Abstract

An approximate expression is derived for the length of a stigmatic final image in multiple-traverse cells of the John U. White type. The length of the final tangential image is, for a point source,

ΔLThb212R2(N-4N),

where h is the height of the “rear” mirrors illuminated, b is the separation of the entrance and exit images, R is the common radius of curvature of the three spherical mirrors, and N is the number of traversals. Direct experimental measurements of image length for two sets of mirrors are in agreement with the calculated values. The results are discussed in terms of design parameters, and two new cells constructed in accordance with these principles are described.

© 1961 Optical Society of America

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References

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  1. John U. White, J. Opt. Soc. Am. 32, 285 (1942).
    [Crossref]
  2. H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
    [Crossref]
  3. T. R. Reesor, J. Opt. Soc. Am. 41, 1059 L (1951).
    [Crossref]
  4. G. S. Monk, Light: Principles and Experiments (McGraw-Hill Book Company, Inc., New York, 1937), pp. 52 and 424.
  5. These expressions may be used to determine the image elongation for a single reflection from a sphere used off-axis (a situation often found in the fore-optic and post-optic arrangements in present day infrared spectrometers).
  6. Wm. G. Fastie, J. Opt. Soc. Am. 42, 647 (1952).
    [Crossref]
  7. Minimum volume multiple-traverse cells are also available commercially, e.g., from the Perkin-Elmer Corporation, Beckman Instrument Company, etc.

1952 (1)

1951 (1)

T. R. Reesor, J. Opt. Soc. Am. 41, 1059 L (1951).
[Crossref]

1948 (1)

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
[Crossref]

1942 (1)

Bernstein, H. J.

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
[Crossref]

Fastie, Wm. G.

Herzberg, G.

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
[Crossref]

Monk, G. S.

G. S. Monk, Light: Principles and Experiments (McGraw-Hill Book Company, Inc., New York, 1937), pp. 52 and 424.

Reesor, T. R.

T. R. Reesor, J. Opt. Soc. Am. 41, 1059 L (1951).
[Crossref]

White, John U.

J. Chem. Phys. (1)

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
[Crossref]

J. Opt. Soc. Am. (3)

Other (3)

Minimum volume multiple-traverse cells are also available commercially, e.g., from the Perkin-Elmer Corporation, Beckman Instrument Company, etc.

G. S. Monk, Light: Principles and Experiments (McGraw-Hill Book Company, Inc., New York, 1937), pp. 52 and 424.

These expressions may be used to determine the image elongation for a single reflection from a sphere used off-axis (a situation often found in the fore-optic and post-optic arrangements in present day infrared spectrometers).

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Figures (7)

Fig. 1
Fig. 1

Optical path of a White-type multiple-traverse absorption cell, set for four traversals. The crossed circles indicate the centers of curvature of the mirrors, the dashed line indicates the chief ray, n and x indicate the entrance and exit images, and b is the total separation of the entrance and exit images. F and B designate front and back mirrors.

Fig. 2
Fig. 2

Modified front mirror showing image positions when the cell is adjusted for 40 traversals (20 images). The images are numbered. The crossed circles indicate centers of curvature of the back mirrors, n and x indicate the entrance and exit images, and b is the total separation of the entrance and exit images. This picture assumes aberrationless images.

Fig. 3
Fig. 3

Astigmatism produced by reflection at a spherical surface, for a point object off-axis in the horizontal plane; as viewed (a) from above, (b) from the side. The crossed circle is the center of curvature of the sphere, the dashed line is the chief ray, d and dT are the distances off-axis of the source and the tangential image, ϕ is the angle of incidence of the chief ray, and h and w are the height and width of the mirror. S, ST, and SS are the distances along the chief ray from the mirror to the source, the tangential image, and the sagittal image. ΔLT and ΔLS are the lengths of the tangential and sagittal images.

Fig. 4
Fig. 4

(a) Image elongation versus number of traversals for a set of mirrors with R=35.8 cm, b=10.4 cm, and h=4.1 cm. The dotted circles are observed values, and the solid curve represents calculated values. (b) Image elongation versus number of traversals for a set of mirrors with R=33.7 cm, b=5.0 cm, and h=5.0 cm. The dotted circles are observed values, and the dashed curve represents calculated values.

Fig. 5
Fig. 5

Front and rear mirror shapes for the two new multiple-traverse cells. F and B designate front and back mirrors.

Fig. 6
Fig. 6

Glass-walled multiple-traverse cell.

Fig. 7
Fig. 7

Brass-walled “minimum volume” multiple-traverse cell. Not shown is the copper cooling coil soldered to the walls.

Equations (8)

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Δ L T h b 2 12 R 2 ( N - 4 N ) ,
1 S T + 1 S = 2 R cos ϕ
1 S S + 1 S = 2 cos ϕ R ,
Δ L T = 2 h R 2 i d i 2 .
Δ L T = 2 h R 2 [ ( b 4 ) 2 + ( b 4 ) 2 ] = h b 2 4 R 2 ,
Δ L T = 4 h b 2 R 2 [ ( N 2 - 1 N ) 2 + + ( 3 N ) 2 + ( 1 N ) 2 ] = h b 2 12 R 2 ( N - 4 N ) = b 2 12 R f V ( N - 4 N ) .
( N 4 - 1 ) w s .
Δ L T N R = N R R 2 N R V o l 2 3 ,