METHOD, COMPUTER PROGRAM, AND APPARATUS FOR ADAPTING AN ESTIMATOR FOR USE IN A MICROSCOPE

Abstract

The present invention is related to a method, a computer program, and apparatus for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample based on a method, in which the sample is illuminated with light at one or more sets of probe positions and fluorescence photons are acquired for the sets of probe positions. The invention is further related to a microscope, which makes use of such a method or apparatus. The sample is illuminated with light at one or more sets of probe positions and fluorescence photons are acquired for the sets of probe positions. Photon counts of the acquired photons are then added to vectors of photon counts or sums of photon counts are determined for the sets of probe positions. A value representative of background noise is determined and used for adapting the estimator in real-time.

Claims

1. A method for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample based on a method, in which the sample is illuminated with light at one or more sets of probe positions (P.sub.i) and fluorescence photons are acquired for the sets of probe positions (P.sub.i), comprising: illuminating the sample with light at one or more sets of probe positions (P.sub.i); acquiring fluorescence photons for the sets of probe positions; adding photon counts of the acquired photons to vectors of photon counts or sums of photon counts for the sets of probe positions; determining a value representative of background noise from the vectors of photon counts or the sums of photon counts; and adapting the estimator in real-time using the value representative of background noise.

2. The method according to claim 1, wherein for determining a value representative of background noise only sets of probe positions are evaluated, for which no fluorescence from an emitter is detected.

3. The method according to claim 2, wherein for determining whether fluorescence from an emitter is detected, the sum of photon counts for a set of probe positions is compared with a threshold derived from a current estimated background.

4. The method according to claim 2, wherein the sums of photon counts are added to a histogram.

5. The method according to claim 4, wherein the histogram is specific for each scanning iteration.

6. The method according to claim 4, wherein the value representative of background noise is derived from a peak of the histogram.

7. The method according to claim 1, wherein the estimator is adapted in such way that an expectancy value of the background noise is subtracted from photon counts before estimating a position of an emitter.

8. The method according to claim 1, wherein the estimator uses a calibration polynomial, which is specific for each of a plurality of scanning iterations.

9. The method according to claim 1, wherein the sets of probe positions are illuminated multiple times.

10. The method according to claim 1, wherein a set of probe positions comprises three or more probe positions, which are arranged rotationally symmetric on a circle.

11. The method according to claim 10, wherein opposing probe positions of a set of probe positions are illuminated in sequential pairs.

12. The method according to claim 1, wherein the estimator is a least-mean-squared estimator.

13. A computer program comprising instructions, which, when executed by a computer, cause the computer to perform a method according to claim 1 for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample based on a method, in which the sample is illuminated with light at one or more sets of probe positions and fluorescence photons are acquired for the sets of probe positions.

14. An apparatus for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample based on a method, in which the sample is illuminated with light at one or more sets of probe positions and fluorescence photons are acquired for the sets of probe positions, the apparatus comprising: illumination means configured to illuminate the sample with light at one or more sets of probe positions; acquisition means configured to acquire fluorescence photons for the sets of probe positions; processing means configured to add photon counts of the acquired photons to vectors of photon counts or sums of photon counts for the sets of probe positions, and to determine a value representative of background noise from the vectors of photon counts or the sums of photon counts; and control means configured to adapt the estimator in real-time using the value representative of background noise.

15. A microscope, wherein the microscope comprises an apparatus according to claim 14 or is configured to perform a method according to claim 1 for adapting an estimator for estimating a position of an emitter in a sample.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Further features of the present invention will become apparent from the following description and the appended claims in conjunction with the figures.

[0071] FIG. 1 schematically illustrates a method for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample;

[0072] FIG. 2 schematically illustrates a first embodiment of an apparatus for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample;

[0073] FIG. 3 schematically illustrates a second embodiment of an apparatus for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample;

[0074] FIG. 4 shows a sample with a number of molecules;

[0075] FIG. 5 shows an exemplary intensity curve over a cross-section through a light distribution;

[0076] FIG. 6 shows an exemplary optical setup of a MINFLUX microscope;

[0077] FIG. 7 illustrates the principle of real-time background compensation;

[0078] FIG. 8 illustrates the principle of MINFLUX localization; and

[0079] FIG. 9 shows targeted coordinate patterns applied in the MINFLUX localization process, with simulated mean position estimates and confidence intervals.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0080] The present description illustrates the principles of the present disclosure. It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the disclosure.

