Method and apparatus for high-resolution localization of single dye molecules in multiple spatial directions

Abstract

The invention relates to MINFLUX nanoscopy. The invention improves the three-dimensional localization of isolated fluorophores. According to the MINFLUX principle, the three-dimensional localization using fluorescence photons of isolated excitable fluorophores (4) is improved by dividing the localization into a series of separate steps using a 3D excitation ring (8), wherein the axial position or the lateral position of the fluorophore is determined in one step. Here, a more precise knowledge of the axial position improves the quality of the subsequent lateral localization, and vice versa. The three-dimensional localization is further improved by the following method: the method performs the axial localization by scanning the axial scanning range with a 3D excitation ring (8) and preferably by forming a vector and subsequently evaluating the measured intensity or photon number.

Description

[0001] Technical Field of the Invention

[0002] The present invention relates to MINFLUX nanoscopy (Nanoskopie), which improves the three-dimensional localization of isolated fluorophores. Existing technology

[0003] MINFLUX nanomicroscopy is a microscopy method that is still emerging in the prior art. MINFLUX nanomicroscopy involves a localization microscopy method. Localization of fluorophores is achieved using a structured excitation light distribution. A fundamental characteristic of MINFLUX nanomicroscopy is that the fluorophores to be localized are always excited near or at a minimum of the excitation light distribution, which ideally is zero, with the excitation light distribution having a region of increased intensity adjacent to the minimum. This allows for particularly effective utilization of fluorescence photons in obtaining information about the position of the corresponding emitting fluorophore. This is also applicable to applications requiring the tracking of fluorophore movement over time. For example, the use of excitation minima for observing samples is known from patents DE 10 2011 055 367 B4 (originally used only for tracking the movement of individual molecules in a sample), EP 3 055 674 B1, and DE 10 2013 114 860 B3, and forms the basis of MINFLUX nanomicroscopy. EP 3 055 674 B1 proposes to use different excitation light distributions alternately in a plurality of spatial directions for tracking particles in a sample, with the particles being tracked in mutually orthogonal directions with these excitation light distributions.

[0004] On this basis, a series of improvements for information acquisition have been developed, which enable the uncertainty of fluorophore localization to be within 2 nm. The magnitude of this uncertainty corresponds to the range of the fluorophore. For a detailed introduction to MINFLUX nanomicroscopy, see Francisco Balzarotti et al., "Nanometerresolution imaging and tracking of fluorescent molecules with minimal photonfluxes," arXiv:1611.03401 [physics.optics] (2016). Experiments demonstrate non-iterative MINFLUX localization and tracking of isolated fluorophores using MINFLUX. Furthermore, the concept of iterative MINFLUX has been proposed. In principle, to localize a fluorophore using MINFLUX nanomicroscopy, intensity minima or zeros must be located at multiple positions relative to the fluorophore's position. To achieve this, the fluorophore's position must be estimated or known initially with low accuracy in a preliminary step. This can be accomplished, for example, using conventional localization microscopy techniques (PALM, STORM) or other known methods. To this end, a method is described in the above-mentioned publication, in which a sample is scanned with a Gaussian intensity distribution until fluorescence from an isolated molecule is detected at the scanning position with a certain probability. The scan is then stopped, and the intensity distribution is subsequently positioned at four positions around the scanning position at a distance from the scanning position that is less than the wavelength of the light. In each case, the position of the isolated emitter relative to the direction of the connecting line is estimated based on the method described in the publication based on the number of photons measured at two separate positions relative to each other relative to the scanning position, thereby determining the emitter position as a whole in two spatial directions perpendicular to the optical axis. Although this method for pre-positioning is described in connection with the subsequent tracking of the movement of the fluorophore, it can also be used in connection with positioning. The estimation in each direction essentially corresponds to an evaluation of the ratio of the number of photons. Then, an intensity distribution of excitation light with a central minimum (for example, an intensity distribution of a donut-shaped shape known from STED microscopy) is placed at a known position, which is selected so 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 steps are repeated for one or more further positions of the intensity distribution. By evaluating the ratio of the intensity ratios, the position of the fluorophore can be determined with greater precision. In principle, the further the fluorophore is from the excitation minimum or the further it is displaced in the region of intensity rise, the greater the emission rate. This more precisely determined position can now be used as the starting point for repeating the above-described sequence of steps, where the position of the minimum in the intensity distribution of the excitation light can be brought closer to the estimated position of the fluorophore.The closer the location of the intensity distribution minimum is to the actual location of the fluorophore, the fewer fluorescent photons are required for localization, given a given uncertainty or precision. The publication indicates that two-dimensional localization can be achieved by first performing localization in one direction using a one-dimensional curve, and then performing localization in the other direction using the same curve, but rotated. It further indicates that future work will involve three-dimensional localization using a z-ring.

[0005] Patent publications relating to MINFLUX microscopy are in particular documents WO 2018 / 069 283 A1, US 2019 / 0235220 A1, US 2019 / 0234882 A1 and US 2019 / 0234879 A1, the U.S. patent applications mentioned therein being all subsequent applications of the aforementioned provisional international patent applications, which also disclose all concepts subsequently mentioned with reference to the U.S. publications.

[0006] US2019 / 0235220 A1 relates to a method using a small or minimal number of positions at which intensity minima of the excitation intensity curve are placed in order to determine the position of a fluorophore, which intensity minimum is adjacent to intensity rise areas on both sides in each spatial direction in which the position of the fluorophore is to be determined.

[0007] US2019 / 0234882 A1 relates to the method further described above, wherein the position information obtained from the first MINFLUX step is used in order to place the minimum of the intensity light distribution closer to the fluorophore in a subsequent step and thereby derive more precise position information.

[0008] US2019 / 0234879 A1 relates to a method in which the intensity minima of the excitation intensity curve are very quickly and almost simultaneously placed at multiple locations around the estimated position of the fluorophore. Then, if the emission rate is determined to be increasing at a single location, the single location is pushed closer to the assumed minimum.

[0009] According to WO 2018 / 069 283 A1, positioning in multiple spatial directions can be performed by performing any of the methods according to the invention for different orientations in sequence, for example first in a first direction with the aid of a one-dimensional excitation intensity curve and then in a direction different from the first direction.

[0010] In the publication by Klaus C. Gwosch et al., “MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells”, Nat Methods 17, 217-224 (2020), https: / / doi.org / 10.1038 / s41592-019-0688-0 (together with the associated “Supplementary Information”), a specific implementation of three-dimensional positioning with the aid of MINFLUX is described. In a sub-area of ​​the sample, an isolated fluorophore is placed in an excitable state with the aid of focused activation light. In a first step, this fluorophore is positioned with the aid of focused excitation light (wherein the intensity distribution at the focus essentially corresponds to a Gaussian distribution) in such a way that the focus of the excitation light is placed at four positions around the activation focus position. Based on the fluorescence signals measured respectively at the two relative positions, the position coordinates of the fluorophore position in the direction of the straight line connecting the two positions are determined accordingly, thereby determining the lateral position overall. Then, in a second step, focused excitation light is applied to the sample, with the focal point having the shape of a 3D donut—i.e., the intensity distribution has a local minimum surrounded by areas of increased intensity in all three spatial directions. The 3D donut is positioned sequentially at a total of two locations, with the local intensity minimum located laterally at the position determined in the first step. Axially, the local minimum is positioned once above and once below the anticipated fluorophore position along the optical axis. This pre-positioning is followed by more precise positioning using a scanning pattern with seven positions: five located in the scanning pattern plane, one of which is located at the center of the scanning pattern plane, and four evenly distributed on a circle around the center. The scanning pattern has two additional positions, which, along with the center of the scanning pattern plane, lie on the scanning pattern axis, for a total of three positions on this axis. The 3D ring is now positioned sequentially at the seven positions of the scan pattern, with the center of the scan pattern positioned at the position of the fluorophore determined during pre-positioning. This positioning is followed by another positioning using a smaller, but otherwise identical, scan pattern. This process can be repeated iteratively until the fluorophore loses its ability to fluoresce.

[0011] In the publication “Multicolor 3D MINFLUX nanoscopy of mitochondrial MICOS proteins” by Jasmin K. Pape et al., PNAS, August 25, 2020, 117(34): 20607-20614, 2020, https: / / doi.org / 10.1073 / pnas.2009364117, further applications of the method proposed in the publication “MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells” are described.

[0012] In image-based localization methods (e.g., PALM or STORM), in which diffraction images of isolated fluorophores are recorded and their positions are then determined from these diffraction images, the resolution is essentially proportional to the wavelength of the light used and inversely proportional to the root of the number of detected photons. In contrast, in iterative MINFLUX methods, the resolution depends on the exact type of iteration. This applies to both two-dimensional and three-dimensional localization. This is because the uncertainty of the fluorophore's position in a given iteration step (i.e., within a given scan pattern range) depends precisely on the scan pattern range. It is important to note that localization is successful only if the distance between the actual position of the fluorophore and the center position is not too large relative to the scan pattern range.

[0013] The aforementioned publication, “Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes,” states that the minimum uncertainty in two-dimensional localization achievable when scanning with a 2D excitation ring using a scanning pattern with a total of four scanning pattern positions (three on the circle and one at the center of the circle) is proportional to the diameter L of the scanning pattern and, in turn, inversely proportional to the root of the number of detected photons. This results in the goal of iteratively reaching a minimum diameter of the scanning pattern, with care being taken to ensure that the diameter of the scanning pattern in subsequent steps is large enough to ensure that the actual position of the fluorophore is not too far from the position determined in the previous iterative step relative to the range of the scanning pattern, otherwise localization in the subsequent step will be unsuccessful. Using maximum likelihood estimation allows for optimal utilization of this information. However, this presupposes that the intensity profile of the excitation ring and, for example, the amount of background fluorescence are known. Furthermore, localization using maximum likelihood methods is time-consuming and therefore unsuitable for iterative applications, as the scanning pattern must be reduced as quickly as possible and the pattern shifted to the position estimated in a given step. Therefore, in practical applications, according to the prior art, the following formula of the so-called modified least mean square estimator (mLMSE) is used:

[0014]

[0015] (In equation S50 of the publication and all equations based thereon, the base is incorrectly referred to as "log(2)" instead of "ln(2)"), where In each case it is normalized to the position fwhm is the full width at half maximum of the region around the local minimum of the excitation ring; k is the order of the estimator, the choice of which affects the region where localization can be performed; and β j is a scalar parameter that is chosen in particular according to the expected signal-to-noise ratio in order to obtain a localization with as small a systematic displacement as possible.

[0016] Such estimators used in practice are based on the so-called linear least mean square (LMS) estimator:

[0017]

[0018] This estimator is in turn derived by linearizing the solution determined by maximum likelihood. According to the information in "MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells", a disadvantage of the LMS estimator is that the number of photons measured in the center of the scan pattern is not included in the position determination. This disadvantage is a decisive disadvantage because, although the value measured in the center does not contain any direct information about the orientation of the fluorophore position in the plane, it does contain information about the distance of the fluorophore position from the center. Therefore, the purpose of the mLMSE expansion is to make the information from the measurement in the center available. This is important because otherwise, existing localization ambiguities can be avoided by measuring in the center. This ambiguity exists if the measurement values ​​obtained in the center are not evaluated because, in some cases, it cannot be determined from the measurement whether the fluorophore is inside or outside the circle of the outer positions of the scan pattern.

[0019] In principle, mLMSE has a bias, i.e. the fluorophore positions determined with the aid of mLMSE are systematically shifted relative to the actual positions. However, this can be minimized by optimally choosing the parameter β according to the assumptions about the background fluorescence and according to the chosen order of the estimator. j , which minimizes this bias. In principle, this estimator can only be used as an estimator if the scanning pattern has positions in the center where the scanning is actually also done. This is because the term This term ensures that the estimator is properly scaled to minimize bias, based on a measurement of the photon count at the center of the scan pattern. While it is possible and common to further analyze the data after the measurement is complete in order to obtain improved estimates of the positions of all fluorophores localized in the manner described above compared to the estimates obtained during the measurement, the quality of the analysis thus obtained still depends crucially on the quality of the estimates obtained during the measurement, since these estimates are the basis of the iterative process and therefore the basis of the minimum possible diameter of the scan pattern and the number of photons that can be measured using this minimum scan pattern.

