# Super-resolution microscopy

Super-resolution microscopy, in light microscopy, is a term that gathers several techniques, which allow images to be taken with a higher resolution than the one imposed by the diffraction limit.[1][2] Due to the diffraction of light, the resolution in conventional light microscopy is limited, as stated (for the special case of widefield illumination) by Ernst Abbe in 1873.[3] In this context, a diffraction-limited microscope with numerical aperture N.A. and light with wavelength λ reaches a lateral resolution of d = λ/(2 N.A.) - a similar formalism can be followed for the axial resolution (along the optical axis, z-resolution, depth resolution). The resolution for a standard optical microscope in the visible light spectrum is about 200 nm laterally and 600 nm axially.[4] Experimentally, the attained resolution can be measured from the full width at half maximum (FWHM) of the point spread function (PSF) using images of point-like objects. Although the resolving power of a microscope is not well defined,[5] it is generally considered that a super-resolution microscopy technique offers a resolution better than the one stipulated by Abbe.

Super-resolution imaging techniques rely on the near-field (photon tunneling microscopy[6] as well as those that utilize the Pendry Superlens and near field scanning optical microscopy) or on the far-field. Among the latter are techniques that improve the resolution only modestly (up to about a factor of two) beyond the diffraction-limit like the confocal microscope (with closed pinhole), or confocal microscopy aided with computational methods such as deconvolution[7] or detector-based pixel reassignment (e.g. re-scan microscopy,[8] pixel reassignment [9]), the 4Pi microscope, and also structured illumination microscopy technologies like SIM and SMI.

There are two major groups of methods for super-resolution microscopy in the far-field that can improve the resolution with a much larger factor:[10]

1. Deterministic super-resolution: The most commonly used emitters in biological microscopy, fluorophores, show a nonlinear response to excitation, and this nonlinear response can be exploited to enhance resolution. These methods include STED, GSD, RESOLFT and SSIM.
2. Stochastic super-resolution: The chemical complexity of many molecular light sources gives them a complex temporal behavior, which can be used to make several close-by fluorophores emit light at separate times and thereby become resolvable in time. These methods include Super-resolution optical fluctuation imaging (SOFI) and all single-molecule localization methods (SMLM) such as SPDM, SPDMphymod, PALM, FPALM, STORM and dSTORM.

On October 8, 2014, the Nobel Prize in Chemistry was awarded to Eric Betzig, W.E. Moerner and Stefan Hell for "the development of super-resolved fluorescence microscopy," which brings "optical microscopy into the nanodimension".[11][12]

## History

In 1978, the first theoretical ideas had been developed to break the Abbe limit using a 4Pi microscope as a confocal laser scanning fluorescence microscope where the light is focused ideally from all sides to a common focus that is used to scan the object by 'point-by-point' excitation combined with 'point-by-point' detection.[13]

Some of the following information was gathered (with permission) from a chemistry blog's review of sub-diffraction microscopy techniques Part I and Part II. For a review, see also reference.[14]

In 1986, the super-resolution optical microscope based on stimulated emission was patented by Okhonin.[15]

## Super-resolution techniques

[6]

### Near-field optical random mapping (NORM) microscopy

NORM (near-field optical random mapping) microscopy is a method of optical near-field acquisition by a far-field microscope through the observation of nanoparticles' Brownian motion in an immersion liquid.[19][20]

NORM utilizes object surface scanning by stochastically moving nanoparticles. Through the microscope, nanoparticles look like symmetric round spots. The spot width is equivalent to the point spread function (~ 250 nm) and is defined by the microscope resolution. Lateral coordinates of the given particle can be evaluated with a precision much higher than the resolution of the microscope. By collecting the information from many frames one can map out the near field intensity distribution across the whole field of view of the microscope. In comparison with NSOM and ANSOM this method does not require any special equipment for tip positioning and has a large field of view and a depth of focus. Due to the large number of scanning "sensors" one can get shorter time of image acquisition.

### 4Pi

A 4Pi microscope is a laser scanning fluorescence microscope with an improved axial resolution. The typical value of 500–700 nm can be improved to 100–150 nm, which corresponds to an almost spherical focal spot with 5–7 times less volume than that of standard confocal microscopy.

