Abstract

A new type of multiple-reflection optical cell is presented. One of the main advantages of this type of cell is that it can be made of standard mirrors without particular tolerance while allowing a great number of reflections and thus a large optical path, only limited by the reflection coefficient of the mirrors. The configuration is simple, compact, stable, and cheap. This cell consists of three mirrors as in a White cell but its principle is different. It behaves as a multiplier of a Herriott cell from which it inherits the opto-mechanical stability qualities. The Herriott cell and the White cell are two particular cases of this type of cell. As examples, a demonstrator and an absorption cell contained in a volume of 5 l are presented. The first device is usable with a laser in visible light. The second device is usable with an infrared laser diode for the detection of atmospheric trace species.

© 2007 Optical Society of America

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References

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  1. H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550-1567 (1966).
    [CrossRef] [PubMed]
  2. P. Connes, "L'étalon de Fabry-Perot Sphérique'," J. Phys. Radium , 19, 262-269 (1958).
    [CrossRef]
  3. D. R. Herriot and H. J. Schulte, "Folded optical delay lines," Appl. Opt. 4, 883-889 (1965).
    [CrossRef]
  4. J. F. Doussin, D. Ritz, and P. Carlier, "Multiple-pass cell for very-long-path infrared spectrometry," Appl. Opt. 38, 4145-4150 (1999).
    [CrossRef]
  5. P. G. Lethbridge and A. J. Stace, "Design considerations for the construction of a reflecting symmetric multipass cell for use in laser molecular-beam experiments," Rev. Sci. Instrum. 58, 2238-2243 (1987).
    [CrossRef]
  6. C. R. Webster, R. D. May, C. A. Trimble, R. G. Chave, and J. Kendall, "Aircraft (ER2) laser infrared absorption spectrometer (ALIAS) for in situ stratospheric measurements of HCl, N2O, CH4, NO2, and HNO3," Appl. Opt. 33, 454-472 (1994).
    [CrossRef] [PubMed]
  7. G. Durry and G. Mégie, "Atmospheric CH4 and H2O monitoring with near-infrared InGaAs laser diodes by the SDLA, a balloon-borne spectrometer for tropospheric and stratospheric in situ measurements," Appl. Opt. 38, 7342-7354 (1999).
    [CrossRef]
  8. G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
    [CrossRef]
  9. C. R. Webster, S. P. Sander, R. Beer, R. D. May, R. G. Knollenberg, D. M. Hunten, and J. Ballard, "Tunable diode laser IR spectrometerfor in situ measurement of the gaz phase composition and particule size distribution of Titan's atmosphere," Appl. Opt. 29, 907-917 (1990).
    [CrossRef] [PubMed]
  10. D. R. Herriot, H. Kogelnik, and R. Kompfner, "Off-axis paths in spherical mirror interferometers," Appl. Opt. 3, 523-526 (1964).
    [CrossRef]
  11. J. B. MacManus, P. L. Kebabian, and M. S. Zahniser, "Astigmatic mirror multipass absorption cells long-pass-length spectroscopy," Appl. Opt. 34, 3336-3348 (1995).
    [CrossRef]
  12. J. U. White, "Long optical path of large aperture," J. Opt. Soc. Am. 32, 285-288 (1942).
    [CrossRef]
  13. L. Grazzi and R. Guzzi, "Theoretical and practical consideration of the construction of a zero-geometric-loss multiple-pass cell based on the use of monolithic multiple-face retroreflectors," Appl. Opt. 33, 6062-6071 (2001).
  14. D. Horn and G. C. Pimentel, "2.5-km low-temperature multiple-reflection cell," Appl. Opt. 10, 1892-1898 (1971).
    [CrossRef] [PubMed]
  15. D. Ritz, M. Haussmann, and U. Platt, "Improved open multireflection cell for the measurement of NO2 and NO3," Proc. SPIE 1715, 200-211 (1992).
    [CrossRef]
  16. E. O. Schulz-DuBois, "Generation of square lattice of focal points by a modified White cell," Appl. Opt. 12, 1391-1393 (1973).
    [CrossRef] [PubMed]
  17. A. L. Vitushkin and L. F. Vitushkin, "Design of a multipass optical cell based on the use of a shift corner cubes and right-angle prisms," Appl. Opt. 37, 162-165 (1998).
    [CrossRef]
  18. S. M. Chernin and E. G. Barskaya, "Optical multipass matrix systems," Appl. Opt. 30, 51-57 (1991).
    [CrossRef] [PubMed]
  19. D. W. Steyert, J. M. Sirota, M. E. Mickelson, and D. C. Reuter, "Two new long-pass cells for infrared and visible spectroscopy," Rev. Sci. Instrum. 72, 4337-4344 (2001).
    [CrossRef]
  20. R. A. Hill and D. L. Hartley, "Focused, multiple-pass cell for Raman scattering," Appl. Opt. 13, 186-192 (1974).
    [CrossRef] [PubMed]
  21. R. B. Zipin, "The apparent thermal radiation properties of an isothermal V-groove with specularly reflecting walls," J. Res. Natl. Bur. Stand. Sect. C 70, 275-280 (1966).
  22. G. Moreau et and C. Robert, "Etude des variations d'un faisceau lumineux dans une cellule à passages multiples," J. Optics 16, 177-183 (1985).

