Method and device for high-resolution location determination of a single dye molecule in multiple spatial directions

Description

TECHNICAL FIELD OF THE INVENTION

[0001] The invention relates to MINFLUX nanoscopy. The invention improves the three-dimensional localization of isolated fluorophores. STATE OF THE ART

[0002] MINFLUX nanoscopy is a relatively new microscopy technique in the state of the art. MINFLUX nanoscopy is a localization microscopy technique. Fluorophores are localized using structured excitation light distributions. A fundamental feature of MINFLUX nanoscopy is that the fluorophores are excited in such a way that the fluorophore to be localized is always positioned close to or within a minimum of the excitation light distribution, which ideally is a zero point, with the excitation light distribution exhibiting a region of increasing intensity adjacent to the minimum. This allows for particularly effective utilization of fluorescence photons to obtain information about the position of the respective emitting fluorophore. This also applies to applications in which the movement of fluorophores is to be tracked over time.The observation of a sample using an excitation minimum, a basis of MINFLUX nanoscopy, is known, for example, from patents DE 10 2011 055 367 B4, initially only for tracking the movement of individual molecules in a sample, EP 3 055 674 B1, and DE 10 2013 114 860 B3. Patent EP 3 055 674 B1 proposes using alternating excitation light distributions to track a particle in a sample in multiple spatial directions, each of which tracks the particle in mutually orthogonal directions.

[0003] Based on this foundation, a number of refinements for information acquisition have been developed that enable the localization of fluorophores with an uncertainty in the range below 2 nm. This uncertainty corresponds to the extent of the fluorophores. A detailed description of MINFLUX nanoscopy can be found in "Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes," Francisco Balzarotti et al., arXiv:1611.03401 [physics.optics] (2016). Non-iterative MINFLUX localization and the tracking of individual fluorophores using MINFLUX are experimentally demonstrated. Furthermore, the concept of iterative MINFLUX is presented. In principle, to localize a fluorophore using MINFLUX nanoscopy, the intensity minimum or zero must be placed at a number of positions relative to the fluorophore's position.For this purpose, the position of the fluorophore must be estimated with an initial, lower degree of accuracy in a preparatory step, or it must be known. This can be done, for example, using conventional localization microscopy (PALM, STORM) or other known methods. The cited publication describes a method in which a sample is scanned with a Gaussian intensity distribution until fluorescence is detected at a scanning position, which with a certain probability originates from an isolated molecule. The scanning is then stopped, and the intensity distribution is subsequently positioned at four locations around the scanning position, each at a distance of less than the wavelength of the light.From the photon counts measured at two individual positions opposite each other with respect to the scanning position, the position of the individual emitter is estimated with respect to the direction of the connecting line using a method described in the publication, so that the emitter position is determined in both spatial directions perpendicular to the optical axis. Although this pre-localization method is described in the context of the subsequent tracking of the movement of a fluorophore, it can also be used in the context of localization. The estimation for each direction essentially corresponds to a ratiometric evaluation of the photon counts.Subsequently, an intensity distribution of excitation light with a central minimum, for example, in the shape of a donut, as known from STED microscopy, is placed at a known position, which is chosen such that the estimated position of the fluorophore is close to the minimum of the intensity distribution. The fluorescence response of the fluorophore is measured. The same process is repeated for one or more additional positions of the intensity distribution. Using a ratiometric evaluation of the intensity ratios, the position of the fluorophore is determined with greater accuracy. In general, the emission rate increases the further the fluorophore is from the excitation minimum or the further the fluorophore is shifted into a range of increasing intensity.This more precisely determined position can now be used as the starting point for repeating the sequence of the aforementioned steps, whereby the positions of the minimum of the intensity distribution of excitation light can be placed closer to the estimated position of the fluorophore. The closer the minimum positions of the intensity distribution are to the actual location of the fluorophore, the fewer fluorescence photons are required for localization with a given uncertainty or accuracy. The publication points out that localization in two dimensions can be achieved by first performing a localization in one direction with a one-dimensional profile and then performing a localization in a different direction with the same profile, but after a rotation.It is further noted that future work would focus on localization in three dimensions using z-donuts.

[0004] Patent publications relating to MINFLUX microscopy include, in particular, WO 2018 / 069 283 A1, US 2019 / 0235220 A1, US 2019 / 0234882 A1 and US 2019 / 0234879 A1, whereby the aforementioned US patent applications are all subsequent applications to the first-mentioned provisional international patent application, in which all concepts subsequently mentioned with reference to the US publications are also disclosed.

[0005] US 2019 / 0235220 A1 is directed to a method with a small or minimal number of positions at which an intensity minimum of an excitation intensity profile, which is adjacent to both sides of intensity increase regions in each spatial direction in which a position of the fluorophore is to be determined, is placed in order to determine the position of the fluorophore.

[0006] US 2019 / 0234882 A1 is directed to the method described above, in which the spatial information obtained from a first MINFLUX step is used to place the minimum of the intensity light distribution closer to the fluorophore in a subsequent step and to derive more precise spatial information from this.

[0007] US 2019 / 0234879 A1 addresses a method in which the intensity minimum of an excitation intensity profile is placed very quickly, almost simultaneously, at a number of positions around the estimated position of the fluorophore. A single position is then moved closer to the presumed minimum if an increased emission rate is detected at that position.

[0008] According to WO 2018 / 069 283 A1, localization can be carried out in several spatial directions by performing any of the methods according to the invention sequentially for different orientations, for example by means of a one-dimensional excitation intensity profile first in a first direction and then in a direction different from the first direction.

[0009] In the publication "MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells," Klaus C. Gwosch et al., Nat Methods 17, 217-224 (2020). https: / / doi.orq / 10.1038 / s41592-019-0688-0, (together with the accompanying "Supplementary Information"), a concrete implementation of three-dimensional localization using MINFLUX is described. In a sub-area of ​​a sample, a single fluorophore is brought into an excitable state using focused activation light. In a first step, this fluorophore is localized using focused excitation light, with the intensity distribution at the focus essentially corresponding to a Gaussian distribution. The focus of the excitation light is placed at four positions around the position of the activation focus.From the measured fluorescence signals at two opposite positions, a spatial coordinate of the fluorophore position is determined in the direction of the straight line connecting the two positions, thus determining an overall lateral position. Subsequently, in a second step, the sample is exposed to focused excitation light. The focus is shaped like a 3D donut, meaning that the intensity distribution exhibits a local minimum surrounded by areas of increasing intensity in all three spatial directions. The 3D donut is placed consecutively at a total of two positions, with the local intensity minimum being located in the lateral direction at the position determined in the first step.In the axial direction, the local minimum is positioned once along the optical axis above and once below the expected fluorophore position (the 3D donut is targeted in two positions above and below the anticipated fluorophore position). This preliminary localization is followed by more precise localization using a scanning pattern with seven positions, five of which lie in a scanning pattern plane, one of which is in the center of the scanning pattern plane, and four of which are evenly distributed in a circle around the central position. The scanning pattern has two further positions that, together with the central position of the scanning pattern plane, lie on a scanning pattern axis, so that a total of three positions lie on the scanning pattern axis.The 3D donut is then sequentially placed at the seven positions of the scanning pattern, with the central position of the scanning pattern being positioned at the fluorophore location determined during pre-localization. This localization is followed by another localization using a reduced but otherwise identical scanning pattern. This can be continued iteratively until the fluorophore loses its fluorescence ability.

[0010] In the publication "Multicolor 3D MINFLUX nanoscopy of mitochondrial MICOS proteins", Jasmin K. Pape et al., PNAS August 25, 2020 117 (34) 20607-20614, 2020 https: / / doi.org / 10.1073 / pnas.2009364117, a further application of the method presented in the publication "MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells" is described.

[0011] While in image-based localization methods such as PALM or STORM, in which diffraction patterns of individual fluorophores are recorded and from which the position of the fluorophore is then determined, the resolution is essentially proportional to the wavelength of the light used and inversely proportional to the square root of the number of detected photons, the resolution of an iterative MINFLUX method depends on the precise type of iteration. This applies to localization in both two and three dimensions. This is because the uncertainty with which the position of a fluorophore in a given iteration step, i.e., for a given extent of the scanning pattern, depends precisely on the extent of the scanning pattern.It should be noted that localization is only successful if the distance between the actual position of the fluorophore and the central position is not too large in relation to the extent of the scanning pattern.

[0012] The publication "Axial Super Resolution Topography of Focal Adhesion by Confocal Microscopy" by C.L. Chiu and E. Gratton (2013, Microsc Res Tech 76(10), 1-16) describes a method for determining the axial position of fluorophores. In this method, the sample is scanned at various axial positions with a Gaussian-shaped excitation light focus, detecting the fluorescence, and evaluating the fluorescence data with a phasor plot analysis to obtain the axial position.

[0013] WO 2020 / 128106 A1 describes a method for point illumination in a microscope, wherein the sample is sequentially illuminated at illumination points of a predefined or predefinable illumination point pattern, in particular with an intensity distribution with a central local minimum. For axial position determination, illumination point patterns can be used in particular, in which the distances in the axial direction are in the order of λ / NA or λ / 2NA, where λ is the wavelength of the excitation light and NA denotes the numerical aperture.

[0014] US 2020 / 0393378 A1 describes a method in which sample structures coupled to positioning aids of known positions are labeled with fluorescent dyes. The dyes are individually localized by scanning with an excitation light intensity distribution with a central local minimum near the known positions of the positioning aids and detecting the respective fluorescent light. In particular, STED and MINFLUX methods can be used alternately.

[0015] The above-mentioned publication "Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes" shows that the smallest uncertainty of the two-dimensional position determination that can be achieved when using a scanning pattern with a total of four scanning pattern positions, three of which are on a circle and one in the center of the circle, when scanning with a 2D excitation donut, is proportional to the diameter L of the scanning pattern and is inversely proportional to the square root of the number of detected photons.This means that the goal must be to iteratively achieve small scanning pattern diameters. It is important to ensure that the scanning pattern diameter in each subsequent step is sufficiently large to ensure that the distance between the actual position of the fluorophore and the position determined in the previous iteration step is not too large relative to the extent of this scanning pattern, as otherwise localization in this subsequent step will fail. Ideal utilization of this information is achieved using maximum likelihood estimation. However, this requires that the intensity profiles of the excitation donut and, for example, the amount of background fluorescence are well known.Furthermore, localizations using maximum-likelihood methods are time-consuming and therefore unsuitable for iterative applications, since the reduction of the sample size and the shifting of the pattern to the location estimated in a single step must be performed as quickly as possible. In practical applications, therefore, a so-called modified least mean squared estimator (mLMSE) of the form . r ¯ ^ mLMS k p ¯ ^ β ¯ = − 1 1 − L 2 ln 2 fwhm 2 ∑ j = 0 k β j p ^ 0 j ∑ i = 1 3 p ^ i ⋅ r ¯ b i , used (in equation S50 of the publication and all equations based on this equation it is mistakenly called "log (2)" without specifying a base instead of "In (2)"), where the p i Photon numbers normalized to the total number of detected photons at the position r b i are. fwhm denotes the full half-width of the region around the local minimum of the excitation donut, k is an order of the estimator, the choice of which influences the range in which localization is possible, and β j is a scalar parameter that must be chosen depending on the expected signal-to-noise ratio in order to obtain localizations that have the smallest possible systematic shift.

