METHOD, SYSTEM, LOCATION MICROSCOPE AND COMPUTER PROGRAMS FOR ABERRATION CORRECTION AND FOR LOCATION OR TRACK OF EMISSORS

Abstract

The invention relates to a method for aberration correction of an illumination light for a localization microscope, wherein the illumination light is focused into a sample, wherein an intensity distribution of the illumination light with a local minimum is generated at the focus of the illumination light in the sample, and wherein the sample is scanned in at least one scanning step with the intensity distribution at scanning positions that form a scanning pattern around a first estimated position of a singular emitter in the sample, and wherein light emissions of the singular emitter are detected for each of the scanning positions, wherein a value of at least one parameter or at least one support point of an aberration correction function is determined on the basis of the detected light emissions.wherein the aberration correction function describes a deviation of a shape of the intensity distribution from a desired shape or a deviation of a phase distribution of the illumination light from a desired phase distribution, as well as a system, a localization microscope, computer program products and a method for localizing or tracking emitters using the aberration correction method.

Description

Technical field of the invention

[0001] The invention relates to a method for aberration correction of an illumination light for a localization microscope, in particular a MINFLUX microscope, as well as a system and a computer program for carrying out the aberration correction method. Further aspects of the invention include a method for localizing or tracking a single emitter in a sample, in particular a MINFLUX method, using the aberration correction method, as well as a localization microscope, in particular a MINFLUX microscope, and a computer program for carrying out the method for localizing or tracking a single emitter. State of the art

[0002] In optics, aberrations are understood as deviations from an ideal optical image produced by an optical system.

[0003] Chromatic aberrations caused by the wavelength dependence of refraction are largely corrected in higher-quality microscope objectives by special lens systems.

[0004] Other aberrations, such as spherical aberrations, astigmatism, and coma, manifest themselves in microscopy primarily as a result of refractive index differences between the sample, coverslip, and immersion medium between the objective lens and coverslip. Spherical aberrations, in particular, have a strong impact when microscopically examining areas deep within the sample, i.e., those located at a relatively large distance from the coverslip.

[0005] Aberrations can distort the excitation and / or detection point spread function (PSF), particularly depending on the microscopy technique, which can lead to lower resolution and reduced image contrast. These effects are especially pronounced when using objectives with high numerical aperture.

[0006] Devices are known in the art that can modify the wavefront of a light beam in such a way as to correct or compensate for aberrations. Such devices can be, for example, deformable mirrors or spatial light modulators (SLMs) with controllable pixels for phase modulation of the wavefront.

[0007] In sensor-based aberration correction, a sensor, such as a Shack-Hartmann sensor, can detect the wavefront of the aberrated light beam. Based on this detected wavefront, a wavefront modulator is then controlled to correct the aberration. Such a method is described, for example, in the publication "3D super-resolution deeptissue imaging in living mice" by MGM Velasco et al., optica 8 (4), 442-450 (2021).

[0008] As an alternative to sensor-based aberration correction, sensorless methods are known, which can, for example, be based on an image metric. In these methods, the control parameters of the wavefront modulator are changed until the image quality parameters approach the desired values.

[0009] For example, US 2015 / 0226950 A1 describes a STED microscopy technique and a corresponding microscope with which a phase pattern displayed on a spatial light modulator is adjusted using an image quality metric to correct aberrations of the STED light beam and, optionally, the excitation light beam. The metric is based on an image sharpness parameter and an image brightness parameter.

[0010] Another sensorless aberration correction method, in which cross-sectional images in planes parallel to the optical axis of the lens are evaluated, is described in patent application US 2022 / 0244515 A1. Among other things, it is proposed there to use the described aberration correction method for a MINFLUX process, wherein the determination of the aberration correction values ​​is based on image acquisition using confocal laser scanning microscopy with the MINFLUX excitation wavelength.

[0011] The article “Aberrations and adaptive optics in super-resolution microscopy” by M. Booth et al., Microscopy (2015) 251-261, provides an overview of the impact of aberrations on various super-resolution microscopy techniques, in which resolutions below the classical light microscopy diffraction limit can be achieved, such as STED (stimulated emission depletion), SMS (single modecule switching) and SI (structured illumination) microscopy.

[0012] Localization microscopy uses a fundamentally different image generation mechanism compared to classical light microscopy. Techniques such as PALM / STORM and MINFLUX do not perform a conventional imaging or scanning of the image field; instead, the positions of individual emitters, e.g., individual fluorophores, are determined, and an image is then generated from these individual localizations.

[0013] Therefore, aberration correction methods based on image analysis are not applicable to localization microscopy. This applies particularly to the MINFLUX technique.

[0014] In the prior art, the term "MINFLUX microscopy" encompasses a family of localization and tracking methods for isolated light-emitting emitters, in which an intensity distribution of illumination light, which induces or modulates light emissions of the emitter, is generated at the focus in the sample, wherein the intensity distribution has a local minimum in at least one spatial direction, and in which the position of an individual emitter is determined by detecting light emissions of the emitter.

[0015] The term "MINFLUX" was first used in the publication "F. Balzarotti et al., 'Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes', Science 355 (6325), 606-612 (2017)". There, the MINFLUX principle described above is implemented by first prelocalizing a single fluorophore by scanning it with a first Gaussian excitation light distribution. Subsequently, a second, donut-shaped excitation light distribution is placed at points that form a symmetrical pattern of four illumination positions around the position of the fluorophore estimated in the prelocalization. From the photon counts recorded for each illumination position, the position of the fluorophore is then determined to within a few nanometers using a maximum likelihood estimator.

[0016] Further variants and embodiments of MINFLUX microscopy are described in patent applications US 2019 / 0234879 A1, US 2019 / 0234882 A1 and US 2019 / 0235220 A1.

[0017] The publication “KC Gwosch et al., “MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells”, Nat. Methods, 17 (2), 217-224 (2020)” describes iterative 2D and 3D MINFLUX microscopy techniques. In this method, the sample is illuminated in several iterative steps at illumination positions with the minimum of a donut-shaped excitation light distribution. These illumination positions form a symmetrical illumination pattern centered around the fluorophore position estimated in the previous step, and the illumination positions are placed closer together around the currently estimated fluorophore position in each iteration. This allows for very high positional accuracy to be achieved in just a few steps.

[0018] Another iterative MINFLUX localization and tracking method using a modified position estimator and based on a commercial microscope setup is described in “R. Schmidt et al., “MINFLUX nanometer-scale 3D imaging and microsecond-range tracking on a common fluorescence microscope”, Nat. Commun. 12 (1), 1478 (2021)”.

[0019] The light that induces or modulates the light emission of the particles can, for example, also be STED (stimulated emission depletion) light. Patent applications US 2018 / 0259458 A1 and US 2020 / 0393378 A1 disclose MINFLUX-like methods based on superimposing an excitation light distribution with a local maximum onto a STED light distribution with a local minimum. The sample is scanned by shifting the STED distribution to the STED minimum, and the position of the fluorophore is determined from the measured fluorescence intensity values ​​at different positions of the STED intensity distribution.

[0020] Patent application DE 10 2021 100 564 A1 describes a 3D-MINFLUX localization method in which lateral and axial localization steps are performed separately. It is further mentioned that aberrations can play a role in the axial localization step or in axial pre-localization, which can lead to distortions of the effective axial intensity profile.

[0021] In the publication “Effects of optical aberrations on localization of MINFLUX super-resolution microscopy” by Chenying He et al. (2022), Optics Express Vol. 30, No. 26, 46849-46860, simulation results investigating the effects of optical aberrations on the MINFLUX localization of emitters are described. According to the study, astigmatism and coma aberrations, in particular, can influence localization precision, localization homogeneity, and systematic positional errors.

[0022] Patent application US 2024 / 0045190 A1 describes a localization microscopy method, in particular a MINFLUX method, in which a systematic deviation in the localization of emitters between early iteration steps and later iteration steps is corrected by means of a position correction.

[0023] This method is in principle capable of correcting localization offsets caused by imaging errors, but requires a relatively high computational effort and therefore has disadvantages for live measurements.