[0020] The method described in "MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells" and the accompanying "Supplementary Information" now builds directly on the above-mentioned method and the theoretical work on this method. To estimate the position of the fluorophores during measurements with 3D annuli, the mLMSE of the following generalized formula is used:

[0021]

[0022] (where the value of index i=0 does not contribute anything to the summation on the right.) For the measurements specifically shown, order k=1 is chosen, so that overall for the measurements as described above (four positions on the circle and three positions on the axis), the formula for the estimator is:

[0023]

[0024] Here, the scalar-valued parameters β are j Numerical optimization was performed for typical signal-to-noise ratios, where the shape of the 3D ring was approximated by a quadratic function, assuming that the intensity increases with the square of the distance from the central intensity minimum of the 3D excitation ring. The optimization parameters for iterative MINFLUX localization (i.e., the number of iterations, the diameter L of the scan pattern per scan stage, and the number N of photons per scan stage) were determined through simulations based on the assumption that the fluorophores are located within an activation volume with a diameter of 360 nm, including the final localization using maximum likelihood estimation. Within the scope of these simulations, Gaussian excitation points and axial variations of the 2D ring were also considered; it was not specified whether the 2D ring was used to investigate the characteristics of the 3D localization.

[0025] MINFLUX nanomicroscopy allows the position of fluorophores to be experimentally determined in three spatial directions with an uncertainty of a few nanometers—that is, the accuracy of the position determination is comparable to the range of the fluorophore itself. Determining the position of individual fluorophores with a given measurement uncertainty requires a shorter time, and in particular, a lower number of fluorescence photons, than is required for determining the position of individual fluorophores using conventional localization microscopy. Prior art localization of individual fluorophores in three spatial directions using the MINFLUX method has only demonstrated a direct coupling of localization with activation of the fluorophore to be localized. In this case, due to localized activation, the axial position of the fluorophore to be localized is often known sufficiently often to allow a more precise estimation of the axial position using a z-ring of excitation light, which is placed once above and once below this axial position. If the axial position of the isolated fluorophore is not sufficiently precisely known from activation, the methods described in the prior art fail. In principle, this method is not suitable for localizing isolated fluorophores without explicit activation of these fluorophores immediately prior to localization. Furthermore, a weakness of the methods known from the prior art is that the quality of the position estimate obtained over time during the measurement is not only degraded by the background signal itself, but also by the background signal if it deviates from the value set in the optimized parameter β. j The quality is systematically further degraded if the assumptions about the background signal are used when performing the spectral estimation.

[0026] Another key weakness of known methods for 3D-MINFLUX nanoscopy is that the real-time estimation of fluorophore positions is based on an approximation of the 3D excitation ring shape by a quadratic function and coupled estimates of the axial and lateral positions. Since this approximation is only good for very small distances from the central minimum, this assumption, combined with the use of known estimators, leads to a reduced utilization of the available information in the fluorescence, especially in the early steps of the MINFLUX iteration when using scanning patterns with large diameters.

[0027] Invention Task

[0028] The object of the present invention is to provide an improved MINFLUX method for localizing isolated fluorophores in three-dimensionally extended samples or sample regions. On the one hand, even those axial positions that are not well known from the outset should be reliably localized. On the other hand, the use of fluorescence for determining the localization of isolated fluorophores in three-dimensionally extended samples or sample regions should be further improved.

[0029] Solution

[0030] The object of the present invention is achieved by a localization microscopy method having the features of independent claim 1 and a further localization microscopy method having the features of parallel claim 5, as well as a microscope having the features of claim 25, which is configured to carry out the method according to the invention. Dependent claims 2 to 4 and 12 to 19 relate to preferred embodiments of the method according to claim 1, dependent claims 6 to 11 to preferred embodiments of the method according to claim 5, dependent claims 20 to 24 to preferred embodiments of the method according to claim 1 and the method according to claim 5, and dependent claim 26 to a preferred embodiment of the microscope according to claim 25.

[0031] Description of the Invention

[0032] To further improve the utilization of fluorescence when determining the localization of isolated fluorophores in a three-dimensionally extended sample or sample region, according to a first aspect of the present invention, when localizing isolated excitable fluorophores in a sample using a 3D excitation ring (i.e., an intensity distribution of excitation light having a local minimum surrounded by areas of increased intensity in all three spatial directions) according to the MINFLUX method, the localization is divided into two steps: an axial localization step and a lateral localization step. While it is known in the prior art to use a 3D excitation ring for axial localization in one step, the lateral position is not newly determined in this step. In the axial localization, the central local minimum of the 3D ring is positioned at two axial sample positions on the axis of the scanning pattern that passes through the estimated position of the excitable fluorophore. This axial localization is then followed by simultaneous localization in the lateral and axial directions, for which the central local minimum of the 3D excitation ring is positioned on a scanning pattern extending in three spatial directions around the estimated position of the excitable fluorophore.

[0033] Therefore, the method according to the first aspect of the invention for determining the position of an excitable fluorophore in three spatial directions in a sample with high resolution by scanning the excitable fluorophore with a 3D excitation ring having a central local minimum comprises an axial positioning step known from the prior art,

[0034] - in the axial positioning step, placing the central local minimum sequentially at two axial sample positions on a scanning pattern axis extending through the estimated position of the excitable fluorophore, wherein the pair of sample positions encompasses the estimated position of the excitable fluorophore,

[0035] wherein in the axial positioning step, the fluorescence emitted by the excitable fluorophore is measured for each of the axial sample positions and the measured value is assigned to the respective axial sample position,

[0036] - wherein in the axial localization step a new estimate of the axial position of the excitable fluorophores is determined from the measured values ​​assigned to the axial sample position.

[0037] However, unlike the prior art, instead of a simultaneous positioning in the lateral and axial directions, a lateral positioning step is then performed.

[0038] - in the lateral positioning step, placing the central local minimum sequentially at at least three lateral sample positions arranged around the position of the excitable fluorophore estimated in one or more previously performed steps, only in the scanning pattern plane oriented perpendicularly to the scanning pattern axis,

[0039] wherein in the lateral localization step, the fluorescence emitted by the excitable fluorophore is measured for each of the lateral sample positions and the measured value is assigned to the respective lateral sample position,

[0040] - 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 sample position.

[0041] At least three lateral sample positions are used, as this is the minimum number of sample positions that allows for lateral localization in both lateral spatial directions. The sample positions are preferably selected so that they lie evenly on a circle around the estimated position of the excitable fluorophore. The selection of six such sample positions is advantageous because this provides very symmetrical recording conditions, resulting in an uncertainty in the estimated fluorophore position that is virtually independent of the fluorophore's exact actual position. In principle, in addition to the sample positions located around the estimated position of the fluorophore, further sample positions corresponding to the estimated position of the fluorophore can also be used.

[0042] In order to now reliably localize fluorophores whose axial position was initially unclear, a second aspect of the invention proposes a method for axial localization, which is suitable for determining the axial position of fluorophores whose axial position was very unclear (with an uncertainty of, for example, ±250 nm or ±500 nm or even greater) before the method according to this aspect of the invention is performed. The method mentioned at the beginning of the description of the invention is not suitable for this purpose, because it can only localize fluorophores that are clearly located in the range between the maxima of the axial intensity curve when the central local minimum of the 3D ring is located at one of the two sample positions on the scanning pattern axis and at the other sample position. In arrangements according to the prior art, this range between the maxima extends to approximately 500 nm.

[0043] According to a second aspect of the present invention, the excitable fluorophore is axially positioned by scanning the excitable fluorophore with focused excitation light, wherein the axial scanning range is greater than 500 nm or greater than 1000 nm. The axial scanning range particularly extends parallel to or along the optical axis along which the sample is illuminated by the excitation light. The axial positioning particularly refers to positioning parallel to or along the optical axis. The optical axis may be the same as or parallel to the scanning pattern axis defined by the method according to the first aspect.

[0044] In principle, the method according to this second aspect of the present invention can be performed with a Gaussian excitation focus. The axial intensity distribution of the excitation light then has a central maximum. As will be explained later, in some cases, the axial intensity profile is not directly decisive for positioning, but rather the effective axial intensity profile, which is derived from the axial intensity profile taking into account the point spread function of the detection. This effective axial intensity profile also has a central maximum.

[0045] During scanning, it is advantageous for adjacent scanning points to be at most half the half-value width of the axial effective intensity curve. This allows, during the scanning process, the excitable fluorophores to be subjected to at least one intensity that is not significantly different from the maximum intensity, one intensity that is reduced, and additionally a very reduced intensity; or to be subjected to two reduced intensities that differ only slightly from the maximum intensity at different positions relative to the scanning position pattern.

[0046] If scanning is performed with a Gaussian excitation focus, this requires that, if a 3D excitation ring is to be applied for MINFLUX localization after the method for axial localization, a switch must be made between the two illumination types. Solutions for such measures exist in the prior art. Conversely, abandoning the switch requires scanning with the same axial intensity profile as used for MINFLUX localization (i.e., an axial intensity profile with a central minimum). The latter initially seems unsuitable for scanning, since the excitation intensity is not concentrated in a narrow area, but rather has a minimum precisely in the central region of the axial intensity profile, so that the excitation intensity provided in the region around the center is particularly low. However, in the inventors' studies, it was found that, despite these apparent disadvantages for scanning, axial localization can be surprisingly successful even when scanning with the axial intensity profile of a 3D ring.

[0047] Therefore, the method according to the second aspect of the present invention can be particularly preferably performed so that the focused excitation light is a 3D excitation ring having an effective axial intensity curve with a central local minimum and a maximum adjacent to the minimum. In this case, the scanning range and the distance of the sample position can also be specified with reference to the distance of the maximum of the effective axial intensity curve. Then, the axial scanning range is greater than the distance of the maximum of the effective axial intensity curve, and preferably, the scanning range is at least twice the distance of the maximum of the effective axial intensity curve.

[0048] Here, the capture range is understood to be the range within which unambiguous positioning can be performed when the relevant scan mode is applied (i.e., when the relevant set of scan points is applied). In the method according to the second aspect of the invention, when the 3D excitation ring is used for axial positioning, the axial capture range is preferably at least as large as the distance to the maximum of the effective axial intensity curve.

[0049] When using a 3D excitation ring for axial localization, the scanning pattern can be preferably selected so that the distance between adjacent scan points is at most half the maximum value of the axial effective intensity curve. However, the pattern may have gaps in the center of the scan position (whose position typically coincides with the estimated position of the excitable fluorophore). This means that the distance between adjacent scan points near the center of the axial range may be greater. This greater distance is at most as great as the distance between the maximum values ​​of the axial effective intensity curve.

[0050] Further preferred embodiments will be given below, since their specific features also correspond to the specific features of the method according to the first aspect of the invention.

[0051] The method according to the first aspect of the present invention (which further improves the use of fluorescence for determining the localization of isolated fluorophores in a three-dimensionally extended sample or sample area) can now preferably be performed so that the step for obtaining an estimated position of the excitable fluorophore includes a step of lateral pre-positioning for estimating the lateral position of the excitable fluorophore, which lateral pre-positioning is performed before the axial positioning step and the lateral positioning step, i.e., before the steps required for performing the first aspect of the present invention. In the prior art, such lateral pre-positioning is performed before performing the MINFLUX method, which is not corresponding to the present invention, using Gaussian excitation light. This requires the possibility of switching the excitation light from Gaussian excitation light to a 3D ring, which is relatively complex technically and therefore economically. Preferably, the pre-positioning is performed by exciting the excitable fluorophore to fluorescence with a 3D excitation ring, wherein the excited fluorescence is detected by a detector, in order to reduce the technical complexity and at the same time increase the measurement speed.

[0052] In this method, the lateral position of the excitable fluorophore can be estimated, preferably based on spatially resolved detection of fluorescence in an image plane containing a point confocal with the excitation focus. For example, a photon-counting avalanche diode array can be used for spatially resolved detection of fluorescence emission in the image plane. Based on the distribution of the measured photon counts, or, in the case of a non-counting detector array or detector array, based on the distribution of measured fluorescence values ​​in the image plane, the position of the fluorophore in the sample can then be estimated, i.e., the position of the excitable fluorophore within the excitation focus. This does not require shifting the excitation focus or adjusting the scanner.

