Bomem-GRAMS User's Guide

APPENDIX A
APODIZATION FUNCTIONS
A.1 Purpose
Bomem-GRAMS uses apodization functions to correct the Fourier transform
process for artifacts that are introduced by the abrupt truncation of
the interferogram when the instrument reaches the limit of its scan. Apodization,
or “foot removal” consists of multiplying the interferogram by a function that
causes its intensity to fall smoothly to zero at its ends. This reduces the feet
(side lobes) of the interferogram, thus reducing the artifacts. However, it also
increases the line width (degrades the resolution) of the spectrum.
Bomem-GRAMS offers a large selection of apodization functions. However, we
recommend that you use the cosine function as a general-purpose apodization
function.
A.2 Functions
available in
Bomem-GRAMS
The following table lists all the apodization functions available in the Bomem-
GRAMS acquisition interface and gives a brief description of how they affect
the spectrum.
FWHH: (Full Width Half Height) is the theoretical width of a monochromatic
line at half its peak height compared with the apodized resolution
requested, in percentage.
SLAM: (Side Lobe Amplitude Maximum) is the theoretical amplitude of
the largest side lobe compared with the amplitude of the main peak, in
percentage.
D: is given by
Optical _ path _ difference
maximum_optical_path_difference
Name and description Function FWH
H (%)
Boxcar
No apodization. Side lobes diminish as 1/x.
Line shape given by sinc x
Bartlett (triangular)
Triangular function; all side lobes positive,
side lobes damped out as 1/x 2 ; intermediate
half width. Line shape given by sinc 2 x
1 60 20
( 1 − D)
89 4.5
SLAM
(%)
Bomem-GRAMS User's Guide 31