### line shape function

(function describing the shape of a spectral line)

A **line shape function** is a function
describing the shape of an absorption line
(the **line shape** or **spectral line shape** or **line profile**).
Characteristics of the source (such as temperature) and of the
medium through which the electromagnetic radiation passes give the spectral line
width (i.e., prevent it from being infinitely thin,
e.g., through Doppler shifts from the
movement of the particles from which the EMR was emitted,
Doppler broadening).
The specific shape of the line, i.e., the intensity at each
wavelength along the width of the line, is determined
by characteristics of the source and the medium.
By mathematically modeling the factors, the shape of
a line given a set of circumstances can be derived,
and conversely, an observed line of that shape can
reveal the characteristics, or if more than one set
of characteristics could create the shape, then
constraints on the characteristics.

The Sobolev approximation is an ingredient to make
it tractable to model Line Shape Functions of sufficient accuracy
for a particular purpose.

A Voigt profile is a line shape created by
the combination of two broadening mechanisms, one a
Gaussian function (such as for Doppler broadening)
and the other Lorentzian (as per **pressure broadening**).
The corresponding mathematical
line shape function is a convolution of mathematical functions for each,
or for an approximation, a linear combination of the two.

(*spectrography,EMR,function,lines*)
http://en.wikipedia.org/wiki/Spectral_line_shape

http://www4.ncsu.edu/~franzen/public_html/CH433/workshop/lineshape/lineshape.html

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