Zeiss LSM 880, Operating Manual

Page: 673 / 690

Resolutionandshotnoise–
resolutionprobability
If the number of photons detected (N) is below 1000, fluo-
rescence 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 contingent on random
events (the random incidence of photons on the detector),
and the gain in resolution obtainable by pinhole constriction
is determined 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 statistics, degrade normally re-
solvable object details in such a way that they are not re-
solved every time in repeated measurements. On the other
hand, objects just outside optical resolvability may appear
resolved because of noise patterns modulated 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 understanding of image formation in the
confocal microscope (PSF) with the influences of shot noise
of the detected light and the scanning and digitization of
the object. The essential criterion is the discernability of
object details.
23
Figure 17 (page 24) shows the dependence of the resolu-
tion 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 sen sible.]
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 num-
ber of photoelectrons obtained from a point object in this
case is about twice the number of photoelectrons 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 tech-
niques (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.
Power
Power
Photon
arrivals
Time
Time
Time
PART 2
SignalProcessing