Super-resolution microscopy

To form an image, light diffracted from the sample must be captured by the imaging lens (Figure 7.1). The angle of the diffracted light from a periodic structure is proportional to the spatial frequency of the structure. There exists a spatial frequency, above which the emerging angle of the diffracted light is too large to enter the lens and an image can no longer be formed. We can decompose any sample we wish to image into multiple overlapping spatial frequencies so this limit holds true for all samples using standard linear microscope systems and defines the Abbe limit [242]:

dmin = λ

2N A (7.1)

where dmin is the smallest distance between two points before they can no longer be

distinguished [243]. We can also imagine a point source emitter as containing all spatial frequencies and so define the same limit for fluorescence microscopy, which this chapter will be primarily concerned with. To exceed Abbe’s limit, we must find a way to access higher spatial frequency information within the sample.

Many techniques can be employed to go beyond this fundamental limit, although they increase the optical system complexity and acquisition time. The advances in bio- logical imaging made using these microscopy methods, however, have proven invaluable. Before the development of optical SR, electron microscopy was the only routinely used sub-diffraction imaging technique. Electron microscopy provides very high resolu- tion of structures but no functional information and require detrimental sample fixation and prohibitively expensive equipment [7]. Functional imaging of electron microscopy samples is possible using immunogold labeling. Antibody-tagged gold nanoparticles bind to the protein of interest and increase contrast in the vicinity. The penetration of the nanoparticles into fixed tissue is low, however, allowing labelling of superficial layers only and the distance between the target and tag is close to the size of the tag itself [244]. These problems can be minimised by using optical microscopy imaging of genetically-encoded fluorescently-tagged proteins instead. Although optical microscopy

A

Sample⊗PSF

information captured

δ(r)⊗PSF=PSF

B

C

Figure 7.1– The Abbe limit defines the smallest spatial frequency that can be captured by an imaging system. A low spatial frequency causes low-angled diffraction, which enters the objective and combines at the imaging plane (A). The image formed is then the sample convolved with the point spread function (PSF) of the imaging system, discussed further in Figure 7.2. If the spatial frequency is high, the diffraction angle will be too great for the imaging lens to capture the higher diffraction orders. Only the zeroth-order will pass through the imaging system, resulting in no spatial information, only a constant term (B). If we instead consider a point source emitter (fluorescence) then the Abbe limit still holds because there is still a loss of information as higher-angled emission cannot pass through the objective. Rather than seeing a perfect point source at the imaging plane, we can instead see the PSF of the imaging system (C). Imaging a point source is a useful way of measuring the PSF of a system. Figure adapted from [243].

can only reach resolutions103 _{times worse than electron microscopy, it can also provide}

invaluable real-time, 3D, functional information about a sample.

By spatially varying the illumination, it is possible to extend the achievable resolu- tion two-fold. Confocal microscopy tightly focuses an excitation laser onto the specimen and passes emitted fluorescence through a pinhole in the confocal image plane before collection at a PMT; the pinhole rejects out-of-focus light and creates optical sectioning. The laser focus is then scanned across the sample to build up an image. The confocal PSF (point-spread function - see Figure 7.2) of the system is then a convolution of the emission and detection PSF, creating a smaller PSF than a standard epi-fluorescence

point source PSF imaging system A B C

Figure 7.2– The point-spread function (PSF) is the image of a point source at the sample plane obtained from an imaging system (A). The PSF can be thought of as a paintbrush that paints all points in a sample passing to the sample plane with the PSF shape, a convolution that creates a lower resolution approximation of the image. If we consider a sample distribution (B), then the image obtained from our imaging system in (A) would be (C). A typical PSF is an airy disc.

microscope. The theoretical lateral resolution of a confocal microscope is twice the Abbe limit but cannot be reached in practice because the pinhole should be infinitely small [245]. Confocal imaging can be extended to SR by using a CCD detector rather than a PMT [246], providing extra information about the sample. Structured illumina- tion microscopy (SIM) uses a spatially varying illumination to bring higher resolution information in the sample into the passband of the objective [247]. A thorough de- scription of the theory behind SIM imaging can be found in Appendix C.2. SIM is a wide-field technique that requires≥9 exposures per image to achieve up to 2 times the lateral resolution limit with increased axial sectioning at rates of approximately 1 Hz.

By breaking the linear dependence of excitation and emission, it is possible to extend beyond the theoretical limit. STED (stimulated emission depletion) microscopy was the first SR technique proposed, using dual illumination to exploit non-linear properties of fluorophores [248]. The STED beam possesses a central point of zero intensity (usually a Laguerre-Gaussian beam). The wavelength of the STED beam is chosen to induce stimulated emission (red-shifted photons that are filtered out) in sample fluorophores.

A second beam induces normal fluorescence emission only in the point where the beams do not overlap (usually 10-70 nm in extent), the other fluorophores are depleted [249]. The necessity for point-scanning limits STED acquisition speed. Single-molecule local- isation techniques, such as PALM and STORM [250, 251], rely on switching on and off individual fluorophores in a field of view. Low-intensity illumination causes a subset of molecules in the field of view to emit. If the PSFs of each fluorophore lit up at any one time do not overlap then each can be localised individually. An image is reconstructed using the knowledge of all the fluorophore positions, many images are taken to collect information from all present fluorophores. Non-linear SR techniques can achieve up to 20 nm resolution but require slow acquisition times and specialised fluorophores.

Owing to accessibility to standard fluorophores and relatively fast acquisition times, combined with modest resolution increase, SIM has been successfully used for many biological scenarios. A commercial SIM (N-SIM, Nikon, UK) is therefore used as a platform to test the suitability of our fibre-based optical trap for combination with fluorescence imaging.

7.2

Integration of optical trapping with a structured