According to A. C. Ferrari and Robertson, Cambridge, BWF and Lorentzian line shape function are best for deconvolution of Raman spectra. Lorentzian function could be used to measure the life time of photoionization process, but what is the physical meaning of Breit Wigner Fano (BWF) line shape function and its importance? Why is it better than Gaussian symmetric function?
Don't Ferrari and Robertson explain why they consider the BWF profile to be best suited? What are their arguments?
There are relationships between line shapes and the effects which contribute to why the line shapes look the way they do. Those frequently employed in spectroscopy include the Gaussian, Lorentz, Voigt and BWF profiles.
In any experiment the final spectral distribution observed will be the convolution of several distributions. A first distinction could be between intrinsic and extrinsic ones.
The apparatus contributes extrinsically to the line shape. Unless a specific apparatus spectral function is known, it is commonplace to assume it is of Gaussian shape. The sample may also possess an extrinsic contribution. Think of the Doppler broadening of atomic spectra for example, which exhibits a Gaussian distribution.
In contrast, intrinsic contributions are those which link the spectral line shape to the excitation/deexcitation processes which give rise to the spectral feature you observe. An emission process is obviously related to a finite life time (otherwise there would not be emission). If the decay is due to (an ensemble of ) non-interacting oscillators and follows an exponential ( exp(-(t-t0)) ) then the corresponding line shape is Lorentzian (the Lorentzian is the Laplace transform of the exponential decay).
The total line shape is then a convolution of Gaussian and Lorentzian which is also called a Voigt profile. So far we have only symmetric profiles (unless asymmetric extrinsic profiles are explicitely present in the experiment).
If the oscillator(s) are interacting with other modes, especially a continuum of modes whose spectral range overlaps with the oscillator frequency, then the line shape may be strongly altered owing to this coupling. The actual spectral shape depends on the coupling strength. The Fano (or BWF) line shapes are obtained in a certain approximation and then parametrized in terms of the Fano- (or coupling or asymmetry-) parameter. The asymmetric shape is characteristic of the presence of coupling and hence cannot properly be captured with Gaussians or Lorentzians alone. Of course, the BWF profile has to be convoluted with the extrinsic contributions to yield the total line shape.
Yet another source of asymmetric line profiles are energetically unresolved inelastic events. In RAMAN spectroscopy these could be due to Stokes and anti-Stokes processes. In Photoelectron spectroscopy of metals, they could result from low energy electron hole excitations.
Summing up: one ought to study the expected line shapes in the experiment and material under scrutiny and learn how to apply them in analyzing data.
Don't Ferrari and Robertson explain why they consider the BWF profile to be best suited? What are their arguments?
There are relationships between line shapes and the effects which contribute to why the line shapes look the way they do. Those frequently employed in spectroscopy include the Gaussian, Lorentz, Voigt and BWF profiles.
In any experiment the final spectral distribution observed will be the convolution of several distributions. A first distinction could be between intrinsic and extrinsic ones.
The apparatus contributes extrinsically to the line shape. Unless a specific apparatus spectral function is known, it is commonplace to assume it is of Gaussian shape. The sample may also possess an extrinsic contribution. Think of the Doppler broadening of atomic spectra for example, which exhibits a Gaussian distribution.
In contrast, intrinsic contributions are those which link the spectral line shape to the excitation/deexcitation processes which give rise to the spectral feature you observe. An emission process is obviously related to a finite life time (otherwise there would not be emission). If the decay is due to (an ensemble of ) non-interacting oscillators and follows an exponential ( exp(-(t-t0)) ) then the corresponding line shape is Lorentzian (the Lorentzian is the Laplace transform of the exponential decay).
The total line shape is then a convolution of Gaussian and Lorentzian which is also called a Voigt profile. So far we have only symmetric profiles (unless asymmetric extrinsic profiles are explicitely present in the experiment).
If the oscillator(s) are interacting with other modes, especially a continuum of modes whose spectral range overlaps with the oscillator frequency, then the line shape may be strongly altered owing to this coupling. The actual spectral shape depends on the coupling strength. The Fano (or BWF) line shapes are obtained in a certain approximation and then parametrized in terms of the Fano- (or coupling or asymmetry-) parameter. The asymmetric shape is characteristic of the presence of coupling and hence cannot properly be captured with Gaussians or Lorentzians alone. Of course, the BWF profile has to be convoluted with the extrinsic contributions to yield the total line shape.
Yet another source of asymmetric line profiles are energetically unresolved inelastic events. In RAMAN spectroscopy these could be due to Stokes and anti-Stokes processes. In Photoelectron spectroscopy of metals, they could result from low energy electron hole excitations.
Summing up: one ought to study the expected line shapes in the experiment and material under scrutiny and learn how to apply them in analyzing data.
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