[0016] This estimator used in practice was based on a so-called linearized least mean squared (LMS) estimator, r ¯ ^ LMS p ¯ ^ = − 1 1 − L 2 ln 2 fwhm 2 ∑ i = 1 3 p ^ i ⋅ r ¯ b i which in turn is derived by linearizing the solution of a maximum likelihood determination. According to the information in "MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells," the LMS estimator has the disadvantage that the number of photons measured at the center of the scanning pattern is not included in the location determination. This disadvantage is a crucial one because, while the value measured at the center does not contain direct information about the direction of a fluorophore's position in a plane, it does contain information about the distance of the fluorophore's position from the center. Accordingly, the goal of developing the mLMSE was to utilize the information from the measurement at the center. This is important because it avoids the ambiguities in localization that would otherwise exist due to the measurement at the center.Such ambiguities exist when no measurement value obtained in the center is evaluated, in that in certain situations it is not possible to decide from the measurement whether a fluorophore is located inside the circle of outer positions of the scanning pattern or outside it.

[0017] The mLMSE does in principle have a bias, i.e. the positions of the fluorophore determined by the mLMSE are systematically shifted with respect to the actual positions, but this bias is minimized by adjusting the parameters β j This estimator can only be used as an estimator if the sampling pattern has a position in the center where a sampling actually takes place. This is because the term is based on the measurement of the number of photons in the center of the sampling pattern. ∑ j = 0 k β j p ^ 0 j , which ensures appropriate scaling of the estimator to minimize bias. While it is possible and common to further analyze the data after measurements have been completed in order to obtain improved estimates of the positions of all fluorophores localized in the manner described above compared to those obtained during the measurements, the resulting quality of the analysis critically depends on the quality of the estimates obtained during the measurements, since these form the basis for the iteration process and thus for the smallest possible diameter of the scanning pattern as well as for the number of photons measurable using this smallest scanning pattern.

[0018] The method described in "MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells" and the accompanying "Supplementary Information" builds directly on the method referred to above and the theoretical work on this method. To estimate the position of the fluorophore during measurement with a 3D donut, the mLMSE is used in the generalized form r ¯ ^ mLMS k p ¯ ^ β ¯ = − 1 1 − L 2 ln 2 fwhm 2 ∑ j = 0 k β j p ^ 0 j ∑ i = 0 m − 1 p ^ i ⋅ r ¯ b i , used (where in the right summand the value for index i=0 makes no contribution). For the measurements presented here, the order k=1 was chosen, so that overall for the measurement as referred to above (four positions on a circle and three on the axis), the estimator has the form r ¯ ^ mLMS k p ¯ ^ β ¯ = − 1 1 − L 2 ln 2 fwhm 2 ∑ j = 0 1 β j p ^ 0 j ∑ i = 0 6 p ^ i ⋅ r ¯ b i , accepts. The parameters β j , which are each scalar values, are numerically optimized for a typical signal-to-noise ratio, where the shape of the 3D donut is approximated by a quadratic function, i.e., where a quadratic increase in intensity with the distance to the central intensity minimum of the 3D excitation donut is assumed. Optimal parameters for iterative MINFLUX localization, i.e., the number of iteration steps, the diameters of the sampling patterns L at each of the sampling steps, and the photon numbers N at each of the sampling steps, are determined from a simulation assuming that a fluorophore is located within the activation volume with a diameter of 360 nm, which also includes the final localization using a maximum likelihood estimation.In this simulation, the variation of both a Gaussian excitation spot and a 2D donut in the axial direction was also considered, although it is unclear whether the properties of 3D localization using a 2D donut were investigated.

[0019] Using MINFLUX nanoscopy, the position of fluorophores in three spatial directions could be experimentally determined with an uncertainty of a few nanometers. This means that the accuracy of the position determination is comparable to the extent of the fluorophores themselves. If the position of a single fluorophore is to be determined with a given measurement uncertainty, less time and, in particular, a smaller number of fluorescence photons are required than for determining the position of a single fluorophore using conventional localization microscopy. Localization of individual fluorophores in three spatial directions using a MINFLUX method has only been demonstrated in the prior art for a direct coupling of the localization to the activation of the fluorophore to be localized.Due to the local activation, the axial position of the fluorophore to be localized is often sufficiently well known to allow the axial position to be estimated more precisely by using a z-donut of excitation light, which is placed once above this axial position and once below. If the axial position of the individual fluorophore is not known with sufficient accuracy from the activation, the method described in the prior art will fail. It is fundamentally not applicable if individual fluorophores are to be localized without them being explicitly activated immediately before localization. Furthermore, the method known from the prior art has the weakness that the quality of the position estimates obtained over time during the measurements is not only reduced by the background signal as such, but also compared to the quality achieved during parameter optimization. β j background signal that deviates from the assumptions used about the background signal is systematically further reduced.

[0020] Another crucial weakness of the known method for 3D MINFLUX nanoscopy arises from the fact that the real-time estimation of a fluorophore's position is based on the approximation of the shape of a 3D excitation donut using a quadratic function and on a coupled estimation of both the axial and lateral positions. Since this approximation is only a good approximation for very small distances to the central minimum, this assumption, in conjunction with the use of the known estimator, leads to a reduced utilization of the information contained in the fluorescence, especially in the early steps of a MINFLUX iteration when using scanning patterns with large diameters. OBJECT OF THE INVENTION

[0021] The invention is based on the object of providing improved MINFLUX methods for the localization of individual fluorophores in three-dimensionally extended samples or sample regions. On the one hand, this should enable the reliable localization of even those fluorophores whose axial position is not well known in advance. On the other hand, the utilization of fluorescence in determining the localization of individual fluorophores in three-dimensionally extended samples or sample regions should be further improved. SOLUTION

[0022] The object of the invention is achieved by a localization microscopy method having the features of independent claim 1 and by a microscope having the features of claim 15, which is configured to carry out a method according to the invention. Dependent claims 2 to 14 relate to preferred embodiments of the method according to claim 1. DESCRIPTION OF THE INVENTION

[0023] To further improve the utilization of fluorescence in determining the localization of individual fluorophores in three-dimensionally extended samples or sample regions, the invention divides the localization into two steps: an axial localization step and a lateral localization step when localizing an individual excitable fluorophore in a sample using a MINFLUX method using a 3D excitation donut, i.e., an intensity distribution of excitation light that exhibits a local minimum surrounded by regions of increasing intensity in all three spatial directions. It is known in the prior art to use a 3D excitation donut for axial localization in one step without redetermining a lateral position in this step.This axial localization, in which the central local minimum of the 3D donut is placed at two axial sample positions on a scanning pattern axis passing through an estimated position of the excitable fluorophore, is then followed by a simultaneous localization in lateral and axial directions, for which the central local minimum of the 3D excitation donut is placed on a scanning pattern extended in three spatial directions around an estimated position of the excitable fluorophore.

[0024] The method for the high-resolution determination of the position of an excitable fluorophore in three spatial directions in a sample by scanning the excitable fluorophore with a 3D excitation donut with a central local minimum according to the invention thus comprises an axial localization step known from the prior art, in which the central local minimum is placed sequentially at two axial sample positions on a scan pattern axis passing through an estimated position of the excitable fluorophore, the pair of sample positions enclosing the estimated position of the excitable fluorophore, wherein in the axial localization step fluorescence emitted by the excitable fluorophore at each of the axial sample positions is measured and the measured value is assigned to the respective axial sample position, wherein in the axial localization step a new estimate of the axial position of the excitable fluorophore is determined from the measured values ​​assigned to the axial sample positions.

[0025] In contrast to the state of the art, there is no simultaneous localization in lateral and axial directions, but rather a lateral localization step follows, in which the central local minimum is placed exclusively in a scanning pattern plane oriented perpendicular to the scanning pattern axis, sequentially at at least three lateral probe positions arranged around a position of the excitable fluorophore estimated in one or more previously performed steps, wherein in the lateral localization step, fluorescence emitted by the excitable fluorophore at each of the lateral probe positions is measured and the measured value is assigned to the respective lateral probe position, wherein in the lateral localization step, a new estimate of the lateral position of the excitable fluorophore is determined from the measured values ​​assigned to the lateral probe positions.

[0026] At least three lateral probe positions are used, as this is the minimum number of probe positions from which a lateral position can be determined in two lateral spatial directions. The probe positions are preferably chosen so that they are evenly located on a circle around the estimated position of the excitable fluorophore. It is advantageous to select six such probe positions, as this provides very symmetrical acquisition conditions, with the result that the uncertainty of the estimation of the position of a fluorophore depends only slightly on the exact actual position of the fluorophore. In principle, in addition to the probe positions located around the estimated fluorophore position, another probe position corresponding to the estimated position of the fluorophore can also be used.

[0027] In order to be able to reliably localize fluorophores whose axial position is not well known in advance, one embodiment of the invention proposes a method for axial localization that is suitable for determining the axial position of fluorophores whose axial position is poorly known prior to carrying out the method according to this aspect of the invention, for example, with an uncertainty of ± 250 nm or ± 500 nm, or with even greater uncertainty. The method mentioned at the beginning of the description of the invention is not suitable for this purpose, since it can only localize fluorophores that are clearly within a range between the maxima of the axial intensity profile, both when the central local minimum of the 3D donut is located at one and when it is located at the other of the two sample positions on the scanning pattern axis.This region between the maxima is approximately 500 nm in the state-of-the-art arrangement.

[0028] According to this embodiment of the invention, axial localization of a stimulable fluorophore is achieved by scanning the stimulable fluorophore with focused excitation light, wherein an axial scanning range is greater than 500 nm or greater than 1000 nm. The axial scanning range extends, in particular, parallel to or along an optical axis along which the sample is illuminated with the excitation light. The axial localization is, in particular, a localization parallel to or along this optical axis. The optical axis can be identical to or parallel to the scanning pattern axis defined in connection with the method according to the invention.

[0029] In principle, the axial localization method can be performed with a Gaussian excitation focus. In this case, the axial intensity profile of the excitation light exhibits a central maximum. It will be explained later that in certain cases, the axial intensity profile is not directly decisive for localization, but rather an effective axial intensity profile, which results from the axial intensity profile taking into account a point spread function of the detection. This effective axial intensity profile also exhibits a central maximum.

[0030] During scanning, it is advantageous for neighboring scanning points to be no more than half the half-width of the axial effective intensity profile. This ensures that the excitable fluorophore is either exposed at least once during the scan with an intensity that does not deviate significantly from the maximum intensity, once with a reduced intensity, and then with a significantly reduced intensity, or, if the scanning position is different relative to the pattern of scanning positions, twice with a reduced intensity that deviates only slightly from the maximum intensity.

