124 4.2  Super-Resolution Microscopy

labeling of samples is not always necessary for SNOM, for example, the latest developments

use label-​free methods employing an infrared (IR)-​SNOM with tuneable IR light source.

Near-​field fluorescence excitation fields can be generated from photonic waveguides.

Narrow waveguides are typically manufactured out of etched silicon to generate channels

of width ~100 nm. A laser beam propagated through the silicon generates an evanescent

excitation field in much the same wave as for total internal reflection fluorescence (TIRF)

microscopy (see Chapter 3). Solutions containing fluorescently labeled biomolecules can

be flowed through a channel and excited by the evanescent near-​field. Many flow channels

can be manufactured in parallel, with surfaces precoated by antibodies, which then recog­

nize different biomolecules, and this therefore is a mechanism to enable biosensing. Recent

improvements to the sensitivity of these optical microcavities utilize the whispering gallery

mode in which an optically guided wave is recirculated in silicon crystal of a circular shape to

enhance the sensitivity of detection in the evanescent near-​field to the single-​molecule level

(Vollmer and Arnold, 2008).

4.2.13  SUPER-​RESOLUTION IN 3D AND 4D

Localization microscopy methods are routinely applied to 2D tracking of a variety of

fluorophore-​labeled biomolecules in live cells. However, to obtain 3D tracking informa­

tion presents more challenges, due in part to mobile particles diffusing from a standard

microscope’s depth of field faster than refocusing can be applied, and so they simply go

out of focus and cannot be tracked further. This, coupled with the normal PSF image of a

fluorophore within the depth of field, results in relative insensitivity to z displacement. With

improvements in cytoplasmic imaging techniques of cellular samples, there is a motivation

to probe biological processes deeper inside relatively large cells and thus a requirement for

developing 3D tracking methods. (Note that these techniques are sometimes referred to as

“4D,” since they generate information from three orthogonal spatial dimensions, in addition

to the dimension of time.)

There are three broad categories of 3D tracking techniques. Multiplane imaging, most

commonly manifested as biplane imaging, splits fluorescence emissions from a tracked par­

ticle to two or more different image planes in which each has a slight focal displacement

offset. This means that the particle will come into sharp focus on each plane at different rela­

tive distances from the lateral focal plane of the sample. In its most common configuration

of just two separate image planes, this can be achieved by forming the two displaced images

onto separate halves of the same camera detector. Standard 2D localization fitting algorithms

can then be applied to each image to measure the xy localizations of the particle as usual and

also estimate the z value from extrapolation of the pixel intensity information compared to

a reference of an in-​focus image of, for example, a surface-​immobilized fluorophore. This

technique works well for bright fluorophores, but in having to split the fluorescence photon

budget between different images, the localization precision is accordingly reduced by a factor

of ~√2. Also, although the real PSF of a fluorescence imaging system shows in general some

asymmetry in z, this asymmetry is normally only noticeable at a few hundred nanometers or

more away from the focal plane. Therefore, unless the different focal planes are configured

to be separated by at least this threshold distance, there is some uncertainty as to whether

a tracked particle very close to the focal plane is diffusing above or below it or, in having to

separate the focal planes by relatively large distances inevitably reduces the sensitivity in z

at intermediate smaller z values. Similarly, there can be reductions in z sensitivity with this

method if separate tracked spots are relatively close to each other in z so as to be difficult to

distinguish (in practice, the threshold separation is the axial optical resolution limit that is

~2.5 times that of the lateral optical resolution limit, close to 1 μm, which is the length scale

of some small cells such as bacteria and cell organelles in eukaryotes such as nuclei).

Astigmatism imaging is a popular alternative method to multiplane microscopy, which

is relatively easy to implement. Here, a long focal length cylindrical lens is introduced in

the optical pathway between the sample and the camera detector to generate an image of

tracked particles on the camera. The cylindrical lens has intrinsic astigmatism, meaning that