The invention relates to an imaging system and an imaging method.

Three-dimensional architectures of organelles and molecules inside cells require microscopes with sufficiently high resolving power in all three spatial dimensions. Conventional microscopy methods when applied to live cell imaging are limited by insufficient spatial resolution in 3D, long recording times and photobleaching.

According to a first aspect of the invention, there is provided an imaging system for imaging a sample, the imaging system comprising an objective lens and an optical arrangement, the optical arrangement including at least one optical component, wherein the optical arrangement is configured to: focus a first pair of coherent light beams onto a back focal plane of the objective lens asymmetrically with respect to an optical axis of the objective lens to create a first light interference pattern tilted with respect to the optical axis; focus a second pair of coherent light beams onto the back focal plane of the objective lens asymmetrically with respect to the optical axis of the objective lens to create a second light interference pattern tilted with respect to the optical axis; and focus a third pair of coherent light beams onto the back focal plane of the objective lens symmetrically about the optical axis of the objective lens to create a third light interference pattern aligned, or substantially aligned, with the optical axis, so as to produce an incoherent superposition of the three light interference patterns to create a three-dimensional (3D) light interference pattern comprising a plurality of peaks and zero-intensity regions, the 3D light interference pattern illuminating the sample.

The configuration of the imaging system of the present invention results in the provision of a highly modulated and regular 3D light interference pattern (also referred to hereon as the "honeycomb" in this specification) that enables light signals from a sample to be simultaneously confined within a plurality of volumes (which are referred to as "confined volumes" in this specification) defined by the zero-intensity regions. Such confinement makes it easier to detect and extract the light signals, thus enhancing imaging speed and enabling high quality image acquisition.

The size of the confined volumes may be reduced down to at least the nanoscale level. For example, each confined volume may have a maximum dimension of sub-100 nm. Thus, the imaging system of the present invention may be configured to have high resolution capable of obtaining 3D images of small spatial details, e.g. features of living cells, that are smaller than the diffraction limit of light. Since the 3D light interference pattern can be readily configured to scale up the number of confined volumes to be in the hundreds, thousands or higher, high parallelisation of the imaging process can be carried out using the plurality of confined volumes to speed up the overall imaging process. Furthermore, the 3D spatial distribution of the confined volumes enables simultaneous, or near-simultaneous imaging, using the confined volumes that speeds up the overall imaging process and provides more precise image information in comparison to a sequential 2D imaging process. Thus, due to its spatial scale and scalability, the 3D light interference pattern may be configured for super resolution imaging in a preferred embodiment of the invention.

The capability of the invention to carry out 3D imaging at high spatial resolution enables the imaging of samples without requiring potentially damaging sample preparation, e.g. slicing the sample to obtain a cross-section. This enables the invention to usefully image live samples, such as live cells.

In contrast to the invention, conventional imaging systems are not powerful or fast enough to work at a spatial scale of sub-100 nm in 3D and also tend to overexpose samples to illumination, thus resulting in phototoxicity and photoinhibition. Furthermore, for conventional imaging systems, the scope of suitable imaging applications may be limited by time-consuming sample preparation with low throughput.

The imaging system of the invention may be configured as a module for retrofitting into an existing imaging device or may be configured as an independent imaging device. Such an imaging device may be, for example, a microscope or nanoscope.

Since the 3D light interference pattern is a periodic pattern with peaks and zero- intensity regions (the latter of which are also referred to as "holes" in this specification), the shapes and sizes of the peaks and holes of the 3D light interference pattern may be varied through reconfiguration of the imaging system of the invention. Particularly, a periodicity of the 3D light interference pattern may be varied by changing the distance between, and the positioning of, the pairs of coherent light beams on the back focal plane of the objective lens.

In a first example, the optical arrangement may be reconfigurable to change a position of at least one of the pairs of coherent light beams on the back focal plane of the objective lens to adjust an axial periodicity of the 3D light interference pattern. In a second example, the optical arrangement may be reconfigurable to change a position of at least one of the pairs of coherent light beams on the back focal plane of the objective lens to adjust a lateral periodicity of the 3D light interference pattern.

Each confined volume is preferably shaped, e.g. spherically shaped, to provide isotropic, or substantially isotropic, confinement but may have other shapes in other embodiments. In embodiments of the invention, the optical arrangement may be configured to, in use, provide a read-out illumination of the sample illuminated by the 3D light interference pattern.

The provision of the read-out illumination in combination with the confined volumes of the 3D light interference pattern not only limits the risk of exposing the sample to high illumination intensities over long image acquisition times that may result in phototoxicity and photoinhibition but also reduces the risk of incomplete photo switching in cell-medium environments. In such embodiments, the optical arrangement may be configured to, in use, provide the read-out illumination to excite light emission from the sample. In a particular example, the light emission may be fluorescence emission.

The imaging system of the present invention is suitable for imaging samples with fluorophores (e.g. negative imaging) or reversibly switchable fluorescent probes (e.g. positive imaging). Such reversibly switchable fluorescent probes may be reversibly switchable fluorescent proteins or dyes. In particular, the 3D light interference pattern created by the imaging system of the present invention permits 3D fluorescence imaging of live cells, such as 3D sub-cellular isotropic fluorescence imaging, to better study the interior cell structure. Preferably such fluorescence imaging is carried out at super resolution. In contrast, conventional super resolution microscopes are limited to 3D imaging of fixed immobile cells or 2D imaging of live cells.

Three exemplary types of read-out illumination may be implemented as follows.

A first exemplary read-out illumination is in the form of a widefield read-out illumination, which may be used to excite parts of the sample corresponding to all or most of the confined volumes. A widefield read-out illumination is relatively straightforward to implement in comparison to the following two types of read-out illumination.

A second exemplary read-out illumination is in the form of a multi-spot read-out illumination, which may be used to excite parts of the sample corresponding to all or a subset of the confined volumes located in a detection focal plane. Preferably the multi-spot read-out illumination is configured to align, or substantially align, peaks of its spots with the zero-intensity regions of the 3D light interference pattern. Due to the smaller imaging volume, the multi-spot read-out illumination permits selective imaging of parts of the sample and reduces the overall illumination exposure of the sample.

The multi-spot read-out illumination may be created using different optical components, such as micro-lenses, spatial light modulators and any other phase or amplitude modulating device. A periodicity of the spots may be adjusted to suppress out-of-focus background and maximise signal detection.

A third exemplary read-out illumination is in the form of a light sheet read-out illumination, which may be used to excite parts of the sample corresponding to the confined volumes located in an optical detection plane of the light sheet. Due to the smaller imaging volume, the light sheet read-out illumination permits faster imaging of the sample and reduces the overall illumination exposure of the sample.

The light sheet read-out illumination may be created using different optical components, such as a cylindrical lens, a spatial light modulator or a lens coupled with a one-dimensional scanner.

Depending on imaging requirements, the shape of the light sheet read-out illumination may vary. For example, the read-out illumination may be an oblique light sheet read out illumination, or may be an orthogonal light sheet read-out illumination.

The reduction in overall illumination exposure by the multi-spot and light sheet read out illuminations enables longer imaging times while reducing the risk of phototoxicity and photoinhibition. In further embodiments of the invention, the optical arrangement may be configured to, in use, provide an on-switching illumination to turn on fluorescent probes of the sample. In such embodiments, the fluorescent probes may be reversibly switchable fluorescent probes. The on-switching illumination may be employed in the imaging system of the invention when the sample includes fluorescent probes that need to be turned on. Typically the on-switching illumination is provided to the sample prior to creation of the 3D light interference pattern.