[0031] If scanning is to be performed with a Gaussian excitation focus, this requires switching between two types of illumination if MINFLUX localization using a 3D excitation donut is to be performed downstream of the axial localization process. State-of-the-art solutions exist for such measures. Conversely, omitting switching requires scanning with the same axial intensity profile as that used for MINFLUX localization, i.e., one with a central minimum. The latter initially appears unsuitable for scanning because the excitation intensity is not concentrated in a narrow area; rather, there is a minimum precisely in the central region of the axial intensity profile, so that particularly little excitation intensity is provided in the area around the center.However, the inventor's investigations have shown that, despite these obvious disadvantages for scanning, axial localization is surprisingly successful even when scanning with the axial intensity profile of a 3D donut.

[0032] Accordingly, the method for axial localization can particularly preferably be carried out such that the focused excitation light is a 3D excitation donut with an effective axial intensity profile with a central local minimum and maxima adjacent to the minimum. In this case, the scanning range and the distances between the sample positions can also be specified with reference to the distance between the maxima of the effective axial intensity profile. An axial scanning range can then be larger than the distance between the maxima of the effective axial intensity profile; preferably, the scanning range is at least twice as large as the distance between the maxima of the effective axial intensity profile.

[0033] A capture region is understood here as an area within which a specific localization is possible when applying a particular scanning pattern, i.e., when applying a particular set of scanning points. In the method for axial localization, when a 3D excitation donut is used for axial localization, it is preferred that an axial capture region be at least as large as the distance between the maxima of the effective axial intensity profile.

[0034] When using a 3D excitation donut for axial localization, the scanning pattern can preferably be selected so that neighboring scanning points are at most half the distance between the maxima of the axial effective intensity profile. However, the pattern of scanning positions in the center, whose location usually coincides with the estimated position of the excitable fluorophore, may then contain a gap. This means that scanning points adjacent to the central position of the axial region may be at a greater distance from each other. This greater distance is then at most as large as the distance between the maxima of the axial effective intensity profile.

[0035] Further preferred embodiments will be given later, since their particular properties also correspond to particular properties of the method according to the invention.

[0036] The method according to the invention, which further improves the utilization of fluorescence in determining the localization of individual fluorophores in three-dimensionally extended samples or sample regions, can now preferably be carried out such that the steps for obtaining the estimated position of the excitable fluorophore include, as a step, a lateral pre-localization for estimating a lateral position of the excitable fluorophore, which is carried out before the axial localization step and the lateral localization step, i.e., before carrying out the steps essential to the invention. In the prior art, such a lateral pre-localization is carried out before carrying out a MINFLUX method not according to the invention using a Gaussian excitation light.This requires a switchable mechanism for switching the excitation light from Gaussian excitation light to a 3D donut, which is technically and thus economically comparatively complex. To reduce technical complexity and also increase measurement speed, prelocalization is preferably performed by exciting the excitable fluorophore to fluorescence with a 3D excitation donut, with the excited fluorescence being detected by a detector.

[0037] With this method, the lateral position of the excitable fluorophore can preferably be estimated from a spatially resolved fluorescence detection in an image plane containing a point confocally located to the excitation focus. The spatially resolved detection of the fluorescence emission in the image plane can be achieved, for example, using an array of photon-counting avalanche diodes. The position of the fluorophore in the sample can then be estimated from the distribution of the measured photon counts, or, when using a non-counting detector array or arrays of detectors, from the distribution of the measured fluorescence values ​​in the image plane. This means that the location of the excitable fluorophore within the excitation focus can be estimated. This does not require any shifting of the excitation focus, nor does it require any scanner adjustment.

[0038] Alternatively, spatially resolved detection of fluorescence emission in the image plane can be achieved by shifting the confocal point in the image plane relative to a pinhole, preferably along a circular path around a center. Fluorescence passing through the pinhole is detected with a detector that does not need to have spatial resolution and assigned to the respective position of the confocal point. Here, too, the location of the fluorophore in the sample can be estimated from the distribution of the measured fluorescence values ​​in the image plane, i.e., the location of the excitable fluorophore within the excitation focus can be estimated. The excitation focus should remain stationary.This can be achieved, for example, by simultaneously shifting the point in the image plane that is confocally located to the excitation focus, by a deflection unit that acts only on the excitation light but not on the fluorescent light, performing a countermovement to a deflection unit that acts on both the excitation light and the fluorescent light.

[0039] Preferably, the method according to the invention can be combined with the method for axial localization, which then enables the reliable localization of fluorophores whose axial position is not well known in advance, while at the same time further improving the utilization of fluorescence in determining the localization of individual fluorophores in three-dimensionally extended samples or sample regions. In this combination, the steps for obtaining the estimated position of the excitable fluorophore comprise, as a step in which the axial coordinate of the estimated position is determined, an axial pre-localization performed before the axial localization step and the lateral localization step performed after the method for axial localization of an excitable fluorophore.

[0040] It is then preferred that the lateral localization step is carried out for the first time after the step of axial pre-localization, preferably immediately thereafter, and before the axial localization step, i.e. in particular before an axial localization step, as mentioned in connection with the invention, is carried out for the first time. For the sake of clarity, it should be noted here that the method for axial localization in itself is referred to in this text as axial localization, which, in combination with the method according to the invention, takes on the role of axial pre-localization and is then also referred to as such. In contrast to axial localization, in connection with the method according to the invention, reference is always made to the axial localization step; this term therefore refers to a step of the method according to the invention.

[0041] Both the method according to the invention as such and this method in conjunction with the method for axial localization can be carried out such that the axial localization step is performed for the first time before the lateral localization step is performed for the first time. Lateral localization according to a MINFLUX method using a 3D excitation donut can be performed more effectively the better the axial position of the excitable fluorophore is already known. In particular, localization with a 3D excitation donut in the axial direction behaves in a certain sense more forgiving than localization in the lateral direction, in that uncertainty in the lateral direction is less critical for the accuracy of axial localization.Therefore, whenever no axial localization is carried out as pre-localization according to the method according to the second aspect or according to the specified alternative in which a switching of the intensity distribution of the excitation light takes place, it is strongly preferred to carry out the axial localization step for the first time before carrying out the lateral localization step for the first time.

[0042] The method according to the invention can preferably be carried out iteratively. If the method according to the invention is combined with the method for axial localization as a pre-localization method, this is generally carried out only once, and the iteration is then directed towards the method according to the invention that follows in the overall process. In the iterative implementation, several axial localization steps, several lateral localization steps, or both several axial localization steps and several lateral localization steps are carried out. Separating the three-dimensional localization into two separate sub-steps allows the sequence of steps to be adapted to the precise observation objective and the sample properties.

[0043] For example, after a lateral localization step, an axial localization step can be performed immediately after the lateral localization step has determined a new estimate of the lateral position of the excitable fluorophore with a specified precision. Depending on the deviation of the actual position of the excitable fluorophore from the estimated position, the specified precision can be achieved in one or more lateral localization steps.

[0044] Furthermore, both in connection with the application of the aforementioned precision criterion and generally with other types of iterative implementation, it may be preferable for several lateral localization steps to be performed in immediate succession. In this case, a new estimated position of the excitable fluorophore is then preferably determined from the estimated position of the excitable fluorophore and the new estimate of the lateral position of the excitable fluorophore obtained in a lateral localization step, which forms the estimated position of the excitable fluorophore for the respective subsequent lateral localization step. This type of iterative implementation is preferred, for example, when good lateral localization is primarily desired.

[0045] In particular, if there is no preferred direction with regard to the desired localization accuracy or if the fluorophore to be localized moves in all spatial directions in the sample and if this movement of the fluorophore is to be tracked, it is preferred that an alternating sequence of axial localization steps and lateral localization steps is carried out, wherein in each case a new estimated position of the excitable fluorophore is determined from the estimated position of the excitable fluorophore and the new estimate of the axial position or the lateral position of the excitable fluorophore obtained in one step, which forms the estimated position of the excitable fluorophore for the respective following step.

[0046] The fact that a new estimated position is determined from the estimated position and a new estimate can mean that, for example, if the new estimate is an estimate of an axial position, a new estimated position is determined by directly replacing the original axial coordinate with the newly estimated axial position, while the lateral coordinate is retained in this example case. However, it is also possible, for example, that the new axial coordinate of the new estimated position is determined from several previously determined estimates, which means, in particular, that the axial coordinate of the original estimated position is also taken into account when determining the new estimated position. The same applies to the reverse case, where the new estimate is the estimate of an axial position, or to cases in which several axial localizations or several lateral localizations are carried out one after the other.In many cases, it is useful to consider more than just the most recent value when determining the position coordinate for a spatial direction. This is especially true when the fluorophore is moving within the sample. Then, from the series of previous axial and lateral estimates, the direction and velocity of the fluorophore's movement can be determined, and the future position—that is, the position where the fluorophore will be in the next step—can be estimated in advance.

[0047] The iterative methods can preferably be performed such that the pair of probe positions surrounds the estimated position of the excitable fluorophore more densely in a later axial localization step than in an earlier axial localization step, or such that in a later lateral localization step, the central local minimum of lateral probe positions is placed more densely around the estimated position of the excitable fluorophore than in an earlier lateral localization step. Both of these measures can also be combined. This means that the basic principle of the iterative MINFLUX methods can be applied separately for both lateral and axial localization.Accordingly, it is also possible, as is known with iterative MINFLUX, to select the intensity of the 3D excitation donut depending on the size of the scanning pattern, i.e., the diameter or, in the case of axial localization, the axial distance between the sample positions. Changing the intensity of the 3D excitation donut has a similar effect, as does changing the respective observation duration, which can also be performed.

[0048] Both when carrying out the method according to the invention and when carrying out the method for axial localization, the respectively necessary displacement of the excitation light in the axial direction can be carried out by directing an excitation light via a deformable mirror through an objective into the sample, wherein the axial positioning is carried out by changing the shape of the deformable mirror.This means that when performing an axial localization step, the 3D excitation donut is preferably positioned at an axial position for sequential placement at the two axial sample positions by appropriately deforming a deformable mirror in the excitation beam path. Likewise, the 3D excitation donut is preferably positioned at an axial position for setting a scanning pattern plane by appropriately deforming a deformable mirror in the excitation beam path. Finally, the focused Gaussian excitation light or the 3D excitation donut is positioned for scanning during axial localization by appropriately deforming a deformable mirror in the excitation beam path. For this purpose, the deformable mirror is preferably placed in a plane of a rear aperture of the objective or a plane conjugate thereto, i.e., in a plane in which a pupil of the objective can be formed.

[0049] The determination of the position from the respective measured values ​​can be carried out in a particularly simple manner, both in methods according to the invention and in methods for axial localization, by evaluating a vector sum. This means that the new estimate of the axial position of the excitable fluorophore or the new estimate of the lateral position of the excitable fluorophore is obtained by evaluating a vector sum, or that the axial coordinate of the estimated position is determined during the axial pre-localization, or that the axial localization is carried out by evaluating a vector sum. The vector sum preferably has the form u → p j b → j = ∑ j = 1 m p j ⋅ b → j ∑ j = 1 m p j , where the pj Photon numbers or represent intensities that correspond to positions bj the 3D excitation donut or the focused excitation light.