[0053] Alternatively, spatially resolved fluorescence emission can be detected in the image plane by displacing the point confocal with the excitation focus in the image plane relative to the aperture diaphragm, preferably along a circular path around the center. The fluorescence light that passes through the aperture diaphragm is detected using a detector that does not necessarily require spatial resolution and is assigned to the corresponding position of the confocal point. Here, the position of the fluorophores in the sample, i.e., the position of the excitable fluorophores within the excitation focus, can also be estimated based on the distribution of fluorescence measurement values ​​in the image plane. The excitation focus should remain fixed in this case. This can be achieved by displacing the point confocal with the excitation focus in the image plane by moving a deflection unit that acts only on the excitation light and not on the fluorescence light in opposite directions from a deflection unit that acts on both the excitation light and the fluorescence light.

[0054] Preferably, the method according to the first aspect of the present invention can be combined with the method according to the second aspect of the present invention, so that fluorophores whose axial positions are not known in advance can be reliably localized, while further improving the utilization of fluorescence when determining the localization of isolated fluorophores in a three-dimensionally extended sample or sample region. In this combination, the step for obtaining an estimated position of the excitable fluorophore includes an axial pre-positioning step for determining the axial coordinates of the estimated position, the axial pre-positioning being performed before the axial localization step and the lateral localization step according to the method for axial localization of an excitable fluorophore according to the second aspect of the present invention.

[0055] The lateral positioning step is then preferably performed for the first time after the axial pre-positioning step (preferably immediately following the axial pre-positioning step) and before the axial positioning step (that is, in particular, before the axial positioning step, which is mentioned only in relation to the first aspect of the invention, is performed for the first time). For the sake of clarity, it is provided that the method according to the second aspect is referred to herein as axial positioning per se, which, in conjunction with the method according to the first aspect, takes on the role of axial pre-positioning and is therefore also referred to as axial pre-positioning. In contrast to the axial positioning according to the second aspect of the invention, the axial positioning step is used for the first aspect; therefore, this term in each case refers to a step of the method according to the first aspect of the invention.

[0056] Whether it is the method according to the first aspect of the invention itself or the method in combination with the method according to the second aspect of the invention, it can be performed in the following way: the axial positioning step is performed for the first time before the lateral positioning step is performed for the first time. The better the axial position of the excitable fluorophore is known, the better the lateral positioning according to the MINFLUX method can be performed using the 3D excitation ring. In particular, in a certain sense, positioning in the axial direction with the 3D excitation ring performs better than positioning in the lateral direction, because the uncertainty in the lateral direction is less critical to the accuracy of the axial positioning. Therefore, whenever the axial positioning is not performed as a pre-positioning according to the method of the second aspect or according to a given alternative scheme (in which the intensity distribution of the excitation light is switched), it is very preferably to perform the axial positioning step for the first time before the lateral positioning step is performed for the first time.

[0057] The method according to the first aspect of the present invention can preferably be performed iteratively. If the method according to the first aspect of the present invention is combined with the method according to the second aspect of the present invention as a method for pre-positioning, the method is typically performed at least once, and then the method according to the first aspect of the present invention is performed iteratively after the overall method. During the iterative execution, multiple axial positioning steps, multiple lateral positioning steps, or both multiple axial positioning steps and multiple lateral positioning steps are performed. The division of the three-dimensional positioning into two separate sub-steps enables the step sequence to be adapted to the precise observation target and sample characteristics.

[0058] For example, after the lateral localization step, if a new estimate of the lateral position of the excitable fluorophore is determined with a given accuracy in the lateral localization step, then the axial localization step can be performed. The predetermined accuracy can be achieved in one or more lateral localization steps based on the deviation of the actual position of the excitable fluorophore from the estimated position.

[0059] Furthermore, whether in conjunction with the application of the aforementioned accuracy criteria or generally in other types of iterative execution, multiple lateral localization steps can preferably be performed consecutively. In this case, it is further preferred to determine a new estimated position of the excitable fluorophore from the estimated position of the excitable fluorophore and the new estimate of the lateral position of the excitable fluorophore obtained in the lateral localization step, with the new estimated position constituting the estimated position of the excitable fluorophore for the corresponding subsequent lateral localization step. This type of iterative execution is preferred, for example, if good lateral localization is primarily sought.

[0060] In particular, if there is no preferred direction with regard to the localization accuracy sought, or if the fluorophore to be localized in the sample moves in all spatial directions and if such movements of the fluorophore are to be tracked, it is preferred to perform an alternating sequence of axial localization steps and lateral localization steps, wherein 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, respectively, which new estimated position constitutes the estimated position of the excitable fluorophore for the corresponding subsequent step.

[0061] Determining the new estimated position from the estimated position and the new estimate, respectively, can mean that, for example, if the new estimate is an estimate of the axial position, the new estimated position is determined by directly replacing the original axial coordinates with the new estimated axial position, while the lateral coordinates remain unchanged in the present example case. However, it is also possible, for example, to determine the new axial coordinates of the new estimated position from a plurality of previously determined estimates, that is, specifically also taking into account the axial coordinates of the original estimated position when determining the new estimated position. This also applies to the opposite case, in which the new estimate is an estimate of the axial position, or also to the case where multiple axial positioning or multiple lateral positioning are performed in sequence. In many cases, it makes sense not only to take into account the last value when determining the position coordinates of a position direction. This applies even when the fluorophore is moving in the sample. Based on a series of previous axial and lateral estimates, the direction and speed of the fluorophore's movement can then be determined, and the future position, i.e. the position of the fluorophore in the next step, can be estimated in advance.

[0062] Preferably, the iterative method can be performed in such a way that in a later axial localization step, the sample position surrounds the estimated position of the excitable fluorophore more closely than in an earlier axial localization step, or in a later lateral localization step, the central local minimum is placed at a lateral sample position that is more closely arranged around the estimated position of the excitable fluorophore than in an earlier lateral localization step. The two measures described above can also be combined. That is, the basic principle of the iterative MINFLUX method can be applied separately to lateral localization and axial localization. Thus, as is known from iterative MINFLUX, the intensity of the 3D excitation ring can be selected depending on the size of the scanning pattern (i.e., the diameter or, in the case of axial localization, the axial distance of the sample position). A change in the corresponding observation duration can also be performed, which has a similar effect to the change in the intensity of the 3D excitation ring.

[0063] When performing the method according to the first aspect of the invention and the method according to the second aspect of the invention, the respective necessary shifts of the excitation light in the axial direction can be achieved by guiding the excitation light through the objective lens to the sample via a deformable mirror, wherein the axial positioning is achieved by changing the shape of the deformable mirror. That is, during the axial positioning step, the 3D excitation ring is preferably positioned at an axial position for sequential placement at two axial sample positions by correspondingly deforming the deformable mirror in the excitation beam path; similarly, the 3D excitation ring is preferably positioned at an axial position for adjusting the scanning pattern plane by correspondingly deforming the deformable mirror in the excitation beam path; and finally, the focused Gaussian excitation light or the 3D excitation ring is positioned for scanning during the axial positioning by correspondingly deforming the deformable mirror in the excitation beam path. For this purpose, the deformable mirror is preferably positioned in the plane of the rear aperture of the objective lens or in a plane conjugate thereto, i.e., in the plane that can form the pupil of the objective lens.

[0064] In the method according to the first aspect of the invention and in the method according to the second aspect of the invention, the determination of the position from the corresponding measured values ​​can be achieved particularly simply by evaluating the vector sum. This means that a new estimate of the axial position of the excitable fluorophore or a new estimate of the lateral position of the excitable fluorophore is obtained by evaluating the vector sum, or the axial coordinates of the estimated position are determined during axial pre-positioning, or the axial positioning is achieved by evaluating the vector sum. Preferably, the formula for the vector sum is where p j Indicates the position of the 3D excitation ring or focused excitation light The number or intensity of photons detected at .

[0065] In a simple calculation of this vector sum, for each method of a given scanning pattern, if the influence of noise is not taken into account and if there is no background signal, a precisely defined value is obtained for each actual position of the fluorophore within a certain range of positions, that is, there is exactly one calculated value for each position. Therefore, in each case, the value of the vector sum can be corrected according to a predetermined calibration function to obtain a new estimate of the axial position or a new estimate of the lateral position, or, in the case of axial prepositioning, the axial coordinates or axial location of the estimated position. Accordingly, the corresponding calibration function to be applied can be determined from the simulation.

[0066] The existing background signal (e.g. background fluorescence, ambient light scattered into the microscope, or light scattered or reflected in the microscope) will not affect the numerator of the vector sum on average, but will affect the denominator. This means that the vector sum in the above formula The value of depends systematically on the amount of background signal. Therefore, when evaluating the vector sum, the amount of background signal is preferably taken into account. This can be achieved particularly simply by subtracting the value of the background signal from the denominator of the above formula. For this purpose, the amount of background signal is preferably determined in a smooth manner from the measurement data.

[0067] The two methods described above, i.e. the method according to the first aspect of the invention and the method according to the second aspect of the invention, are preferably performed in real time. This is advantageous because, in the method according to the first aspect of the invention, the new position can be obtained by evaluating a simple vector sum, or, in the method according to the second aspect of the invention, the positioning can be obtained by evaluating a simple vector sum.

[0068] After executing the real-time method, or at any time after executing the real-time method, further data analysis can be performed. For this purpose, the data of each step obtained during execution is permanently stored. For example, more accurate positioning can be obtained from such data analysis. However, the achievable accuracy depends on the quality of the obtained data. This means that the method according to the present invention not only enables better real-time evaluation, but also improves the quality of subsequent analysis results.

[0069] The microscope according to the present invention is characterized in that it has a control device configured to control the microscope to perform the method according to the first aspect of the present invention or the method according to the second aspect of the present invention. Preferably, the control device is configured so that the method according to the first aspect of the present invention and the method according to the second aspect of the present invention or a combination of the methods can be performed, depending on the user's selection.

[0070] Particularly preferably, the microscope according to the invention has a deformable mirror for axially displacing the excitation focus in the sample (this also includes axially displacing the 3D excitation annulus). The deformable mirror is preferably placed in the plane of the rear aperture of the objective or in a plane conjugate thereto, i.e., in the plane that can form the pupil of the objective.

[0071] Advantageous developments of the invention are apparent from the patent claims, the description and the drawings and the associated explanation of the drawings, some of which are flow charts, based on which the method according to the invention is explained in greater detail as a whole.

[0072] The claims should not be interpreted as meaning that possible developments of the invention are only the subject matter of devices or methods which, in addition to the features of independent method claims 1 and 5 and device claim 25, have only all the features of the dependent claims or none of the features of the dependent claims. Rather, further developments can be derived from the features mentioned in the description and from the features that can be taken from the drawings and the associated explanations, which can have an effect individually or cumulatively. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 The flowchart of two-dimensional positioning using the iterative MINFLUX method in the prior art is shown.

[0075] Figure 2 FIG. 1 is a diagram illustrating a process of three-dimensional MINFLUX positioning according to the prior art.

[0076] Figure 3 FIG. 4 is a diagram illustrating a process of three-dimensional MINFLUX positioning according to an embodiment of the present invention.

[0077] Figure 4 is an illustration of a method for axial pre-positioning using a 3D excitation ring according to one aspect of the present invention.

[0078] Figure 5 is an illustration of a method of axial pre-positioning according to one aspect of the present invention having a much more expanded capture range.

[0079] Figure 6 3D excitation ring 8 is a contour plot of the cross section of the effective intensity distribution along the optical axis.

[0080] Figures 7 to 10 Shown are simulation results for determining the axial position of excitable fluorophores using a 3D excitation ring and various scanning modes.

[0081] Figures 11 to 13 The corresponding results for the preferred scanning mode with an increased capture range are shown.

[0082] Figure 14 It is an illustration of another method for axial pre-positioning with an expanded capture range based on continuous or fine grid scanning with a 3D excitation ring.

[0083] Figure 15 is a schematic diagram of an embodiment of a microscope according to the present invention.

[0084] Description of the drawings and explanation of the invention based on the drawings

[0085] The present invention is further explained and described below based on the embodiments shown in the accompanying drawings. Figure 1 and Figure 2 Explain the prior art.

