Method of determining the arrangement of a plurality of point sources

Abstract

In one method for determining the arrangement of point sources in a sample, the point sources are scanned (3) with a probe signal including the probe signal intensity. The spatial intensity distribution of the probe signal intensity has a local probe signal intensity minimum, which is bounded on both sides by the probe signal intensity maximum in at least one spatial direction. The local probe signal intensity minimum is located at different probe signal intensity minimum locations spaced apart by distance in the at least one spatial direction. For each of the different probe signal intensity minimum locations, the measurement intensity of the measurement signal from the point source is recorded (4). The measurement intensity depends on the probe signal intensity at the point source location. The point sources are limited (2) to a number of at least 2 and to such a small spatial area of ​​the sample that the spatial progression of the recorded measurement intensity at different probe signal intensity minimum locations has only one local measurement signal intensity minimum. The arrangement of the point sources is determined (5) from the spatial progression of the recorded measurement intensity at different probe signal intensity minimum locations using prior knowledge of the point source arrangement.

Description

Technical Field

[0001] This invention relates to a method for determining the arrangement of identical point sources in a sample with high precision. More particularly, this invention relates to the method described according to the preamble of claim 1.

[0002] Many embodiments of this method belong to the field of microscopy, and more particularly to the field of ultra-high resolution optical microscopy. Other embodiments of this method belong to the field of sonography, and more particularly to the field of ultrasound imaging. Background Technology

[0003] For example, in the study of biological processes, it is of interest to determine the arrangement of different or identical structures or structural portions, and particularly to determine the temporal evolution of such arrangements. The structures or structural portions may be, for example, different proteins and / or different regions of a single protein or any other larger molecule. To determine the arrangement of interest, these structures may be labeled with point sources, or these structures may inherently include point sources that provide measurement signals, and using these measurement signals, the arrangement of these point sources can be determined as an image of the arrangement of the structure of interest.

[0004] A set of point sources used for this purpose are fluorophores. Fluorophores can be detected by excitation light, or more specifically, excited by excitation light, and can be located based on the fluorescence emitted in response to excitation by the excitation light. However, fluorescence can only be assigned to a single fluorophore if its distance to adjacent fluorophores is at least approximately λ / (2n sinα), where λ is the wavelength of the fluorescence, n is the refractive index of the optical material between the sample and the objective lens used for imaging the fluorescence, and α is half the objective aperture. This is a strong limitation on the determinable arrangement of fluorophores used as point sources.

[0005] This limitation can be overcome by using different fluorophores for adjacent structures, which can be detected and / or emit fluorescence at different wavelengths of excitation light. However, this concept is limited by crosstalk between the excitation cross-sections of different fluorophores and by the overlap of their emission spectra. This is especially true if labeling of more than two structures arranged at a distance less than λ / (2n sinα) is required. Furthermore, this concept requires additional expenditure for excitation and / or recording at different wavelengths, and the number of other similar fluorophores that can be excited and / or emitted at easily distinguishable wavelengths is strongly limited.

[0006] Another concept for individually locating fluorophores arranged in very close proximity utilizes switchable fluorophores, i.e., fluorophores that can switch between an on state where they can be excited to emit fluorescence and an off state where they cannot be excited to emit fluorescence. If, at a given time, only one fluorophore in an arrangement of multiple fluorophores is in its on state, its position can be determined with high precision from the fluorescence it emits, since the fluorescence originates uniquely from that fluorophore. Once all positions of all fluorophores are determined in this way, the fluorophore arrangement is known. However, this concept inherently does not allow for determining the positions of all fluorophores at the same time. Furthermore, the switching signal always affects all fluorophores in the arrangement. Therefore, it is impossible to switch fluorophores one after another. Instead, which fluorophore will actually be switched is determined by the transition probability. For a large number of fluorophores, determining the positions of all fluorophores requires some additional time, i.e., much more time than the time required to determine the position of one fluorophore multiplied by the number of fluorophores. In addition, some switchable fluorophores tend to flicker between their on and off states in an uncontrolled manner.

[0007] US 9,719,928B2 discloses a method for high-resolution fluorescence microscopy using a structured excitation beam. To determine the position of individual fluorescent molecules in a sample that maintain a minimum distance from each other, the individual fluorescent molecules are excited by an excitation beam to emit fluorescence. Fluorescence is recorded at different positions of the zero point of the excitation beam intensity distribution. The distance between these positions is at least half of the minimum distance between the fluorescent molecules. The position of the fluorescent molecule is derived from the change in fluorescence intensity at the zero point of the excitation beam. In practice, the distance between individual fluorescent molecules is adjusted to maintain a minimum value d = λ / (2n sin α √(1+I / I)). S ), where λ is the wavelength of the excitation light, n is the refractive index of the optical material forming the excitation light intensity distribution having at least one minimum value, α is the half-angle of the aperture of the optical arrangement that guides the excitation light to the sample, I is the maximum intensity of the excitation light within the sample, and I S This is the material-dependent fluorescence excitation saturation intensity of the excitation light. The adjustment of the distance between individual fluorescent molecules to a minimum value d is achieved by using a low concentration of fluorescent molecules in the sample or by using molecules that can transfer or switch between non-fluorescent and fluorescent states. With this known method, the arrangement of fluorescent molecules used as the same point source can only be determined without switching if the point sources maintain a minimum distance d. In this case, the change in fluorescence intensity at the excitation zero point position involves individual local minima for each fluorescent molecule, i.e., at each position corresponding to the position of the corresponding fluorescent molecule in the sample. However, the arrangement of many structures of interest does not maintain a minimum distance d. These arrangements can only be determined using different fluorescent molecules or switchable fluorescent molecules, and have all the drawbacks explained above.

[0008] US 10,962,479B2 discloses a method for determining the position (in n spatial dimensions) of a single molecule in a sample that can be excited to emit fluorescence with high spatial resolution. Excitation light is directed onto the sample, and its intensity distribution has a zero point and regions of increasing intensity adjacent to that zero point in each of the n spatial dimensions. The zero point is arranged at no more than n × 3 distinct locations. The fluorescence emitted by the single molecule is recorded individually for each distinct location of the zero point. The position of the single molecule in the n spatial dimensions of the sample is derived from the individually recorded fluorescence intensities for no more than n × 3 distinct zero point locations. The single molecule has a minimum distance from other similar molecules that can be excited by the same excitation light to emit fluorescence in the same wavelength range. This minimum distance is reliably maintained if the distance of the single molecule to such similar molecules is at least as high as the diffraction barrier at the emission wavelength, i.e., at least λ / (2n sinα), as described above. Therefore, this known method is only applicable to determining the arrangement of the same point sources at significantly smaller distances, if different or interchangeable molecules are used, and if the associated problems are accepted, see above. On the other hand, this known method, also known as MINFLUX (minimum photon flux) microscopy, allows for the determination of the position of a single molecule with very high precision without requiring the molecule to emit many photons.

[0009] Matthew P. Gordon et al., "Single-molecule high-resolution imaging with photobleaching", PNAS 101(17)6462-6465, April 19, 2004, https: / / doi.org / 10.1073 / pnas.0401638101, disclosed how to use the quantified photobleaching behavior of a single fluorescent dye molecule to locate the positions of two dyes and determine their spacing with an accuracy of 5 nm. By fitting images of one dye before and after photobleaching, the two dyes can be located simultaneously, and their spacing can be calculated.

[0010] WO2011 / 106323A2 discloses a method for photobleaching and intermittent localization microscopy (PhILM). A "reverse subtraction film" is obtained by sequentially subtracting one frame from another from a film of fluorophores transitioning between fluorescent and dark states. Dark and bright spots are detected in the reverse subtraction film, where bright spots correspond to transitions from a fluorescent to a dark state ("photobleaching" events) and dark spots correspond to transitions from a dark to a fluorescent state ("flickering" events), and the corresponding frame numbers and positions of these photobleaching or flickering events are stored. The positions of the fluorophore transition events are located at subpixel resolution; and a high-resolution image is created by plotting the located positions of the fluorophore transition events in the final image.

[0011] Purpose of the invention The purpose of this invention is to provide a method for determining the arrangement of identical point sources in a sample with high accuracy, even if the point sources are arranged at very small distances, and the method does not require switchable point sources.

[0012] Solution According to the present invention, the objective of the present invention is achieved by the method of independent claim 1.

[0013] Preferred embodiments of the method according to the invention are defined in the dependent claims. Summary of the Invention

[0014] In the method for determining the arrangement of point sources in a sample according to the invention, the point sources are scanned with a probe signal including probe signal strength. The spatial intensity distribution of the probe signal strength has a local probe signal strength minimum, which is bounded on both sides by the probe signal strength maximum in at least one spatial direction. During the step of scanning the point sources with the probe signal, the local probe signal strength minimum is located at different probe signal strength minimum locations spaced apart in the at least one spatial direction. Furthermore, for each of the different probe signal strength minimum locations, the measurement intensity of the measurement signal from the point source is recorded. The recorded measurement signal can be any measurement signal whose measurement intensity depends on the probe signal strength at the point source location. The arrangement of the point sources to be determined is limited to a known number of at least two point sources, and is limited to such a small spatial area of ​​the sample that the spatial progression of the recorded measurement intensity at the different probe signal strength minimum locations has only one measurement signal minimum. The arrangement of the point sources is determined from the spatial progression of the recorded measurement intensity at the different probe signal strength minimum locations using prior knowledge of the point source arrangement.

[0015] The recorded changes in measurement intensity are spatial because the measurement intensity is recorded for the minimum position of different detection signals in space.

[0016] The prior knowledge preferably includes at least one of the following: the expected contribution of each point source to the measured intensity, the actual number of point sources, a variety of different possible basic geometries for the arrangement of point sources, or (at least when the number of point sources is greater than 4) the geometry of the arrangement of point sources. The actual number of point sources can be known, for example, from the fact that a protein containing a known fixed number of point sources is being studied. Point sources can be, for example, fluorophores that are coupled to a fixed number of coupling sites introduced into the protein in a generally known protein engineering manner. In this embodiment, coupling sites introduced at specific locations in the protein can also inherently limit the different possible basic geometries of the arrangement of point sources to certain basic geometries, i.e., provide further prior knowledge for determining the arrangement of point sources from the spatial progression of the recorded measured intensity at different locations of minimum detection signal.

[0017] The prior knowledge must be known before determining the arrangement of point sources from the spatial progression of the recorded measurement intensities at different locations of minimum detection signals. However, it is not necessary to know the prior knowledge before recording the measurement intensities of the measurement signals from the point sources for each of the different locations of minimum detection signals. Instead, the actual number of point sources can be obtained, for example, by evaluating the total measurement intensity of the measurement signal and / or the discrete reduction in the total measurement intensity of the measurement signal due to the successive bleaching of fluorescent point sources one after another. The total number of these discrete reductions indicates the actual number of point sources. Furthermore, the magnitude of these discrete reductions indicates the contribution of each point source to the measurement signal intensity. Discrete increases and decreases in the measurement signal caused by flickering fluorescent point sources can also be evaluated to determine the contribution of each point source to the measurement signal intensity. These contributions may depend on various factors, such as the orientation of the individual point sources or the local environment, and they can be used as further prior knowledge when determining the arrangement of point sources from the spatial progression of the recorded measurement intensities at different locations of minimum detection signals.

