Voigtprofilen

Voigtprofilen, also known as Voigt profiles, are mathematical functions used to describe the shape of spectral lines in spectroscopy. They are named after the German physicist Woldemar Voigt, who first derived the formula in 1912. The Voigt profile is a convolution of a Gaussian function, which represents the Doppler broadening of spectral lines, and a Lorentzian function, which represents the pressure broadening. This combination allows the Voigt profile to accurately model the broadening effects that occur in real-world spectra.

The Voigt profile is particularly useful in astrophysics, where it is used to analyze the spectra of stars and other celestial objects. By fitting Voigt profiles to observed spectral lines, astronomers can determine the physical properties of these objects, such as their temperature, density, and composition. The Voigt profile is also used in other fields of spectroscopy, including atomic and molecular physics, and laser spectroscopy.

The Voigt profile is defined by two parameters: the Gaussian width, which is related to the temperature of the gas, and the Lorentzian width, which is related to the pressure and collision rates. The shape of the Voigt profile depends on the relative magnitudes of these two parameters. When the Gaussian width is much larger than the Lorentzian width, the Voigt profile resembles a Gaussian function. Conversely, when the Lorentzian width is much larger, the Voigt profile resembles a Lorentzian function. In the intermediate case, the Voigt profile has a characteristic asymmetric shape with a broad wing on one side and a sharp peak on the other.

Despite its usefulness, the Voigt profile has some limitations. The convolution of the Gaussian and Lorentzian functions does not have an analytic form, which makes it difficult to work with mathematically. Instead, the Voigt profile is typically evaluated using numerical methods or approximate formulas. Additionally, the Voigt profile assumes that the broadening mechanisms are independent and that the spectral line is isolated from other lines. In practice, these assumptions may not hold, which can lead to errors in the analysis of spectral data.