[0086] exist Figure 1 A possible workflow for iterative two-dimensional MINFLUX localization according to the prior art is shown in FIG. A Gaussian excitation intensity distribution 3 is applied to an isolated fluorophore 4. This Gaussian excitation intensity distribution 3 is placed at four locations around the fluorophore's estimated position 16, such that two locations in a first position direction 5 and two locations in a second position direction 6 are opposite each other relative to the estimated position 16. Based on the fluorescence intensity or photon count measured for each pair, the position of the excitable fluorophore in the first position direction 5 and the second position direction 6 is determined. This step of pre-positioning 10 involving lateral pre-positioning 17 is known, for example, from the publication "Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes" mentioned in the prior art section regarding the subsequent tracking of the fluorophore's movement. The pre-positioning 10 is followed by an iterative real-time MINFLUX positioning 33, which comprises three steps: lateral MINFLUX positioning 30, 30', 30". For the lateral MINFLUX positioning 30, 30', 30", the excitation light distribution (which has a local intensity minimum in the lateral direction at the center of the focus, ideally a zero value, referred to as a 2D excitation ring 32) is placed at three positions on a circle around the position of the fluorophore 4 determined in the pre-positioning and at the position of the fluorophore 4 determined in the pre-positioning itself. Thus, the scanning pattern 9 comprises four scanning positions. Fluorescence is detected until the position of the excitable fluorophore 4 can be estimated more accurately from the measurement results (e.g., by a predetermined amount). How this assessment is performed is described in this publication and mentioned in the prior art section. Subsequently, before performing the lateral MINFLUX positioning 30', the scanning pattern 9 is shifted so 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; at the same time, the diameter 19 of the scanning pattern 9 is reduced. The fluorescence is detected again until the position of the excitable fluorophore 4 can be estimated more accurately from the measurement results (e.g., by a predetermined amount), and then the diameter 19 of the scanning pattern 9 is shifted and reduced in the same manner, and finally a further lateral MINFLUX localization 30 is performed. The iterative real-time MINFLUX localization 33 is followed by a final localization 43, which obtains the measurement data obtained in the iterative real-time MINFLUX localization 33 during analysis.

[0087] exist Figure 2The process of iterative three-dimensional real-time MINFLUX localization with a pre-localization step is shown in FIG, which essentially corresponds to the process described in the publication “MINFLUX nanoscopy delivers 3D multicolornanometer resolution in cells” mentioned in the prior art section. In a sub-region of the sample, isolated fluorophores are placed in an excitable state with the aid of focused activating light. Alternatively, the first step is to find 1 an excitable fluorophore 4. As combined Figure 1 As described above, in the pre-positioning of the lateral pre-positioning step 17, by means of the Gaussian excitation intensity distribution 3 (in Figure 2The excitable fluorophore 4 is located in real time (indicated by a black square star in the figure). To this end, a Gaussian excitation intensity distribution 3 is placed at two lateral positions 11, 11' in the first position direction 5 and at two lateral positions 12, 12' in the second position direction 6. Then, in the step of axial pre-positioning 18, focused excitation light is applied to the sample, wherein the focus has the shape of a 3D ring, that is, the intensity distribution has a local minimum surrounded by intensity rise areas in all three spatial directions. Therefore, the sample is irradiated with a 3D excitation ring 8. Here, the 3D excitation ring 8 is placed in sequence at a total of two axial positions 15, 15', wherein the local intensity minimum is located in the lateral direction at the position determined in the lateral pre-positioning 17. In the axial position direction 7, the local minimum is placed once above and once below the expected fluorophore position along the optical axis. Although the distance between these two positions is not explicitly stated in the above-mentioned disclosure on the prior art, it can be concluded from the information on setting the axial focus position of the 3D excitation ring 8 that the distance 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, the excitable fluorophore 4 must be located between the upper and lower intensity maxima of the axial intensity curve of the 3D excitation ring 8 for both positions of the 3D excitation ring 8. The axial position of the excitable fluorophore 4 is determined based on the fluorescence signals measured at the axial positions 15, 15'. This pre-positioning 10 is followed by a more precise 3D localization 20 performed in real time using a scan pattern with seven positions 21 to 27. Five of these positions 21 to 25 lie in a scan pattern plane 29, one of which is the center position 25 at the center of the scan pattern plane 29, and four positions are evenly distributed on a circle around the center position 25. The scan pattern 9 has two more positions 26, 27, which, along with the center position 25 of the scan pattern plane 29, lie on the scan pattern axis 28, resulting in a total of three positions 25, 26, and 27 lying on the scan pattern axis 28. The 3D excitation ring 8 is now positioned sequentially at the seven positions 21 to 27 of the scan pattern 9, with the center position 25 of the scan pattern 9 being positioned at the position of the excitable fluorophore 4 determined in the pre-positioning 10. This 3D positioning 20 is followed by a further 3D positioning 20', in which a reduced, but otherwise identical, scan pattern 9 with positions 21' to 27' is used. This can be continued iteratively until the excitable fluorophore 4 loses its fluorescence capability. Here, the 3D positioning 20, 20' is performed in the first position direction 5, the second position direction 6, and the axial position direction 7 using an estimator according to the following formula:

[0088]

[0089] Among them, β jis a scalar calibration value, which is selected so that the deviations occurring in the real-time positioning are as small as possible on average. Since the intensity distribution of the 3D excitation ring 8 is not spherically symmetrical, this results in the calibration value β j Either the selection is made to favor a better axial position determination, so that the lateral position determination is suboptimal, or vice versa, so that the axial position determination is suboptimal. Another difficulty is that the intensity profile of the 3D excitation ring 8 along a line perpendicular to the axis strongly depends on the axial distance of this line from the center of the 3D excitation ring 8. Therefore, the prior art method using the above-mentioned estimator makes poorer use of the emitted photons than in the case of a two-dimensional comparison method.

[0090] exist Figure 3 , in conjunction with a pre-positioning step, shows a process for iterative three-dimensional MINFLUX localization according to one embodiment of the present invention. The method starts with the discovery 1 of an excitable fluorophore 4. This can be done in different ways, for example by excitation and observation in a wide field of view or by confocal scanning of the sample. Depending on the sample, in addition to the excitation light, activation light can also be used for discovery. If the sample is scanned with excitation light, a Gaussian excitation intensity distribution 3 can be used for this. However, a 3D excitation ring 8 can also preferably be used. This is preferred because the need for multiple light paths, between which rapid switching can be performed, is thereby avoided. If an excitable fluorophore 4 is found, the position of the excitable fluorophore 4 is generally known with an uncertainty in the order of magnitude of the diffraction limit.

[0091] After finding 1, prepositioning 10 is performed. When performing the method according to the present invention, this prepositioning 10 can also be performed according to methods known from the prior art. In the illustrated embodiment, prepositioning is performed using a 3D excitation ring 8. Lateral prepositioning 17 is performed using the 3D excitation ring. The position of the excitable fluorophore 4 in the first positional direction 5 and the second positional direction 6 is estimated based on spatially resolved detection of the fluorescence emission in an image plane confocal with the excitation focus (i.e., the diffraction disk in the image plane). This spatially resolved detection can be performed, for example, using a photon-counting avalanche diode array, or, as shown, by scanning a diffraction disk with an aperture in the detection plane. Advantageously, the center of the aperture is guided along a circular path around the center, or the apertures are sequentially positioned at at least three (e.g., six) preferably evenly distributed positions along such a circular path. The center is thus the center of an imaginary image of an imaginary point light source located exactly at the center of the 3D excitation ring 8. The circular track is represented in the figure as an aperture track 13 by three smaller circles marked on a circumferential section and an arrow. The diameter of the smaller circles does not represent the diameter of the aperture track. Rather, the aperture track can be large enough so that the image of the aperture track in the sample always includes the center of the excitation focus. The diameter of the aperture track 13 is advantageously selected to be as large as possible, the specific conditions of which may depend on the available fluorescence signal and fluorescence background, but also, in particular, on the actual boundary conditions. For example, the applicant uses an arrangement in which the 3D excitation ring 8 is both deflected by an electro-optical scanner (by means of which it is moved to the individual points of the scanning pattern 9) and guided to a galvanometer scanner for scanning the sample. Here, the galvanometer scanner is also located in the detection beam path, but the electro-optical scanner is not. Specifically, the aperture track 13 is now scanned while simultaneously maintaining the excitation position using the 3D excitation ring 8. This is achieved by sequentially positioning the projection of the aperture placed in the detection beam path toward the sample at selected positions on the aperture track 13 using a galvanometer scanner, while the electro-optical scanner imparts a counter-motion to the excitation beam, thereby maintaining the 3D excitation ring in a fixed position within the sample. This results in a maximum range for the aperture track 13, corresponding to the size of the scanning field driven solely by the electro-optical scanner. Since, in this type of position determination, regardless of its specific implementation, the 3D excitation ring 8 remains fixed in position, the excitable fluorophores 4 are always exposed to the same excitation intensity during localization. Consequently, the shape of the intensity distribution of the 3D excitation ring 8 does not directly influence the quality of lateral pre-localization 17, but is at most indirectly affected by varying signal-to-background ratios depending on the actual position of the excitable fluorophores 4 relative to the center of the 3D excitation ring 8.

[0092] The discovery 1 and the lateral pre-positioning 17 can also be performed simultaneously in a single step. For example, the 3D excitation ring 8 can be moved to a position in the sample and fluorescence can be detected in the above-described manner. Based on the signal, in particular, based on whether fluorescence is detected or how much fluorescence is detected, it can be determined whether an excitable fluorophore 4 is present in the focal region of the 3D excitation ring 8. However, based on the measured values ​​obtained in this case, the position of the excitable fluorophore 4 within the focal region can also be directly determined. If no fluorescence is detected or only a small amount of signal is detected, the sample can be moved to another (e.g., adjacent) position in the sample and the above-described measurement can be repeated at that position.

[0093] In research conducted by the present applicants, it was discovered that iterative real-time MINFLUX localization 33 can be performed even if multiple excitable fluorophores 4 are actually present within the focal region of the 3D excitation ring and contribute to the signal during discovery 1 or lateral pre-localization 17, or even during a later localization step. Although the position of no single excitable fluorophore is determined with the best possible accuracy in that step, and instead an average position is obtained, there is a certain probability that one of two favorable situations will occur 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 co-located within a range of the scan pattern 9 within which MINFLUX localization can be performed using the given scan pattern 9. The average position of the excitable fluorophores 4 is then obtained during the iterative real-time MINFLUX localization 33. This situation particularly arises when the distance between the contributing fluorophores is small compared to the size of the resolvable biological structure. In other cases, the multiple excitable fluorophores 4 are relatively far apart. When the excitation mode 9 is narrowed, the excitable fluorophores 4 located outside are then in a region of very high excitation light intensity or excitation light quantity. This causes these fluorophores located outside (if they are normally corresponding switchable fluorophores) to be placed in a dark state, so that they then no longer contribute to the fluorescence signal, so that ultimately only isolated excitable fluorophores 4 or a plurality of closely adjacent excitable fluorophores 4 are localized.

[0094] The lateral pre-positioning 17 may be followed by the axial pre-positioning 18. A particularly advantageous method of performing the axial pre-positioning 18 is in Figure 4 and Figure 5 shown in the figure and will be combined with Figure 4 and Figure 5 However, Figure 3The method shown in assumes that the axial position of the excitable fluorophores 4 is known with sufficient accuracy without axial pre-positioning 18 to enable MINFLUX localization to be performed without axial pre-positioning 18. This situation arises, for example, if the sample to be investigated is thin, or if excitable fluorophores 4 are found during discovery 1 that are activated only during discovery 1 with the aid of activating light (in particular short-wavelength activating light), or if activation is achieved with the aid of a thin light sheet incident from the side. Lateral pre-positioning 17 can then be followed directly by iterative, real-time MINFLUX localization 33. 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, the MINFLUX localization is performed with the aid of an intensity curve having a local central intensity minimum (here specifically the 3D excitation ring 8) surrounded by an intensity rise region in all three position directions, but the lateral MINFLUX localization 30, 30', 30" is performed separately from the axial MINFLUX localization 40, 40', 40" in the axial position direction 7, that is, one after the other in a time series. According to the invention, when the axial MINFLUX localization 40, 40', 40" is the next step, the information obtained in the lateral MINFLUX localization 30, 30', 30" is used in order to optimally position the axial sample position (i.e., position 15, 15') taking into account the utilization of the information contained in the fluorescence photons to be detected in this next step. Conversely, when lateral MINFLUX positioning 30, 30', 30" is the next step, the information obtained in the axial MINFLUX positioning 40, 40', 40" is used in order to optimally place the axial sample position 31, in particular the center of the scanning pattern 9, taking into account the utilization of the information contained in the fluorescence photons to be detected in this next step.