[0018] Furthermore, the location of the last bleached fluorescent spot source can be determined with high precision from the spatial progression of measurement intensity recorded by measurement signals at different minimum detection signal positions, or by positioning, and used as prior knowledge when determining the arrangement of spot sources from the spatial progression of recorded measurement intensity at different minimum detection signal positions. More specifically, the location of the last bleached fluorescent spot source, determined with high precision, can be used as prior knowledge when determining the location of the penultimate bleached fluorescent spot source with increased precision. For example, the location of the penultimate bleached fluorescent spot source can be determined from the spatial progression of measurement intensity recorded by measurement signals at different minimum detection signal positions, using the location of the last bleached fluorescent spot source as prior knowledge. Then, the locations of the last bleached and penultimate bleached fluorescent spot sources can be used as prior knowledge when determining the location of the third-to-last bleached fluorescent spot source with increased precision, and so on. For example, the location of the fluorescent source for the penultimate bleaching can be determined from three point sources—only from the last bleaching, the penultimate bleaching, and the penultimate bleaching—the spatial progression of the measured intensity recorded by the measurement signals at different minimum detection signal positions, and the two locations of the fluorescent source for the last bleaching and the penultimate bleaching, which serve as prior knowledge. At least, the arrangement of point sources determined from the spatial progression of the recorded measured intensity at different minimum detection signal positions can be used to reverse-engineer the location of the fluorescent source for the last bleaching, based on the point source only from the last bleaching, the spatial progression of the measured intensity recorded by the measurement signals at different minimum detection signal positions, or the location of the fluorescent source for the last bleaching precisely determined by positioning.

[0019] Furthermore, for scintillation fluorophores, PhILM can be used to determine the precise location of one or more point sources individually with high accuracy. However, for the arrangement of point sources, whose arrangement is determined by the spatial progression of changes in the measured intensities at different detection signal minimum positions, bleach-based reverse lookup is only possible (if possible) at the very end of these changes for the final arrangement of the point sources. On the other hand, for scintillation fluorophores, tracking changes in the entire arrangement of point sources becomes difficult. Therefore, the actual arrangement of most point sources will have to be determined from the spatial progression of the recorded measured intensities from all point sources at different detection signal minimum positions, without prior knowledge of the precise locations of one or more point sources that have been individually determined with high accuracy.

[0020] Another indication of the actual number of point sources can be obtained by analyzing photon statistics, i.e., the timing of individual photons emitted by point sources.

[0021] The distances between the different probe signal minimum locations in the at least one spatial direction are selected such that the shape of the localized measurement signal minimum can be determined from the measurement intensities recorded at these different probe signal minimum locations. For two point sources, the shape of the localized measurement signal minimum can typically be determined solely from the measurement intensities recorded at three different probe signal minimum locations in the at least one spatial direction, one of which is located on either side of the arrangement of interest, and the third is located within the arrangement of interest. The distances between these different probe signal minimum locations will be on the typical order of magnitude of the FWHM of the probe signal minimum, i.e., one or several tenths. The FWHM of any minimum is determined as the width of the corresponding intensity variation process at half the depth of the minimum, compared to the adjacent maximum. Therefore, the FWHM is effectively the "full width at half-minus".

[0022] The fact that the recorded measurement signal depends on the strength of the probe signal at the point source location means that all point sources whose arrangement is to be determined continuously contribute to the measurement signal unless their point source locations are the same as the current minimum probe signal location, i.e., all point sources are in a state of being on in response to the probe signal to provide the measurement signal.

[0023] The measurement intensity can depend linearly on the probe signal intensity at the respective point source location, and can start from zero or measurement intensity noise when the probe signal intensity is zero. However, the dependence of the measurement intensity on the probe signal intensity can also be nonlinear. In particular, this nonlinearity may exist at higher probe signal intensities. In the region of minimum probe signal intensity, there will be very small probe signal intensities, and at small probe signal intensities, there will generally be a linear dependence of the measurement intensity on the probe signal intensity. However, if the probe signal excites the point source to emit the measurement signal via a two-photon or multi-photon process, then even at low probe signal intensities, the measurement intensity exhibits a nonlinear dependence on the probe signal intensity.

[0024] Furthermore, given the same depth of minimum localized probe signal intensity, if the probe signal is excited by a point source via a two-photon or multi-photon process to emit the measurement signal, the background or baseline of the measurement signal will be significantly reduced compared to a single-photon process. This allows for more accurate determination of the point source arrangement in a sample, as discussed below. On the other hand, if the probe signal is excited by a point source via a two-photon or multi-photon process to emit the measurement signal, the excitation probability is much lower compared to a single-photon process, and the excitation light intensity required to obtain the specific measurement signal intensity from the point source needed to reduce statistical errors is much higher. As a result, the risk of photochemical bleaching of the point source is much higher when using a two-photon or multi-photon process.

[0025] Therefore, in one embodiment of the method for determining the arrangement of point sources in a sample, a further detection signal is used to excite the point sources via a single-photon process to emit a measurement signal, and the arrangement of point sources in the sample is determined or monitored sequentially or alternately with lower precision (i.e., with lower spatial resolution but higher temporal resolution) using the detection signal to excite the point sources via a two-photon or multi-photon process to emit a measurement signal, and the arrangement of point sources in the sample is determined with higher precision (i.e., with higher spatial resolution but lower temporal resolution) using the detection signal to excite the point sources via a two-photon or multi-photon process.

[0026] More generally, the method according to the invention for determining the arrangement of point sources in a sample can be combined with any other known method for determining or imaging the arrangement of point sources in a sample in a different manner and / or with a different level of precision, particularly with lower precision, so as to, for example, first locate the arrangement of point sources in the sample to be determined. Other known methods for determining or imaging the arrangement of point sources in a sample include, for example, point source-compatible epifluorescence microscopy, laser scanning microscopy, STED microscopy, and other types of RESOLFT microscopy.

[0027] In the method according to the invention, at least some prior knowledge of the arrangement of point sources is utilized. The minimum prior knowledge of the point sources is the actual number of point sources. The actual number of point sources may be known due to the nature of the arrangement of the same point sources of interest. In another embodiment, the number of point sources can be obtained from the measurement of the total strength of the measured signal. For example, the measured total strength of the measured signal can be divided by the known expected contribution of each point source to the measured strength. The known number of point sources is not merely known to be in the range of 2 to (e.g.) 32. Rather, the exact number of point sources is prior knowledge utilized in the method according to the invention.

[0028] At least when the number of point sources is greater than 4, prior knowledge can further include the basic geometry of the point source arrangement. This known basic geometry can be point sources arranged at equal distances along a straight line, a circle, or a grid. For a number of point sources not exceeding 4, and particularly not exceeding 3, the geometry of the point source arrangement is inherently limited and can generally be determined from the spatial progression of the recorded measured intensity at different locations of minimum detection signal. For a number of point sources of 2, the geometry of the point source arrangement is inherently known because the two point sources are always arranged at a distance to be determined along a straight line. In testing the method of the present invention, it can be demonstrated that even for a number of point sources of 3, the geometry of the point source arrangement can be determined with high precision from the spatial progression of the recorded measured intensity at different locations of minimum detection signal, as described below.

[0029] Alternatively, the prior knowledge may include a variety of different possible basic geometries for the arrangement of point sources, and these different possible basic geometries may even include known arrangements of different but fixed numbers of point sources.

[0030] The fact that the spatial progression of the recorded measurement intensity at different locations of minimum probe signal has only one local measurement signal minimum means that, compared to the FWHM of the local probe signal intensity minimum, the point sources are arranged in a very small spatial region of the sample. Furthermore, the measurement signals from all point sources contribute to this spatial progression of the recorded measurement intensity. Therefore, a considerably high total measurement signal can be obtained without requiring high contributions from individual point sources.

[0031] The spatial progression of the recorded measurement intensity at different locations of minimum detection signals, determined by the arrangement of its point sources, is the shape of the minimum value of that local measurement signal.

[0032] Using the prior knowledge, the arrangement of point sources in at least one spatial direction can be determined from the depth and / or width of the minimum local measurement signal. The parameters depth and width are interrelated to the minimum local measurement signal. Both respond strongly to increases in point source distance starting from zero. The depth of the minimum local measurement signal decreases with increasing point source distance, while its width increases with increasing point source distance. Because the decrease in depth and increase in width are particularly strong as the point source distance increases from zero, the method according to the invention is particularly suitable for determining point source distances very close to zero, whereas prior art methods require a minimum point source distance.

[0033] In one embodiment of the method of the invention, the minimum value of a local measurement signal is compared with a minimum value of a local detection signal intensity or with a minimum value of a comparative local measurement signal, the minimum value of which corresponds to a comparative arrangement of point sources in which all point source positions are the same in at least one spatial direction, i.e., where the point source positions are arranged at zero distance in at least one spatial direction. Each difference noted in such a comparison indicates the distance of the actual point source position. For many detection signals, the minimum value of the local detection signal intensity can be easily determined by scanning a single gold bead with the detection signal intensity distribution and recording the detection signal reflected by the gold bead. Alternatively or additionally, the minimum value of a local measurement signal can be compared with at least one minimum value of a comparative local measurement signal corresponding to a certain basic geometry of the arrangement of point sources in order to determine whether, or with what probability, the actual basic geometry of the arrangement of point sources is the corresponding certain basic geometry.

[0034] The steps of determining the arrangement of point sources may include fitting a curve to the recorded measured intensities. More specifically, at least one fitting variable tuned when fitting the curve to the recorded measured intensities may be a parameter that directly describes the arrangement of the point sources. For example, this parameter may be the distance between the point sources in the at least one spatial direction.

[0035] In one embodiment of the method of the present invention, the prior knowledge includes a variety of different possible basic geometries for the arrangement of point sources. The spatial progression of the recorded measured intensities at different locations of minimum detection signals is compared with each of a variety of different comparative spatial progressions to determine the arrangement of the point sources. Each of the variety of different comparative spatial progressions corresponds to one of the variety of different possible basic geometries for the arrangement of point sources and can be generated through computational simulation using a measured, estimated, or hypothetical arrangement of the point sources. For example, the measured arrangement of the point sources may include the location of each point source previously measured with high precision using the positioning of switchable fluorophores. In another embodiment, the arrangement of the point sources used in the computational simulation may be purely hypothetical. It should be understood that in any computational simulation, the spatial intensity distribution of the detection signals in the sample must be considered.

