Zeiss LSM 880 Operating Manual page 213

LSM 880
D. Diffusion terms
Diffusion is driven by Brownian motion. We can distinguish translational, rotational and flow diffusion.
D.1 Rotational diffusion
In the most general form, rotation can be described as the sum of 5 exponential terms
5
∑
t
= − + ⋅
g ( ) 1 R R c
r a a
=
m 1
with R being the amplitude, c
a
diffusion time.
However, there are special cases that are of more use.
In symmetric rotation, the general formula reduces to:
t
−
t
= 1 − + ⋅
G ( ) R R e
r a a
t
−
t
⋅
R e
r
t
= + normalized
a
G ( ) 1
r −
1 R
a
being the rotational amplitude and t
with R
a
and t
R are both fit parameters.
a r
If rotation occurs dependent from other processes, the formula used as an additive term is defined as:
t
−
t
t = ⋅
G ( ) R e
r
r a
R in this case is either a fit parameter or a fixed value and often takes the value 4/5.
a
In case of asymmetric rotation, the term is as follows:
t
= − + ⋅
G ( ) 1 R R ( c
r a a 1
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− ⋅ t t
⋅ r /
m r , m
e
m
the relative amplitude, r
m
t
not normalized
r
⋅ t ⋅ t
r r
− −
1 2
t t
⋅ + ⋅
r 1 , r 2 ,
e c e )
2
000000-2071-464
the frequency factor and t
m
the rotational diffusion time.
r
not normalized
ZEISS
(8a)
the rotational
r,m
(8b)
(8c)
(8d)
(8e)
207