2005 (1)

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

2001 (2)

L. Grazzi and R. Guzzi, "Theoretical and practical consideration of the construction of a zero-geometric-loss multiple-pass cell based on the use of monolithic multiple-face retroreflectors," Appl. Opt. 33, 6062-6071 (2001).

D. W. Steyert, J. M. Sirota, M. E. Mickelson, and D. C. Reuter, "Two new long-pass cells for infrared and visible spectroscopy," Rev. Sci. Instrum. 72, 4337-4344 (2001).
[CrossRef]

1999 (2)

1998 (1)

A. L. Vitushkin and L. F. Vitushkin, "Design of a multipass optical cell based on the use of a shift corner cubes and right-angle prisms," Appl. Opt. 37, 162-165 (1998).
[CrossRef]

1995 (1)

1994 (1)

1992 (1)

D. Ritz, M. Haussmann, and U. Platt, "Improved open multireflection cell for the measurement of NO2 and NO3," Proc. SPIE 1715, 200-211 (1992).
[CrossRef]

1991 (1)

1990 (1)

1987 (1)

P. G. Lethbridge and A. J. Stace, "Design considerations for the construction of a reflecting symmetric multipass cell for use in laser molecular-beam experiments," Rev. Sci. Instrum. 58, 2238-2243 (1987).
[CrossRef]

1985 (1)

G. Moreau et and C. Robert, "Etude des variations d'un faisceau lumineux dans une cellule à passages multiples," J. Optics 16, 177-183 (1985).

1974 (1)

R. A. Hill and D. L. Hartley, "Focused, multiple-pass cell for Raman scattering," Appl. Opt. 13, 186-192 (1974).
[CrossRef] [PubMed]

1973 (1)

1971 (1)

1966 (2)

H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550-1567 (1966).
[CrossRef] [PubMed]

R. B. Zipin, "The apparent thermal radiation properties of an isothermal V-groove with specularly reflecting walls," J. Res. Natl. Bur. Stand. Sect. C 70, 275-280 (1966).

1965 (1)

1964 (1)

1958 (1)

P. Connes, "L'étalon de Fabry-Perot Sphérique'," J. Phys. Radium , 19, 262-269 (1958).
[CrossRef]

1942 (1)

Ballard, J.

Barskaya, E. G.

Beer, R.

Camy-Peyret, C.

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

Carlier, P.

Catoire, V.

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

Chartier, M.

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

Chave, R. G.

Chernin, S. M.

Connes, P.

