Zeiss LSM 880 Operating Manual page 663

seite 7
.
PSF (x,y,z) = PSF (x,y,z)
tot ill
seite 9
0.88 .
exc
FWHM =
Geometricopticalconfocality
ill,axial
(n- n 2 -NA 2 )
Optical slice thickness (depth discrimination) and stray light
suppression (contrast improvement) are basic properties of
1.77 . n .
a confocal LSM, even if the pinhole diameter is not an
2
NA
ideal point (i.e. not infinitely small). In this case, both depth
discrimination and stray light suppression are determined
exclusively by PSF . This alone brings an improvement in
det
exc
FWHM = 0.51
the separate visibility of object details over the conventional
ill,lateral
NA
microscope.
Hence, the diameter of the corresponding half-intensity
area and thus the optical slice thickness is given by:
seite 11
0.88 .
FWHM =
det,axial
n- n
λ
= emission wavelength
em
PH = object-side pinhole diameter [µm]
= refractive index of immersion liquid
n
NA = numerical aperture of the objective
seite 12
Equation (4) shows that the optical slice thickness comprises
a geometric-optical and a wave-optical term. The wave-
optical term (first term under the root) is of constant value
(
PSF (x,y,z) = PSF (x,y,z)
tot ill
for a given objective and a given emission wavelength.
The geometric-optical term (second term under the root)
is dominant; for a given objective lens it is influenced ex-
.
clusively by the pinhole diameter.
em exc
2
2 2
+
exc em
0.64 .
FWHM =
tot,axial
2 2
(n- n -NA )
FWHM = 0.37
tot,lateral
NA
Fig.9 Optical slice thickness as a function of the pinhole diameter
(red line). Parameters: NA = 0.6; n = 1; λ = 520 nm.
The X axis is dimensioned in Airy units, the Y axis (slice thickness)
in Rayleigh units (see also: Details "Optical Coordinates").
In addition, the geometric-optical term in equation 4 is shown
separately (blue line).
PSF (x,y,z)
det
exc
2 2
2 . n . PH
(4)
em +
NA
2 2
-NA
) 2
1.28 . n .
OpticalImageFormation
Likewise, in the case of geometric-optical confocality, there
is a linear relationship between depth discrimination and
pinhole diameter. As the pinhole diameter is constricted,
depth discrimination improves (i.e. the optical slice thick-
ness decreases). A graphical representation of equation (4)
is illustrated in figure 9. The graph shows the geometric-
optical term alone (blue line) and the curve resulting from
eq. 4 (red line). The difference between the two curves is
a consequence of the waveoptical term.
Above a pinhole diameter of 1 AU, the influence of diffrac-
tion effects is nearly constant and equation (4) is a good
approximation to describe the depth discrimination. The
interaction between PSF
ill
with pinhole diameters smaller than 1 AU.
Let it be emphasized that in case of geometric optical con-
focality the diameters of the half-inten sity area of PSF
allow no statement about the separate visibility of object
details in axial and lateral direction.
In the region of the optical section (FWHM
details are resolved (imaged separately) only unless they are
spaced not closer than described by equations (2) / (2a) / (3).
7.0
6.3
5.6
4.9
NA 2
4.2
3.5
2.8
2.1
1.4
0.7
0
1.2 1.48 1.76 2.04 2.32 2.6
and PSF becomes manifest only
det
), object
det,axial
2.88 3.16 3.44 3.72
Pinhole diameter [AU]
PART 1
det
4.0
13