditions for Using a Fabry-Perot Photo-Electric Spectrometer,” AERE Lib. Trans., 778Harwell (1958).

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

1948 (1)

P. Jacquinot, C. Dufour, “Optical Conditions in the Use of Photo-Electric Cells in Spectrographs and Interferometers,” J. Rech. CNRS 6, 91 (1948).

Ananev, Y. A.

Y. A. Ananev, “The Maximum Attainable Resolution of a Real Fabry-Perot Etalon,” Opt. Spectrosc. 20, 89 (1966).

Ballik, E. A.

Bayer-Helms, F.

F. Bayer-Helms, “Analyse von Linienprofilen. I. Grundlagen und Messeinrichtungen,” Z. Angew.Phys. 15, 330 (1963).

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 (1974).
[CrossRef]

K. Singh, G. S. Bhatnagar, “Sparrow Limit of Spectral Resolution in the Reflection Echelon and the Fabry-Perot Interferometer Having Surface Imperfections,” Appl. Opt. 9, 2326 (1970).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

Bray, R. J.

Brown, N.

Bruce, C. F.

Chabbal, R.

R. Chabbal, “Finesse Limite d'un Fabry-Perot Formé de Lames Imparfaites,” J. Phys. Radium 19, 295 (1958).
[CrossRef]

Chabbal, R. J.

R. J. Chabbal, “Recherche des Meilleures Conditions d'Utilisation d'un Spectromètre Fabry-Perot,” J. Rech. CNRS 24, 138 (1953).English translation, “Research on the Best Conditions for Using a Fabry-Perot Photo-Electric Spectrometer,” AERE Lib. Trans., 778Harwell (1958).

Connes, P.

P. Connes, “L'étalon de Fabry-Perot Sphérique,” J. Phys.Radium 19, 262 (1958).
[CrossRef]

Del Piano, V. N.

Dufour, C.

P. Jacquinot, C. Dufour, “Optical Conditions in the Use of Photo-Electric Cells in Spectrographs and Interferometers,” J. Rech. CNRS 6, 91 (1948).

Duong, H. T.

H. T. Duong, S. Gerstenkorn, J. M. Helbert, “Cartes des Lames d'un Fabry-Perot,” J. Phys. Paris 28, 266 (1967).
[CrossRef]

Dupoisot, H.

Fox, A. G.

A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453 (1961).

Gerstenkorn, S.

H. T. Duong, S. Gerstenkorn, J. M. Helbert, “Cartes des Lames d'un Fabry-Perot,” J. Phys. Paris 28, 266 (1967).
[CrossRef]

Goorvitch, D.

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 (1974).
[CrossRef]

Helbert, J. M.

H. T. Duong, S. Gerstenkorn, J. M. Helbert, “Cartes des Lames d'un Fabry-Perot,” J. Phys. Paris 28, 266 (1967).
[CrossRef]

Hercher, M.

Hernandez, G.

Hill, R. M.

R. M. Hill, “Some Fringe-Broadening Defects in a Fabry-Perot Etalon,” Opt. Acta 10, 141 (1963).
[CrossRef]

Hodgkinson, I. J.

Ikenoue, J.

Y. Yoshida, H. Ogura, J. Ikenoue, “Fabry-Perot Resonator with Slightly Tilted Mirrors,” Jpn. J. Appl. Phys. 8, 285 (1969).
[CrossRef]

H. Ogura, Y. Yoshida, J. Ikenoue, “Theory of Deformed Fabry-Perot Resonator,” J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

Jacquinot, P.

P. Jacquinot, “New Developments in Interference Spectroscopy,” Rep. Prog. Phys. 23, 267 (1960).
[CrossRef]

P. Jacquinot, “Luminosity of Spectrometers with Prisms, Gratings, or Fabry-Perot Etalons,” J. Opt.Soc. Am. 44, 761 (1954).
[CrossRef]

P. Jacquinot, C. Dufour, “Optical Conditions in the Use of Photo-Electric Cells in Spectrographs and Interferometers,” J. Rech. CNRS 6, 91 (1948).

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

Johnson, J. R.

Krebs, K.

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

Li, T.

A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453 (1961).

Lotsch, H. K. V.

H. K. V. Lotsch, “The Fabry-Perot Interferometer with a Large Fresnel Number,” Ann. Phys. 16, 7 (1965).
[CrossRef]

Loughhead, R. E.

Minkwitz, G.

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen. I,” Opt. Acta 13, 103 (1966).
[CrossRef]

Neuhaus, H.