P. Connes, "L'étalon de Fabry-Perot Sphérique'," J. Phys. Radium , 19, 262-269 (1958).
[CrossRef]

Doussin, J. F.

Durry, G.

Grazzi, L.

L. Grazzi and R. Guzzi, "Theoretical and practical consideration of the construction of a zero-geometric-loss multiple-pass cell based on the use of monolithic multiple-face retroreflectors," Appl. Opt. 33, 6062-6071 (2001).

Guzzi, R.

L. Grazzi and R. Guzzi, "Theoretical and practical consideration of the construction of a zero-geometric-loss multiple-pass cell based on the use of monolithic multiple-face retroreflectors," Appl. Opt. 33, 6062-6071 (2001).

Hartley, D. L.

R. A. Hill and D. L. Hartley, "Focused, multiple-pass cell for Raman scattering," Appl. Opt. 13, 186-192 (1974).
[CrossRef] [PubMed]

Haussmann, M.

D. Ritz, M. Haussmann, and U. Platt, "Improved open multireflection cell for the measurement of NO2 and NO3," Proc. SPIE 1715, 200-211 (1992).
[CrossRef]

Herriot, D. R.

Hill, R. A.

R. A. Hill and D. L. Hartley, "Focused, multiple-pass cell for Raman scattering," Appl. Opt. 13, 186-192 (1974).
[CrossRef] [PubMed]

Horn, D.

Hunten, D. M.

Huret, N.

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

Kebabian, P. L.

Kendall, J.

Knollenberg, R. G.

Kogelnik, H.

Kompfner, R.

Lethbridge, P. G.

P. G. Lethbridge and A. J. Stace, "Design considerations for the construction of a reflecting symmetric multipass cell for use in laser molecular-beam experiments," Rev. Sci. Instrum. 58, 2238-2243 (1987).
[CrossRef]

Li, T.

MacManus, J. B.

May, R. D.

Mégie, G.

Mickelson, M. E.

D. W. Steyert, J. M. Sirota, M. E. Mickelson, and D. C. Reuter, "Two new long-pass cells for infrared and visible spectroscopy," Rev. Sci. Instrum. 72, 4337-4344 (2001).
[CrossRef]

Moreau, G.

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

Moreau et, G.

G. Moreau et and C. Robert, "Etude des variations d'un faisceau lumineux dans une cellule à passages multiples," J. Optics 16, 177-183 (1985).

Pimentel, G. C.

Pirre, M.

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

Platt, U.

D. Ritz, M. Haussmann, and U. Platt, "Improved open multireflection cell for the measurement of NO2 and NO3," Proc. SPIE 1715, 200-211 (1992).
[CrossRef]

Pomathiod, L.

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

Reuter, D. C.

D. W. Steyert, J. M. Sirota, M. E. Mickelson, and D. C. Reuter, "Two new long-pass cells for infrared and visible spectroscopy," Rev. Sci. Instrum. 72, 4337-4344 (2001).
[CrossRef]

Ritz, D.

J. F. Doussin, D. Ritz, and P. Carlier, "Multiple-pass cell for very-long-path infrared spectrometry," Appl. Opt. 38, 4145-4150 (1999).
[CrossRef]

D. Ritz, M. Haussmann, and U. Platt, "Improved open multireflection cell for the measurement of NO2 and NO3," Proc. SPIE 1715, 200-211 (1992).
[CrossRef]

Robert, C.

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

G. Moreau et and C. Robert, "Etude des variations d'un faisceau lumineux dans une cellule à passages multiples," J. Optics 16, 177-183 (1985).

Sander, S. P.

Schulte, H. J.

Schulz-DuBois, E. O.

Sirota, J. M.

D. W. Steyert, J. M. Sirota, M. E. Mickelson, and D. C. Reuter, "Two new long-pass cells for infrared and visible spectroscopy," Rev. Sci. Instrum. 72, 4337-4344 (2001).
[CrossRef]

Stace, A. J.