Optionally a pattern of the on-switching illumination may be further configured to match a pattern of the read-out illumination. Matching the patterns of the on-switching and read-out illuminations ensures that only the fluorescent probes to be read are switched on, thus further reducing illumination dosage for the sample.

Non-limiting examples of the on-switching illumination include a widefield on-switching illumination, a multi-spot on-switching illumination and a light sheet on-switching illumination (such as an oblique light sheet on-switching illumination or an orthogonal light sheet on-switching illumination). The advantages of such exemplary on-switching illuminations are as described above and in the rest of the specification with reference to their read-out illumination counterparts. The choice of the type of on-switching illumination may depend on imaging requirements, such as imaging speed, lower overall illumination exposure, sample type and type of image information required.

The 3D light interference pattern may be used in different ways and in different imaging sequences to carry out sample imaging.

In embodiments of the invention, the optical arrangement may be configured to, in use, provide the 3D light interference pattern to switch one or more parts of the sample to an inactive state, e.g. a state in which the one or more parts of the sample do not emit detectable photons. This provides a reliable way of simultaneously confining light signals from specific regions of interest in the sample within the confined volumes of the 3D light interference pattern. In such embodiments, the optical arrangement may be configured to, in use, provide a read-out illumination to excite light emission from the or each remaining active part of the sample. Such light emission may be fluorescence emission.

In further embodiments of the invention, the optical arrangement may be configured to, in use, provide the 3D light interference pattern to suppress light emission from the sample in volumes defined by its peaks and allow light emission from the sample in volumes defined by its zero-intensity regions. Such selectivity is made possible by the confined volumes defined by the zero-intensity regions of the 3D light interference pattern, thus enabling the imaging system to focus on specific regions of interest in the sample. This is especially the case when selective light emission from the light sample is difficult to achieve, such as when a widefield illumination is used to excite light emission from the sample.

The 3D light interference pattern may rely on photophysical mechanisms, or other mechanisms, to suppress fluorescence emission. Non-limiting examples of such photophysical mechanism include reversible saturable optical fluorescence transitions (RESOLFT) and stimulated emission.

Non-limiting examples of applications of the imaging system of the invention include:

• Observation of fluorescently labelled small organelles and/or macromolecular complexes inside living cells;

• Imaging of cell cultures, tissues, organoids and cells in multi-cellular organisms;

• Visualisation of cellular processes such as cytoskeleton rearrangement, endocytosis, exocytosis, cell connection, organelles dynamics, cytoskeleton nucleus interaction;

• Visualisation of cellular mechanisms in health-related and diseased samples with molecular specificity.

• Observation of volumetric structural alterations and synaptic protein plasticity in hippocampal neurons.

It will be appreciated that there are many possible configurations of the optical arrangement, non-limiting examples of which are described throughout the specification. Different optical components and different configurations of such optical components may be employed to create the 3D light interference pattern in accordance with the invention. In embodiments of the invention, the optical arrangement may include, but is not limited to, at least one light source, at least one diffraction grating, at least one spatial light modulator and/or at least one beam splitter cube.

Each pair of coherent light beams may be created by splitting a single light beam into the two coherent light beams. This may be achieved using a diffraction grating, a spatial light modulator, beam splitter cubes, or a combination thereof. Other techniques for creating each pair of coherent light beams may be used. According to a second aspect of the invention, there is provided an imaging method using the imaging system in accordance with any one of the first aspect of the invention and its embodiments, the method comprising the steps of: by the optical arrangement, focusing a first pair of coherent light beams onto a back focal plane of the objective lens asymmetrically with respect to an optical axis of the objective lens to create a first light interference pattern tilted with respect to the optical axis; focusing a second pair of coherent light beams onto the back focal plane of the objective lens asymmetrically with respect to the optical axis of the objective lens to create a second light interference pattern tilted with respect to the optical axis; and focusing a third pair of coherent light beams onto the back focal plane of the objective lens symmetrically about the optical axis of the objective lens to create a third light interference pattern aligned, or substantially aligned, with the optical axis, so as to produce an incoherent superposition of the three light interference patterns to create a 3D light interference pattern comprising a plurality of peaks and zero-intensity regions, the 3D light interference pattern illuminating the sample.

In embodiments of the second aspect of the invention, the imaging method may include the steps of, by the optical arrangement: providing an illumination to excite light emission from the sample; and providing the 3D light interference pattern to suppress light emission from the sample in volumes defined by its peaks and allow light emission from the sample in volumes defined by its zero-intensity regions, wherein the method further includes the step of detecting the allowed light emission from the sample.

In further embodiments of the second aspect of the invention, the imaging method may include the steps of, by the optical arrangement: providing an on-switching illumination to turn on fluorescent probes of the sample; providing the 3D light interference pattern to switch one or more parts of the sample to an inactive state; and providing a read-out illumination to excite light emission from the or each remaining active part of the sample. In such embodiments, the fluorescent probes may be reversibly switchable fluorescent probes.

The features of the imaging system of the first aspect of the invention and its embodiments apply mutatis mutandis to the features and advantages of the imaging method of the second aspect of the invention and its embodiments.

It will be appreciated that the use of the terms "first" and "second", and the like, in this patent specification is merely intended to help distinguish between similar features, and is not intended to indicate the relative importance of one feature over another feature, unless otherwise specified.

Within the scope of this application it is expressly intended that the various aspects, embodiments, examples and alternatives set out in the preceding paragraphs, and the claims and/or the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and all features of any embodiment can be combined in any way and/or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and/or incorporate any feature of any other claim although not originally claimed in that manner.

Preferred embodiments of the invention will now be described, by way of non-limiting examples, with reference to the accompanying drawings in which:

Figure 1 shows the creation of a 3D light interference pattern by an imaging system of the invention;

Figure 2 shows imaging properties of the imaging system of the invention;

Figures 3 to 6 show different embodiments of sample illumination by a 3D light interference pattern created by the imaging system of the invention;

Figures 7 to 9 show exemplary implementations of the imaging system of the invention;

Figure 10 shows the use of the imaging system of the invention in live cell imaging;

Figures 11 to 17 illustrate exemplary properties of the 3D light interference pattern created by an imaging system of the invention.

The figures are not necessarily to scale, and certain features and certain views of the figures may be shown exaggerated in scale or in schematic form in the interests of clarity and conciseness.

The following embodiments of the invention are described with reference to the use of an imaging system as a microscope in 3D super resolution imaging. It will be appreciated that the following description of the invention applies mutatis mutandis to the use of the imaging system in other imaging applications and at other resolution levels. The goal of the new microscope is to image small spatial details in living cells (preferably sub-100 nm, more preferably in the range of 10-50 nm) far beyond the diffraction limit of light, rapidly and most importantly, in 3D. Existing super resolution microscopes are too slow to volumetrically image cells in 3D with fine details.

Embodiments of the present invention achieve 3D spatial resolution by designing a new interference pattern, which is modulated in 3D, featuring "holes" or zero-intensity regions in a 3D volume. Preferably the holes are spherical, or substantially spherical, in shape. This illumination, when coupled with optically controllable fluorescent molecules, can be used to "turn off" the ability of the molecules to be detected. This way, small volumes can be confined in a distributed manner over the 3D volume, where the molecules can emit fluorescence and be detected. These volumes can theoretically be infinitesimally small. Practical demonstrations show, for example, an average spatial resolution of sub-80 nm in 3D with features as small as 40 nm (about 10 times better axially and 5-6 times in XY). In practice, using current fluorescent molecules, confinements of 55 nm laterally and 80 nm axially have been measured.

