Abstract

The theory of the multiple-pass cell based on the use of retroreflectors is presented. As a result of this study, it is shown that it is possible to construct an enhanced White cell with zero geometric loss. Starting from theoretical considerations of the design of a new monolithic multiple-face retroreflector, a multiple-pass cell is proposed. Ray-tracing simulations indicate that this cell is easy to align and has zero geometric loss over a very long optical path.

© 2001 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, 285–288 (1942).
    [CrossRef]
  2. D. Horn, G. C. Pimental, “2.5-km low-temperature multiple-reflection cell,” Appl. Opt. 10, 1892–1898 (1971).
    [CrossRef] [PubMed]
  3. E. O. Schulz-DuBois, “Generation of square lattice of focal points by a modified White cell,” Appl. Opt. 12, 1391–1393 (1973).
    [CrossRef] [PubMed]
  4. P. L. Hanst, “Spectroscopic methods for air pollution measurements,” in Advances in Environmental Science and Technology, J. N. Pitts, R. L. Metcalf, eds. (Wiley, New York, 1971), vol. 2, pp. 91–213.
  5. D. R. Herriott, H. J. Schulte, “Folded optical delay lines,” Appl. Opt. 4, 883–889 (1965).
    [CrossRef]
  6. P. L. Hanst, A. S. Lefohn, B. W. Gay, “Detection of atmospheric pollutants at part-per-billion levels by infrared spectroscopy,” Appl. Spectrosc. 27, 188–198 (1973).
    [CrossRef]
  7. J. U. White, “Very long optical paths in air,” J. Opt. Soc. Am. 66, 411–416 (1976).
    [CrossRef]
  8. D. Ritz, M. Hausmann, U. Platt, “An improved open path multi-reflection cell for the measurement of NO2 and NO3,” in Optical Methods in Atmosphere Chemistry: Proceedings of the Meeting, Berlin, Germany, June 22–24, 1992, H. I. Schiff, U. Platt, eds., Proc. SPIE1715, 200–211 (1992).
    [CrossRef]
  9. J.-F. Doussin, D. Ritz, C. Patrick, “Multiple-pass cell for very-long-path infrared spectrometry,” Appl. Opt. 38, 4145–4150 (1999).
    [CrossRef]
  10. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).
  11. “Quartz glass for optics. data and properties,” , Heraeus Quarzglas GmbH, Hanau, Germany (1994).

1999

1976

1973

1971

1965

1942

Doussin, J.-F.

Gay, B. W.

Hanst, P. L.

P. L. Hanst, A. S. Lefohn, B. W. Gay, “Detection of atmospheric pollutants at part-per-billion levels by infrared spectroscopy,” Appl. Spectrosc. 27, 188–198 (1973).
[CrossRef]

P. L. Hanst, “Spectroscopic methods for air pollution measurements,” in Advances in Environmental Science and Technology, J. N. Pitts, R. L. Metcalf, eds. (Wiley, New York, 1971), vol. 2, pp. 91–213.

Hausmann, M.

D. Ritz, M. Hausmann, U. Platt, “An improved open path multi-reflection cell for the measurement of NO2 and NO3,” in Optical Methods in Atmosphere Chemistry: Proceedings of the Meeting, Berlin, Germany, June 22–24, 1992, H. I. Schiff, U. Platt, eds., Proc. SPIE1715, 200–211 (1992).
[CrossRef]

Herriott, D. R.

Horn, D.

Lefohn, A. S.

Patrick, C.

Pimental, G. C.

Platt, U.

D. Ritz, M. Hausmann, U. Platt, “An improved open path multi-reflection cell for the measurement of NO2 and NO3,” in Optical Methods in Atmosphere Chemistry: Proceedings of the Meeting, Berlin, Germany, June 22–24, 1992, H. I. Schiff, U. Platt, eds., Proc. SPIE1715, 200–211 (1992).
[CrossRef]

Ritz, D.

J.-F. Doussin, D. Ritz, C. Patrick, “Multiple-pass cell for very-long-path infrared spectrometry,” Appl. Opt. 38, 4145–4150 (1999).
[CrossRef]

D. Ritz, M. Hausmann, U. Platt, “An improved open path multi-reflection cell for the measurement of NO2 and NO3,” in Optical Methods in Atmosphere Chemistry: Proceedings of the Meeting, Berlin, Germany, June 22–24, 1992, H. I. Schiff, U. Platt, eds., Proc. SPIE1715, 200–211 (1992).
[CrossRef]

Schulte, H. J.

Schulz-DuBois, E. O.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

White, J. U.

Appl. Opt.

Appl. Spectrosc.

