Abstract

The realization that the usual optical geometry of an absorption cell is the frustrum of a cone and that a requirement can be put on any transfer optics system that eliminates the need for a field lens at the cell input leads to a powerful method of first-order optical system design through (1) determination of a required ray transfer matrix, unique except for sign, which requires a single concave spherical mirror (or lens) to implement and (2) getting additional degrees of freedom to make the system more practical at the expense of additional spherical mirrors (or lenses). Two successful applications of the method are described.

© 1987 Optical Society of America

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References

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  1. R. Clark Jones, “Immersed Radiation Detectors,” Appl. Opt. 1, 607 (1962); A. Zachor, “Throughput: A Figure of Merit for Optical Systems,” J. Opt. Soc. Am. 54, iv (1964); F. E. Nicodemus, H. J. Kostkowski, in “Self-Study Manual on Optical Radiation Measurements,” Natl. Bur. Stand. U.S. Tech. Note 910-1, U.S. Department of Commerce, Washington, DC (1976), Appendix 2, Chap. 2.
    [CrossRef]
  2. H. Sakai, “Consideration of the Signal-to-Noise Ratio in Fourier Spectroscopy,” in Aspen Conference on Fourier Spectroscopy, 1970, G. A. Vanasse, A. T. Stair, D. J. Baker, Eds. (Air Force Cambridge Research Laboratories, Hanscom Field, Bedford, MA, 1970), pp. 19–41.
  3. H. Kogelnik, T. Li, “Laser Beams and Resonators,” Appl. Opt. 5, 1550 (1966); W. Brower, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964); E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, MA, 1963); R. S. Longhurst, Geometrical and Physical Optics, (Longman, London, 1973).
    [CrossRef] [PubMed]

1966 (1)

1962 (1)

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Figures (1)

Fig. 1
Fig. 1

Relevant geometry of the interferometer and sample system. In the case of a White-type multiple-reflection cell, the geometry of the sample cell illustrated is that for the first pass only. The beam splitter is shown only for the purpose of visualizing the collimated beam leaving the fixed mirror of the interferometer. The space from A to B along the optic axis will be spanned by the transfer optics system.

Equations (31)

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G c = π 2 r a 2 r b 2 / d 2 .
g = r a r b / d
g = G 1 / 2 / π .
Ω = π sin 2 α ,
Ω = π α 2 .
r i = α f c ,
α = ( ν m L ) - 1 / 2 .
g = α r 0
G = π 2 r 0 2 α 2 .
R = ν m L = ν m / δ ν .
α r 0 = r a r b / d .
( T 11 T 12 T 21 T 22 ) ( r 0 - α ) = ( - r a X ) .
( 1 d 0 1 ) ( T 11 T 12 T 21 T 22 ) ( r a - α ) = ( - r b Y ) ,
T 11 r 0 - T 12 α = - r a ,
( T 11 + T 21 d ) r 0 - ( T 12 + T 22 d ) α = - r b .
T 11 = 0 ,
T 12 = r a / α ,
T 12 = r 0 d / r b .
T 21 = - 1 / T 12 = - r b / r 0 d .
T 22 = - r 0 / r b .
T = ( 0 r 0 d / r b - r b / r 0 d - r 0 / r b ) .
f 12 = - 1 / T 21 = r 0 d / r b = ( r a / α ) ,
d 1 = f 12 ( 1 + r 0 / r b ) ,
d 2 = f 12 .
f 1 = d 12 C / ( C - d 23 - d 12 A ) ,
f 2 = d 12 d 23 / ( d 12 + d 23 - C ) ,
f 3 = d 23 C / ( C - d 12 - d 23 B ) ,
A = T 11 - d 2 T 21 ,
B = T 22 - d 1 T 21 ,
C = T 12 - d 1 T 11 - d 2 T 22 + d 1 d 2 T 21 .
T = ( 0.00000 - 284.308 0.0035173 1.846154 ) .

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