[0081] All examples and conditional language recited herein are intended for educational purposes to aid the reader in understanding the principles of the disclosure and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions.

[0082] Moreover, all statements herein reciting principles, aspects, and embodiments of the disclosure, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure.

[0083] Thus, for example, it will be appreciated by those skilled in the art that the diagrams presented herein represent conceptual views of illustrative circuitry embodying the principles of the disclosure.

[0084] The functions of the various elements shown in the figures may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term “processor” or “controller” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, read only memory (ROM) for storing software, random access memory (RAM), and nonvolatile storage.

[0085] Other hardware, conventional and/or custom, may also be included. Similarly, any switches shown in the figures are conceptual only. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context.

[0086] In the claims hereof, any element expressed as a means for performing a specified function is intended to encompass any way of performing that function including, for example, a combination of circuit elements that performs that function or software in any form, including, therefore, firmware, microcode or the like, combined with appropriate circuitry for executing that software to perform the function. The disclosure as defined by such claims resides in the fact that the functionalities provided by the various recited means are combined and brought together in the manner which the claims call for. It is thus regarded that any means that can provide those functionalities are equivalent to those shown herein.

[0087] FIG. 1 schematically illustrates a method according to the invention for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample. For example, the estimator may be a least-mean-squared estimator. In this method, the sample is illuminated S1 with light at one or more sets of probe positions and fluorescence photons are acquired S2 for the sets of probe positions. Advantageously, the sets of probe positions are illuminated S1 multiple times. Opposing probe positions of a set of probe positions may be illuminated S1 in sequential pairs. Preferably, a set of probe positions comprises three or more probe positions, which are arranged rotationally symmetric on a circle. Photon counts of the acquired S2 photons are then added S3 to vectors of photon counts or sums of photon counts for the sets of probe positions. Subsequently, a value representative of background noise is determined S4 from the vectors of photon counts or the sums of photon counts. For example, the sums of photon counts may be added to a histogram, which preferably is specific for each of a plurality of scanning iterations. The value representative of background noise can then be derived from a peak of a histogram. The value representative of background noise is used for adapting S5 the estimator in real-time. For example, the estimator may be adapted S5 in such way that an expectancy value of the background noise is subtracted from photon counts before estimating a position of an emitter. Preferably, the estimator uses a calibration polynomial, which is specific for each scanning iteration. Advantageously, for determining a value representative of background noise only sets of probe positions are evaluated, for which no fluorescence from an emitter is detected. For determining whether fluorescence from an emitter is detected, the sum of photon counts for a set of probe positions may be compared with a threshold derived from a current estimated background.

[0088] FIG. 2 schematically illustrates a block diagram of a first embodiment of an apparatus 40 according to the invention for adapting an estimator 35 for use in a microscope 10 for estimating a position of an emitter in a sample. For example, the estimator 35 may be a least-mean-squared estimator. The apparatus 40 has an interface 41 for exchanging data with components of the microscope 10. An illumination means 42 is configured to illuminate the sample with light at one or more sets of probe positions, e.g. by instructing a light source and position control elements of the microscope accordingly. Advantageously, the sets of probe positions are illuminated S1 multiple times. Opposing probe positions of a set of probe positions may be illuminated S1 in sequential pairs. Preferably, a set of probe positions comprises three or more probe positions, which are arranged rotationally symmetric on a circle. An acquisition means 43 is configured to acquire fluorescence photons for the sets of probe positions, e.g. by evaluating signals of one or more detectors of the microscope. A processing means 44 is configured to add photon counts of the acquired photons to vectors of photon counts or sums of photon counts for the sets of probe positions, and to determine a value representative of background noise from the vectors of photon counts or the sums of photon counts. For example, the sums of photon counts may be added to a histogram, which preferably is specific for each of a plurality of scanning iterations. A control means 45 is configured to adapt the estimator 35 in real-time using the value representative of background noise. For example, the estimator may be adapted in such way that an expectancy value of the background noise is subtracted from photon counts before estimating a position of an emitter. Preferably, the estimator uses a calibration polynomial, which is specific for each scanning iteration. Advantageously, for determining a value representative of background noise only sets of probe positions are evaluated, for which no fluorescence from an emitter is detected. For determining whether fluorescence from an emitter is detected, the sum of photon counts for a set of probe positions may be compared with a threshold derived from a current estimated background.