[0050] With a simple calculation of this vector sum, each method for given scanning patterns, provided the influence of noise is ignored and no background signal is present, yields a specific value for exactly one actual position of a fluorophore within a specific range of positions. This means that each calculated value corresponds to exactly one position. Therefore, it is possible in each case to correct the value of the vector sum according to a predetermined calibration function in order to obtain the new estimate of the axial position or the new estimate of the lateral position, or in the case of axial pre-localization, the axial coordinate of the estimated position or the axial localization. The respective calibration function to be applied can be determined from a simulation.

[0051] An existing background signal, such as background fluorescence, scattered ambient light, or light scattered or reflected within the microscope, does not affect the term in the numerator of the vector sum on average, but it does affect the denominator. This means that the value of the vector sum u ( pj, bj ) in the above form is systematically dependent on the amount of background signal. Therefore, the amount of background signal is preferably taken into account when evaluating the vector sum. This can be done particularly easily by subtracting the value of the background signal from the denominator in the above formula. For this purpose, the amount of background signal is preferably determined using a sliding scale from measured data.

[0052] Both of these methods, i.e., the method according to the invention and the method for axial localization, are preferably carried out in real time. This is facilitated by the fact that, in methods according to the invention, the new positions can be obtained by evaluating simple vector sums, or by the fact that, in methods for axial localization, the localization can be obtained from an evaluation of a simple vector sum.

[0053] Further data analysis can follow the real-time process or any time period after the real-time process has been carried out. For this purpose, data obtained for each individual step during the process is permanently stored. Such data analysis can, for example, yield even more precise localizations. However, the achievable accuracy depends on the quality of the collected data. This means that the methods according to the invention enable not only better real-time evaluation but also improved quality of subsequent analysis results.

[0054] A microscope according to the invention is characterized in that it comprises a control device configured to control the microscope such that a method according to the invention is carried out. Preferably, the control device is configured such that both a method according to the invention and a method for axial localization or a combined method can be carried out, depending on the user's choice.

[0055] Particularly preferably, a microscope according to the invention comprises a deformable mirror for axially displacing an excitation focus, which also includes the axial displacement of a 3D excitation donut, in a sample. The deformable mirror is preferably positioned in a plane of a rear aperture of the objective or a plane conjugate thereto, i.e., in a plane in which a pupil of the objective can be formed.

[0056] Advantageous developments of the invention will become apparent from the patent claims, the description, the drawings, and the accompanying explanations of the drawings. Some of the drawings are flowcharts that explain the inventive methods in great detail.

[0057] The claims are not to be understood as meaning that only those objects, devices, or methods that each have all or none of the features of a subclaim in addition to the features of independent method claim 1 and device claim 15 can be possible developments of the invention. Rather, further developments can result from features mentioned in the description and from the drawings and the associated explanations, which can be effective individually or cumulatively. BRIEF DESCRIPTION OF THE CHARACTERS

[0058] Fig. 1The process of localization in two dimensions using an iterative MINFLUX method, as it results from the state of the art, is shown. Fig. 2 is a representation of the process of a MINFLUX localization in three dimensions according to the state of the art. Fig. 3 is a representation of the process of a MINFLUX localization in three dimensions according to an embodiment of the invention. Fig. 4 is an illustration of a method for axial pre-localization according to one aspect of the invention using a 3D excitation donut. Fig. 5 is an illustration of a method for axial pre-localization according to one aspect of the invention having a more extended capture range. Fig. 6 is a contour plot of a section of an effective intensity distribution of a 3D excitation donut 8 along an optical axis. Fig. 7 - 10present results of simulation calculations to determine the axial position of an excitable fluorophore using a 3D excitation donut and different scanning patterns. Fig. 11 - 13 show corresponding results for preferred scanning patterns with extended capture range. Fig. 14 is a representation of another method for axial pre-localization with an extended capture area based on continuous or finely rasterized scanning with a 3D excitation donut. Fig. 15 is a schematic representation of an embodiment of a microscope according to the invention. DESCRIPTION OF THE FIGURES AND EXPLANATION OF THE INVENTION WITH THE FIGURES

[0059] In the following, the invention is further explained and described with reference to exemplary embodiments shown in the figures. To clarify the differences from the prior art, the latter is first described with reference to the Figures 1 and 2 explained.

[0060] In Fig. 1A possible sequence of iterative MINFLUX localization in two dimensions is shown, as it results from the state of the art. An isolated fluorophore 4 is exposed to a Gaussian excitation intensity distribution 3, which is placed at four positions around an estimated position 16 of the fluorophore, such that two of the positions in a first spatial direction 5 and a second spatial direction 6 are opposite each other with respect to the estimated position 16. From two measured fluorescence intensities or photon numbers, a position of the excitable fluorophore in the first spatial direction 5 and in the second spatial direction 6 is determined.This pre-localization step 10, which here is a lateral pre-localization 17, is known, for example, from the publication "Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes" cited in the prior art section in connection with subsequent tracking of the movement of a fluorophore. Pre-localization 10 is followed by an iterative real-time MINFLUX localization 33, which here comprises three steps of lateral MINFLUX localizations 30, 30', 30". For a lateral MINFLUX localization 30, 30', 30", an excitation light distribution that has a local intensity minimum, ideally a zero, in the lateral direction at the center of the focus, referred to as a 2D excitation donut 32, is placed at three positions on a circle around the position of the fluorophore 4 determined during pre-localization and at the fluorophore itself. The scanning pattern 9 thus contains four scanning positions.Fluorescence light is detected until the position of the excitable fluorophore 4 can be estimated more accurately, for example, by a predetermined amount. How this estimation is performed is described in the same publication and is referenced in the prior art section. Subsequently, before performing a lateral MINFLUX localization 30', the scanning pattern 9 is shifted such that its center coincides with the position of the excitable fluorophore 4 determined in the previous step, which is closer to the actual position of the excitable fluorophore 4; the diameter 19 of the scanning pattern 9 is simultaneously reduced.Fluorescence light is again detected until the position of the excitable fluorophore 4 can be estimated more accurately from the measurements, for example by a predetermined amount. Subsequently, the diameter 19 of the scanning pattern 9 is shifted and reduced in size in the same way before finally another lateral MINFLUX localization 30" is performed. The iterative real-time MINFLUX localization 33 is finally followed by a final localization 43, which is obtained by analyzing the measurement data obtained during the iterative real-time MINFLUX localization 33.

[0061] In Fig. 2A sequence of iterative real-time MINFLUX localization in three dimensions is shown together with pre-localization steps, which essentially corresponds to the sequence described in the publication "MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells" mentioned in the prior art section. In a partial area of ​​a sample, an isolated fluorophore is brought into an excitable state using focused activation light. Alternatively, the first step is the detection 1 of an excitable fluorophore 4. This excitable fluorophore 4 is pre-localized 10 in a step towards lateral pre-localization 17 using a Gaussian excitation intensity distribution 3 (in Figure 2 symbolized by a black four-pointed star) in real time, as in connection with Figure 1described. For this purpose, the Gaussian excitation intensity distribution 3 is placed at two lateral positions 11, 11' in a first spatial direction 5 and at two lateral positions 12, 12' in a second spatial direction 6. Subsequently, in a step of axial pre-localization 18, the sample is exposed to focused excitation light, wherein the focus has the shape of a 3D donut, i.e., wherein the intensity distribution has a local minimum that is surrounded by areas of increasing intensity in all three spatial directions. The sample is thus illuminated with a 3D excitation donut 8. The 3D excitation donut 8 is placed successively at a total of two axial positions 15, 15', wherein the local intensity minimum is located in the lateral direction at the position determined during the lateral pre-localization 17.In the axial spatial direction 7, the local minimum is placed once along the optical axis above and once below the expected fluorophore position. Although the distance between the two positions is not explicitly stated in the cited prior art publication, it follows from the information on setting the axial focus position of the 3D excitation donut 8 that this can be a maximum of 400 nm. This means that if the axial position of the excitable fluorophore 4 is to be determined more precisely using this method, its axial position must be located between the upper and lower intensity maximum of the axial intensity profile of the 3D excitation donut 8 for both positions of the 3D excitation donut 8. An axial position of the excitable fluorophore 4 is determined from the fluorescence signals measured at the axial positions 15, 15'.This pre-localization 10 is followed by a more precise, real-time 3D localization 20, using a scanning pattern with seven positions 21 to 27, of which five positions 21 to 25 lie in a scanning pattern plane 29, one of which is a central position 25 in the center of the scanning pattern plane 29, and four of which are evenly distributed on a circle around the central position 25. The scanning pattern 9 has two further positions 26, 27, which, together with the central position 25 of the scanning pattern plane 29, lie on a scanning pattern axis 28, so that a total of three positions 25, 26, 27 lie on the scanning pattern axis 28. The 3D excitation donut 8 is now sequentially placed at the seven positions 21 to 27 of the scanning pattern 9, whereby the central position 25 of the scanning pattern 9 is placed at the position of the excitable fluorophore 4 determined during pre-localization 10.This 3D localization 20 is followed by another 3D localization 20', in which a reduced, but otherwise identical scanning pattern 9 with the positions 21' to 27' is used. This can be continued iteratively until the excitable fluorophore 4 loses its fluorescence capability. The 3D localizations 20, 20' are performed in the first spatial direction 5, the second spatial direction 6, and the axial spatial direction 7 using an estimator of the form . r ¯ ^ mLMS k p ¯ ^ β ¯ = − 1 1 − L 2 ln 2 fwhm 2 ∑ j = 0 1 β j p ^ 0 j ∑ i = 0 6 p ^ i ⋅ r ¯ b i , where the β j are scalar calibration values ​​that are chosen so that, on average, the bias during real-time localization is as low as possible. Since the intensity distribution of a 3D excitation donut 8 is not spherically symmetric, this leads to the calibration values β j either be chosen in favor of better axial location determinations such that the lateral location determination is not optimal, or conversely such that the axial location determination is not optimal. A further difficulty is that the intensity profile of a 3D excitation donut 8 along a perpendicular to the axis strongly depends on the axial distance of this perpendicular to the center of the 3D excitation donut 8. The state-of-the-art method with the above-mentioned estimator therefore makes less efficient use of the emitted photons than is the case with the comparison method in two dimensions.

[0062] In Fig. 3, together with pre-localization steps, a sequence of iterative MINFLUX localization in three dimensions according to one embodiment of the invention is shown. The method begins with the detection 1 of an excitable fluorophore 4. This can be done in various ways, for example by excitation and observation in the wide field or by confocal scanning of the sample. Depending on the sample, activation light can also be used for detection in addition to the excitation light. If the sample is scanned with excitation light, a Gaussian excitation intensity distribution 3 can be used for this purpose. However, a 3D excitation donut 8 can also preferably be used. This is preferred because it avoids the need for multiple light paths between which one can quickly switch.Once an excitable fluorophore 4 has been found, the position of the excitable fluorophore 4 is usually known with an uncertainty in the order of the diffraction limit.

