FWHM
tot,lateral
= 0.37
NA
FWHM
tot,axial
=
0.64 .
(n- n
2
-NA
2
)
≈
1.28 . n .
NA
2
Thus, equations (2) and (3) for the widths of the
axial and lateral half-intensity areas are trans-
formed into:
Axial:
If NA < 0.5, equation (7) can be approximated by
Lateral:
PSF
tot
(x,y,z) =
(
PSF
ill
(x,y,z)
)
2
Wave-optical confocality
If the pinhole is closed down to a diameter of
< 0.25 AU (virtually “infinitely small”), the charac-
ter of the image changes. Additional diffraction
effects at the pinhole have to be taken into
account, and PSF
det
(optical slice thickness) shrinks
to the order of magnitude of PSF
ill
(Z resolution)
(see also figure 7c).
In order to achieve simple formulae for the range
of smallest pinhole diameters, it is practical to
regard the limit of PH = 0 at first, even though it is
of no practical use. In this case, PSF
det
and PSF
ill
are identical.
The total PSF can be written as
In fluorescence applications it is furthermore
necessary to consider both the excitation wave-
length
λ
exc
and the emission wavelength
λ
em
. This
is done by specifying a mean wavelength
1
:
(6)
1
For rough estimates, the expression
λ
≈ √
λ
em
·
λ
exc
suffices.
em
.
exc
2
exc
+
2
em
≈
2
12
Note:
With the object being a mirror, the factor in
equation 7 is 0.45 (instead of 0.64), and 0.88
(instead of 1.28) in equation 7a. For a fluores-
cent plane of finite thickness, a factor of 0.7
can be used in equation 7. This underlines
that apart from the factors influencing the
optical slice thickness, the type of specimen
also affects the measurement result.
(6)
(5)
(7)
(7a)
(8)
337_Zeiss_Grundlagen_e 25.09.2003 16:16 Uhr Seite 15
