Abstract

Laser based spectroscopic diagnostic tools offer the possibility of spatially and temporally resolved measurements of species concentrations in complex reacting gas flows of engineering interest. The major problem associated with such measurements is the effect of quenching reactions on the fluorescence signal. To overcome this difficulty operating in the saturation mode is proposed. For suitable systems the fluorescence signal is then no longer a function of quenching rates or laser power. Very low detectability limits appear possible.

© 1977 Optical Society of America

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References

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  1. D. L. Hartley, AIP Conf. Proc. 25 (1975).
  2. C. P. Wang, Combust. Sci. Technol. 13, 211 (1976).
    [CrossRef]
  3. C. M. Penny et al., “Study of Resonance Light Scattering for Remote Optical Probing,” NASA CA-132363 (1973).
  4. J. W. Daily, Appl. Opt. 15, 955 (1976).
    [CrossRef] [PubMed]
  5. Only the quantum mechanical density matrix formulation is exactly correct for describing energy level populations in the transient case. This is because the off diagonal elements of the density matrix which give rise to induced absorption and emission are themselves time dependent. In the steady state limit or when the characteristic time for the process considered is long compared to the relaxation time for the cross terms, the density matrix formulation reduces to rate equations of the form of Eq. (4). See, for example, T. J. McIlrath, J. L. Carlsten, Phys. Rev. A 6, 1091 (1972).
    [CrossRef]
  6. It should be noted that the scattered radiation does not have the simple single peaked spectrum of the lower laser intensity case but displays a complicated three peaked spectrum. The present results, however, are concerned only with the integrated intensity which is always proportional to the Einstein A coefficient for the transition involved. B. R. Mollow, Phys. Rev. A 2, 76 (1970) and J. L. Carlsten, A. Szöke, Phys. Rev. Lett. 36, 667 (1976).
    [CrossRef]
  7. F. Robben, “Comparison of Density and Temperature Measurement Using Raman Scattering and Rayleigh Scattering,” SQUID Workshop on Combustion Measurements in Jet Propulsion Systems, Purdue University, 22–23 May 1975.
  8. C. C. Wang, L. I. Davis, Phys. Rev. Lett. 32, 349 (1974).
    [CrossRef]

1976 (2)

C. P. Wang, Combust. Sci. Technol. 13, 211 (1976).
[CrossRef]

J. W. Daily, Appl. Opt. 15, 955 (1976).
[CrossRef] [PubMed]

1975 (1)

D. L. Hartley, AIP Conf. Proc. 25 (1975).

1974 (1)

C. C. Wang, L. I. Davis, Phys. Rev. Lett. 32, 349 (1974).
[CrossRef]

1973 (1)

C. M. Penny et al., “Study of Resonance Light Scattering for Remote Optical Probing,” NASA CA-132363 (1973).

1972 (1)

Only the quantum mechanical density matrix formulation is exactly correct for describing energy level populations in the transient case. This is because the off diagonal elements of the density matrix which give rise to induced absorption and emission are themselves time dependent. In the steady state limit or when the characteristic time for the process considered is long compared to the relaxation time for the cross terms, the density matrix formulation reduces to rate equations of the form of Eq. (4). See, for example, T. J. McIlrath, J. L. Carlsten, Phys. Rev. A 6, 1091 (1972).
[CrossRef]

1970 (1)

It should be noted that the scattered radiation does not have the simple single peaked spectrum of the lower laser intensity case but displays a complicated three peaked spectrum. The present results, however, are concerned only with the integrated intensity which is always proportional to the Einstein A coefficient for the transition involved. B. R. Mollow, Phys. Rev. A 2, 76 (1970) and J. L. Carlsten, A. Szöke, Phys. Rev. Lett. 36, 667 (1976).
[CrossRef]

Carlsten, J. L.

Only the quantum mechanical density matrix formulation is exactly correct for describing energy level populations in the transient case. This is because the off diagonal elements of the density matrix which give rise to induced absorption and emission are themselves time dependent. In the steady state limit or when the characteristic time for the process considered is long compared to the relaxation time for the cross terms, the density matrix formulation reduces to rate equations of the form of Eq. (4). See, for example, T. J. McIlrath, J. L. Carlsten, Phys. Rev. A 6, 1091 (1972).
[CrossRef]

Daily, J. W.

Davis, L. I.

C. C. Wang, L. I. Davis, Phys. Rev. Lett. 32, 349 (1974).
[CrossRef]

Hartley, D. L.

D. L. Hartley, AIP Conf. Proc. 25 (1975).

McIlrath, T. J.

Only the quantum mechanical density matrix formulation is exactly correct for describing energy level populations in the transient case. This is because the off diagonal elements of the density matrix which give rise to induced absorption and emission are themselves time dependent. In the steady state limit or when the characteristic time for the process considered is long compared to the relaxation time for the cross terms, the density matrix formulation reduces to rate equations of the form of Eq. (4). See, for example, T. J. McIlrath, J. L. Carlsten, Phys. Rev. A 6, 1091 (1972).
[CrossRef]

Mollow, B. R.