[0089] The illumination means 42, the acquisition means 43, the processing means 44, and the control means 45 may be controlled by a controller 46. A local storage unit 47 is provided, e.g. for storing data during processing. A user interface 48 may be provided for enabling a user to modify settings of the various elements 42-46 of the apparatus 40. The different elements 42-46 of the apparatus 40 can be embodied as dedicated hardware units. Of course, they may likewise be fully or partially combined into a single unit or implemented as software running on a processor, e.g. a CPU or a GPU.

[0090] A block diagram of a second embodiment of an apparatus 50 according to the invention for adapting an estimator for use in a microscope for estimating a position of an emitter in a sample is illustrated in FIG. 3. The apparatus 50 comprises a processing device 51 and a memory device 52. For example, the apparatus 50 may be a computer, an electronic control unit or an embedded system. The memory device 52 has stored instructions that, when executed by the processing device 51, cause the apparatus 50 to perform steps according to one of the described methods. The instructions stored in the memory device 52 thus tangibly embody a program of instructions executable by the processing device 51 to perform program steps as described herein according to the present principles. The apparatus 50 has an input 53 for receiving data. Data generated by the processing device 51 are made available via an output 54. In addition, such data may be stored in the memory device 52. The input 53 and the output 54 may be combined into a single bidirectional interface.

[0091] The processing device 51 as used herein may include one or more processing units, such as microprocessors, digital signal processors, or a combination thereof.

[0092] The local storage unit 47 and the memory device 52 may include volatile and/or non-volatile memory regions and storage devices such as hard disk drives, optical drives, and/or solid-state memories.

[0093] In the following, aspects of the invention shall be explained in more detail with reference to FIG. 4 to FIG. 9.

[0094] FIG. 4 shows a sample 1 with a number of emitters 2, e.g. molecules marked with fluorophores or acting as fluorophores themselves. In this example, five emitters 2 are shown, whose positions M.sub.1 to M.sub.5 are to be determined. The fluorophores can be excited with light of a suitable wavelength to emit photons. 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 range adjacent to the minimum. In this way a better utilization of the fluorescence photons is achieved with regard to obtaining information about the position of the respective emitting fluorophore. Ideally, the minimum of the excitation light distribution is a zero point.

[0095] FIG. 5 shows an exemplary intensity curve over a cross-section through a light distribution 3 of a suitable structured optical beam, in this case a donut. The intensity I is plotted against the position within the light distribution 3, here along the x-axis. The intensity curve of the light distribution 3 shows a central intensity minimum 4, which is surrounded on all sides by intensity increase areas 5.

[0096] FIG. 6 shows an exemplary optical setup of a MINFLUX microscope 10. The optical setup is based on a common fluorescence microscope. Typical microscopy workflows also entail prior steps before a nanometer resolution image is recorded, in particular the selection of regions of interest based on eyepiece inspection of a sample in the widefield mode or by confocal scanning. Realizing MINFLUX on top of a standard inverted microscope platform 11 facilitates the combination of practicability with ultimate resolution, as a common fluorescence microscope provides routinely needed features such as compatibility with standard stages, probe holders, bright field and epi-fluorescence illumination with employable filters and eyepieces for quickly checking large regions of interest in the sample. The MINFLUX microscope 10 is controlled by controller 12.

[0097] An excitation beam 13 emitted by a laser 14 is focused into the focal plane of an objective lens, which is part of the microscope platform 11. In order to allow both flexible pre-views of large regions of interest and precise measurements in desired regions applying the MINFLUX scheme, beam scanning with respect to the stationary sample is achieved by a galvanometer scanning unit 16 and electro-optical beam deflectors 17, 18 operating in concert. To enable lateral fast scanning for MINFLUX measurements in the x-y-plane, the excitation beam 13 passes through a λ/2-plate 15 and is deflected by two electro-optical beam deflectors 17, 18, which are installed in series and rotated by 90° relative to their respective axes. A λ/2-plate 20 in between the electro-optical beam deflectors 17, 18 rotates the laser beam polarization by 90° to accommodate for that rotation. The accessible field of view of the deflector array in the focal plane is small and is extended via an additional galvanometer scanning unit 16 installed at the camera port of the microscope body, which serves as the coarser basis for additional finer and much faster electro-optic x- and y-displacements. To switch between a Gaussian shape of the excitation beam 13 and a donut shape, a phase-modulating spatial light modulator 21 is used, which introduces a helical phase shift onto the beam 13. Following that, a λ/4-plate 22 shapes a circular polarization of the excitation light. Subsequently, the excitation beam 13 is superimposed with the detection beam path with a beam splitter 23 and steered into the microscope 11 via the galvanometer scanning unit 16. Jointly, both the galvanometer scanning unit 16 and the electro-optical beam deflectors 17, 18 are used to position the excitation beam 13 in the microscope 11, either as a normally focused beam for confocal scanning, or as a donut with a central zero-point intensity for the MINFLUX protocol.