The improvement in resolution is achieved by using two opposing objective lenses, both of which are focused to the same geometrical location. Also, the difference in optical path length through each of the two objective lenses is carefully aligned to be minimal. By this, molecules residing in the common focal area of both objectives can be illuminated coherently from both sides and also the reflected or emitted light can be collected coherently, i.e. coherent superposition of emitted light on the detector is possible. The solid angle ${\displaystyle \Omega }$ that is used for illumination and detection is increased and approaches the ideal case. In this case the sample is illuminated and detected from all sides simultaneously.[21][22]

Up to now, the best quality in a 4Pi microscope was reached in conjunction with the STED principle in fixed cells[23] and RESOLFT microscopy with switchable proteins in living cells.[24]

### Structured illumination microscopy (SIM)

There is also the wide-field structured-illumination (SIM) approach.[25][26][27][28]

SI enhances spatial resolution by collecting information from frequency space outside the observable region. This process is done in reciprocal space: The Fourier transform (FT) of an SI image contains superimposed additional information from different areas of reciprocal space; with several frames with the illumination shifted by some phase, it is possible to computationally separate and reconstruct the FT image, which has much more resolution information. The reverse FT returns the reconstructed image to a super-resolution image.

A number of applications have recently surfaced, in which SIM microscopy could potentially replace electron microscopy as part of routine diagnosis. These include diagnosis of kidney disorders,[29] kidney cancer,[30] and blood diseases.[31]

Although the term "structured illumination microscopy" was coined by others in later years, Guerra (1995) first published results [25] in which light patterned by a 50 nm pitch grating illuminated a second grating of pitch 50 nm, with the gratings rotated with respect to each other by an angular amount to achieve magnification. Although the illuminating wavelength was 650 nm, the 50 nm grating was easily resolved. This showed a nearly 5X improvement over the Abbe resolution limit of 232 nm that should have been the smallest obtained for the N.A. and wavelength used. In an extension and further development of this work, Guerra showed that super-resolved lateral topography is attained by phase-shifting the evanescent field. Several U.S. patents[32] were issued to Guerra individually or with colleagues and assigned to Polaroid Corp. Licenses to this technology were procured by Dyer Energy Systems, Calimetrics Inc. and then Nanoptek Corp. for use of this super-resolution technique in optical data storage and microscopy.

### Spatially modulated illumination (SMI)

One implementation of structured illumination is known as spatially modulated illumination. Like standard structured illumination, the SMI technique modifies the point spread function (PSF) of a microscope in a suitable manner. In this case however, "the optical resolution itself is not enhanced";[33] instead structured illumination is used to maximize the precision of distance measurements of fluorescent objects, to "enable size measurements at molecular dimensions of a few tens of nanometers".[33]

The Vertico SMI microscope achieves structured illumination by using one or two opposing interfering laser beams along the axis. The object being imaged is then moved in high-precision steps through the wave field, or the wave field itself is moved relative to the object by phase shift. This results in an improved axial size and distance resolution.[33][34][35]

SMI can be combined with other super resolution technologies, for instance with 3D LIMON or LSI-TIRF as a total internal reflection interferometer with laterally structured illumination (this last instrument and technique is essentially a phase-shifted photon tunneling microscope, which employs a total internal reflection light microscope with phase-shifted evanescent field (Guerra, 1996)[32]). This SMI technique allows one to acquire light-optical images of autofluorophore distributions in the sections from human eye tissue with previously unmatched optical resolution. Use of three different excitation wavelengths (488, 568 and 647 nm), enables one to gather spectral information about the autofluorescence signal. This has been used for human eye tissue affected by macular degeneration.[36]

## Deterministic functional techniques

RESOLFT microscopy is an optical microscopy with very high resolution that can image details in samples that cannot be imaged with conventional or confocal microscopy. Within RESOLFT the principle of STED microscopy[37][38] and GSD microscopy are generalized. Also, there are techniques with other concepts than RESOLFT or SSIM, for example fluorescence microscopy using optical AND gate property of nitrogen-vacancy center.[39]

### Stimulated emission depletion (STED)

STED (stimulated emission depletion microscopy) uses two laser pulses, the excitation pulse for excitation of the fluorophores to their fluorescent state and the STED pulse for the de-excitation of fluorophores by means of stimulated emission.[15][40][41][42][43][44] In practice, the excitation laser pulse is first applied whereby a STED pulse soon follows (But STED without pulses using continuous wave lasers is also used). Furthermore, the STED pulse is modified in such a way that it features a zero-intensity spot, which coincides with the excitation focal spot. Due to the non-linear dependence of the stimulated emission rate on the intensity of the STED beam, all the fluorophores around the focal excitation spot will be in their off state (the ground state of the fluorophores). By scanning this focal spot one retrieves the image. The FWHM of the PSF of the excitation focal spot can theoretically be compressed to an arbitrary width by raising the intensity of the STED pulse, according to equation (1).