It should be noted that the scattered radiation does not have the simple single peaked spectrum of the lower laser intensity case but displays a complicated three peaked spectrum. The present results, however, are concerned only with the integrated intensity which is always proportional to the Einstein A coefficient for the transition involved. B. R. Mollow, Phys. Rev. A 2, 76 (1970) and J. L. Carlsten, A. Szöke, Phys. Rev. Lett. 36, 667 (1976).
[CrossRef]

Penny, C. M.

C. M. Penny et al., “Study of Resonance Light Scattering for Remote Optical Probing,” NASA CA-132363 (1973).

Robben, F.

F. Robben, “Comparison of Density and Temperature Measurement Using Raman Scattering and Rayleigh Scattering,” SQUID Workshop on Combustion Measurements in Jet Propulsion Systems, Purdue University, 22–23 May 1975.

Wang, C. C.

C. C. Wang, L. I. Davis, Phys. Rev. Lett. 32, 349 (1974).
[CrossRef]

Wang, C. P.

C. P. Wang, Combust. Sci. Technol. 13, 211 (1976).
[CrossRef]

AIP Conf. Proc. (1)

D. L. Hartley, AIP Conf. Proc. 25 (1975).

Appl. Opt. (1)

Combust. Sci. Technol. (1)

C. P. Wang, Combust. Sci. Technol. 13, 211 (1976).
[CrossRef]

NASA CA-132363 (1)

C. M. Penny et al., “Study of Resonance Light Scattering for Remote Optical Probing,” NASA CA-132363 (1973).

Phys. Rev. A (2)

Only the quantum mechanical density matrix formulation is exactly correct for describing energy level populations in the transient case. This is because the off diagonal elements of the density matrix which give rise to induced absorption and emission are themselves time dependent. In the steady state limit or when the characteristic time for the process considered is long compared to the relaxation time for the cross terms, the density matrix formulation reduces to rate equations of the form of Eq. (4). See, for example, T. J. McIlrath, J. L. Carlsten, Phys. Rev. A 6, 1091 (1972).
[CrossRef]

It should be noted that the scattered radiation does not have the simple single peaked spectrum of the lower laser intensity case but displays a complicated three peaked spectrum. The present results, however, are concerned only with the integrated intensity which is always proportional to the Einstein A coefficient for the transition involved. B. R. Mollow, Phys. Rev. A 2, 76 (1970) and J. L. Carlsten, A. Szöke, Phys. Rev. Lett. 36, 667 (1976).
[CrossRef]

Phys. Rev. Lett. (1)

C. C. Wang, L. I. Davis, Phys. Rev. Lett. 32, 349 (1974).
[CrossRef]

Other (1)

F. Robben, “Comparison of Density and Temperature Measurement Using Raman Scattering and Rayleigh Scattering,” SQUID Workshop on Combustion Measurements in Jet Propulsion Systems, Purdue University, 22–23 May 1975.

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Figures (2)

Fig. 1
Fig. 1

Energy level diagram.

Fig. 2
Fig. 2

Detectability limits under saturation conditions.

Tables (2)

Tables Icon

Table I Numerical Values Used in Uncertainty Analysis

Tables Icon

Table II Suitable Species of Importance in Combustion Systems

Equations (25)

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N k + h ν B k l I ν N l , l > k ,
N l A l k N k + h ν , l > k ,
N l + M Q l i N i + M * , i = 1 , 2 , 3 < l ,
( d N l ) / ( d t ) = N k B k l I ν - ( Q l + A l + B l k I ν ) N l ,
N l = B k l I ν Q l + A l + B l k I ν N k .
N l = B k l B l k N k ,
N l = g l g k N k .
B l k I ν Q l + A l .
I l = h ν A l 4 π Ω c V c N l ,
I l = h ν A l 4 π Ω c V c ( g l g k ) N k .
I 2 = h ν A 2 4 π Ω c V c ( 1 1 + g 1 / g 2 ) N 0 .
( d N 3 ) / ( d t ) = B 13 I ν N 1 - ( Q 31 + Q 32 + A 31 + A 32 + B 31 I ν ) N 3 ,
( d N 2 ) / ( d t ) = Q 32 N 3 - ( Q 21 + A 21 ) N 2 ,
N 0 = N 1 + N 2 + N 3 ,
N 3 = { g 1 g 3 + Q 32 Q 21 + A 21 + 1 } - 1 N 0 .
I 3 = h ν A 3 / 4 π Ω c V c { g 1 / g 3 + Q 32 / ( Q 21 + A 21 ) + 1 } N 0 .
N 2 = Q 32 ( g 1 / g 3 + 1 ) ( Q 21 + A 21 ) + Q 32 N 0 .
I 3 = h ν A 3 4 π Ω c V c N 3
I 2 = h ν A 21 4 π Ω c V c N 2 .
N 0 = { 1 + g 1 / g 3 } I 3 h ν ( A 3 / 4 π ) Ω c V c + I 2 h ν ( A 21 / 4 π ) Ω c V c .
W I l / I l C - 1 / 2 ,
W N l / N l { η A l 4 π Ω c V c Δ t N l } - 1 / 2 ,
N l { η A l 4 π Ω c V c Δ t ( W N l N l ) 2 } - 1 .
N l { η P A Ω c V c σ Δ t ( W N l N l ) 2 } - 1 .
I Fluor I Ray 2 × 10 9 P ( λ 0 ) P ( λ ) ( λ 0 λ ) 4 N l N tot ,

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