[0095] exist Figure 3 In the embodiment shown, for a first axial MINFLUX positioning 40, a 3D excitation ring 8 (advantageously identical to the 3D excitation ring 8 used in the lateral pre-positioning 17) is placed at two positions 15, 15' along a perpendicular line relative to the focal plane of the lateral pre-positioning 17, one below the focal plane and the other above the focal plane. The position of the perpendicular line in the direction of the first position 5 and the direction of the second position 6 corresponds to the lateral position of the excitable fluorophore 4 determined in the lateral pre-positioning 17, which generally does not correspond exactly to the actual lateral position of the excitable fluorophore 4. The axial distance is selected such that the axial position of the excitable fluorophore 4 can be determined from the fluorescence values ​​measured at the two positions 15, 15'. The corresponding steps are known from the prior art and are described in detail in detail in the accompanying drawings. Figure 2axial pre-positioning 18 is described in

[17] . To this end, the lower position 15 is selected so that it lies below the actual axial position of the excitable fluorophore 4 with sufficient certainty (e.g., with a probability of approximately 90% or greater), and correspondingly, the upper position 15′ lies above this axial position. The maximum distance between the two positions 15, 15′ suitable for MINFLUX localization is determined by the fact that the excitable fluorophore 4 should ideally be close to the central minimum of the 3D excitation ring 8 and should under no circumstances be exposed to the region of maximum intensity of the 3D excitation ring 8 or to a region further from the central minimum than the first local axial maximum of the 3D excitation ring 8. The axial position of the excitable fluorophore 4 is determined based on the photon count or intensity measured at the positions 15, 15′. Lateral MINFLUX localization 30 is then performed. To this end, the 3D excitation ring 8 is positioned in a plane perpendicular to the optical axis at six lateral sample positions 31 arranged regularly on a circle, the center of which corresponds to the position of the excitable fluorophore 4 determined in the lateral pre-positioning 17. The plane of the lateral sample positions is arranged so that its axial position corresponds to the position of the excitable fluorophore 4 determined in the axial MINFLUX localization 40. This ensures that the lateral intensity profile of the 3D excitation ring 8 has the most pronounced local intensity minimum possible, which is ideally suited for the lateral MINFLUX localization 30. The scanning pattern used in this step has no sample positions directly outside the plane of the lateral sample positions 31. In the illustrated embodiment, this lateral MINFLUX localization 30 is followed by an axial MINFLUX localization 40', which is performed based on the first axial MINFLUX localization 40. The axial positions 15, 15' at which the 3D excitation ring 8 is positioned during this axial MINFLUX localization 40' are selected such that the midpoint between these two positions 15, 15' in the axial direction corresponds to the axial position of the excitable fluorophore 4 determined in the preceding axial MINFLUX localization 40, and their lateral position corresponds to the position of the excitable fluorophore 4 determined in the preceding lateral MINFLUX localization 30. In the embodiment shown, this is followed accordingly by a further lateral MINFLUX positioning 30', a further axial MINFLUX positioning 40", and a final lateral MINFLUX positioning 30". All positioning is performed in real time according to the MINFLUX principle using a suitable estimator. As in the prior art, in many cases the iterative real-time MINFLUX positioning 33 can and will be followed by a final positioning 43, which is obtained during a subsequent data analysis. This is not shown in this figure.

[0096] Dividing the MINFLUX positioning in three spatial directions into axial MINFLUX positioning 40, 40', 40' and lateral MINFLUX positioning 30, 30', 30' allows for iterative execution, for example, by performing two axial MINFLUX positionings in quick succession. Thus, for example, it may be advantageous to perform a second axial MINFLUX positioning 40' after a first axial MINFLUX positioning 40, wherein only the distance between the corresponding positions 15, 15' or the axial position of the midpoint between the two positions 15, 15' is changed between the two axial MINFLUX positionings 40, 40', without changing the lateral positions of these positions 15, 15'. This may be advantageous because, in a 3D excitation annulus 8 generated with the aid of a 3D annular phase plate, the radial intensity curve strongly depends on the axial position of the radial section, while the axial intensity curve 45 is less dependent on the radial position. This means that, in order to utilize the information contained in the fluorescence photons, it may be advantageous to first determine the axial position with a lower uncertainty before performing the lateral MINFLUX positioning 30. Publications from the prior art have shown that iterative position determination is generally advantageous in every case, even if the position determination is only carried out in one position direction.

[0097] Typically, in the iterative MINFLUX method 33 according to the present invention, each individual localization is based on measurements of sample positions around the previously estimated position of the excitable fluorophore 4, where the scan pattern does not contain a sample position at the location of the excitable fluorophore 4. This is because, according to the inventors' findings, real-time localization without measurements in the center of the scan pattern is generally more successful than the methods of the scientific publications cited in the prior art. The method according to the present invention described herein also makes it easier to separate MINFLUX localization into axial and lateral MINFLUX localization, since measurements in the center are not required for calibration of the overall localization performed in real time. However, this does not preclude measurements from also being taken at the center during individual or all steps of the method according to the present invention. Such measurements can be advantageously performed for control purposes, particularly for background signal checking, e.g., estimating the magnitude of the background signal, or based on knowledge of whether one or more excitable fluorophores are present in the detection region. Typically, the determination of the position of the excitable fluorophore 4 does not directly depend on such measurements in the center. This should not mean that the division of the localization into axial MINFLUX localization 40 , 40 ′, 40 ″ and lateral MINFLUX localization 30 , 30 ′, 30 ″ according to the invention is not possible if the determination of the position of the excitable fluorophore 4 also depends directly on the measurement in the center.

[0098] exist Figure 4 In FIG, the process of axial pre-positioning 18 is shown. For pre-positioning, a 3D excitation ring 8 is used, preferably the same 3D excitation ring 8 as is subsequently used for the iterative real-time MINFLUX positioning 33. The 3D excitation ring 8 has an effective axial intensity curve 45 with a central local minimum 46. If only the excitation curve is displaced axially, but the detection aperture remains in a fixed position, the effective axial intensity curve 45 corresponds to the actual intensity curve in the sample. If the detection aperture is displaced axially together with the excitation curve, the effective axial intensity curve 45 is the product of the detection point spread function and the actual axial intensity curve. In practice, also occurring aberrations need to be taken into account.

[0099] A typical 3D excitation ring 8 has a maximum in the radial direction in the focal plane, and the distance of the maximum is larger than the corresponding distance of the 2D excitation ring, for example, it can be 520 nm at an excitation wavelength of 642 nm. Depending on the width of the 3D excitation ring 8, the axially parallel intensity curve 45 is very similar in the range of radial distances from the axis. Figure 6 This applies to distances above ±100 nm, as shown as a contour diagram in FIG and explained further below for the effective intensity distribution 44. In this range, the local minimum increases only slowly with increasing distance from the axis. Figure 4 The method shown in can be used in the following situation: after discovery 1 and, if necessary, after lateral pre-positioning, the lateral position is known with an uncertainty that matches the above-mentioned radial distance range, and the axial position of the excitable fluorophore 4 is known with an uncertainty that is at most slightly greater than half the distance of the maximum value of the effective intensity curve 45.

[0100] The estimated position 16 of the excitable fluorophore is the axial sample position 50. Thus, in the illustrated embodiment, the 3D excitation ring 8 is sequentially positioned at four axial sample positions along the optical axis: axial sample position 48, axial sample position 49, axial sample position 51, and axial sample position 52. The set of axial sample positions 48, 49, 51, and 52 forms an axial scan pattern 59. The central axial sample position 50, corresponding to the estimated position 16 of the excitable fluorophore, is omitted. 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 between the central local minimum 46 and the maximum of the effective intensity curve 45, for example, 360 nm. This distance also depends on the wavelength of the excitation light used and the refractive index of the sample. Axial sample positions 48 and 52 are each at twice the distance from the estimated position 16 of the excitable fluorophore 4. Based on the set of fluorescence measurement values ​​obtained in this manner, a reliable estimate of the axial position of the excitable fluorophore 4 can be made. For example, if a vector sum is formed over the measured values, an estimated value is assigned to each actual position of the excitable fluorophore 4 , with each estimated value being assigned to exactly one position. This is ensured by the selected distances between the axial sample positions. The distances can also be selected to be smaller, but preferably not larger. Specifically specified distances are a particularly good choice in this regard because, at these distances, the capture range (i.e., the range within which a fluorophore must lie in order to be localized using the method) is very large relative to the number of scan points. Due to the uniqueness of the assignment, the vector sum can be modified by calibration (e.g., by means of simulation calculations) via a correction function so that the resulting estimator provides an unbiased estimate of the actual position of the excitable fluorophore 4 . In the absence of background fluorescence, two widely spaced axial sample positions are, in principle, sufficient for axial localization of a single excitable fluorophore. However, in practice, it is necessary to excite the fluorophore to be localized relatively strongly relative to the background during the localization process. This is achieved using the four selected scan positions. For example, the intensity maxima of the 3D excitation ring 8 placed at axial sample positions 49 and 51 are used to detect the fluorophore that actually has the estimated position 16 . Then, as the distance from this location increases, the intensity of excitation experienced by the excitable fluorophore 4 from one of the two further spaced 3D excitation rings 8 increases.

[0101] exist Figure 5 , another axial pre-positioning 18 process is shown. In this axial pre-positioning 18, the requirement for knowing the axial position of the excitable fluorophore 4, as set forth in the above method, does not need to be met. Therefore, this method is particularly suitable for positioning excitable fluorophores 4 that have been pre-positioned laterally by means of a wide-field positioning method with a low depth of field.

[0102] Likewise, in the method, the axial sample positions have a distance from one another which corresponds to the distance of the central local minimum 46 from the maximum of the effective intensity curve 45. Here too, the distance selected is a particularly suitable distance, but in principle a smaller distance can also be chosen. In the method, a central axial sample position 50 which can correspond to the estimated position of the excitable fluorophore 4 is not excluded. The number of axial sample positions is at least six, seven are specifically shown, but a larger number can be chosen. The restrictions here are set by the device possibilities of displacing the excitation focus in the axial direction relative to the sample and by the optical aberrations that occur. By an odd number of axial sample positions 47-53 and one central axial sample position 50 at the estimated position 16 of the excitable fluorophore 4, it is achieved that the capture range (within which axial positioning can be performed) is symmetrical with respect to the estimated position 16 of the excitable fluorophore 4. If there are two axial sample positions in both directions of the actual position of the excitable fluorophore 4, the axial position of the excitable fluorophore 4 can be determined unambiguously in any case using the method; the calculation results for the axial scanning pattern 59' formed by the set of all axial sample positions 47 to 53 are as follows Figure 13 As shown, the capture range is even greater. Thus, in the specifically shown example, if the excitable fluorophore is actually located in the region between the axial sample positions 48 and 52, it can always be reliably localized in each case. In the case shown, the excitable fluorophore 4 is located directly between the axial sample positions 51 and 52. Axial localization can again be performed with the aid of the calibrated vector sum.

[0103] In a simple implementation, this can be done in two steps by first roughly determining the axial position and then performing a more precise position determination by vector summing the measurements of four axial sample positions, which are chosen so that the arrangement used for this evaluation corresponds to Figure 4 The arrangement shown. Instead of evaluating the measured values ​​of the axial sample positions adjacent to the roughly estimated position of the excitable fluorophore 4, the two nearest neighboring positions remaining in each axial direction are then evaluated; thus, in the case shown, the axial sample positions 49, 50, 52 and 53 are evaluated. This is harmless if the rough estimate is ambiguous as to whether the excitable fluorophore 4 is slightly above or below an axial sample position (e.g., axial sample position 51). Subsequently, in a more precise axial localization, this sample position is not taken into account, in the example described (not shown). In a more precise localization, the sample position that is closest to the roughly determined position of the excitable fluorophore can usually be disregarded.

