Abstract

Multiple-pass optical cells with dense spot patterns are useful for many applications, especially when the cell volume must be minimized relative to the optical path length. Present methods to achieve these dense patterns require expensive, highly precise astigmatic mirrors and complex alignment procedures. This work describes a new, simpler, and less demanding mirror system, comprising either a pair of cylindrical mirrors or one cylindrical and one spherical mirror.

© 2005 Optical Society of America

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References

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  5. D. Herriott, H. Kogelnik, R. Kompfner, “Off-axis paths in spherical mirror interferometers,” Appl. Opt. 3, 523–526 (1964).
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    [CrossRef]
  7. A. Yariv, “The propagation of rays and spherical waves,” in Introduction to Optical Electronics (Holt, Reinhart, & Winston, New York, 1971), pp. 18–29.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. P. L. Kebabian, “Off-axis cavity absorption cell,” U.S. Patent5,291,265 (1March1994).
  14. L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
    [CrossRef]
  15. J. A. Silver, “Dense pattern optical multipass cell,” U.S. patent application 10/896,608 (21July2004) and “Near re-entrant dense pattern optical multipass cell,” U.S. patent application 10/948, 660 (22September2004).

2002 (1)

L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
[CrossRef]

1995 (1)

1991 (1)

1990 (1)

1988 (1)

R. M. Abdullin, A. V. Lebedev, “Use of an integrating sphere as a multiple pass optical cell,” Sov. J. Opt. Technol. 55, 139–141 (1988).

1981 (1)

1980 (1)

W. R. Trutna, R. L. Byer, “Multiple-pass Raman gain cell,” Appl. Opt. 2, 301–312 (1980).
[CrossRef]

1977 (1)

M. M. Salour, “Multipass optical cavities for laser spectroscopy,” Laser Focus 13(10), 50–55 (1977).

1965 (1)

1964 (1)

1942 (1)

Abdullin, R. M.

R. M. Abdullin, A. V. Lebedev, “Use of an integrating sphere as a multiple pass optical cell,” Sov. J. Opt. Technol. 55, 139–141 (1988).

Altmann, J.

Barskaya, E. G.

Baumgart, R.

Bohren, A.

M. W. Sigrist, A. Bohren, I. G. Calasso, M. Nägele, A. Romann, M. Seiter, “Laser spectroscopic sensing of air pollutants,” in 13th Symposium and School on High-Resolution Molecular Spectroscopy, L. N. Sinitsa, ed., Proc. SPIE4063, 17–25 (2000).
[CrossRef]

Byer, R. L.

W. R. Trutna, R. L. Byer, “Multiple-pass Raman gain cell,” Appl. Opt. 2, 301–312 (1980).
[CrossRef]

Calasso, I. G.

M. W. Sigrist, A. Bohren, I. G. Calasso, M. Nägele, A. Romann, M. Seiter, “Laser spectroscopic sensing of air pollutants,” in 13th Symposium and School on High-Resolution Molecular Spectroscopy, L. N. Sinitsa, ed., Proc. SPIE4063, 17–25 (2000).
[CrossRef]

Chernin, S. M.

Feng, D.

L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
[CrossRef]

Hao, L.-Y.

L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
[CrossRef]

Herriott, D.

Herriott, D. R.

Kebabian, P. L.

Kogelnik, H.

Kompfner, R.

Lebedev, A. V.

R. M. Abdullin, A. V. Lebedev, “Use of an integrating sphere as a multiple pass optical cell,” Sov. J. Opt. Technol. 55, 139–141 (1988).

McManus, J. B.

Nägele, M.

M. W. Sigrist, A. Bohren, I. G. Calasso, M. Nägele, A. Romann, M. Seiter, “Laser spectroscopic sensing of air pollutants,” in 13th Symposium and School on High-Resolution Molecular Spectroscopy, L. N. Sinitsa, ed., Proc. SPIE4063, 17–25 (2000).
[CrossRef]

Qi, L.

L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
[CrossRef]

Qiang, S.

L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
[CrossRef]

Romann, A.