The imaging speed comes from having thousands of these volumes confined at the same time. In fact, the interference pattern features many holes and peaks. A single volume can potentially be recorded in a few seconds.

Embodiments of the invention allow the multiple 3D confined volumes to be probed and detected. In fact, the read-out illumination can be done with widefield illumination for simple implementation, multi-spots to ensure optical sectioning and the highest detection efficiency or with a light sheet for the fastest recording. The last two illuminations allow minimisation of light dosage, thus providing a gentle super resolution approach.

The invention comprises a sequential illumination with differently shaped light patterns.

The present invention features a light pattern which is modulated in 3D. This is done by focusing three beam pairs of light on the back focal plane (BFP) of the objective lens. Two of the beam pairs are shifted laterally with respect to the optical axis, resulting in an interference pattern that is tilted with respect to the optical axis, which is key for the resolution improvement along the optical axis. The third beam pair can then be placed symmetrically around the optical axis. The polarisation of the beams are rotated so as to give optimal modulation. The paired beams are created by a diffraction grating which splits the beam in different orders. The beam pair can also be created using a spatial light modulator or beam splitter cubes. As long as two fully coherent beams are created, the concept will work. Beam pairs with the same polarisation are kept incoherent by using separate, mutually incoherent sources. The final resulting interference at the specimen plane will be a periodic light pattern with holes and peaks, herein called the honeycomb. The periodicity can be tweaked by changing the distance between, and the positioning of, the paired-spots in the BFP.

The illumination pattern can be used to suppress fluorescence emission, allowing only emission from the volumes defined by the holes in the pattern. Optical fluorescence suppression is commonly used in super resolution microscopy, and any method to achieve this is compatible with the illumination pattern described above. If reversibly switchable fluorescent probes are used for fluorescence suppression, a sequential illumination scheme may be needed to (1) switch on, (2) suppress, and (3) excite and read out the fluorescence from the confined volumes. In this case, the read-out light is applied sequentially in time (e.g. few micro-seconds later) to record the fluorescence emitted by all, or a subset of, the multiple confined volumes.

For use with reversibly switchable fluorescent probes, different read-out illuminations can be used. For example, the read-out (type 1) may be a widefield illumination that excites all the confined volumes in the sample. In another example, the read-out (type 2) may be a multi-spot array created with micro-lenses, spatial light modulators or other phase or amplitude modulating device. The multi-spots are preferably aligned with the honeycomb such that the peaks of the spots match the holes of the honeycomb. The periodicity of the spots can be adjusted to suppress out-of-focus background and maximise signal detection. The multi-spot array excites fluorescence from all or a subset of volumes located in the detection focal plane of the sample. In yet another example, the read-out (type 3) may be a light sheet illumination, defined as a thin sheet of light illuminating only a section of the sample volume that coincides with the optical detection plane. This type of read-out excites only the volumes located in the plane of the light sheet. The light sheet can be generated using any conventional method for light sheet generation. Examples include using a cylindrical lens, using a spatial light modulator or using a conventional lens coupled with a one-dimensional scanner.

For use with probes that need to be actively switched on, on-switching illumination is required prior to applying the honeycomb pattern. The on-switching light can be either widefield, switching on all the probes in the sample, or it can be matched to the read- out pattern, in order to only switch on the volumes that are to be read out in the read out step of the sequence. The latter approach further minimises illumination dosage.

For use ith conventional, spontaneously emitting fluorophores, the imaging scheme can be summarised as (1) a widefield, multi-spot or light sheet illumination excites fluorescence from the probes, (2) the honeycomb pattern suppresses emission from all regions except the zero-intensity volumes, (3) emission is detected from the remaining emitting regions.

For use with reversibly switchable fluorescent probes, the imaging scheme can be summarised as: (1) an illumination pattern suitable for the application is used to switch probes on, (2) the honeycomb illumination functions as a patterned light switch, i.e. it switches the fluorescent molecules to an inactive state where they do not emit detectable fluorescent photons, (3) the read out pattern of choice is used to excite fluorescence from the volumes remaining in the active/on state.

Since the honeycomb pattern acts to confine the fluorescence in 3D in a parallelised way, it needs to target a mechanism that suppresses the fluorescence from the probes. Common photophysical mechanisms used to suppress fluorescence include reversible saturable optical fluorescence transitions (RESOLFT) and stimulated emission. The concept is however not limited to these photophysical mechanisms.

For complete planar or volumetric imaging, the illuminations need to be repeatedly shifted with respect to the sample so as to record information from the whole area or volume being imaged. Thus, a scanning system for scanning either the sample or the illuminations shifts their relative position to each other in order to record information from all regions of interest. In order to reconstruct the image volume, the detected emissions are reassigned to their correct volumetric elements. The final reconstruction can be further improved by applying iterative deconvolution algorithms such as Richardson-Lucy or similar.

The current invention features a 3D pattern highly modulated and more regular which enables confinement of the fluorescence signal in 3D. Previous 3D patterns were either not highly modulated or less regular making the extraction of the signal harder. The coupling of the 3D modulated light pattern with reversibly switchable fluorescent probes was never done before and demonstrates for the first time that 3D theoretically- unlimited super resolution imaging of living cells with minimal light dosage is possible. The multi-foci and oblique light sheet read-out illuminations minimise further the specimen exposure to light, thereby making the technique able to record longer time- lapse images and to minimize cellular photo-toxicity. The current invention can be used to observe small organelles or macromolecular complexes fluorescently labelled inside the 3D architecture of living cells. It can image cell culture, tissues, organoids and cells in multi-cellular organisms. Cellular processes, such as cytoskeleton rearrangement, endocytosis/exocytosis, cell connection, organelles dynamics, cytoskeleton nucleus interaction and many others can be studied with unprecedented level of temporal/spatial precision.

Further non-limiting details of implementations of the imaging system (also referred to as the "3D-pRESOLFT" imaging system in this specification) of the invention are set out as follows:

Figure la shows a schematic illustration of how different combinations of coherent beams can create light interference patterns with different tilts. Below the objectives in Figure la, the corresponding placement of the focused beams on the back focal plane is shown together with their polarisation (indicated by double arrows). The tilt of the final patterns depends on the angles cu and 02, which are defined here as the angle between the direction of propagation of the beam and the optical axis (z-axis).

The 2D-plots in Figure lb show the lateral and axial periodicities of the resulting interference pattern as a function of the angles Oi and 02. Marked by red circles is the combination of angles used for the tilted interference patterns.

Figure lc shows a schematic illustration of each of the three light interference patterns P l, P2, P3 with corresponding beam placements on the back focal plane of the objective lens. The solid planes illustrate the geometry of zero-intensity planes within each of the three light interference patterns RI,RS,RB.

Figure Id shows a schematic illustration of the incoherent superposition of Pi, P2 and P3 to create the 3D light interference pattern ("honeycomb") that results in three- dimensionally confined volumes.

Figure le shows a schematic illustration of the imaging sequence that shows simulated illumination patterns in the X-Z-plane in the correct temporal order. From left to right, the full sequence of illuminations starts with an on-switching illumination, then a honeycomb illumination that functions as an off-switching illumination, and finally a read-out illumination for excitation. The pattern of the on-switching illumination matches the pattern of the read-out illumination. The rightmost image shows the calculated expected emission distribution during read-out resulting from the full sequence of illuminations.