[0063] After detection 1, a pre-localization 10 is carried out. This pre-localization 10 can also be carried out when carrying out a method according to the invention using a method known from the prior art. In the illustrated embodiment, it is carried out using a 3D excitation donut 8. With this, a lateral pre-localization 17 is carried out. The position of the excitable fluorophore 4 in a first spatial direction 5 and a second spatial direction 6 is estimated from a spatially resolved detection of the fluorescence emission, i.e. of the diffraction disk in the image plane, in an image plane located confocally to the excitation focus. Such spatially resolved detection can be carried out, for example, with an array of photon-counting avalanche diodes, i.e. with an SPAD array, or it can be carried out, as shown in the figure, by scanning the diffraction disk with a pinhole in the detection plane.It is advantageous to guide the pinhole with its center on a circular path around a center or to place it sequentially at a number of at least three, for example six, preferably evenly distributed positions on such a circular path. The center is the center of the imaginary image of an imaginary point light source located exactly in the center of the 3D excitation donut 8. The circular path is marked in the figure as a pinhole orbit 13 by three smaller circles drawn on a section of a circle's circumference and an arrow. The diameter of the smaller circles does not represent the diameter of the pinhole. Rather, the pinhole can be large enough that the image of the pinhole in the sample encompasses the center of the excitation focus at all times.The diameter of the pinhole orbit 13 is preferably chosen to be as large as possible, although the exact conditions may depend on the available fluorescence signal and the fluorescence background, but will also depend on practical constraints. For example, the applicant uses a device in which the 3D excitation donut 8 is deflected by an electro-optical scanner, which is used to move to the individual points of the scanning pattern 9, and is also guided over a galvo scanner, which is used to scan the sample. The galvo scanner is also located in the detection beam path, but the electro-optical scanner is not.Specifically, the pinhole orbit 13 is scanned while simultaneously fixing the excitation location with the 3D excitation donut 8. Using the galvo scanner, the projection of the pinhole placed in the detection beam path is sequentially placed into the sample at the selected positions of the pinhole orbit 13. The electro-optical scanner imposes a counter-movement on the excitation light such that the 3D excitation donut remains stationary in the sample. This results in a maximum extension of the pinhole orbit 13, which corresponds to the size of the scan field controllable by the electro-optical scanner alone.Since with this type of location determination, regardless of how it is actually implemented, the 3D excitation donut 8 remains stationary and thus the excitable fluorophore 4 is always exposed to the same excitation intensity during localization, the shape of the intensity distribution of the 3D excitation donut 8 does not directly affect the quality of the lateral prelocalization 17, but at most indirectly through different signal-to-background ratios depending on the actual position of the excitable fluorophore 4 relative to the center of the 3D excitation donut 8.

[0064] The detection 1 and the lateral pre-localization 10 can also occur in a single step. For example, it is possible to target a location in the sample with the 3D excitation donut 8 and detect fluorescence in the manner described above. Depending on the signal, in particular depending on whether or how much fluorescence is detected, it can be determined whether or not an excitable fluorophore 4 is present in the focal region of the 3D excitation donut 8. However, the measured values ​​obtained in this way can also directly determine the position of the excitable fluorophore 4 within the focal region. If no fluorescence or only a weak signal is detected, another location, for example a neighboring location in the sample, can be targeted, where the aforementioned measurement is repeated.

[0065] The applicant's investigations have shown that iterative real-time MINFLUX localization 33 can be performed even if, during detection 1 or during lateral pre-localization 17, or even during a later localization step, several excitable fluorophores 4 are actually present within the focal area of ​​the 3D excitation donut and contribute to the signal. In this case, although the position of none of the excitable fluorophores 4 present is determined with the best possible accuracy in that step, a sort of average position is obtained, one of two favorable situations will occur with a certain probability in subsequent steps.In one case, the multiple excitable fluorophores 4 are so close to one another that they are not separated during the entire iterative real-time MINFLUX localization 33, i.e., they are collectively located within the region of the scanning pattern 9 in which MINFLUX localization can occur with the given scanning pattern 9. Then, during the iterative real-time MINFLUX localization 33, a central position of the excitable fluorophores 4 is obtained. Such a case occurs in particular when the distance between the contributing fluorophores is small compared to the size of the resolvable biological structures. In other cases, the multiple excitable fluorophores 4 are further apart. Then, as the excitation pattern 9 is reduced in size, outer excitable fluorophores 4 enter a region where the intensity of the excitation light, or the amount of excitation light to which they are actually exposed, is very high.This leads to these outer fluorophores, if they are corresponding switchable fluorophores, as is usual, being put into a dark state so that they subsequently no longer contribute to the fluorescence signal, so that finally only an isolated excitable fluorophore 4 or closely spaced excitable fluorophores 4 are localized.

[0066] The lateral pre-localization 17 can be followed by an axial pre-localization 18. Particularly advantageous methods for performing an axial pre-localization 18 are described in the Figures 4 and 5 and will be explained in connection with these. The Figure 3However, the method presented assumes that the axial position of the excitable fluorophore 4 is already known with sufficient accuracy without an axial pre-localization 18 in order to be able to carry out a MINFLUX localization without an axial pre-localization 18. Such a situation can arise, for example, if the sample to be examined is thin or if, during detection 1, precisely those excitable fluorophores 4 are found that were only activated during detection 1 by means of activation light, in particular short-wave activation light, or even if activation occurs by means of thin light sheets irradiated from the side. In this case, an iterative real-time MINFLUX localization 33 can follow directly after the lateral pre-localization 17.In contrast to the methods known from the prior art, in this embodiment of the iterative real-time MINFLUX localization 33 according to the invention, a MINFLUX localization is carried out by means of an intensity profile with a local, central intensity minimum surrounded by intensity increase regions in all three spatial directions, here specifically a 3D excitation donut 8, whereby a lateral MINFLUX localization 30, 30', 30" is nevertheless carried out separately from an axial MINFLUX localization 40, 40', 40" in the axial spatial direction 7, i.e. in a temporal sequence one after the other.According to the invention, the information obtained during a lateral MINFLUX localization 30, 30', 30" is used when an axial MINFLUX localization 40, 40', 40" is the next step to optimally position the axial sample positions, i.e., positions 15, 15', with regard to the utilization of the information contained in this next step. Conversely, the information obtained during an axial MINFLUX localization 40, 40', 40" is used when a lateral MINFLUX localization 30, 30', 30" is the next step to optimally position the axial sample positions 31, in particular the center of the scanning pattern 9, with regard to the utilization of the information contained in this next step.

[0067] At the Figure 3In the embodiment shown, for a first axial MINFLUX localization 40, a 3D excitation donut 8, which is advantageously identical to the 3D excitation donut 8 used in the lateral pre-localization 17, is placed at two positions 15, 15', which lie along a perpendicular to the focal plane of the lateral pre-localization 17, one below and the other above the focal plane. The position of the perpendicular in the first spatial direction 5 and the second spatial direction 6 corresponds to the lateral position of the excitable fluorophore 4 determined in the lateral pre-localization 17, which generally does not exactly correspond to the actual lateral position of the excitable fluorophore 4. The axial distance is selected such that an axial position of the excitable fluorophore 4 can be determined from the fluorescence values ​​measured at the two positions 15, 15'. A corresponding step is known from the state of the art and is described in Figure 2described as axial pre-localization 18. For this purpose, the lower position 15 is selected such that it lies with sufficient certainty, for example with a probability of approximately 90% or more, below the actual axial position of the excitable fluorophore 4, and correspondingly the upper position 15' above this axial position. The maximum distance between the two positions 15, 15', which is suitable for MINFLUX localization, results from the fact that the excitable fluorophore 4 should ideally be located close to the central minimum of the 3D excitation donut 8 and in any case should not be exposed to an area of ​​the 3D excitation donut 8 with maximum intensity or an area that is further away from the central minimum than a first local axial maximum of the 3D excitation donut 8. From the number of photons or intensities measured at positions 15,15', an axial position of the excitable fluorophore 4 is determined.This is followed by lateral MINFLUX localization 30. For this purpose, the 3D excitation donut 8 is placed in a plane perpendicular to the optical axis at six lateral probe positions 31 regularly arranged on a circle whose center corresponds to the position of the excitable fluorophore 4 determined during lateral pre-localization 17. The plane of the lateral probe positions is positioned such that its axial position corresponds to the position of the excitable fluorophore 4 determined during axial MINFLUX localization 40. This ensures that the lateral intensity profile of the 3D excitation donut 8 has the most pronounced local intensity minimum possible, which is well suited for lateral MINFLUX localization 30. The scanning pattern used in this step has no probe positions outside the plane of the lateral probe positions 31.In the illustrated embodiment, this lateral MINFLUX localization 30 is followed by an axial MINFLUX localization 40', which is carried out in accordance with the first axial MINFLUX localization 40; the axial positions 15, 15' at which the 3D excitation donut 8 is placed during this axial MINFLUX localization 40' are selected such that the center between the two positions 15, 15' in the axial direction corresponds to the axial position of the excitable fluorophore 4 obtained during the previous axial MINFLUX localization 40, and such that their lateral position corresponds to the position of the excitable fluorophore 4 obtained in the preceding lateral MINFLUX localization 30. In the illustrated embodiment, a further lateral MINFLUX localization 30', a further axial MINFLUX localization 40" and a final lateral MINFLUX localization 30" follow accordingly.All localizations are performed in real time according to the MINFLUX principle using a suitable estimator. As in the prior art, the iterative real-time MINFLUX localization 33 can and often will be followed by a final localization 43, which is obtained as part of a subsequent data analysis. This is not shown in this figure.

[0068] Dividing the MINFLUX localization in three spatial directions into axial MINFLUX localizations 40, 40', 40' and lateral MINFLUX localizations 30, 30', 30' offers the possibility of iteratively performing, for example, two axial MINFLUX localizations in immediate succession. For example, it may be advantageous to perform a second axial MINFLUX localization 40' after the first axial MINFLUX localization 40'. Between the two axial MINFLUX localizations 40, 40', only the distance between the respective positions 15, 15' or the axial position of the center point between the two positions 15, 15' is changed, but not the lateral position of these positions 15, 15'. This can be advantageous because in a 3D excitation donut 8 generated by means of a vortex phase plate, a radial intensity profile depends strongly on the axial position of the radial section, while an axial intensity profile 45 depends less on the radial position.This means that, with regard to the utilization of the information contained in the fluorescence photons, it may be advantageous to first determine the axial position with low uncertainty before performing a lateral MINFLUX localization 30. It has been shown in the publications on the state of the art that an iterative position determination is generally advantageous, even when determining the position in only one spatial direction.

