### line shape function

(function describing the shape of a spectral line)

A **line shape function** is a (mathematical) function
that models the shape of a spectral line
(the **line shape** or **spectral line shape** or **line profile**).
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.
For example, a source of line broadening is Doppler broadening
due to movement of particles emitting or absorbing,
which temperature contributes to.
By mathematically modeling each such factor (each with
its own characteristic *line shape function*),
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 one technique to make such models
tractable given some situations.

A Voigt profile is a model line-shape created by
the combination of model line-shapes of two
broadening mechanisms:
a Gaussian function for Doppler broadening
and a **Lorentzian function** for **pressure broadening**.
The combined line shape function is a convolution
of mathematical functions for each, but
a linear combination of the two serves as an approximation.

(*spectrography,EMR,function,lines*)
**Further reading:**

http://en.wikipedia.org/wiki/Spectral_line_shape

http://www.sjsu.edu/faculty/watkins/lineshape.htm

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