A.
Fitting Functions
Figure A.3.: The function
sech
(
t
)
2
and its normalized autocorrelation
3csch
(
τ
)
3
(
τ
cosh
(
τ
)
−
sinh
(
τ
)
(dotted line)
Equating the normalized functions with
1
2
gives the time value at half amplitude.
S
(
a
) =
1
2
⇒
a
=
0
.
881374
(A.12)
L
ACF
(
b
)
3
4
=
1
2
⇒
b
=
1
.
35979
(A.13)
The quotient of these time values supplies the transformation factor between the pulse width and
the FWHM value of its autocorrelation function.
a
b
=
0
.
648
(A.14)
Pulse
Scout2 Version 1.1
50
July 2015