[0069] As a rule, in the iterative MINFLUX method 33 according to the invention, each individual localization is based on a measurement at sample positions located around the previously estimated position of the excitable fluorophore 4, wherein the scanning pattern does not contain a sample position at the position of the excitable fluorophore 4. This is because, according to the inventor's finding, real-time localization without a measurement in the center of the scanning pattern is generally more successful than with a method according to the scientific publications cited in the prior art. With regard to the inventive method described here, this also makes it easier to divide the MINFLUX localization into an axial and a lateral MINFLUX localization, since the measurement in the center is not required for calibrating an overall localization performed in real time.However, this does not preclude the possibility of a measurement also being performed at a central position when carrying out a method according to the invention in individual steps or in all steps. This measurement can advantageously be performed for control purposes, in particular with regard to a check for the background signal, for example, an estimation of the size of the background signal, or with a view to detecting whether one or more excitable fluorophores are located in the detection range. As a rule, the determination of the position of the excitable fluorophore 4 will not directly depend on this measured value in the center. This should not mean that the inventive separation of the localization into an axial MINFLUX localization 40, 40', 40" and a lateral MINFLUX localization 30, 30', 30" is not also possible if the determination of the position of the excitable fluorophore 4 is also based directly on a measurement in the center.

[0070] In Fig. 4A sequence of axial pre-localization 18 is shown. For the pre-localization, a 3D excitation donut 8 is used, preferably the same 3D excitation donut 8 that is subsequently used for iterative real-time MINFLUX localization 33. The 3D excitation donut 8 has an effective axial intensity profile 45 with a central local minimum 46. If only the excitation profile is axially displaced, but the detection aperture remains stationary, the effective axial intensity profile 45 corresponds to the actual intensity profile in the sample. If the detection aperture is axially displaced together with the excitation profile, the effective axial intensity profile 45 results as a product of the detection point spread function and the actual axial intensity profile. In practice, any aberrations that may occur must also be taken into account.

[0071] A typical 3D excitation donut 8 exhibits maxima in the radial direction in the focal plane, the distance between which is large compared to the corresponding distance in a 2D excitation donut, for example, at an excitation wavelength of 642 nm, it can be 520 nm. Depending on the width of the 3D excitation donut 8, axis-parallel intensity profiles 45 are very similar for a range of radial distances from the axis. For the Figure 6 This applies to distances of up to more than ± 100 nm in the example of an effective intensity distribution 44 shown as a contour plot and explained in more detail below. The value in the local minimum also increases only slowly within this range with larger distances from the axis. Figure 4The method described can be applied if, after the detection 1 and, if necessary, after a lateral pre-localization, the lateral position is known with an uncertainty that matches the range of radial distances outlined above, and the axial position of the excited fluorophore 4 is known with an uncertainty of up to slightly more than half the distance of the maxima of the effective intensity profile 45.

[0072] The estimated position 16 of the excitable fluorophore is assumed to be at the axial probe position 50. Then, in the illustrated embodiment, the 3D excitation donut 8 is sequentially placed at four axial probe positions along the optical axis: at the axial probe position 48, the axial probe position 49, the axial probe position 51, and the axial probe position 52. The set of axial probe positions 48, 49, 51, and 52 forms an axial scan pattern 59. A central axial probe position 50, which corresponds to the estimated position 16 of the excitable fluorophore, is omitted. The axial sample positions 49 and 51 are at a distance from the estimated position 16 of the excitable fluorophore 4 that corresponds to the distance of the central local minimum 46 from a maximum of the effective intensity profile 45, for example 360 ​​nm, wherein this distance depends, among other things, on the wavelength of the excitation light used and on the refractive index of the sample.The axial sample positions 48 and 52 are each twice the distance from the estimated position 16 of the excitable fluorophore 4. From the set of fluorescence measurement values ​​obtained in this way, an axial position of the excitable fluorophore 4 can be reliably estimated. If, for example, a vector sum is formed over the measurement values, an estimated value is assigned to each actual position of the excitable fluorophore 4, whereby an estimated value is always assigned to only one position. This is ensured by the selection of the distances between the axial sample positions. The distances can also be selected to be smaller, but preferably not larger. The specifically specified distances are a particularly good choice because the capture range, i.e. the area in which a fluorophore must be located in order to be localized using the method, is very large in relation to the number of sampling points.To ensure the uniqueness of the assignment, the vector sum can be modified using a correction function via calibration, for example, using a simulation calculation, so that the resulting estimator estimates the actual position of the excitable fluorophore 4 without bias. In the absence of background fluorescence, two axial probe positions, which should be far apart, would in principle suffice for axial localization of a single existing excitable fluorophore. In practice, however, it is necessary to excite the fluorophore to be localized comparatively strongly compared to the background during the localization process. This is achieved using the four selected probe positions. A fluorophore that actually has the estimated position 16 is detected, for example, with intensity maxima of the 3D excitation donuts 8 placed at the axial probe positions 49 and 51.With increasing distance from this position, the excitation intensity that the excitable fluorophore 4 experiences from one of the two further spaced 3D excitation donuts 8 increases.

[0073] In Fig. 5 A sequence of a further axial prelocalization 18 is shown. This does not require the prior knowledge of the axial position of the excitable fluorophore 4, as required in the previously described method. The method is therefore particularly suitable, for example, for localizing excitable fluorophores 4 that were laterally prelocalized using a wide-field localization method with a shallow depth of field.

[0074] In this method, too, axial sample positions are spaced apart by a distance corresponding to the distance between the central local minimum 46 and a maximum of the effective intensity profile 45. Here, too, the selected distances are particularly suitable, but smaller distances can also be selected in principle. The central axial sample position 50, which can correspond to the estimated position of the excitable fluorophore 4, is not omitted in this method. The number of axial sample positions is at least six; seven are specifically shown, but the number can be larger. Limits are set by the technical capabilities for shifting the excitation focus in the axial direction relative to the sample, as well as by optical aberrations that may occur.By using an odd number of axial probe positions 47-53 and positioning a central axial probe position 50 at the estimated position 16 of the excitable fluorophore 4, the capture range within which axial localization can occur is symmetrical to the estimated position 16 of the excitable fluorophore 4. An unambiguous determination of the axial position of the excitable fluorophore 4 is possible with this method if there are two axial probe positions in both directions from the actual position of the excitable fluorophore 4; calculations for the axial scanning pattern 59', which is formed by the set of all axial probe positions 47 to 53, the results of which are shown in . Figure 13The images shown show that the capture range is even larger. In the specific example shown, an excitable fluorophore can therefore always be reliably localized if it is actually located within the area between the axial probe positions 48 and 52. In the case shown, the excitable fluorophore 4 is located directly between the axial probe positions 51 and 52. Axial localization can again be achieved using a calibrated vector sum.

[0075] In a simple implementation, a two-stage approach can be used: first, the axial position is roughly determined and then the more precise position determination is carried out by performing a vector sum of the measured values ​​for four of the axial test positions, which are selected in such a way that the arrangement of the Figure 4shown. The measured value for an axial sample position that is adjacent to the roughly estimated position of the excitable fluorophore 4 is then not evaluated, while the remaining next two neighbors in each axial direction are evaluated; in the case shown, the axial sample positions 49, 50, 52 and 53 would therefore be evaluated. If the rough estimate is ambiguous as to whether the excitable fluorophore 4 is located just above or below an axial sample position, for example the axial sample position 51, this is harmless. Then precisely this sample position, in the described (not shown) example the axial sample position 51, is not considered in the more precise axial localization. In general, the sample position that is closest to the roughly determined position of the excitable fluorophore can be disregarded in the more precise localization.

[0076] The displacement of the 3D excitation donut 8 to the axial sample positions 47-53 can be carried out in each case, both in connection with Figure 4 as well as in connection with Figure 5explained embodiments, on the one hand, in such a way that the projection of the pinhole or generally of structures in the detection plane is displaced into the sample together with the 3D excitation donut 8, or on the other hand, in such a way that the projection of the pinhole or of structures in the detection plane remains fixed in the plane of the estimated position 16 of the excitable fluorophore 4. Solutions are also conceivable in which the projection of the pinhole or of structures in the detection plane is displaced to a different extent than the 3D excitation donut 8. If only the 3D excitation donut 8 is displaced, the actual intensity profile of the excitation light in the sample is decisive for determining the distances between the axial sample positions, i.e. for establishing the axial sample positions.If the projection of the pinhole or of detection structures in the detection plane, such as detector elements of a detector that spatially resolves a diffraction image, is shifted together with the 3D excitation donut 8, the effective intensity profile 45 is decisive, which results from a product of the actual intensity profile of the excitation light with a point spread function of the detection.

[0077] In particular, if the distances between the axial scanning positions 47-53 are chosen to be smaller than in the examples shown and thus more scanning points are chosen in relation to the capture area, it is not necessary for a central axial scanning position 50 to be present which coincides with the estimated position 16 of the excitable fluorophore.

[0078] In many cases, by repeating the MINFLUX localization step(s) with the smallest scanning pattern(s) 9, highly accurate localization, i.e., a highly accurate determination of the position of the excitable fluorophores 4, can be performed multiple times. This means that the method can be performed iteratively, whereby, particularly with small scanning patterns 9, a further reduction of the scanning pattern 9 from one step to the next, in which localization is performed in the same orientation, i.e., lateral or axial, is omitted. In many cases, however, a lower uncertainty in the position determination is achieved in the later steps.

[0079] In Fig. 6A contour plot of a section of a calculated effective intensity distribution 44 of a 3D excitation donut 8 is shown. For the calculation, it was assumed that the central minimum of the 3D excitation donut 8 is displaced both axially and laterally together with the detection aperture, so that the detection aperture and the central minimum are always arranged confocally to each other. Furthermore, an excitation wavelength of 642 nm and a certain, unspecified diameter of the detection aperture, i.e., a confocal pinhole, were assumed. For the selected parameters, the actual distance between the lateral maxima of the 3D excitation donut 8 is approximately 520 nm, whereas in the illustrated effective intensity distribution 44 it is approximately 400 nm. These lateral maxima cannot be seen in the contour plot shown, simply because no closed contour exists for the corresponding maxima value in the axial section.The contour plot shows that a line of equal effective intensity close to the center is approximately rectangular in shape with rounded corners. Above and below are regions with egg-shaped lines of equal effective intensity. The contour plot also reveals that an axial intensity profile has two distinct maxima. It can be seen that intensity profiles at radially displaced parallels to the axis each exhibit a distinct minimum and two plateau-like maxima regions, with the center of the plateau being at almost the same position in the axial direction as the maximum on the axis. This applies to a range of approximately ± 100 nm.For the more practically relevant case in which the detection aperture is fixed in the lateral, i.e., radial, direction, when the 3D excitation donut 8 is axially displaced for axial prelocalization 18, this range in which axial effective intensity profiles 45 exhibit the aforementioned properties is indeed wider. The same applies when a very large detection aperture is used, i.e., when no confocal detection is used. If the lateral position of an excitable fluorophore 4 is known with an uncertainty corresponding to the width of the range, it can be axially prelocalized using the 3D excitation donut 8.

[0080] In Fig. 7 to Fig. 10 Results of various simulation calculations for axial prelocalization 18 using a 3D excitation donut 8 are shown. In each case, the result of the calculation of the axial coordinate of a vector sum of photon numbers or fluorescence intensities pj ,which for different scanning positions bj , which are to be expected as measured values ​​under the respective assumed measurement conditions, are plotted against the assumed axial position of the excitable fluorophore. The vector sum can be written as u → p j b → j = ∑ j = 1 m p j ⋅ b → j ∑ j = 1 m p j .