Figure 2a shows the experimentally measured intensity pattern when illuminating the sample with the two tilted interference patterns. On the right of Figure 2a, the measurement is placed in a larger context showing a simulation of a larger area. Here, the effect of a refractive index interface between the cover glass and sample is also illustrated, resulting in an axial compression of the pattern.

Figure 2b shows the axial line profile of the three different illumination patterns as well as the resulting relative expected emission distribution along the same line with the FWHM of the central Gaussian calculated as ~78 nm. Figure 2c shows the dependence of the central FWHM on off-illumination energy where the energy represents the energy delivered at the maxima of the intensity pattern shown in Figure 2a.

Figure 2d shows simulated and measured 3D-pRESOLFT imaging. The virtual sample used in the simulations attempt to mimic the structure and labelling of the sample observed in the measured data and is created as two labelled sheets with varying axial separation. The sheets are labelled with 20 fluorophores per 20x20x20 nm voxel. Both measured and simulated data are acquired without the Y-confining pattern. Figure 2d shows line profiles along lines 1,2, 3, 4 marked in Figure 2d. Data is fitted with the expected effective point spread function (PSF) of the imaging system. Results show good correspondence between simulations and measured data both in terms of subjective image quality and measured values of fitted curves. Figure 3 shows that the honeycomb pattern suppresses fluorescence everywhere but in small volume elements that, following honeycomb illumination 100, spontaneously emit fluorescence which can be detected on a camera and provides high resolution information about the sample structure. The combination of the honeycomb illumination and the widefield read-out illumination may be implemented by scanning the honeycomb periodicity. Shorter periodicities may need deconvolution for signal extraction from cross-talk and reconstruction. The fluorescence label can be reversibly switchable proteins or dyes for positive imaging. Fluorophores can be relied upon for negative imaging. Figure 4 shows that, if used with reversibly switchable probes, the confined volu es resulting from the honeycomb illumination 102 can be read out with a widefield illumination leading to emission from all the volume elements.

The combination of the honeycomb illumination and the multi-spot read-out illumination permits volumetric time-lapse imaging with theoretically unlimited spatial resolution. Its efficiency in providing background suppression is ideal for 3D sample imaging, including 3D tissue imaging. Also, it minimises unwanted protein switching, which make it suitable for longer time-lapse imaging. Figure 5 shows that, if used with reversibly switchable probes, the confined volumes resulting from the honeycomb illumination 104 can be read out with a multi-spot illumination 106 leading to emission from a subset of volume elements located in the focal plane of detection.

The combination of the honeycomb illumination and the light sheet read-out illumination may be implemented by firstly using the honeycomb illumination to provide spatial confinement of the fluorescence emittance and then using the light sheet read-out illumination to image the sample section-by-section. The light sheet can be created with a cylindrical lens or by rapidly scanning the beam. A Bessel beam can also be used. The image plane is the one illuminated by the light sheet and it is achieved with remote focusing. This plane will be imaged by a fast and sensitive camera detector. The final image reconstruction can be done with photon reassignment with or without Richardson and Lucy deconvolution. Figure 6 shows that, if used with reversibly switchable probes, the confined volumes resulting from the honeycomb illumination 108 can be read out with an orthogonal light sheet 110 or oblique light sheet 112 leading to emission from volume elements located in the focal plane of detection.

Figure 7 shows a schematic illustration of the optical setup showing the module for creating the honeycomb pattern. In this embodiment, the honeycomb pattern is coupled to a multi-spot on-switching illumination 114 and a multi-spot read-out illumination 116. The feature 118 is a non-polarising beam splitter, the feature 120 is a polarising beam splitter, the feature 122 is a dielectric mirror, and the feature 124 is a silver mirror. Figure 7 shows three-dimensional and top-down illustrations of the configuration of optical components used to achieve the asymmetry giving rise to the tilted patterns. Beams 126,128 are reflected off elevated and lowered mirrors 130 in order to hit the diffractive grating 132 at the correct angle. Figure 8 shows a schematic illustration of a possible optical design for coupling of the honeycomb pattern 134 with an orthogonal light sheet read-out illumination 136. The design is also coupled to a widefield on-switching illumination. The plane of the light sheet 136 and the plane of detection are kept co-aligned by using a scanning mirror for moving the light sheet 136 and a remote refocus system to move the detection plane.

Figure 9 shows a schematic illustration of a possible optical design for coupling of the honeycomb pattern 138 with an oblique light sheet read-out 140. The design is coupled to a widefield on-switching illumination. The plane of the light sheet 140 and the plane of detection are intrinsically co-aligned by using a scanning mirror to shift both the light sheet 140 and the detection plane in a coupled manner.

An exemplary implementation of the invention lies in an optical scheme enabling volumetric nanoscopy of living cells with resolutions approaching or surpassing 100 nm while maintaining high imaging speed (sec/frame), large field of view and minimal illumination intensities (W/cm ² -kW/cm ² ) by utilising reversibly switchable fluorescent molecules.

Optical microscopes primarily convey higher spatial information in the lateral directions due to the intrinsic principles of optical imaging. The advent of optical nanoscopy has demonstrated the possibility to extract finer axial information using interferometry and point spread function engineering approaches in both deterministic and single molecule stochastic switching. However, he systems capable of conveying truly super resolved 3D information from within the sample today are not suitable for imaging living samples over longer times, either because of phototoxic illumination intensities and/or too long image acquisition times and/or incomplete photo-switching in cell-medium environment.

To tackle this challenge, the invention is configured to create an illumination pattern covering whole cells with intensity modulation along all three dimensions. The pattern exhibits an array of small zero-intensity regions co-aligned with the focal plane of detection with sharp and nearly isotropic 3D-confinement, making it more suitable for coordinate targeted switching scheme as in STED and RESOLFT nanoscopy than previously presented patterns. The 3D modulated illumination is used to switch reversibly switchable fluorescent proteins (rsFP) from a fluorescent (on) to a non- fluorescent (off) state, which is long-lived and require minimal intensities (W/cm ² - kW/cm ² ) to be completely populated; thus enabling parallelised optical schemes covering fields of view of 50-100 pm ² .

The theoretically unlimited 3D resolution of the imaging system of the invention is preferably based on the off-switching pattern which is created using the incoherent superposition of three different standing wave patterns. Each standing wave pattern creates planes of zero intensity in the illuminated volume. The points where planes from all three patterns intersect will be the centers of the resulting zero intensity volumes. Each standing wave pattern is generated by the interference of two coherent plane waves, exiting the objective in carefully chosen directions. Two of the standing wave patterns RI,RS are tilted with respect to the optical axis. This tilt gives the final pattern its axial modulation. The tilt is achieved by shifting the two focused spots on the back focal plane so that they are asymmetrically positioned with respect to the optical axis. The third pattern P3, which is symmetric on the back focal plane, confines the volumes in the final lateral dimension. The exact axial and lateral periodicities of the pattern can be tuned by changing the position of the foci on the back focal plane. Since the periodicity of the pattern in a given direction is inversely proportional to the fluorescence confinement at a certain intensity, tuning the periodicities will affect the properties of the imaging system. For the imaging demonstrated here, a configuration is chosen that minimises the axial periodicity and thus maximises the potential axial resolution. Exemplarily the axial and lateral periodicities may be 480 nm and 360 nm respectively.