[0036] In the method according to the invention, all comparison steps can be implemented automatically by utilizing at least one of artificial intelligence, neural networks, artificial neural networks, or machine learning. These techniques are well-known powerful tools for pattern recognition, and they can be particularly used to determine the correct basic geometry of the arrangement of point sources from a variety of different possible basic geometries. The techniques used in practice can be trained with actual measured and / or simulated data.

[0037] In the method of the present invention, it is preferable that the number of point sources does not exceed 32, 16, 8, or 4, and for 3 or 2 point sources, their arrangement can be determined with high accuracy most readily from the spatial progression of the recorded measurement intensity at different locations of minimum detection signal without any further prior knowledge. Alternatively or in addition to a low number of point sources, further prior knowledge of the arrangement of point sources will be utilized when determining the arrangement of point sources from the spatial progression of the recorded measurement intensity at different locations of minimum detection signal. This prior knowledge includes a certain basic geometry of the arrangement of point sources. For example, point sources may be arranged on a ring, and the parameters of the arrangement of point sources to be determined may be the diameter of the ring or the point source distance along the circumference of the ring.

[0038] Furthermore, prior knowledge of the arrangement of point sources may include the relative scattering cross sections of each point source. Preferably, these relative scattering cross sections of each point source are equal, i.e., all point sources may be identical. However, the method according to the invention can be performed in parallel with two or more sets of different point sources that can be detected by different probe signals and / or provide distinguishable measurement signals. These different sets of point sources may, for example, be used to label different structural subsets of macromolecules. Therefore, in a dual-channel embodiment of the method according to the invention, in addition to the arrangement of point sources, a further arrangement of further point sources is determined. The further point sources are selected to provide further measurement signals distinguishable from the measurement signals, and / or to be selectively detected by further probe signals different from the probe signals. For example, the further measurement signals and the measurement signals may be light of different wavelengths, and / or the further probe signals and the probe signals may be light of different wavelengths, such that the further point sources and the point sources can be detected separately by the further probe signals and the probe signals, respectively.

[0039] Furthermore, although the point sources used in the method according to the invention are generally not switchable (see below), they can be inactivated, for example, by photochemical bleaching. The sample can then include further activatable point sources, which are also limited to a known number of at least two point sources and confined to such a small spatial region of the sample that the spatial progression of the recorded measurement intensity at different locations of minimum detection signal has a local minimum measurement signal. The further point sources can be, for example, fluorophores that can be activated by decageing. Suitable fluorophores can be, for example, selected from caged quantum dots. Once the arrangement of the point sources has been determined and the point sources have been inactivated, the further point sources can be activated, and their arrangement can be determined according to the method of the invention to obtain further information about the sample. Here, the activation of all further point sources is not a randomized process. Instead, all further point sources will be activated before their arrangement is determined.

[0040] As previously stated, the arrangement of point sources can be determined with respect to their point source distances in the at least one spatial direction. If the arrangement of point sources is further determined with respect to their centroids in the at least one spatial direction, then the locations of all point sources in the sample are known.

[0041] The method according to the invention does not require a switchable point source that can switch between an on state providing a measurement signal and an off state not providing a measurement signal, and which is typically hydrophobic. Therefore, the point source can also be readily selected to be non-flickering, i.e., to switch between the on and off states in an uncontrolled manner. Conversely, the point source can be readily selected from those having a fixed dependence of the measurement intensity on the intensity of the detected signal at the respective point source location. Furthermore, the point source can be readily selected from hydrophilic point sources suitable for biomolecular labeling.

[0042] Typically, the probe signal will have wave-like properties, i.e., it will have a wavelength. Therefore, destructive interference of the probe signal can be used to form a local minimum probe signal intensity. This formation of a local minimum probe signal intensity allows for a small FWHM (Frequency Wavelength). Furthermore, the sample space region within which the point source is confined can preferably be no larger than 1 / 10 of the wavelength in at least one spatial direction. Alternatively, the sample space region within which the point source is confined can be no larger than 1 / 25, 1 / 50, or even 1 / 75 of the wavelength in at least one spatial direction. Therefore, the size of the sample space region within which the point source is confined can be much smaller than the diffraction barrier of λ / (2n sinα).

[0043] Most preferably, the minimum local probe signal strength includes the zero point of the probe signal strength. In this case, the shape of the at least one local minimum measurement signal strength is most dependent on the distances of point sources that are not zero in the at least one spatial direction. In fact, in this case, the spatial resolution or accuracy of the method according to the invention in the at least one spatial direction depends only on the background or baseline of the measurement signal. In particular, when all point sources are located at the zero point of the minimum probe signal strength, there will be no statistical noise, as if there were no measurement signal. This is a significant difference from all methods that use the maximum probe signal strength to scan the arrangement of point sources of interest. Using the maximum probe signal strength, when all point sources are located at the maximum probe signal strength, there will be a maximum measurement signal and a maximum absolute statistical measurement signal noise.

[0044] As previously stated, the method according to the invention is particularly suitable for determining small distances of point sources in at least one spatial direction. Therefore, the sample space region within which the point source is confined is preferably no larger than 1 / 2, 1 / 3, or 1 / 5 of the FWHM of the minimum local detection signal strength. Optionally, the sample space region within which the point source is confined is no larger than 1 / 10 or even no larger than 1 / 20 of the FWHM of the minimum local detection signal strength.

[0045] In many embodiments of the method of the present invention, the detection signal will be an electromagnetic signal. Very commonly, this electromagnetic signal will be light. The light may have wavelengths in the infrared, visible, or ultraviolet range. In another embodiment, the electromagnetic signal includes x-rays. In yet another embodiment, the detection signal is an acoustic signal or any other pressure signal of a fluctuating nature.

[0046] The measurement signal can be fluorescent light, and the point source can be a fluorophore. In another embodiment, the measurement signal is any light or other electromagnetic signal inelastically scattered by the point source. For example, the measurement signal can be light Raman scattered by the point source. Furthermore, the measurement light can be elastically scattered light, such as light scattered by a latex bead used as a point source, or any other electromagnetic signal elastically scattered by the point source. In yet another embodiment, the measurement signal can be sound scattered by the point source, optionally ultrasound.

[0047] In all embodiments, the point source acts as a point source of the measurement signal, i.e., a source whose size is very small compared to the wavelength of the measurement signal. Typically, these sizes will not be greater than 1 / 16, 1 / 32, 1 / 64, 1 / 128, 1 / 256, or 1 / 512 of the wavelength of the measurement signal.

[0048] In the method according to the invention, the steps of scanning point sources with probe signals, recording the measurement intensity of measurement signals from the point sources, and determining the arrangement of point sources from the spatial progression of the recorded measurement intensity at different locations of minimum probe signals are typically performed not only once, but repeatedly. These steps can be repeated to determine the arrangement of other point sources. In other embodiments, the above steps are repeated to track changes in the arrangement of point sources. Changes can be tracked to study the effects of external influences (e.g., physical or chemical influences, including drugs) on the sample. Furthermore, changes can be tracked along with the movement of entities to which point sources are attached within the sample. Such movement may cause the entities to enter different regions of the sample subject to different external influences.

[0049] In one embodiment of the method of the present invention, point sources can be attached to different sites on an object selected from the group consisting of macromolecules, proteins, complexes, drug candidates, and potential drug targets. Therefore, the point source location will be the actual location of the site to which the point source is attached. Determining the arrangement of point sources will provide information about the conformational state of the corresponding object, and tracking changes in the arrangement of point sources will provide information about changes in that conformational state, such as in response to some external influence or interaction with some other object. This embodiment of the method of the present invention can be used for drug screening, wherein the ability of various drug candidates to interact with a certain drug target and change its conformational state is to be tested.

[0050] The method of the present invention can utilize many measures known from MINFLUX microscopy to reduce the baseline or background of the measurement signal and / or improve spatial resolution or accuracy by reducing the size of the local minimum probe signal intensity (from which the probe signal intensity increases to the maximum in at least one spatial direction). For example, the measurement signal can be recorded confocally with respect to the local minimum probe signal intensity. Furthermore, once the arrangement of the point sources has been determined to such an accuracy that new minimum probe signal locations can be selected to ensure that the point sources in the arrangement are not subjected to more probe signal intensity than the maximum (although the total intensity of the probe signal increases), the total intensity of the probe signal can be increased.

[0051] The local minimum intensity of the probe signal can be bounded by the maximum intensity of the probe signal in one, two, or all three spatial directions. All techniques known from STED- and MINFLUX-microscopy for forming local minimum intensities can be applied. These techniques include, but are not limited to: forming a ring-shaped or bottle-shaped spatial intensity distribution including a central zero; shaping the wavefront of the probe signal into a 2π or higher-order phase vortex; and directing the probe signal onto the sample from different or even opposite directions, such as in 4Pi-microscopy.

[0052] If the minimum local probe signal strength is bounded only in one spatial direction, the point source can be scanned first in the first spatial direction with the minimum local probe signal strength (i.e., the bounded spatial direction) oriented in that first spatial direction. Then, the point source can be scanned again in the second spatial direction with the minimum local probe signal strength (i.e., the bounded spatial direction) oriented in that second spatial direction, where the second spatial direction may be orthogonal to the first spatial direction. Additionally, the point source can be scanned in a third spatial direction with the minimum local probe signal strength (i.e., the bounded spatial direction) oriented in that third spatial direction, where the third spatial direction may be at a 45° angle to the first and second spatial directions. The point source can also be scanned in a fourth spatial direction with the minimum local probe signal strength (i.e., the bounded spatial direction) oriented in that fourth spatial direction, where the fourth spatial direction may be orthogonal to the third spatial direction. Each spatial progression of the measurement signal strength recorded during each scan in an additional spatial direction provides additional usable information about the arrangement of the point source of interest. Furthermore, the characteristics of individual fluorophores, such as their spatial orientation, can be obtained from the spatial progression of the measurement intensity of the measurement signal recorded during several scans in different spatial directions. Therefore, scanning the region of interest of the sample with the minimum or maximum value of the detection signal intensity confined only in one spatial direction is known from existing techniques.

[0053] If the minimum local probe signal strength is bounded in only one spatial direction, then a three-dimensional sample can be scanned in at least three spatial scanning directions, wherein the minimum local probe signal strength (i.e., the spatial direction in which it is bound) will be oriented in the corresponding scanning direction, and wherein the three scanning directions can be orthogonal to each other.

[0054] Furthermore, the minimum probe signal intensity, which is bounded only in one or two spatial directions, can be rotated during the arrangement of the scanning point sources, as is generally known from prior art methods, see, for example, WO 2016 / 156541A1. For example, the minimum probe signal intensity can be rotated around each different minimum probe signal position so that the measured intensity of the measured signal from the point source is recorded for some or all of the different spatial orientations of the minimum probe signal intensity.