P. G. Lethbridge and A. J. Stace, "Design considerations for the construction of a reflecting symmetric multipass cell for use in laser molecular-beam experiments," Rev. Sci. Instrum. 58, 2238-2243 (1987).
[CrossRef]

Steyert, D. W.

D. W. Steyert, J. M. Sirota, M. E. Mickelson, and D. C. Reuter, "Two new long-pass cells for infrared and visible spectroscopy," Rev. Sci. Instrum. 72, 4337-4344 (2001).
[CrossRef]

Trimble, C. A.

Vitushkin, A. L.

A. L. Vitushkin and L. F. Vitushkin, "Design of a multipass optical cell based on the use of a shift corner cubes and right-angle prisms," Appl. Opt. 37, 162-165 (1998).
[CrossRef]

Vitushkin, L. F.

A. L. Vitushkin and L. F. Vitushkin, "Design of a multipass optical cell based on the use of a shift corner cubes and right-angle prisms," Appl. Opt. 37, 162-165 (1998).
[CrossRef]

Webster, C. R.

White, J. U.

Zahniser, M. S.

Zipin, R. B.

R. B. Zipin, "The apparent thermal radiation properties of an isothermal V-groove with specularly reflecting walls," J. Res. Natl. Bur. Stand. Sect. C 70, 275-280 (1966).

Appl. Opt. (4)

G. Moreau, C. Robert, V. Catoire, C. Camy-Peyret, N. Huret, M. Pirre, L. Pomathiod, and M. Chartier, "SPIRALE: A multi-species in situ balloon-borne instrument with six tunable diode laser spectrometers," Appl. Opt. 30, 5972-5989 (2005).
[CrossRef]

L. Grazzi and R. Guzzi, "Theoretical and practical consideration of the construction of a zero-geometric-loss multiple-pass cell based on the use of monolithic multiple-face retroreflectors," Appl. Opt. 33, 6062-6071 (2001).

A. L. Vitushkin and L. F. Vitushkin, "Design of a multipass optical cell based on the use of a shift corner cubes and right-angle prisms," Appl. Opt. 37, 162-165 (1998).
[CrossRef]

R. A. Hill and D. L. Hartley, "Focused, multiple-pass cell for Raman scattering," Appl. Opt. 13, 186-192 (1974).
[CrossRef] [PubMed]

Appl. Opt. (11)

S. M. Chernin and E. G. Barskaya, "Optical multipass matrix systems," Appl. Opt. 30, 51-57 (1991).
[CrossRef] [PubMed]

D. Horn and G. C. Pimentel, "2.5-km low-temperature multiple-reflection cell," Appl. Opt. 10, 1892-1898 (1971).
[CrossRef] [PubMed]

C. R. Webster, R. D. May, C. A. Trimble, R. G. Chave, and J. Kendall, "Aircraft (ER2) laser infrared absorption spectrometer (ALIAS) for in situ stratospheric measurements of HCl, N2O, CH4, NO2, and HNO3," Appl. Opt. 33, 454-472 (1994).
[CrossRef] [PubMed]

G. Durry and G. Mégie, "Atmospheric CH4 and H2O monitoring with near-infrared InGaAs laser diodes by the SDLA, a balloon-borne spectrometer for tropospheric and stratospheric in situ measurements," Appl. Opt. 38, 7342-7354 (1999).
[CrossRef]

C. R. Webster, S. P. Sander, R. Beer, R. D. May, R. G. Knollenberg, D. M. Hunten, and J. Ballard, "Tunable diode laser IR spectrometerfor in situ measurement of the gaz phase composition and particule size distribution of Titan's atmosphere," Appl. Opt. 29, 907-917 (1990).
[CrossRef] [PubMed]

D. R. Herriot, H. Kogelnik, and R. Kompfner, "Off-axis paths in spherical mirror interferometers," Appl. Opt. 3, 523-526 (1964).
[CrossRef]

