Effect of Selfabsorption on lineshapes:
absorption appears when light emitted by some atoms in a light source
is absorbed by atoms in the source. This effect not only reduces the
light emission, but also changes the line shape to differ from the
typical Gaussian profile. Predicting the exact emission line shape in
the presence of self absorption is quite difficult as it requires
information on the spatial distribution of the emitting and absorbing
species, including their velocity (or temperature). The effect can,
however, be illustrated by assuming a simplified model of the real
situation. If we assume the emission cell to consist of two different
layers, an inner layer emitting light and an outer layer partly
re-absorbing this light before it can reach the detector, the effect on
the line shape can be calculated rather easily using Lambert-Beers law
and the frequency dependence of the emission and absorption profiles.
The shape of the emission line IE(n) before it is affected by re-absorption, will be given by a Gaussian profile with a total line intensity of IL:
line shape of the absorbing medium will be described by the same
function. The temperature of the atoms in the absorbing medium,
however, may be different from the temperature in the emitting region.
Note that the temperature influences the line width. The line width is
proportional to the inverse of the square root of the temperature.
In order to calculate the transmission coefficient T(n,d), we apply Lambert-Beers law.
T in the above formula describes the fraction of light transmitted
while passing through the absorbing medium of thickness d. The absorption is strongest in the centre of the absorbing line and becomes smaller at frequencies away from the centre.
To calculate the transmitted light IT(n), and its line shape, we need to multiply the emission profile by the absorption profile:
the example shown in the above figure, we have assumed that the gas
temperature in the emitting region is twice the temperature in the
absorbing region. The ratio of line widths or the emitting and
absorbing light, respectively, is therefore a square root of two. For
this example, absorption coefficient was chosen just strong enough to
generate a dip the line shape of the transmitted line profile.
Depending on the strength of the absorption, the dip may be more
pronounced or not observed at all, as shown in the experimental
spectral profiles below.
of these recordings from a high resolution spectrometer show the
hyperfine doublet of the 324.75nm Cu I transition. The recording on the
left was acquired using a hollow cathode source at moderate operation
conditions, whereas the spectrum on the right was acquired using a
typical Grimm type source in end-on view. The 324.75 nm line is
obviously affected by severe self absorption in the Grimm source as can
be seen in the (misleading) dips of each of the two hyperfine
components of the electronic transition.
A different model for
the distribution of the emitting and absorbing species which can be
easily described is the homogeneous emitter absorber system. Here we
assume a constant distribution of emitting and absorbing species.
Emitting and absorbing species have the same temperature. To see the
main difference from the situation described above with distinct
emitting and absorbing areas, we calculate the effect of emission and
For this situation we can write the differential equation:
Where dI is the change in light intensity in a space interval dx. El is the linear emission density (emitted light intensity per length unit) and ka is the proportionality factor describing the portion of light intensity absorbed by a thin slice dx. The frequency dependence of ka is not specifically mentioned here.
By rearranging this equation we obtain:
Integrating this equation we find
Assuming now that I(0)=0, there is no light emitted yet at x=0. We get
increasing thickness, the intensity approaches a constant value given
by the ratio of the emission density and the absorption coefficient.
Once this limit is reached in each slice, the amount of absorbed light
equals the amount of emitted light. The transmitted light intensity
does not vary anymore.
We can now use this formula to describe the effect on the line shape.
above figure displays the effect of self-absorption by a homogenous
emitter/absorber system on the line shape. The line shape is calculated
for two strength or thickness. As the source gets (optically) thicker
the emitted intensity reaches a limit at the emission profile centre.
The profile therefore shows a flat top.
The following two graphics
summarise the effect of self absorption on the emission intensity and
the line shape in an emission cell. Here we assumed, for the two cases,
that the density of both emitters and absorbers is continuously
increased. In the first case, separated emission and absorption
regions, the intensities first increase until a clear dip in the line
centre is developed. In the second case, mixed emitters and absorber,
again the transmitted intensity first increases and then a flat top
|case 1: evolution of lineshape towards self reversal
||case 2: evolution of lineshape towards a flat top profile
discharge sources are used as light sources both effects are likely to
be present. Emitters (excited atoms or ions) are present in the same
region as the absorbers (ground state atoms or ions). Their absolute
and relative density however will vary over the entire discharge region
observed by the spectrometer. Additionally the gas temperature will not
be constant in the different discharge regions. It is therefore rather
difficult to predict the exact line shape observed by a high resolution
spectrometer. The effect of stimulated emission, necessary to make the
transition towars black body radiation, has been neglected in this
First published on the web: 09. 01. 2008.
Author: Thomas Nelis. The text resumes and extends topics presented by Prof. E.B Steers during the first
GLADNET Training course held in Antwerp, Be, in September 2007.