[0055] Furthermore, the arrangement of point sources can be scanned with a probe signal by making the minimum intensity of the ring probe signal surround the arrangement of point sources, and the center of the circular motion is adjusted after at least one full circle. Therefore, multiple projections of the distance from the point source to the center of the ring minimum are recorded as the recorded measured intensities at different locations of the probe signal minimum. This can be understood as a Lardon transform convolved with the PSF of the spatial intensity distribution of the probe signal, and allows the arrangement of point sources to be reconstructed by deconvolving and inverse transforming (inverse Lardon transform) the spatial progression of the recorded measured intensities at different locations of the probe signal minimum.

[0056] The direction of scanning the point source, i.e., the direction in which different detection signal minimum positions follow successively, can be defined in any coordinate system, including Cartesian, polar, cylindrical, and spherical coordinates. Furthermore, the point source can be scanned along any straight line or curve. Alternatively, the point source can be scanned by aiming at the individual detection signal minimum positions in any order (i.e., without a specific scanning direction). The number of different detection signal minimum positions can be relatively small to record more measurement signals from the point source, such as more fluorescence photons, for each different detection signal minimum position. The minimum number of different detection signal minimum positions is 3 for the arrangement of the two-dimensional point source to be determined, and 4 for the arrangement of the two-dimensional point source to be determined. Typically, the number of different detection signal minimum positions will be at least 4 for the arrangement of the two-dimensional point source to be determined, and at least 5 or 6 for the arrangement of the two-dimensional point source to be determined. Typically, the number of different detection signal minimum positions will be higher than 6. However, as the number of different detection signal minimum positions increases, more measurement signals from the point source are required. If the minimum local detection signal strength is bounded only in one spatial direction, the measurement signal from the point source can be recorded at each location of the minimum detection signal strength with a first orientation of the minimum local detection signal strength and at least one further orientation of the minimum local detection signal strength, wherein the at least one further orientation is different from the first orientation with respect to the spatial direction in which the minimum local detection signal strength is bound and can be orthogonal to the first orientation.

[0057] The measurement intensity of the measurement signal from the point source can be recorded using a point detector arranged in a confocal array with respect to the minimum intensity of the local detection signal.

[0058] In one embodiment, by modifying the detection of the measurement signal to obtain more information about the arrangement of the point source from the measurement signal, the amount of prior knowledge required to determine the arrangement of the point source from the spatial process of recording measurement intensities at different locations of minimum detection signals is reduced. In the first step, for each of the different locations of minimum detection signals, not only is one measurement intensity recorded, but also the spatial distribution of the measurement intensity of the measurement signal from the point source is recorded. In other words, the measurement signal from the point source is recorded using a spatially resolved detector array (e.g., a digital camera). The spatially resolved detector array can be confocal about the local minimum detection signal intensity or fixed about the arrangement of the point source.

[0059] In the second step, a spatial pattern is imprinted onto the measurement signals from the point sources, and for each of the minimum locations of different probe signals, the resulting spatial measurement intensity distribution is recorded using a spatially resolved detector array. This spatial pattern is imprinted on all components of the measurement signals from each point source in the same manner, and the recorded spatial measurement intensity distribution is a superposition of the patterned components of the measurement signals from all point sources. The intensity of these components, and therefore their superposition, i.e., the recorded spatial measurement intensity distribution, depends on the current distance from each point source to the local minimum of the probe signal intensity. These distances change when the point sources are scanned with the local minimum of the probe signal intensity, and therefore the recorded spatial measurement intensity distribution also changes. Therefore, by using a suitable spatial pattern imprinted on the measurement signals from the point sources, additional information about the arrangement of the point sources can be derived from the recorded spatial measurement intensity distribution and its variations.

[0060] For example, if the point source is a fluorophore, if the detection signal is fluorescent excitation light, if the measurement signal is fluorescent light, and if a scanning fluorescence microscope is used, the detection path of the microscope can be modified. Instead of collecting photons of the fluorescent light at a simple confocal or bucket detector (e.g., an APD), a phase mask is placed in the back aperture of the microscope or any other Fourier plane, and the camera is placed in the image plane of the microscope. The phase mask placed in the Fourier plane allows the same pattern to be imprinted on the fluorescence emitted by all fluorophores, resulting in a spatially shifted copy of that pattern superimposed on the camera. Combined with the spatial intensity distribution of the excitation light having a local minimum detection signal intensity, this allows the determination of the location and brightness of more than two fluorophores, such as three, four, or five fluorophores. This has been demonstrated through simulations under realistic conditions and photon budgets. The basic idea is that the local minimum detection signal intensity modulates the emission intensity differences between fluorophores, and the phase mask in the Fourier plane of the microscope allows additional information about the location of the fluorophores to be imprinted, which can be extracted by evaluating its image with a continuous spatial blend of the distribution determined by the phase mask in the detection path. The camera image changes as the fluorophore is scanned with the minimum local detection signal intensity, and the fluorescence intensity differences between fluorophores are modulated. This can be understood as a series of superimposed images of spatially shifted phase masks along the detection path. This series of superimposed images uniquely encodes the arrangement of the fluorophores.

[0061] A phase mask can be imprinted with patterns of localized intensity minima with strong spatial constraints, such as linear intensity minima. For a single fluorophore, the location of the localized intensity minima on the camera indicates the location of the fluorophore emitting patterned fluorescence. In the spatial fluorescence intensity distribution recorded by the camera, the superposition of spatially shifted pattern copies results in deformed localized intensity minima with reduced depth. However, it is precisely these spatial fluorescence intensity distributions recorded by the camera and the deformation of the localized intensity minima in their spatial progression at different locations of detection signal minima that contain additional information about the fluorophore arrangement.

[0062] If a pattern with a minimum linear intensity is printed, the point source can be scanned using a fixed orientation of that minimum linear intensity, or by using more than one orientation of the minimum linear intensity of the pattern, one after another. Each orientation of the minimum linear intensity of the pattern can be parallel to or at an arbitrary angle to the local minimum linear intensity of the probe signal. For example, a semi-circular phase mask with a π-phase step can be placed in the back aperture of a microscope to print a pattern with a minimum linear intensity.

[0063] Advantageous developments of the present invention are derived from the claims, description and drawings.

[0064] The advantages of the features and combinations of features mentioned at the beginning of the specification are for illustrative purposes only and can be used alternatively or cumulatively without requiring these advantages to be obtained according to embodiments of the invention.

[0065] The following applies to the disclosure of the original application and patent, but not to the scope of protection: Further features can be obtained from the drawings, particularly from the illustrated design and the dimensions of the various components relative to each other, their relative arrangement, and their functional connections. Combinations of features from different embodiments of the invention or features from different claims (independent of selected references in the claims) are also possible and are set forth herein. This also applies to features shown in separate drawings or mentioned in their description. These features may also be combined with features from different claims. Furthermore, further embodiments of the invention may not have the features mentioned in the claims; however, this does not apply to the independent claims of the granted patent.

[0066] The number of features mentioned in the claims and specification should be understood to include both the exact number and a number greater than the mentioned number, without explicitly using the adverb "at least". For example, if a minimum local detection signal strength is mentioned, it should be understood that there is exactly one minimum local detection signal strength, or that there are two or more minimum local detection signal strengths. (However, the feature of one minimum local detection signal strength only relates to the different minimum detection signal locations of one minimum local detection signal strength.) Additional features may be added to these features listed in the claims, or these features may be unique features of the corresponding product.

[0067] The reference numerals included in the claims do not limit the scope of the subject matter protected by the claims. Their sole function is to make the claims easier to understand. Attached Figure Description

[0068] The invention is further explained and described below with reference to the preferred exemplary embodiments shown in the accompanying drawings.

[0069] Figures 1a to 1d illustrate how to distinguish two inelastic point scatterers using diffraction maxima and minima.

[0070] Figures 2a to 2c illustrate the theoretical positioning accuracy of two point scatterers detected using the diffraction maximum (max) or diffraction minimum (min) for N=100 detected photons.

[0071] Figures 3a to 3i illustrate the measurement of the distance between two simultaneously emitting fluorescent molecules by using (x,y-) scans with minimum illumination intensity.

[0072] Figures 4a to 4f illustrate two fluorophores with constant emission at a resolution as low as 8 nm.

[0073] Figures 5a to 5h illustrate the uninterrupted resolution and localization of the two mobile fluorophores.

[0074] Figures 6a to 6h illustrate the sub-diffraction localization of multiple point sources scattering simultaneously.

[0075] Figures 7a to 7c illustrate distance measurements via line scanning and control measurements via the bleaching step.

[0076] Figures 8a to 8c illustrate the correlation between measurement uncertainty and production variability.

[0077] Figure 9 is a flowchart of a method for determining the arrangement of identical point sources in a sample according to the present invention.

[0078] Figure 10a and 10b will compare the arrangement of three identical point sources in a two-dimensional sample determined in the computational simulation of the method of the present invention with the actual arrangement of the three identical point sources from which the computational simulation begins.

[0079] Figure 11 a and 11b will compare another arrangement of three identical point sources in a two-dimensional sample determined in the computational simulation of the method of the present invention with another actual arrangement of the three identical point sources from which the computational simulation begins; and Figure 12 a and 12b will compare another arrangement of three identical point sources in a two-dimensional sample determined in the computational simulation of the method of the present invention with another actual arrangement of the three identical point sources from which the computational simulation begins. Detailed Implementation

[0080] The use of free-propagating waves to resolve two or more identical, constant-scattering point sources is considered to be limited by diffraction. This disclosure shows, both theoretically and experimentally, that by employing diffraction minimums instead of maximums to resolve a given number of point sources, it is possible to resolve them at a very small fraction of the wavelength used. Specifically, a distance of 8 nm between two constant-emission (non-flickering, non-switchable) fluorescent molecules was identified, corresponding to 1 / 80th of the wavelength. Furthermore, this disclosure shows that, contrary to naive expectations, measurement accuracy increases with decreasing distance between point sources and may even increase with increasing point source density, thus opening the way for clusters of (optical) point sources that can be resolved at very small fractions of the wavelength.

[0081] A prominent problem in physics is how small the distance *d* between two simultaneously scattering point sources must be for them to be separated by a focused (light) wave (wavelength λ). Separating two inelastic optical scatterers, or two other similar point sources, and measuring their distance is important in many fields, particularly in fluorescence microscopy, the most widely used imaging modality in the life sciences. Fluorescent molecules, also known as fluorophores, are considered inelastic optical scatterers here because they annihilate any phase information of the incident light field by dissipating some of the absorbed photon energy and emitting photons of longer wavelengths. In any case, the textbook answer regarding the minimum resolvable distance is the Rayleigh criterion, see references 1 and 2. It states that the distance between the diffraction maxima of the scatterers in an image should not be less than *d* = 0.61λ / (nsinα), where *n* and *sinα* represent the refractive index of the immersion medium and the sine of the lens's half-aperture angle, respectively. Although introduced for wide-field microscopy, the Rayleigh limit also applies to popular scanning optical microscopy, in which an object is scanned with a focused beam of wavelength λ, and the image is given by the number of photons recorded at each scan position (see reference 3).

