METHOD, COMPUTER PROGRAM AND DEVICE FOR ESTIMATE THE POSITION OF AN EMERT OR REFLECTOR IN A SAMPLE

Description

[0001] The present invention relates to a method, a computer program with instructions, and a device for estimating the position of an emitter or reflector in a sample. The present invention also relates to a microscope that uses a method or device according to the invention.

[0002] EP 0 485 803 A1 describes a device for three-dimensional examination using a confocal beam path. An illumination grid is projected into a focal plane located on or near the surface of the object. The radiation reflected in the focal plane is projected directly onto the receiving surface of a CCD detector via a beam splitter. The device can be used, among other things, for fluorescence measurements.

[0003] Fluorescence microscopy has experienced a significant boost in achievable resolution through the synergistic combination of the specific strengths of coordinate-targeted and coordinate-stochastic microscopy techniques, particularly single-molecule-based super-resolution microscopy and nanoscopy techniques. Coordinate-oriented super-resolution microscopy techniques [1] include STED (STimulated Emission Depletion) [2] and RESOLFT (REversible Saturable OpticaL Fluorescence Transitions) [3]. Coordinate-stochastic super-resolution microscopy techniques include PALM (PhotoActivated Localization Microscopy) / STORM (STochastic Optical Reconstruction Microscopy) [4] and PAINT (Point Accumulation for Imaging in Nanoscale Topography) [5].The resulting nanoscopy technique, called MINFLUX (MINimal photon FLUXes) [6], has closed the existing resolution gap of -20-30 nm in STED, PALM / STORM and other fluorescence nanoscopy techniques to the size of the molecules themselves in the range of 1-5 nm.

[0004] At its core, MINFLUX localization is based on the idea of ​​injecting a reference coordinate into the sample using a structured optical beam, e.g., a donut with a central intensity minimum, i.e., a zero. The position of the zero in the sample defines the targeted sample coordinate. The MINFLUX concept applies equally to entire sets of reference coordinates, i.e., line- and point-like zeros, as well as to parallelized detection in the wide-field. Targeting coordinates enables controlled and thus photon-efficient localization of fluorescent molecules, because the fluorophore coordinate to be determined is no longer determined by determining the center of a weak, diffraction-limited fluorescence spot captured by a camera. Instead, the fluorophore is localized by actively aligning the zero of the excitation light onto the fluorophore.Specifically, the zero point of the excitation light is moved as close as possible to the molecule in several iterations until the detected fluorescence rate approximately equals that of the background noise. At this closest proximity, only a minimal number of fluorescence photons is needed to achieve maximum localization precision, since determining the remaining distance between the coordinate targeted by the zero point and the molecule position requires far fewer detected photons. Thus, "injecting" or targeting a reference coordinate shifts the requirement of many fluorescence photons for localization to the virtually unlimited number of photons in the excitation light.

[0005] Since MINFLUX localization is no longer limited by the requirement of a large number of fluorescence photons, this nanometer-precise localization is much faster than the camera-based localization used in PALM / STORM. The idea of ​​optically injecting a coordinate using a zero is also fundamentally present in the original STED concept. In STED microscopy, in the absence of background noise, a single detected photon is sufficient to demonstrate the presence of a fluorophore at the coordinate targeted by the zero. Here, too, the emitting fluorophore is precisely localized by the photons injected by the STED light.

[0006] One possible approach for MINFLUX localization uses iterative localization. In this approach, the position of an emitter in a sample is inferred from the photon counts measured at a series of positions by applying a stochastic estimator to the data. To obtain an unbiased result, i.e., one without systematic error, a measurement scheme is used that provides near-unadvertent localization in real time.

[0007] For a target coordinate pattern with m Beam positions b i ( i = 0 ... m - 1) and associated photon counts p i can the position u For example, it can be estimated using an uncalibrated symmetric estimator as follows: u → x → b → i = u → p i x → , b → i = ∑ i = 0 m − 1 p i ⋅ b → i ∑ i = 0 m − 1 p i .

[0008] Further information on this estimator can be found, for example, in [6].

[0009] A simulation is used to determine the systematic deviation between the actual position of a fluorophore and the position determined by the estimator. The estimator is calibrated using this deviation. This means that, in a MINFLUX measurement, the raw estimate is corrected for the deviation, resulting in an estimate that is free of bias.

[0010] This works when each uncalibrated estimate corresponds to exactly one actual fluorophore position. This condition is met when there is certainty that a fluorophore is actually located within a specific region of the target coordinate pattern. If a fluorophore is located further outside, the estimate may again be identical to an estimate obtained for the inner region. Therefore, if the actual position of the fluorophore is known with insufficient certainty before the measurement, no unambiguous estimate of the fluorophore's position can be obtained from the subsequent measurement.

[0011] In other words, the position estimate of the estimator given above is also under perfect conditions, ie infinitely many photons, no background noise, non-injective with respect to x → u. It is only injective for | x | ≤ xlim . To avoid ambiguities, measures must be taken to ensure that the emitters to be located are always at radial distances of less than x lim from the center of the target coordinate pattern.

[0012] Using the MINFLUX approach, not only emitters but also reflecting particles can be located. This is particularly useful for detecting any drift. The above-mentioned problem also arises when locating such reflectors.

[0013] It is an object of the invention to provide improved solutions for estimating a position of an emitter or reflector in a sample.

[0014] The invention is set forth in the independent claims. Preferred embodiments of the invention are the subject of the dependent claims.

