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Generalized Lorentzian approximations for the Voigt line shape.
Applied Optics
|March 24, 2010
Summary
Researchers developed a simple Padé approximation for the Voigt function. This generalized Lorentzian approximation offers an easier calculation for experiments not needing high precision.
Area of Science:
- Computational physics
- Spectroscopy
- Applied mathematics
Background:
- The Voigt function is crucial in spectroscopy for modeling spectral line shapes.
- Accurate calculation of the Voigt function can be computationally intensive.
- Approximations are needed for practical applications where high precision is not critical.
Purpose of the Study:
- To develop a computationally simple and accurate approximation for the Voigt function.
- To utilize the Padé method for approximating the complex Voigt function.
- To provide a viable alternative to the exact Voigt function in specific experimental contexts.
Main Methods:
- Calculation of the multipole approximation to the complex Voigt function.
- Expressing the approximation in terms of the error function and plasma dispersion function.
- Employing the Padé approximant technique.
Main Results:
- A simplified, easy-to-calculate approximation to the Voigt function was derived.
- The approximation is a generalized Lorentzian function.
- The derived approximation demonstrates utility in experimental settings.
Conclusions:
- The Padé approximation provides a practical alternative to the exact Voigt function.
- This method simplifies calculations in experiments where high accuracy is not paramount.
- The generalized Lorentzian approximation is suitable for various spectroscopic applications.
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