[0082] Unlike many other microscopy methods, fluorescence microscopy does not map the molecules of interest themselves, such as proteins in cells, but rather the fluorophores that are already attached to these molecules as markers. While this may seem disadvantageous at first glance, this aspect is crucial for super-resolution fluorescence microscopy, or nanomicroscopy, because these methods manipulate the state of the fluorophore to achieve sub-diffraction resolution. Specifically, fluorophores residing closer to the diffraction barrier are resolved by instantaneously shifting a portion of them to a molecular state that emits photons (on), while the remaining portion remains in a non-emitting state (off). The immediate placement of the fluorophore in different states during the brief detection period provides separability, rendering separation by focusing on tiny points obsolete (see references 4 and 5). This on / off state transition is a key physical element of all known diffraction-limited fluorescence microscopy methods to date, including those called STED, PALM / STORM, and more recently introduced methods called MINFLUX (see reference 6) and DNA-PAINT (see reference 7). Without this element, none of these methods can provide nanoscale resolution.

[0083] Unfortunately, separation by switching molecular states on / off introduces fundamental limitations, hindering the extension of super-resolution beyond fluorescence, such as to other types of (inelastic) optical scattering like Raman scattering, not to mention to other physical domains resolved by diffraction waves. Even within the field of fluorescence microscopy, the on / off principle inevitably requires that adjacent fluorophores be recorded sequentially. This limitation is intolerable if adjacent fluorophores need to be observed and resolved simultaneously, a situation commonly encountered in biophysical experiments involving molecular tracing. Therefore, driven by fundamental and practical reasons, and the recent success of MINFLUX (see Reference 6), the ability of optical microscopy to resolve individual scatterers that remain identical (i.e., on) during observation has been re-examined.

[0084] This disclosure shows that scanning with a focused light field having a (central) diffraction minimum—instead of a maximum—allows for the measurement of distances down to single-digit nanometers between optically identical fluorophores. By measuring the positions of two fluorophores separated by only 8 nm (λ / 80), it can be demonstrated that the Rayleigh criterion significantly overestimates the minimum distance at which two inelastic scatterers can be resolved in practice. The fundamental physical reason is that probing the scatterers with the diffraction minimum modulates the scattering signal without modulating their state, while preventing the modulation from being drowned out by noise. As a result, continuous tracking of at least two fluorophores at nanometer distances becomes feasible.

[0085] This disclosure also shows that, for a given signal-to-noise ratio (SNR) and background, the precision of separability actually increases as the distance between scatterers decreases. Contrary to naive expectations, this potentially surprising property also allows the method to be extended to a greater number of scatterers, which has great potential for studying the dynamic (re)arrangement and conformational changes of individual proteins and other molecules at the nanoscale using conventional optics.

[0086] This indicates that the diffraction maxima of two fluorophores located at a distance d < λ / 2 significantly overlap in an optical microscope image. This applies both to images formed by diffracted fluorescence photons from a camera and to maxima obtained by scanning a focused excitation beam across the focal plane and recording the fluorescence photons with a confocal detector. In both cases, the identification of each individual fluorophore depends heavily on the noise in the image, which is typically Poisson distributed, see [link to relevant documentation]. Figure 1 a and 1b. If the signal-to-noise ratio (SNR) is infinite and the point spread function (PSF) of the imaging system is perfectly known, then fluorophores can always be resolved by deconvolving with the PSF. However, in practice, the knowledge of the PSF is impaired by aberrations, and the SNR is too low to reliably resolve fluorophores; see references 8 and 9.

[0087] Typically, altering the distance *d* between two inelastic point scatterers modulates the spatial distribution and amplitude of their joint image signal *I(d)*. For the overlapping diffraction maxima, see... Figure 1 c, noise is added, and modulation is only noticeable for approximately d ≥ λ / 2. Fortunately, modulation is more easily detected by comparing the joint image signal with a zero-signal baseline. Using this idea, scanning of the excitation beam of the focal spot light field with a central intensity minimum was investigated. Figure 1 b). Since the generated fluorescence signal is proportional to the illumination intensity, the signal of each individual fluorophore is minimum (zero) at the central node. Furthermore, due to the additive (incoherent) summation of signals from inelastic scatterers, scanning two scatterers with d < λ / 2 also produces a joint signal I(d) with a single minimum. Figure 1 d). In the absence of background, the minimum is truly zero only when d=0. Therefore, any deviation of the fluorescence minimum from zero indicates a finite d.

[0088] First, consider scanning a complete cycle on the x-axis to obtain a sinusoidal excitation (stripe) pattern of two fluorophores spaced d apart. For simplicity, see... Figure 1 d. The resulting joint signal is obtained from Given, where a0 represents a constant offset, and a1 is the magnitude of the change with d. Parameters Give the phase of the joint signal relative to the sinusoidal illumination pattern. The phase difference is ν = 4πx / λ. a0 and a1 depend on many parameters, including the brightness of the fluorophores, their spacing, the background, and the initial fringe contrast of the (typically finite) illumination. Furthermore, the modulation visibility is expressed as ν(d) = a1(d) / a0.

[0089] The finite d causes the sinusoidal fluorescence signals of the individual fluorophores to spatially shift relative to each other, thus altering the visibility ν(d) of the joint modulation. Interestingly, contrary to the case of separation by the maximum value, decreasing d increases ν(d), meaning that measuring d with the minimum value actually performs well at small d values. In the limiting case of d=0 and zero background, the joint signal is zero, meaning that even tiny d values ​​can be measured due to the inherently low noise at the minimum. In contrast, for the overlapping maximum values ​​at d=λ / 4, ν(d) approaches zero, and separation is most challenging due to noise. Regardless, sampling at three locations... Sufficient to determine a0, a1 and And distinguished by d.

[0090] The lower bound for estimating the positions of the two emitters can be provided by the Cramér-Rao bound (CRB), see reference 10. The CRB is directly related to Fisher information (FI), which provides statistical samples of their signals and... In the case of the model, it can be obtained from The model measures how much information about the parameters (including the location of the fluorophore) is inferred. The inelastic scattering signal can be viewed as a non-homogeneous Poisson process, with its underlying mean specified by the convolution of the illumination pattern with the imaging system's PSF.

[0091] For a Poisson process, FI is related to the model gradient (squared). With absolute model value The ratio is proportional. This relationship maximizes the FI of scattered photons from the minimum and makes it provide more information than photons from near the maximum. For two sources with a spacing of d, the CRB, as the accuracy σ of the distance estimate, is approximately proportional to the minimum and maximum values, respectively. and Scaling. Therefore, for the minimum value, the relative error of the d estimate is constant, but for the maximum value, the relative error diverges at small distances ( Figure 2 a) is obtained. This only holds true within the limits of the scan range L→0 and with an ideal contrast ν0=1 for the illumination pattern. Larger (finite) scan ranges L>0 and imperfect initial contrast ν0<1 will reduce the estimation quality, see [link to documentation]. Figure 2 a to 2c. However, the estimate of d provided by the minimum value is at least two orders of magnitude more accurate than the estimate provided by the maximum value. Figure 2 a). It should be noted that this finding is related to is independent of the shape, because the decisive factor is the minimum of the illumination beam, which has a parabolic spatial intensity distribution in the first-order approximation.

[0092] The CRB does not guarantee the existence of an estimator that reaches this precision bound. However, among a range of options, it has been found that the polynomial maximum likelihood estimators for parameters a0, a1 and are sufficient to retrieve the estimate of d with constant relative error from photons near the minimum. This advantage is also maintained in the presence of non-negligible background and non-zero intensity at the minimum of the illumination diffraction, see Figure 2 b.

[0093] To experimentally find the minimum distance at which two inelastic scatterers can be resolved, two fluorophores (Atto647N molecules) were placed at a controlled distance 66nm < d < 90nm, that is, a distance that is absolutely considered unresolvable due to the Rayleigh limit. This spatial arrangement is achieved by attaching fluorophores to a DNA origami structure (a so-called nanoruler), see Reference 11. The DNA structure serves as a scaffold for attaching fluorophores at a given d. Next, by illuminating opposite halves of the entrance pupil of a 1.4 numerical aperture oil immersion objective with two interfering excitation beams, a linear interference pattern is obtained in the focal plane of a scanning confocal microscope ( Figure 3 a). This setup was originally developed for MINFLUX, see Reference 12, and has been described in detail previously. In brief, the linear focal spot interference pattern can be oriented along the x or y direction, and can be quickly switched by changing the x and y orientations of the two beams using an electro-optic device ( Figure 3 b). Destructive interference at the focal point provides a central linear diffraction minimum, while constructive interference provides a maximum. Linearly changing the phase difference between the beams allows scanning this pattern over the fluorophores (along the x or y axis, Figure 3 c), so that the separation result provided by the minimum can be easily compared with the separation result provided by the maximum.

[0094] These line scans are successively repeated for the x-axis and y-axis until both molecules are bleached; a stack of all x or y line scans constitutes an x or y trajectory respectively ( Figure 3 d). Therefore, each trajectory allows consideration of all photons or only photons originating from near the diffraction minimum. For both cases, the projection of the distance between fluorophores onto each axis is determined, and d is calculated. The sudden bleaching of individual fluorophores during measurement is also recorded ( Figure 3 e). The subsequent sudden shift of the signal centroid allows d to also be extracted ( Figure 3 f to 3i). Pioneered in camera-based single-molecule localization, see Reference 13, this on / off-based separation provides independent control for d measurement.

[0095] Experiments show that for d < 30 nm, separation by scanning the entire interference pattern across the entire sample becomes inaccurate, while selecting photons from the region near the minimum of the stacked line scan (trajectory) (for d down to 10 nm) can resolve fluorophores. Furthermore, the results agree well with those obtained through bleaching control. Figure 7 Consistent with theory, this finding suggests that photons recorded from the minimum value perform exceptionally well in resolving small d-type fluorophores. Perhaps more notably, using additional photons not only consumes time and limits the fluorescence budget but also impairs resolution.

[0096] Therefore, we will now use only the excitation minimum to detect the two fluorophores. As with previous MINFLUX records, x on each axis... - =x COM -L / 2, x0=x COM , x + =x COM Sampling was performed at three locations: +L / 2, where the value of L was iteratively decreased. The centroids (x, y, y) of the two fluorophores were then estimated using the fluorescence minimum. COM To estimate d, a certain number of such triplet positions and counts are combined into a binary number with a certain number of photons. This process allows for a single-digit nanometer precision in d estimation using approximately 5000 photons. Figure 4 Furthermore, it paves the way for resolution in dynamic environments where the distance and position of two fluorophores must be continuously determined, i.e., uninterrupted by on / off state transitions.

