Abstract

A simple model is presented as an aid in understanding, first, the relative noise performance and, second, the noise reduction achievable by referencing, in different experimental approaches to single shot broadband coherent anti-Stokes Raman scattering (CARS). Qualitative agreement is obtained with previous experimental investigations of CARS noise. The broadband dye laser radiation is described as the sum of independent modes with random phases. The dye laser contribution to the CARS noise is then approximately inversely proportional to the square root of the number of dye laser modes generating the detected signal. A fundamental idea is that in Raman resonant spectra only the number of Stokes modes actually participating in driving the Raman resonance should be counted. This means, e.g., that for narrow Raman resonances, as in an atmospheric flame, the noise generated by the dye laser will be higher for a single-mode pump laser than for a multimode pump laser with the experimental CARS configuration normally employed. The implications of the model for the dual broadband type CARS techniques are also discussed.

© 1987 Optical Society of America

Full Article  |  PDF Article

Errata

S. Kroll, M. Alden, T. Berglind, and R. J. Hall, "Noise characteristics of single shot broadband Raman-resonant CARS with single- and multimode lasers: erratum," Appl. Opt. 29, 4434-4434 (1990)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-29-30-4434

References

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  1. S. A. J. Druet, J.-P. E. Taran, “CARS Spectroscopy,” Prog. Quantum. Electron. 7, 1 (1981).
    [CrossRef]
  2. R. J. Hall, A. C. Eckbreth, “Coherent Anti-Stokes Raman Spectroscopy (CARS) Application to Combustion Diagnostics,” Laser Appl. 5, 213 (1984).
  3. R. L. Farrow, R. P. Lucht, G. L. Clark, R. E. Palmer, “Species Concentration Measurements Using CARS with Non-resonant Susceptibility Normalization,” Appl. Opt. 24, 2241 (1985).
    [CrossRef] [PubMed]
  4. M. Pealat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of Multiplex CARS Temperature Measurements,” Appl. Opt. 24, 1012 (1985).
    [CrossRef] [PubMed]
  5. A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS Temperature and Species Measurements in Augmented Jet Engine Exhausts,” Appl. Opt. 23, 1328 (1984).
    [CrossRef] [PubMed]
  6. L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10-Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
    [CrossRef]
  7. M. Alden, S. Wallin, “CARS Experiments in a Full-Scale (10 × 10 m) Industrial Coal Furnace,” Appl. Opt. 24, 3434 (1985).
    [CrossRef] [PubMed]
  8. E. J. Beiting, “Multiplex CARS Temperature Measurements in a Coal-Fired MHD Environment,” Appl. Opt. 25, 1684 (1986).
    [CrossRef] [PubMed]
  9. W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-Pulse Coherent Anti-Stokes Raman Scattering,” Appl. Phys. Lett. 29, 174 (1976).
    [CrossRef]
  10. R. E. Teets, “Accurate Convolutions of Coherent Anti-Stokes Raman Spectra,” Opt. Lett. 9, 226 (1984).
    [CrossRef] [PubMed]
  11. L. A. Rahn, R. L. Farrow, R. P. Lucht, “Effects of Laser Field Statistics on Coherent Anti-Stokes Raman Spectroscopy Intensities,” Opt. Lett. 9, 223 (1984).
    [CrossRef] [PubMed]
  12. R. L. Farrow, L. A. Rahn, “Interpreting Coherent Anti-Stokes Raman Spectra Measured with Multimode Nd:YAG Pump Lasers,” J. Opt. Soc. Am. B 2, 903 (1985).
    [CrossRef]
  13. D. R. Snelling, R. A. Sawchuk, R. E. Mueller, “Single Pulse CARS Noise: a Comparison Between Single-Mode and Multimode Pump Lasers,” Appl. Opt. 24, 2771 (1985).
    [CrossRef] [PubMed]
  14. D. A. Greenhalgh, S. T. Whittley, “Mode Noise in Broadband CARS Spectroscopy,” Appl. Opt. 24, 907 (1985).
    [CrossRef] [PubMed]
  15. R. J. Hall, D. A. Greenhalgh, “Noise Properties of Single-Pulse Coherent Anti-Stokes Raman Spectroscopy with Multimode Pump Sources,” J. Opt. Soc. Am. B 3, 1637 (1986).
    [CrossRef]
  16. D. R. Snelling, G. I. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” AGARD Conf. Proc.00, 000 (198x), to be published.
  17. S. Kröll, “The influence of mode beating and pump mode fluctuations on noise in broadband CARS,” in progress.
  18. A. C. Eckbreth, T. J. Anderson, “Dual Broadband CARS for Simultaneous, Multiple Species Measurements,” Appl. Opt. 24, 2731 (1985).
    [CrossRef] [PubMed]
  19. A. C. Eckbreth, T. J. Anderson, “Dual broadband USED CARS,” Appl. Opt. 25, 1534 (1986).
    [CrossRef] [PubMed]
  20. A. C. Eckbreth, T. J. Anderson, “Simultaneous Rotational Coherent Anti-Stokes Raman Spectroscopy and Coherent Stokes Raman Spectroscopy with Arbitrary Pump–Stokes Spectral Separation,” Opt. Lett. 11, 496 (1986).
    [CrossRef] [PubMed]
  21. M. Aldén, P.-E. Bengtsson, H. Edner, “Rotational CARS Generation Through a Multiple Four-Color Interaction,” Appl. Opt. 25, 4493 (1986).
    [CrossRef] [PubMed]
  22. A. V. Masalov, “Spectral and Temporal Fluctuations of Broadband Laser Radiation,” Prog. Opt. 22, 145 (1985).
    [CrossRef]
  23. R. E. Teets, “CARS Signals: Phase Matching, Transverse Modes, and Optical Damage Effects,” Appl. Opt. 25, 855 (1986).
    [CrossRef] [PubMed]
  24. E. E. Whiting, “An Empirical Approximation to the Voigt Profile,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
    [CrossRef]
  25. M. Alden, K. Fredriksson, S. Wallin, “Application of a Two-Color Dye Laser in CARS Experiments for Fast Determinations of Temperatures,” Appl. Opt. 23, 2053 (1984).
    [CrossRef] [PubMed]
  26. M. A. Yuratich, “Effects of Laser Linewidth on Coherent Anti-Stokes Raman Spectroscopy,” Mol. Phys. 38, 625 (1979).
    [CrossRef]
  27. H. Kataoka, S. Maeda, C. Hirose, “Effects of Laser Linewidth on the Coherent Anti-Stokes Raman Spectroscopy Spectral Profile,” Appl. Spectrosc. 36, 565 (1982).
    [CrossRef]
  28. J. H. Churnside, “Second Harmonic Generation Using Partially Coherent Light,” Opt. Commun. 51, 207 (1984).
    [CrossRef]
  29. R. J. Hall, “The Statistical Behaviour of Nonresonant CARS Intensities,” Opt. Commun. 56, 127 (1985).
    [CrossRef]
  30. R. J. Hall, “Theoretical Analysis of Non-Thermal Pump Effects in Broadband CARS Spectroscopy,” Opt. Quantum Electron. 18, 319 (1986).
    [CrossRef]
  31. G. S. Agarwal, R. L. Farrow, “Theoretical Modeling of Two-Color Coherent Anti-Stokes Raman Spectroscopy Spectra Measured with a Frequency-Doubled, Multimode Pump Laser,” J. Opt. Soc. Am. B 3, 1596 (1986).
    [CrossRef]
  32. D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Precision of Multiplex CARS Temperatures Using Both Single-Mode and Multimode Pump Lasers,” Appl. Opt. 26, 99 (1987).
    [CrossRef] [PubMed]