[0015] According to a first aspect of the invention, a method for estimating a position of an emitter or reflector in a sample comprises the steps of: Illuminating the sample with excitation light at at least one set of target coordinates; detecting fluorescence photons or reflected photons for each of the set of target coordinates; and estimating a position of an emitter or reflector from the detected fluorescence photons or reflected photons; wherein estimating the position of the emitter or reflector comprises comparing vector sums determined for subsets of the set of target coordinates and / or sums over vectors of the detected fluorescence photons or reflected photons, and / or wherein the excitation light has an intensity distribution comprising a central minimum and three or more local maxima arranged around the central minimum, the angular positions of the three or more local maxima changing along the optical axis.

[0016] According to a further aspect of the invention, a method for estimating a position of an emitter or reflector in a sample comprises the steps of: Illuminating the sample with excitation light at at least one set of target coordinates, wherein the excitation light has a donut-shaped intensity distribution; detecting fluorescence photons or reflected photons for the individual target coordinates of the set of target coordinates; determining an uncalibrated first estimated position of an emitter or reflector from the fluorescence photons or reflected photons detected for a first subset of the set of target coordinates; determining an uncalibrated second estimated position of the emitter or reflector from the fluorescence photons or reflected photons detected for a second subset of the set of target coordinates; and estimating a position of the emitter or reflector by comparing the first estimated position and the second estimated position, wherein the position estimated by comparing the first estimated position and the second estimated position is calibrated.

[0017] According to a further aspect of the invention, a method for estimating a position of an emitter or reflector in a sample comprises the steps of: Illuminating the sample with excitation light at at least one set of target coordinates; detecting fluorescence photons or reflected photons for each of the set of target coordinates; and estimating a position of an emitter or reflector from the detected fluorescence photons or reflected photons; wherein the excitation light has an intensity distribution comprising a central minimum and three or more local maxima arranged around the central minimum, wherein the angular positions of the three or more local maxima vary along the optical axis. Preferably, estimating the position of the emitter or reflector comprises comparing estimated positions for the emitter or reflector determined from fluorescence photons or reflected photons detected for subsets of the set of target coordinates.

[0018] According to a further aspect of the invention, a computer program includes instructions which, when executed by a computer, cause the computer to perform the following steps for estimating a position of an emitter or reflector in a sample: Illuminating the sample with excitation light at at least one set of target coordinates; detecting fluorescence photons or reflected photons for each of the set of target coordinates; and estimating a position of an emitter or reflector from the detected fluorescence photons or reflected photons; wherein estimating the position of the emitter or reflector comprises comparing vector sums determined for subsets of the set of target coordinates and / or sums over vectors of the detected fluorescence photons or reflected photons, and / or wherein the excitation light has an intensity distribution comprising a central minimum and three or more local maxima arranged around the central minimum, the angular positions of the three or more local maxima changing along the optical axis.

[0019] According to a further aspect of the invention, a computer program includes instructions which, when executed by a computer, cause the computer to perform the following steps for estimating a position of an emitter or reflector in a sample: Illuminating the sample with excitation light at at least one set of target coordinates, wherein the excitation light has a donut-shaped intensity distribution; detecting fluorescence photons or reflected photons for the individual target coordinates of the set of target coordinates; determining an uncalibrated first estimated position of an emitter or reflector from the fluorescence photons or reflected photons detected for a first subset of the set of target coordinates; determining an uncalibrated second estimated position of the emitter or reflector from the fluorescence photons or reflected photons detected for a second subset of the set of target coordinates; and estimating a position of the emitter or reflector by comparing the first estimated position and the second estimated position, wherein the position estimated by comparing the first estimated position and the second estimated position is calibrated.

[0020] According to a further aspect of the invention, a computer program includes instructions which, when executed by a computer, cause the computer to perform the following steps for estimating a position of an emitter or reflector in a sample: Illuminating the sample with excitation light at at least one set of target coordinates; detecting fluorescence photons or reflected photons for each of the set of target coordinates; and estimating a position of an emitter or reflector from the detected fluorescence photons or reflected photons; wherein the excitation light has an intensity distribution comprising a central minimum and three or more local maxima arranged around the central minimum, wherein the angular positions of the three or more local maxima vary along the optical axis. Preferably, estimating the position of the emitter or reflector comprises comparing estimated positions for the emitter or reflector determined from fluorescence photons or reflected photons detected for subsets of the set of target coordinates.

[0021] The term "computer" should be understood broadly. In particular, it also includes microcontrollers, embedded systems, and other processor-based data processing devices. The execution of these steps can be performed directly by the computer or involve the computer controlling a component intended to execute a step, such as a light source or a detector.

[0022] The computer program may, for example, be made available for electronic retrieval or stored on a computer-readable storage medium.

[0023] According to another aspect of the invention, an apparatus for estimating a position of an emitter or reflector in a sample comprises: Illumination means for illuminating the sample with excitation light at at least one set of target coordinates; detection means for detecting fluorescence photons or reflected photons for the individual target coordinates of the set of target coordinates; and an estimator for estimating a position of an emitter or reflector from the detected fluorescence photons or reflected photons; wherein the estimation device is configured to compare vector sums determined for subsets of the set of target coordinates and / or sums over vectors of the detected fluorescence photons in order to estimate the position of the emitter or reflector, and / or wherein the excitation light has an intensity distribution having a central minimum and three or more local maxima arranged around the central minimum, the angular positions of the three or more local maxima changing along the optical axis.