J. Opt. Soc. Am.

Other

P. L. Hanst, “Spectroscopic methods for air pollution measurements,” in Advances in Environmental Science and Technology, J. N. Pitts, R. L. Metcalf, eds. (Wiley, New York, 1971), vol. 2, pp. 91–213.

D. Ritz, M. Hausmann, U. Platt, “An improved open path multi-reflection cell for the measurement of NO2 and NO3,” in Optical Methods in Atmosphere Chemistry: Proceedings of the Meeting, Berlin, Germany, June 22–24, 1992, H. I. Schiff, U. Platt, eds., Proc. SPIE1715, 200–211 (1992).
[CrossRef]

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

“Quartz glass for optics. data and properties,” , Heraeus Quarzglas GmbH, Hanau, Germany (1994).

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Figures (12)

Fig. 1
Fig. 1

Three-dimensional view of the field and objective optics. Left, field mirror B and three retroreflectors D, E, and F; right, two objective mirrors A and C.

Fig. 2
Fig. 2

Numbered pattern of the light spots on the field surface for the 144-pass configuration.

Fig. 3
Fig. 3

Upper, β as function of ΔIO for p 1 = 68.5 mm and p 2 = 61.5 mm; lower, β as function of p p for Δ1 = 31 mm and for Δ2 = 17 mm.

Fig. 4
Fig. 4

Side and top views of the multiple-face retroreflector D.

Fig. 5
Fig. 5

Front view of the two objective mirrors in the single-ray source case. Upper, MMF configuration; middle, Ritz configuration; lower, computer-optimized Ritz configuration.

Fig. 6
Fig. 6

Front view of the objective mirror A in the MMF retroreflector configuration and the five-parallel-rays source case. The pictures show the behavior that is due to the succession of the prism reflections; the picture sequence is from left to right and from top to bottom.

Fig. 7
Fig. 7

Front view of the objective mirror A in the MMF retroreflector configuration and the five parallel f/40 cones of rays source case. The pictures show the behavior that is due to the succession of the prism reflections; the picture sequence is from left to right and from top to bottom.

Fig. 8
Fig. 8

Front view of the field surface, i.e., field mirror and retroreflectors, in the five f/40 parallel cones of rays source case.

Fig. 9
Fig. 9

Maximum spot distance from the center on an objective-mirror surface versus a retroreflector configuration (iteration step). Here Δd max = d max - d max,0, where d max,0 is evaluated for the exact MMF retroreflector configuration.

Fig. 10
Fig. 10

Focus position along the x axis versus the wavelength in the MMF retroreflector configuration. The value d focus is the difference between the focus position along the x axis at wavelength λ and the value at λ = 300 nm.

Fig. 11
Fig. 11

View of the prism in the plane perpendicular to its apex that contains the input and output points on the prism-field surface.

Fig. 12
Fig. 12

The center of the prism-field surface P and the center of the objective-mirror surface P 0 in a Cartesian coordinate system.

Tables (3)

Tables Icon

Table 1 Parameters for the Exact Solution of Retroreflector D

Tables Icon

Table 2 Parameters of the MMF Retroreflector D

Tables Icon

Table 3 Parameters of the MMF Retroreflector E

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

f=1-2RnIΔIO+nIsinnI90-απ/180+hp-ΔIOΔIO1+sin90-απ/180,
β=arcsin2pp-mptannI90-απ/180/ΔIOCproj180/π,
x0=R-ΔIO2 tannI90-απ/180 Cproj cosβ π180,
Cproj1-2zf tannI90-απ/180/ΔIO21/2.
H=1+2nh,
ω1+ω2+ϕ/nI=180,
α=90-ϕ2nI.
b=ΔIO2+a sinϕ0/π/360=ΔIO2+hp-ΔIO2sinϕ/π/nI 360,
l=ΔIO/2sinϕ/π/360.
a+bnI+l=R.
R=1nIΔIO2+hp-ΔIO21+sinϕ/π/nI 360+ΔIO/2sinϕ/π/360,
1-2RnIΔIO+hp-ΔIOΔIO1+sin90-απ/180+nIsinnI90-απ/180=0.
d=d cosθπ/180, zf=d sinθπ/180, pp-mp=d sinβπ/180,
d=ΔIO/2tannI90-απ/180.
d=d1-zf/d21/2=d Cproj,
Cproj1-zf/d21/2=1-2zf tannI90-απ/180/ΔIO21/2.
β=arcsinpp-mp/d1-zf/d21/2180/π=arcsin2pp-mptannI90-απ/180/ΔIOCproj180/π.
x0=R-ΔIO/2tannI90-απ/180 Cproj cosβπ/180.

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