1987

1986

1985

1984

1983

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10-Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

1982

1981

S. A. J. Druet, J.-P. E. Taran, “CARS Spectroscopy,” Prog. Quantum. Electron. 7, 1 (1981).
[CrossRef]

1979

M. A. Yuratich, “Effects of Laser Linewidth on Coherent Anti-Stokes Raman Spectroscopy,” Mol. Phys. 38, 625 (1979).
[CrossRef]

1976

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-Pulse Coherent Anti-Stokes Raman Scattering,” Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

1968

E. E. Whiting, “An Empirical Approximation to the Voigt Profile,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[CrossRef]

Agarwal, G. S.

Alden, M.

Aldén, M.

Anderson, T. J.

Beiting, E. J.

Bengtsson, P.-E.

Bouchardy, P.

Churnside, J. H.

J. H. Churnside, “Second Harmonic Generation Using Partially Coherent Light,” Opt. Commun. 51, 207 (1984).
[CrossRef]

Clark, G. L.

Dobbs, G. M.

Druet, S. A. J.

S. A. J. Druet, J.-P. E. Taran, “CARS Spectroscopy,” Prog. Quantum. Electron. 7, 1 (1981).
[CrossRef]

Eckbreth, A. C.

Edner, H.

Farrow, R. L.

Fredriksson, K.

Goss, L. P.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10-Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Greenhalgh, D. A.

Hall, R. J.

R. J. Hall, D. A. Greenhalgh, “Noise Properties of Single-Pulse Coherent Anti-Stokes Raman Spectroscopy with Multimode Pump Sources,” J. Opt. Soc. Am. B 3, 1637 (1986).
[CrossRef]

R. J. Hall, “Theoretical Analysis of Non-Thermal Pump Effects in Broadband CARS Spectroscopy,” Opt. Quantum Electron. 18, 319 (1986).
[CrossRef]

R. J. Hall, “The Statistical Behaviour of Nonresonant CARS Intensities,” Opt. Commun. 56, 127 (1985).
[CrossRef]

R. J. Hall, A. C. Eckbreth, “Coherent Anti-Stokes Raman Spectroscopy (CARS) Application to Combustion Diagnostics,” Laser Appl. 5, 213 (1984).