[0024] However, it would be desirable to be able to correct the effects of aberrations on localization microscopy techniques such as MINFLUX microscopy in an improved manner, especially with regard to flexible correction of diverse aberrations dependent on sample and environmental conditions, as well as rapid correction during live measurements. Object of the invention

[0025] In view of the disadvantages of the prior art discussed above, the object of the present invention is to provide a method for aberration correction of an illumination light for a localization microscope and a corresponding method for localizing or tracking emitters in a sample, which makes it possible to locate individual emitters quickly and with high accuracy in a simple and flexible manner, especially deep within a sample, and in particular to improve the quality of live measurements. Solution

[0026] This problem is solved by the subject matter of the independent claims. Advantageous further developments are specified in the dependent claims and described below. Description of the invention

[0027] A first aspect of the invention relates to a method for aberration correction of an illumination light for a localization microscope, in particular a MINFLUX microscope, wherein the illumination light is focused into a sample, wherein an intensity distribution of the illumination light with at least one local minimum is generated at the focus of the illumination light in the sample, and wherein the sample is scanned in at least one scanning step with the intensity distribution at scanning positions that form a scanning pattern around a first estimated position of a singular emitter in the sample, wherein, for each of the scanning positions, light emissions of the singular emitter induced or modulated by the illumination light are detected.and wherein, based on the light emissions recorded for the different sampling positions, a value of at least one parameter (in particular values ​​of several parameters) or at least one support point (in particular several support points) of an aberration correction function is determined, wherein the aberration correction function describes a deviation of a form of the intensity distribution of the illuminating light from a desired form of the intensity distribution or a deviation of a phase distribution of the illuminating light from a desired phase distribution.

[0028] According to the invention, data acquisition for aberration correction is performed similarly to a MINFLUX method for localizing or tracking individual emitters. However, unlike the prior art, the acquired light emissions are used to determine parameter values ​​or support points for an aberration correction function. This allows aberration correction to be performed simply and accurately with a localization microscope without additional hardware components. In particular, this makes it possible to quickly and with very high accuracy locate or track individual emitters, even deep within a relatively thick sample.

[0029] In contrast to aberration correction methods, which iteratively perform and optimize image acquisitions in order to maximize an image quality metric, the inventive method allows usable parameters for aberration correction to be determined in a single measurement cycle.

[0030] Since an intensity distribution is used that can also be used for localization (especially using a MINFLUX method), the recorded light emissions can optionally be used twice – firstly for aberration correction and secondly for localizing the corresponding emitters, e.g., through subsequent data processing. In other words, a portion of the already available localization data can advantageously be used for aberration correction as well.

[0031] The aberration correction function can be a continuous or a discrete function. It describes a deviation of a shape of the intensity distribution or a phase distribution of the illumination light from a desired shape. The aberration correction function can describe the shape of the intensity distribution at the focus in the sample, such as a point spread function, where the parameter determined according to the invention can be, for example, a shape parameter that can describe, for example, a skewness of the intensity distribution or an intensity value at the minimum of the intensity distribution.

[0032] The desired shape of the intensity distribution at the focus in the sample can, in particular, be point-symmetric with respect to the local minimum and / or the local minimum of the desired shape of the intensity distribution can be a zero point. Such a desired shape can, in particular, correspond to a shape of the intensity distribution that would result under ideal illumination without aberrations.

[0033] As an alternative to describing an intensity distribution in the sample, the aberration correction function can, for example, describe a phase distribution of the illumination light in a back aperture of an objective focusing the illumination light into the sample, or in a plane conjugate to the back aperture (pupil plane). In particular, the aberration correction function can have an orthogonal system of correction terms, e.g., Zernike polynomials.

[0034] The aberration correction function can also be defined, for example, by a matrix of parameter values ​​or support points. These values ​​can correspond, for example, to the values ​​with which mechanical actuators of a deformable mirror or pixels of a controllable spatial light modulator must be controlled in such a way that they compensate for the deviation of the intensity distribution shape from the desired shape, so that the desired shape results in the sample.

[0035] In the context of this specification, the term "localization microscope" refers to a light microscope designed to determine the positions of isolated emitters in a sample.

[0036] In the context of this specification, a "MINFLUX microscope" is a localization microscope designed to determine the positions of isolated emitters in a sample according to a MINFLUX method.

[0037] In the context of this specification, a "MINFLUX method" is a method for locating or tracking a single emitter in a sample, wherein an illumination light, in particular in a region around a first estimated position of a single emitter, is focused into a sample, wherein an intensity distribution of the illumination light with a local minimum is generated at the focus of the illumination light in the sample, and wherein, for different sampling positions of the intensity distribution or different shapes and / or arrangements of the intensity distribution, respective light emissions of the single emitter induced or modulated by the illumination light are detected.and wherein, based on the light emissions and the associated scanning positions or shapes and / or arrangements, a further estimated position of the isolated emitter is determined with higher accuracy than the first estimated position using a position estimator.

[0038] The term "emitter" refers to an object within the sample that acts as a point light source when illuminated. Light emission can occur directly from the emitter itself (especially if the emitter is a fluorescent dye molecule) or indirectly through a marker coupled to the emitter (e.g., fluorescent dye molecules covalently or non-covalently bound to a protein) or multiple such markers. An emitter can therefore also be an object to which several fluorophores are bound at a distance below the diffraction limit. Light emission can refer not only to the active emission of light by the emitter or markers in the sense of luminescence (especially fluorescence), but also, for example, to light emission caused by (Raman or Rayleigh) scattering. Specifically, the emitter or marker can be...The markers coupled to the emitter are in particular molecules of a fluorescent dye, fluorescent nanoparticles (e.g. quantum dots) or light-scattering nanoparticles such as gold nanoparticles or gold nanorods.

[0039] In the context of this specification, "isolated" emitters are emitters that can be separated by optical means. This can mean, in particular, that the emitters have a spatial separation above the optical diffraction limit. However, emitters are also considered isolated in this sense if they can be detected sequentially, for example, by detecting light emitted by a first emitter at a time when a neighboring second emitter is not emitting light because it is (in the case of fluorophores) in a dark state. In this way, even emitters that are separated below the diffraction limit but blink asynchronously can be separated by light microscopy.Finally, it is also possible to separate emitters that are separated below the diffraction limit but emit light of different wavelengths by spectral separation of the emitted light using a light microscope, or to excite two emitters with different excitation spectra at different wavelengths in order to optically separate the emitters. Finally, emitters with different emission lifetimes can be distinguished from one another by measuring their lifetimes (e.g., by time-resolved single-photon counting) and thus detected separately. All of these examples fall under the term "isolated emitters".

[0040] The sample can be illuminated in particular with an illumination light beam (e.g. a laser beam of illumination light), whereby the illumination light can be focused into the sample by an objective of the localization microscope.

[0041] The illumination light can be, for example, excitation light that excites emitters in the sample to luminescence, especially fluorescence, or that is reflected or scattered by emitters in the sample, thus inducing light emissions. Alternatively, the illumination light can also be suppression light (e.g., STED light) that returns the emitters from an excited state (especially by excitation light different from the illumination light) to a ground state. Suppression light is light that modulates the light emissions of the emitters.

[0042] The illumination light can, in particular, be the same illumination light used in the fourth-aspect method for locating or tracking individual emitters. This facilitates the correction of aberrations occurring in the single-emitter locating or tracking method using the determined parameters or support points of the aberration correction function. Specifically, the illumination light can have the same wavelength or spectrum in both methods, although the intensities of the illumination light may differ between the aberration correction method and the single-emitter locating or tracking method. However, it can also be advantageous to use different illumination lights for the first-aspect and fourth-aspect methods.

[0043] At the focal point of the illumination light in the sample, an intensity distribution of the illumination light with a local minimum is generated. This local minimum can be, in particular, a central local minimum, which can be located, for example, at the geometric focus. Ideally, the minimum is a zero point of intensity. However, due to the influence of aberrations, for example, the intensity of the illumination light at the minimum can be greater than zero. Areas of increasing intensity can be adjacent to the local minimum on both sides in at least one spatial direction. Specifically, the intensity distribution can be, for example, a donut shape, in which areas of increasing intensity in all directions in the focal plane perpendicular to the optical axis of the objective are adjacent to a central zero point. A donut shape is particularly suitable for 2D localization in the focal plane.The intensity distribution can also be a so-called bottle beam or 3D donut, in which areas of increasing intensity border the central zero point both in the focal plane (laterally) and along the optical axis (axially), i.e., in all three spatial directions. Further examples are light distributions with two intensity maxima separated by an area of ​​zero intensity, where the area intersects the geometric focus.

[0044] The intensity distribution can be generated, for example, by phase modulation of the illumination light beam with a phase plate or a spatial light modulator and subsequent focusing through the objective of the localization microscope.

[0045] The same intensity distribution can be used for both the aberration correction method and the method for locating or tracking individual emitters. This has the advantage that the effects of aberrations can be particularly well accounted for in the aberration correction. Alternatively, a different intensity distribution can be used for aberration correction than for locating or tracking individual emitters. For example, an optimized intensity distribution can be used for aberration correction, allowing for particularly accurate estimation of the aberration correction parameters. The determined aberration correction function can then be applied to the intensity distribution used in the method for locating or tracking individual emitters, such as a donut or a bottle beam.

