Zeiss LSM 880 Operating Manual page 674

A resolution probability of 90% is considered ne cessary for
resolving the two point images. Accordingly, the two-point
object defined above can only be resolved if each point
produces at least about 25 photoelectrons. With pinhole
diameters smaller than 0.25 AU, the drastic increase in shot
noise (decreasing intensity of the detected light) will in any
case lead to a manifest drop in resolution probability, down
to the level of indeterminateness (≤ 50% probability) at
PH = 0.
As another consequence of shot noise, the curve maximum
shifts toward greater pinhole diameters as the number of
photoelectrons drops.
The general slight reduction of resolution probability to-
wards greater pinhole diameters is caused by the decreasing
effectiveness of the pinhole (with regard to suppression of
out-of-focus object regions, see Part 1).
Resolution
probability
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.25 0.5
24
0.75 1 1.25
The pinhole diameter selected in practice will therefore al-
ways be a trade-off between two quality parameters: noise
(SNR as a function of the intensity of the detected light)
and resolution (or depth discrimination). The pinhole always
needs a certain minimum aperture to allow a minimum of
radiation (depending on the intensity of fluorescence) to
pass to the detector.
Where fluorescence intensities are low, it may be sensible
to accept less than optimum depth discrimination so as to
obtain a higher signal level (higher intensity of detected light
= less noise, better SNR). For most fluorescent applications
a pinhole diameter of about 1 AU has turned out to be the
best compromise.
Fig. 17 The graph shows the computed resolution prob-
ability of two self-luminous points (fluorescence objects)
spaced at 1/2 AU, as a function of pinhole size and for
various photoelectron counts per point object (e-).
The image raster conforms to the Nyquist theorem (critical
100e-
raster spacing = 0.25 AU); the rasterized image is subjected
50e-
to interpolation. The photoelectron count per point object
is approximately twice that per pixel (referred to the pixel
30e-
at the center of the Airy disk). Each curve has been fitted
to a fixed number of discrete values, with each value
20e-
computed from 200 experiments.
10e-
6e-
The resolution probability is the quotient between suc-
cessful experiments (resolved) and the total number of
4e-
experiments. A resolution probability of 70% means that 7
3e-
out of 10 experiments lead to resolved structures.
2e-
A probability > 90% is imperative for lending certainty
to the assumption that the features are resolved. If we
assume a point-like fluorescence object containing 8 FITC
fluorescence molecules (fluorochrome concentration of
about 1 nMol) a laser power of 100 µW in the pupil and
an objective NA of 1.2 (n = 1.33), the result is about 45
photoelectrons / point object on the detection side.
Pinhole
1.5
size [AU]