J. B. MacManus, P. L. Kebabian, and M. S. Zahniser, "Astigmatic mirror multipass absorption cells long-pass-length spectroscopy," Appl. Opt. 34, 3336-3348 (1995).
[CrossRef]

H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550-1567 (1966).
[CrossRef] [PubMed]

D. R. Herriot and H. J. Schulte, "Folded optical delay lines," Appl. Opt. 4, 883-889 (1965).
[CrossRef]

J. F. Doussin, D. Ritz, and P. Carlier, "Multiple-pass cell for very-long-path infrared spectrometry," Appl. Opt. 38, 4145-4150 (1999).
[CrossRef]

E. O. Schulz-DuBois, "Generation of square lattice of focal points by a modified White cell," Appl. Opt. 12, 1391-1393 (1973).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Optics (1)

G. Moreau et and C. Robert, "Etude des variations d'un faisceau lumineux dans une cellule à passages multiples," J. Optics 16, 177-183 (1985).

J. Phys. Radium (1)

P. Connes, "L'étalon de Fabry-Perot Sphérique'," J. Phys. Radium , 19, 262-269 (1958).
[CrossRef]

J. Res. Natl. Bur. Stand. Sect. C (1)

R. B. Zipin, "The apparent thermal radiation properties of an isothermal V-groove with specularly reflecting walls," J. Res. Natl. Bur. Stand. Sect. C 70, 275-280 (1966).

Proc. SPIE (1)

D. Ritz, M. Haussmann, and U. Platt, "Improved open multireflection cell for the measurement of NO2 and NO3," Proc. SPIE 1715, 200-211 (1992).
[CrossRef]

Rev. Sci. Instrum. (2)

D. W. Steyert, J. M. Sirota, M. E. Mickelson, and D. C. Reuter, "Two new long-pass cells for infrared and visible spectroscopy," Rev. Sci. Instrum. 72, 4337-4344 (2001).
[CrossRef]

P. G. Lethbridge and A. J. Stace, "Design considerations for the construction of a reflecting symmetric multipass cell for use in laser molecular-beam experiments," Rev. Sci. Instrum. 58, 2238-2243 (1987).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

The present cell. M1, M1′ and M2 are spherical mirrors. The beam enters and leaves the cell through two opening in M1. The reflections patterns are represented on the mirrors. The curved arrow shows the M1′ rotation axis. This rotation adjusts the total path length.

Fig. 2
Fig. 2

The Herriott cell. M1 and M2 are two spherical mirrors. The beam enters in the cell by the hole pierced in M1. The beam undergoes multiple reflections on the two mirrors. The traces on the mirrors draw ellipses centered on the optical axis.

Fig. 3
Fig. 3

Characteristics of the reflections in the Herriott cell. M1 and M2 are the mirrors of the Herriott cell. The spots are the reflections pattern. The numbers are the reflection index. The beams enter and leave M1 through the spot numbered 0. Two successive reflections on a mirror are separated angularly by 2θ. Two contiguous reflections on a mirror are separated angularly by 2θ∕K. Two symmetrical reflections about the optical axis have the same diameter (Simulation parameters: N = 22, K = 5, R1 = 1000 mm, R2 = 3000 mm, d = 352.7 mm, mirror diameter = 50 mm).

Fig. 4
Fig. 4

Recirculations in the cell. The reflection spots are numbered in the order of the reflections. The beam enters focused on spot 0. (a) Reflections on the M1 mirror of a Herriott cell. (b) The M1 mirror is cut in two parts on the x-axis. The upper half mirror is turned around the y-axis. The optical centers C1 and C1′ are the intersection of the two optical axis with M1. (c) Inversion of the reflection ellipses when one of them passes between the two optical centers. (d) Three recirculations in the Herriott cell. The beam are injected and recovered through two diametrically opposite openings. (Simulation parameters: K = 1 and N = 31).