[0046] The sample is scanned in at least one sampling step using the intensity distribution at sampling positions that form a scanning pattern around a first estimated position of a single emitter within the sample. The illumination light can be moved (e.g., with a beam scanner), the sample can be moved (e.g., using a stage scanner), or both. The first estimated position can be determined using an independent method of lower accuracy, analogous to a MINFLUX method, such as scanning with a Gaussian focus, wide-field microscopy, or pinhole orbit scanning. In the sampling step, the local minimum of the intensity distribution is successively positioned at the sampling positions. This can be done stepwise, for example, by successively shifting the intensity distribution to the sampling positions and recording light emissions during a waiting period at each position.Alternatively, the intensity distribution can also be continuously moved, e.g., along a circular path or other closed path around the first estimated position. In this variant, the sampling positions do not need to be fixed, but can be determined from the times of detection of the light emissions (especially individual photons) and the measured or calculated positions of the minimum of the intensity distribution assigned to those times.

[0047] As explained below, the localization or tracking method according to the fourth aspect (e.g., the MINFLUX method), for which the aberration correction according to the invention is performed, can also include steps in which the intensity distribution with the local minimum is positioned at different sampling positions in the sample. However, this is not mandatory. The localization or tracking method can also be performed with a stationary intensity distribution of the illumination light in the sample by changing the shape and / or orientation of the intensity distribution. For example, an intensity distribution with two maxima separated by an area of ​​minimum intensity can be rotated around the geometric focus, and the light emissions can be detected for the different orientations.

[0048] The detected light emissions can be, in particular, single photons or groups of photons. Single photons can be detected, for example, with avalanche photodiodes (APDs) or two-dimensional arrays of APDs, while groups of photons can be detected, for example, by so-called hybrid photodetectors or arrays of hybrid photodetectors.

[0049] According to one embodiment, the value of the at least one parameter or the at least one support point of the aberration correction function is determined by a function fit of the light emissions detected for the different sampling positions to the desired intensity distribution of the illumination light at the focus in the sample.

[0050] For example, intensity values ​​of a stored intensity distribution at positions corresponding to the sampling positions can be compared with the measured light emissions, and parameter values ​​(especially aberration terms representing different aberrations) can be adjusted until the deviation is minimal. Specifically, several stored intensity distributions with different aberrations can be compared with the measured values, and the intensity distribution with the greatest match can be selected. The parameter values ​​of an aberration correction function stored for this intensity distribution, e.g., in a lookup table, can then be used for aberration correction.

[0051] According to a further embodiment, the at least one parameter value or the at least one support point is determined by a trained data processing network, e.g., an artificial neural network, wherein the data processing network can, in particular, receive the light emissions recorded for the various sampling positions as input values ​​and can output the value of the at least one parameter or the at least one support point of the aberration correction function. Such a network can, for example, be trained with simulated light emission data. Alternatively or additionally, the data processing network can be trained or further trained based on measurement data, i.e., light emissions recorded for various sampling positions within the framework of an aberration correction method according to the invention, e.g., using reinforcement learning.Various parameters are conceivable as evaluation measures for the training of the data processing network, e.g. a residual deviation between the desired intensity distribution and the actual intensity distribution of the illumination light after aberration correction.

[0052] According to one embodiment, a beam shaping device is controlled such that a specific intensity distribution of the illumination light is adapted based on the aberration correction function. Here, the at least one parameter value or the at least one support point of the aberration correction function is adjusted such that the adapted illumination light, combined with the aberrations of the optical system from the beam path of the localization microscope and, if applicable, the sample itself, results in an intensity distribution in the sample that approximates a desired intensity distribution. Such a desired intensity distribution is, in particular, point-symmetric about the geometric focus within the focal plane. Furthermore, the local minimum of the desired intensity distribution, especially the central minimum, can be a zero point.

[0053] Aberration correction by controlling a beamforming device has the advantage that localization data is acquired directly under near-optimal conditions. This makes position estimation from the localization data possible in the first place, even in cases of strong aberrations. Additionally, the effort required for subsequent data processing can be reduced. Furthermore, this type of aberration correction is extremely advantageous for live position determination of emitters, as well as for tracking experiments and iterative localization methods, where the accuracy of the estimated emitter position is crucial for the subsequent steps and there is usually insufficient time for live data processing. While the aberration correction is primarily based on previously acquired data, it can be performed promptly and under the specific acquisition conditions on the sample under investigation.

[0054] According to a further embodiment, the beam shaping device comprises a deformable mirror and / or a spatial light modulator. A spatial light modulator can modulate the amplitude and / or the phase of the illumination light. When the illumination light beam is reflected by the appropriately adjusted deformable mirror, deviations from a plane wavefront caused by aberrations can be corrected in a manner known from the prior art. The spatial phase distribution of the illumination light can be modulated with a spatial light modulator. Aberrations can also be corrected in this way in a manner known from the prior art, e.g., by imprinting phase distributions corresponding to the Zernike polynomials.

[0055] According to a further embodiment, a position estimator for estimating the position of a singular emitter in a sample, in particular according to a MINFLUX method, is adapted on the basis of the aberration correction function, in particular wherein an expression of the position estimator describing a form of the intensity distribution is adapted on the basis of the aberration correction function.

[0056] The position estimator is an estimation algorithm for the position of an isolated emitter. It uses, in particular, light emissions (e.g., photon numbers or photon rates) and associated sampling positions (positions of the local minimum of the intensity distribution of the illumination light) or associated shapes and / or orientations of the intensity distribution of the illumination light as input data. The position estimator can be, for example, a maximum likelihood estimator or a least mean squares estimator. According to the invention, the position estimator can be adapted to correct the effects of aberrations of the illumination light on the position estimation of isolated emitters. The adaptation of the position estimator can, in particular, also be carried out in combination with or in addition to the control of a beam shaping device, especially to correct residual errors.In prior art MINFLUX position estimators, the intensity distribution of the illumination light is often assumed to be parabolic, which is a good approximation for a certain region around the local minimum. According to the invention, an expression for the shape of the intensity distribution adapted to the aberration correction function can now be used in the position estimator to account for the effects of aberrations on the position estimation.

[0057] According to another embodiment, the sampling step is performed sequentially on different isolated emitters. In principle, the method according to the invention can also be carried out on a single emitter, particularly if it is a particularly photostable emitter that can emit a large number of photons before transitioning to a dark state. However, performing the method on different emitters has the advantage that, even compared to a single photostable emitter, a much larger amount of data can be collected, which increases the accuracy with which the value of the at least one parameter or the at least one support point of the aberration correction function is determined. In particular, the light emissions detected at a sampling position can be a sum of light emissions from several emitters.

[0058] According to a further embodiment, a second estimated position of the isolated emitter is determined with increased accuracy compared to the first estimated position, wherein, based on the second estimated position, the sampling positions used in the at least one sampling step are shifted by a respective difference vector between the respective first estimated position and the respective second estimated position, and wherein the value of the at least one parameter or the at least one support point of the aberration correction function is determined based on the light emissions detected for the shifted sampling positions.

[0059] The second estimated position is considered the actual position of the corresponding emitter, and the sampled positions, particularly those from the sampling steps of a large number of emitters, are normalized to this position. This means a coordinate transformation is performed to analyze the distribution of light emissions around the actual emitter position. If the light emissions of multiple emitters are used for aberration correction, all light emissions can be related to their respective actual positions in this way. This allows for the evaluation of more light emissions, thus increasing the accuracy of the aberration correction.

[0060] In the described embodiment, the higher positional uncertainty of the first estimated position is exploited to obtain a large number of sampling positions. This is because, due to the positional uncertainty, the first estimated position is randomly shifted relative to the second estimated position; that is, the difference vector has randomly different lengths and directions. For different emitters, or when the first estimated position of an emitter is determined multiple times, the randomly shifted sampling pattern results in different (shifted) sampling positions relative to the second estimated position. In this way, even with a sampling pattern with relatively few (e.g., three to six) sampling positions, the point spread function can be sampled at many points. This has the advantage that the values ​​of a large number of parameters or a large number of support points of an aberration correction function (e.g.,the parameters of a large number of Zernike polynomials) can be determined.

[0061] The sampling positions shifted by the difference vector can, in particular, be assigned to different sampling steps with different sampling patterns, and furthermore, in particular to sampling patterns of different sizes.

[0062] Furthermore, between determining the first estimated position and the second estimated position from the light emissions of at least one sampling step, at least one further estimated position of the isolated emitter can be determined. In this way, the accuracy of the position determination can be successively increased.

[0063] According to a further embodiment, the second estimated position is determined using a MINFLUX method. This allows the second estimated position to be determined with very high accuracy (e.g., a deviation of a few nanometers), so that it corresponds very well to the actual position of the corresponding emitter. This improves the accuracy of determining the value of the at least one parameter or the at least one support point of the aberration correction function. In addition to its use for aberration correction, the second estimated position can advantageously also be used for the high-resolution imaging of sample structures in a method for locating a single emitter according to the fourth aspect.

[0064] If the second estimated position is determined using a MINFLUX method, an iterative MINFLUX method can in particular be carried out by determining at least one further position of the isolated emitter from the light emissions of at least one sampling step between the determination of the first estimated position and the determination of the second estimated position, and by placing the sampling pattern of each subsequent step depending on the further estimated position, in particular by centering it at the further estimated position.