[0104] The displacement of the 3D excitation ring 8 to the axial sample position 47-53 can be combined with Figure 4 and combination Figure 5 In the described embodiments, the projection of the apertured aperture or, more generally, the structure in the detection plane is displaced into the sample together with the 3D excitation ring 8, or, alternatively, the projection of the apertured aperture or structure in the detection plane remains fixed in the plane of the estimated position 16 of the excitable fluorophores 4. Solutions are also conceivable in which the projection of the apertured aperture or structure in the detection plane is displaced to different degrees than the 3D excitation ring 8. If only the 3D excitation ring 8 is displaced, the actual excitation light intensity curve in the sample plays a decisive role in determining the distance to the axial sample position (i.e., for determining the axial sample position). If the projection of the apertured aperture or the detection structure (e.g., the detector elements of a detector that locally resolves the diffraction image) in the detection plane is displaced together with the 3D excitation ring 8, the effective intensity curve 45, which results from the product of the actual excitation light intensity curve and the detected point spread function, plays a decisive role.

[0105] In particular, if the distances of the axial scan positions 47-53 are smaller than in the example shown and therefore more scan points are selected relative to the capture range, there need not be a central axial scan position 50 coinciding with the estimated position 16 of the excitable fluorophore.

[0106] In many cases, a high-precision localization, i.e., a high-precision determination of the position of the excitable fluorophore 4, can be performed multiple times by repeating a MINFLUX localization step or multiple MINFLUX localization steps using one or more minimum scanning patterns 9. This means that the method can be performed iteratively, wherein, in particular with small scanning patterns 9, further reduction from one step to the next (in which the localization is performed in the same orientation, i.e., lateral or axial) is omitted. In many cases, a low uncertainty in the position determination is still achieved in the subsequently performed steps.

[0107] exist Figure 6, a contour plot of a cross-section of the calculated effective intensity distribution 44 of the 3D excitation ring 8 is shown. The calculation assumes that the central minimum of the 3D excitation ring 8 is shifted axially and laterally together with the detection aperture, so that the detection aperture and the central minimum are always confocally aligned with each other. Furthermore, an excitation wavelength of 642 nm and a defined diameter of the detection aperture (i.e., the confocal aperture stop) are assumed (not further specified here). For the selected parameters, the actual distance between the lateral maxima of the 3D excitation ring 8 is approximately 520 nm, while in the shown effective intensity distribution 44, this distance is approximately 400 nm. These lateral maxima cannot be derived from the contour plot shown, simply because there are no closed contour lines of the relevant maxima in the axial cross-section. It can be seen in the contour plot that the shape of the lines near the center of the same effective intensity is approximately a rectangle with rounded corners. Above and below are regions of oval lines with the same effective intensity. Based on the contour plot, it can be further seen that the axial intensity curve has two distinct maxima. As can be seen, the intensity curves of parallel lines radially displaced relative to the axis have distinct minima and in each case two plateau-like maximum regions, where the center of the plateau in the axial direction is approximately at the same position as the maximum on the axis. This applies to a range of approximately ±100 nm. For the more practically relevant case, i.e., when the 3D excitation ring 8 used for axial prepositioning 18 is axially displaced, the region in which the axial effective intensity curve 45 has the above-described characteristics is actually wider. The same is true if a very large detection aperture is used, i.e., if confocal detection is not used. As long as the lateral position of the excitable fluorophore 4 is known with an uncertainty corresponding to the width of the region, it is possible to axially preposition this excitable fluorophore with the aid of the 3D excitation ring 8.

[0108] exist Figures 7 to 10 , the results of various simulations of axial pre-positioning 18 using a 3D excitation ring 8 are shown. Here, the axial coordinate p of the vector sum of the number of photons or fluorescence intensities is j The calculated results are plotted at the assumed axial position of the excitable fluorophore. The photon number or fluorescence intensity is the result of different scanning positions under the assumed measurement conditions. The expected measurement value of . The vector sum can be written as

[0109] Here, for all axial coordinates for which calculations are performed, the calculations are performed for a plurality of radial coordinates in the range corresponding to the radial distance from the optical axis from 0 nm to 100 nm. Thus, for each value of the abscissa, a plurality of values ​​of the ordinate are determined, whereby the calculated values ​​may also be very close. For reasons of symmetry, these values ​​for the abscissa value 0 in principle completely coincide with one another. The axis scale is 10 -7m, which is 10 2 nm, so a value of 1 corresponds to 100 nm.

[0110] Figure 7 The illustration is now based on an assumed axial scanning pattern with two scanning points, at which the central local minimum of the 3D excitation ring 8 is placed, each scanning point being located at a distance of 256 nm above and below the center. This distance corresponds approximately to one-quarter of the distance of the maximum of the axial intensity curve based on the simulated 3D excitation ring 8. Observation conditions are further assumed in which the effective intensity distribution 44 corresponds to the actual intensity distribution in the sample. Under these conditions, fluorophore positions closer to or further from the center than approximately 260 nm cannot be distinguished. Therefore, axial positioning or axial pre-positioning 18 based on a simple vector sum and on the basis of an assumed axial scanning pattern and assumed initial conditions is only possible if the axial positions of the excitable fluorophores are known in advance to better than approximately ±260 nm. This range in which unambiguous positioning can be performed is subsequently referred to as the capture range or the capture range of the axial scanning pattern.

[0111] Figure 8 The illustration of is now based on an assumed axial scanning pattern with three scanning points. Figure 7 In addition to the scanning points of the axial scanning pattern, the axial scanning pattern used here also includes a scanning point in the center. As can be seen from the figure, for the evaluation based on a simple vector sum, the capture range of this axial scanning pattern is smaller than the capture range of the axial scanning pattern with only two scanning points.

[0112] Figure 9 The illustration is now based on an assumed axial scanning pattern with two scanning points, which corresponds to Figure 7 The simulation was modified with respect to the observation conditions, assuming observation with a confocal aperture diaphragm that is axially displaced together with the 3D excitation ring 8. Here, the effective axial intensity curve 45 is active, with a maximum distance of Figure 7 The maximum distance of the intensity curve on which the simulation was based is reduced. Figure 9 Assume that the distance between each scanning point and the center is 180nm. The trend of the data curve corresponds to Figure 7 The data curve is narrowed and supplemented by Figure 7 According to the change of effective axial strength curve 45, Figure 7 Compared to the intensity curve based on ΔV, the capture range is reduced to approximately ±180 nm.

[0113] Figure 10 The diagram is now also based on Figure 9The two scanning points and observation conditions assume an axial scanning pattern, but the distance between the two scanning points and the center is doubled, to 360 nm. Consequently, the distance between the two scanning points corresponds to the maximum value of the effective axial intensity curve 45 of the 3D excitation ring 8. As can be seen from the figure, this axial scanning pattern is not suitable for localizing fluorophores based on vector sums, because, particularly for fluorophores close to the center of the axial scanning pattern, the value obtained from the vector sum has little correlation with the actual position of the fluorophore.

[0114] exist Figures 11 to 13 In FIG. 1 , the results of various simulation calculations of the axial pre-positioning 18 with an expanded capture range of the 3D excitation ring 8 are shown. All three figures relate to the Figure 9 Assumed observation conditions, i.e. using axially co-movable confocal aperture diaphragms or equivalent detection schemes. Figure 10 shows that the capture range known in the prior art (approximately equivalent to that according to Figure 9 The relevant enlargement of the axial capture range 61 compared to the capture range of the axial sample is not achieved simply by spreading the scanning points, whose measured values ​​are evaluated ratio-wise, further apart from each other. The inventors have now discovered that by scanning the sample in the axial direction with a 3D excitation ring 8, precise axial pre-positioning 18 can be achieved in a surprisingly simple manner within the enlarged axial capture range 61. For this purpose, a scan is selected with axial sample positions which are spaced apart from each other by no more than half the distance to the maximum of the effective intensity curve 45, wherein no scanning point has to be present at the central sample position, so that the distance between two central axial scanning positions can correspond to the distance of the maximum of the effective axial intensity curve 45. This has already been done based on Figure 4 and Figure 5 A specific example of evaluating the data obtained during scanning has been described.

[0115] about Figure 11 The assumed axial scanning pattern corresponds to the Figure 10 The assumed axial scanning pattern is supplemented with an additional scanning point at a distance of 360 nm above and below (i.e., half the distance of the maximum value of the effective axial intensity curve 45 of the 3D excitation ring 8); therefore, the axial scanning pattern has four scanning points, two of which are located at a distance of 360 nm above and below the center of the axial scanning pattern, and the other two scanning points are located at a distance of 720 nm above and below the center of the axial scanning pattern. Therefore, this scanning pattern based on the simulation corresponds to Figure 4Axial scan pattern 59 is shown. The axial capture range 61 of this axial scan pattern 59 used for evaluation based on the vector sum is approximately ±400 nm, which means that a fluorophore can still be unambiguously localized even if it is located outside the region between the inner scan pattern points for up to approximately 10% of the scan point distance. The cloud of points belonging to the various abscissa values ​​includes a slightly wider range of values, particularly at the edge of the capture range, indicating that for a given fluorophore axial position, the axial value obtained from the vector sum depends on the lateral position of the fluorophore. Substantial deviations of the axial position obtained by the vector sum from the axial position on which it is based can be compensated by a calibration curve, so that after calibration, the value obtained from the vector sum reflects the actual position of the fluorophore without systematic errors. The dependence on the lateral position leads to uncertainty in axial localization. In contrast, a large slope of the curve (i.e., the vector sum overestimates the axial distance from the center of the axial scan pattern 59) is advantageous because it means that the vector sum is sensitive to changes in the fluorophore position.

[0116] about Figure 12 is based on an axial scanning mode, which Figure 11 This axial scanning mode is derived by adding a scanning point at the center. This axial scanning mode extends the capture range even beyond ±500 nm, but has lower sensitivity for the position of the fluorophores from approximately ±400 nm to the edge. This axial scanning mode 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 fluorophores in the data representation.

[0117] about Figure 13 is based on an axial scanning mode, which Figure 12 is obtained by adding one additional scanning point at each edge. Therefore, the axial scanning pattern obtained in this way corresponds to Figure 5 The axial scanning pattern 59' is shown. Simulations show that the capture range of this axial scanning pattern includes the entire range for which the simulation calculations were performed, i.e. greater than ±500 nm. Figure 5 Based on the basic considerations stated, it can be assumed that the capture range is actually at least about ±720nm. Figure 12 From the simulation results shown in , one can further assume that the capture range is actually larger.

[0118] Overall, Figures 11 to 13 The results shown in show that the 3D excitation ring 8 is surprisingly well suited for axial localization of fluorophores whose lateral positions are known with an uncertainty of at least up to ±100 nm.

[0119] Figures 7 to 10 and Figures 11 to 13The simulation calculations on which the illustration of is based do not explicitly include the effects of photon noise and background signals. However, the applicant knows from other studies that the vectors and depend on the background signal in each case. He obtained the following conclusions by observing that the vectors and This can be easily seen. The background signal can be considered constant, or at least approximately constant, over the entire axial scanning pattern. While this background signal does not cause the vector in the numerator of the above equation to change, it does cause the denominator to change, i.e., to increase. Therefore, the larger the background signal, the smaller the length of the calculated vector. For this reason, the applicant has developed a method that can correct for the background signal during MINFLUX measurements. This method is the subject of European patent application No. 21190113.7, which was not published at the date of filing this application. The entire content of this European patent application is hereby incorporated by reference into this application. According to the method described in the aforementioned patent application, an average background signal is determined in a smoothed manner during the measurement. This background signal is now 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 already stated above, the positioning can then be calibrated by applying a calibration function. This can be described, for example, by a polynomial or a lookup table.