[0097] To demonstrate the tracking of two moving fluorophores, the sample stage is translated along a defined trajectory. Since they are attached to a nanoscale, each fluorophore produces a slightly offset copy of its corresponding trajectory. The time-resolved distance between the fluorophores can be extracted by tracing their centroids and evaluating the signal at specific time points. Distance estimation is readily available for fluorophores with d = 30 nm (moving along a circle with a diameter of 30 nm) and d = 15 nm (moving along a higher-order Lissajous trajectory with an amplitude of 15 nm). Figure 5These results (which are clearly unattainable with popular camera-based tracking) demonstrate time-resolved distance measurements of fluorophores with identical spectra and constant emission well below the diffraction barrier. In other words, to establish nanoscale distances as a function of time, on / off switching or separation by excitation / emission wavelengths is unnecessary. This finding greatly relaxes the requirements for fluorophores, as stable, non-switching, and non-flickering fluorophores can be used. Stable fluorophores typically offer higher photon emissivity and larger photon emission budgets. Furthermore, the emission variation of individual fluorophores is much smaller, which improves the accuracy of distance estimation. Moreover, from a practical standpoint, on / off switchable and activatable fluorophores are often hydrophobic, which greatly limits their utility in biomolecular labeling. By abandoning the on / off requirement, the range of stable, hydrophilic dyes automatically opens the door to nanoscale resolution.

[0098] As a crucial next step, it was investigated whether diffraction minimum scanning could still locate the positions of three or more identical scatterers within a geometrically known constellation and distance in the region ≪2λ. Therefore, measurements were performed on DNA scaffolds with three and four labeled sites. The fluorophores were arranged in linear, triangular, or square formations. Expected scaling parameters, such as side lengths and distances to the nearest fluorophores, were recovered. Figure 6 (a to 6f), ranging from approximately 20 nm.

[0099] To avoid being limited by the samples at hand and to explore the generalizability of our concept, we also simulated constellations of other equally bright fluorophores ( Figure 6 (g and h). These arrangements are parameterized by a single scaling parameter d. For a linear arrangement of scatterers, d corresponds to the nearest neighbor distance, or the diameter of the circle circumscribed by m scatterers forming a regular polygon. The beneficial scaling of the relative error σ / d = RMSE(d) / d is found to remain valid for more than two scatterers. Conceptually, a smaller distance parameter d allows for the resolution of a larger number of scatterers. In practice, achievable accuracy is limited by lower bounds imposed by experimental limitations such as finite background, variations in the brightness of a single source, and reduced initial contrast of the illumination pattern, i.e., a finite “depth” of the intensity minimum. However, numerical data show that for d ≪ λ / 2 and the commonly encountered SNR, the location of a single inelastic scatterer can be identified in a variety of geometries. For scatterers arranged linearly at a given repeating distance d, the relative error increases with increasing d, as the overall error extends significantly into a larger intensity region outside the detection minimum. Interestingly, not only linear arrangements, but also polygonal or grid-like arrangements of a known number of identical scatterers, allow for the identification of their mutual distances with a given number of probe photons.

[0100] In short, using diffraction minimums instead of maximums, in principle, allows for the separation of two spectrally identical incoherent point scatterers without diffraction limits—even with a finite number of photons. This finding also applies to arrangements of a known number of scatterers confined to a sub-diffraction region at a distance d ≪ λ / 2, provided the geometry of the arrangement is substantially known. Since the structures of many proteins can now be known from X-ray crystallography, NMR, cryo-electron microscopy, or computational prediction, and since multiple protein sites can now be labeled with the best stable fluorophores, this disclosure offers entirely new opportunities to probe the dynamic (re)arrangements of proteins using visible light and conventional lenses. In fact, this disclosure has the potential, for the first time, to directly quantify the internal mechanics of a single protein with minimal intrusion.

[0101] The physical reason for this potentially surprising result is that scanning the illumination minimum across point scatterers at distances ≪λ / 2 automatically modulates the signal of each scatterer, thus enabling separation without the need for state transitions. This modulation is easily detectable because it manifests at the minimum of the scattered signal, where the Poisson noise level is inherently low. Since the modulation vanishes at larger sub-diffraction distances (d>λ / 4), our method performs exceptionally well at small sub-diffraction scales, which, for visible light, is precisely the size of a single biomolecule (1–50 nm), at which other optical and non-optical methods have failed to date. On / off based methods remain the preferred approach for resolving fluorophores at larger sub-diffraction distances and for imaging large fields of view.

[0102] Because the method of this disclosure relies entirely on the interaction between the patterned illumination light and the scatterer, only the absorption of fluorophores is important for studying them. Subsequent emission (patterning) is irrelevant. In other words, as long as the detected signal is proportional to the illumination intensity, it is irrelevant which fluorophore is the actual source of the detected signal. Therefore, the energy transfer (FRET) between fluorophores that often occurs at distances <10 nm does not affect our results. This is another major reason why the method of this disclosure is powerful at the nanoscale. In contrast, in popular camera-based super-resolution methods that rely on evaluating fluorescence emission patterns, any energy transfer leads to positional misrepresentation. Furthermore, the large noise of the fluorescence overlap diffraction maxima requires on / off transitions for separation, making temporally continuous separation impossible.

[0103] On the other hand, the spatial intensity distribution near the minimum is parabolic. Therefore, the effect of aberrations on the parabolic function is more easily identified in the method of this disclosure. In contrast, popular deconvolution methods that employ diffraction maxima require detailed knowledge of the system's aberration PSF and need to identify these details in the shot noise of the maxima. Since there is no fundamental difference between fluorescence and other types of inelastic optical scattering (e.g., Raman scattering) under similar signal and background conditions, the method of this disclosure can be transferred to these important optical fields.

[0104] Furthermore, this disclosure emphasizes that the ability to resolve individual scatterers using freely propagating light waves is severely underestimated due to the widespread acceptance of the Rayleigh criterion. This may be partly due to the fact that, when using the diffraction maxima, resolution becomes increasingly difficult as d decreases, making the prospect of extracting dimensions d≪λ / 2 using propagating (light) waves impractical. In stark contrast, this disclosure shows that measurements using the diffraction minima immediately open a measurement window in the range d≪λ / 2, resolving distances at 1 / 80th of the wavelength.

[0105] Besides the low noise level at the minimum, a key factor in the success of this method is the robustness of the minimum to aberrations. The spatial intensity distribution of the minimum is approximately parabolic and is sampled only near the minimum, making it less susceptible to distortion. In contrast, popular deconvolution methods that utilize diffraction maxima require detailed knowledge of the system's (aberration) PSF and must identify these details within the shot noise at the maxima. Since there is no fundamental difference between fluorescence and other types of inelastic optical scattering (e.g., Raman scattering) under similar signal and background conditions, our results should also be transferable to these important optical domains.

[0106] Last but not least, the principle of separation by minimum also applies to elastic scatterers at small distances, where the distance-dependent phase difference between light scattered from different sources is negligible. Equally interesting is that by achieving separation by avoiding state transitions in the material under study, the method of identifying point scatterer locations using diffraction minimums will be applicable to any type of point scatterer for any type of propagating wave, thus opening up super-resolution for many other wave-based imaging methods.

[0107] Now refer to the attached diagram for more details. Figure 1 The illustration shows how to distinguish two inelastic point scatterers using diffraction maximum and minimum values. Figure 1a: When probed with the diffraction maximum of a focused illumination light having a specific full width at half maximum (FWHM), two closely spaced scatterers (shown as a star in the diagram) are indistinguishable for spacings below the diffraction limit of d ≈ 1 FWHM ≈ 280 nm. For spacings below this limit, changing the position of the scatterers only slightly alters the combined emission (note the similarity of the difference images shown in the lower panel row for two spacing values ​​d1 = 0.03 FWHM and d2 = 0.3 FWHM). For each image, N = 10 is considered in the calculations. 6 One detected photon. Figure 1 b: When probed with the minimum value, the same difference in dd significantly alters the joint signal; note the increase in signal in the correlated difference image by 6. Figure 1 c: The one-dimensional intensity distribution of the scattered light when the scatterer is illuminated with the diffraction maximum. Modulating the joint signal intensity by changing d keeps both d within the (Poisson) noise band of the average signal, meaning the two sources cannot be distinguished in the noise. Figure 1 d: When the same scatterer is illuminated with a diffraction minimum, the modulation at the resulting signal minimum is outside the noise band, allowing for separation. Decreasing d results in a deeper minimum of the joint signal. The insets in panels c and d show the individual average intensity distribution of the scattering from each point scatterer and the distribution of its joint signal.

[0108] Figure 2 The illustration shows the theoretical positioning accuracy of two point scatterers detected using the maximum or minimum diffraction value for N=100 detected photons. Figure 2 a: For different initial visibility ν0, the Cramér Rao-boundary (CRB) divided by the spacing d, i.e., the relative CRB (σ CRB / d). When probing with the minimum value, the relative CRB of the resolution remains constant, while it diverges for the maximum value. The imperfect contrast of the illumination minimum (ν0=0.95) degrades accuracy; however, the relative CRB is improved by approximately two orders of magnitude compared to the counterpart using the maximum value. Figure 2 b: The effect of visibility ν0 on the resolvable distance d. Measuring small distances requires high contrast in the illumination pattern, i.e., a minimum with sufficient “depth.” Here, a successful distance measurement (“resolvable”) is required to exhibit a relative CRB < 0.5. The table in the interpolation provides example values ​​for the minimum visibility required to measure dd (λ = 640 nm). Figure 2 c: For various d examples, the relative CRB with respect to the scan range L near the joint signal minimum. Accuracy increases as L decreases, meaning that probing as close as possible to the joint signal minimum improves range estimation.

[0109] Figure 3The illustration shows the measurement of the distance between two simultaneously emitting fluorescent molecules using (x,y-) scans with minimum illumination intensity. Figure 3 a: Scanning fluorescence microscope with photon counting detection (APD) of fluorescence passing through a dichroic mirror (DM) and a confocal pinhole (PH). The interference of two beams with an adjustable phase difference φ entering the entrance pupil of the objective produces an illumination intensity pattern on the focal plane, which has linear diffraction minimums and maximums (MINFLUX apparatus) oriented in either x or y. The two fluorophores are schematically star-shaped. Figure 3 b: Change Scan for the minimum linear values ​​in the y and x directions. c: Top: Line scan principle: A linear ramp on 2π causes the minimum to shift across the scatterer, producing a sinusoidal distribution of fluorescence (or scattering signal). Bottom: Continuous line scans can be appropriately replaced by probing three points near the scatterer with the minimum (MINFLUX recording). Figure 3 d: Normalized counts measured during repeated line scans. The absolute number of counts decreases progressively with each individual fluorophore bleaching. Repeated ramps are performed on the scatterer in both the x and y directions. Exceeding 2π resulted in a line scan stack. Figure 3 e: Average count per line, normalized over the entire stack. The two bleaching steps are clearly visible, marking the transition from two molecules to one molecule and then to zero (background). Figure 3 f: Exemplary lines from two molecules and a single molecule show the sinusoidal distribution of fluorescence counts and the shift of the spatial centroid after the first bleaching step. Each line allows for information extraction based on photons near the minimum, near the maximum, or along the entire line. Figure 3 g: Thermal image of the centroid localization of two fluorophores 20 nm apart. Inset: Two localized clusters are visible, showing the centroid shift after bleaching one fluorophore. Figure 3 h: Average counts of the x and y axes from each 3-point MINFLUX measurement, normalized over the entire measurement. Fluorescence fluctuations in bleaching steps and fluorophore brightness are clearly visible. Figure 3 i: Normalized count for each segment. Second-order polynomial fitting shows the change in parabolic shape and the location of the minimum after the bleaching step. The measurement of d depends only on photons from the first (two-molecule) segment; the bleaching step is used for independent control only.