${\displaystyle \Delta r\approx {\frac {\Delta }{\sqrt {1+I_{\max }/I_{s}}}}}$   (1)

∆r is the lateral resolution, ∆ is the FWHM of the diffraction limited PSF, Imax is the peak intensity of the STED laser, and ${\displaystyle I_{s}}$ is the threshold intensity needed in order to achieve saturated emission depletion.

The main disadvantage of STED, which has prevented its widespread use, is that the machinery is complicated. On the one hand, the image acquisition speed is relatively slow for large fields of view because of the need to scan the sample in order to retrieve an image. On the other hand, it can be very fast for smaller fields of view: Recordings with up to 80 frames per second have been shown. [45][46] Due to a large Is value associated with STED, there is a need for a high-intensity excitation pulse, which may cause damage to the sample.

### Ground state depletion (GSD)

GSD microscopy or ground state depletion microscopy, uses the triplet state of a fluorophore as the off-state and the singlet state as the on-state, whereby an excitation laser is used to drive the fluorophores at the periphery of the singlet state molecule to the triplet state. This is much like STED, where the off-state is the ground state of fluorophores, which is why equation (1) also applies in this case. The ${\displaystyle I_{s}}$ value is smaller than in STED making super-resolution imaging possible at a much smaller laser intensity. Compared to STED though, the fluorophores used in GSD are generally less photostable and the saturation of the triplet state may be harder to realize.[47]

### Saturated structured illumination microscopy (SSIM)

SSIM (saturated structured-illumination microscopy) exploits the nonlinear dependence of the emission rate of fluorophores on the intensity of the excitation laser.[48] By applying a sinusoidal illumination pattern[49] with a peak intensity close to that needed in order to saturate the fluorophores in their fluorescent state one retrieves Moiré fringes. The fringes contain high order spatial information that may be extracted by computational techniques. Once the information is extracted a super-resolution image is retrieved.

SSIM requires shifting the illumination pattern multiple times, effectively limiting the temporal resolution of the technique. In addition there is a need of very photostable fluorophores due to the saturating conditions. These conditions also induce radiation damage to the sample that restricts the possible applications in which SSIM may be used.

Examples for this microscopy are shown under section Structured illumination microscopy (SIM), Images of cell nuclei and mitotic stages recorded with 3D-SIM Microscopy.

## Stochastic functional techniques

### Localization microscopy

Single-molecule localization microscopy (SMLM) summarizes all microscopical techniques that achieve super-resolution by isolating emitters and fitting their images with the point spread function (PSF). Normally, the width of the point spread function (~ 250 nm) limits resolution. However, given an isolated emitter, one is able to determine its location with a precision only limited by its intensity according to equation (2).[50]

${\displaystyle \Delta \mathrm {loc} \approx {\frac {\Delta }{\sqrt {N}}}}$   (2)

Here, Δloc is the localization precision, Δ is the FWHM of the PSF and N is the number of collected photons. This fitting process can only be performed reliably for isolated emitters (see Deconvolution), and interesting biological samples are so densely labeled with emitters that fitting is impossible when all emitters are active at the same time. SMLM techniques solve this dilemma by activating only a sparse subset of emitters at the same time, localizing these few emitters very precisely, deactivating them and activating another subset.