When combined with rsFP such as rsEGFP2, this blue-light induced off-switching enables imprinting of patterns of state distributions into the sample which then, under fluorescent excitation, translates into a spatial pattern of expected emission. In the imaging system of the invention, a multi-foci pattern at 405 nm is used for switching the rsFP located at the focal spots. The sharp zero regions of the off-switching pattern are used to sharply confine the on-state rsFP population and create a pattern of emission consisting primarily of distinctly separated but sharply 3D-confined regions located in the focal plane of the microscope. As these regions are probed with a second multi-foci illumination, the relative fluorophore density is detected at that coordinate in the sample. The effective off-switching pattern is measured by scanning fluorescent beads embedded in Mowiol ^® . Due to the mismatch of the refractive index of the sample (1.33 sample versus 1.51 oil), the resulting periodicity is compressed from 680 nm to 480 nm, which is used to achieve even higher isotropic confinement. Given the rsEGFP2 switching kinetics and a peak energy of 0.7 1/cm ² each for the patterns Pi,P2,P3, this results in a confined fluorescent volume with an axial and lateral FWHM of around 78 nm and 59 nm respectively. These are values that roughly describe the potential resolution of the imaging system at given label and imaging parameters. The dependence of axial FWHM and energy of off-switching illumination is shown in Figure 2c.

Although the resolution extension beyond the diffraction limit stems from the off- switching pattern described above, the final image quality is highly dependent on the multi-foci patterns. Adding the multi-foci on-switching and read-out means that fluorophores are only switched on in, and excited from, the confined volumes located in the focal plane of detection. This minimises the amount of out-of-focus emission that deteriorates the image SNR, and also gives the flexibility of switching on and reading out a subset of zero-volumes, which minimises emission cross-talk and enhances image SNR.

U20S cells labelled with LifeAct-rsEGFP2 were imaged to compare the resulting resolving power with theoretical calculations and computational simulations. The results confirm that the imaging system is able to distinguish axially separated structures sized 70-80 nm at a distance approaching 100 nm. This is corroborated by measuring a modulation depth of 62% for structures separated by 118 nm and measuring a FWHM of the confined central Gaussian of around 80 nm. All values are in good agreement with theory and simulations. The amount of high frequency information can be extended by increasing the energy of the off-switching light i.e. increasing the confinement. This will however alter the signal to noise and signal to background levels in ways that depend on the fluorophore and labelling characteristics. Other parameters like labelling density and type of structure being imaged also alters the effective resolution of the system.

To further explore and demonstrate the imaging ability of 3D-pRESOLFT in living cells, the whole three dimensional mitochondria network in U20S cells transfected with OMP25-rsEGFP2 as outer membrane marker was recorded. The ability of the system to accurately measure the 3D shape and "hollow" volume of each distinct mitochondria even in closely packed regions, such as the nuclear proximity, is highlighted. Time- lapse imaging of an X-Z slice using Pi and P _å shows the axial organization and dynamics of several mitochondria over time. Not only mitochondria but also intermediate filaments are distributed across the entire 3D cellular architecture. The x-z slice of the cell demonstrate (imaged using Pi and P2) that the extended resolution of the system is retained also when imaging endogenously labelled structures such as Vimentin filaments, which are not resolved in the confocal image recorded without off-pattern. Finally full 3D-volumetric imaging (with P1-P3) was performed at dual time points of a different part of the sample labelled with LifeAct- rsEGFP2 showing both dynamics and packed 3D intertwined filaments.

Figure 10a shows a large field of view volumetric image of a mitochondrial network in a live LJ20S cell labelled with rsEGFP2-Omp25. The zoom-in shows a mitochondrial complex in high 3D-resolution. The three-dimensional resolution enhancement enables the distinction and segmentation of a smaller spherical mitochondrial fragment/vesicle located just beneath the larger one and to accurately quantify the volume of the different component individually.

Figure 10b shows, from top to bottom, an x-z-slice from a time-lapse recording of U20S cells labelled with rsEGFP2-Omp25 over 2 minutes. The series demonstrated specifically the ability of the system to unveil mitochondrial reorganization in 3D at high temporal resolution. Images are acquired at 5-6 second intervals.

Figure 10c shows that the x-z-slice of a U20S cell endogenously expressing Vimentin- rsEGFP2 images in 3D-pRESOLFT and enhanced confocal mode demonstrates that both the lateral and axial resolution extension is retained also in the notoriously dim endogenously labelled filamentous Vimentin structure. Line profiles plotted in the graph are measured along the line marked with arrows in the zoom and are each normalised to the maximum intensity of the curve.

Figure lOd shows dual time point volumetric imaging of U20S cells labelled with LifeAct-rsEGFP2. The difference images on the right is acquired by subtraction one time points from the other and displaying the magnitude of the result. The difference image reveals regions of the volume where significant reorganisation has occurred between the time points. The extended resolution also unveils geometrical structures within where the cell protrusions interact and e.g. form a helical structure as shown in the zoom in at the bottom of the panel.

The imaging system of the invention represents a new approach to 3D super resolution imaging with minimal illumination intensities over large fields of view that for the first time enables volumetric studies of whole living cells at resolutions far surpassing the diffraction limit in all three dimensions. The technique may rely on the use of reversibly switchable fluorophores and is demonstrated here using rsEGFP2. The spatial distribution of fluorescent emission from these labels can be finely controlled in 3D using a novel combination of interference patterns. The resulting images show both lateral and axial resolutions below 100 nm without prior information or processing. The invention is applicable to cellular biology studies, which aims to dissect the dynamic position in 3D of organelles and molecules in both living cells and tissues. For deeper tissue imaging, adaptive wavefront corrections may be implemented for the preservation of the light patterns within these complex media.

The patterned illumination used for switching off the rsFPs in the sample is created by letting several beam pairs interfere, both coherently and incoherently, with each other as described above and below.

A point in the object space of a microscope is defined by its coordinates x,y,z in a coordinate system with the orthonormal basis x, y and z. The vector z points away from the objective and the focal plane of the objective coincides with the plane z = 0.

Disregarding polarisation, the electric field of a monochromatic plane wave passing through the space can be described as where r = (x _r ,yr,z _r ) is the position vector, k _n is the wave vector in radians per meter (\k _n \ = g), An is the amplitude of the wave and con is the angular frequency. For two coherent and equally polarised plane waves Ei and Ez of a given frequency, we have ah = 0)2 º w and thus \k _x \ = \k ₂ \. Where the two waves coincide, the total electric field, E _t o _t (r,f) will be given by:

¾.ot(r, t) = E ₁ (r, t) + E ₂ ( r, t)

Knowing that the sum of same frequency sinusoids gives a new sinusoidal, it can be rewritten as: for some (in the following results irrelevant) F(G)) and

If Ai = A2 º A, the intensity distribution of the resulting field ends up being: From this equation, Itot will have its highest modulation frequency along the K = kl - k2 vector and will have constant values on any plane to which is the normal vector.

Of specific interest are the planes with zero intensity, appearing where cos (K r) = - 1, i.e. where K r = nr + 2 ph, h E Z.