[0024] According to another aspect of the invention, an apparatus for estimating a position of an emitter or reflector in a sample comprises: Illumination means for illuminating the sample with excitation light at at least one set of target coordinates, the excitation light having a donut-shaped intensity distribution; detection means for detecting fluorescence photons or reflected photons for the individual target coordinates of the set of target coordinates; and an estimator for estimating a position of an emitter or reflector from the detected fluorescence photons or reflected photons. wherein the estimation device is configured to determine an uncalibrated first estimated position of the emitter or reflector from the fluorescence photons or reflected photons detected for a first subset of the set of target coordinates, to determine an uncalibrated second estimated position of the emitter or reflector from the fluorescence photons or reflected photons detected for a second subset of the set of target coordinates, and to estimate the position of the emitter or reflector by comparing the first estimated position and the second estimated position, wherein the position estimated by comparing the first estimated position and the second estimated position is calibrated.

[0025] According to another aspect of the invention, an apparatus for estimating a position of an emitter or reflector in a sample comprises: Illumination means for illuminating the sample with excitation light at at least one set of target coordinates, wherein the excitation light has an intensity distribution that includes a central minimum and three or more local maxima arranged around the central minimum, wherein the angular positions of the three or more local maxima vary along the optical axis; detection means for detecting fluorescence photons or reflected photons for the individual target coordinates of the set of target coordinates; and an estimator for estimating a position of an emitter or reflector from the detected fluorescence photons or reflected photons. Preferably, the estimator is configured to compare estimated positions for the emitter or reflector, which are determined from fluorescence photons or reflected photons detected for subsets of the set of target coordinates, to estimate the position of the emitter or reflector.

[0026] In the solution according to the invention, the size of the usable range within which the estimator implemented in the estimator is unambiguously assigned to an actual position can be increased by comparing vector sums or sums over vectors over subsets of the set of target coordinates. Additionally or alternatively, the use of a specific intensity distribution creates the possibility of determining depth information for the emitter or reflector as an additional parameter without having to shift the focal plane relative to the sample. Both allow for faster localization of the emitter or reflector. Preferably, the vector sums are weighted vector sums. It is assumed that the vector sums are each composed of positive summands. "Positive" here means that no summand is assigned a negative weight. Equivalently, all weights could, of course, be negative.The direction vectors themselves can have either a negative or positive sign.

[0027] If the implemented estimator based on subsets of the set of target coordinates is used together with a donut-shaped intensity distribution, one advantage of this estimator is that the capture range, i.e., the range in which a unique, calibratable or calibrated position estimate is obtained, is larger. At the same time, however, a conventional estimator based on a vector sum over the entire set of target coordinates provides a more accurate estimate if the emitter or reflector is clearly located within the capture range of this estimator. If the estimator based on subsets of the set of target coordinates provides a position well within the capture range of the conventional estimator, it is therefore advantageous to improve the position estimate using the conventional estimator. Different estimators can thus be applied iteratively.

[0028] According to one aspect of the invention, a difference is determined or a ratio is formed for the comparison. Equivalent to forming a difference between two vector sums, a vector sum with summands with positive and summands with negative weights can also be formed. According to formula (1), for at least two subsets of the set of target coordinates, which at least partially comprise different target coordinates, the associated estimated values u 0 and u 1. The absolute difference d = | u 0 - u 1 | of these two functions also depends on x The value range for | x |, for which an injective function x → d ( x ) but extends over xlim. The value d can therefore be used directly as an estimate of the radial distance of the position of an emitter from the center of the set of target coordinates. However, it can also be used to decide on which side of x lim where the emitter or reflector is located. To reduce the required overhead, the position of the emitter or reflector can be calculated directly from the mean value of u 0 and u 1, which is usually a good approximation, instead of also u for the entire set of target coordinates. Instead of calculating the difference, a ratio of the estimated values ​​can also be calculated u 0 and u 1 to expand the usable area.

[0029] According to one aspect of the invention, the set of target coordinates comprises four or more target coordinates, and the subsets of the set of target coordinates each comprise three or more target coordinates. At least three target coordinates are required to estimate a position. To form two non-identical subsets from the set of target coordinates, the set of target coordinates must therefore comprise at least four target coordinates. Increasing the number of target coordinates increases the isotropy of the localization accuracy.

[0030] According to one aspect of the invention, the subsets of the set of target coordinates are disjoint. Thus, the subsets have information content independent of each other.

[0031] According to one aspect of the invention, the set of target coordinates comprises six target coordinates arranged in a hexagon. In this case, the subsets of the set of target coordinates preferably each comprise three target coordinates arranged in an equilateral triangle. By using six target coordinates arranged in a hexagon, very consistent localization accuracy is achieved regardless of the angular position of the emitter or reflector.

[0032] According to one aspect of the invention, depth information for the emitter or reflector is determined from the vector sums determined for the subsets of the set of target coordinates and / or sums over vectors of the detected fluorescence photons or reflected photons. In this way, in addition to localizing the emitter or reflector in a plane perpendicular to the optical axis, localization along the optical axis is also performed without requiring a focal plane to be displaced relative to the sample.

[0033] According to one aspect of the invention, a combined vortex and trefoil phase is impressed on the excitation light to generate the intensity distribution. This is preferably done using an adjustable spatial light modulator (SLM). The phase shift of the trefoil phase is, for example, between 10% and 200% of the phase shift of the vortex phase, preferably between 20% and 150%, more preferably between 30% and 120%, more preferably between 80% and 110%, preferably 100%. By combining a vortex phase and a trefoil phase, an intensity distribution can be easily generated that is particularly well suited for determining depth information for the emitter or reflector. The ratio of the phase shifts influences in particular the lateral position of the local maxima relative to the optical axis as well as the distance between the local maxima along the optical axis.The greater the phase shift of the trefoil phase, the further the local maxima shift outward. At the same time, their length increases. The use of an adjustable area light modulator has the advantage that the imposed phases can be adjusted as needed.

[0034] According to one aspect of the invention, the central minimum extends along the optical axis. This has the advantage that the depth information for the emitter or reflector can be reliably determined over a comparatively large depth range.