[0065] Alternatively, the second estimated position can also be a previously known position of the corresponding emitter, for example, when the emitter is coupled to a sample structure with a known position. In this case, the second estimated position does not need to be determined by a localization method but can, for example, be retrieved from a data storage device. Even in this case, the position is referred to as the "estimated position" because, again, the previously known position cannot be specified with arbitrarily high accuracy.

[0066] According to another embodiment, the sampling positions are arranged around a position randomly shifted from the first estimated position. This increases the variability of the sampling, thus generating more distinct sampling positions, for example, if the random variation of the first estimated position is lower than desired.

[0067] According to another embodiment, the sampling step is performed with different sampling patterns, in particular sampling patterns of different sizes. For example, three to six sampling positions arranged on a circle around the first estimated position can be used, with the diameter of the circle being adjusted. This also results in a larger number of sampling positions relative to the actual position of the respective emitter, which improves the determination of these positions and thus the determination of the value of the at least one parameter or the at least one support point for the aberration correction function. A similar approach is used in iterative MINFLUX methods according to the prior art to incrementally increase the positional accuracy. With a suitable sampling pattern size, MINFLUX data from different iteration steps could therefore also be used for aberration correction.

[0068] According to a further embodiment, the scanning pattern is a continuous path around the first estimated position, in particular wherein a corresponding scanning position is determined each time the light emissions are detected. As the continuous path is traversed, the intensity distribution performs a uniform movement, e.g., a uniform circular motion. The scanning positions are then not fixed but result from the times at which light emissions, e.g., individual photons, were detected. The scanning movement of the intensity distribution then yields a corresponding scanning position for each light emission. The scanning positions at specific times can be obtained, for example, from the control signal of a scanner or from a measurement with a position sensor.For the method according to the invention, this type of sampling has the advantage that, due to stochastic photon emission, different sampling positions are obtained for each sampling step, even relative to the first estimated position. This increases the variability, i.e., leads to a larger number of sampling positions. Thus, an improved determination of the at least one parameter or the at least one support point of the aberration correction function results.

[0069] Different continuous paths, particularly those of varying sizes, can be used around the first estimated position in different sampling steps. Specifically, the sampling pattern (here, the continuous path) can be successively reduced in size in an iterative process. The sampling pattern can also be recentered, for example, if a further estimated position with higher accuracy than the first estimated position is determined from the light emissions. In this case, the sampling pattern can be centered on this further estimated position.

[0070] According to another embodiment, the illumination light is excitation light that excites emitters in the sample to luminescence, in particular fluorescence, or that is scattered or reflected by emitters in the sample.

[0071] According to another embodiment, the scanning pattern has scanning positions with different coordinates along or parallel to an optical axis of a lens with which the sample is illuminated with the illumination light.

[0072] That is, an axial, and in particular three-dimensional, scanning pattern is used. With such a scanning pattern (possibly in combination with another lateral scanning pattern), it is possible to spatially scan the intensity distribution of the illumination light, in particular to obtain an aberration correction for a three-dimensional localization or tracking method in which individual emitters are localized in all three spatial directions.

[0073] According to another embodiment, the intensity distribution of the illumination light has areas of increased intensity adjacent to the local minimum in all spatial directions, in particular wherein the intensity distribution is a bottle beam.

[0074] A bottle beam (sometimes also called a 3D donut) is an intensity distribution resulting from phase modulation of the illumination light (particularly in a pupil plane conjugate to a back aperture of the objective lens) with a ring-shaped phase pattern having a phase shift of π (particularly where an outer and an inner region of the phase pattern have the same area) and focusing the illumination light onto the sample. A bottle beam can advantageously be used for the 3D localization or 3D tracking of individual emitters, since an intensity gradient of the illumination light is also present along the optical axis, thus providing information about the axial coordinate of the emitter. In contrast to a (2D) donut beam, a bottle beam generates additional intensity at the central minimum, primarily due to spherical aberrations, so that there is no longer a zero intensity point there.This worsens the position estimate.

[0075] According to a further embodiment, the value of the at least one parameter or the at least one support point of the aberration correction function is determined based on light emissions from different emitters, wherein data sets are stored in which the value of the at least one parameter or the at least one support point is assigned to a position in the sample, such that the data sets represent a one-dimensional, two-dimensional, or three-dimensional map of parameter values ​​or support points, in particular wherein the positions in the sample form a regular grid with spacings of at least 500 nm, more specifically at least 1 µm. In particular, the different emitters have spacings of at least 500 nm, more specifically at least 1 µm. The position in the sample to which the parameter values ​​or support points are assigned can correspond to the position of the respective emitter (e.g.,(The highly accurate second estimated position can be used for this purpose) or the position can be derived from the position of the emitter, e.g. by an interpolation method.

[0076] For example, spherical aberration increases with depth in the sample (i.e., the axial distance to the coverslip). Additionally, aberrations within a sample can differ significantly from one another locally in a plane perpendicular to the optical axis, e.g., due to an inhomogeneous refractive index distribution. With the embodiment described above, position-specific aberration correction is advantageously possible under such conditions, e.g., by selecting the appropriate data set depending on the position at which an emitter to be localized is found (especially at the position determined by pre-localization) and using the corresponding parameter values ​​or support points for the aberration correction function.

[0077] According to another embodiment, the aberration correction function comprises at least one Zernike polynomial.

[0078] According to another embodiment, the scanning pattern has a maximum extent of 250 nm or more, in particular 300 nm or more. The maximum extent can be, for example, the diameter of a circle or sphere, or the major axis of an ellipse or ellipsoid. A maximum extent in the specified range offers the advantage that information about the point spread function of an emitter illuminated by the illumination light can be efficiently collected, thus providing meaningful values ​​for determining the value of the at least one parameter or the at least one support point of the aberration correction function. In iterative MINFLUX methods, the scanning pattern is typically significantly smaller than 100 nm, at least in the last iteration; for example, scanning patterns with a diameter of 40 nm are described in the prior art.Therefore, if the aberration correction method according to the invention is carried out in parallel with an iterative MINFLUX method for localizing or tracking individual emitters, the data for determining the value of the at least one parameter or the at least one support point of the aberration correction function are obtained in particular from "early" to "middle" iteration steps to ensure sufficient sampling, while the later iteration steps are used in particular exclusively for localizing the emitter.

[0079] According to a further embodiment, the intensity distribution of the illumination light in a focal plane perpendicular to an optical axis of a lens illuminating the sample has at least two intensity maxima, with a maximum extent of the scan pattern being 75% to 125% of the distance between the intensity maxima in the focal plane. In this way, information about the point spread function of an emitter illuminated by the illumination light can be efficiently collected. The distance between the maxima of the intensity distribution depends in particular on the wavelength of the illumination light.

[0080] A second aspect of the invention relates to a system for aberration correction of an illumination light for a localization microscope, in particular a MINFLUX microscope, according to a method according to the first aspect, wherein the system has a computing unit which is configured to determine a value of at least one parameter or at least one support point of an aberration correction function on the basis of light emissions detected by means of a detector of the localization microscope during at least one sampling step, wherein the aberration correction function describes a deviation of a shape of the intensity distribution of the illumination light from a desired shape of the intensity distribution or a deviation of a phase distribution of the illumination light from a desired phase distribution.

[0081] According to one embodiment, the system has a control unit configured to control a beam shaping device of the localization microscope in such a way that a shape of the intensity distribution of the illumination light is adapted based on the aberration correction function.

[0082] According to another embodiment, the computing unit or another computing unit of the system is configured to adapt a position estimator for estimating the position of a single emitter in a sample, in particular according to a MINFLUX method, based on the aberration correction function.

[0083] A third aspect of the invention relates to a computer program comprising instructions that cause the system according to the second aspect to carry out the method according to the first aspect.

[0084] Further embodiments and advantages of the system according to the second aspect and of the computer program according to the third aspect result analogously from the description of the method according to the first aspect.

[0085] A fourth aspect of the invention relates to a method for locating or tracking isolated emitters in a sample, wherein an illumination light is focused into a sample, wherein an intensity distribution of the illumination light with a local minimum is generated at the focus of the illumination light in the sample, and wherein, for different sampling positions of the intensity distribution or different shapes and / or arrangements of the intensity distribution, respective light emissions induced or modulated by the illumination light of an isolated emitter are detected, and wherein, based on the light emissions and the associated sampling positions or shapes and / or arrangements, a third estimated position of the isolated emitter is determined by means of a position estimator, and wherein the intensity distribution of the illumination light and / or the position estimator is adapted based on an aberration correction function.wherein a value of at least one parameter or at least one support point of the aberration correction function is or is determined using the first-aspect aberration correction method.