The interference pattern created by two plane waves results in zero intensity planes periodically distributed in space, i.e. confines the zero-volumes in one dimension. To achieve three dimensional confinement of the zero-volumes, at least three linearly independent patterns are needed. In an implementation, two patterns were used to confine the zero-volumes in two lateral but ninety degrees rotated dimensions (e.g. x and y dimensions), and both these patterns thus fulfil K i z . In the 3D implementation, two patterns that do not fulfil K i z are used to confine the zero-volumes in one lateral dimension and the axial dimension (x and z) and a third pattern, fulfilling K i z to confine in the other lateral dimension (y). The patterns are indexed as pattern i = 1, 2 and 3, following the order in which they were mentioned above. Disregarding the absolute intensities, each pattern can then be fully described by its K vector, hereafter indexed as K, for pattern i. To create an array of zero-volumes that is coplanar with the focal plane of the objective (where z=0), we take a look at cases where Ki for both patterns 1 and 2 lie in the plane spanned by x and z and where Ki and Kå are each other's reflections with respect to z (This gives zeros in the focal plane). Since all kn have equal magnitude (same wavelength lasers), each Ki maps onto a unique (disregarding permutations) pair of ki and kå. It follows that the pairs of ki and k2-vectors of patterns 1 and 2 are reflections of each other. Given these constraints, the incoherent sum of patterns 1 and 2 can be described by the two angles Oi and 02 formed between the kn-vectors and z.

B is defined as the angle between the K- vector of a pattern and the z-vector. In order to achieve efficient on-state confinement, it is desirable to have a steep intensity gradient surrounding the zero intensity point. To confine efficiently in along both x and z, a steep intensity gradient is needed in both directions. It can be shown that the superposition of the two sinusoidal interference patterns discussed above will result in an elliptical confinement in the x - z plane with the amount of ellipticity defined by the ratio between the periodicities of the sinusoidal patterns along x and z respectively. The £ and z periodicities can be expressed as: This allows the isotropy of the confined region to be defined as:

Px _ cos(i T - b)

Pz cos{fi - f )

The superimposed patterns only confines the emitting regions in two dimensions. In order to achieve fully three-dimensional confinement, the emitting regions are confined along the y-direction. This is done by superimposing a third interference pattern P3 with a K-vector fulfilling K || y. P3 will then add a sinusoidal intensity modulation along the y-direction enabling confinement of the emitting region also in the third dimension. The intensity distribution of the incoherent superposition of two equally intense interference patterns as (normalising the maximum intensity to 1) can be expressed as: where the intensity zero is shifted to the origin by changing the sign in front of the cosines to minus. In the vicinity of the origin (1 - cos(x)) can be well approximated by a parabolic function:

Thus in the vicinity of the zero intensity it follows that: Introducing the saturation intensity Isat and the vector r _sat where this intensity is reached.

Where Oi and 02 are the angles between Ki and r and K2 and r respectively. By introducing y and Q as: and enforcing the symmetry between Ki and K2 giving:

The distance |r| to a predefined saturation intensity Isat will have an elliptical shape in the general case of arbitrary g, q, K _n values with its half axes along z (y = o) and x [g = For the special case where Q = i.e. the K-vectors are orthogonal, |r| will assume a perfectly circular shape.

Figure 11 illustrates that the derived elliptical shape corresponds well with the shape of the zero regions in the saturated simulated pattern. The symmetry of the 2D intensity pattern, i.e. that Ki and K2 are reflections of each other in z, which means that the intensity profile along x and z will both be pure sinusoidal functions with equal maximum intensity but different periodicity. Thus the confinement can be compared along these lines since it will be proportional to the periodicity of the pure sinusoidal, and the isotropy can be defined as the ratio between the periodicities along the two axes. In the experimentally created patterns, a pattern is produced where the axial periodicity is 480 nm and the lateral one is 360 nm, as shown in Figure lib.

Reversibly switchable fluorescent proteins are specific fluorophores that can be modelled as a two state Markov system where the two states are on and off. Fluorescent emission can only occur from fluorophores in the on-state. Different wavelengths of light induce specific switching rates between the two states. As a consequence, patterned (spatially varying) illuminations can be used to create a spatially dependent probability function of fluorophores being in one or the other state. The probability of the two state Markov system being in the on-state at a certain time can be described as: Where row is the rate of switching from off to on, TOFF is the rate of switching from on to off, p is the probability of the system starting in the on-state and t is time.

The fluorophores used with the 3D-pRESOLFT system are so-called negative switchers, meaning that the wavelength with largest absorption cross section for fluorescence excitation coincides with the peak of the absorption cross section spectra for switching the fluorophores back to the off-state. Using experimental measurements, the different switching rates induced by the specific wavelengths used can be estimated. We see from these measurements that, although 488 nm light induces a large off-switching rate, the off-switching is never fully complete, indicating that under 488 nm illumination, a small residual on-switching rate is still also present.

In order to estimate the different rates induced by the different illuminations, we use a biological sample labelled with the fluorophore of interest, which in this cases is the fluorescent protein rsEGFP2. The sample is first illuminated with 405 nm light to push most of the proteins to the on-state. Small consecutive pulses of 488 nm light are then applied to the sample while simultaneously exposing the camera in detection. Since only fluorophores in the on-state are able to emit fluorescence, the amount of fluorescence detected will be proportional to the relative amount of fluorophores in the on-state. The time trace of detected emission light thus represents the exponential decay of on-state population. By measuring/ calculating the illumination intensity at the sample, the decay constant for the given intensity can be estimated by fitting a function of the above probability equation to the decaying fluorescent signal. By changing the illumination intensity, the off-switching rate seems to scale linearly with increased intensity. Similarly, the rate of -switching is measured by pulsing the 405 nm laser and probing the relative emission from a trailing 488 nm pulse. For this measurement, 4.3 W/cm ² 488 nm pulse that only switches about 3% of the on-state fluorophores back off with each pulse is used. When extracting on-rate, this minor off-switching effect is disregarded.

Figure 12 is a graph that shows the evolution of off- state population under three different 491 nm illumination powers and their respective exponential fits. All curves are normalised to the emission detected at the first data point representing the emission from 100% of the on-state population prior to measurement start.

Table 1 below shows estimated off-switching rates under 491 nm illumination extracted from the fitted curves in Figure 12 illustrating the relatively constant ratio between off- rate and intensity. Table 2 below shows estimated on-switching rates under 491 nm illumination extracted from the fitted curves in Figure 12 illustrating the relatively constant ratio between on-rate and intensity.

Table 1

Table 2

Figure 13 is a graph showing the evolution of on-state population under 405 nm illumination. Data is acquired by pulsing the 405 nm laser with interleaved 488 nm pulses to probe the fluorescence emission. 488 nm pulses are weak enough to not induce any significant off-switching. Table 3 below shows extracted on-switching rates from the fitted curves in Figure 13 illustrating the relatively constant ratio between on- rate and intensity.

Table 3

From these values, it is demonstrated that the ratio between off-switching rate and intensity is fairly steady between 0.007-0.008 and the ratio between on-switching rate and intensity is fairly steady between 3e-4 to 4e-4. Under 405 nm illumination, a 72% activation after 1 ms illumination with 252 W/cm ² intensity is measured as shown in Figure 13. With a good estimate of switching rates, it can be calculated how the probability of fluorophores residing in one or the other states evolves over time under a spatially varying illumination intensity. Using the above probability equation, the probabilities of different states after certain sequences of illuminations are calculated. By inserting the illumination patterns used for on-switching and off-switching, the spatially dependent probabilities Pon(x,y,z) are calculated, where RON describes the probability of a fluorophore residing in the on-state if it is located at coordinate (x,y,z). Since negative switchers are used, the fluorophores will also undergo switching during the read-out phase of the illumination sequence. The total expected emission of a fluorophore is therefore calculated by first calculating the total expected time that the fluorophore resides in the on-state during the read out illumination, and then multiplying with the rate of fluorescence emission resulting from the read out illumination intensity, giving :

Emit) = Tfi * T _0N where is the expected total time in the on-state, Em(t) is the expected number of emitted photons and rn is the rate of fluorescent emission under a given illumination. Using these equations, the expected emission from different spatial coordinates that are exposed to different illumination intensities can be calculated.

