Abstract

A multipass cell for absorption measurements with laser light is described. The number of passes is adjusted by variation of the distance of two parallel concave mirrors. The position and direction of the exit beam do not change when the path length is varied. A cell of 1-m length was used for infrared absorption measurements with an effective path length between 3 and 150 m.

© 1981 Optical Society of America

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References

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  1. J. U. White, J. Opt. Soc. Am. 32, 285 (1942).
    [CrossRef]
  2. D. R. Herriott, H. Kogelnik, R. Kompfner, Appl. Opt. 3, 523 (1964).
    [CrossRef]
  3. D. R. Herriott, H. J. Schulte, Appl. Opt. 4, 883 (1965).
    [CrossRef]
  4. J. Brochard, P. Cahuzac, J. Phys. B: 9, 2027 (1976).
    [CrossRef]
  5. J. Brochard, P. Cahuzac, J. Opt. Paris 8, 207 (1977).
    [CrossRef]
  6. B. Wellegehausen, Dissertation, Technische UniversitätHannover (1972).
  7. J. Altmann, Dissertation, Universität Hamburg (1980).
  8. J. Altmann, P. Pokrowsky, Appl. Opt. 19, 3449 (1980).
    [CrossRef] [PubMed]

1980 (1)

1977 (1)

J. Brochard, P. Cahuzac, J. Opt. Paris 8, 207 (1977).
[CrossRef]

1976 (1)

J. Brochard, P. Cahuzac, J. Phys. B: 9, 2027 (1976).
[CrossRef]

1965 (1)

1964 (1)

1942 (1)

Altmann, J.

J. Altmann, P. Pokrowsky, Appl. Opt. 19, 3449 (1980).
[CrossRef] [PubMed]

J. Altmann, Dissertation, Universität Hamburg (1980).

Brochard, J.

J. Brochard, P. Cahuzac, J. Opt. Paris 8, 207 (1977).
[CrossRef]

J. Brochard, P. Cahuzac, J. Phys. B: 9, 2027 (1976).
[CrossRef]

Cahuzac, P.

J. Brochard, P. Cahuzac, J. Opt. Paris 8, 207 (1977).
[CrossRef]

J. Brochard, P. Cahuzac, J. Phys. B: 9, 2027 (1976).
[CrossRef]

Herriott, D. R.

Kogelnik, H.

Kompfner, R.

Pokrowsky, P.

Schulte, H. J.

Wellegehausen, B.

B. Wellegehausen, Dissertation, Technische UniversitätHannover (1972).

White, J. U.

Appl. Opt. (3)

J. Opt. Paris (1)

J. Brochard, P. Cahuzac, J. Opt. Paris 8, 207 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. B (1)

J. Brochard, P. Cahuzac, J. Phys. B: 9, 2027 (1976).
[CrossRef]

Other (2)

B. Wellegehausen, Dissertation, Technische UniversitätHannover (1972).

J. Altmann, Dissertation, Universität Hamburg (1980).

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Figures (7)

Fig. 1
Fig. 1

Schematic multipass arrangement of two concave mirrors. Mirror 0 has a hole for the beam entrance and exit, mirror 1 can be shifted in the z direction. In the drawing the distance d is equal to the focal length f; this leads to N = 6 passes through the cell.

Fig. 2
Fig. 2

Coordinate system; the z axis points through the mirror centers, the x axis is defined by the entrance hole at x0.

Fig. 3
Fig. 3

Projections of the reflex spots on the mirrors into the x-y plane lie on an ellipse, shown here for N = 6 passes (circles); the even reflexes lie on mirror 0, the odd reflexes on mirror 1. As the mirror distance is increased, the reflexes wander clockwise further around the ellipse (crosses), the sixth reflex misses the entrance hole and produces a series of new reflexes (no. 7, etc., triangles). The next closed path is given when the distance is such that the (N + 4)th reflex on mirror 0 has moved onto the entrance hole. Then the ray leaves the cell without further passes, and the projection point has made one additional turn around the ellipse.

Fig. 4
Fig. 4

Photograph of the multipass cell. In the front flange is the entrance window before mirror 0. Between the tube rails the spindle which shifts the sliding carriage with mirror 1 can be seen. The rear flange contains the feedthroughs for vacuum and gas feed and drain and also for the pressure gauges.

Fig. 5
Fig. 5

Decrease, on a logarithmic scale, of the average ratio A / B ¯ of the exiting and entering light pulse energies with pass number, from N = 10 to N = 50, empty cell. Each point is an average of 20 laser pulses. The slope of the best straight line fitted to the experimental averages gives the mirror reflectance R.

Fig. 6
Fig. 6

Reflectance measurement as in Fig. 5, for pass numbers N from 14 to 154.

Fig. 7
Fig. 7

Absorption measurement: logarithmically scaled decrease of the average pulse energy ratio A / B ¯ with path length, from L = 10.99 m to L = 46.78 m (full circles). Gas mixture: 37.1-mbar SO2 with 960-mbar N2, DF line P4(6) at 3.9843 μm. Correcting for the reflectance losses results in the open circles. The slope of the straight line fit to these points gives the absorption coefficient α.

Equations (18)

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x n = x 0 cos n θ + d 4 f d ( x 0 + 2 f x 0 ) sin n θ ,
cos θ = 1 ( d / 2 f ) .
N = 2 ( 2 j + 1 ) ,
θ = 2 j π N = N 2 2 N π .
d N = 2 f ( 1 cos N 2 2 N π ) ,
x N 1 = x 0 f + x 0 , y N 1 = y 0 f + y 0 .
x 0 = x 0 2 f , y 0 = x 0 2 f ; x N 1 = x 0 2 f , y N 1 = x 0 2 f ,
a = x 0 , b = x 0 4 f d d .
Δ x N = N 2 2 x 0 4 d f f 2 ( Δ d ) 2 .
Δ y N = N x 0 4 f d Δ d .
| Δ x N | N 2 x 0 6 f 2 ( Δ d ) 2 ,
| Δ y N | N x 0 2 f | Δ d | .
L n = d 2 + ( x n x n 1 ) 2 + ( y n y n 1 ) 2 ,
L = n = 1 N L n = N d + x 0 2 4 f d [ n 1 N sin 2 n θ + n = 1 N sin 2 ( n 1 ) θ ] .
L = N d + N x 0 2 4 f d .
Δ L = N Δ d .
Δ L = N d f 4 f d ( Δ x 0 ) 2 N d x 0 4 f d Δ y 0 ,
| Δ L | N f ( Δ x 0 ) 2 + N x 0 | Δ y 0 | .

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