Abstract

Several designs of infrared sensors use a Fabry–Perot interferometer (FPI) to modulate the incident light. In this work we analyze the particular case where the FPI fringes are matched with very well defined rovibrational absorption lines of a target molecule such as CO2, C O, N 2O, or CH4. In this kind of sensor, modulation is induced by scanning the FPI cavity length over one half of the reference wavelength. Here we present an analytical method based on the Fourier transform, which simplifies the procedure to determine the sensor response. Furthermore, this method provides a simple solution to finding the optimal FPI cavity length and mirror reflectivity. It is shown that FPI mirrors with surprisingly low reflectivity (<50%) are generally the optimum choice for target gases at atmospheric pressure. Finally, experimental measurements and simulation results are presented.

© 2007 Optical Society of America

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References

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  1. J. J. Barrett and S. A. Myers, "New interferometric method for studying periodic spectra using a Fabry-Perot interferometer," J. Opt. Soc. Am. B 61, 1246-1251 (1971).
    [CrossRef]
  2. W. Jin, G. Stewart, B. Culshaw, S. Murray, and D. Pinchbeck, "Absorption measurement of methane gas with a broadband ligth and interferometric signal processing," Opt. Lett. 18, 1364-1366 (1993).
    [CrossRef] [PubMed]
  3. C. R. Batchellor and J. P. Dakin, "Wavelength scanning optical sensor," UK Patent Application GB 2181536A (1987).
  4. A. Mohebati and T. A. King, "Remote detection of gases by diode laser spectroscopy," J. Mod. Opt. 35, 319-324 (1998).
    [CrossRef]
  5. J. P. Dakin, Review of Fibre Optic Gas Sensors (Plessey, 1988).
  6. W. Jin, G. Stewart, B. Culshaw, and S. Murray, "Source-noise limitation of fiber-optic methane sensors," Appl. Opt. 34, 2345-2349 (1995).
    [CrossRef] [PubMed]
  7. E. Vargas-Rodriguez and H. N. Rutt, "Method to minimize spurious background signals in gas detectors based on correlation spectroscopy using a Fabry-Perot bandpass filter shape optimization," Opt. Eng. 44, 103002 (2005).
    [CrossRef]
  8. E. Hecht, Optics (Addison-Wesley, 1998).
  9. M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).
  10. J. M. Vaughan, The Fabry-Perot Interferometer History, Theory, Practice, and Applications (Adam Hilger, 1989).
  11. J. H. Jaffe, "Concerning the use of the Fabry-Perot interferometer for wave-number measurement in the infrared," J. Opt. Soc. Am. 43, 1170-1173 (1953).
    [CrossRef]
  12. J. Spelman, S. Skrien, and T. E. Parker, "Design methodology for a Fabry-Perot interferometer used as a concentration sensor," Appl. Opt. 41, 2847-2857 (2002).
    [CrossRef] [PubMed]

2005 (1)

E. Vargas-Rodriguez and H. N. Rutt, "Method to minimize spurious background signals in gas detectors based on correlation spectroscopy using a Fabry-Perot bandpass filter shape optimization," Opt. Eng. 44, 103002 (2005).
[CrossRef]

2002 (1)

1998 (1)

A. Mohebati and T. A. King, "Remote detection of gases by diode laser spectroscopy," J. Mod. Opt. 35, 319-324 (1998).
[CrossRef]

1995 (1)

1993 (1)

1971 (1)

J. J. Barrett and S. A. Myers, "New interferometric method for studying periodic spectra using a Fabry-Perot interferometer," J. Opt. Soc. Am. B 61, 1246-1251 (1971).
[CrossRef]

1953 (1)

Appl. Opt. (2)

J. Mod. Opt. (1)

A. Mohebati and T. A. King, "Remote detection of gases by diode laser spectroscopy," J. Mod. Opt. 35, 319-324 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

J. J. Barrett and S. A. Myers, "New interferometric method for studying periodic spectra using a Fabry-Perot interferometer," J. Opt. Soc. Am. B 61, 1246-1251 (1971).
[CrossRef]

Opt. Eng. (1)

E. Vargas-Rodriguez and H. N. Rutt, "Method to minimize spurious background signals in gas detectors based on correlation spectroscopy using a Fabry-Perot bandpass filter shape optimization," Opt. Eng. 44, 103002 (2005).
[CrossRef]

Opt. Lett. (1)

Other (5)

