Zeiss LSM 880 Operating Manual page 215

LSM 880
D.2 Translational diffusion
In its general form, translational diffusion is defined as:





3
∑
t
=

G ( )
d

=
i 1



 t
+

1

t



 d , i

with t
representing the diffusional correlation time of molecule species i, S the structural parameter that
d,i
is the ratio of axial to lateral focus radii, α
species I, e , e fixed exponentials to define dimensionality of diffusion (1-D: e
d1 d2
e =0; 3-D: e =1; e =1)
d2 d1 d2
e and e are fixed values and have to be user defined. The following values define 1-, 2-and 3-D
d1 d2
diffusion:
e e dimensionality
d1 d2
1/2 0 1-D
1 0 2-D
1 1 3-D
Note that in the FCS software these values are automatically selected with the choice of dimensionality.
S is either a fit parameter or a fixed value. It is an instrumental parameter and can be determined by a
calibration experiment using a dye solution with a known diffusion as a fit result.
α
is either a fitted value for anomalous diffusion or a fixed value (set to "1") for free diffusion. The
i
following relation exists
α Diffusion process
=1 Free diffusion
<1 Anomalous sub-diffusion
>1 Anomalous super-diffusion
Note that α
is set automatically to "1", if free diffusion is selected. If anomalous diffusion is selected, the
i
parameter will float.
10/2014 V_01
CHAPTER 1 - SYSTEM OPERATION
Left Tool Area and Hardware Control Tools
Φ
i

e
α α
 

d 1
  
i i
  t
⋅ +
   
1
t
 
  

 
d , i

the anomaly parameter or temporal component of molecule
i
000000-2071-464





with the constraint

e


d 2
1


2


⋅
1 


2
S 




ZEISS
∑
(8g)
Φ =
1
i
i
=1/2; e =0; 2-D: e
d1 d2
=1;
d1
209