[0120] The influence of photon noise directly depends on the number of photons measured. In this respect, the applicant has performed further simulations which show that, for example, with the aid of Figure 12 The proposed scanning pattern with five scanning points and a confocal aperture diaphragm that is jointly moved axially allows for axial localization with an uncertainty of between 20 nm and 35 nm, depending on the position of the fluorophore within the volume of interest. For each ±100 nm lateral range of the fluorophore in a first direction and a second direction orthogonal thereto, only 400 photons are detected within an axial capture range of approximately ±500 nm. This is certainly sufficient to subsequently perform, for example, iterative three-dimensional real-time MINFLUX localization.

[0121] Furthermore, the applicant has learned from experiments that, in particular, Figure 12 Based on an axial scanning pattern with five points, deviations of the actual scanning pattern distances from the simulation-based distances can be tolerated. Consequently, aberrations can occur in real samples, which can distort the effective axial intensity curve 45. These distortions depend on the axial position considered. Nevertheless, using the above-described method for axial prepositioning 18, particularly in combination with aberration correction, the applicants have succeeded in achieving sufficiently accurate axial prepositioning of fluorophores to subsequently perform iterative three-dimensional, real-time MINFLUX localization 33.

[0122] Figure 14Another scanning method for axial pre-positioning 18 using a 3D excitation ring 8 is shown. Figure 4 and Figure 5 While the method described was based on a discrete scanning pattern with the greatest possible distance in order to achieve the largest possible axial capture range 61 with just a few scan points, the present method is based on a finer gridding or a continuous scanning motion. With the 3D excitation ring 8, an axial scanning range 60 is scanned, wherein the central local minimum 46 of the effective axial intensity curve 45 sweeps across the entire axial scanning range. Here, the displacement 64 of the central local minimum 46 can be performed in discrete steps or continuously. According to one aspect of the invention, the axial scanning range 60 is greater than the distance of the maximum of the axial effective intensity curve 45. In Figure 4 In the method shown, the axial scanning range 60 (not specified in detail for the sake of clarity) is twice the distance of the maximum value of the axial intensity curve 45. Figure 5 and Figure 14 In the method shown, this is three times the distance to the maximum of the axial intensity curve 45. The axial capture range 61 is derived from the axial scanning range 60. Now, in each case, if the excitable fluorophore 4 is located within a pre-positioning volume 63 (which is a cuboid or cylinder resulting from the lateral pre-positioning range 62 and the axial capture range 61), the excitable fluorophore 4 can be axially pre-positioned. The lateral pre-positioning range 62 depends on the effective intensity distribution 44, which can be exemplified by Figure 6 As mentioned above, the lateral pre-positioning range can include a square with a side length of twice 100 nm or a circular area with a radius greater than 100 nm. If the scanning motion is continuous, the photons detected during a part of the scanning motion can be cumulatively recorded and assigned to the swept range. The determination of the axial position can now also be done by evaluating the vector sum This can be achieved particularly simply by applying a calibration function. In principle, the axial position of the excitable fluorophore can also be determined by adapting the effective axial intensity curve 45 to the course of the measured intensity. However, in this case, there is the problem that the shape of the effective axial intensity curve depends on the radial distance from the central local minimum of the entire effective intensity distribution 44 of the 3D excitation ring 8. Furthermore, such position determination is computationally complex and therefore more time-consuming.

[0123] The method for axial pre-positioning 18 can also be advantageously combined with subsequent two-dimensional MINFLUX localization. It has been demonstrated that using a 3D excitation ring 8 can achieve comparable results as using a 2D excitation ring. This is important because it eliminates the need for complex devices that can rapidly switch between different excitation intensity profiles. Furthermore, as long as the axial position of the fluorophore is sufficiently well known, a 3D excitation ring generally provides a larger lateral capture range for MINFLUX localization than a 2D excitation ring.

[0124] exist Figure 15, an embodiment of a microscope 70 according to the present invention is schematically shown. The microscope 70 has an excitation light unit 76, which includes a light source and a beam shaping element, so that the excitation light forms a 3D excitation ring 8 in the sample 75. The beam shaping element can be adjustable so that an excitation focus with a central maximum can be formed in the sample 75. Furthermore, the excitation light unit 76 can have a deflection unit which is configured to rapidly displace the 3D excitation ring 8 or, more generally, the excitation focus in the sample, in particular in the lateral direction, i.e., for example, in order to move it sequentially to the lateral sample positions 31, 31', 31". The microscope 70 also has an element with the aid of which the excitation light is coupled into a common beam path for excitation and detection and which guides the fluorescence emitted from the sample 75 in the direction of the detection unit 72. By way of example, in the figure, this element is configured as a dichroic element 78. Furthermore, the microscope 70 has a deformable mirror 73. Here, the deformable mirror is placed between the scanning unit 77 and the objective lens 74. The placement and configuration of the deformable mirror are such that, by deformation of the deformable mirror 73, the excitation focus, in particular the 3D excitation ring, can be displaced in the axial direction in the sample 75. The scanning unit 77 can comprise, for example, a galvanometer scanner; the scanning unit is designed to displace the excitation focus in the lateral direction in the sample 75. The detection unit 72 can be arranged in a plane The plane into which the excitation focus is imaged by means of an objective lens 74 and other optical elements (not shown in the figures) contains an apertured aperture or, for example, a photon-counting avalanche diode array. Both the scanning unit 77 and the deformable mirror 73 are positioned so that they act on the excitation light and the fluorescence to be detected. Thus, in the image plane, a point confocal with a fixed position in the specimen 75 can be displaced in the image plane by means of the scanning unit 77, for example, along a circular path around the center. If the excitation light unit 76 includes a deflection unit, the excitation focus can be held fixed in the specimen 75 by the combined action of this deflection unit and the scanning unit 77, while the image of the excitation focus position can be displaced in the image plane relative to, for example, the apertured aperture. Furthermore, the microscope 70 includes a control unit 71, which is configured to control the microscope 70 to carry out the method according to the present invention. The control unit 71 can be connected to the elements to be driven via control lines (not shown) or wirelessly, for example, by radio.

[0125] Reference Mark List

[0126] 1 Discovery of fluorophores

[0127] 2 Gaussian activation intensity distribution

[0128] 3 Gaussian excitation intensity distribution

[0129] 4 Excitable fluorophores

[0130] 5 First position direction

[0131] 6 Second position direction

[0132] 7 Axial position direction

[0133] 8 3D excitation ring

[0134] 9 Scan Mode

[0135] 10 Pre-positioning

[0136] 11, 11' lateral position

[0137] 12, 12' lateral position

[0138] 13 Aperture track with holes

[0139] 15, 15' axial position

[0140] 16 Estimated Location

[0141] 17 Lateral pre-positioning

[0142] 18 Axial pre-positioning

[0143] 19 diameter

[0144] 20, 20' 3D positioning

[0145] 21, 21' first position

[0146] 22, 22' Second position

[0147] 23, 23' Third position

[0148] 24, 24' Fourth position

[0149] 25, 25' center position

[0150] 26, 26' Sixth position

[0151] 27, 27' 7th position

[0152] 28, 28' scanning mode axis

[0153] 29, 29' Scanning Mode Plane

[0154] 30, 30', 30" lateral MINFLUX positioning

[0155] 31, 31', 31" lateral sample positions

[0156] 32 2D excitation ring

[0157] 33-iteration real-time MINFLUX positioning

[0158] 34 round

[0159] 40, 40', 40" axial MINFLUX positioning

[0160] 43 Final Positioning

[0161] 44 Effective intensity distribution

[0162] 45 Axial Strength Curve

[0163] 46 Central local minimum

[0164] 47 Axial sample position

[0165] 48 axial sample position

[0166] 49 Axial sample position

[0167] 50 Axial sample position

[0168] 51 Axial sample position

[0169] 52 Axial sample position

[0170] 53 Axial sample position

[0171] 59, 59' Axial scanning mode

[0172] 60 axial scanning range

[0173] 61 Axial capture range

[0174] 62 Lateral pre-positioning range

[0175] 63 Pre-positioning volume

[0176] 64 Shift

[0177] 70 Microscope

[0178] 71 Control Device

[0179] 72 Detection Unit

[0180] 73 Deformable Mirror

[0181] 74 objective lens

[0182] 75 samples

[0183] 76 excitation light unit

[0184] 77 Scanning Unit

[0185] 78 dichroic elements.

Claims

1. A method for determining the position of an excitable fluorophore (4) in three spatial directions in a sample with high resolution by scanning the excitable fluorophore (4) with a 3D excitation ring (8) having a central local minimum (46), in, In an axial positioning step, the central local minimum (46) is sequentially placed at two axial sample positions (15, 15') on a scanning pattern axis (28) extending through the estimated position (16) of the excitable fluorophore (4), wherein the pair of axial sample positions (15, 15') surrounds the estimated position (16) of the excitable fluorophore (4), wherein, in the axial positioning step, the fluorescence emitted by the excitable fluorophore (4) is measured for each of the axial sample positions (15, 15') and the measured value is assigned to the corresponding axial sample position (15, 15'), wherein, in the axial positioning step, a new estimate of the axial position of the excitable fluorophore (4) is determined from the measured values ​​assigned to the axial sample position (15, 15'), It is characterized in that In a lateral positioning step, the central local minimum (46) is sequentially placed at at least three lateral sample positions (31) arranged around the position (16) of the excitable fluorophore (4) estimated in one or more previously performed steps, only in a scanning pattern plane (29) oriented perpendicularly to the scanning pattern axis (28), wherein, in the lateral positioning step, the fluorescence emitted by the excitable fluorophore (4) is measured for each of the lateral sample positions (31), and the measured value is assigned to the corresponding lateral sample position (31), Therein, in the lateral localization step, a new estimate of the lateral position of the excitable fluorophore (4) is determined from the measured value assigned to the lateral sample position (31).

2. The method according to claim 1, characterized in that The method further comprises a step of lateral pre-positioning (17) for estimating the lateral position of the excitable fluorophore (4), wherein the step of lateral pre-positioning is performed before the step of axial positioning and the step of lateral positioning, in which the excitable fluorophore (4) is excited to emit fluorescence using a 3D excitation ring, and wherein the excited fluorescence is detected.

3. The method according to claim 2, characterized in that In the step of lateral pre-positioning, the lateral position of the excitable fluorophore (4) is estimated based on spatially resolved detection of fluorescence in an image plane containing a point confocal with the excitation focus.

4. The method according to claim 3, characterized in that Spatially resolved detection of fluorescence emission in the image plane is achieved using a photon counting avalanche diode array.

5. The method according to claim 3, characterized in that: Spatially resolved detection of fluorescence emission in the image plane is achieved by shifting a point in the image plane that is confocal with the excitation focus relative to the aperture diaphragm, wherein the fluorescence passing through the aperture diaphragm is detected by a detector and assigned to the corresponding position of the confocal point.

6. The method according to claim 1, characterized in that The method further comprises a step of axial pre-positioning (18) for determining the axial coordinates of the estimated position, which is performed before the axial positioning step and the lateral positioning step, wherein in the axial pre-positioning (18), the excitable fluorophore is scanned with focused excitation light within an axial scanning range (60) greater than 500 nm.

7. The method according to claim 2, characterized in that The method further comprises a step of axial pre-positioning (18) for determining the axial coordinates of the estimated position, which is performed before the axial positioning step and the lateral positioning step, wherein in the axial pre-positioning (18), the excitable fluorophore is scanned with focused excitation light within an axial scanning range (60) greater than 500 nm.

8. The method according to claim 3, characterized in that The method further comprises a step of axial pre-positioning (18) for determining the axial coordinates of the estimated position, which is performed before the axial positioning step and the lateral positioning step, wherein in the axial pre-positioning (18), the excitable fluorophore is scanned with focused excitation light within an axial scanning range (60) greater than 500 nm.

9. The method according to claim 4, characterized in that The method further comprises a step of axial pre-positioning (18) for determining the axial coordinates of the estimated position, which is performed before the axial positioning step and the lateral positioning step, wherein in the axial pre-positioning (18), the excitable fluorophore is scanned with focused excitation light within an axial scanning range (60) greater than 500 nm.

10. The method according to claim 5, characterized in that The method further comprises a step of axial pre-positioning (18) for determining the axial coordinates of the estimated position, which is performed before the axial positioning step and the lateral positioning step, wherein in the axial pre-positioning (18), the excitable fluorophore is scanned with focused excitation light within an axial scanning range (60) greater than 500 nm.