Considering background and camera pixelation, and using Gaussian approximation for the point spread function (Airy disk) of a typical microscope, the theoretical resolution is proposed by Thompson et al.[51] and fine-tuned by Mortensen et al.:[52]

${\displaystyle \sigma ^{2}={\frac {\sigma _{PSF}^{2}+a^{2}/12}{N_{sig}}}({\frac {16}{9}}+{\frac {8\pi N_{bg}(\sigma _{PSF}^{2}+a^{2}/12)}{N_{sig}a^{2}}})}$

where

• σ is the Gaussian standard deviation of the center locations of the same molecule if measured multiple times (e.g. frames of a video). (unit m)
• σPSF is the Gaussian standard deviation of the point spread function, whose FWHM following the Ernst Abbe equation d = λ/(2 N.A.). (unit m)
• a is the size of each image pixel. (unit m)
• Nsig is the photon counts of the total PSF over all pixels of interest. (unitless)
• Nbg the average background photon counts per pixel (dark counts already removed), which is approximated to be the square of the Gaussian standard deviation of the Poisson distribution background noise of each pixel over time or standard deviation of all pixels with background noise only, σbg2. The larger the σbg2, the better the approximation (e.g. good for σbg2 >10, excellent for σbg2 >1000). (unitless)
• Resolution FWHM is ~2.355 times the Gaussian standard deviation.

Generally, localization microscopy is performed with fluorophores. Suitable fluorophores for e.g. STORM reside in a non-fluorescent dark state for most of the time and are activated stochastically, typically with an excitation laser of low intensity. A readout laser stimulates fluorescence and bleaches or photoswitches the fluorophores back to a dark state, typically within 10–100 ms. In PAINT, the fluorophores are nonfluorescent before binding and fluorescent after. The photons emitted during the fluorescent phase are collected with a camera and the resulting image of the fluorophore (which is distorted by the PSF) can be fitted with very high precision even on the order of a few Angstroms.[53] Repeating the process several thousand times ensures that all fluorophores can go through the bright state and are recorded. A computer then reconstructs a super-resolved image.

The desirable traits of fluorophores used for these methods, in order to maximize the resolution, are that they should be bright. That is, they should have a high extinction coefficient and a high quantum yield. They should also possess a high contrast ratio (ratio between the number of photons emitted in the light state and the number of photons emitted in the dark state). Also, a densely labeled sample is desirable according to the Nyquist criteria.

The multitude of localization microscopy methods differ mostly in the type of fluorophores used.

#### Localization microscopy SPDM

A single, tiny source of light can be located much better than the resolution of a microscope: Although the light will produce a blurry spot, computer algorithms can be used to accurately calculate the center of the blurry spot, taking into account the point spread function of the microscope, the noise properties of the detector, and so on. However, this approach does not work when there are too many sources close to each other: The sources all blur together.

SPDM (spectral precision distance microscopy) is a family of techniques in fluorescence microscopy which gets around this problem by measuring just a few sources at a time, so that each source is "optically isolated" from the others (i.e., separated by more than the microscope's resolution, typically ~200-250 nm).[54][55][56] Then, the above technique (finding the center of each blurry spot) can be used.

If the molecules have a variety of different spectra (absorption spectra and/or emission spectra), then it is possible to look at light from just a few molecules at a time by using the appropriate light sources and filters. Molecules can also be distinguished in more subtle ways based on fluorescent lifetime and other techniques.[54]

The structural resolution achievable using SPDM can be expressed in terms of the smallest measurable distance between two in their spatial position determined punctiform particle of different spectral characteristics ("topological resolution"). Modeling has shown that under suitable conditions regarding the precision of localization, particle density etc., the "topological resolution" corresponds to a "space frequency" which in terms of the classical definition is equivalent to a much improved optical resolution.

SPDM is a localization microscopy which achieves an effective optical resolution several times better than the conventional optical resolution (approx. 200-250 nm), represented by the half-width of the main maximum of the effective point image function. By applying suitable laser optical precision processes, position and distances significantly smaller than the half-width of the point spread function (conventionally 200-250 nm) can be measured with nanometer accuracy between targets with different spectral signatures.[54] An important area of application is genome research (study of the functional organization of the genome). Another important area of use is research into the structure of membranes.

