Abstract

An aperture system is described which executes a spectral scan for a Fabry-Perot spectrometer. Overlapping Fabry-Perot patterns produce straight-line moiré fringes; hence, a linear ruling placed over a Fabry-Perot pattern generates a second, displaced Fabry-Perot pattern, consisting of segments of the rings of the first pattern. The segmented rings expand or contract as the ruling is moved past the mask. The result is a wavelength scan, and the system can therefore be used as a Fabry-Perot spectrometer. The theory is developed, the results of a preliminary application described, and an indication of some possible applications given.

© 1967 Optical Society of America

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References

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  1. J. G. Hirschberg, J. Opt. Soc. Am. 50, 514 (1960).
  2. J. Katzenstein, Appl. Opt. 4, 253 (1965).
    [CrossRef]
  3. G. G. Shepherd, C. W. Lake, J. R. Miiller, L. L. Cogger, Appl. Opt. 4, 267 (1965).
    [CrossRef]
  4. J. G. Hirschberg, P. Platz, Appl. Opt. 4, 1375 (1965).
    [CrossRef]
  5. J. G. Hirschberg, Colloque Sur les Methodes Nouvelle de Spectroscopie Instrumentale, sponsored by C.N.R.S. at Orsay, April 1966.
  6. D. J. Bradley, B. Bates, C. O. L. Juulman, S. Majumdar, Appl. Opt. 3, 1461 (1964).
    [CrossRef]
  7. G. Oster, Y. Nishijima, Sci. Am. 208, No. 5, 54 (1963).
    [CrossRef]
  8. J. Guild, The Interference Systems of Crossed Diffraction Gratings—Theory of Moiré Fringes (Clarendon Press, Oxford, 1956).
  9. J. Guild, Diffraction Gratings as Measuring Scales—Practical Guide to the Metrological Use of Moiré Fringes (Oxford University Press, London, 1960).
  10. G. Oster, Appl. Opt. 4, 1359 (1965).
    [CrossRef]
  11. G. Oster, J. Opt. Soc. Am. 55, 1329 (1965).

1965 (5)

1964 (1)

1963 (1)

G. Oster, Y. Nishijima, Sci. Am. 208, No. 5, 54 (1963).
[CrossRef]

1960 (1)

J. G. Hirschberg, J. Opt. Soc. Am. 50, 514 (1960).

Bates, B.

Bradley, D. J.

Cogger, L. L.

Guild, J.

J. Guild, Diffraction Gratings as Measuring Scales—Practical Guide to the Metrological Use of Moiré Fringes (Oxford University Press, London, 1960).

J. Guild, The Interference Systems of Crossed Diffraction Gratings—Theory of Moiré Fringes (Clarendon Press, Oxford, 1956).

Hirschberg, J. G.

J. G. Hirschberg, P. Platz, Appl. Opt. 4, 1375 (1965).
[CrossRef]

J. G. Hirschberg, J. Opt. Soc. Am. 50, 514 (1960).

J. G. Hirschberg, Colloque Sur les Methodes Nouvelle de Spectroscopie Instrumentale, sponsored by C.N.R.S. at Orsay, April 1966.

Juulman, C. O. L.

Katzenstein, J.

Lake, C. W.

Majumdar, S.

Miiller, J. R.

Nishijima, Y.

G. Oster, Y. Nishijima, Sci. Am. 208, No. 5, 54 (1963).
[CrossRef]

Oster, G.

G. Oster, J. Opt. Soc. Am. 55, 1329 (1965).

G. Oster, Appl. Opt. 4, 1359 (1965).
[CrossRef]

G. Oster, Y. Nishijima, Sci. Am. 208, No. 5, 54 (1963).
[CrossRef]

Platz, P.

Shepherd, G. G.

Appl. Opt. (5)

J. Opt. Soc. Am. (2)

J. G. Hirschberg, J. Opt. Soc. Am. 50, 514 (1960).

G. Oster, J. Opt. Soc. Am. 55, 1329 (1965).

Sci. Am. (1)

G. Oster, Y. Nishijima, Sci. Am. 208, No. 5, 54 (1963).
[CrossRef]

Other (3)

J. Guild, The Interference Systems of Crossed Diffraction Gratings—Theory of Moiré Fringes (Clarendon Press, Oxford, 1956).

J. Guild, Diffraction Gratings as Measuring Scales—Practical Guide to the Metrological Use of Moiré Fringes (Oxford University Press, London, 1960).

J. G. Hirschberg, Colloque Sur les Methodes Nouvelle de Spectroscopie Instrumentale, sponsored by C.N.R.S. at Orsay, April 1966.

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Figures (4)

Fig. 1
Fig. 1

Illustrating the formation of straight-line moiré fringes by overlapping Fabry-Perot patterns. The quantities n and p are defined in the text.

Fig. 2
Fig. 2

Showing the geometry and coordinate system used in the calculations and as applied to a pair of intersecting rings.

Fig. 3
Fig. 3

Two ways of determining the aperture spectral function. (a) The aperture formed by the intersection of a Fabry-Perot ring and a linear mask ruling, and filled with a band of light. Lines of constant λ are shown. (b) The same as in (a) but for a monochromatic source.

Fig. 4
Fig. 4

Experimental spectra obtained from the 5461-Å line of natural Hg using the moiré fringe method and the refractive index variation method, using the same aperture finesse in both cases.

Equations (22)

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Δ x = λ F 2 / ( 2 u d t ) ,
m λ = 2 u t cos θ ,
m λ = 2 u t ( 1 - θ 2 / 2 ) ,
= 2 u t ( 1 - r 2 / 2 F 2 ) ,
( m 0 - n ) λ = 2 u t ( 1 - r n 2 / 2 F 2 ) ,
r n 2 = λ n / k + r 0 2 ,
k = u t / F 2 .
r 1 a 2 = n 1 ( λ / k ) + r 0 2 ( λ ) ,
r 2 a 2 = n 2 ( λ / k ) + r 0 2 ( λ ) .
n 1 ( λ / k ) + r 0 2 ( λ ) = ( x a + d / 2 ) 2 + y a 2 ,
n 2 ( λ / k ) + r 0 2 ( λ ) = ( x a - d / 2 ) 2 + y a 2 .
x a = ( 1 / 2 k d ) [ n 1 λ - n 2 λ - m 0 ( λ - λ ) ] .
x b = ( 1 / 2 k d ) [ n 1 λ - n 2 λ + m 0 ( λ - λ ) ] ,
x c = ( 1 / 2 k d ) [ n 1 λ - n 2 λ ] = p λ / 2 k d ,
x d = ( 1 / 2 k d ) [ n 1 λ = n 2 λ ] = p λ / 2 k d .
x b - x a = ( λ - λ ) [ 2 m 0 - ( n 1 + n 2 ) ] / 2 k d .
( x b - x a ) / Δ x = 2 m 0 ( λ - λ ) / λ .
x = p λ / 2 k d + r 01 2 - r 02 2 .
p = [ k 1 / λ 1 - k 2 / λ 2 ] ( x 2 + y 2 + d 2 / 4 ) + [ k 1 / λ 1 + k 2 / λ 2 ] x d .
x 0 - x = [ ( k 1 λ 2 - k 2 λ 1 ) / ( k 1 λ 2 + k 2 λ 1 ) ] ( y 2 / d ) ,
( x 0 - x ) / Δ x = ( k y 2 / λ 2 ) ( λ 2 - λ 1 ) = ( u t / λ 2 ) ( γ / F ) 2 ( λ 2 - λ 1 ) .
λ 2 - λ 1 = 10 / N Å .

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