[0098] For activation of single fluorophores, an activation laser 24 is used. The intensity of this laser 24 is reduced into the nanowatts region by a neutral-density filter 25. After passing through a λ/4 plate 26, the activation laser beam 27 is superimposed with the detection laser beam path as well as the excitation laser beam path by means of a beam splitter 28. The activation laser beam 27 is provided to the microscope 11 without passing the electro-optical beam deflectors 17, 18

[0099] Fluorescence light 29 emitted by the sample is collected by the objective lens, descanned by the galvanometer scanning unit 16, transmitted by the aforementioned beam splitters 23, 28 and passed to a variable pinhole 30 for confocalized detection using two avalanche photodiodes 31, 32, which detect photons in distinct spectral ranges defined by a dichroic mirror 33.

[0100] In order to estimate positions of the emitters in the sample, the controller 12 comprises an estimator 35. The estimator 35 can be adapted in real-time by an apparatus 40 according to the invention for adapting the estimator 35. In this example, the apparatus 40 is also included in the controller 12. Of course, it may likewise be provided as a self-contained apparatus.

[0101] As indicated before, one possible modality for superresolving imaging is to use iterative MINFLUX imaging with power ramping. This approach derives the position of an emitter in a sample from the photon counts measured at a set of probe positions by applying a stochastic estimator to the data. In order to arrive at an unbiased result, i.e. a result without a systematic error, a measuring scheme is used, which offers virtually unbiased localization in real-time.

[0102] For a targeted coordinate pattern with m beam positions {right arrow over (b)}.sub.j (j=1 . . . m) on a circle with radius L and associated photon counts p.sub.j collected during equal dwell times, a least-mean-squared estimator (LMSE) for the (relative) emitter position u within the targeted coordinate pattern can be written as the product

{right arrow over (r)}(p.sub.j)=c(L,w).Math.{right arrow over (u)}(p.sub.j,{right arrow over (b)}.sub.j)  (2)

of a normalized vector sum

[00002]$\begin{array}{cc}\stackrel{.fwdarw.}{u}\left(p_j,{\stackrel{.fwdarw.}{b}}_j\right)=\frac{{.Math.}_{j=1}^m{p}_j.Math.{\stackrel{.fwdarw.}{b}}_j}{{.Math.}_{j=1}^m{p}_j}& \left(3\right)\end{array}$

with a scaling constant c that accounts for L and the full-width-half-maximum (FWHM) w of the point spread function. According to one aspect of the present invention, the scaling constant c is replaced with an iteration dependent calibration polynomial P.sub.k of second degree, which is inexpensive to compute on the microscope hardware, to obtain an unbiased emitter position from the calibrated least-mean-squared estimator:

{right arrow over (r)}({right arrow over (u)})={right arrow over (u)}.Math.P.sub.k(|{right arrow over (u)}|.sup.2)  (4)

[0103] For each iteration k, optimized coefficients for P.sub.k may be obtained by a Monte Carlo simulation that accounts for the known experimental parameters such as the precise shape of the donut, the geometry of the targeted coordinate pattern and the photon limit N.sub.k. Preferably, the microscope probes at the targeted coordinate pattern multiple times during each localization step until the actual number of collected photons surpassed the preset N.sub.k. The dwell times and the excitation powers may be adjusted such that the distribution of the actual number of collected photons stays close enough to this limit to warrant the use of P.sub.k. For m=3 off-center beam positions as used in previous MINFLUX implementations, the estimator bias significantly deviates from radial symmetry. Therefore, m is preferably increased to 6 for all iterations. An exception may be made for iterations where the aim are highest localization rates and the added overhead should be avoided. The increased angular uniformity of the localization precision becomes noteworthy in particular for emitters that reside at the periphery of the targeted coordinate pattern.

[0104] In providing the unbiased emitter position, equation (4) does not, however, account for the inevitable background that is present in typical applications. A uniform background would introduce a bias towards the center of the targeted coordinate pattern, as its mean contribution to the numerator of u would amount to 0, while the denominator would now overestimate the number of photons that came from the localized emitter. Based on this notion, a MINFLUX control logic with a real-time background estimation algorithm is used to mitigate sufficiently homogeneous, quasi-static background.