H. Neuhaus, P. Nylén, “The Theoretical Instrument Function of a Fabry-Perot Etalon with Finite Aperture,” Opt. Acta 18, 637 (1971).
[CrossRef]

H. Neuhaus, “Zur Theorie der Vielstrahlinterferometer einschliesslich Betrachtungen über das theoretische Auflösungsvermögen des Pérot-Fabryschen Etalons,” Ark. Fys. 31, 91 (1966);H. Neuhaus, P. Nylén, “Zur Apparatfunktion des Fabry-Pérotschen Interferometers,” Ark. Fys. 37, 59 (1968);H. Neuhaus, P. Nylén, “Die Apparatfunktion eines aus Fabry-Pérotschen Etalons zusammengesetzten Systems bei endlicher Apertur. Teil III,” Ark. Fys. 40, 405 (1970).

Nylén, P.

H. Neuhaus, P. Nylén, “The Theoretical Instrument Function of a Fabry-Perot Etalon with Finite Aperture,” Opt. Acta 18, 637 (1971).
[CrossRef]

Nylén, P. S.

P. S. Nylén, “Scanning Aperture Correction in Fabry-Perot Interferometry,” Optik 37, 123 (1973);P. S. Nylén, “On the Scanning Fabry-Perot Interferometer,” Phys. Scr. 8, 81 (1973).
[CrossRef]

Ogura, H.

Y. Yoshida, H. Ogura, J. Ikenoue, “Fabry-Perot Resonator with Slightly Tilted Mirrors,” Jpn. J. Appl. Phys. 8, 285 (1969).
[CrossRef]

H. Ogura, Y. Yoshida, J. Ikenoue, “Theory of Deformed Fabry-Perot Resonator,” J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

Prat, R.

Primak, W.

Quesada, A. F.

Ramsay, J. V.

Rautian, S. G.

S. G. Rautian, “Real Spectral Apparatus,” Sov. Phys. Usp. 66, 245 (1958).
[CrossRef]

Riekher, R.

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen. I,” Opt. Acta 13, 103 (1966).
[CrossRef]

Roesler, F. L.

Roychoudhuri, C.

Sandercock, J. R.

J. R. Sandercock, “Simple Stabilization Scheme for Maintenance of Mirror Alignment in a Scanning Fabry-Perot Interferometer,” J. Phys. E 9, 566 (1976).
[CrossRef]

Sauer, A.

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

Schulz, G.

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen. I,” Opt. Acta 13, 103 (1966).
[CrossRef]

Schwider, J.

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen. I,” Opt. Acta 13, 103 (1966).
[CrossRef]

Sharples, F. P.

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 (1974).
[CrossRef]

K. Singh, G. S. Bhatnagar, “Sparrow Limit of Spectral Resolution in the Reflection Echelon and the Fabry-Perot Interferometer Having Surface Imperfections,” Appl. Opt. 9, 2326 (1970).
[CrossRef] [PubMed]

Slansky, S.

Sloggett, G. J.

Stoner, J. O.

J. O. Stoner, “PEPSIOS Purely Interferometric High-resolution Scanning Spectrometer. III. Calculation of Interferometer Characteristics by a Method of Optical Transients,” J. Opt.Soc. Am. 56, 370 (1966).
[CrossRef]

Traub, W.

Vaughan, A. H.

A. H. Vaughan, “Astronomical Fabry-Perot Interference Spectroscopy,” Ann. Rev. Astron. Astrophys. 5, 139 (1967).
[CrossRef]

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

Yamada, R.

R. Yamada, “On the Plane Fabry-Perot Interferometer,” Jpn. J. Appl. Phys. 6, 904 (1967).
[CrossRef]

Yoshida, Y.

Y. Yoshida, H. Ogura, J. Ikenoue, “Fabry-Perot Resonator with Slightly Tilted Mirrors,” Jpn. J. Appl. Phys. 8, 285 (1969).
[CrossRef]

H. Ogura, Y. Yoshida, J. Ikenoue, “Theory of Deformed Fabry-Perot Resonator,” J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

Ann. Phys. (2)

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

H. K. V. Lotsch, “The Fabry-Perot Interferometer with a Large Fresnel Number,” Ann. Phys. 16, 7 (1965).
[CrossRef]

Ann. Rev. Astron. Astrophys. (1)

A. H. Vaughan, “Astronomical Fabry-Perot Interference Spectroscopy,” Ann. Rev. Astron. Astrophys. 5, 139 (1967).
[CrossRef]

