Abstract

The signal improvement obtained for a spectroscopic measurement with a multipass cell can be expressed as the gain over a single pass measurement. We develop a unified analysis of amplitude gain and signal-to-noise ratio (SNR) gain for both cw and pulsed systems with application to Rayleigh/Raman spectroscopy, fluorescence, and similar techniques. Our analysis reveals that the SNR gain is dependent on the single pass efficiency, number of passes, and temporal overlap. Increasing the single pass efficiency of a multipass system will increase both the amplitude and SNR gains. While increasing the number of passes always improves the amplitude gain, the SNR gain actually has an optimal number of passes. In particular, what has not been recognized for pulsed systems is that increasing the pulse overlap fraction is equally or even more significant than the number of pass or efficiency increases. For cw systems, the amplitude gain and SNR gain are identical.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  5. W. Demtroder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer-Verlag, 1981).
  6. D. A. Santavicca, “A high energy, long pulse Nd:YAG laser multipass cell for Raman scattering diagnostics,” Opt. Commun. 30, 423-425 (1979).
    [CrossRef]
  7. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus Press, 1988).
  8. A. Gulati, “Raman measurements at the exit of a combustor sector,” J. Propul. Power 10, 169-175 (1994).
    [CrossRef]

1994 (1)

A. Gulati, “Raman measurements at the exit of a combustor sector,” J. Propul. Power 10, 169-175 (1994).
[CrossRef]

1980 (1)

W. T. Hill III, F. A. Abreu, T. W. Hänsch, and A. L. Schawlow, “Sensitive intracavity absorption of reduced pressures,” Opt. Commun. 32, 96-100 (1980).
[CrossRef]

1979 (1)

D. A. Santavicca, “A high energy, long pulse Nd:YAG laser multipass cell for Raman scattering diagnostics,” Opt. Commun. 30, 423-425 (1979).
[CrossRef]

1978 (1)

1974 (1)

1942 (1)

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Propul. Power (1)

A. Gulati, “Raman measurements at the exit of a combustor sector,” J. Propul. Power 10, 169-175 (1994).
[CrossRef]

Opt. Commun. (2)

W. T. Hill III, F. A. Abreu, T. W. Hänsch, and A. L. Schawlow, “Sensitive intracavity absorption of reduced pressures,” Opt. Commun. 32, 96-100 (1980).
[CrossRef]

D. A. Santavicca, “A high energy, long pulse Nd:YAG laser multipass cell for Raman scattering diagnostics,” Opt. Commun. 30, 423-425 (1979).
[CrossRef]

Other (2)

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus Press, 1988).

W. Demtroder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer-Verlag, 1981).

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Figures (9)

Fig. 1
Fig. 1

Example diagram of a multipass light cell using opposing corner mirror assemblies and showing collection optics [1].

Fig. 2
Fig. 2

Example diagram of a multipass light cell using cavity mirrors [6].

Fig. 3
Fig. 3

Multipass amplitude gain versus the number of passes for different single pass efficiencies.

Fig. 4
Fig. 4

Diagram showing parameter definitions relevant to consecutive pulse addition; (a) the individual pulses from each pass, and (b) the combined pulse.

Fig. 5
Fig. 5

Theoretical single pulse shape and effective pulse shape after 20 passes (a 1% power loss per pass has been assumed).

Fig. 6
Fig. 6

Multipass SNR gain as a function of the number of passes for different pulse overlaps and single pass efficiency.

Fig. 7
Fig. 7

Pulse overlap fraction versus the number of passes for different SNR gains. All plots used η = 0.996 .

Fig. 8
Fig. 8

Maximum achievable SNR gain versus the normalized pulse delay for different values of single pass efficiency. The number of passes at these maxima is also shown as contours.

Fig. 9
Fig. 9

Maximum achievable SNR gain versus the single pass optical loss for different values of overlap fraction. The number of passes at these maxima is also shown as contours.

Equations (15)

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η = ( i = 1 m R i ) ( j = 1 k T j ) ,
G A = i = 1 n P i P 1 = 1 + η + η 2 + + η ( n - 1 ) = 1 - η n 1 - η .
lim η 1 G A = n .
lim n G A = 1 1 - η .
τ n = τ 1 + ( n - 1 ) τ D = [ 1 + ( n - 1 ) ( 1 - v ) ] τ 1 .
SNR n = f SP i = 1 n P i P B τ n / τ 1 + f LI i = 1 n P i = f SP G A P 1 P B τ n / τ 1 + f LI G A P 1 .
G SNR ( P B , f LI ) = SNR n SNR 1 = G A P B + f LI P 1 P B τ n / τ 1 + f LI G A P 1 .
G SNR ( P B , 0 ) = G A τ 1 τ n = 1 - η n 1 - η 1 1 + ( n - 1 ) ( 1 - v ) .
lim n G SNR ( P B , 0 ) = 0 ,
lim η 1 G SNR ( P B , 0 ) = n τ 1 τ n = 1 1 - ( 1 - 1 / n ) v .
f Raman = N ( σ Ω ) Raman Ω ε ,
f Fluor N Ω B 12 B 12 + B 21 A 21 A 21 + Q 21 ,
P n P 0 = η ( n - 1 ) exp ( - n α L ) ,
η ( n - 1 ) P 0 - P n = η ( n - 1 ) P 0 [ 1 - exp ( - n α L ) ] η ( n - 1 ) P 0 [ n α L ] ,
G A = η ( n - 1 ) I 0 - I n I 0 - I 1 η ( n - 1 ) I 0 n α I 0 α = n η ( n - 1 ) .

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