Abstract

This paper describes a new type of filter radiometer—the Selective Interferometer Filter (SIF)—which has extremely high selectivity to the radiation from a given gas. The basic device is a double output Michelson interferometer, with mirrors fixed at zero geometrical path difference. It is shown that if a cell containing a gas is placed in each of the arms, the ensemble can be made to operate as a highly selective filter, passing radiation only very near the center frequencies corresponding to the absorption lines of this gas. This is a result of direct absorption effects and of the variation of refractive index with frequency and consequent modification of the optical path difference of the two arms of the interferometer. The device may, therefore, after calibration be operated as a highly selective ir radiometer; and a feature of importance in atmospheric and space applications is that it requires no internal moving parts to achieve this selectivity. Details of the device are presented, and a thorough examination of the practical realization of it is given.

© 1976 Optical Society of America

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References

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  1. A. R. Barringer, J. H. Davies, Investigations in Correlation Spectroscopy and Interferometry in Proceedings of the Joint Conference on Environmental Pollutants Paper 71-1105 (Am. Inst. Aeronautics and Astronautics, New York, 1971).
  2. A. W. Goldstein, M. H. Bortner, R. N. Grenda, A. M. Karger, P. J. LeBel, Paper 73-515 in Proceedings of the Joint AIAA/AMS Conference June 1973, Denver (Am. Inst. Aeronautics and Astronautics, New York, 1973).
  3. S. D. Smith, C. R. Pigeon, Mem. Soc. R. Sci. Liege 9, 336 (1964).
  4. P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).
  5. F. W. Taylor, J. T. Houghton, G. Peskett, C. D. Rodgers, E. J. Williamson, Appl. Opt. 11, 135 (1972).
    [CrossRef] [PubMed]
  6. R. M. Goody, J. Opt. Soc. Am. 58, 900 (1968).
    [CrossRef]
  7. M. Françon, Optical Interferometry (Academic, New York, 1966).
  8. L. Kaplan, J. Opt. Soc. Am. 49, 1004 (1959).
    [CrossRef]
  9. J. T. Houghton, F. W. Taylor, Rep. Prog. Phys. 36, 827 (1973).
    [CrossRef]
  10. International Critical Tables (McGraw Hill, New York, 1930), Vol. 7, p. 9.
  11. C. Statescu, Philos. Mag. 30, 737 (1915).

1973 (1)

J. T. Houghton, F. W. Taylor, Rep. Prog. Phys. 36, 827 (1973).
[CrossRef]

1972 (1)

1970 (1)

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

1968 (1)

1964 (1)

S. D. Smith, C. R. Pigeon, Mem. Soc. R. Sci. Liege 9, 336 (1964).

1959 (1)

1915 (1)

C. Statescu, Philos. Mag. 30, 737 (1915).

Abell, P. G.

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

Barringer, A. R.

A. R. Barringer, J. H. Davies, Investigations in Correlation Spectroscopy and Interferometry in Proceedings of the Joint Conference on Environmental Pollutants Paper 71-1105 (Am. Inst. Aeronautics and Astronautics, New York, 1971).

Bortner, M. H.

A. W. Goldstein, M. H. Bortner, R. N. Grenda, A. M. Karger, P. J. LeBel, Paper 73-515 in Proceedings of the Joint AIAA/AMS Conference June 1973, Denver (Am. Inst. Aeronautics and Astronautics, New York, 1973).

Davies, J. H.

A. R. Barringer, J. H. Davies, Investigations in Correlation Spectroscopy and Interferometry in Proceedings of the Joint Conference on Environmental Pollutants Paper 71-1105 (Am. Inst. Aeronautics and Astronautics, New York, 1971).

Ellis, P.

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

Françon, M.

M. Françon, Optical Interferometry (Academic, New York, 1966).

Goldstein, A. W.

A. W. Goldstein, M. H. Bortner, R. N. Grenda, A. M. Karger, P. J. LeBel, Paper 73-515 in Proceedings of the Joint AIAA/AMS Conference June 1973, Denver (Am. Inst. Aeronautics and Astronautics, New York, 1973).

Goody, R. M.

Grenda, R. N.