[0035] According to one aspect of the invention, the angular positions of the three or more local maxima along the optical axis change monotonically, preferably strictly monotonically, more preferably proportionally to the axial position. This simplifies the determination of the depth information for the emitter or reflector from the determined vector sums and / or sums over vectors of the detected fluorescence photons or reflected photons.

[0036] According to one aspect of the invention, the three or more local maxima are evenly distributed around the central minimum. Preferably, the angular positions of the three or more local maxima along the optical axis vary over a designated axial detection range [ z ; -z ] by an amount equal to 180° divided by the number of maxima. In the case of three local maxima, the angular position of each maximum thus changes from z until -zby 60°. If the number and position of the target coordinates of the target coordinate pattern are matched to the number and position of the local maxima, it is possible to apply an intensity to the emitter or reflector that is a function of the axial position of the emitter or reflector with a maximized range of values. It is particularly advantageous if the number of target coordinates is twice as large as the number of local maxima.

[0037] Preferably, a microscope uses a device or method according to the invention for estimating a position of an emitter or reflector in a sample.

[0038] Further features of the present invention will become apparent from the following description and the appended claims taken in conjunction with the figures. Fig. 1 schematically shows a method for estimating the position of an emitter or reflector in a sample; Fig. 2 shows a first embodiment of a device for estimating the position of an emitter or reflector in a sample; Fig. 3 shows a second embodiment of a device for estimating the position of an emitter or reflector in a sample; Fig. 4 shows a sample with a plurality of emitters or reflectors; Fig. 5 shows a basic structure of a MINFLUX microscope in which a solution according to the invention is implemented; Fig. 6 shows an example of a hexagonal target coordinate pattern; Fig. 7 shows example position estimates for a group of simulated emitters; Fig. 8 shows an intensity distribution of the excitation light in the x-y -plane for different axial positions; Fig. 9 shows the intensity distribution of the excitation light in the x-z -plane; Fig. 10 shows the intensity distribution of the excitation light in the y-z -plane; Fig. 11 shows the value of an uncalibrated estimator according to the invention depending on the position in a lateral plane for different axial positions; Figs. 12-14 show simulations of the behavior of an estimator according to the invention and an estimator according to the prior art for different axial positions and a diameter of the target coordinate pattern of L =486 nm; Fig. 15-17 show corresponding simulations for a diameter of the target coordinate pattern of L =288 nm; and Fig. 18-20 show simulations of the behavior of another estimator according to the invention and an estimator according to the prior art for different axial positions and a diameter of the target coordinate pattern of L =486 nm.

[0039] To better understand the principles of the present invention, embodiments of the invention are explained in more detail below with reference to the figures. It is understood that the invention is not limited to these embodiments and that the described features may also be combined or modified without departing from the scope of the invention as defined in the appended claims.

[0040] Fig. 1 shows a schematic of a method for estimating a position of an emitter or reflector in a sample. In the method, the sample is illuminated with excitation light at at least one set of target coordinates S1. Fluorescence photons or reflected photons are detected S2 for the individual target coordinates of the set of target coordinates. A position of an emitter or reflector is estimated S3 from the detected fluorescence photons or reflected photons. The estimation S3 of the position of the emitter or reflector comprises a comparison of vector sums determined for subsets of the set of target coordinates and / or sums over vectors of the detected fluorescence photons or reflected photons. For the comparison, for example, a difference can be determined or a ratio can be formed. The vector sums can in particular be weighted vector sums.Alternatively or additionally, the excitation light has an intensity distribution comprising a central minimum and three or more local maxima arranged around the central minimum, with the angular positions of the three or more local maxima varying along the optical axis. From the vector sums determined for the subsets of the set of target coordinates and / or sums over vectors of the detected fluorescence photons or reflected photons, depth information for the emitter or reflector can be determined in conjunction with such an intensity distribution. To generate the intensity distribution, a combined vortex and trefoil phase can be impressed on the excitation light, for example, using an adjustable area light modulator.

[0041] Fig. 2 shows a simplified schematic representation of a first embodiment of a device 40 for estimating a position of an emitter or reflector in a sample. The device 40 has an interface 41 for communication with external components. Illumination means 42 are configured to illuminate the sample with excitation light at at least one set of target coordinates. For this purpose, the illumination means 42 can control a light source 14 and an area light modulator 21 via the interface 41. Detection means 43 are configured to detect fluorescence photons or reflected photons for the individual target coordinates of the set of target coordinates. For this purpose, the detection means 43 can evaluate signals from photodiodes 31, 32 received via the interface 41. The photodiodes 31, 32 can be avalanche photodiodes, for example.An estimator 44 is configured to estimate a position of an emitter or reflector from the detected fluorescence photons or reflected photons. To do so, the estimator 44 compares vector sums determined for subsets of the set of target coordinates and / or sums over vectors of the detected fluorescence photons or reflected photons. For the comparison, the estimator 44 can, for example, determine a difference or form a ratio. The vector sums can, in particular, be weighted vector sums. Alternatively or additionally, the excitation light has an intensity distribution that includes a central minimum and three or more local maxima arranged around the central minimum, wherein the angular positions of the three or more local maxima vary along the optical axis.From the vector sums determined for the subsets of the set of target coordinates and / or sums over vectors of the detected fluorescence photons or reflected photons, the estimator 44 can determine depth information for the emitter or reflector in conjunction with such an intensity distribution. To generate the intensity distribution, a combined vortex and trefoil phase can be impressed on the excitation light, for example, using the area light modulator 21.