Figure 14 shows the different probability distributions along an axial line passing through the intensity zero of the off-switching pattern. These calculations use illumination intensities that follow the illumination applied in the 3D-pRESOLFT imaging scheme. Figure 14a shows an axial illumination profile of on-switching (405 nm) illumination and resulting on-state distribution after a 0.192 3/cm ² peak energy pulse. Figure 14b shows an axial illumination profile of off-switching (491 nm) illumination and resulting on-state distribution after a 1.424 3/cm ² peak energy pulse. Figure 14c shows an axial read-out (488 nm) illumination profile and resulting expected relative emission distribution after a 0.1883/cm ² pulse. All curves in a-c are normalised to their individual maximum value. Figure 14d shows simulated data that is normalised to its maximum value and fits calculated for the normalised data.

Table 4 below sets out the parameters used to calculate the curves in Figure 14. Table 4

^Off-switcliing rate under 405 mil illumination was not measured. In simulations and calculations of probabilities it is assumed to be zero

The expected relative emission can be well approximated as a sum of two Gaussian functions, a larger one resulting from the background emission due to the small residual on-switching under 488 nm illumination, and a small one resulting from the spatial confinement of on-state fluorophores in the zero-intensity region of the off- switching pattern. The wellness of this approximation is illustrated in Figure 12d, where the accurately simulated data is shown to be well approximated by the sum of two Gaussian functions of FWHM values 401 nm and 78 nm respectively.

The expected emission function describing the relative expected number of emitted photons from a given spatial coordinate is derived above. Due to the selective activation and read-out, the spatial separation between emitting regions is well above the optical diffraction limit of the system allowing for independent quantification of each emitting volume. The quantification is done by segmenting the camera frame into sub-regions centered on the emitting volumes. Digital pin-holing is then done by pixelwise multiplication between a pinhole function and the acquired image and the resulting value is assigned to the corresponding volume element (voxel) in the raw data volume. The transformation between the sample density and the raw image volume is thus described as where D(r) is the fluorophore density at point r and h(u) is the impulse response (or a p pa re nt/effect i ve point spread function) of the imaging system. The three- dimensional impulse response of the system is calculated by first convolving each plane of the detection PSF of the system with the two-dimensional pinhole function used in the quantification step and then multiplying with the relative expected emission function given by the illumination scheme.

G (x, y, z) = PSF _t (x, y, _å )P{x - i , y - j)didj

(i,j)e

L(M) = Em (it) G (ii)

Where PSF _d et(x,y,z) is the detection point spread function, P(x,y) is the pinhole function and Em(u) is the relative expected emission from point u with a given pulse scheme and illuminations. The detection PSF as a Gaussian in all planes with z-dependent width is approximated as:

The pinhole function is set to be a Gaussian minus a constant: Meaning that G(x,y,z) will in each plane be a Gaussian with larger width minus a constant:

With the approximation of Em(u) as a sum of a small Gaussian and a large Gaussian, h(u) will resemble Em(u), again being a sum of two Gaussian with the width of each Gaussian scaled according to:

Thus h(u) is also well approximated by a sum of two Gaussians, where each Gaussian will be slightly smaller than in Em(u). However, evaluated for the emission functions resulting from the illumination scheme, the shrinking effect on the small central Gaussian of Em(u) will be on the order of 1-2% axially and around 3-5% laterally. The larger Gaussian however, will be shrunk by approximately 10-15% both laterally and axially.

It can be readily reasoned that h(u) will be very similar to Em(u), since G(u) is the plane by plane convolution of the PSF which can be approximated as a Gaussian in each plane and P(x,y) which is a Gaussian minus a constant, resulting in a G(u) closely resembling Gaussian of width Gaussian function in each plane. Thus h(u) should also be well approximated with a small central Gaussian. Since the reconstruction is simply the quantified total emission from the region assigned to the correct pixel, the final image can be accurately described as a convolution between the label distribution in the sample and the expected emission function:

It can be seen that the emission function acts as the effective PSF in the system in the sense that the final 3D image is expected to be the convolution of the underlying label distribution with the emission function. When performing curve fitting on line profiles, certain properties of the underlying structure and image formation model are assumed, and a set of parameters is fit to the given model. The theoretically expected line profile however, will depend on the three-dimensional structure of the sample. For a point source, the line profile will simply be the line profile through the three-dimensional PSF. For a line or sheet structure, the expected line profile will be projections through the PSF. When fitting functions to line profiles, a fit with the expected PSF of that image is desired. By simulating the x-z image of a single very densely labelled slice, the expected line profile of such structures can be estimated. The PSF can still be nearly perfectly approximated as a sum of Gaussians, although in this case, the larger confocal Gaussian is stronger compared to the thinner diffraction limited Gaussian. The height of the larger Gaussian is measured to be 38% of the height of the thinner Gaussian. In Figure 15, the dual membrane structure seen as two sheets is modelled, and thus the line profiles are fit using the above mentioned effective PSF, i.e. a double Gaussian function. For these curve fits, the ratio of the Gaussians is fixed to 0.38 and the width of the large Gaussian is fixed to 400 nm. The width of the small Gaussian, as well as the center of all double Gaussian functions, varies.

Figure 15 shows that the expected intensity profile along a line depends both on the three-dimensional expected emission distribution but also the type of sample being imaged. Figure 15 shows the resulting axial intensity profile across a virtual sample consisting of a thin sheet, mimicking e.g. a membrane structure.

The emission probability function of 3D-pRESOLFT imaging can be approximated very well as a sum of Gaussian functions. The super resolution ability of the system comes from the sharp central Gaussian function. Since a Gaussian function, unlike an airy function, has theoretically infinite frequency support, there is no absolute cut-off frequency for which above that, the system carries zero information. Information content will however decrease with increasing frequency and the question of interest is whether the frequency distribution of the information content is sufficient to answer the biological question at hand. Apart from the shape of the emission probability function, which depends on the switching parameters of the fluorophore, this parameter is heavily influenced by the properties of the labeling, i.e. labelling density, label brightness etc., but also on the structure of the sample imaged i.e. sparsity, shape etc.

Figure 16 demonstrates the effect of changing labelling parameters on image quality and effective resolution. Specifically, Figure 16 is a demonstration using simulations of how labelling density, label brightness and sample structure affects the useful resolution in rsFP based imaging. The simulations use the imaging parameters presented in Table 4 above. Figure 16a shows that increasing labelling density does not affect the image quality in the same way as increasing label brightness due to the stochastic nature of photoswitching. Low labelling density with bright labels suppresses the Poisson photon emission noise but does not suppress switching noise. High labelling density however suppresses both noise sources. Figure 16b shows that, at low labelling density, sparse structures like cross-sections of filaments are hardly distinguishable whereas sheet like structures can be both distinguished and separated at 80 nm distance. At 5x higher labelling density, the sparse structure can be clearly distinguished and separated.

In order to explore and test different illumination schemes, a tool was developed to simulate imaging data of samples labelled with reversibly switchable fluorophores. A voxelised virtual sample is created containing a certain number of fluorophores in each voxel. Illumination patterns are defined on the same voxel grid as the sample and interactions between the illuminations and the fluorophores follow specific spectral responses preassigned to the fluorophores. The binary states of the fluorophores are tracked during the different illuminations applied using randomly generated numbers and fluorescent emission is calculated according to the applied imaging sequence. The fluorescent emission is virtually recorded on a camera after propagation through an ideal diffraction limited optical system and with camera properties mimicking the camera used in the real optical setup. By simulating the data in this way, the true stochastic nature of the fluorophore switching is incorporated, giving realistic simulated data. As shown in Figure 16, the simulations correspond very well with the recorded data.