J. P. Dakin, Review of Fibre Optic Gas Sensors (Plessey, 1988).

E. Hecht, Optics (Addison-Wesley, 1998).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).

J. M. Vaughan, The Fabry-Perot Interferometer History, Theory, Practice, and Applications (Adam Hilger, 1989).

C. R. Batchellor and J. P. Dakin, "Wavelength scanning optical sensor," UK Patent Application GB 2181536A (1987).

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Figures (12)

Fig. 1
Fig. 1

(Color online) Fabry–Perot fringes and target molecule rovibrational absorption lines. (a) FPI's fringes matched with the rovibrational lines. (b) FPI's fringes shifted along the wavenumber axis. The rovibrational lines are shifted up for clarity.

Fig. 2
Fig. 2

(Color online) FPI transmission fringes characteristics and its Fourier transform. (a) Transmission fringe profile considering R = 0.30 and n d = 0.28   cm . (b) Fourier transform of the FPI fringes.

Fig. 3
Fig. 3

(Color online) (a) Function G(ν) profile showing the filter performance and the rovibrational absorption lines of CO 2 and considering a flat source. (b) Fourier transform of G(ν); here the magnitude of the sidelobes centered at ξ = 0.56 cm clearly increases with the CO 2 concentration.

Fig. 4
Fig. 4

(Color online) Amplitude modulation for a CO 2 sensor evaluated using both the direct numerical evaluation of Eq. (1) and using the convolution method. Here R = 0.30 and n d = 0.28   cm .

Fig. 5
Fig. 5

(Color online) Amplitude modulation as a function of the reflectivity with a constant optical thickness n d = 0.28   cm . Different CO 2 concentrations are shown.

Fig. 6
Fig. 6

(Color online) Magnitude of the FPI fringes impulses as a function of the reflectivity.

Fig. 7
Fig. 7

(Color online) Experimental setup.

Fig. 8
Fig. 8

Measured FPI mirror reflectivity.

Fig. 9
Fig. 9

FPI fringe patterns evaluated for a collimated beam ( θ max = 0   rad ) and for a converging beam with θ max = 0.0416   rad .

Fig. 10
Fig. 10

(Color online) (a) Function G(ν) for the CH 4 sensor for different gas concentrations. (b) Magnitude of the Fourier transform | G ( ξ ) | .

Fig. 11
Fig. 11

(Color online) Simulated and measured amplitude modulation values for the CH 4 sensor. Here we use R = 0.30 and CH 4 concentration of 50%.

Fig. 12
Fig. 12

(Color online) Simulated and measured AM values as a function of the CH 4 concentration.

Equations (14)

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I D ( R , n , d , δ ) = 0 I F P ( ν , R , n , d , δ ) T ( ν ) F i l ( ν ) × S ( ν ) d ν ,
A M = I D ( R , n , d , δ ) max I D ( R , n , d , δ ) min .
I D ( R , n , d , Δ ν ) = 0 I F P ( ν , R , n , d , Δ ν ) T ( ν ) F i l ( ν ) × S ( ν ) d ν .
G ( ν ) = S ( ν ) F i l ( ν ) T ( ν ) .
I D ( R , n , d , Δ ν ) = 0 I F P ( ν , R , n , d , Δ ν ) G ( ν ) d ν .
I D ( R , n , d , Δ ν ) = 0 I F P ( Δ ν ν , R , n , d ) G ( ν ) d ν .
h ( t ) = f ( τ t ) k ( t ) d τ ,
FT { f ( t ) * k ( t ) } = H ( ω ) = F ( ω ) K ( ω ) .
FT { I D ( R , n , d , Δ ν ) } = I D ( R , n , d , ξ ) = I F P ( ξ , R , n , d ) G ( ξ ) .
I F P ( ν , R , n , d , θ ) = ( 1 R ) ( 1 + R ) { 1 + 2 m = 1 R m × cos [ m 4 π n d ν   cos ( θ ) ] } ,
A m = ( 1 R ) ( 1 + R ) 2 R m ,   m = 1 , 2 .
I F P ( ξ , R , n , d ) = { A m 2 | ξ | = m 2 n d 0 | ξ | m 2 n d .
| I F P ( 2 n d , R , n , d ) | = ( 1 R ) ( 1 + R ) R .
I F P ( ν , R , n , d ) = 2 sin 2 ( θ max ) 0 θ max I F P ( ν , R , n , d , θ ) × sin   θ   cos   θ d θ .

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