[0081] For all axial coordinates for which a calculation was performed, calculations were performed for several radial coordinates within a range corresponding to radial distances from the optical axis from 0 to 100 nm. Therefore, for each abscissa value, several ordinate values ​​are determined, whereby the calculated values ​​can coincide very closely. For an abscissa value of 0, the values ​​generally coincide exactly for reasons of symmetry. The scale of the axes is 10 -7 < m, i.e., 10 2 < nm; a value of 1 therefore corresponds to 100 nm.

[0082] The representation of the Fig. 7This is based on an assumed axial scanning pattern with two scanning points, at which the central local minimum of the 3D excitation donut 8 is placed, each at a distance of 256 nm above and below a center. This distance corresponds to approximately a quarter of the distance between the maxima of an axial intensity profile of a 3D excitation donut 8 used as the basis for the simulation. Furthermore, observation conditions were assumed under which the effective intensity distribution 44 corresponds to the actual intensity distribution in the sample. Under these conditions, it is not possible to distinguish between positions of a fluorophore that are closer than approximately 260 nm or further than 260 nm from the center.Therefore, based on the assumed axial scanning pattern and the assumed initial conditions, axial localization or axial pre-localization 18 based on a simple vector sum is only possible if the axial position of the excitable fluorophore is known in advance to better than approximately ± 260 nm. This range, within which unambiguous localization is possible, is hereinafter referred to as the capture range or capture range of the axial scanning pattern.

[0083] The representation of the Fig. 8 is now based on an assumed axial scanning pattern with three sampling points. In addition to the sampling points of the axial scanning pattern of the Fig. 7 The underlying axial scanning pattern contains one more sampling point in the center. The plot shows that the capture range of this axial scanning pattern for evaluation based on a simple vector sum is smaller than that of an axial scanning pattern with only two sampling points.

[0084] The representation of the Fig. 9 is now based on an assumed axial scanning pattern with two scanning points, which corresponds to the axial scanning pattern of the Figure 7 The simulation was modified with regard to the observation conditions, in that an observation was assumed using a confocal pinhole axially shifted with the 3D excitation donut 8. In this case, an effective axial intensity profile 45 is effective, the maxima spacing of which is different from that of the simulation for Fig. 7 Accordingly, the intensity profile used has now been reduced for Fig. 9 Sampling points are assumed to be 180 nm apart from a center. The data curve corresponds to a reduced scale of the data curve from Fig. 7 supplemented by a Fig. 7 not included. The capture range is determined according to the change in the effective axial intensity profile 45 compared to the Fig. 7underlying intensity profile to approximately ± 180 nm.

[0085] The representation of the Fig. 10 There is now also an assumed axial sampling pattern with two sampling points and observation conditions as for Fig. 9 However, the distance between the two sampling points and the center was doubled, i.e., increased to 360 nm. The two sampling points are thus spaced apart by a distance that corresponds to the distance between the maxima of the effective axial intensity profile 45 of the 3D excitation donut 8. It can be seen from the illustration that this axial scanning pattern is not suitable for localizing a fluorophore based on a vector sum, since, particularly for fluorophores located close to the center of the axial scanning pattern, the values ​​obtained from the vector sum depend only weakly on the actual position of the fluorophore.

[0086] In Fig. 11 to Fig. 13Results of various simulation calculations for axial pre-localization 18 with extended capture range using a 3D excitation donut 8 are shown. All three representations are based on observation conditions such as for Fig. 9 assumed, i.e. with an axially moving confocal pinhole or an equivalent detection scheme. Figure 10 It was shown that a relevant extension of the axial capture range compared to the axial capture range known from the state of the art, which is approximately the capture range according to Figure 9corresponds, is not simply possible by placing the sampling points, whose measured values ​​are evaluated ratiometrically, at a greater distance from each other. The inventor has now discovered that by scanning the sample in the axial direction with a 3D excitation donut 8, a precise axial pre-localization 18 within an extended axial capture range 61 can be achieved in a surprisingly simple manner. For this purpose, a scan is selected with axial sample positions whose distance from each other is not greater than half the distance between the maxima of the effective intensity profile 45, whereby no sampling point needs to be located at a central sample position, so that the distance between two central axial sampling positions can correspond to the distance between the maxima of the effective axial intensity profile 45. Concrete examples of the evaluation of the data obtained during a scan have already been described above with reference to the Figures 4 and 5 explained.

[0087] The for Fig. 11 The assumed axial scanning pattern corresponds to the axial scanning pattern used for Fig. 10 was assumed, supplemented by one further sampling point above and below at a distance of 360 nm, i.e. half the distance of the maxima of the effective axial intensity profile 45 of the 3D excitation donut 8; the axial sampling pattern therefore has four sampling points, two of which are at a distance of 360 nm above and below the center of the axial sampling pattern and two further at a distance of 720 nm above and below the center of the axial sampling pattern. This sampling pattern on which the simulation is based thus corresponds to the axial sampling pattern 59, which in Figure 4is shown. The axial capture range 61 of this axial scanning pattern 59 for an evaluation based on a vector sum is approximately ± 400 nm, which means that fluorophores can still be clearly localized even if they lie outside the area between the inner scanning pattern points by up to approximately 10% of the scanning point spacing. The fact that the point clouds belonging to the individual abscissa values ​​cover a somewhat broader range of values, particularly at the edge of the capture range, shows that the axial value obtained from the vector sum for a given axial position of a fluorophore depends on the lateral position of the fluorophore. The fundamental deviation of the axial position obtained from the vector sum from the underlying axial position can be compensated for by a calibration curve, so that after calibration, the value obtained from the vector sum reflects the actual position of the fluorophore without any systematic error.The dependence on the lateral position leads to uncertainty in the axial localization. The large slope of the curve, meaning that the vector sum overestimates the axial distances to the center of the axial scanning pattern 59, is favorable, as it indicates that the vector sum is sensitive to a change in the position of the fluorophore.

[0088] For Fig. 12 An axial scanning pattern was used, which consists of the Fig. 11The capture range of this axial scanning pattern extends beyond ± 500 nm, although the sensitivity to the position of the fluorophore is only low from approximately ± 400 nm toward the edge. This axial scanning pattern has the advantage that, within the investigated radial range of ± 100 nm, the axial position obtained from the vector sum shows no visible dependence on the radial position of the fluorophore in the data representation.

[0089] For Fig. 13 An axial scanning pattern was used, which consists of the Fig. 12 by adding one more sampling point at each edge. The resulting axial sampling pattern corresponds to the one in Figure 5The simulation shows that the capture range of this axial scanning pattern covers the full range for which simulation calculations were carried out, i.e., more than ± 500 nm. Due to the fundamental considerations related to Figure 5 It can be assumed that the capture range is actually at least about ± 720 nm. Based on the simulation results presented in Fig. 12 shown, it can be further assumed that the catch area is actually even larger.

[0090] Overall, the Figures 11 to 13 The results presented show that a 3D excitation donut 8 is surprisingly well suited for axial localization of a fluorophore whose lateral position is known with an uncertainty of at least up to ± 100 nm.

[0091] The simulation calculations that correspond to the representations of the Figures 7 to 10 and 11 to 13do not explicitly include the effects of photon noise and background signal. However, the applicant knows from other studies that the vector sums depend on the background signal. This can be easily determined by considering the vector sum u → p j b → j = ∑ j = 1 m p j ⋅ b → j ∑ j = 1 m p j can be seen. A background signal that can be considered constant, at least to a good approximation, across the entire axial scanning pattern does not lead to a change in the vector in the numerator of the above equation, but to a change, namely an increase, in the denominator. The larger the background signal, the smaller the length of the calculated vector. For this reason, the applicant has developed a method that enables correction for the background signal while performing the MINFLUX measurements. This method is the subject of European patent application EP 3 951 470 A1. According to the method described in the cited patent application, an average background signal is determined on a sliding basis during the measurement. This background signal is then taken into account by subtracting it from the denominator. This results in a corrected vector sum whose value no longer systematically depends on the background signal.As explained above, the calibration of the localization can then be performed by applying a calibration function. This can be described, for example, by a polynomial or a look-up table.

[0092] The influence of photon noise depends directly on the number of photons measured. In this regard, the applicant has carried out further simulations, which show, for example, that by means of the Figure 12The underlying scanning scheme with five sampling points and an axially moving confocal pinhole, with the detection of only 400 photons over an axial capture range of approximately ± 500 nm for fluorophores within a lateral range of ± 100 nm each in a first direction and in a second direction orthogonal to the first, achieves an axial localization with an uncertainty between 20 nm and 35 nm, depending on the position of the fluorophore within the volume under consideration. This is certainly sufficient to subsequently perform, for example, iterative real-time MINFLUX localization in three dimensions.

[0093] Furthermore, the applicant is aware from experiments that, in particular for an axial scanning pattern with five points such as Fig. 12As a basis, a deviation of the actual scanning pattern spacing from those used in the simulations can be tolerated. For example, aberrations occur in real samples that lead to distortions of the effective axial intensity profiles 45. These distortions depend on the axial position under consideration. Nevertheless, using the aforementioned methods for axial pre-localization 18, particularly in conjunction with a correction of the aberrations, the applicant succeeds in axially pre-localizing fluorophores with sufficient accuracy to subsequently perform iterative real-time MINFLUX localization 33 in three dimensions.

[0094] Fig. 14 illustrates another scanning method for axial pre-localization 18 using a 3D excitation donut 8. While the Figures 4 and 5While the methods explained above are based on a discrete scanning pattern with the largest possible spacing in order to achieve the largest possible axial capture range 61 with a few sampling points, this method is based on a more finely rasterized or continuous scanning movement. With the 3D excitation donut 8, an axial scanning range 60 is scanned, wherein the central local minimum 46 of the effective axial intensity profile 45 covers the entire axial scanning range. In this case, the displacement 64 of the central local minimum 46 can take place in discrete steps or continuously. According to one aspect of the invention, the axial scanning range 60 is greater than the spacing of the maxima of the axial effective intensity profile 45. In the Figure 4In the method shown, the axial scanning range 60 (which is not explicitly noted there for reasons of clarity) is twice as large as the distance between the maxima of the axial intensity profile 45, in the Figures 5 and 14 As shown, it is three times as large as the distance between the maxima of the axial intensity profile 45. The axial scanning range 60 results in an axial capture range 61. An excitable fluorophore 4 can now be axially prelocalized if it is located within a prelocalization volume 63, which here is a cuboid or cylinder consisting of a lateral prelocalization range 62 and the axial capture range 61. The lateral prelocalization range 62 depends on the effective intensity distribution 44, for which an example is shown in Figure 6As explained above, it can comprise a square with an edge length of twice 100 nm or a circular area with a radius of more than 100 nm. If the scanning movement is continuous, photons detected during a part of the scanning movement can be accumulated and assigned to the swept area. The determination of the axial position can now also be carried out particularly easily by evaluating a vector sum u → p j b → j = ∑ j = 1 m p j ⋅ b → j ∑ j = 1 m p j and applying a calibration function. In principle, the axial position of the excitable fluorophore could also be determined by fitting an effective axial intensity profile 45 to the measured intensity profile. However, this poses, among other problems, that the shape of the effective axial intensity profile depends on the radial distance to the central local minimum of the overall effective intensity distribution 44 of the 3D excitation donut 8. Furthermore, such a determination of the position is fundamentally more computationally intensive and thus more time-consuming.