##### SPDMphymod

Localization microscopy for many standard fluorescent dyes like GFP, Alexa dyes and fluorescein molecules is possible if certain photo-physical conditions are present. With this so-called SPDMphymod (physically modifiable fluorophores) technology a single laser wavelength of suitable intensity is sufficient for nanoimaging[57] in contrast to other localization microscopy technologies that need two laser wavelengths when special photo-switchable/photo-activatable fluorescence molecules are used. A further example for the use of SPDMphymod is an analysis of Tobacco mosaic virus (TMV) particles[58] or the study of virus–cell interaction.[59][60]

Based on singlet triplet state transitions it is crucial for SPDMphymod that this process is ongoing and leading to the effect that a single molecule comes first into a very long-living reversible dark state (with half-life of several seconds even) from which it returns to a fluorescent state emitting many photons for several milliseconds before it returns into a very long-living so-called irreversible dark state. SPDMphymod microscopy uses fluorescent molecules that are emitting the same spectral light frequency but with different spectral signatures based on the flashing characteristics. By combining two thousands images of the same cell, it is possible using laser optical precision measurements to record localization images with significantly improved optical resolution.[61]

Standard fluorescent dyes already successfully used with the SPDMphymod technology are GFP, RFP, YFP, Alexa 488, Alexa 568, Alexa 647, Cy2, Cy3, Atto 488 and fluorescein.

#### Cryogenic Optical Localization in 3D (COLD)

Cryogenic Optical Localization in 3D (COLD) is a method that allows localizing multiple fluorescent sites within a single small- to medium-sized biomolecule with Angstrom-scale resolution.[53] The localization precision in this approach is enhanced because the slower photochemistry at low temperatures leads to higher number of photons that can be emitted from each fluorophore before photobleaching.[62][63] As a result, cryogenic stochastic localization microscopy reaches the required sub-molecular resolution to resolve the 3D positions of several fluorophores attached to a small protein. By employing algorithms known from electron microscopy, the 2D projections of fluorophores are reconstructed into a 3D configuration. COLD brings fluorescence microscopy to its fundamental limit given by the size of the label. The method can also be combined with other structural biology techniques such as X-ray crystallography, magnetic resonance spectroscopy and electron microscopy to provide valuable complementary information and specificity.

#### BALM

BALM (Binding Activated Localization Microscopy) is a general concept for Single Molecule localization Microscopy (SMLM) super-resolved imaging of DNA-binding dyes based on modifying the properties of DNA and the dye.[64] By careful adjustment of the chemical environment leading to local, reversible DNA melting and hybridization control over the fluorescence signal of the DNA-binding dye molecules can be introduced. Intercalating and minor-groove binding DNA dyes can be used to register (optically isolate) only a few DNA-binding dye signals at a time. DNA structure fluctuation-assisted BALM (fBALM) has been used to nanoscale differences in nuclear architecture with an anticipated structural resolution of approximately 50 nm. Imaging chromatin nanostructure with binding-activated localization microscopy based on DNA structure fluctuations.[65] Recently, significant enhancement of fluorescence quantum yield of NIAD-4 upon binding to amyloid was exploited to BALM imaging of amyloid fibrils[66] and oligomers.[67]

#### STORM, PALM and FPALM

Stochastic optical reconstruction microscopy (STORM), photo activated localization microscopy (PALM) and fluorescence photo-activation localization microscopy (FPALM) are super-resolution imaging techniques that utilize sequential activation and time-resolved localization of photoswitchable fluorophores to create high resolution images. During imaging, only an optically resolvable subset of fluorophores is activated to a fluorescent state at any given moment, such that the position of each fluorophore can be determined with high precision by finding the centroid position of the single-molecule images of particular fluorophore. The fluorophore is subsequently deactivated, and another subset is activated and imaged. Iteration of this process allows numerous fluorophores to be localized and a super-resolution image to be constructed from the image data. These three methods were published independently during a short period of time and their principle is identical. STORM was originally described using Cy5 and Cy3 dyes attached to nucleic acids or proteins,[68] while PALM and FPALM was described using photoswitchable fluorescent proteins.[69][70] In principle any photoswitchable fluorophore can be used, and STORM has been demonstrated with a variety of different probes and labeling strategies. Using stochastic photoswitching of single fluorophores, such as Cy5,[71] STORM can be performed with a single red laser excitation source. The red laser both switches the Cy5 fluorophore to a dark state by formation of an adduct[72][73] and subsequently returns the molecule to the fluorescent state. Many other dyes have been also used for STORM.[74][75][76][77][78][79] In addition to single fluorophores, dye-pairs consisting of an activator fluorophore (such as Alexa 405, Cy2, and Cy3) and a photoswitchable reporter dye (such as Cy5, Alexa 647, Cy5.5, and Cy7) can be used for STORM.[68][80][81] In this scheme, the activator fluorophore, when excited near its absorption maximum, serves to reactivate the photoswitchable dye to the fluorescent state. Multicolor imaging has been performed by using different activation wavelengths to distinguish dye-pairs based on the activator fluorophore used[80][81][82] or using spectrally distinct photoswitchable fluorophores either with or without activator fluorophores.[74][83][84] Photoswitchable fluorescent proteins can be used as well.[69][70][84][85] Highly specific labeling of biological structures with photoswitchable probes has been achieved with antibody staining,[80][81][82][86] direct conjugation of proteins,[87] and genetic encoding.[69][70][84][85] STORM has also been extended to three-dimensional imaging using optical astigmatism, in which the elliptical shape of the point spread function encodes the x, y, and z positions for samples up to several micrometers thick,[81][86] and has been demonstrated in living cells.[84] To date, the spatial resolution achieved by this technique is ~20 nm in the lateral dimensions and ~50 nm in the axial dimension and the temporal resolution is as fast as 0.1–0.33s.

