Fluorescence Phase Microscopy (FPM) and Nanoscopy - Biomedical Optical Phase Microscopy and Nanoscopy - page 378

with high precision, thereby enabling the precise localization of the source along the z axis.
In general, the axial localization precision is determined by the detected signal-to-noise
ratio (SNR) and roughly increases inversely with its square root [4] . Finally, it is worth
mentioning that FPM based on phase-shifting methods has recently showed localization of
single fluorescent markers at 10 nm precision in 3D, thereby demonstrating the power

of FPM for 3D optical nanoscopy [2,4] .

,

The TD-FPM system consists of three main components: (i) excitation optics, (ii) a self-
referencing interferometer, and (iii) a detection module. The excitation optics comprises a
wide-field or point-scanning illumination depending on the application. Next, the self-
referencing interferometer has two opposing matched lenses, which collect fluorescent light
from both sides of the specimen, and two mirrors that direct the light to a beam splitter
where the fluorescent fields are recombined. Low-numerical-aperture lenses are employed
when a large depth of field is required and a moderate transversal resolution is sufficient.
Moderately high-numerical-aperture lenses may be used for providing improved optical
sectioning capabilities without scarifying transversal resolution but at the expense of the
confocal length. Finally, the detection module comprises imaging and focusing optics as
well as a photodetector, for example, a two-dimensional (2D) charge-coupled device (CCD)
camera or a point detector, depending on the application.

It is important to point out that 4Pi and I5M microscopy systems combine the fluorescence
self-interference process with high-numerical-aperture microscope objectives to
achieve high axial resolution of approximately 100 nm [34 37] , whereas TD-FPM uses
the resolving power of optical path-length difference measurements to image fluorophores
with mesoscopic resolution for applications in depth-resolved optical imaging of thick
specimens or to precisely localize fluorescent emitters for applications in optical nanoscopy.
We also note that in contrast to 4Pi and I5M microscopy systems, TD-FPM requires the
translation of the sample along the optical axis and the demodulation of the recorded data
to obtain the depth information from the sample.

18.3.2 Spectral-Domain Fluorescence Phase Microscopy

An alternative setup of FPM can be realized in the spectral (Fourier) domain by using
spectrally resolved interferometry. An SD-FPM system is shown in Figure 18.3 .
The detector output in the case of a single fluorescent point source is expressed using the
Wiener Khintchine theorem [43] as:

I ð x ; y ; k Þ 5 I 0 ð x ; y Þ S ð k Þf 1 1 cos ð 2kz Þg (18.2)

Here, k denotes the wavenumber of the source, I 0 (x,y) is the transversal image of the
source, S(k) is the power spectral density (PSD) of the source which is closely related to the
Fourier transform of γ ( ), and z is the position of the source (relative to the zero