[0095] The methods for axial prelocalization 18 can also be advantageously used in conjunction with subsequent MINFLUX localization in two dimensions. It has been shown that comparable results can be achieved with a 3D excitation donut 8 as with a 2D excitation donut. This is important because it eliminates the need for a complex setup that enables rapid switching between different excitation intensity distributions. Furthermore, a 3D excitation donut, provided the axial position of the fluorophore is sufficiently well known, generally has a larger lateral capture area for MINFLUX localization than a 2D excitation donut.

[0096] In Fig. 15An embodiment of a microscope 70 according to the invention is shown schematically. The microscope 70 has an excitation light unit 76 containing a light source and beam-shaping elements such that the excitation light forms a 3D excitation donut 8 in a sample 75. The beam-shaping elements can be adjustable, thus enabling an excitation focus with a central maximum to be formed in the sample 75. Furthermore, the excitation light unit 76 can have a deflection unit configured to quickly displace the 3D excitation donut 8, or more generally the excitation focus, in particular laterally within the sample, i.e., for example, to sequentially control lateral sample positions 31, 31', 31".The microscope 70 further comprises an element with which excitation light is coupled into a beam path common to excitation and detection, and which guides the fluorescent light emitted by the sample 75 toward a detection unit 72. By way of example, in the figure, the element is embodied as a dichroic element 78. Furthermore, the microscope 70 comprises a deformable mirror 73. This is positioned here between a scanning unit 77 and an objective lens 74. It is positioned and configured such that, by deforming the deformable mirror 73, the excitation focus, in particular the 3D excitation donut, can be displaced in the axial direction within the sample 75. The scanning unit 77 can comprise, for example, a galvo scanner; it is configured to displace the excitation focus in the lateral direction within the sample 75.The detection unit 72 can contain a pinhole or, for example, an array of photon-counting avalanche diodes in a plane into which the excitation focus is imaged by means of the objective 74 and other optical elements not shown in the figure. Both the scanning unit 77 and the deformable mirror 73 are positioned such that they act on the excitation light and the fluorescent light to be detected. Therefore, by means of the scanning unit 77, a point confocally located at a fixed location in the sample 75 can be displaced in the image plane, for example, on a circular path around a center.If the excitation light unit 76 has a deflection unit, the interaction of this deflection unit and the scanning unit 77 can hold an excitation focus in the sample 75 in a fixed position, while the scanning unit 77 can be used to shift the image of the location of the excitation focus in an image plane relative to, for example, a pinhole. Furthermore, the microscope 70 has a control unit 71 configured to control the microscope 70 such that a method according to the invention is carried out. The control unit 71 can be connected to the elements to be controlled via control lines (not shown) or wirelessly, for example via radio. LIST OF REFERENCE SYMBOLS

[0097] 1Detecting a fluorophore 2Gaussian activation intensity distribution 3Gaussian excitation intensity distribution 4Excitable fluorophore 5First spatial direction 6Second spatial direction 7Axial spatial direction 83D excitation donut 9Scanning pattern 10Pre-localization 11,11'lateral position 12,12'lateral position 13Pinhole orbit 15,15'axial position 16Estimated position 17Lateral pre-localization 18Axial pre-localization 19Diameter 20,20'3D localization 21,21'first position 22,22'second position 23,23'third position 24,24'fourth position 25,25'central position 26,26'sixth position 27,27'seventh position 28,28'sampling pattern axis 29,29'sampling pattern plane 30,30',30"lateral MINFLUX localization 31,31',31"lateral sample positions 322D excitation donut 33iterative real-time MINFLUX localization 34circle 40,40',40‴axial MINFLUX localization 43final localization 44effective intensity distribution 45axial intensity profile 46central local minimum 47axial sample position 48axial sample position 49axial sample position 50axial sample position 51axial sample position 52axial sample position 53axial sample position 59, 59'axial scanning pattern 60axial scanning range 61axial capture range 62lateral pre-localization range 63pre-localization volume 64displacement 70microscope 71control device 72detection unit 73deformable mirror 74objective lens 75sample 76excitation light unit 77scanning unit 78dichroic element,

Claims

1. Method for high-resolution determination of the position of an excitable fluorophore (4) in three spatial directions in a sample by scanning the excitable fluorophore (4) with a 3D excitation donut (8) having a central local minimum (46), - wherein, in an axial localisation step, the central local minimum (46) is sequentially placed at two axial sample positions (15,15') on a scan pattern axis (28) passing through an estimated location (16) of the excitable fluorophore (4), the pair of sample positions (15,15') enclosing the estimated location (16) of the excitable fluorophore (4), - wherein in the axial localisation step, fluorescence emitted by the excitable fluorophore (4) is measured at each of the axial sample positions (15, 15') and the measured value is assigned to the respective axial sample position (15, 15'), - wherein in the axial localisation step, a new estimate of the axial position of the excitable fluorophore (4) is determined from the measured values assigned to the axial sample positions (15, 15'), characterised in that - in a lateral localisation step following the axial localisation step, the central local minimum (46) is placed exclusively in a scan pattern plane (29) oriented perpendicular to the scan pattern axis (28) sequentially at at least three lateral sample positions (31) arranged around a estimated position (16) of the excitable fluorophore (4) estimated in one or more steps performed earlier, - wherein in the lateral localisation step, fluorescence emitted by the excitable fluorophore (4) is measured at each of the lateral sample positions (31) and the measured value is assigned to the respective lateral sample position (31), - wherein in the lateral localisation step, a new estimate of the lateral position of the excitable fluorophore (4) is determined from the measured values assigned to the lateral sample positions (31).

2. The method according to claim 1, characterised in that the steps for obtaining the estimated position (16) of the excitable fluorophore (4) comprises as a step a lateral pre-localisation (17) for estimating a lateral position of the excitable fluorophore (4), which is performed prior to the axial localisation step and the lateral localisation step, wherein the excitable fluorophore (4) is excited to fluorescence with a 3D excitation donut, and wherein excited fluorescence is detected.

3. Method according to claim 2, characterised in that the lateral position of the excitable fluorophore (4) is estimated from a spatially resolved detection of the fluorescence in an image plane which contains a point confocal to the excitation focus, in particular wherein the spatially resolved detection of the fluorescence emission in the image plane is carried out with an array of photon-counting avalanche diodes or by displacing the point in the image plane which is confocal to the excitation focus relative to a pinhole aperture, preferably on a circular path around a centre, wherein fluorescence passing through the pinhole aperture is detected with a detector and assigned to the respective position of the confocal point.

4. The method according to any one of claims 1 to 3, characterised in that the steps for obtaining the estimated position (16) of the excitable fluorophore (4) comprises an axial pre-localisation (18) as a step in which the axial coordinate of the estimated position is determined, which is carried out before the axial localisation step and the lateral localisation step according to a method for the axial localisation of an excitable fluorophore (4), the method for axial localisation being carried out by scanning the excitable fluorophore with focused excitation light, an axial scanning range being greater than 500 nm, in particular greater than 1000 nm.

5. Method according to claim 4, characterised in that the lateral localisation step is carried out for the first time after the axial pre-localisation step (18) and before the axial localisation step is carried out for the first time.

6. Method according to one of claims 1 to 4, characterised in that the axial localisation step is carried out for the first time before the lateral localisation step is carried out for the first time.

7. Method according to one of the preceding claims, characterised in that several axial localisation steps and / or several lateral localisation steps are carried out.

8. Method according to claim 7, characterised in that, after a lateral localisation step, an axial localisation step is carried out next if a new estimate of the lateral position of the excitable fluorophore (4) was determined with a predetermined precision in the lateral localisation step.

9. Method according to claim 7 or 8, characterised in that a plurality of lateral localisation steps are carried out in direct succession, wherein a new estimated position of the excitable fluorophore (4) is determined from the estimated position (16) of the excitable fluorophore (4) and the new estimate of the lateral position of the excitable fluorophore (4) obtained in a lateral localisation step, which forms the estimated position (16) of the excitable fluorophore (4) for the respective following lateral localisation step.

10. Method according to claim 7, characterised in that an alternating sequence of axial localisation steps and lateral localisation steps is carried out, wherein in each case a new estimated position (16) of the excitable fluorophore (4) is determined from the estimated position (16) of the excitable fluorophore (4) and the new estimate of the axial position or the lateral position of the excitable fluorophore (4) obtained in one step, which new estimated position (16) forms the estimated position (16) of the excitable fluorophore (4) for the respective following step.

11. The method according to any one of claims 7 to 10, characterised in that the pair of sample positions (15, 15') surrounds the estimated position (16) of the excitable fluorophore (4) more closely in a later axial localisation step than in an earlier axial localisation step and / or in that in a later lateral localisation step the central local minimum (46) is placed at lateral sample positions (31) which are arranged more closely around the estimated position (16) of the excitable fluorophore (4) than in an earlier lateral localisation step.

12. Method according to one of the preceding claims, characterised in that a positioning of the 3D excitation donut (8) at an axial position for the sequential placement at the two axial sample positions (15,15') and / or for setting the scan pattern plane (29) and / or for scanning at the axial localisation and / or the axial pre-localisation (18) and / or in that positioning of the focused excitation light for scanning at the axial localisation is performed by directing an excitation light via a deformable mirror through an objective into the sample, wherein the axial positioning being performed by changing the shape of the deformable mirror.

13. Method according to one of the preceding claims, characterised in that the new estimate of the axial position of the excitable fluorophore (4) and / or the new estimate of the lateral position of the excitable fluorophore (4) is obtained by evaluating a vector sum and / or in that a determination of the axial coordinate of the estimated position in the axial pre-localisation (18) and / or in that the axial localisation is performed by evaluating a vector sum, in particular wherein the vector sum has the form u → p j b → j = ∑ j = 1 m p j ⋅ b → j ∑ j = 1 m p j , wherein the pj represent photon counts or intensities, which were detected at positions bj of the 3D excitation donut (8) or the focussed excitation light, wherein the value of the vector sum is corrected according to a predetermined calibration function, in order to obtain the new estimate of the axial position or the new estimate of the lateral position or, in the case of the axial pre-localisation (18), the axial coordinate of the estimated position or the axial localisation, furthermore, in particular, the quantity of the background signal being taken into account when evaluating the vector sum, the quantity of the background signal being determined on a sliding basis from measurement data.

14. Method according to one of the preceding claims, characterised in that it is carried out in real time.

15. Microscope, characterised in that it has a control device which is set up to control the microscope so that a method according to one of claims 1 to 14 is carried out, in particular wherein the microscope has a deformable mirror for axial displacement of an excitation focus in a sample.