22
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 resolu-
tion probability, down to the level of indetermi-
nateness (
≤
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 proba-
bility towards 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).
The pinhole diameter selected in practice will
therefore always be a trade-off between two qual-
ity 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 fluores-
cence) to pass to the detector.
Where fluorescence intensities are low, it may be
sensible to accept less than optimum depth dis-
crimination so as to obtain a higher signal level
(higher intensity of detected light = less noise, bet-
ter SNR). For most fluorescent applications a pin-
hole diameter of about 1 AU has turned out to be
the best compromise.
Fig. 17 The graph shows the computed resolution
probability 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 raster spacing = 0.25 AU); the rasterized image
is subjected to interpolation. The photoelectron count per
point object is approximately twice that per pixel (referred
to the pixel at the center of the Airy disk). Each curve has
been fitted to a fixed number of discrete values, with each
value computed from 200 experiments.
The resolution probability is the quotient between successful
experiments (resolved) and the total number of experiments.
A resolution probability of 70% means that 7 out of 10
experiments lead to resolved structures. 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 mole-
cules (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.
Resolution
probability
Pinhole
size [AU]
0.25
0.5
0.75
1
1.25
1.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
100e-
30e-
50e-
20e-
10e-
6e-
3e-
2e-
4e-
337_Zeiss_Grundlagen_e 25.09.2003 16:16 Uhr Seite 25