Hirose, C.

Kataoka, H.

Kröll, S.

S. Kröll, “The influence of mode beating and pump mode fluctuations on noise in broadband CARS,” in progress.

Lefebvre, M.

Lucht, R. P.

MacDonald, B. G.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10-Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Maeda, S.

Masalov, A. V.

A. V. Masalov, “Spectral and Temporal Fluctuations of Broadband Laser Radiation,” Prog. Opt. 22, 145 (1985).
[CrossRef]

Mueller, R. E.

Palmer, R. E.

Parameswaran, T.

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Precision of Multiplex CARS Temperatures Using Both Single-Mode and Multimode Pump Lasers,” Appl. Opt. 26, 99 (1987).
[CrossRef] [PubMed]

D. R. Snelling, G. I. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” AGARD Conf. Proc.00, 000 (198x), to be published.

Pealat, M.

Rahn, L. A.

Roh, W. B.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-Pulse Coherent Anti-Stokes Raman Scattering,” Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

Sawchuk, R. A.

Schreiber, P. W.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-Pulse Coherent Anti-Stokes Raman Scattering,” Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

Smallwood, G. I.

D. R. Snelling, G. I. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” AGARD Conf. Proc.00, 000 (198x), to be published.

Smallwood, G. J.

Snelling, D. R.

Stufflebeam, J. H.

Switzer, G. L.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10-Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Taran, J. P. E.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-Pulse Coherent Anti-Stokes Raman Scattering,” Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

Taran, J.-P.

Taran, J.-P. E.

S. A. J. Druet, J.-P. E. Taran, “CARS Spectroscopy,” Prog. Quantum. Electron. 7, 1 (1981).
[CrossRef]

Teets, R. E.

Tellex, P. A.

Trump, D. D.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10-Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Wallin, S.

Whiting, E. E.

E. E. Whiting, “An Empirical Approximation to the Voigt Profile,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[CrossRef]

Whittley, S. T.

Yuratich, M. A.

M. A. Yuratich, “Effects of Laser Linewidth on Coherent Anti-Stokes Raman Spectroscopy,” Mol. Phys. 38, 625 (1979).
[CrossRef]

Appl. Opt.

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS Temperature and Species Measurements in Augmented Jet Engine Exhausts,” Appl. Opt. 23, 1328 (1984).
[CrossRef] [PubMed]

D. A. Greenhalgh, S. T. Whittley, “Mode Noise in Broadband CARS Spectroscopy,” Appl. Opt. 24, 907 (1985).
[CrossRef] [PubMed]

M. Pealat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of Multiplex CARS Temperature Measurements,” Appl. Opt. 24, 1012 (1985).
[CrossRef] [PubMed]

R. L. Farrow, R. P. Lucht, G. L. Clark, R. E. Palmer, “Species Concentration Measurements Using CARS with Non-resonant Susceptibility Normalization,” Appl. Opt. 24, 2241 (1985).
[CrossRef] [PubMed]

A. C. Eckbreth, T. J. Anderson, “Dual Broadband CARS for Simultaneous, Multiple Species Measurements,” Appl. Opt. 24, 2731 (1985).
[CrossRef] [PubMed]

D. R. Snelling, R. A. Sawchuk, R. E. Mueller, “Single Pulse CARS Noise: a Comparison Between Single-Mode and Multimode Pump Lasers,” Appl. Opt. 24, 2771 (1985).
[CrossRef] [PubMed]

R. E. Teets, “CARS Signals: Phase Matching, Transverse Modes, and Optical Damage Effects,” Appl. Opt. 25, 855 (1986).
[CrossRef] [PubMed]

E. J. Beiting, “Multiplex CARS Temperature Measurements in a Coal-Fired MHD Environment,” Appl. Opt. 25, 1684 (1986).
[CrossRef] [PubMed]

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Precision of Multiplex CARS Temperatures Using Both Single-Mode and Multimode Pump Lasers,” Appl. Opt. 26, 99 (1987).
[CrossRef] [PubMed]

M. Aldén, P.-E. Bengtsson, H. Edner, “Rotational CARS Generation Through a Multiple Four-Color Interaction,” Appl. Opt. 25, 4493 (1986).
[CrossRef] [PubMed]

M. Alden, K. Fredriksson, S. Wallin, “Application of a Two-Color Dye Laser in CARS Experiments for Fast Determinations of Temperatures,” Appl. Opt. 23, 2053 (1984).
[CrossRef] [PubMed]

M. Alden, S. Wallin, “CARS Experiments in a Full-Scale (10 × 10 m) Industrial Coal Furnace,” Appl. Opt. 24, 3434 (1985).
[CrossRef] [PubMed]

A. C. Eckbreth, T. J. Anderson, “Dual broadband USED CARS,” Appl. Opt. 25, 1534 (1986).
[CrossRef] [PubMed]

Appl. Phys. Lett.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-Pulse Coherent Anti-Stokes Raman Scattering,” Appl. Phys. Lett. 29, 174 (1976).
[CrossRef]

Appl. Spectrosc.