[0086] A method for localizing isolated emitters is understood to be a method in which the positions of isolated emitters are determined, in particular separately, and from which a localization map of sample structures can be created that resembles a high-resolution image of the sample, but in particular without optical imaging of the sample onto a detector and without conventional scanning in the sense of a raster scan of the sample (e.g. with confocal laser scanning microscopy).

[0087] In "tracking" (also called tracing), an emitter that can move within the sample is located multiple times in succession to obtain a trajectory of the emitter.

[0088] The method according to the fourth aspect of the invention is a MINFLUX method according to the definition used in this specification.

[0089] The illumination light is, in particular, excitation light that excites emitters in the sample to luminescence, especially fluorescence, or is reflected and / or scattered by emitters in the sample. Alternatively, the illumination light can also be, for example, suppression light (e.g., STED light) or switching light.

[0090] The illumination light is, in particular, the same illumination light used for the first-aspect aberration correction method. Specifically, the illumination light used in the first-aspect method has the same wavelength as the illumination light used in the fourth-aspect method. However, a different illumination light may be used for localization or tracking than for aberration correction.

[0091] The emitters localized or tracked using the fourth-aspect method can belong to the same species as the emitters used in the aberration correction method. However, this is not mandatory. For example, the aberration correction method can be used to scan nanoparticles labeled with a multitude of fluorophores, while the fourth-aspect method can be used to localize biological sample structures labeled with individual fluorophores. These fluorophores can belong to the same species or to a different species, and in the latter case, they can be excited by the same illumination.

[0092] The first-aspect aberration correction method and the fourth-aspect emitter localization or tracking method can be performed on the same sample. This has the advantage that the data for aberration correction and high-precision structural analysis can be collected at the same location within the sample. In this case, the aberration correction takes the spatial refractive index distribution of the sample area of ​​interest into account particularly well.

[0093] Alternatively, a separate sample, e.g., a calibration sample, can be used for the aberration correction procedure according to the first aspect. In this case, the value of at least one parameter or at least one support point of the aberration correction function can be stored in order to then apply the aberration correction function to measurements on other samples according to the procedure according to the fourth aspect.

[0094] If the sample and emitter species match in both the first and fourth aspect procedures, at least some of the acquired measurement data can advantageously be used twice – for determining the value of at least one parameter of the aberration correction function and for localizing sample structures to create a high-resolution localization map. In this case, the third estimated position determined in the fourth aspect procedure can coincide with the second estimated position determined in the first aspect procedure.

[0095] According to one embodiment, at least some of the light emissions used to determine the third estimated position are also used to determine the value of the at least one parameter or the at least one support point of the aberration correction function. Advantageously, the measurement data are used twice, which increases the efficiency of the method. In the case of an iterative method, it is not necessarily required that the light emissions from all iteration steps be used twice.

[0096] When a beam shaping device is controlled based on a specific aberration correction function, this function can be iteratively improved during the execution of the procedure according to the fourth aspect. The improved aberration correction, based on previous measurements, is applied to subsequent measurement steps, resulting in a further refined aberration correction function. In the case of adjusting a position estimator based on the aberration correction function, all localization data can even be corrected with the final aberration correction function during post-processing.

[0097] According to a further embodiment, the method for locating or tracking a single emitter comprises at least a first iteration step and a second iteration step, wherein in the second iteration step the third estimated position is determined with higher accuracy than in the first iteration step, and wherein the second iteration step is performed based on the third estimated position determined in the first iteration step, and wherein the light emissions detected in the first iteration step (in particular, only the light emissions detected in the first iteration step, but not the light emissions detected in the second iteration step) are also used to determine the value of the at least one parameter or the at least one support point of the aberration correction function. In particular, in the first iteration step a scanning pattern with a first maximum extent (e.g.,In the first iteration, a larger sample pattern (e.g., a circle with a first diameter) is used, and in the second iteration, a sample pattern with a second maximum extent (e.g., a circle with a second diameter) is used, where the second maximum extent is smaller than the first. For the fourth-aspect method, this has the advantage of achieving higher positional accuracy. However, for aberration correction according to the first aspect, the data from the first iteration with the larger sample pattern can be used, since the sample points cover a larger area, allowing for a better determination of at least one parameter value or at least one support point for the aberration correction function.

[0098] Due to the size of the point spread function of an emitter, it is advantageous to use only the early or middle iteration steps, where a maximum extent, in particular a diameter, of the sampling pattern corresponds to at least 250 nm or at least the distance between two maxima adjacent to the local minimum of the intensity distribution, for aberration correction, and to use the later iteration steps exclusively for localization or tracking.

[0099] According to a further embodiment, light emissions from first emitters are used to determine the value of the at least one parameter or the at least one support point of the aberration correction function, while light emissions from second emitters are used to determine the third estimated position of the second emitters. The first emitters can belong to a different species than the second emitters. Alternatively, the first and second emitters can also belong to the same species but, for example, be located in different regions of the sample. The use of first and second emitters has the advantage that, in principle, the first emitters can be exposed during scanning to determine the value of the at least one parameter or the at least one support point of the aberration correction function until they bleach or enter a dark state.Due to the larger number of light emissions, the parameter determination can be carried out more accurately.

[0100] If the first and second emitters belong to different species, they can be illuminated with light of different wavelengths according to a further embodiment. In this case, the light of the wavelength used in the aberration correction method has little or no effect on the second emitters (in particular, it does not excite them). This has the advantage that data acquisition for aberration correction can first be performed on the same sample without damaging the second emitters or rendering them dark. Subsequently, for example, a localization experiment with a high labeling density of the sample can be carried out using the aberration correction.It is advantageous if the illumination light of the wavelength used in the localization or tracking method does not affect (especially does not excite) the first emitters, thus preventing interference signals from affecting the localization of the second emitters. The first emitters can, in particular, exhibit higher photostability than the second emitters. For example, the first emitters could be nanoparticles labeled with fluorescent markers or reflective / light-scattering nanoparticles, while the second emitters could be fluorophores that can be coupled to sample structures of interest.

[0101] According to another embodiment, the first emitters are reversibly coupled to structures in the sample, and after the light emissions have been detected, the first emitters are exchanged for the second emitters to determine the value of the at least one parameter or the at least one support point of the aberration correction function. Methods known from the prior art, such as "Exchange-Paint," can be used for this reversible labeling. The first and second emitters can be of the same species or different.

[0102] In this way, data for aberration correction can be acquired at precisely the same locations where the sample structures to be localized are situated. The aberration correction function thus takes into account the local refractive index distribution of the sample with exceptional accuracy. Furthermore, parameter values ​​can be determined with a large number of light emissions and therefore with high precision. It is irrelevant if the emitters are damaged or enter a dark state, as they are subsequently replaced with new emitters, which can then be used to analyze the sample structures of interest using the aberration correction according to the invention.

[0103] According to another embodiment, the first and second emitters differ in their excitation mechanism (e.g., fluorescence and scattering / reflection), their excitation spectrum, their emission spectrum, and / or their emission lifetime. This also has the advantage that the emitters used for localizing the sample structures of interest are not damaged or switched to a dark state, since the data acquisition for aberration correction is performed with other emitters. Wavelength differences in the excitation and / or emission spectrum can be taken into account, if necessary, by appropriately adjusting the aberration correction function. Advantageously, this is not required when evaluating the emission lifetime, since the aberrations do not depend on the emission lifetime.

[0104] According to another embodiment, depending on the position (e.g., a position roughly estimated in a pre-localization) of the isolated emitter, at least one value of a parameter or at least one support point of the aberration correction function is selected from stored data sets. In this way, position-dependent aberration correction can be performed (see above).

[0105] A fifth aspect of the invention relates to a localization microscope for locating or tracking isolated emitters in a sample, in particular according to a method according to the fourth aspect.The localization microscope comprises an illumination optic designed to focus an illumination light, in particular an excitation light, into a sample and to generate an intensity distribution of the illumination light with a local minimum at the focus of the illumination light in the sample, a detector designed to detect, for different sampling positions of the intensity distribution or different shapes and / or arrangements of the intensity distribution, respective light emissions induced or modulated by the illumination light of a single emitter, and a computing unit designed to estimate a third estimated position of the single emitter based on the light emissions using a position estimator.The localization microscope further comprises a system for aberration correction according to the fourth aspect, wherein the computing unit of the system is designed to determine a value of at least one parameter or at least one support point of an aberration correction function on the basis of light emissions detected by the detector of the localization microscope during at least one sampling step.

[0106] The localization microscope may in particular be a MINFLUX microscope according to the definition used in this specification.

[0107] The illumination optics comprise, in particular, an illumination light source, especially a laser, and a lens configured to focus the illumination light into the sample. Additionally, the illumination optics comprise, in particular, a light modulator configured to spatially modulate the phase and / or amplitude of the illumination light, such that the illumination light focused by the lens into the sample exhibits the intensity distribution with the local minimum.

