21
Resolution and shot noise –
resolution probability
If the number of photons detected (N) is below
1000, fluorescence emission should be treated as
a stochastic rather than a continuous process; it is
necessary, via the shot noise, to take the quantum
nature of light into account (the light flux is
regarded as a photon flux, with a photon having
the energy E = h
⋅ν
). Resolution becomes contin-
gent on random events (the random incidence of
photons on the detector), and the gain in resolu-
tion obtainable by pinhole constriction is deter-
mined by the given noise level. Figure 16 will help
to understand the quantum nature of light.
As a possible consequence of the shot noise of the
detected light, it may happen, for example, that
noise patterns that change because of photon sta-
tistics, degrade normally resolvable object details
in such a way that they are not resolved every time
in repeated measurements. On the other hand,
objects just outside optical resolvability may
appear resolved because of noise patterns modu-
lated on them. Resolution of the “correct” object
structure is the more probable the less noise is
involved, i.e. the more photons contribute to the
formation of the image.
Therefore, it makes sense to talk of resolution
probability rather than of resolution. Consider a
model which combines the purely optical under-
standing of image formation in the confocal
microscope (PSF) with the influences of shot noise
of the detected light and the scanning and digiti-
zation of the object. The essential criterion is the
discernability of object details.
Figure 17 (page 22) shows the dependence of the
resolution probability on signal level and pinhole
diameter by the example of a two-point object
and for different numbers of photoelectrons per
point object. [As the image of a point object is
covered by a raster of pixels, a normalization
based on pixels does not appear sensible.]
Thus, a number of 100 photoelectrons/point
object means that the point object emits as many
photons within the sampling time as to result in
100 photoelectrons behind the light-sensitive
detector target (PMT cathode). The number of
photoelectrons obtained from a point object in
this case is about twice the number of photoelec-
trons at the maximum pixel (pixel at the center of
the Airy disk). With photoelectrons as a unit, the
model is independent of the sensitivity and noise
of the detector and of detection techniques
(absolute integration time / point sampling / signal
averaging). The only quantity looked at is the
number of detected photons.
Fig. 16 The quantum nature of light can be made visible in two ways:
• by reducing the intensity down to the order of single photons and
• by shortening the observation time at constant intensity, illustrated
in the graph below: The individual photons of the light flux can be
resolved in their irregular (statistical) succession.
Signal Processing
Part 2
Photon
arrivals
Power
Power
Time
Time
Time
337_Zeiss_Grundlagen_e 25.09.2003 16:16 Uhr Seite 24