J. Opt. Soc. Am. B

J. Quant. Spectrosc. Radiat. Transfer

E. E. Whiting, “An Empirical Approximation to the Voigt Profile,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[CrossRef]

Laser Appl.

R. J. Hall, A. C. Eckbreth, “Coherent Anti-Stokes Raman Spectroscopy (CARS) Application to Combustion Diagnostics,” Laser Appl. 5, 213 (1984).

Mol. Phys.

M. A. Yuratich, “Effects of Laser Linewidth on Coherent Anti-Stokes Raman Spectroscopy,” Mol. Phys. 38, 625 (1979).
[CrossRef]

Opt. Commun.

J. H. Churnside, “Second Harmonic Generation Using Partially Coherent Light,” Opt. Commun. 51, 207 (1984).
[CrossRef]

R. J. Hall, “The Statistical Behaviour of Nonresonant CARS Intensities,” Opt. Commun. 56, 127 (1985).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

R. J. Hall, “Theoretical Analysis of Non-Thermal Pump Effects in Broadband CARS Spectroscopy,” Opt. Quantum Electron. 18, 319 (1986).
[CrossRef]

Prog. Opt.

A. V. Masalov, “Spectral and Temporal Fluctuations of Broadband Laser Radiation,” Prog. Opt. 22, 145 (1985).
[CrossRef]

Prog. Quantum. Electron.

S. A. J. Druet, J.-P. E. Taran, “CARS Spectroscopy,” Prog. Quantum. Electron. 7, 1 (1981).
[CrossRef]

Rev. Sci. Instrum.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10-Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Other

D. R. Snelling, G. I. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” AGARD Conf. Proc.00, 000 (198x), to be published.

S. Kröll, “The influence of mode beating and pump mode fluctuations on noise in broadband CARS,” in progress.

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Figures (3)

Fig. 1
Fig. 1

Schematic view of the CARS process employing (a) a single-mode pump laser and (b) a multimode pump laser. The figure is a visualization of how the multimode pump laser enables a larger number of Stokes laser modes to participate in the excitation of the Raman resonance. Vertical scale is energy, vertical arrows and piles represent energies of the photons used in each step in the CARS process. One Raman resonance is indicated. Horizontal lines represent laser modes. These lines have different lengths symbolizing the randomness in intensity of the individual modes.

Fig. 2
Fig. 2

Dye laser modes, a narrow isolated Lorentzian Raman resonance, and a wider Gaussian slit function are shown. L is the (optical) length of the dye laser cavity. The intensity in the nonresonant spectra will be determined by the total intensity in the modes selected by the detection slit function. The intensity in the resonant spectra, however, is determined only by the total intensity in the smaller subgroup selected by the Raman resonance.

Fig. 3
Fig. 3

Noise, as defined in the text, in two nonresonant CARS spectra recorded using (a) normal vibrational CARS and (b) dual broadband rotational CARS is shown. In a spectra with no noise all points would have intensity 1.0. The noise in the two spectra is 9.3% and 4.5%, respectively. The slope in the upper spectra arises from shot-to-shot fluctuations in the position of the dye laser spectral peak. The dispersion is 0.6 Å/channel.

Tables (1)

Tables Icon

Table I CARS Noise Obtained for Different Experimental Situations by Snelling

Equations (10)

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

I T = k = 1 l I k , σ k ( I k 2 - I k 2 ) 1 / 2 = I k , σ T = ( k = 1 l σ k 2 ) 1 / 2 ;
σ T I T = k = 1 l I k 2 k = 1 l I k = 1 l .
W Δ · Γ r Ω s
W Δ · Γ ( r + p ) Ω s .
Δ Γ r single - mode laser , Δ Γ ( r + p ) multimode laser .
noise N R , S M noise N R , M M · Δ Γ r Δ Γ ( r + p ) = noise N R , S M noise N R , M M · Γ ( r + p ) Γ r = noise R , S M noise R , M M .
W V W L 2 + ( W L 2 ) 2 + W G 2 ,
Γ ( r + p ) Γ r 2 + ( Γ r 2 ) 2 + Γ p 2 0.12 cm - 1 .
6.4 8.6 0.12 0.04 1.4 ,
22 15.6 1.4.

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