[0108] According to one embodiment, the localization microscope has at least one scanning device configured to shift the intensity distribution of the illumination light at scanning positions in the sample. This can be, for example, a fast scanning device based on electro-optic or acousto-optic deflectors. For axial shifting of the intensity distribution, the beam shaping device can be used, particularly if it is configured as a deformable mirror or a spatial light modulator. Alternatively, a separate axial scanning device can be used, such as a deformable mirror or a lens with variable focus. In addition to the fast scanning device, a further lateral scanning device, such as a [missing information], can be used.a galvanometer scanning device shall be provided which can be used in particular for coarse positioning of the illumination light and / or for pre-localization (determining the first estimated position), for example by pinhole orbit scanning or raster scanning.

[0109] Alternatively or additionally, the localization microscope can have a switching device for changing the shape and / or orientation of the intensity distribution, e.g. using a biaxial crystal.

[0110] According to another embodiment, the localization microscope has a control unit and a beam shaping device coupled to the control unit, in particular a deformable mirror or a spatial light modulator, wherein the control unit is configured to control the beam shaping device in such a way that a shape of the intensity distribution of the illumination light is adapted based on the aberration correction function.

[0111] According to another embodiment, the computing unit or another computing unit of the localization microscope is configured to adapt the position estimator based on the aberration correction function.

[0112] A sixth aspect of the invention relates to a computer program comprising commands that cause the localization microscope according to the fifth aspect to perform the method for localizing or tracking emitters in a sample according to the fourth aspect.

[0113] Further embodiments of the method according to the fourth aspect result from the above description of the method according to the first aspect. Further embodiments of the localization microscope according to the fifth aspect and of the computer program according to the sixth aspect result from the above description of the method according to the fourth aspect.

[0114] Advantageous developments of the invention will become apparent from the patent claims, the description, the drawings, and the accompanying explanations of the drawings. The described advantages of features and / or combinations of features of the invention are merely exemplary and may be effective alternatively or cumulatively.

[0115] Regarding the disclosure content (but not the scope of protection) of the original application documents and the patent, the following applies: Further features can be seen in the drawings – in particular the depicted relative arrangements and functional connections. The combination of features from different embodiments of the invention or from features of different claims is also possible, deviating from the chosen cross-references in the claims, and is hereby encouraged. This also applies to features that are illustrated in separate drawings or mentioned in their description. These features can also be combined with features from different claims. Likewise, features listed in the claims can be omitted for further embodiments of the invention, but this does not apply to the independent claims of the granted patent.

[0116] The reference signs contained in the patent claims do not represent a limitation of the scope of the subject-matter protected by the patent claims. They serve solely to make the patent claims easier to understand.

[0117] Exemplary embodiments of the invention are described below with reference to figures. These do not limit the subject matter of this disclosure or the scope of protection. Short description of the characters Fig. Figure 1 shows a schematic representation of an embodiment of a scanning pattern according to the invention; Fig. Figure 2 shows a schematic representation of an embodiment of the aberration correction method according to the invention; Fig. Figure 3 shows an embodiment of the localization microscope according to the invention with an aberration correction system according to the invention. Description of the characters

[0118] Fig. Figure 1 schematically shows a scanning pattern 6 consisting of scanning positions 5, at which a sample 2 is scanned in a focal plane with an intensity distribution 3 of an illumination light B.

[0119] The intensity distribution 3 is schematically represented as a cross-section in the focal plane and exhibits a central minimum 4 (ideally a zero point in intensity) and an annular maximum (not shown) at a geometric focus F of the illumination beam. The intensity distribution 3 can, for example, be a so-called donut beam or a so-called bottle beam. These intensity distributions are known from the prior art of STED and MINFLUX microscopy.

[0120] The minimum 4 of the intensity distribution 3 is arranged successively at six symmetrically positioned sampling positions 5 on a circle, according to the embodiment, which form a sampling pattern 6 around a first estimated position P1 of a single emitter E.

[0121] The first estimated position P1, whose accuracy may be far lower than the accuracy of the final position of the emitter E to be determined, can be determined in advance, for example, using an independent method such as confocal scanning of sample 2 with a regular Gaussian focus, wide-field microscopy, or pinhole orbit scanning. This can be done, for example, as part of a so-called prelocalization.

[0122] In a MINFLUX method for localizing a single emitter E, in particular, light emissions L of the emitter E can be detected for each sampling position 5, whereby the position of the emitter E can be estimated using a position estimator with the known coordinates of the sampling positions 5 and the respective light emissions L detected at these positions (e.g. photon numbers).

[0123] Such a procedure can be carried out iteratively, wherein in each iteration step the scanning pattern 6 is arranged around a position determined in the previous iteration. The scanning pattern 6 can be successively reduced in size to increase the positional accuracy; for example, the diameter of the circle on which the scanning positions 5 lie can be reduced, and in particular, the light intensity of the illumination B can also be increased.

[0124] In particular, aberrations of the illumination light B can occur due to misalignments in the illumination beam path and differences between the refractive index of the sample and the immersion medium, which can lead, for example, to a non-zero intensity at the local minimum 4 of the intensity distribution 3 and / or to a distortion of the intensity distribution 3.

[0125] To correct aberrations, a beam shaping device 7, such as a deformable mirror 8 or a spatial light modulator 9, can be controlled using an aberration correction function, e.g. using the Zernike polynomials, to shape the wavefront to produce an aberration-corrected intensity distribution 3.

[0126] Parameter values ​​or support points of an aberration correction function (such as the coefficients of the Zernike polynomials) can be determined in various ways according to the state of the art. For example, the wavefront of the illumination light could be measured directly using a Shack-Hartmann sensor. However, this solution would require additional components and installation space and has the disadvantage that effects of the refractive index in the sample are difficult to determine.

[0127] An alternative known from classical light microscopy is sensorless aberration correction based on an image metric (e.g., based on image brightness, resolution, and / or sharpness). However, since localization microscopy according to the MINFLUX principle does not involve actual image acquisition but rather the localization of individual emitters, there is no generally applicable measure of image quality.

[0128] Therefore, according to the invention, the value of at least one parameter or at least one support point of an aberration correction function for the illumination light B (which may be altered by aberrations) is determined by scanning the sample 2 with the intensity distribution 3 with the local minimum 4 and detecting light emissions.

[0129] Such a determination is similar to confocal scanning of a point center with a regular focus, with the difference that the point spread function here is not a Gaussian distribution, but reflects the intensity distribution of the illumination light B and therefore has a central local minimum.

[0130] Accordingly, parameter values ​​or support points of an aberration correction function, which describes a deviation of the shape of the intensity distribution 3 from a desired intensity distribution (in particular a symmetrical distribution with a central zero) or a deviation of a phase distribution of the illumination light B from a desired phase distribution, can be determined, e.g., by a function fit to the light emissions obtained for the different sampling positions 5.

[0131] For example, the light intensities L measured for the different sampling positions 5 in the inventive method can be fitted to the desired intensity distribution 3 of the illumination light B in the sample 2. This functional fit can be performed, for example, successively with intensity distributions 3 containing different aberration terms, whereby the coefficients of the aberration terms are adjusted until the deviation between the measured light emissions and the respective function is minimal. Then the intensity distribution 3 with the smallest deviation can be selected. Based on this intensity distribution 3, the parameter values ​​of the aberration correction function can be determined.

[0132] Subsequently, the beam shaping device 7 can be controlled based on the aberration correction function to adjust the wavefront of the illumination light and compensate for the aberrations. Alternatively, or additionally, the position estimator for a MINFLUX method can be adjusted based on the aberration correction function to correct localization errors caused by the aberrations.

[0133] The sampling pattern 6 has a suitable extent for determining the parameter values ​​or support points of the aberration correction function, such that the sampling positions cover the emitter's point spread function well enough to determine parameter values ​​or support points. The sampling pattern 6 can, in particular, have a diameter that corresponds approximately to the distance between the opposite maxima of the intensity distribution 3, in this case, the diameter of the annular maximum. This diameter can, for example, be in the range between 250 nm and 450 nm, and especially between 300 nm and 400 nm.

[0134] In principle, if the emitter position is known, it is possible to determine the intensity distribution 3 of the illumination light B by evaluating the data from the six in Fig. To determine the total number of light emissions detected at the 5 scan positions shown (from one or more emitters), provided the scan pattern 6 is of sufficient size to sample enough positions. The known emitter position can be determined, for example, by an independent method or by high-precision MINFLUX localization.

[0135] In the method described above, the six sampling positions would be 5 of the in Fig. However, the sampling pattern shown in Figure 1 is not sufficient to determine more complex aberration correction functions. For example, when using Zernike polynomials to correct various aberrations, it may be necessary to determine far more than six independent parameters, for which a system of equations with six sampling positions would be underdetermined.

