Abstract

Conditions are derived for minimum volume and astigmatism of White-type multiple reflection absorption cells, with multiple row and column image arrays, for the case of circular images and apertures.

© 1984 Optical Society of America

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References

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  1. J. U. White, “Long Optical Paths of Large Aperture,” J. Opt. Soc. Am. 32, 285 (1942).
    [CrossRef]
  2. H. J. Bernstein, G. Hertzberg, “Rotation-Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths,” J. Chem. Phys. 16, 30 (1948).
    [CrossRef]
  3. D. Horn, G. C. Pimental, “2.5-km Low-Temperature Multiple-Reflection Cell,” Appl. Opt. 10, 1892 (1971).
    [CrossRef] [PubMed]
  4. T. H. Edwards, “Multiple-Traverse Absorption Cell Design,” J. Opt. Soc. Am. 51, 98 (1961).
    [CrossRef]
  5. T. R. Reesor, “Astigmatism of a Multiple Path Absorption Cell,” J. Opt. Soc. Am. 41, 1059L (1951).
    [CrossRef]

1971 (1)

1961 (1)

1951 (1)

T. R. Reesor, “Astigmatism of a Multiple Path Absorption Cell,” J. Opt. Soc. Am. 41, 1059L (1951).
[CrossRef]

1948 (1)

H. J. Bernstein, G. Hertzberg, “Rotation-Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths,” J. Chem. Phys. 16, 30 (1948).
[CrossRef]

1942 (1)

Bernstein, H. J.

H. J. Bernstein, G. Hertzberg, “Rotation-Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths,” J. Chem. Phys. 16, 30 (1948).
[CrossRef]

Edwards, T. H.

Hertzberg, G.

H. J. Bernstein, G. Hertzberg, “Rotation-Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths,” J. Chem. Phys. 16, 30 (1948).
[CrossRef]

Horn, D.

Pimental, G. C.

Reesor, T. R.

T. R. Reesor, “Astigmatism of a Multiple Path Absorption Cell,” J. Opt. Soc. Am. 41, 1059L (1951).
[CrossRef]

White, J. U.

Appl. Opt. (1)

J. Chem. Phys. (1)

H. J. Bernstein, G. Hertzberg, “Rotation-Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths,” J. Chem. Phys. 16, 30 (1948).
[CrossRef]

J. Opt. Soc. Am. (3)

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Figures (3)

Fig. 1
Fig. 1

Pictorial view of a White type multiple reflection cell with two rows of images. It is not a minimum volume cell. The cell here shown is for reference purposes with regard to dimension parameters defined in the text. The front mirror is cut in a T shape. An external source focuses an image at the input labeled 0. Images on the front mirror are labeled by the number of passes completed.

Fig. 2
Fig. 2

(a) Positions of images for 54 passes on the front mirror of a White cell of four rows of images as originally described by Horn and Pimentel. The images are labeled by the number of passes completed at that image. The row changing folding field mirror is at the upper left corner. The two small dots on the horizontal center line are the centers of curvature of the two back mirrors. (b) New modification of the arrangement which uses all available image space and gives several more transits. The row changing mirror is below the input image in this arrangement. For a practical arrangement one would cut out the lower left corner to take out image 58.

Fig. 3
Fig. 3

Composite diagram showing the optical requirement of a row-stepping mirror pair. A is the center of a back mirror of the White cell. Options for the mirrors with surfaces along BCE and BCE′ are given in the text.

Equations (59)

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T = m ( 2 n - 1 ) d = N d ,
N = m ( 2 n - 1 ) ,
G = π 2 r 1 2 r 2 2 / d 2 ,
r 1 r 2 / d = G 1 / 2 / π = g .
A 2 = w 2 h 2 = 4 r 2 2 r 2 = 8 r 2 2 .
w 1 = 2 n r 1 ,
h 1 = 2 m r 1 ,
A 1 = w 1 h 1
= 4 m n r 1 2 .
A 0 = [ A 1 A 2 ] 1 / 2
= [ 4 m n r 1 2 8 r 2 2 ] 1 / 2
= 4 r 1 r 2 [ 2 m n ] 1 / 2 .
A 0 = 4 g d [ 2 m n ] 1 / 2 .
K = [ N + m ] 1 / 2 = [ 2 m n ] 1 / 2 .
A 0 = 4 g T K / N .
V = ( d / 6 ) ( 2 w 2 h 2 + w 1 h 2 + w 2 h 1 + 2 w 1 h 1 ) .
p = r 1 [ 2 m n ] 1 / 2 / r 2 = K r 1 / 2 r 2 ,
q = [ 2 m / n ] 1 / 2 = K / n .
2 w 1 h 1 = 8 n m r 1 2 = 2 p A 0 ,
w 1 h 2 = 4 n r 1 r 2 = A 0 / q ,
w 2 h 1 = 8 m r 1 r 2 = q A 0 ,
2 w 2 h 2 = 16 r 2 2 = 2 p A 0 .
V = [ A 0 d / 6 ] [ 2 ( p + 1 / p ) + q + 1 / q ] .
A 4 g T / N 1 / 2 .
V p = ( A 0 d / 6 ) ( 4 + q + 1 / q ) .
V p q = A 0 d = 4 g T 2 K / N 2
4 g T 2 / N 3 / 2 .
1 / z + 1 / d t = 2 / d cos ( ϕ ) ,
1 / z + 1 / d s = 2 cos ( ϕ ) / d ,
d t = d cos ( ϕ ) / [ 2 - cos ( ϕ ) ] ;
d s = d / [ 2 cos ( ϕ ) - 1 ] .
r a = 2 r 2 [ 1 - cos ( ϕ ) ] ,
r a = r 2 ϕ 2 .
Δ r 1 = r 2 ϕ i 2 .
F x = N x 2 = ( 1 / 6 ) m ( 2 n - 1 ) ( m 2 - 1 ) .
F x = ( 1 / 6 ) N ( m 2 - 1 ) .
F y = N y 2 = ( 1 / 6 ) ( 2 n - 1 ) ( n 2 - n )
= ( 1 / 6 ) N ( n 2 - n ) .
F = F x + F y
= ( 1 / 6 ) N ( n 2 - n + m 2 - 1 ) .
Δ r 1 = r 2 ( r 1 2 / d 2 ) F .
Δ r 1 = r 1 g F / d .
= r 1 g N F / T .
r 1 = r 1 + Δ r 1 .
u 1 = g N F / T ,
r 1 = r 1 + r 1 u 1
= r 1 ( 1 + u 1 ) .
R 1 = 1 + u 1 .
E a = R 1 - 2 .
n = m + 1 / 2 ,
R m = 1 + ( g / T ) N 2 ( 1 / 6 ) ( N - 1 ) .
Δ r 2 = 2 r 1 ( N - 2 ) ( r 2 2 / d 2 )
= 2 r 2 ( N - 2 ) N g / T ,
u 2 = ( N - 2 ) N g / T .
r 2 = r 2 + r 2 u 2
= r 2 ( 1 + u 2 ) .
R 2 = [ 1 + u 2 ] .
k 1 r 1 = r 1 + r 1 k 1 2 u 1 .
k 1 = 2 / [ 1 + ( 1 - 4 u 1 ) 1 / 2 ] .

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