[0110] Figure 4 The illustration shows two fluorophores with constant emission at a resolution as low as 8 nm. Figure 4a: The measured distance d relative to the expected distance (the line specified by the DNA nanoscale scaffold manufacturer). Photons originating near the illumination minimum are sufficient to resolve simultaneously emitted fluorophores, down to d = 8.4 nm, within the manufacturer-specified uncertainty (shaded area). Circles represent the median distance, and error bars represent twice the median absolute deviation (MAD) of the median. Figure 4 b: Exemplary localization of two fluorophores attached to a single nanoscale with expected distances of 8.4 nm, 10.4 nm, and 14.8 nm. The mean distance d and the mean single-molecule localization accuracy (standard deviation of localization) dn, dn are indicated. Figure 4 c: The corresponding histogram of the distance estimate. The standard deviation is indicated for each nanoscale. Figure 4 d: Box plot of the mean standard error (SEM) for all nanoscales. The box plot extends from the lower quartile to the upper quartile. Error bars mark the interval from the median (the line within the box) to the last point within 1.5 times the interquartile range (IQR). Outliers are shown as points. Number of independent measurements per box: 8.4nm: 307; 10.2nm: 322; 14.3nm: 218; 20.1nm: 272; 25nm: 231; 31.8nm: 283. For all systems studied, the SEM median was less than 0.5nm, and 1.5 IQR was always <1nm. Figure 4 e: Box plot of the measured distance d relative to the expected distance 7 specified by the DNA nanoscale scaffold manufacturer. Data originating from photons near the illumination minimum (see inset) sufficient to resolve simultaneously emitted fluorophores, down to d = 8.4 nm, within the manufacturer-specified uncertainty 8. Box lines 9 extend from the lower quartile to the upper quartile values ​​of the data. Error bars mark the interval from the median 10 (the line within the box) to the last point within 1.5 times the interquartile range (IQR). Outliers are shown as points. Number of independent measurements per box: 8.4 nm: 307; 10.2 nm: 322; 14.3 nm: 218; 20.1 nm: 272; 25 nm: 231; 31.8 nm: 283. Figure 4 f: a distance histogram obtained from the 8.4 nm fluorophore spacing, superimposed with a scaled probability density function 11. The corresponding data comes from... Figure 4 The box plot for e is shown above. Comparing the total dispersion of the obtained deviations with the significantly different average values ​​of individual nanoscales within a batch indicates that the total dispersion can be divided into low measurement uncertainty and high production variability of the nanoscales. Figure 7 and 8 ).

[0111] Figure 5 The diagram illustrates the continuous resolution and localization of two moving fluorophores. Figure 5a: Measurement schematic: A nanoscale with two fluorophores is moved along a predefined trajectory (circle) using a microscope stage. The centroids of the two fluorophores are traced using a minimum illumination intensity of 12. The distance d2 along the obtained trajectory is estimated using a bootstrap method. Figure 5 b: Then calculate the position of the fluorophore relative to the current centroid coordinates. This results in the trajectory 13 of each fluorophore. Figure 5 c: An exemplary trajectory of a d2=32nm nanometer scale moving along a circle with a diameter d1=30nm. Time-averaged images of the two fluorophores result in two offset circles. Figure 5 The Lissajous figure moves along the x and y directions with amplitudes of 15 nm and 20 nm, respectively, with a nanometer scale of d:d2=15 nm. Figure 5 e: The trajectories of each fluorophore cause a shift in the center of mass motion. Figure 5 f: An exemplary trajectory of a d2=15nm nanometer scale moving along the Lissajous figure. Time-averaged images of the two fluorophores result in two offset copies of the Lissajous figure. Figure 5 g: Measurement distance time series for a 50ms time window (thick line). Error bands correspond to the moving standard deviation (200ms window). For each window, the corresponding tuple is selected based on its timestamp, and the distance and orientation of the fluorophore are estimated. Figure 5 h: Histograms of the measured distances (without average) produce clearly distinguishable populations for nanoscales of d=32nm (red) and d=15nm (blue). The histograms are superimposed with scaled probability density functions.

[0112] Figure 6 The diagram illustrates the sub-diffraction localization of multiple point sources scattering simultaneously. Figure 6 a: Experimental positioning with four emitters arranged in a square with a side length of 22nm. Figure 6 b: The three emitters are arranged in a straight line, with the nearest neighbor distance being 18nm. Figure 6 c: The three emitters are arranged in a triangle with a side length of 18 nm. Individual fluorophores are clearly visible. Figure 6 d to 6f: Histograms of all pairwise distances between the locations of each fluorophore. The histograms are overlaid with a Gaussian mixture model fitted to the data. The histograms show single peaks, such as in the case of triangles, or double peaks, such as in the case of squares and lines. For squares, the expected patterns are d and d√2, while for lines, the expected patterns are d and 2d. The average distances of the Gaussian mixture model components are marked in their respective panels. Figure 6 g: Numerical simulation. Spatial arrangement of up to m=5 point scatterers (fluorophores): straight lines and regular polygons. The scaling parameter d represents the nearest neighbor distance between point sources on a straight line, or, for polygons, the diameter of all circumscribed source circles. Figure 6h: Numerical simulation of the relative distance error σ / d = RMSE(⟨d>) / d for the arrangements shown in the same grayscale encoding 14 to 17. Note that at a fixed distance d < 0.018λ, five scatterers in a straight line can be resolved more precisely than two scatterers, indicating that as long as the whole does not significantly extend beyond the minimum of the detected intensity beam (d > 0.02λ) (compare lines 14 and 16), the resolution favorably depends on the number of scatterers. For regular polygons, adding scatterers increases the emitter density, i.e., without changing the overall spatial extent, thus improving the accuracy of d estimation at small d (lines 15 vs. 17). Similarly, this means that at small distances d, such as d < 20 nm, it is more advantageous to locate and measure the distance for a larger number of scatterers than for a smaller number. The numerical distance values ​​were obtained under the conditions of N = 500 detected photons, an actual detection range of L = 30 nm, the average background emission equivalent to β = 0.1 background emitting molecules, and λ = 640 nm.

[0113] Figure 7 The diagram illustrates distance measurement via line scanning and control measurement via the bleaching step. Figure 7 a: Box plot of distance estimates obtained from line-scan experiments relative to expected distances up to 90 nm. Here, the distance between two fluorophores is determined by selecting photons near the line-scan minimum (minimum, see inset). The box plot extends from the lower quartile to the upper quartile values ​​of the data. Error bars mark the interval from the median (the black line inside the box) to the last point within 1.5 times the interquartile range. Outliers are shown as dots. The experiments are consistent with expected d down to 10 nm. For d < 10 nm, the estimates saturate and cannot distinguish between shorter and longer nanoscales; this can be attributed to experimental limitations, such as the non-zero minimum intensity of the probe pattern. Figure 7 b: The correlation between the obtained distance estimate and the control of the centroid shift due to one-molecule bleaching. While the two methods agree well on the distance estimate, the method in this disclosure, which relies on the minimum value, is more accurate than the control and uses only a small fraction (5%) of the available photons across the entire line scan. The illustration depicts how the centroid shift allows d to be determined via the bleaching step. Figure 7 c: A half-violin plot of the deviation between the obtained distance estimate and the expected distance. The distance estimate18 obtained by using all available photons from the full-line scan is compared with the estimate19 obtained by using only photons near the emission minimum. Considering more photons does not improve co-localization accuracy or precision because photons from the maximum value do not add information. On the contrary, longer measurement sequences and exposure to higher illumination intensities increase molecular scintillation and impair measurements through, for example, emission saturation.

[0114] Figure 8 The diagram illustrates the correlation between measurement uncertainty and production variability. Figure 8a: A violin plot of the average distance deviation obtained from a single nanometer scale. The black box marks the interquartile range, the white dots represent the median deviation, and the whisker line extends from the median to the nearest point within 1.5 times the interquartile range (IQR). Figure 8 b: Comparison of the standard deviation of the average distance estimate obtained within a batch ("x", the standard deviation of the i-th batch, which takes into account the average distance by averaging k estimates on a single nanoscale across j nanoscales) with the standard deviation of a single nanoscale (the standard deviation of a single k estimates on the j-th nanoscale in the i-th batch). The batch bias is much greater than the dispersion of consecutive distance estimates on a single nanoscale. Figure 8 c: Results of the analysis of variance (ANOVA). The high F-score in the last column indicates that the estimated total spread can be divided into the spread of the mean (“production variability”) and the spread estimated on a single nanometer scale (“measurement uncertainty”). Control measurements ( Figure 7 The comparable dispersion of the sample and the dispersion observed by the manufacturer, as shown in reference 11, further support this finding.

[0115] In method 1 for determining the arrangement of identical point sources in a sample according to this disclosure (the flowchart is shown in Figure 9), the point sources are limited to 2 to a known number of at least 2 and no more than 32 (i.e., no more than 2). 5 The number of point sources is determined and restricted to a small spatial region of the sample. Then, the point sources are scanned with a probe signal, including the probe signal intensity. The spatial intensity distribution of the probe signal intensity has a local probe signal intensity minimum, which is bounded on both sides by the probe signal intensity maximum in at least one spatial direction. The local probe signal intensity minimum is located at different probe signal intensity minimum locations spaced apart in the at least one spatial direction. For each of the different probe signal intensity minimum locations, the measurement intensity of the measurement signal from the point sources is recorded. The measurement intensity depends on the probe signal intensity at the point source location. The arrangement of the point sources is determined from the spatial progression of the recorded measurement intensity at different probe signal intensity minimum locations. In the step of restricting the two point sources, the point sources have been restricted to such a small spatial region of the sample that the spatial progression of the recorded measurement intensity at different probe signal intensity minimum locations has only one local measurement signal intensity minimum.