#### Points accumulation for imaging in nanoscale topography (PAINT)

Points accumulation for imaging in nanoscale topography (PAINT) is a single-molecule localization method that achieves the stochastic single-molecule fluorescence by molecular adsorption/absorption and photobleaching/desorption.[88] The first dye used is Nile red which is nonfluorescent in aqueous solution but is fluorescent when inserted into a hydrophobic environment such as micelles or living cell walls. Thus when the concentration of the dye is small, in the order of nanomolar level, such that the molecule's sorption rate to the diffraction-limited area is in the millisecond region. The stochastic binding of single dye molecules (probes) to an immobilized target can be spatially and temporally resolved under a typical widefield fluorescence microscope. Each dye is photobleached to return the field to dark for the next dye to bind and be observed. The advantage of this method comparing to other stochastic method is in addition to obtaining the super-resolved image of the fixed target, it can measure the dynamic binding kinetics of the diffusing probe molecules in the solution to the target. Combining with 3D super-resolution technique (e.g. the double-helix point spread function develop in Moerner's group) and using photo-activated dyes, power-dependent active intermittency and points accumulation for imaging in nanoscale topography (SPRAIPAINT) can super-resolve live-cell walls.[89] PAINT works by maintaining a balance between the dye adsorption/absorption and photobleaching/desorption rates. This balance can be estimated with stochastic statistical principles.[90] The adsorption or absorption rate of a dilute solute to a surface or interface in a (gas or liquid) solution can be calculated using Fick's laws of diffusion. The photobleaching/desorption rate can be measured for a given solution condition and illumination power density.

PAINT has been further extended to regular dyes termed as DNA-PAINT when the dynamic binding and unbinding of a dye-labeled DNA probe to a fixed DNA origami is used to achieve the stochastic single-molecule imaging.[91][92] DNA-PAINT is no longer limited to the environment-sensitive dyes and can measure both the adsorption and the desorption kinetics of the probes to the target. The method utilizes the camera blurring effect of moving dyes. When a regular dye is diffusing in the solution, its image on a typical CCD camera is blurred because of its relatively fast moving speed and the relatively long camera exposure time, thus it contributes to the fluorescence background. However, when it binds to a fixed target, the dye stop moving and a clear point spread function can be taken by the camera. Thus, a general term for this modification is (motion blur) mbPAINT.[93] When a total internal reflection fluorescence microscope (TIRF) is used to imaging, the excitation depth is limited to ~100 nm from the substrate, which further reduces the fluorescence background from the blurred dyes near the substrate and the background in the bulk solution. Very bright dyes can be used for mbPAINT which gives typical single-frame spatial resolutions ~20 nm and single-molecule kinetic temporal resolution ~20 ms under relatively mild photoexcitation intensities, which is useful in studying molecular separation of single proteins.[94]

The temporal resolution has been further improved (20 times) using a rotational phase mask placed in the Fourier plane during data acquisition and resolve the distorted point spread function that contains temporal information. The method was named Super Temporal-Resolved Microscopy (STReM).[95]

#### Label-free localization microscopy

Optical resolution of cellular structures in the range of about 50 nm can be achieved even in label-free cells using the localization microscopy SPDM.

