User guide

LBA-USB User Guide Document No: 11294 Page 101
4.13 Gauss Fit
LBA-USB can perform a least squares bivariate normal equation (Gaussian equation) fit
using all of the data when doing a Whole beam fit. Or it can perform two univariate
normal equation fits using orthogonal Lines of data through the Centroid Location.
With the Elliptical results disabled, the Gaussian fitter may be set to Disabled, Whole
Beam, or X/Y aligned.
With the Elliptical results enabled, the choices are Disabled, Whole Beam, or
Major/Minor aligned.
The Gauss Fit results are displayed as follows:
Whole Beam Fits Line Fits Are X/Y or Major/Minor aligned
Centroid X,Y Centroid X or Major Centroid Y or Minor
Width X,Y Width X or Major Width Y or Minor
Height Height X or Major Height Y or Minor
Deviation Deviation X or Major Deviation Y or Minor
Correlation Correlation X or Major Correlation Y or Minor
The Centroid Major value is the distance from the fitted Major axis centroid to the
origin axis, which is most perpendicular to the Major axis. The Centroid Minor value
is the distance from the fitted Minor axis centroid to the origin axis, which is most
perpendicular to the Minor axis. At 45° the Centroid Major value is the distance to
the X-axis and the Centroid Minor is the distance to the Y-axis.
Whole beam fits are always X and Y aligned.
Line fits can be either X/Y aligned where the fits will be performed upon the data in
the X & Y directions passing through the Centroid. Or the fits can be Major/Minor axes
aligned with the fits performed upon the data on the Major and Minor axes passing
through the Centroid.
All fits are least square fits, meaning that the algorithm minimizes the sum of the square
of the differences between the data and the fitted surface or line, as described in the
following equation.
(
)
∑
∑
−=
xy
xyxy
SZA
2
min
Where: Z
xy
= Amplitude of the pixel data at (x,y)
S
xy
= Amplitude of fitted surface at (x,y)