11. The method according to any one of claims 6 to 10, characterized in that: In the step of axial pre-positioning (18), the focused excitation light is the 3D excitation ring (8), and the 3D excitation ring has an effective axial intensity curve (45), and the effective axial intensity curve has the central local minimum (46) and a maximum value adjacent to the central local minimum (46).

12. The method according to any one of claims 6 to 10, characterized in that: In the step of axial pre-positioning (18), the focused excitation light is the 3D excitation ring (8), the 3D excitation ring has an effective axial intensity curve (45), wherein the axial scanning range (60) is greater than the distance of the maximum value of the effective axial intensity curve (45).

13. The method according to any one of claims 6 to 10, characterized in that: In the step of axial pre-positioning (18), the focused excitation light is the 3D excitation ring (8), the 3D excitation ring having an effective axial intensity curve (45), wherein the axial scanning range (60) is at least twice the distance of the maximum value of the effective axial intensity curve (45), and the axial capture range (61) is at least as large as the distance of the maximum value of the effective axial intensity curve (45).

14. The method according to claim 11, characterized in that The distance between adjacent scanning points is at most half the distance of the maximum value of the effective axial intensity curve (45), wherein scanning points adjacent to the center position of the axial scanning range can have a larger distance from each other, which is at most equivalent to the distance of the maximum value of the effective axial intensity curve.

15. The method according to claim 13, characterized in that The distance between adjacent scanning points is at most half the distance of the maximum value of the effective axial intensity curve (45), wherein the distance between scanning points adjacent to the center position of the axial scanning range can be larger, and the larger distance is at most equivalent to the distance of the maximum value of the effective axial intensity curve.

16. The method according to any one of claims 6 to 10, characterized in that: After the step of axial pre-positioning (18) and before the first execution of the step of axial positioning, the step of lateral positioning is first executed.

17. The method according to claim 11, characterized in that After the step of axial pre-positioning (18) and before the first execution of the step of axial positioning, the step of lateral positioning is first executed.

18. The method according to claim 13, characterized in that After the step of axial pre-positioning (18) and before the first execution of the step of axial positioning, the step of lateral positioning is first executed.

19. The method according to claim 14, characterized in that After the step of axial pre-positioning (18) and before the first execution of the step of axial positioning, the step of lateral positioning is first executed.

20. The method according to claim 1, characterized in that Multiple axial positioning steps and / or multiple lateral positioning steps are performed.

21. The method according to claim 2, characterized in that Multiple axial positioning steps and / or multiple lateral positioning steps are performed.

22. The method according to claim 3, characterized in that Multiple axial positioning steps and / or multiple lateral positioning steps are performed.

23. The method according to claim 4, characterized in that Multiple axial positioning steps and / or multiple lateral positioning steps are performed.

24. The method according to any one of claims 6 to 10, characterized in that Multiple axial positioning steps and / or multiple lateral positioning steps are performed.

25. The method according to any one of claims 20 to 23, characterized in that After the lateral localization step, if a new estimate of the lateral position of the excitable fluorophore (4) was determined with a given accuracy in the lateral localization step, an axial localization step is subsequently performed.

26. The method according to claim 24, characterized in that After the lateral localization step, if a new estimate of the lateral position of the excitable fluorophore (4) was determined with a given accuracy in the lateral localization step, an axial localization step is subsequently performed.

27. The method according to any one of claims 20 to 23, characterized in that A plurality of lateral localization steps are performed in succession, wherein a new estimated position of the excitable fluorophore (4) is determined from the estimated position (16) of the excitable fluorophore (4) and a new estimate of the lateral position of the excitable fluorophore (4) obtained in the lateral localization step, and the new estimated position constitutes the estimated position (16) of the excitable fluorophore (4) for a corresponding subsequent lateral localization step.

28. The method according to claim 24, characterized in that A plurality of lateral localization steps are performed in succession, wherein a new estimated position of the excitable fluorophore (4) is determined from the estimated position (16) of the excitable fluorophore (4) and a new estimate of the lateral position of the excitable fluorophore (4) obtained in the lateral localization step, and the new estimated position constitutes the estimated position (16) of the excitable fluorophore (4) for a corresponding subsequent lateral localization step.

29. The method according to any one of claims 20 to 23, characterized in that An alternating sequence of axial positioning steps and lateral positioning steps is performed, wherein a new estimated position (16) of the excitable fluorophore (4) is determined from the estimated position (16) of the excitable fluorophore (4) and a new estimate of the axial position or lateral position of the excitable fluorophore (4) obtained in one step, respectively, and the new estimated position constitutes the estimated position (16) of the excitable fluorophore (4) for the corresponding subsequent step.

30. The method according to claim 24, characterized in that An alternating sequence of axial positioning steps and lateral positioning steps is performed, wherein a new estimated position (16) of the excitable fluorophore (4) is determined from the estimated position (16) of the excitable fluorophore (4) and a new estimate of the axial position or lateral position of the excitable fluorophore (4) obtained in one step, respectively, and the new estimated position constitutes the estimated position (16) of the excitable fluorophore (4) for the corresponding subsequent step.

31. The method according to any one of claims 20 to 23, characterized in that In a later axial positioning step, a pair of the axial sample positions (15, 15') surround the estimated position (16) of the excitable fluorophore (4) more closely than in an earlier axial positioning step, and / or, in a later lateral positioning step, the central local minimum (46) is placed at lateral sample positions (31) that are more closely arranged around the estimated position (16) of the excitable fluorophore (4) than in an earlier lateral positioning step.

32. The method according to claim 24, characterized in that In a later axial positioning step, a pair of the axial sample positions (15, 15') surround the estimated position (16) of the excitable fluorophore (4) more closely than in an earlier axial positioning step, and / or, in a later lateral positioning step, the central local minimum (46) is placed at lateral sample positions (31) that are more closely arranged around the estimated position (16) of the excitable fluorophore (4) than in an earlier lateral positioning step.

33. The method according to claim 1, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

34. The method according to claim 2, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

35. The method according to claim 3, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

36. The method according to claim 4, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

37. The method according to claim 5, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

38. The method according to any one of claims 6 to 10, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

39. The method according to claim 11, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

40. The method according to claim 13, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

41. The method according to claim 14, characterized in that By directing the excitation light through an objective lens into the sample via a deformable mirror, the 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') and / or the scanning pattern plane (29) is adjusted and / or scanned in the axial positioning and / or axial pre-positioning (18), wherein the axial positioning is achieved by changing the shape of the deformable mirror.

42. The method according to claim 1, characterized in that The method is performed in real time.

43. The method according to claim 42, characterized in that A new estimate of the axial position of the excitable fluorophore (4) and / or a new estimate of the lateral position of the excitable fluorophore (4) is obtained by evaluating the vector sum, and / or the axial coordinates of the estimated position are determined in an axial pre-positioning (18), and / or the axial positioning is achieved by evaluating the vector sum.

44. The method according to claim 43, characterized in that The formula for the vector sum is where p j Indicates the position of the 3D excitation ring (8) or the focused excitation light The number or intensity of photons detected at the location is further characterized in that the value of the vector sum is corrected according to a predetermined calibration function to obtain a new estimate of the axial position or a new estimate of the lateral position, or to obtain the axial coordinates of the estimated position or the axial positioning in the case of the axial pre-positioning (18).

45. The method according to claim 43, characterized in that The amount of the background signal is taken into account when evaluating the vector sum, wherein the amount of the background signal is determined in a smoothed manner from the measurement data.

46. ​​The method according to claim 44, characterized in that The amount of the background signal is taken into account when evaluating the vector sum, wherein the amount of the background signal is determined in a smoothed manner from the measurement data.

47. The method according to claim 46, characterized in that Multiple axial positioning steps and / or multiple lateral positioning steps are performed.

48. The method according to claim 47, characterized in that After the lateral localization step, if a new estimate of the lateral position of the excitable fluorophore (4) was determined with a given accuracy in the lateral localization step, an axial localization step is subsequently performed.

49. The method according to claim 48, characterized in that The 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') by directing excitation light through an objective lens into the sample via a deformable mirror, wherein the axial positioning is achieved by changing the shape of the deformable mirror.

50. The method according to claim 3, characterized in that The method is performed in real time.

51. The method according to claim 50, characterized in that A new estimate of the axial position of the excitable fluorophore (4) and / or a new estimate of the lateral position of the excitable fluorophore (4) is obtained by evaluating the vector sum, and / or the axial coordinates of the estimated position are determined in an axial pre-positioning (18), and / or the axial positioning is achieved by evaluating the vector sum.

52. The method according to claim 51, characterized in that The formula for the vector sum is where p j Indicates the position of the 3D excitation ring (8) or the focused excitation light The number or intensity of photons detected at the location is further characterized in that the value of the vector sum is corrected according to a predetermined calibration function to obtain a new estimate of the axial position or a new estimate of the lateral position, or to obtain the axial coordinates of the estimated position or the axial positioning in the case of the axial pre-positioning (18).

53. The method according to claim 51, characterized in that The amount of the background signal is taken into account when evaluating the vector sum, wherein the amount of the background signal is determined in a smoothed manner from the measurement data.

54. The method according to claim 52, characterized in that The amount of the background signal is taken into account when evaluating the vector sum, wherein the amount of the background signal is determined in a smoothed manner from the measurement data.

55. The method according to claim 54, characterized in that Multiple axial positioning steps and / or multiple lateral positioning steps are performed.

56. The method according to claim 55, characterized in that After the lateral localization step, if a new estimate of the lateral position of the excitable fluorophore (4) was determined with a given accuracy in the lateral localization step, an axial localization step is subsequently performed.

57. The method according to claim 56, characterized in that The 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') by directing excitation light through an objective lens into the sample via a deformable mirror, wherein the axial positioning is achieved by changing the shape of the deformable mirror.

58. The method according to claim 8, characterized in that The method is performed in real time.

59. The method according to claim 58, characterized in that A new estimate of the axial position of the excitable fluorophore (4) and / or a new estimate of the lateral position of the excitable fluorophore (4) is obtained by evaluating the vector sum, and / or the axial coordinates of the estimated position are determined in an axial pre-positioning (18), and / or the axial positioning is achieved by evaluating the vector sum.

60. The method according to claim 59, characterized in that The formula for the vector sum is where p j Indicates the position of the 3D excitation ring (8) or the focused excitation light The number or intensity of photons detected at the location is further characterized in that the value of the vector sum is corrected according to a predetermined calibration function to obtain a new estimate of the axial position or a new estimate of the lateral position, or to obtain the axial coordinates of the estimated position or the axial positioning in the case of the axial pre-positioning (18).

61. The method according to claim 59, characterized in that The amount of the background signal is taken into account when evaluating the vector sum, wherein the amount of the background signal is determined in a smoothed manner from the measurement data.

62. The method according to claim 60, characterized in that The amount of the background signal is taken into account when evaluating the vector sum, wherein the amount of the background signal is determined in a smoothed manner from the measurement data.

63. The method according to claim 62, characterized in that Multiple axial positioning steps and / or multiple lateral positioning steps are performed.

64. The method according to claim 63, characterized in that After the lateral localization step, if a new estimate of the lateral position of the excitable fluorophore (4) was determined with a given accuracy in the lateral localization step, an axial localization step is subsequently performed.

65. The method according to claim 64, characterized in that The 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') by directing excitation light through an objective lens into the sample via a deformable mirror, wherein the axial positioning is achieved by changing the shape of the deformable mirror.

66. The method of claim 25, wherein: The 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') by directing excitation light through an objective lens into the sample via a deformable mirror, wherein the axial positioning is achieved by changing the shape of the deformable mirror.

67. The method according to claim 26, characterized in that The 3D excitation ring (8) is positioned at an axial position so as to be sequentially placed at two axial sample positions (15, 15') by directing excitation light through an objective lens into the sample via a deformable mirror, wherein the axial positioning is achieved by changing the shape of the deformable mirror.

68. A microscope, characterized in that: The microscope has a control device configured to control the microscope to perform the method according to any one of claims 1 to 67.

69. The microscope according to claim 68, characterized in that The microscope has a deformable mirror for axially displacing the excitation focus in the sample.

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