Fig. 5
Fig. 5

Configuration I1M. Various cases of cells with injection on the side of the single mirror M2. In black: reflections on M2. In green: on the higher figure, reflections on M1 and M1′. In red: the trace of the first and the last reflection on M1 and M1′. The upper left case corresponds to the White cell.

Fig. 6
Fig. 6

Configuration I2M. Various cases with injection on the side of the two mirrors M1 and M1′

Fig. 7
Fig. 7

Spot diagrams of the exit beam. Input beam f-number: f∕54. Coordinates are in mm. (Simulation parameters: N = 11, K = 5, R1 = R2 = 1000 mm. Mirror diameters: 60 mm. Mirrors spacing: 857.6 mm. Configuration: I2M. Recirculation number: 16. Optical path: 301.8 m. M1′ rotation: 77 arc seconds.).

Fig. 8
Fig. 8

Spot diagrams of the exit beam. Input beam f-number: f∕31. (Simulation parameters: N = 5, K = 3, R1 = R2 = 1000 mm. Mirror Diameters: 70 mm. Mirrors spacing: 690.8 mm. Configuration: I2M. Recirculation number: 16. Optical path: 110.5 m. M1′ rotation: 208 arc seconds.).

Fig. 9
Fig. 9

Mechanical configuration with plane mirrors. M1 and M1′ are bonded on a monolithic piece having a flexible part for M′1. The adjusting screw allows the recirculation number choice thanks to the M1′ rotation.

Fig. 10
Fig. 10

Two plane mirrors configuration. Top: reflections on the plane mirrors, Bottom : reflections on the spherical mirror. (cell parameters: N = 16, K = 3, total number of reflections :128.).

Fig. 11
Fig. 11

Remarkable patterns drawn by reflections for various M1′ adjustments. Left: reflections on M1 and M1′. Right: reflection on M2. The number of reflections on each mirror are, from the top to the bottom: 17, 34, 51, 68, 170, 238. Bottom photography: beams in the cell. The total optical path is 216.1 m. (Cell parameters: N = 17, K = 9, R1 = R2 = 500 mm, distance between the mirrors: 453.9 mm. Mirror diameter: 80 mm.).

Fig. 12
Fig. 12

Other remarkable patterns drawn by the reflections for a small recirculation number.

Fig. 13
Fig. 13

Example of absorption spectrum by atmospheric CO and C O 2 . Left: one second averaged signal of 220 elementary spectra. Solid curve: optical signal obtained with atmospheric air in the cell. Dashed curve: optical signal obtained with no absorption (vacuum in the cell). Lower curve: fringes obtained with a germanium etalon of 300 MHz free spectral range (or 0.01 c m 1 ). Middle: normalized spectra. Solid curve: the absorption spectrum is divided by the vacuum spectrum and the residual baseline is removed after polynomial fitting of the absorption outside the absorption lines. The fringes and the position of the CO line give the wave number scale. Dashed curve: synthetic spectrum obtained with the HITRAN database and experimental parameters (pressure and temperature) for 375 ppm of C O 2 and 128 ppb of CO. the two curves difference cannot be discerned in this graph. Right: zoomed spectra in the 0.3% absorption range with a limit of detection about 2.10 4 .

Equations (11)

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

cos ( K π / N ) = g 1 g 2 ,
g 1 = 1 d R 1 ,
g 2 = 1 d R 2 .
g 1 = g 2 = 1 d / R ,
g 1 / g 2 = 1 .
d = R ( 1 cos θ ) w i t h θ = K π / N θ ] 0 , π [
g 1 g 2 .
x i = r cos ( i θ ) and y i = r sin ( i θ ) .
Δ P i = | i r R sin ( θ ) Δ d | = | i r t g ( θ / 2 ) Δ d d | .
L 2 N d N a 4 d R 2 .
y i = x 0 sin ( i θ ) .

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