A. W. Goldstein, M. H. Bortner, R. N. Grenda, A. M. Karger, P. J. LeBel, Paper 73-515 in Proceedings of the Joint AIAA/AMS Conference June 1973, Denver (Am. Inst. Aeronautics and Astronautics, New York, 1973).

Houghton, J. T.

J. T. Houghton, F. W. Taylor, Rep. Prog. Phys. 36, 827 (1973).
[CrossRef]

F. W. Taylor, J. T. Houghton, G. Peskett, C. D. Rodgers, E. J. Williamson, Appl. Opt. 11, 135 (1972).
[CrossRef] [PubMed]

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

Kaplan, L.

Karger, A. M.

A. W. Goldstein, M. H. Bortner, R. N. Grenda, A. M. Karger, P. J. LeBel, Paper 73-515 in Proceedings of the Joint AIAA/AMS Conference June 1973, Denver (Am. Inst. Aeronautics and Astronautics, New York, 1973).

LeBel, P. J.

A. W. Goldstein, M. H. Bortner, R. N. Grenda, A. M. Karger, P. J. LeBel, Paper 73-515 in Proceedings of the Joint AIAA/AMS Conference June 1973, Denver (Am. Inst. Aeronautics and Astronautics, New York, 1973).

Peckham, G.

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

Peskett, G.

Pigeon, C. R.

S. D. Smith, C. R. Pigeon, Mem. Soc. R. Sci. Liege 9, 336 (1964).

Rodgers, C. D.

F. W. Taylor, J. T. Houghton, G. Peskett, C. D. Rodgers, E. J. Williamson, Appl. Opt. 11, 135 (1972).
[CrossRef] [PubMed]

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

Smith, S. D.

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

S. D. Smith, C. R. Pigeon, Mem. Soc. R. Sci. Liege 9, 336 (1964).

Statescu, C.

C. Statescu, Philos. Mag. 30, 737 (1915).

Taylor, F. W.

Williamson, E. J.

F. W. Taylor, J. T. Houghton, G. Peskett, C. D. Rodgers, E. J. Williamson, Appl. Opt. 11, 135 (1972).
[CrossRef] [PubMed]

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Mem. Soc. R. Sci. Liege (1)

S. D. Smith, C. R. Pigeon, Mem. Soc. R. Sci. Liege 9, 336 (1964).

Philos. Mag. (1)

C. Statescu, Philos. Mag. 30, 737 (1915).

Proc. R. Soc. (1)

P. G. Abell, P. Ellis, J. T. Houghton, G. Peckham, C. D. Rodgers, S. D. Smith, E. J. Williamson, Proc. R. Soc. A320, 35 (1970).

Rep. Prog. Phys. (1)

J. T. Houghton, F. W. Taylor, Rep. Prog. Phys. 36, 827 (1973).
[CrossRef]

Other (4)

International Critical Tables (McGraw Hill, New York, 1930), Vol. 7, p. 9.

M. Françon, Optical Interferometry (Academic, New York, 1966).

A. R. Barringer, J. H. Davies, Investigations in Correlation Spectroscopy and Interferometry in Proceedings of the Joint Conference on Environmental Pollutants Paper 71-1105 (Am. Inst. Aeronautics and Astronautics, New York, 1971).

A. W. Goldstein, M. H. Bortner, R. N. Grenda, A. M. Karger, P. J. LeBel, Paper 73-515 in Proceedings of the Joint AIAA/AMS Conference June 1973, Denver (Am. Inst. Aeronautics and Astronautics, New York, 1973).

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Figures (5)

Fig. 1
Fig. 1

A schematic diagram of the Selective Interferometer Filter (SIF). Radiation from a source S is modulated by a simple chopper C, passed through an interference filter F to isolate a chosen spectral band, and then into a Michelson interferometer. Cells of length l1 and l2 are placed in the arms containing pressures p1 and P2 of gas x, respectively. The interferograms that would be obtained if one of the reflectors were scanned away from zero optical path difference are shown against outputs 1 and 2.

Fig. 2
Fig. 2

The effective normalized transmittance for a single absorption line X2 (σ) seen at output 2 (Fig. 1) for a single cell (A) and double cell (B) SIF. Case A: l1 = l2 = 1.0 cm, p1 = 1 mb, p2 =0; case B: l1 = l2= 1.0cm, p1=1 mb, p2=5 mb.

