Zeiss LSM 880 Operating Manual page 670

Nyquisttheorem
It is known from Part 1 that the information content of the
signal is limited by the resolving power of the microscope
optics. A realistic estimate for the resolving power is the
full width at half maximum intensity (FWHM
image (see equation 3).
To avoid a loss of information during the scanning process,
it is necessary to stick to the Nyquist theorem. The optimal
pixel spacing in scanning a periodic signal, as defined by the
Nyquist theorem, is half the period of the feature spacing
to be resolved, or two pixels per resolvable structure detail.
Together with the resolving power defined above, this re-
sults in a maximum pixel spacing of d
With a two-point object (see explanation on page 18), the
pixel spacing needed to separate the two Airy discs in the
digitized image is 0.25 AU (figure 13).
Fig. 13 The graph illustrates the scanning of a two-point object
with the minimum number of sampling points needed to avoid
a loss of resolution (spacing of sampling points 0.25 AU).
1
0.8
0.6
0.4
0.2
0.25 0.5
20
) of a point
lat
= 0.5 x FWHM
pix
0.75 1 1.25 1.5
If the number of sampling points per feature size is smaller
than that given by the Nyquist theorem (undersampling),
part of the information will be lost. This is evident in
Figure 14c especially by the unresolved fine features.
A greater number of sampling points per feature size (overs-
ampling) means a greater number of readings without a
gain in information; simultaneously, the time per pixel be-
comes shorter. Thus, the volume of data to be processed is
inflated, and the noise of the measurement signal increases
(see page 22).
Under unfavorable conditions, also artefacts may result out
of the digitization process (aliasing). As a rule, this is the
case if the feature spacing in the specimen is equal, or
nearly equal, to the pixel spacing.
.
lat
AU
1.75
Fig. 14 Oversampling, correct
sampling and undersampling
of a continous signal.
a)
150
100
50
0 50 100 150
Pixels
Oversampling