[0136] As in Fig. As shown schematically in Figure 2, according to one embodiment of the method according to the invention, the positional uncertainty of determining the first estimated position (prelocalization) can be used to obtain light emissions at a plurality of displaced sampling positions 5' from the scanning of several emitters E with the illumination light B, with which the parameter values ​​of even complex aberration correction functions can be determined.

[0137] Fig. Figure 2 schematically illustrates the scanning of three different emitters E with the intensity distribution of the illumination light B. The coordinate system was normalized or transformed to the highly accurate second estimated position P2, which closely approximates the actual emitter position. This was achieved by shifting the scanning positions 5 assigned to each emitter E using a difference vector V between the respective first estimated position P1 and the respective second estimated position P2, in order to obtain shifted scanning positions 5'. Thus, for all three emitters E, the second estimated position P2 is located at the origin in this representation.

[0138] However, due to their positional uncertainty, the first estimated positions P1, which are estimated with lower accuracy in the pre-localization, deviate randomly from the second estimated position P2.

[0139] The sampling pattern 6 was centered on the first estimated positions P1 during sampling with intensity distribution 3, i.e., the first estimated position P1 is the center of the circle on which the sampling positions 5 lie.

[0140] Therefore, eighteen different shifted sampling positions 5' are obtained relative to the second estimated position P2 (here the origin), each of which occupies the minimum of the intensity distribution relative to the respective sampled emitter E. With a sufficient number of detected photons for each shifted sampling position 5', 18 independent measurements are obtained in this way, with which the parameter values ​​or support points of the aberration correction function can be determined.

[0141] The second estimated position P2 can be identical to a third estimated position P3, which was determined using a MINFLUX method and can be used, for example, for high-resolution imaging of sample structures.

[0142] Fig. Figure 3 shows an embodiment of a localization microscope 1 according to the invention, namely a MINFLUX microscope, with a system 10 according to the invention (comprising a computing unit 11, a control unit 13 and a beam shaping device 7) for aberration correction.

[0143] The localization microscope 1 has a light source 16, in particular a laser, for generating the illumination light B, which is in particular excitation light that excites emitter E in the sample 2 to luminescence, in particular fluorescence, or is reflected or scattered by emitters E in the sample 2.

[0144] The illumination light B passes through a first scanning device 15a, e.g. having at least one electro-optic or acousto-optic deflector, wherein the first scanning device 15a is configured to shift the focus F of the illumination light B focused by the objective 20 in the sample 2 laterally, i.e. perpendicular to an optical axis O of the objective 20.

[0145] In the beam path behind the first scanning device 15a, a spatial light modulator 9 is arranged, which can be used, for example, to phase-modulate the illumination light B with a phase pattern such that the illumination light B, focused by the objective 20, forms an intensity distribution 3 with a local minimum 4 (e.g., a donut or a bottle beam) at the focus F in the sample 2. For this purpose, the illumination light B can be modulated, for example, with a vortex phase pattern (creating a donut) or a ring-shaped phase pattern (creating a bottle beam).

[0146] In addition, the spatial light modulator 9 alone or in combination with the deformable mirror 8 can also be used as a beam shaping device 7 to correct certain aberrations according to the invention, controlled by the control unit 13, i.e. to shape the wavefront of the illumination light B in such a way that these aberrations are corrected.

[0147] The potentially deflected and modulated illumination light B passes through a beam splitter 18 and then through a second scanning device 15b, e.g., a galvanometric scanning device. For the sake of clarity, only one controllable scan mirror 19 of the second scanning device 15b is shown, although the second scanning device 15b has, in particular, at least two such scan mirrors 19 that deflect the illumination light B, especially laterally, in two orthogonal directions.

[0148] The second scanning device 15b can be used, in particular, for the slower coarse positioning of the illumination light B in the sample 2, while the first scanning device 15a is used for the rapid repositioning of the illumination light B to the scanning positions 5 during the scanning of the sample 2. Furthermore, the second scanning device 15b, especially in combination with the first scanning device 15a, can also be used for repositioning the illumination light B during prelocalization, e.g., by pinhole orbit scanning.

[0149] A deformable mirror 8 is arranged in the beam path between the second scanning device 15b and the lens 20. The illumination light B is thrown onto the deformable mirror 8 by a deflecting mirror 21, and the light reflected by the deformable mirror 8 is then directed to the lens 20 by another deflecting mirror 21.

[0150] The deformable mirror 8 can be used on the one hand as a beam shaping device 7 according to the invention, in that the control unit 13 controls the deformable mirror 8 in such a way that it corrects the aberrations of the illumination light B with the aberration correction function.

[0151] On the other hand, the deformable mirror 8 can also be used to focus the intensity distribution 3 in the sample 2, i.e., to axially shift the focus along the optical axis O of the objective 20, e.g., to implement a three-dimensional MINFLUX localization method.

[0152] The lens 20 focuses the illumination light B into the sample 2, so that the intensity distribution 3 with the local minimum 4 is formed in the sample 2.

[0153] The light emissions L emitted by emitters E in sample 2 are focused by the objective 20 and pass via the deformable mirror 8 and the second scanning device 15b to the beam splitter 18, in particular a dichroic beam splitter, which reflects the emission light into a detection beam path. In the detection beam path is an optional pinhole 17 (possibly with additional lens optics for focusing on the pinhole 17, not shown here) and a detector 12, e.g., an avalanche photodiode, a hybrid detector, or an array of individual detectors, for detecting the light emissions L.

[0154] The detector 12 is connected to a computing unit 11, which is designed to estimate the position of an emitter E in the sample 2 on the basis of the light emissions L recorded for different sampling positions 5 using a position estimator, e.g. a maximum likelihood estimator or a least mean square estimator.

[0155] The detector 12 is still connected to a control unit 13 (directly or as shown in Fig. 3 represented via the computing unit 11), which controls the first scanning device 15a, the second scanning device 15b, the deformable mirror 8 and the spatial light modulator 9.

[0156] In the execution of the method according to the invention, the computing unit 11 determines parameter values ​​or support points of an aberration correction function from light emissions L detected by the detector 12 for different sampling positions 5, in particular from several emitters E in the sample 2 (see Fig. 2 and associated description) and, based on the specified parameter values ​​or support points, controls the deformable mirror 8, the spatial light modulator 9 or both in combination to adjust the wavefront of the illumination light B so that the aberrations are corrected for the subsequent acquisition of localization data.

[0157] Additionally, the position estimator can be adjusted using the computation unit 11 based on the aberration correction function. Reference symbol list 1 Localization microscope 2 Sample 3,3a-3f intensity distribution 4.4a-4f Minimum 5 scanning positions 5' Shifted scanning position 6 scanning patterns 7 Beam shaping device 8. Deformable Mirror 9 Spatial Light Modulator 10 Aberration correction system 11 Computing unit 12 Detector 13 Control unit 14 Lighting optics 15a First scanning device 15b Second scanning device 16 light sources 17 pinhole aperture 18 beam splitters 19 scan mirrors 20 lenses 21 deflecting mirrors B Illumination light E Emitter L Light emissions Optical axis P1 First estimated position P2 Second estimated position P3 Third estimated position V Difference vector