The simulations are used to illustrate the impact of different sample and imaging parameters on the quality of the final data. Figure 16 illustrates the potential increase in image quality achievable by increasing the labelling density or the label brightness. Due to the stochastic nature of photoswitching, an increased labelling density is preferable to an increased label brightness. Although the difference between these images are purely in terms of signal to noise ratio, it is clear that there is a strong coupling between signal to noise ratio and useful resolution. Sample composition also has an impact on the perceived ability of a system to distinguish different structures. In Figure 16, the two labelled sheets can just be distinguished, while the single filaments can be hard to detect. If labelling density is increased, single filaments can just be perceived while sheets are very well separable. Given the framework presented and accurate characterization of fluorophore properties, the image formation model can be concisely described as a convolution between the sample fluorophore density and the expected relative emission distribution as presented in the above equations. This accurate description of the image formation process allows us to estimate the underlying sample density using a custom designed Richardson-Lucy algorithm.

The optical setup shown in Figure 7 used to create the illumination pattern and detect the emitted fluorescence can be divided into three main parts:

• The two microlens paths used to create the multi-foci patterns for on-switching (405 nm laser) and read-out (488 nm laser)

• The laser paths used to create the off-switching pattern (491 nm lasers)

• The detection path that images the emitted fluorescence onto the sCMOS camera.

The two microlens paths each contain a fiber coupled laser source (Cobolt 06-MLD 488 nm and 405 nm filtered with Chroma ET405/10X and ET488/10X respectively) that after a collimating lens passes through the microlens array (Thorlabs MLA150-7AR-M) with a 150 pm distance between lenslets. The image plane after the microlenses is demagnified by a factor of two using a 4f telescope. The beams are then coupled into the main optical path using a 50/50 non-polarizing beam splitter (Thorlabs CCM1- BS013/MB) and a dichroic mirror (Semrock Di03-R442-t 1-25x36). The main optical path then contains an optimized scan lens and objective pair (Leica STED-Orange 1.4 NA Oil objective) giving around 104x demagnification. The final periodicity of the multi foci pattern in the sample is 720 nm.

The off-switching paths consist of three separate paths originating from two different but identical laser sources (Cobolt Calypso 491 nm DPSS). Using a 50/50 polarizing beam splitter (Thorlabs CCM1-PBS251/M), one of the beams is divided into two to give the total of three beams. Two of them, beam 1 and beam 2, have horizontal polarization and the last one, beam 3, has vertical polarization. The two beams with horizontal polarization are directed onto a diffraction grating (phase-diffraction gratings of 437-nm-high Si02 lines with a 25-pm period from Laser Laboratorium Gottingen) with horizontal grating lines. These beams will create the partial pattern Pi and P2. The mirrors preceding the diffraction grid are placed so that these beams hit the grid at an angle of 1.125 degrees in opposite direction. This small tilt at the plane of the diffraction grids is what gives the asymmetry in the back focal plane. Since these two beams originate from different laser sources, they will be temporally incoherent and thus will not interfere with each other. The beam with vertical polarization is directed onto a diffraction grating with vertical grating lines. This beam is aligned symmetrically with the optical axis and creates the partial pattern P3. After passing through the two gratings, the beams are combined with a second polarising beam splitter. The combined beams pass through a telescope between which a physical mask is placed to block everything except the +1 and -1 diffraction orders of the gratings. Since the -1 order of beam 1 and +1 order of beam 2 will both fall on the optical axis at the plane of the mask and need to be let pass, while the 0 order of beam three should be blocked, a very small intentional misalignment of beam 3 is introduced to allow blocking of the 0 order without blocking the -1 and + 1 order of beam 1 and 2 respectively. This will introduce a minor tilt in also the partial pattern P3. This will however have no significant influence on the final pattern and performance of the system.

The detection is designed as a widefield detection. As the main excitation path is reflected off a long pass dichroic mirror (Semrock Di03-R488-tl-25x36) before entering the objective, the emitted fluorescent light will pass through the dichroic mirror and is imaged onto a sCMOS camera (Hamamatsu ORCA-Fusion) using a standard 200 mm tube lens. The detection path also contains an additional band pass filter (Chroma ET535/70m) to minimize any ambient light and two notch filters (Chroma ZET405NF and ZET488NF) to eliminate any reflections.

The performance of the 3D-pRESOLFT imaging system relies on an accurate co alignment of the three different illumination patterns. This preferably requires both that the periodicities of the patterns match as well as the translational positioning. Matching the periodicities is mainly a matter of designing the optical paths to achieve magnifications that give matching patterns. However optical components are never 100% perfect (resulting from e.g. chromatic differences), which is why some manual craftsmanship may be needed to achieve perfect matching. In our case, we achieve this final minor tuning of periodicities using the telescopes following the microlens arrays. By slightly tuning axial positions of these lenses, we can tune the final periodicities to exactly equal double the periodicity of the off- pattern. Alternatively, a third lens with long focal length (200-300 mm) can be positioned in the focal plane of the two lenses forming the above mentioned 4f telescope. This lens will change the position of the back focal plane of the telescope requiring an axial repositioning of the microlens array.

The periodicity of the array in the sample can be fine-tuned by moving the axial position of the inserted lens. For the translational positioning (x-y-z overlap), the off- pattern to the detection in terms of rotation and axial positioning is first aligned by tuning the rotation and axial position of the diffraction gratings (mounted on rotation and z- translation mounts). We then tune the rotation and xy-translation of the two multi-foci patterns by physically rotating and moving the microlenses on their rotational and translational mounts. The precise co-alignment of the patterns is inspected and tuned using a conventional bead scan procedure, where a fluorescent bead is scanned through the illumination patterns to probe their intensity at different positions.

The co-alignment of the patterns can also be visualized using a fluorescent layer that is excitable using both 405 nm and 488/491 nm lasers, e.g. Alexa 430.

Figure 17 shows two images with the different light patterns superimposed and color coded. The images show that both the on-switching and read-out patterns (left image) as well as read-out and off-switching pattern (right image) co-align well throughout the vast majority of the field of view. Slight pattern shifts can appear in the edges of the field of view due to minor aberrations and optical imperfections. This may cause a slight decrease in image contrast in these areas.

In Figure 17, the illumination patterns used for switching and reading out fluorophores are visualized by illuminating a fluorescent layer. Co-alignment between both multifoci patterns (488 nm read-out and 405 nm on switch) as well as between multifoci pattern and off-switching pattern (488 nm read-out pattern and 488 nm off pattern) is shown over the 40 x 40 pm ² field-of-view. Pattern images have been high pass filtered to aid visualization. Bottom row shows five line profiles taken across the off-switching (blue), read-out (red) and on-switching (green) patterns at the five positions indicated by the white arrows.

It will be appreciated that the above numerical values are merely intended to help illustrate the working of the invention and may vary depending on the requirements of the imaging system and the imaging application.

The listing or discussion of an apparently prior-published document or apparently prior- published information in this specification should not necessarily be taken as an acknowledgement that the document or information is part of the state of the art or is common general knowledge.

Preferences and options for a given aspect, feature or parameter of the invention should, unless the context indicates otherwise, be regarded as having been disclosed in combination with any and all preferences and options for all other aspects, features and parameters of the invention.