Appl. Opt. (21)

G. Hernandez, “Analytical Description of a Fabry-Perot Spectrometer. 3: Off-Axis Behavior and Interference Filters,” Appl. Opt. 13, 2654 (1974).
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H. Dupoisot, R. Prat, S. Slansky, “Luminous Flux Amplification in Fabry-Perot Spectrometry,” Appl. Opt. 17, 3930 (1978).
[CrossRef] [PubMed]

H. Dupoisot, R. Prat, “High Resolvance Interference Spectrometry with a High Factor of Merit in the Visible Spectrum,” Appl. Opt. 18, 85 (1979).
[CrossRef] [PubMed]

C. Roychoudhuri, M. Hercher, “Stable Multipass Fabry-Perot Interferometer: Design and Analysis,” Appl. Opt. 16, 2514 (1977).
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R. E. Loughhead, R. J. Bray, N. Brown, “Instrumental Profile of a Triple Fabry-Perot Interferometer for use in Solar Spectroscopy,” Appl. Opt. 17, 415 (1978).
[CrossRef] [PubMed]

G. Hernandez, “Analytical Description of a Fabry-Perot Spectrometer. 5: Optimization for Minimum Uncertainties in the Determination of Doppler Widths and Shifts,” Appl. Opt. 18, 3826 (1979).
[PubMed]

G. Hernandez, “Analytical Description of a Fabry-Perot Spectrometer. 3: Off-Axis Behavior and Interference Filters: Erratum,” Appl. Opt. 18, 3364 (1979).
[CrossRef] [PubMed]

F. L. Roesler, W. Traub, “Precision Mapping of Pairs of Uncoated Optical Flats,” Appl. Opt. 5, 463 (1966).
[CrossRef] [PubMed]

W. Primak, “The Determination of the Absolute Contours of Optical Flats,” Appl. Opt. 6, 1917 (1967).
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I. J. Hodgkinson, “A Method for Mapping and Determining the Surface Defects Function of Pairs of Coated Optical Flats,” Appl. Opt. 8, 1373 (1969).
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C. F. Bruce, F. P. Sharples, “Relative Flatness Measurement of Uncoated Optical Flats,” Appl. Opt. 14, 3082 (1975).
[CrossRef] [PubMed]

V. N. Del Piano, A. F. Quesada, “Transmission Characteristics of Fabry-Perot Interferometers and a Related Electrooptic Modulator,” Appl. Opt. 4, 1386 (1965).
[CrossRef]

K. Singh, G. S. Bhatnagar, “Sparrow Limit of Spectral Resolution in the Reflection Echelon and the Fabry-Perot Interferometer Having Surface Imperfections,” Appl. Opt. 9, 2326 (1970).
[CrossRef] [PubMed]

G. J. Sloggett, “Fringe Broadening in Fabry-Perot Interferometers,” Appl. Opt. 23, 2427 (1984).
[CrossRef] [PubMed]

C. F. Bruce, “On Automatic Parallelism Control in a Scanning Fabry-Perot Interferometer,” Appl. Opt. 5, 1447 (1966).
[CrossRef] [PubMed]

E. A. Ballik, “The Response of Scanning Fabry-Perot Interferometers to Atomic Transition Profiles,” Appl. Opt. 5, 170 (1966).
[CrossRef] [PubMed]

J. V. Ramsay, “Aberrations of Fabry-Perot Interferometers when Used as Filters,” Appl. Opt. 8, 569 (1969).
[CrossRef] [PubMed]

G. Hernandez, “Analytical Description of a Fabry-Perot Photoelectric Spectrometer,” Appl. Opt. 5, 1745 (1966).
[CrossRef] [PubMed]

D. Goorvitch, “Galatry Profile Convolved with the Fabry-Perot Instrument Function,” Appl. Opt. 16, 1732 (1977).
[CrossRef] [PubMed]

J. R. Johnson, “A High Resolution Scanning Confocal Interferometer,” Appl. Opt. 7, 1061 (1968).
[CrossRef] [PubMed]

M. Hercher, “The Spherical Mirror Fabry-Perot Interferometer,” Appl. Opt. 7, 951 (1968).
[CrossRef] [PubMed]

Ark. Fys. (1)

H. Neuhaus, “Zur Theorie der Vielstrahlinterferometer einschliesslich Betrachtungen über das theoretische Auflösungsvermögen des Pérot-Fabryschen Etalons,” Ark. Fys. 31, 91 (1966);H. Neuhaus, P. Nylén, “Zur Apparatfunktion des Fabry-Pérotschen Interferometers,” Ark. Fys. 37, 59 (1968);H. Neuhaus, P. Nylén, “Die Apparatfunktion eines aus Fabry-Pérotschen Etalons zusammengesetzten Systems bei endlicher Apertur. Teil III,” Ark. Fys. 40, 405 (1970).