M. W. Sigrist, A. Bohren, I. G. Calasso, M. Nägele, A. Romann, M. Seiter, “Laser spectroscopic sensing of air pollutants,” in 13th Symposium and School on High-Resolution Molecular Spectroscopy, L. N. Sinitsa, ed., Proc. SPIE4063, 17–25 (2000).
[CrossRef]

Salour, M. M.

M. M. Salour, “Multipass optical cavities for laser spectroscopy,” Laser Focus 13(10), 50–55 (1977).

Schulte, H. J.

Seiter, M.

M. W. Sigrist, A. Bohren, I. G. Calasso, M. Nägele, A. Romann, M. Seiter, “Laser spectroscopic sensing of air pollutants,” in 13th Symposium and School on High-Resolution Molecular Spectroscopy, L. N. Sinitsa, ed., Proc. SPIE4063, 17–25 (2000).
[CrossRef]

Sigrist, M. W.

M. W. Sigrist, A. Bohren, I. G. Calasso, M. Nägele, A. Romann, M. Seiter, “Laser spectroscopic sensing of air pollutants,” in 13th Symposium and School on High-Resolution Molecular Spectroscopy, L. N. Sinitsa, ed., Proc. SPIE4063, 17–25 (2000).
[CrossRef]

Silver, J. A.

J. A. Silver, “Dense pattern optical multipass cell,” U.S. patent application 10/896,608 (21July2004) and “Near re-entrant dense pattern optical multipass cell,” U.S. patent application 10/948, 660 (22September2004).

Trutna, W. R.

W. R. Trutna, R. L. Byer, “Multiple-pass Raman gain cell,” Appl. Opt. 2, 301–312 (1980).
[CrossRef]

Weitkamp, C.

White, J. U.

Wu, G.-R.

L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
[CrossRef]

Yariv, A.

A. Yariv, “The propagation of rays and spherical waves,” in Introduction to Optical Electronics (Holt, Reinhart, & Winston, New York, 1971), pp. 18–29.

Zahniser, M. S.

Zhu, Q.-S.

L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
[CrossRef]

Appl. Opt. (7)

J. Opt. Soc. Am. (1)

Laser Focus (1)

M. M. Salour, “Multipass optical cavities for laser spectroscopy,” Laser Focus 13(10), 50–55 (1977).

Rev. Sci. Instrum. (1)

L.-Y. Hao, S. Qiang, G.-R. Wu, L. Qi, D. Feng, Q.-S. Zhu, “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum. 73, 2079–2085 (2002).
[CrossRef]

Sov. J. Opt. Technol. (1)

R. M. Abdullin, A. V. Lebedev, “Use of an integrating sphere as a multiple pass optical cell,” Sov. J. Opt. Technol. 55, 139–141 (1988).

Other (4)

P. L. Kebabian, “Off-axis cavity absorption cell,” U.S. Patent5,291,265 (1March1994).

M. W. Sigrist, A. Bohren, I. G. Calasso, M. Nägele, A. Romann, M. Seiter, “Laser spectroscopic sensing of air pollutants,” in 13th Symposium and School on High-Resolution Molecular Spectroscopy, L. N. Sinitsa, ed., Proc. SPIE4063, 17–25 (2000).
[CrossRef]

A. Yariv, “The propagation of rays and spherical waves,” in Introduction to Optical Electronics (Holt, Reinhart, & Winston, New York, 1971), pp. 18–29.

J. A. Silver, “Dense pattern optical multipass cell,” U.S. patent application 10/896,608 (21July2004) and “Near re-entrant dense pattern optical multipass cell,” U.S. patent application 10/948, 660 (22September2004).

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Figures (12)

Fig. 1
Fig. 1

Cylindrical–cylindrical mirror cell having an on-axis input hole, set for an initial alignment condition of four passes, with focal lengths initially orthogonal.

Fig. 2
Fig. 2

Plot of relative reentrant intensity for a cylindrical–cylindrical mirror cell as a function of dimensionless mirror separation d/2f, with the mirror axes at δ = π/2 and an off-axis input hole.

Fig. 3
Fig. 3

Map of allowed reentrant pass number as a function of mirror separation d and mirror twist angle δ. The magnitude of N is denoted (logarithmically) by the diameter of each spot and by color ranging from dark blue (6 passes, largest) to red (200 passes, smallest).