[0116] Figures 10, 11, and 12 each show the arrangement of three identical point sources in a two-dimensional sample determined in a computational simulation of the method of the present invention (the computational simulation is based on the actual arrangement of three voluntarily selected identical point sources, respectively). Figure 10 (a, 11a or 12a) starting) and the actual arrangement of the three identical point sources (respectively) Figure 10Comparisons were made between b, 11b, or 12b). The computational simulations assumed scanning a two-dimensional sample with linear probe signal intensity minimums of standard shapes in the x and y directions. In determining the arrangement of point sources from the spatial progression of recorded measured intensities at different probe signal minimum locations in the computational simulations, no further prior knowledge was used beyond the actual number of point sources (3) of the same fluorophore, and, of course, the actual arrangement of those three identical point sources was unknown at the time of arrangement determination. This was achieved by... Figure 10 The arrangement of point sources obtained by the methods of the present invention, a, 11a, and 12a (displayed as a heatmap of the probabilities of three individual point source locations), very accurately images their actual locations and... Figure 10 The distances d1, d2, and d3 indicated in b, 11b, and 12. Figures 10 to 12 This is merely an example of a larger series of corresponding simulations for other distances d1, d2, and d3 of the point sources, and for other orientations of the arrangement in the x and y directions. Therefore, it has been shown that for three point sources, no additional prior knowledge is required beyond the actual number of identical point sources.

[0117] References 1. Rayleigh, Lord. On the Theory of Optical Images, with special reference to the Microscope. Journal of the Royal Microscopical Society 23,474--482 (1903). 2. Abbe, E. Beiträge zur Theorie des Mikroskops und dermikroskopischen Wahrnehmung. Archiv f. mikrosk. Anatomie 9, 413--468 (1873). 3. Wilson, T. & Sheppard, C. Theory and practice of scanning optical microscopy . London: Academic Press (1984). 4. Hell, SW Far-Field Optical Nanoscopy. Science 316, 1153--1158 (2007). 5. Hell, SW Nobel Lecture: Nanoscopy with freely propagating light. Rev. Mod. Phys. 87, 1169--1181 (2015). 6. Balzarotti, F. et al. Nanometer resolution imaging and tracking offluorescent molecules with minimal photon fluxes. Science (2017). 7. Jungmann, R. et al. Single-Molecule Kinetics and Super-ResolutionMicroscopy by Fluorescence Imaging of Transient Binding on DNA Origami. Nano Lett. 10, 4756--4761 (2010). 8. Carrington, W. A. et al. Superresolution Three-Dimensional Imagesof Fluorescence in Cells with Minimal Light Exposure. Science 268, 1483--1487(1995). 9. Pawley, J. Handbook of Biological Confocal Microscopy . (SpringerScience&Business Media, 2013). 10. Ram, S., Ward, E. S.&Ober, R. J. Beyond Rayleigh‘s criterion: Aresolution measure with application to single-molecule microscopy. Proceedings of the National Academy of Sciences 103, 4457--4462 (2006). 11. Raab, M. et al. Using DNA origami nanorulers as traceabledistance measurement standards and nanoscopic benchmark structures. Sci Rep 8, 1780 (2018). 12. Wolff, J. O. et al.MINFLUX dissects the unimpeded walking ofkinesin-1. Science 379, 1004--1010 (2023). 13. Gordon, M. P., Ha, T.&Selvin, P. R. Single-molecule high-resolution imaging with photobleaching. Proceedings of the National Academy of Sciences 101, 6462--6465 (2004). 14. Hensel, T. A. Diffraction minima resolve point scatterers at tinyfractions (1 / 80) of the wavelength - Datasets. (2024) doi:10.5281 / zenodo.10625021. 15. Hensel, T. A. Diffraction minima resolve point scatterers at tinyfractions (1 / 80) of the wavelength - Software and documentation. (2024) doi:10.5281 / zenodo.10639211. 16. Truong, C., Oudre, L.&Vayatis, N. Selective review of offlinechange point detection methods. Signal Processing 167, 107299 (2020).

Claims

1. A method for determining the arrangement of point sources in a sample, comprising: - Scan the point source (3) with a probe signal that includes the probe signal strength. - The spatial intensity distribution of the detected signal strength has a localized minimum detected signal strength, which is bounded on both sides by the maximum detected signal strength in at least one spatial direction. - The minimum local detection signal strength is located at different minimum detection signal positions spaced apart by distance in the at least one spatial direction. - For each of the minimum positions of different detection signals, record (4) the measurement intensity of the measurement signal from the point source. The measured intensity depends on the detection signal strength at the point source location. - The arrangement of point sources (5) is determined from the spatial progression of the recorded measurement intensity at different locations of minimum detection signals. The method is characterized in that it further includes: - Its arrangement is determined by the point source constraint (2) based on the spatial progression of the recorded measurement intensity at different locations of minimum detection signals: - The number of point sources must be at least 2, and - The small spatial region of the sample ensures that the spatial progression of the recorded measurement intensity at different locations of minimum detection signal has a local minimum measurement signal value, and - When determining the arrangement of point sources from the spatial progression of recorded measurement intensities at different locations of minimum detection signals, prior knowledge of the arrangement of point sources is utilized.

2. The method according to claim 1, wherein, The prior knowledge includes at least one of the following: - The expected contribution of each point source to the measured intensity. - Number of point sources - The various possible basic geometric shapes for arranging point sources, or - At least when the number of point sources is greater than 4, the basic geometry of the point source arrangement.

3. The method according to claim 1 or 2, wherein, The arrangement of point sources is determined from at least one of the following: - The shape of the minimum value of a local measurement signal, or - At least one of the depth or width of the minimum value of a local measurement signal.

4. The method of claim 2 or 3, further comprising comparing the minimum value of the one local measurement signal with at least one of the following: - The minimum value of the comparative local measurement signal, which corresponds to the comparative arrangement of point sources whose positions are the same in at least one spatial direction. - Minimum local detection signal strength, or - At least one comparative local measurement signal minimum, which corresponds to a certain basic geometry of the arrangement of point sources.

5. The method according to any one of the preceding claims, wherein, The steps for determining the placement of point sources include fitting a curve to the recorded measured intensities.

6. The method according to claim 5, wherein, At least one fitting variable tuned when fitting the curve to the recorded measured intensity is a parameter describing the arrangement of the point sources, optionally distance.

7. The method according to any one of the preceding claims, wherein the prior knowledge includes a variety of different possible basic geometries for the arrangement of point sources, and further includes, when determining the arrangement of point sources, comparing the spatial progression of the recorded measurement intensity at different locations of minimum detection signal with each of a variety of different comparative spatial progressions, wherein, Each of the various comparative spatial processes corresponds to one of the various possible basic geometries of the arrangement of point sources.

8. The method according to claim 7, wherein, Each of the various comparative spatial processes is generated by simulation using the arrangement of measured or estimated point sources.

9. The method of claim 4, 7 or 8 further comprises automatically performing the comparison step by means of at least one of artificial intelligence, neural network, artificial neural network or machine learning.

10. The method according to any one of the preceding claims, wherein, - The number of point sources does not exceed 32, 16, 8, or 4, and / or Prior knowledge of the arrangement of point sources includes the relative scattering cross sections of each point source, wherein, optionally, the relative scattering cross sections of the point sources are equal.

11. The method according to any one of the preceding claims, wherein, The arrangement of point sources is determined with respect to their point source distances in the at least one spatial direction, and optionally, with respect to their centroids in the at least one spatial direction.

12. The method according to any one of the preceding claims, wherein, The point source must neither be switched nor flicker in relation to the dependence of the measurement intensity on the intensity of the detected signal at the point source location.

13. The method according to any one of the preceding claims, wherein, The point source is hydrophilic.

14. The method according to any one of the preceding claims, wherein, The detection signal has a wavelength, and in which, - The minimum local probe signal strength is formed using the destructive interference of the probe signals, and / or - The sample space region within which the point source is confined is not greater than 1 / 10, 1 / 25, 1 / 50, or 1 / 75 of the wavelength in at least one spatial direction.

15. The method according to any one of the preceding claims, wherein, The minimum local detection signal strength includes the zero point of the detection signal strength.

16. The method according to any one of the preceding claims, wherein, - The minimum local detection signal strength is limited only in one spatial direction. - The point source is first scanned in a first spatial direction, wherein the minimum local detection signal strength is bounded by the spatial direction oriented in the first spatial direction, and - A point source is scanned in a second spatial direction, which is orthogonal to a first spatial direction, wherein the minimum local detection signal strength is bounded by the first spatial direction oriented in the second spatial direction.

17. The method according to any one of claims 1 to 15, wherein, - The minimum local detection signal strength is circular, and - The arrangement of point sources is scanned with a probe signal by making the ring probe signal intensity minimum to move in a circle around the arrangement of point sources, wherein, optionally, the center of the circle is adjusted after at least one full circle.

18. The method according to any one of the preceding claims, wherein, A spatial pattern is imprinted on the measurement signal from a point source, wherein, for each of the different minimum locations of the detection signal, a spatial measurement intensity distribution including the measurement intensity is recorded with spatial resolution, and wherein the recorded spatial measurement intensity distribution and its spatial progression at the different minimum locations of the detection signal are evaluated to determine the arrangement of the point source, wherein, optionally, the spatial pattern includes the linear local intensity minimum of the measurement signal.

19. The method according to any one of the preceding claims, wherein, The sample space region within which the point source is confined is no greater than 1 / 2, 1 / 3, 1 / 5, 1 / 10, or 1 / 20 of the FWHM of the minimum local detection signal strength.

20. The method according to any one of the preceding claims, wherein, The detection signal is either an electromagnetic signal or a sound signal.

21. The method according to any one of the preceding claims, wherein, The measurement signal is: - Fluorescent light, the point source is a fluorophore, or - Inelastic scattered light, optionally Raman scattered light, or - Elastically scattered light, or - Scattered sound, optionally scattered ultrasound.

22. The method according to any one of the preceding claims, wherein, The detection signal is emitted by exciting a point source via a two-photon or multi-photon process to emit a measurement signal, wherein, optionally, the further detection signal is emitted by exciting a point source via a single-photon process to emit a measurement signal, and wherein the further detection signal is used to successively or alternately determine or monitor the arrangement of point sources in the sample with lower precision, and the detection signal is used to determine the arrangement of point sources in the sample with higher precision.

23. The method according to any one of the preceding claims, wherein, Steps - Scan point sources using probe signals. - Record the measurement intensity of the measurement signal from the point source, and - Determine the arrangement of point sources by the spatial progression of recorded measurement intensity at different locations of minimum detection signal. It is repeated to track changes in the arrangement of point sources, optionally with respect to at least one of external influences on the sample or the movement of entities to which point sources are attached within the sample.

24. The method according to any one of the preceding claims further comprises attaching a point source to a different site of an object selected from the group consisting of macromolecules, proteins, complexes, drug candidates, and potential drug targets.

25. The method according to any one of the preceding claims further includes determining a further arrangement of further point sources, wherein the further point sources are also limited to: - The number of known point sources is at least 2, and - Such a small spatial region as the sample ensures that the spatial progression of the recorded measurement intensity at different locations of minimum detection signal has a local minimum measurement signal value. - in, The further point source provides a further measurement signal that can be distinguished from the measurement signal, and / or - Wherein, the further point source can be selectively detected by a further detection signal different from the detection signal, and / or - Wherein, the point source is deactivated, and wherein, the further point source is activated.

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