Bell Syst. Tech. J. (1)

A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453 (1961).

J. Opt.Soc. Am. (2)

J. O. Stoner, “PEPSIOS Purely Interferometric High-resolution Scanning Spectrometer. III. Calculation of Interferometer Characteristics by a Method of Optical Transients,” J. Opt.Soc. Am. 56, 370 (1966).
[CrossRef]

P. Jacquinot, “Luminosity of Spectrometers with Prisms, Gratings, or Fabry-Perot Etalons,” J. Opt.Soc. Am. 44, 761 (1954).
[CrossRef]

J. Phys. E (1)

J. R. Sandercock, “Simple Stabilization Scheme for Maintenance of Mirror Alignment in a Scanning Fabry-Perot Interferometer,” J. Phys. E 9, 566 (1976).
[CrossRef]

J. Phys. Paris (1)

H. T. Duong, S. Gerstenkorn, J. M. Helbert, “Cartes des Lames d'un Fabry-Perot,” J. Phys. Paris 28, 266 (1967).
[CrossRef]

J. Phys. Radium (1)

R. Chabbal, “Finesse Limite d'un Fabry-Perot Formé de Lames Imparfaites,” J. Phys. Radium 19, 295 (1958).
[CrossRef]

J. Phys. Soc. Jpn. (1)

H. Ogura, Y. Yoshida, J. Ikenoue, “Theory of Deformed Fabry-Perot Resonator,” J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

J. Phys.Radium (1)

P. Connes, “L'étalon de Fabry-Perot Sphérique,” J. Phys.Radium 19, 262 (1958).
[CrossRef]

J. Rech. CNRS (2)

P. Jacquinot, C. Dufour, “Optical Conditions in the Use of Photo-Electric Cells in Spectrographs and Interferometers,” J. Rech. CNRS 6, 91 (1948).

R. J. Chabbal, “Recherche des Meilleures Conditions d'Utilisation d'un Spectromètre Fabry-Perot,” J. Rech. CNRS 24, 138 (1953).English translation, “Research on the Best Conditions for Using a Fabry-Perot Photo-Electric Spectrometer,” AERE Lib. Trans., 778Harwell (1958).

Jpn. J. Appl. Phys. (2)

R. Yamada, “On the Plane Fabry-Perot Interferometer,” Jpn. J. Appl. Phys. 6, 904 (1967).
[CrossRef]

Y. Yoshida, H. Ogura, J. Ikenoue, “Fabry-Perot Resonator with Slightly Tilted Mirrors,” Jpn. J. Appl. Phys. 8, 285 (1969).
[CrossRef]

Nouv. Rev. Opt. (1)

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 (1974).
[CrossRef]

Opt. Acta (3)

R. M. Hill, “Some Fringe-Broadening Defects in a Fabry-Perot Etalon,” Opt. Acta 10, 141 (1963).
[CrossRef]

H. Neuhaus, P. Nylén, “The Theoretical Instrument Function of a Fabry-Perot Etalon with Finite Aperture,” Opt. Acta 18, 637 (1971).
[CrossRef]

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen. I,” Opt. Acta 13, 103 (1966).
[CrossRef]

Opt. Spectrosc. (1)

Y. A. Ananev, “The Maximum Attainable Resolution of a Real Fabry-Perot Etalon,” Opt. Spectrosc. 20, 89 (1966).

Optik (1)

P. S. Nylén, “Scanning Aperture Correction in Fabry-Perot Interferometry,” Optik 37, 123 (1973);P. S. Nylén, “On the Scanning Fabry-Perot Interferometer,” Phys. Scr. 8, 81 (1973).
[CrossRef]

Rep. Prog. Phys. (1)

P. Jacquinot, “New Developments in Interference Spectroscopy,” Rep. Prog. Phys. 23, 267 (1960).
[CrossRef]

Rev. Sci. Instrum. (1)

C. F. Bruce, “Aperture Correction in Fabry-Perot Interferometer Measurements,” Rev. Sci. Instrum. 37, 349 (1966).
[CrossRef]

Sov. Phys. Usp. (1)

S. G. Rautian, “Real Spectral Apparatus,” Sov. Phys. Usp. 66, 245 (1958).
[CrossRef]

Z. Angew.Phys. (1)

F. Bayer-Helms, “Analyse von Linienprofilen. I. Grundlagen und Messeinrichtungen,” Z. Angew.Phys. 15, 330 (1963).

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

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Figures (4)

Fig. 1
Fig. 1

Diagram showing how plate surface irregularities modify the transmission of the interferometer. The Airy transmission A(m) should be imagined as a function of position in the (l,λ) plane. A triangular defect function is used as an example. Symbols are defined in the text.