Claims

[1] Method for aberration correction of an illuminating light (B) for a localization microscope (1), wherein the illuminating light (B) is focused into a sample (2), wherein an intensity distribution (3) of the illuminating light (B) with at least one local minimum (4) is generated at the focus (F) of the illuminating light (B) in the sample (2), and wherein the sample (2) is scanned in at least one scanning step with the intensity distribution (3) at scanning positions (5) which form a scanning pattern (6) around a first estimated position (P1) of an isolated emitter (E) in the sample (2), and wherein light emissions (L) of the isolated emitter (E) are respectively detected for the scanning positions (5), characterized bythat a value of at least one parameter or at least one support point of an aberration correction function is determined on the basis of the light emissions (L) detected for the different scanning positions (5), wherein the aberration correction function describes a deviation of a shape of the intensity distribution (3) of the illuminating light (B) from a desired shape of the intensity distribution (3) or a deviation of a phase distribution of the illuminating light (B) from a desired phase distribution. [2] Method according to claim 1, characterized by that the value of the at least one parameter or the at least one support point of the aberration correction function is determined by a function fit of the light emissions (L) detected for the different scanning positions (5) to the desired intensity distribution (3) of the illumination light (B) in the sample (2). [3] Method according to claim 1, characterized bythat the value of the at least one parameter or the at least one support point of the aberration correction function is determined by means of a trained data processing network, in particular an artificial neural network. [4] Method according to one of claims 1 to 3, characterized by that a beam shaping device (7) is controlled such that a shape of the intensity distribution (3) of the illumination light (B) is adapted on the basis of the aberration correction function. [5] Method according to claim 4, characterized by that the beam-shaping device (7) comprises a deformable mirror (8) and / or a spatial light modulator (9). [6] Method according to one of the preceding claims, characterized bythat on the basis of the aberration correction function, a position estimator for estimating a position of an isolated emitter (E) in a sample (2) is adapted, in particular wherein an expression of the position estimator describing a form of the intensity distribution (3) is adapted on the basis of the aberration correction function. [7] Method according to one of the preceding claims, characterized by that the scanning step is carried out successively on different isolated emitters (E), wherein the value of the at least one parameter or the at least one support point of the aberration correction function is determined on the basis of the light emissions (L) of the different isolated emitters (E). [8] Method according to one of the preceding claims, characterized bythat a second estimated position (P2) of the isolated emitter is determined with an accuracy that is increased compared to the first estimated position (P1), wherein on the basis of the second estimated position (P2) the sampling positions (5) used in the at least one sampling step are shifted by a respective difference vector (V) between the respective first estimated position (P1) and the respective second estimated position (P2), and wherein the value of the at least one parameter or the at least one support point of the aberration correction function is determined on the basis of the light emissions (L) detected for the shifted sampling positions (5'). [9] Method according to claim 8, characterized by that the second estimated position (P2) is determined using a MINFLUX method. [10] Method according to one of the preceding claims, characterized bythat the sampling positions (5) are arranged around a position randomly shifted from the first estimated position (P1). [11] Method according to one of the preceding claims, characterized by that the scanning pattern (6) is a continuous path around the first estimated position (P1), in particular wherein a corresponding scanning position (5) is determined upon detection of the light emissions (L). [12] Method according to one of the preceding claims, characterized by that the scanning step is carried out with different scanning patterns (6), in particular scanning patterns (6) of different sizes. [13] Method according to one of the preceding claims, characterized by that the illumination light (B) is excitation light which excites emitters (E) in the sample (2) to luminescence, in particular fluorescence, or which is scattered or reflected by emitters (E) in the sample (2). [14] Method according to one of the preceding claims, characterized by that the scanning pattern (6) has scanning positions (5) with different coordinates along or parallel to an optical axis (O) of an objective (20) with which the sample (2) is illuminated with the illumination light (B). [15] Method according to claim 14, characterized by that the intensity distribution (3) of the illuminating light (B) has intensity increase regions adjacent to the local minimum in all spatial directions, in particular wherein the intensity distribution (3) is a bottle beam. [16] Method according to one of the preceding claims, characterized bythat the value of the at least one parameter or the at least one support point of the aberration correction function is determined on the basis of light emissions (L) of different emitters (E), wherein data records are stored in which the value of the at least one parameter or the at least one support point is assigned to a position in the sample (2), so that the data records represent a one-dimensional, two-dimensional or three-dimensional map of parameter values ​​or support points, in particular wherein the positions in the sample form a regular grid with spacings of at least 500 nm, in particular at least 1 µm. [17] Method according to one of the preceding claims, characterized by that the aberration correction function includes at least one Zernike polynomial. [18] Method according to one of the preceding claims, characterized bythat the scanning pattern (6) has a maximum extension of 250 nm or more, in particular 300 nm or more. [19] Method according to one of the preceding claims, characterized by that the intensity distribution (3) of the illuminating light (B) in a focal plane of the illuminating light (B) perpendicular to an optical axis (O) of an objective (20) with which the sample (2) is illuminated with the illuminating light (B) has at least two intensity maxima, wherein a maximum extension of the scanning pattern (6) is 75% to 125% of the distance between the intensity maxima in the focal plane. [20] System (10) for a localization microscope (1) arranged for aberration correction of an illuminating light (B) according to a method according to one of claims 1 to 19, characterized byin that the system (10) has a computing unit (11) which is designed to determine a value of at least one parameter or at least one support point of an aberration correction function on the basis of light emissions (L) detected by means of a detector (12) of the localization microscope (1) during the at least one scanning step, wherein the aberration correction function describes a deviation of a shape of the intensity distribution (3) of the illumination light (B) from a desired shape of the intensity distribution (3) or a deviation of a phase distribution of the illumination light (B) from a desired phase distribution. [21] System (10) according to claim 20, characterized bythat the system (10) has a control unit (13) which is designed to control a beam shaping device (7) of the localization microscope (1) such that a shape of the intensity distribution (3) of the illumination light (B) is adapted on the basis of the aberration correction function. [22] System (10) according to claim 20 or 21, characterized by that the computing unit (11) is designed to adapt a position estimator for estimating the position of an isolated emitter (E) in a sample (2) on the basis of the aberration correction function. [23] A computer program comprising instructions that cause the system (10) according to any one of claims 20 to 22 to carry out the method according to any one of claims 1 to 19. [24] Method for locating or tracking individual emitters (E) in a sample (2), wherein an illuminating light (B) is focused into a sample (2), wherein an intensity distribution (3) of the illuminating light (B) with a local minimum (4) is generated at the focus (F) of the illuminating light (B) in the sample (2), and wherein for different scanning positions (5) of the intensity distribution (3) or different shapes and / or arrangements of the intensity distribution (3), respective light emissions (L) of an individual emitter (E) are detected, and wherein on the basis of the light emissions (L) and the associated scanning positions (5) or shapes and / or arrangements, a third estimated position (P3) of the emitter (E) is determined by means of a position estimator, characterized bythat the intensity distribution (3) of the illumination light (B) and / or the position estimator is adapted on the basis of an aberration correction function, wherein a value of at least one parameter of or at least one support point of the aberration correction function is determined using the method for aberration correction according to one of claims 1 to 19. [25] Method according to claim 24, characterized by that at least a part of the light emissions (L) used to determine the third estimated position (P3) are also used to determine the value of the at least one parameter or the at least one support point of the aberration correction function. [26] Method according to claim 25, characterized byin that the method for locating or tracking an isolated emitter (E) comprises at least a first iteration step and a second iteration step, wherein in the second iteration step the third estimated position (P3) is determined with a higher accuracy than in the first iteration step, and wherein the second iteration step is carried out on the basis of the third estimated position (P3) determined in the first iteration step, and wherein the light emissions (L) detected in the first iteration step are also used to determine the value of the at least one parameter or the at least one support point of the aberration correction function. [27] Method according to one of claims 24 to 26, characterized bythat light emissions (L) of the first emitter are used to determine the value of the at least one parameter or the at least one support point of the aberration correction function, wherein light emissions (L) of the second emitter are used to determine the third estimated position (P3) of the second emitter. [28] Method according to claim 27, characterized by that the first emitters and the second emitters are illuminated with illuminating light (B) of different wavelengths. [29] Method according to claim 27 or 28, characterized by that the first emitters are reversibly coupled to structures in the sample (2), wherein the first emitters are exchanged for the second emitters after the detection of the light emissions (L) for the determination of the value of the at least one parameter or the at least one support point of the aberration correction function. [30] Method according to one of claims 27 to 29, characterized bythat the first emitters and the second emitters differ in the mechanism of excitation, in their excitation spectrum, their emission spectrum and / or their emission lifetime. [31] Localization microscope (1) for localizing or tracking isolated emitters (E) in a sample (2), in particular according to a method according to one of claims 24 to 30, comprising - an illumination optics (14) designed to focus an illumination light (B) into a sample (2) and to generate an intensity distribution (3) of the illumination light (B) with a local minimum (4) at the focus (F) of the illumination light (B) in the sample (2), - a detector (12) which is designed to detect respective light emissions (L) of an isolated emitter (E) for different scanning positions (5) of the intensity distribution (3) or different shapes and / or arrangements of the intensity distribution (3), and - a computing unit (11) designed to estimate a third estimated position (P3) of the isolated emitter (E) on the basis of the light emissions (L) by means of a position estimator, characterized by that the localization microscope (1) has a system (10) for aberration correction according to one of claims 20 to 22, wherein the computing unit (11) of the system (10) is designed to determine a value of at least one parameter or at least one support point of an aberration correction function on the basis of light emissions (L) detected by the detector (12) of the localization microscope (1) during the at least one scanning step. [32] Localization microscope (1) according to claim 31, characterized by that the localization microscope (1) has at least one scanning device (15a, 15b) which is designed to shift the intensity distribution (3) of the illumination light (B) at scanning positions (5) in the sample (2). [33] Localization microscope (1) according to claim 31 or 32, characterized by in that the localization microscope (1) has a control unit (13) and a beam-shaping device (7) coupled to the control unit (13), in particular a deformable mirror (8) and / or a spatial light modulator (9), wherein the control unit (13) is designed to control the beam-shaping device (7) such that a shape of the intensity distribution (3) of the illumination light (B) is adapted on the basis of the aberration correction function. [34] Localization microscope (1) according to one of claims 31 to 33, characterized by that the computing unit (11) or a further computing unit of the localization microscope (1) is designed to adapt the position estimator on the basis of the aberration correction function. [35] Computer program comprising instructions which cause the localization microscope (1) according to one of claims 31 to 34 to carry out the method for localizing or tracking emitters (E) in a sample (2) according to one of claims 24 to 30.

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