Beside a substantial resolution improvement of autofluorescent structures, using two different laser wavelengths SPDM reveals cellular objects which are not detectable under conventional fluorescence wide-field imaging conditions.

As a control the positions of the detected objects in the localization image match these in the bright-field image.[96]

Label-free superresolution microscopy has also been demonstrated using the fluctuations of surface enhanced Raman scattering signal on a highly uniform plasmonic metasurface. [97]

#### Direct stochastical optical reconstruction microscopy (dSTORM)

dSTORM utilizes the photoswitching of a single fluorophore. In dSTORM, fluorophores are embedded in an oxidizing and reducing buffer system (ROXS) and fluorescence is excited. Sometimes, stochastically, the fluorophore will enter a triplet or some other dark state which is sensitive to the oxidation state of the buffer. As the molecules return stochastically they can be excited to fluoresce so that single molecule positions can be recorded.[98] Development of the dSTORM method occurred in 3 independent laboratories at about the same time and was called 'Reversible photobleaching microscopy -RPM",[99] "Ground state depletion microscopy followed by individual molecule return" -GSDIM[100] as well as the now generally accepted moniker dSTORM.[101]

#### Software for localization microscopy[102]

Localization microscopy depends heavily on software that can precisely fit the point spread function (PSF) to millions of images of active fluorophores within a few minutes. Since the classical analysis methods and software suites used in natural sciences are too slow to computationally solve these problems, often taking hours of computation for processing data measured in minutes, specialised software programs have been developed. Many of these localisation software packages are open-source, they are listed at SMLM Software Benchmark. Once molecule positions have been determined, the locations need to be displayed and several algorithms for display have been developed e.g.[103]

### Super-resolution optical fluctuation imaging (SOFI)

It is possible to circumvent the need for PSF fitting inherent in single molecule localization microscopy (SMLM) by directly computing the temporal autocorrelation of pixels. This technique is called super-resolution optical fluctuation imaging (SOFI) and has been shown to be more precise than SMLM when the density of concurrently active fluorophores is very high.

### Omnipresent Localization Microscopy (OLM)[104]

Omnipresent Localisation Microscopy (OLM) is an extension of Single Molecule Microscopy (SMLM) techniques that allow high-density single molecule imaging with an incoherent light source (such as Mercury arc lamp) and a conventional epifluorescence microscope setup. A short burst of deep blue excitation (350-380 nm instead of 405 nm laser) can for a prolonged reactivation of molecules. A resolution of 90 nm on test specimens. Finally, correlative STED and SMLM imaging can be performed on the same biological sample using a simple imaging medium, which can provide a basis for a further enhanced resolution. These findings can democratise superresolution imaging and help any scientist to generate high-density single molecule images even with a limited budget.

## Combination of techniques

### 3D light microscopical nanosizing (LIMON) microscopy

3 D LIMON (Light MicrOscopical nanosizing microscopy) images using the Vertico SMI microscope are made possible by the combination of SMI and SPDM, whereby first the SMI and then the SPDM process is applied.

The SMI process determines the center of particles and their spread in the direction of the microscope axis. While the center of particles/molecules can be determined with a 1–2 nm precision, the spread around this point can be determined down to an axial diameter of approx. 30–40 nm.

Subsequently, the lateral position of the individual particle/molecule is determined using SPDM, achieving a precision of a few nanometers.[105]

As a biological application in the 3D dual color mode the spatial arrangements of Her2/neu and Her3 clusters was achieved. The positions in all three directions of the protein clusters could be determined with an accuracy of about 25 nm.[106]

### Integrated correlative light and electron microscopy

Combining a super-resolution microscope with an electron microscope enables the visualization of contextual information with the labelling provided by fluorescence markers. This overcomes the problem of the black backdrop that the researcher is left with when using only a light microscope. In an integrated system, the sample is measured by both microscopes simultaneously.[107]

## Enhancing of techniques using neural networks

Recently, owing to advancements in artificial intelligence computing, deep learning neural networks have been used for super-resolution enhancing of photographic images,[108] optical microscopy from 40x to 100x,[109] 20x optical microscope to 1500x scanning electron microscope via a neural lens,[110] positron-emission tomography and fluorescence microscopy.[111]

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