[0042] The illumination means 42, the detection means 43, and the estimation device 44 can be controlled by a control unit 45. Settings of the illumination means 42, the detection means 43, the estimation device 44, or the control unit 45 can be changed if necessary via a user interface 47. The data generated in the device 40 can be stored in a memory 46 of the device 40, for example, for later evaluation or for use by the components of the device 40. The illumination means 42, the detection means 43, the estimation device 44, and the control unit 45 can be implemented as dedicated hardware, for example, as integrated circuits. Of course, they can also be partially or completely combined or implemented as software running on a suitable processor, for example, a GPU or a CPU.The interface 41 can also be implemented in the form of separate inputs and outputs.

[0043] Fig. 3 shows a simplified schematic representation of a second embodiment of a device 50 for estimating the position of an emitter or reflector in a sample. The device 50 has a processor 52 and a memory 51. For example, the device 50 is a microcontroller, a computer, or an embedded system. Instructions are stored in the memory 51 which, when executed by the processor 52, cause the device 50 to carry out the steps according to one of the described methods. The instructions stored in the memory 51 thus embody a program executable by the processor 52 which implements the method according to the invention. The device 50 has an input 53 for receiving information. Data generated by the processor 52 are provided via an output 54. Furthermore, they can be stored in the memory 51.The input 53 and the output 54 can be combined to form a bidirectional interface.

[0044] The processor 52 may include one or more processor units, such as microprocessors, digital signal processors, or combinations thereof.

[0045] The memories 46, 51 of the described embodiments can have both volatile and non-volatile memory areas and can comprise a wide variety of storage devices and storage media, for example hard disks, optical storage media or semiconductor memories.

[0046] Fig. 4 shows a sample 1 with a large number of emitters or reflectors 2. Five emitters or reflectors 2 are shown as an example. The emitters 2 can be, for example, fluorophores or molecules labeled with fluorophores. The fluorophores can be excited to emit photons using light of a suitable wavelength. In MINFLUX microscopy, the fluorophores are excited in such a way that a fluorophore to be localized is always placed close to or in a minimum of a light distribution used for excitation, whereby the light distribution must have an intensity increase region adjacent to the minimum. This achieves better utilization of the fluorescence photons with regard to obtaining information about the position of the respective emitting fluorophore. Ideally, the minimum of the excitation light distribution is a zero.

[0047] Fig. 5 shows the basic structure of a MINFLUX microscope 10 in which a solution according to the invention is implemented. The optical setup is based on a standard fluorescence microscope. Implementing the MINFLUX concept on a standard inverted microscope platform 11 facilitates practical implementation of high resolution, as a standard fluorescence microscope provides all routinely required functions, such as compatibility with standard stages, sample holders, brightfield and epifluorescence illumination with insertable filters and eyepieces for quickly examining large areas of interest in the sample. The MINFLUX microscope 10 is controlled by a controller 12.

[0048] An excitation light beam 13 emitted by a laser 14 is focused into the focal plane of an objective lens that is part of the microscope platform 11. To enable both flexible previews of large areas of interest and precise measurements in desired areas using the MiNFLUX concept, the beam scanning with respect to the stationary sample is realized by a combination of a galvanometer scanning unit 16 and electro-optical beam deflectors 17, 18. To enable lateral fast scanning for MINFLUX measurements in the x-y -plane, the excitation light beam 13 passes through a λ / 2 plate 15 and is deflected by two electro-optical beam deflectors 17, 18, which are arranged in series and rotated by 90° to their respective axes. A λ / 2 plate 20 between the electro-optical beam deflectors 17, 18 rotates the polarization of the light beam by 90° to account for this rotation. The field of view in the focal plane accessible by means of the beam deflectors 17, 18 is small and is expanded via an additional galvanometer scanning unit 16 at the camera port of the microscope platform 11. The galvanometer scanning unit 16 serves as a coarser basis for further finer and significantly faster electro-optical x and y shifts. A phase-modulating area light modulator 21 serves to imprint desired phases on the excitation light beam 13. Subsequently, a λ / 4 plate 22 forms a circular polarization of the excitation light.The excitation light beam 13 is then superimposed on the detection beam path using a beam splitter 23 and guided into the microscope platform 11 via the galvanometer scanning unit 16. The galvanometer scanning unit 16 and the electro-optical beam deflectors 17, 18 together serve to position the excitation light beam 13 in the microscope platform 11, either as a normally focused beam for confocal scanning or with an intensity distribution suitable for the MINFLUX concept.

[0049] An activation laser 24 is used to activate individual fluorophores. The intensity of this laser 24 can be reduced to the nanowatt range if necessary, depending on the sample or the fluorophores used, e.g., using a neutral density filter 25. After passing through a λ / 4 plate 26, the activation light beam 27 is superimposed on the detection beam path and the excitation beam path by means of a beam splitter 28. The activation light beam 27 is guided to the microscope platform 11 without passing through the electro-optical beam deflectors 17, 18.

[0050] The fluorescent light 29 emitted by the sample is collected by the objective, scanned by the galvanometer scanning unit 16, passed through the aforementioned beam splitters 23, 28 and guided to a variable pinhole 30 for confocal detection with two avalanche photodiodes 31, 32, which detect photons in different spectral ranges defined by a dichroic mirror 33.

[0051] In order to estimate the positions of the emitters in the sample, the controller 12 comprises a device 40 according to the invention for estimating a position of an emitter or reflector.

[0052] Fig. 6 shows an example of a hexagonal target coordinate pattern TCP. The target coordinate pattern TCP comprises target coordinates P i at six positions 0 to 5, each symbolized by the open circles. The six target coordinates P i lie on a circle with the diameter L.The center of the target coordinate pattern TCP is also marked, but it is not necessarily used as the target coordinate.

