Abstract

Many workers have used channeled spectra produced by a Fabry-Perot interferometer to calibrate infrared spectrometers. In this paper the effects of the finite height of the spectrometer slit and the finite aperture of the condensing lens on the visibility of the spectra are discussed. The way in which maximum accuracy of calibration is to be obtained for any given experimental arrangement is indicated.

© 1953 Optical Society of America

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References

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  1. H. Rubens, Pogg. Ann. 45, 238 (1892).
  2. J. W. Ellis, J. Opt. Soc. Am. 23, 88 (1933).
    [Crossref]
  3. C. V. Cooper and J. D. Stroupe, J. Opt. Soc. Am. 41, 427 (1951).
    [Crossref]
  4. Rank, Rix, and Wiggins, J. Opt. Soc. Am. 43, 157 (1953).
    [Crossref]
  5. K. W. Meissner, J. Opt. Soc. Am. 31, 405 (1941).
    [Crossref]
  6. S. Tolansky, Phil. Mag. 34, 555 (1943).

1953 (1)

1951 (1)

1943 (1)

S. Tolansky, Phil. Mag. 34, 555 (1943).

1941 (1)

1933 (1)

1892 (1)

H. Rubens, Pogg. Ann. 45, 238 (1892).

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Figures (6)

Fig. 1
Fig. 1

The interferometer placed in collimated light. T, extended source; L1, collimating lens; FP, interferometer; L2, condensing lens; S, spectrometer slit.

Fig. 2
Fig. 2

Visibility V of the channeled spectrum plotted against the fraction of a fringe embraced by the spectrometer slit for a series of values of the reflectivity R. ( stands for either S or L—see text.)

Fig. 3
Fig. 3

Visibility V of the channeled spectrum plotted against the number of fringes embraced by the slit, for three values of the reflectivity R. ( stands for either S or L—see text).

Fig. 4
Fig. 4

The interferometer placed in convergent light. L2, condensing lens; FP, interferometer; S, spectrometer slit.

Fig. 5
Fig. 5

The utility U of the channeled spectrum plotted against the fraction of a fringe embraced by the spectrometer slit for a series of values of the reflectivity R. ( stands for either S or L—see text).

Fig. 6
Fig. 6

(a) Fringe field as seen from a point 0ϕ′ on the spectrometer slit (exaggerated). (b) Notation for the calculation of the intensity of the light falling on the slit point 0ϕ′.

Equations (20)

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I ϕ = 1 / ( 1 + F sin 2 ( 2 π t ν cos ϕ ) ) ,
δ = 4 π t ν cos ϕ ,
I δ = 1 / ( 1 + F sin 2 δ / 2 ) .
I δ 0 = 1 / ( 1 + F sin 2 δ 0 / 2 ) .
V = I max - I min I max + I min .
S = 2 π t ν Φ 2 .
I = 1 S δ 0 δ 0 + S d δ 1 + F sin 2 δ / 2 ,
I = 2 S ( 1 + F ) 1 2 × tan - 1 { ( 1 + F ) 1 2 ( tan δ 0 + S 2 - tan δ 0 / 2 ) 1 + ( 1 + F ) tan δ 0 + S 2 · tan δ 0 / 2 } .
I max = 8 S ( 1 + F ) 1 2 tan - 1 { ( 1 + F ) 1 2 tan S / 4 } ,
I min = 8 S ( 1 + F ) 1 2 tan - 1 { tan S / 4 ( 1 + F ) 1 2 } .
V = tan - 1 { ( 1 + F ) 1 2 tan S / 4 } - tan - 1 { tan S / 4 ( 1 + F ) 1 2 } tan - 1 { ( 1 + F ) 1 2 tan S / 4 } + tan - 1 { tan S / 4 ( 1 + F ) 1 2 } .
( 2 n + 1 ) 2 π < S < 2 ( n + 1 ) 2 π ,             ( n = 0 , 1 , 2 , ) ,
L = 2 π t ν Θ 2 ,
I 0 = 1 L δ 0 δ 0 + L d δ 1 + F sin 2 δ / 2 ,
L = ( Θ 2 / Φ 2 ) S .
U = V ,
I ψ = 1 / ( 1 + F sin 2 ( 2 π t ν cos ψ ) ) = G ( ψ ) , say .
G ( ψ ) = G ( θ ) + ( ϕ 2 2 θ sin 2 α + ϕ cos α ) d G ( θ ) d θ .
J ϕ = 1 A A G ( ψ ) d A = 2 Θ 2 0 Θ G ( θ ) θ d θ + ϕ 2 2 Θ 2 [ G ( Θ ) - G ( 0 ) ] ,
J = 1 Φ 0 Φ J ϕ d ϕ .