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).
Geometric optical confocality
Optical slice thickness (depth discrimination) and
stray light suppression (contrast improvement) are
basic properties of a confocal LSM, even if the
pinhole diameter is not an ideal point (i.e. not infi-
nitely small). In this case, both depth discrimina-
tion and stray light suppression are determined
exclusively by PSF
det
. This alone brings an improve-
ment in the separate visibility of object details over
the conventional microscope.
Hence, the diameter of the corresponding half-
intensity area and thus the optical slice thickness
is given by:
(4)
λ
em
= emission wavelength
PH = object-side pinhole diameter [µm]
n
= refractive index of immersion liquid
NA = numerical aperture of the objective
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 for a given objective and
a given emission wavelength. The geometric-opti-
cal term (second term under the root) is dominant;
for a given objective it is influenced exclusively by
the pinhole diameter.
Likewise, in the case of geometric-optical confo-
cality, there is a linear relationship between depth
discrimination and pinhole diameter. As the pin-
hole diameter is constricted, depth discrimination
improves (i.e. the optical slice thickness decreases).
A graphical representation of equation (4) is illus-
trated in figure 9. The graph shows the geometric-
optical term alone (blue line) and the curve resul-
ting from eq. 4 (red line). The difference between
the two curves is a consequence of the wave-
optical term.
FWHM
det,axial
=
0.88 .
em
n- n
2
-NA
2
+
2 . n . PH
NA
2
2
Above a pinhole diameter of 1 AU, the influence
of diffraction effects is nearly constant and equa-
tion (4) is a good approximation to describe the
depth discrimination. The interaction between
PSF
ill
and PSF
det
becomes manifest only with pin-
hole diameters smaller than 1 AU.
Let it be emphasized that in case of geometric
optical confocality the diameters of the half-inten-
sity area of PSF
det
allow no statement about the
separate visibility of object details in axial and
lateral direction.
In the region of the optical section (FWHM
det,axial
),
object details are resolved (imaged separately) only
unless they are spaced not closer than described
by equations (2) / (2a) / (3).
Pinhole diameter [AU]
FWHM [R
U]
1.2
1.48 1.76
2.04 2.32 2.6
2.88 3.16 3.44
3.72
4.0
0
0.7
1.4
2.1
2.8
3.5
4.2
4.9
5.6
6.3
7.0
11
Optical Image Formation
Part 1
(4)
337_Zeiss_Grundlagen_e 25.09.2003 16:16 Uhr Seite 14