[0053] Fig. 7 shows example position estimates for a group of simulated emitters. The emitters each have a similar radial coordinate r The figures show estimates of r against the actual radial coordinate r for a hexagonal target coordinate pattern from Fig. 6 . The filled circles show the mean uncalibrated estimate of the radial position, the open circles show the mean calibrated estimate of the radial position. The value of r lim , which can be read off from the abscissa of the maxima of the two curves, is approximately 0.9×10 -7< m. Also shown by filled triangles are the values ​​of d = | u 0 - u 1 |, which for two subsets b i ( i = 0,2,4) and b i ( i = 1,3,5) of the target coordinate pattern with three target coordinates arranged in a triangle. d ( r lim ) is approximately 50. The difference d between the values ​​of the two subsets is fanned out because for an estimator based on only three points, the estimated radial coordinate also depends more strongly on the angular position. However, it is clearly visible that the range of values ​​for r , for which an injective function r → d ( r ) is available, about r lim extends beyond.

[0054] Fig. 8 bis Fig. 10 exhibit a special intensity distribution of the excitation light, which also allows the z-coordinate to be determined without shifting the focal plane relative to the sample. The intensity distribution has a central minimum and three or more local maxima arranged around the central minimum, with the angular positions of the three or more local maxima changing along the optical axis. To generate such an intensity distribution, a combined vortex and trefoil phase can be impressed on the excitation beam, e.g., using a surface light modulator. Based on the donut caused by the vortex phase, the resulting intensity distribution can be called a trenut.

[0055] Fig. 8 shows the intensity distribution of the excitation light in the x-y -plane for different axial positions. The intensity distributions for three axial positions are shown z =-240 nm,z =0 nm and z =240 nm for a wavelength of 642 nm and a numerical aperture NA =1.4 . On the left, the intensity distribution is shown in grayscale, on the right as a contour plot. Fig. 9 and Fig. 10 show the intensity distribution of the excitation light in the x-z -level and the y-z -level. Also shown are Fig. 8 the six positions 0 to 5 of the target coordinate pattern, the two subsets α =(0,2,4) and β =(1,3,5). The diameter of the target coordinate pattern used, which is adapted to the position of the local maxima, is L=486 nm. The number of positions is adjusted to the number of local maxima. Preferably, the number of positions is twice as large as the number of local maxima, thus six positions for a three-slot, and correspondingly more positions for a multi-slot with more than three local maxima. The positions of the target coordinate pattern and the position of the local maxima are adjusted to each other so that z =0 nm position pairs from the two subsets of the target coordinate pattern, e.g. the position pairs (1,2), (3,4) and (5,0), are each exposed to the same intensity. For increasing or decreasing values ​​of z the local maxima shift in such a way that the positions of one of the two subsets are exposed to a high intensity, while the positions of the other subset are exposed to a low intensity. This is shown in Fig. 8 well on the intensity distributions for the axial positionsz =-240 nm and z =240 nm.

[0056] Assuming a fluorophore is now located at the center of the target coordinate pattern at position (0,0,0) and the center of the intensity distribution is shifted to the right to position 0 of the target coordinate pattern, the fluorophore is exposed to the intensity that corresponds to position 3 of the target coordinate pattern in the representation of the unshifted intensity distribution. The same applies to pairs 1-4 and 2-5, and vice versa. Thus, if a fluorophore is scanned at a target coordinate pattern with points 0 to 5, the corresponding intensities can be read from the figure. This also applies to fluorophores at axial positions other than 0.

[0057] If a fluorophore is located laterally in the center, then it will be used for point 0 of the target coordinate pattern with the Fig. 8 at point 3, at point 4 with the intensity of point 1, at point 2 with the intensity of point 5 and accordingly 1-4, 3-0, 5-2. It is now already from the Fig. 8 It is evident that such a fluorophore z =240 nm at the odd points 1, 3, 5 of the target coordinate pattern with the small intensities of points 4, 2, 0 and at the even points 0, 2, 4 of the target coordinate pattern with the large intensities of points 1, 3, 5. z =0 nm, however, it is exposed to the same intensities. z =-240 nm the behavior is exactly the opposite of z =240 nm. Due to the diameter used L of the target coordinate pattern ensures that the fluorophore in the considered area of z =240 nm to z =-240 nm with an intensity that strongly depends on the axial position zThe same applies if the fluorophore is not exactly on-axis. Therefore, the Trenut can easily be used to estimate the position based on subsets of the target coordinate pattern. z- Coordinate can be estimated. In Fig. 8 It is clearly visible that the intensity distribution near the axis behaves quite well, so that a lateral position determination following an axial position determination with a smaller diameter L of the target coordinate pattern, e.g. with L =288 nm.

[0058] Analogous to the formula (1) above, an uncalibrated estimator based on a trenut for the subsets α =(0,2,4) and β =(1,3,5) of the positions b i of the target coordinate pattern can be formulated as: u ′ → xy x → b → i : = u → x → , b → i , i ∈ α − u → x → , b → i , i ∈ β u ′ → z x → b → i : = ∑ i ∈ α p i − ∑ i ∈ β p i ∑ i p i .

[0059] The two summands u ( x, b i , i ∈ α ) and u ( x, b i , i ∈ β ) are formed according to formula (1), ie for u' xy ( x, b i ) In the denominator, only the photon counts of the respective subset of the target coordinate pattern are summed.

[0060] Fig. 11 shows on the right side the value of the uncalibrated estimator using contour lines u' z depending on the position in a lateral plane for z =-240 nm, z =-120 nm and z =0 nm. On the left side, the values ​​are shown in grayscale. Especially in the grayscale representation, it is clearly visible that an axial coordinate of the fluorophores can be easily determined even without precise knowledge of the lateral position. To utilize the asymmetry of the intensity distribution to determine the axial position, the diameter of the target coordinate pattern is adjusted to the position of the local maxima.