Fig. 4
Fig. 4

Map of allowed reentrant pass number as a function of separation d/f = near 1.1 and mirror twist angle δ near 98 deg. Selected spots are denoted by the indices N M y M x.

Fig. 5
Fig. 5

Plot of reentrant solutions for 182 passes as a function of reduced advance angles ϕx and ϕy for (a) matched cylindrical cell and (b) astigmatic cell. Solutions for various twist angles shown as solid lines and curves.

Fig. 6
Fig. 6

Plot of exit pass number of a cylindrical–spherical mirror cell as a function of mirror separation 0.5 ≤ d/f ≤ 1.5, with the ratio of input hole diameter to maximum spot pattern size being (a) 0.05, (b) 0.025, (c) 0.0125. For this calculation, the same focal length is assumed for both mirrors.

Fig. 7
Fig. 7

Plot of beam exit locations in the xy plane just outside the input mirror for case (b) of Fig. 6, noting the exit pass number and quadrant. The × in the lower left quadrant denotes the location of the input beam in this plane.

Fig. 8
Fig. 8

(a) Spot pattern for 26 passes with a 90 deg crossed cylindrical–cylindrical mirror cell at d/f = 0.88. (b) Dense spot pattern of 122 passes created by rotating front mirror by 9 deg.

Fig. 9
Fig. 9

Plot of a 174-pass dense spot pattern computed and observed at d/f = 1.13 and mirror twist angle δ = 98.3 deg.

Fig. 10
Fig. 10

2f WMS absorption spectrum of O2 near 763 nm in cylindrical multipass cell with N = 142.

Fig. 11
Fig. 11

Cylindrical–spherical mirror cell having an on-axis input hole and set for an initial alignment condition having two rows of spots.

Fig. 12
Fig. 12

Cylindrical–spherical mirror cell dense spot pattern computed and observed for 166 passes.

Equations (13)

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θ R = 2 π M / N ,             d = 2 f ( 1 - cos θ R ) ,
x i = X max sin ( i θ x ) , y i = Y max sin ( i θ y ) , θ x R = cos - 1 ( 1 - d / 2 f x ) = π M x / N , θ y R = cos - 1 ( 1 - d / 2 f y ) = π M y / N ,
r i + 1 = [ x i + 1 x i + 1 y i + 1 y i + 1 ] = M · r i = [ 4 × 4 ] [ x i x i y i y i ] .
D = [ 1 d 0 0 0 1 0 0 0 0 1 d 0 0 0 1 ] , R = [ 1 0 0 0 - 1 / f x 1 0 0 0 0 1 0 0 0 - 1 / f y 1 ] .
C = [ A B C D ] .
x n + 2 - 2 b x n + 1 + γ x n = 0 , b = 1 / 2 ( A + D ) ,             γ = A D - B C = 1.
T ( δ ) = [ cos δ 0 sin δ 0 0 cos δ 0 sin δ - sin δ 0 cos δ 0 0 - sin δ 0 cos δ ] .
θ R = cos - 1 ( 1 - d / 2 f ) ,             0 d 2 f .
cos ( 2 θ x R ) = 1 2 ( F - ξ ) ,             cos ( 2 θ y R ) = 1 2 ( G + ξ ) ,
F = 2 ( d f cos 2 τ - 1 ) 2 - ( d f ) 2 cos 2 τ , G = 2 ( d f sin 2 τ - 1 ) 2 - ( d f ) 2 sin 2 τ , ξ = 1 2 ( G - F ) { - 1 + [ 1 - 4 ɛ 2 ( G - F ) 2 ] 1 / 2 } , ɛ = - ( d 2 f ) 2 sin ( 4 τ ) ,             τ = δ 2 .
ϕ x , y = θ x R , y R - π 2 = π ( M x , y N - 1 2 ) .
0 ( d 2 f sph ) 1 , x axis , 0 ( 1 - d 2 f sph ) ( 1 - d 2 f cyl ) 1 , y axis ,
x n + 2 - 2 ( 1 - d f sph ) x n + 1 + x n = 0 , y n + 2 - 2 ( 1 - d f sph - d f cyl + d 2 f sph f cyl ) y n + 1 + y n = 0.

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