Fig. 3
Fig. 3

The effective normalized transmittance X2(σ) for different pressures in the two cells. Case B: l1 = l2 = 1.0 cm, p1 = 1 mb, p2 = 5 mb; case C: l1 = l2 = 1.0 cm, p1 = 2 mb, p2 = 12 mb; case D: l1 = l2 =1.0 cm, p1 = 4 mb, p2 = 40 mb.

Fig. 4
Fig. 4

The effective normalized transmittance X2(σ) at high pressures and pathlengths. Case E: l1 = l2 = 1.0 cm, p1 = 1 atm, p2 = 0; case F: l1 = l2 = 2.0 cm, p1 = 1 atm, p2 = 0; case G: l1 = l2 = 3.0 cm, p1 = 1 atm, p2 = 0; case H: l1 = l2 = 4.0 cm, p1 = 1 atm, p2 = 0; case I: l1 = l2 = 5.0 cm, p1 = 1 atm, p2 = 0.

Fig. 5
Fig. 5

The effect of ϕ ≠ 1. The effective normalized transmittance X2(σ). Case A: l1 = l2 = 1.0 cm, p1 = 1 mb, p2 = 0, ϕ = 1.0; case J: l1 = l2 = 1.0 cm, p1 = 1 mb, p2 = 0, ϕ = 0.9; case K: l1 = l2 = 1.0 cm, p1 = 1 mb, p2 = 0, ϕ = 0.7; case L: l1 = l2 = 1.0 cm, p1 = 1 mb, p2 = 0, ϕ = 0.5.

Equations (14)

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I 1 ( x ) = I 1 + F ( x ) = - 2 r ^ 2 t ^ 2 B o d σ + - 2 r ^ 2 t ^ 2 B o cos 2 π σ x d σ .
I 2 ( x ) = I 2 - F ( x ) = - ( r ^ 4 + t ^ 4 B o d σ - - 2 r ^ 2 t ^ 2 B o cos 2 π σ x d σ .
I 2 ( 0 ) = - ( r ^ 4 - 2 r ^ 2 t ^ 2 + t ^ 4 ) B o d σ 0 if r ^ 2 = t ^ 2 .
L ^ = S exp ( - i ψ ) loss due to cell windows × exp [ - 2 π i σ ( n ^ - 1 ) l ] loss due to gas in cell of length l .
I 2 ( 0 ) = - ( r ^ 4 L ^ 2 2 + t ^ 4 L ^ 1 2 ) B 0 d σ - - 2 r ^ 2 t ^ 2 L ^ 1 L ^ 2 B o cos 2 π σ [ ( n 2 - 1 ) l 2 - ( n 1 - 1 ) l 1 ] d σ ;
= - S 2 B o t ^ 4 { ϕ 2 exp ( - α 2 l 2 ) + exp ( - α 1 l 1 ) - 2 ϕ exp [ - 1 2 ( α 1 l 1 + α 2 l 2 ) ] cos 2 π σ [ ( n 2 - 1 ) l 2 - ( n 1 - 1 ) l 1 } d σ .
X 2 ( σ ) = I 2 ( 0 ) S 2 B o t ^ 4 = ϕ 2 exp ( - α 2 l 2 ) + exp ( - α 1 l 1 ) - 2 ϕ exp [ - 1 2 ( α 1 l 1 + α 2 l 2 ) ] cos 2 π σ [ ( n 2 - 1 ) l 2 - ( n 1 - 1 ) l 1 ] .
r ^ t ^
l 1 l 2 ,
α ( σ ) = S o p π · γ o p ( σ - σ o ) 2 + ( γ o p ) 2 ,
n ( σ ) = n o + S o ( σ - σ o ) p 4 π 2 σ o [ ( σ - σ o ) 2 + ( γ o p ) 2 ] .
l 1 = l 2 = 1 cm , p 1 = 2 mb , p 2 = 12 mb ( C )
l 1 = l 2 = 1 cm , p 1 = 4 mb , p 2 = 40 mb ( D ) .
X 2 ( σ o ) = 1 + 0 ( 0 ) - 0 ( 0 ) 1

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