[0061] Fig. 12 bis Fig. 14 show simulations of the estimator's behavior u according to formula (1) and the estimator according to the invention u' according to formula (2) for the axial positions z =-240 nm, z =-120 nm and z =0 nm. The simulations are based on a wavelength of 642 nm and a diameter of the target coordinate pattern of L =486 nm. The figures show from top to bottom the uncalibrated estimate of the angular position ϕ with the estimator u, the uncalibrated estimate of the angular position ϕ with the estimator u', the uncalibrated estimate of the radial position r with the estimator u and the uncalibrated estimate of the radial position r with the estimator u'. Fig. 15 bis Fig. 17 show corresponding simulations for a diameter of the target coordinate pattern of L =288 nm. As can be clearly seen from the figures, the behavior of uand u' very much on the choice of diameter L The more benign the estimators are, ie the larger the injective range, the larger the effective measurement range. For a typical measurement range of r For wavelengths ≤75 nm, the sets of curves for emitter or reflector positions within this range are shown as solid lines, while those outside this range are shown as dashed lines. This makes it much easier to assess the injectivity in the relevant range. Regarding the angular coordinate ϕ is the estimator u' over the entire range of - π to + π injective. The diameter L =486 nm is optimized for the determination of z. The appraiser u' behaves much more kindly than the appraiser u . The diameter L =288 nm leads to a less accurate determination of z, so that the use of the estimator u'is necessary. The coordinates x and y or r and ϕ can also be easily estimated with the estimator u determine.

[0062] As an alternative to the formula (2) above, an uncalibrated estimator based on a trenut for the subsets α =(0,2,4) and β =(1,3,5) of the positions b i of the target coordinate pattern can also be formulated as: u ′ → xy x → b → i : = ∑ j ∈ α p j b → j − ∑ k ∈ β p i b → k ∑ i p i u ′ → z x → b → i : = ∑ i ∈ α p i − ∑ i ∈ β p i ∑ i p i .

[0063] In this case, u' xy ( x , b i ) in the denominator is summed over the photon counts of all positions of the target coordinate pattern.

[0064] Fig. 18 bis Fig. 20 show simulations of the estimator's behavior u according to formula (1) and the further estimator according to the invention u' according to formula (3) for the axial positions z =-240 nm, z =-120 nm and z=0 nm. The simulations are based on a wavelength of 642 nm and a diameter of the target coordinate pattern of L =486 nm. The figures show from top to bottom the uncalibrated estimate of the angular position ϕ with the estimator u, the uncalibrated estimate of the angular position ϕ with the estimator u', the uncalibrated estimate of the radial position r with the estimator u and the uncalibrated estimate of the radial position r with the estimator u'. As can be seen from the figures, the estimator according to formula (3) behaves even more benignly than the estimator according to formula (2). Referenzen

[0065] [1] S.W. Hell: "Far-Field Optical Nanoscopy", Science 316, S. 1153-1158 (2007). [2] S.W. Hell et al.: "Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy", Optics Letters 19, S. 780-782 (1994). [3] S.W. Hell: "Toward fluorescence nanoscopy". Nat Biotech 21, S. 1347-1355 (2003). [4] E. Betzig et al.: "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution", Science 313, S. 1642-1645 (2006). [5] A. Sharonov et al: "Wide-field subdiffraction imaging by accumulated binding of diffusing probes", Proceedings of the National Academy of Sciences 103, S. 18911-18916 (2006). [6] F. Balzarotti et al.: "Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes", Science 355, S. 606-612 (2017). [7] R. Schmidt et al.: " MINFLUX nanometer-scale 3D imaging and microsecond-range tracking on a common fluorescence microscope", Nature Communications 12, S. 1-12 (2021). Bezugszeichenliste

[0066] 1 Sample 2 Emitter / Reflector 10 Microscope 11 Inverted microscope platform 12 Controller 13 Excitation light beam 14 Laser 15 λ / 2 plate 16 Galvanometer scanning unit 17 Electro-optical beam deflector 18 Electro-optical beam deflector 20 λ / 2 plate 21 Area light modulator 22 λ / 4 plate 23 Beam splitter 24 Activation laser 25 Neutral density filter 26 λ / 4 plate 27 Activation light beam 28 Beam splitter 29 Fluorescent light 30 Variable pinhole 31 Avalanche photodiode 32 Avalanche photodiode 33 Dichroic mirror 40 Device 41 Interface 42 Illumination means 43 Detection means 44 Estimator 45 Control unit 46 Storage 47User interface 50Device 51Memory 52Processor 53Input 54Output P i Target coordinate TCPSet of target coordinates S1Illuminating a sample with excitation light at target coordinates S2Detecting fluorescence photons or reflected photons S3Estimating a position of an emitter or reflector

Claims

1. A method for estimating a position of an emitter or reflector (2) in a sample (1), comprising the steps of: - illuminating (S1) the sample (1) with excitation light (13) at at least one set (TCP) of target coordinates (Pi), wherein the excitation light (13) has an intensity distribution in the form of a donut; - detecting (S2) fluorescence photons or reflected photons for the individual target coordinates (Pi) of the set (TCP) of target coordinates (Pi); - determining a first uncalibrated estimated position of an emitter or reflector from the fluorescence photons or reflected photons detected for a first subset of the set (TCP) of target coordinates (Pi); - determining a second uncalibrated estimated position of the emitter or reflector from the fluorescence photons or reflected photons detected for a second subset of the set (TCP) of target coordinates (Pi); and - estimating (S3) a position of the emitter or reflector (2) by comparing the first estimated position and the second estimated position, wherein the position estimated by comparing the first estimated position and the second estimated position is calibrated.

