decreasing importance: 
a) Diffraction loss . The media and the spec- 
imen exhibit inhomogeneous refraction indi- 
ces, this introduces an elongation of the focal 
spot (spherical aberration). Combined with 
the illumination and registration process, this 
leads to a massive light loss in thick 
specimen, rendering sound observation 
almost impossible. 
b) Fluorophore decay (photobleaching). Bach 
fluorophore has a specific mean-excitation 
lifetime, i.e. it shows a probability p to be 
destroyed by an excitation process. 
c) Aperture function of the microscope. A 
scanned voxel does not represent a cubic 
area of space over which the light flux has 
been integrated (scanned). It is a complicated 
and geometrically extended structure from 
which the light has been gathered. 
Mathematically this ‘resolution function’ is 
referred to as the point spread function (PSF) 
8(x,y,z). It describes how the instrument 
accumulates its samples. The response I' for 
an original intensity I at a specific coordinate 
(x,y,z) is 
rz) fepe t3 9 nva dxdya: 
; 
d) Light scattering in the specimen. Solid 
particles bend the light flux both for 
irradiation and emission. This has exactly the 
same effects as the spherical aberration 
discussed in a). 
e) Attenuation. Specimens are not perfectly 
transparent, they consume a certain amount 
of light due to cross-excitation and thermal 
oscillation. The resulting effect is the same 
as a) and d). 
f) Excitation loss. Irradiated light is absorbed 
by fluorophores during excitation. This 
means that areas behind bright zones appear 
darker. The influence is related to a), d) and 
e). 
The orders of magnitude in falsification of 
the final results vary considerably between the 
different effects. With 20 um thick specimen 
slices a) may cause for the deepest layer a loss 
of up to 75% of the total light. In a standard 
setup b) is less destructive. For a large number 
of layers it may consume an unlimited fraction 
of the efficiency (e.g. more than 80% for a stack 
of 100 slices). c) is harmful especially for fine 
structures, but as a rule of thumb it is 
proportional to the oversampling. d) and e) are 
difficult to separate from a) and b), but are 
reported to be less than 10% for 20um and 
about 2:107 - zoom factor of objective, (20% for 
a 100x objective). Finally f) is less than 5% 
even for extended and bright volumes under 
observation. 
Note that a) and d) have no meaning at all 
for non-confocal arrangements, b) almost none, 
c) is much simpler and of inferior magnitude, 
whereas e) and f) remain unchanged. This 
explains the much better quantification behavior 
of 2D fluorescence microscopy. 
All these effects which degrade the 
quantification process can be accounted for, if 
they are precisely determined. A general 
reconstruction scheme may be pseudo-coded as 
follows: 
Read specimen data 
(attenuation, scatter, refraction mean & 
variance) 
Read fluorophore data 
(photoefficiency, bleach, wavelength) 
Read instrument data 
(sensitivity, NA, PSF) 
ResetCounters 
(scatter, attenuation, bleach, excitation) 
FOR each layer DO 
GetLocalData 
316 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
  
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