Abstract

Interferograms, the information directly available from lamellar grating and Michelson interferometertype spectrometers, are derived on the basis of an absorption spectrum whose lines are sharp, symmetrical, and reasonably well isolated from each other. The formulation shows that if the absorption spectrum is periodic in wavenumber, the interferogram will also have periodic structure characterized by features called signatures. The results are used to predict the interferogram for the pure rotational spectrum of a molecule whose rotational constants approximate those of carbon monoxide. It is found for an absorption spectrum consisting of equally spaced lines (rigid rotor model) that the shape of the individual signatures should be almost identical although damped out exponentially. However when centrifugal distortion is taken into account (nonrigid rotor model), which cause the absorption lines for a linear or diatomic molecule to converge slightly at higher wavenumbers, it is found to lead to a distortion of the signatures, the distortion becoming more pronounced toward large differences of optical path between the interfering beams.

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  1. J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 49, 844 (1959).
  2. J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 50, 113 (1960).
  3. H. A. Gebbie, J. Phys. Radium 19, 230 (1958). See also, "Submillimeter Wave Spectroscopy Using a Michelson Interferometer," in Advances in Quantum Electronics, edited by J. R. Senger (Columbia University Press, New York, 1961).
  4. J. Connes, Rev. Opt. 40, 45–47, 116–140, 171–190, 231–265 (1961). Although nearly all of Mme. Connes' experimental observations are in the near infrared portion of the spectrum, the theory and experimental analysis discussion presented apply equally well to the far infrared.
  5. T. Williams, J. Opt. Soc. Am. 50, 1159 (1960).
  6. H. S. Carslaw, Fourier Series (Dover Publications Inc., New York, 1939), Chap. IX.
  7. H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).
  8. E. V. Lowenstein, J. Opt. Soc. Am. 50, 1163 (1960).
  9. Should the absorption lines overlap too badly for this to be a good approximation, it is possible to extend this treatment to include the binary cross terms, i.e., cross terms of the form γiγk. This will provide the first-order correction for overlapping. The necessary integrals are given in reference 10.
  10. W. Gröbner and N. Hofreiter, Integraltafel, Zweiter Teil, Bestimmte Integrale, (Springer-Verlag, Berlin, 1959), Sec. 333, p. 128, No. 67b.
  11. C. Townes and A. Schawlow, Microwave Spectroscopy (McGraw-Hill Book Company, Inc., New York, 1955), Chap. 13, p. 360.

Carslaw, H. S.

H. S. Carslaw, Fourier Series (Dover Publications Inc., New York, 1939), Chap. IX.

Connes, J.

J. Connes, Rev. Opt. 40, 45–47, 116–140, 171–190, 231–265 (1961). Although nearly all of Mme. Connes' experimental observations are in the near infrared portion of the spectrum, the theory and experimental analysis discussion presented apply equally well to the far infrared.

Gebbie, H. A.

H. A. Gebbie, J. Phys. Radium 19, 230 (1958). See also, "Submillimeter Wave Spectroscopy Using a Michelson Interferometer," in Advances in Quantum Electronics, edited by J. R. Senger (Columbia University Press, New York, 1961).

Genzel, L.

H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).

Gröbner, W.

W. Gröbner and N. Hofreiter, Integraltafel, Zweiter Teil, Bestimmte Integrale, (Springer-Verlag, Berlin, 1959), Sec. 333, p. 128, No. 67b.

Happ, H.

H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).

Hofreiter, N.

W. Gröbner and N. Hofreiter, Integraltafel, Zweiter Teil, Bestimmte Integrale, (Springer-Verlag, Berlin, 1959), Sec. 333, p. 128, No. 67b.

Lowenstein, E. V.

E. V. Lowenstein, J. Opt. Soc. Am. 50, 1163 (1960).

Schawlow, A.

C. Townes and A. Schawlow, Microwave Spectroscopy (McGraw-Hill Book Company, Inc., New York, 1955), Chap. 13, p. 360.

Strong, J.

J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 50, 113 (1960).

J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 49, 844 (1959).

Townes, C.

C. Townes and A. Schawlow, Microwave Spectroscopy (McGraw-Hill Book Company, Inc., New York, 1955), Chap. 13, p. 360.

Vanasse, G. A.

J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 49, 844 (1959).

J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 50, 113 (1960).

Williams, T.

T. Williams, J. Opt. Soc. Am. 50, 1159 (1960).

Other (11)

J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 49, 844 (1959).

J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 50, 113 (1960).

H. A. Gebbie, J. Phys. Radium 19, 230 (1958). See also, "Submillimeter Wave Spectroscopy Using a Michelson Interferometer," in Advances in Quantum Electronics, edited by J. R. Senger (Columbia University Press, New York, 1961).

J. Connes, Rev. Opt. 40, 45–47, 116–140, 171–190, 231–265 (1961). Although nearly all of Mme. Connes' experimental observations are in the near infrared portion of the spectrum, the theory and experimental analysis discussion presented apply equally well to the far infrared.

T. Williams, J. Opt. Soc. Am. 50, 1159 (1960).

H. S. Carslaw, Fourier Series (Dover Publications Inc., New York, 1939), Chap. IX.

H. Happ and L. Genzel, Infrared Phys. 1, 39 (1961).

E. V. Lowenstein, J. Opt. Soc. Am. 50, 1163 (1960).

Should the absorption lines overlap too badly for this to be a good approximation, it is possible to extend this treatment to include the binary cross terms, i.e., cross terms of the form γiγk. This will provide the first-order correction for overlapping. The necessary integrals are given in reference 10.

W. Gröbner and N. Hofreiter, Integraltafel, Zweiter Teil, Bestimmte Integrale, (Springer-Verlag, Berlin, 1959), Sec. 333, p. 128, No. 67b.

C. Townes and A. Schawlow, Microwave Spectroscopy (McGraw-Hill Book Company, Inc., New York, 1955), Chap. 13, p. 360.

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