2. A method for estimating a position of an emitter or reflector (2) in a sample (1), comprising the steps of: - illuminating (S1) the sample (1) with excitation light (13) at at least one set (TCP) of target coordinates (Pi); - detecting (S2) fluorescence photons or reflected photons for the individual target coordinates (Pi) of the set (TCP) of target coordinates (Pi); and - estimating (S4) a position of an emitter or reflector (2) from the detected fluorescence photons or reflected photons; wherein the excitation light (13) has an intensity distribution comprising a central minimum and three or more local maxima arranged around the central minimum, wherein the angular positions of the three or more local maxima vary along the optical axis.

3. The method according to claim 2, wherein estimating (S3) the position of the emitter or reflector (2) comprises comparing estimated positions for the emitter or reflector (2) determined from fluorescence photons or reflected photons detected for subsets of the set (TCP) of target coordinates (Pi).

4. The method according to claim 1 or 3, wherein a difference is determined or a ratio is formed for the comparison.

5. The method according to any one of claims 1, 3, and 4, wherein the set (TCP) of target coordinates (Pi) comprises four or more target coordinates (Pi) and the subsets of the set (TCP) of target coordinates (Pi) each comprise three or more target coordinates (Pi), or wherein the subsets of the set (TCP) of target coordinates (Pi) are disjoint.

6. The method according any one of the preceding claims, wherein the set (TCP) of target coordinates (Pi) comprises six target coordinates (Pi) arranged in a hexagon, and wherein the subsets of the set (TCP) of target coordinates (Pi) preferably each comprise three target coordinates (Pi) arranged in an equilateral triangle.

7. The method according to claim 3 or according to claim 3 and any one of claims 4 to 6, wherein a depth information for the emitter or reflector (2) is determined from vector sums and / or sums over vectors of the detected fluorescence photons or reflected photons determined for the subsets of the set (TCP) of target coordinates (Pi).

8. The method according to claim 2 or according to claim 2 and any one of claims 3 to 7, wherein a combined vortex and trefoil phase is imposed on the excitation light (13) to generate the intensity distribution, preferably by means of an adjustable spatial light modulator (21).

9. The method according to claim 8, wherein the phase shift of the trefoil phase is between 10% and 200% of the phase shift of the vortex phase, preferably between 20% and 150%, more preferably between 30% and 120%, more preferably between 80% and 110%, preferably 100%.

10. The method according to claim 2 or according to claim 2 and any one of claims 3 to 9, wherein: - the central minimum is extended along the optical axis; or - the angular positions of the three or more local maxima change monotonically, preferably strictly monotonically, along the optical axis, further preferably proportional to the axial position; or - the three or more local maxima are evenly distributed around the central minimum, wherein the angular positions of the three or more local maxima preferably change along the optical axis over an intended axial detection range by an amount corresponding to 180° divided by the number of maxima.

11. A computer program comprising instructions which, when executed by a computer, cause the computer to perform the steps of a method according to any one of claims 1 to 10 for estimating a position of an emitter or reflector (2) in a sample (1).

12. An apparatus (40) for estimating a position of an emitter or reflector (2) in a sample (1), comprising: - illuminating means (42) for illuminating (S1) the sample (1) with excitation light (13) at at least one set (TCP) of target coordinates (Pi), wherein the excitation light (13) has an intensity distribution in the form of a donut; - detecting means (43) for detecting (S2) fluorescence photons or reflected photons for the individual target coordinates (Pi) of the set (TCP) of target coordinates (Pi); and - estimating means (44) for estimating (S3) a position of an emitter or reflector (2) from the detected fluorescence photons or reflected photons; wherein the estimating means (44) is configured to determine a first uncalibrated estimated position of an emitter or reflector from the fluorescence photons or reflected photons detected for a first subset of the set (TCP) of target coordinates (Pi), determine a second uncalibrated estimated position of the emitter or reflector from the fluorescence photons or reflected photons detected for a second subset of the set (TCP) of target coordinates (Pi), and estimate (S3) a position of the emitter or reflector (2) by comparing the first estimated position and the second estimated position, wherein the position estimated by comparing the first estimated position and the second estimated position is calibrated.

13. An apparatus (40) for estimating a position of an emitter or reflector (2) in a sample (1), comprising: - illuminating means (42) for illuminating (S1) the sample (1) with excitation light (13) at at least one set (TCP) of target coordinates (Pi), wherein the excitation light (13) has an intensity distribution comprising a central minimum and three or more local maxima arranged around the central minimum, wherein the angular positions of the three or more local maxima vary along the optical axis; - detecting means (43) for detecting (S2) fluorescence photons or reflected photons for the individual target coordinates (Pi) of the set (TCP) of target coordinates (Pi); and - estimating means (44) for estimating (S3) a position of an emitter or reflector (2) from the detected fluorescence photons or reflected photons.

14. The apparatus (40) according to claim 13, wherein the estimating means (44) is configured to compare estimated positions for the emitter or reflector (2) determined from fluorescence photons or reflected photons detected for subsets of the set (TCP) of target coordinates (Pi) for estimating (S3) the position of the emitter or reflector (2), or wherein the illuminating means (42) comprises an adjustable spatial light modulator (21) for imposing a combined vortex and trefoil phase on the excitation light (13).

15. A microscope (10), characterized in that the microscope (10) comprises an apparatus (40) according to any one of claims 12 to 14 or is configured to perform a method according to any one of claims 1 to 10 for estimating a position of an emitter or reflector (2) in a sample (1).