Teledyne LeCroy AORM - Advanced Optical Recording Measurements - Manual (Page 39)

AORM Software Package
923133 Rev A ISSUED: June 2013
37
BESS BEGINNING EDGE SHIFT SIGMA
Description
BESS provides a measurement of the mean, normalized standard deviation of the Beginning
Edge Shift measurements (see BES). When a single n is specified, or when you are in ‘nT Table’
Show
mode, the value calculated for the n th index is calculated using the following equation for
standard deviation:
Beginning Edge Shift Sigma cannot be calculated for a given index n unless there are at least two
Beginning Edge Shift values calculated or that n index.
When Beginning Edge Shift is configured as a custom parameter with a range of n, the value
calculated is the standard deviation of the distribution that results by normalizing each independent
distribution categorized by the space (pit) nT preceding the subject pit (space). Distributions are
normalized by subtracting the mean of the distribution from all of the elements in the distribution. This
results in the following equation for overall Beginning Edge Shift Sigma resulting from the individually
categorized Beginning Edge Shift Sigma values:
( ) ( )
BESS
BESS N
N
overall
n n
n
1
1
2
=
⋅ −
−
∑
∑
Note: The value calculated by BESS will generally not be the same as the sigma of the BES measurement displayed on
the parameter line when a range of n is used and statistics is on. This is because the two measurements are not the
same. The BESS measurement normalizes the results for each n by subtracting the mean BES from each BES in the n
th
distribution. This results in a superposition of mean-centered distributions, not a superposition of 0-centered distributions
contributing to BES measurements. BESS will always be less than or equal to the standard deviation of BES
measurements.
( )
( )
BESS
BESS
BES
BES
N
N
n
n
n
n
n
n
1
2
2
=
=
−
−
∑
∑
σ
BES
n