Apr-09
69
Avantes
www.avantes.com
Setup Menu: Smoothing and Spline
The Cubic Spline Interpolation Algorithm can be
applied to get a better estimation for the spectral data
between the pixels on the detector array.
Smoothing is a procedure, which averages the spectral
data over a number of pixels on the detector array.
For example, if the smoothing parameter is set to 2,
the spectral data for all pixels x
n
on the detector array
will be averaged with their neighbor pixels x
n-2
, x
n-1
,
x
n+1
and x
n+2
.
Cubic Spline Interpolation
In the figure at the right, the
effect of spline interpolation is
illustrated. The Master data shows
the AD counts for 4 pixels,
connected by a straight line
(linear interpolation). The Slave1
data is for these 4 pixels exactly
the same as for the Master data,
but this time the cubic spline
interpolation algorithm has been
applied, resulting in data which is
smooth in the first derivative and
continuous in the second
derivative.
The spline interpolation can be
useful for applications in which
the output of line sources, like
laser diodes is displayed, or for
other applications, which require a high resolution. Note that for the AvaSpec-2048 with 2048 pixels,
the effect of spline interpolation is not visible if the data is shown at full scale. The monitor
resolution is much less than 2048 pixels. The effect of spline interpolation can only be visualized if
the number of detector pixels that are displayed is smaller than the number of monitor pixels at the
x-axis.
Smoothing
To get a smoother spectrum without losing information it is important to set in the software the
right smoothing parameter. The optimal smoothing parameter depends on the distance between the
pixels at the detector array and the light beam that enters the spectrometer. For the AvaSpec-2048,
the distance between the pixels on the CCD-array is 14 micron.
With a 200 micron fiber (no slit installed) connected, the optical pixel resolution is about 14.3 CCD-
pixels. With a smoothing parameter set to 7, each pixel will be averaged with 7 left and 7 right
neighbor pixels. Averaging over 15 pixels with a pitch distance between the CCD pixels of 14 micron
will cover 15*14 = 210 micron at the CCD array. Using a fiber diameter of 200 micron means that we
will lose resolution when setting the smoothing parameter to 7. Theoretically the optimal smoothing
parameter is therefore 6.
The formula is ((slit size/pixel size)
– 1)/2
In the table below, the recommended smoothing values for the AvaSpecs spectrometer are listed as
function of the light beam that enters the spectrometer. This light beam is the fiber core diameter,
or if a smaller slit has been installed in the spectrometer, the slit width. Note that this table shows