Fig. 2
Fig. 2

Diagram showing how the finite fringe-sampling aperture modifies the transmission of the interferometer. The etalon transmission E(m) should be imagined as a function of position in the (ξ,λ) plane. A rectangular aperture function is used as an example. Symbols are defined in the text.

Fig. 3
Fig. 3

Diagram showing how the source spectral radiance contributes to the output of the spectrometer. The instrument transmission I(m) should be imagined as a function of position in the (l,λ) plane. A Gaussian source function is used as an example. Symbols are defined in the text.

Fig. 4
Fig. 4

Diagram summarizing the formation of the recorded function from the Airy, defect, aperture, and source functions, using examples similar to those in Figs. 13.

Equations (48)

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O ( x ) = T ( x x ) F ( x ) d x .
R ( x x 0 ) = T ( x x ) δ ( x x 0 ) d x = T ( x 0 x ) .
O ( x ) = R ( x x ) F ( x ) d x ,
O ( x ) = R ( x ) * F ( x ) .
m = 2 μ l ξ / λ + ϕ / π ,
A ( m ) = τ A / [ 1 + F sin 2 ( π m ) ] ,
τ A = T 2 / ( 1 R ) 2 ,
F = 4 R / ( 1 R ) 2 .
A Δ = T 2 / ( 1 R 2 ) .
w A = ( 1 R ) / ( π R ) .
m 0 = 2 μ l 0 ξ 0 / λ 0 ,
d s = D ( x ) d x ,
l Δ λ 0 / ( 2 μ ξ 0 ) = l 0 / m 0 ,
d E = A ( m + x / l Δ ) D ( x ) d x / S .
m x = x / l Δ .
d s / S = D ̂ ( m x ) d m x .
D ̂ ( m x ) = ( l Δ / S ) D ( l Δ m x ) .
w D = δ x / l Δ .
d E = A ( m m x ) D ̂ ( m x ) d m x ,
E ( m ) = D ̂ ( m ) * A ( m ) .
d ω = F ( ξ f ) d ξ .
d ω = 2 π d ξ f ,
F ( ξ f ) = 2 π , δ ξ ξ f 0 , = 0 , otherwise ,
ξ Δ λ 0 / ( 2 μ l 0 ) = ξ 0 / m 0 .
m ξ = ξ f / ξ Δ ,
d ω / Ω = F ̂ ( m ξ ) d m ξ .
F ̂ ( m ξ ) = ( ξ Δ / Ω ) F ( ξ Δ m ξ ) .
w F = δ ξ / ξ Δ ,
w F = Ω / ( 2 π ξ Δ ) .
d I = E ( m m ξ ) F ̂ ( m ξ ) d m ξ ,
I ( m ) = F ̂ ( m ) * E ( m ) .
d L = B ( λ b ) d λ .
λ Δ λ 0 2 / ( 2 μ l 0 ξ 0 ) = λ 0 / m 0 .
m λ = λ b / λ Δ ,
d L / L = B ̂ ( m λ ) d m λ .
B ̂ ( m λ ) = ( λ Δ / L ) B ( λ Δ m λ ) ,
w B = δ λ / λ Δ .
d Y = I ( m m λ ) B ̂ ( m λ ) d m λ ,
Y ( m ) = B ̂ ( m ) * I ( m ) .
m / m 0 = λ / λ 0 ,
Φ ( m ) = L S Ω τ c Y ( m ) ,
Φ M = L S Ω τ c τ Y ,
τ Y = τ B τ F τ D τ A ,
Φ Δ = L S Ω τ c A Δ ,
Φ ( l , ξ , λ ) = A ( m ) d s d ω d L ,
Φ ( l , ξ , λ ) = B ( λ b ) F ( ξ f ) D ( x ) τ A ( 1 + F sin 2 π m a ) 1 dxd ξ f d λ b ,
= m 0 / w I = m 0 N I ,
2 π / Ω .

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