Chemistry Reference
In-Depth Information
three-dimensional function but in TIRF microscopy at the focal plane, variations
along the optical axis are not relevant. The theoretical PSF for a well-focused
individual
fluorophore is an Airy disk, similar to a two-dimensional Gaussian
shape, as described earlier. At visible optical wavelengths and with a high-aperture,
well-corrected objective lens, the full width at half-intensity of the PSF is
250 nm.
This value sets the classical lower limit of spatial resolution in optical microscopy
for resolving nearby objects. When two objects are closer than this distance, their
emission distributions overlap and they appear fused.
An additional piece of information about the object, however, can enable its
location to be determinedmuchmore precisely than 250 nm. If the object is known to
be a single sub-resolution emitter, such as a single
fluorescent probe, then its lateral
(x
-
y) location can be determined from the detected distribution of emission intensity
with precision considerably less than classical resolution and less than the pixel size.
This idea has become known as Fluorescence Imaging to One Nanometer Accuracy
(FIONA). For an optically well-corrected image of an in-focus or unpolarized point
emitter, the center of the recorded intensity distribution corresponds to the physical
position of the probe at sub-pixel resolution. Several groups utilized this idea to
localize
fluorescent spots to within tens of nm [31, 32] and P. R. Selvin and colleagues
first achieved precision of 1
-
2 nm [27]. FIONA and its derivatives have been reviewed
in [33].
The theoretical uncertainty,
s
m
, of position in a FIONA experiment is given
approximately by [32]
s
s
i
þ
s
i
b
2
a
2
N
2
a
2
=
12
8
p
s
m
i
¼
þ
ð
3
:
4
Þ
N
where the index i refers to the x or y direction, si
i
is the width (standard deviation)
of the image intensity distribution in direction i, N is the number of collected
photons, b is the standard deviation of the background, including photon
counting statistics and camera readout noise, and a is the pixel size of the
imaging detector. The
rst term (s
i
=
N) is the photon noise; the second term is the
effect of the
finite detector pixel size of the detector; and the last term is the effect
of the background. This relation assumes that other sources of error, such as
mechanical vibrations and thermal drift in the microscope are negligible. As can
be seen from this expression, when the pixel size, a, becomes smaller than s
x
and
s
y
, the effect of pixelation on position uncertainty is small. Practical values of the
pixel size for s
x
, s
y
¼
120 nm are 75
-
150 nm referred to as the sample plane. For a
camera with 13-
m square pixels, this situation corresponds to overall magnifi-
-
cation of 80
-
170. Figure 3.5A shows how the expected uncertainty (standard
deviation,
m
s
m
) in determination of position decreases as the number of photons is
increased in a practical situation with 0.5-s image integration, s.d. of the
background b
¼
11
-
33 per pixel, and effective pixel size of a
¼
86 or 43 nm [27].
With the lower background, a precision of
1.5 nm is reached when the image
accumulates 11 000 photoelectron counts. In this condition, 80% of the uncer-
s
m
¼
