13
From equations (7) and (7a) it is evident that depth
resolution varies linearly with the refractive index
n
of the immersion liquid and with the square of the
inverse value of the numerical aperture of the
objective
{
NA = n
· sin(
α
)}.
To achieve high depth discrimination, it is impor-
tant, above all, to use objectives with the highest
possible numerical aperture.
As an NA > 1 can only be obtained with an immer-
sion liquid, confocal fluorescence microscopy is
usually performed with immersion objectives (see
also figure 11).
A comparison of the results stated before shows
that axial and lateral resolution in the limit of
PH = 0 can be improved by a factor of 1.4. Further-
more it should be noted that, because of the
wave-optical relationships discussed, the optical
performance of a confocal LSM cannot be
enhanced infinitely. Equations (7) and (8) supply
the minimum possible slice thickness and the best
possible resolution, respectively.
From the applications point of view, the case of
strictly wave-optical confocality (PH = 0) is irrele-
vant (see also Part 2).
By merely changing the factors in equations (7)
and (8) it is possible, though, to transfer the equa-
tions derived for PH = 0 to the pinhole diameter
range up to 1 AU, to a good approximation. The
factors applicable to particular pinhole diameters
can be taken from figure 10.
It must also be noted that with PH <1 AU, a dis-
tinction between optical slice thickness and resolu-
tion can no longer be made. The thickness of the
optical slice at the same time specifies the resolu-
tion properties of the system. That is why in the
literature the term of depth resolution is frequently
used as a synonym for depth discrimination or
optical slice thickness. However, this is only correct
for pinhole diameters smaller than 1 AU.
axial
lateral
To conclude the observations about resolution and
depth discrimination (or depth resolution), the
table on page 15 provides an overview of the for-
mulary relationships developed in Part 1. In addi-
tion, figure 11a shows the overall curve of optical
slice thickness for a microscope objective of
NA = 1.3 and n = 1.52 (
λ
= 496 nm).
In figure 11b-d, equation (7) is plotted for
different objects and varied parameters (NA,
λ
, n).
Fig. 10 Theoretical factors for equations (7) and (8),
with pinhole diameters between 0 and 1 AU.
Optical Image Formation
Part 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pinhole diameter [AU]
Factor
0.30
0.45
0.40
0.35
0.50
0.60
0.55
0.65
0.70
0.75
0.80
0.85
337_Zeiss_Grundlagen_e 25.09.2003 16:16 Uhr Seite 16