[0105] The implementation of the algorithm is depicted in FIG. 7. The current fluorescence baseline per iteration is deduced from a running histogram of detected fluorescence intensity during localization. Variables with index k are iteration specific, where k is the current iteration, starting at 0. NIT indicates the number of iterations in the MINFLUX sequence. TCP.sub.k refers to the targeted coordinate pattern, i.e. the relative coordinates of the probe positions. EPE is the emitter position estimate relative to POS, i.e. the measurement position in the sample, which is the origin of the TCP. POS is also the starting emitter position estimate. SIP refers to the last signal from pattern, which is a vector of photon counts. ΣSIP is the total photon count of the last signal. SIA refers to the accumulated SIPs over the current iteration. Accordingly, ΣSIA is the total photon count of the current iteration over the estimated background. PHL.sub.k is a photon limit, HST.sub.k is the (running) histogram of acquired ΣSIPs. DKT refers to a dark time counter, DKL to a dark time limit. EBG is the estimated background count of a single pattern in the current iteration. TBG.sub.k refers to a background threshold. STA is the status of the measurement. If the status is “bright”, the algorithm is trying to localize an emitter. If the status is “dark”, the algorithm is estimating background. CLMSE.sub.k refers to the calibrated least mean square estimator.

[0106] The implementation uses a vector “signal from pattern” SIP=(p.sub.1, . . . p.sub.m) of photon counts that were acquired during a single probing of the targeted coordinate pattern as the smallest unit of data on which decisions are based. For a single SIP probing, every needs to be addressed at least once. However, typically the targeted coordinate pattern is scanned multiple times during a single SIP acquisition to ensure that a time-fluctuating background signal is effectively probed at all {right arrow over (b)}.sub.j, to mitigate a directional distortion that would occur if a short burst of background would concentrate into a subset of the {right arrow over (b)}.sub.j. For the same reason, it is beneficial to choose the scan order such that opposing {right arrow over (b)}.sub.j are probed in sequential pairs.

[0107] To estimate the background, a histogram-type baseline estimation is used. For each MINFLUX iteration k, record is kept of the number of photons ΣSIP=Σ.sub.j=1.sup.m p.sub.j that have been collected during each individual SIP by entering every measured ΣSIP into an iteration specific, running histogram HST.sub.k. A running histogram is a histogram that is built from a limited number of entries in a first-in-first-out manner. While a region of interest is scanned in search for fluorescing emitters, the microscope acquires 0-th iteration SIPs at different locations in the sample, until a fluorescent signal is detected. The imaging conditions, e.g. activation levels, etc., are chosen such that during this process, most of the non-background emitters are in their dark state. Therefore, most of the acquired SIPs in 0-th iteration contain background-only signal. For higher iterations k>0, the corresponding histograms HST.sub.k are built from only those SIPs that were measured after the measurement status changed to “dark”, i.e. no significant signal above background has been detected. Consequently, all histograms will, iteration specifically, develop a maximum at a value EBG of ΣSIP that is an estimate for the current, averaged background level.

[0108] During each MINFLUX iteration, one or more SIPs are acquired until enough photons are acquired to proceed with the localization. During this process, an emitter that is currently being localized, i.e. the current emitter, may emit fluorescence intermittently in (micro-)bursts, a property well known for fluorescent proteins, and may cease to emit at any time. To allow only those SIPs to contribute to the localization that have a high probability of carrying signal from the current emitter, it is determined whether an individual SIP contains significant signal over background by comparing ΣSIP to the sum of the current value EBG and a threshold TBG.sub.k. If the answer is yes, SIP is added to a vector SIA that holds the accumulated, vectorial signal for this iteration, which later contributes to the numerator of equation (3). For the denominator of equation (3), ΣSIP is background corrected and then added to the accumulated total signal ΣSIA.fwdarw.ΣSIA+ΣSIP−EBG. If the answer is no, SIP is discarded, as the current emitter apparently entered a non-fluorescing dark state. A counter DKT measures the number of consecutive SIPs that fall under this case and is now incremented by one. If the counter DKT surpasses a preset dark-time-limit DKL, which determines the longest time to wait for the current emitter to re-emit, the measurement status is set to dark. In this state, the microscope skips localization and probes a single SIP in each subsequent iteration to fill the respective histogram HST.sub.k. The measurement status will return to bright, i.e. it expects signal from a current emitter, during initialization of the next localization event.

[0109] While less well-behaved background structures may require additional effort, such as multiple instances of background estimation assigned to different areas of the region of interest, it is noteworthy that already this simple approach proves efficient for the imaging tasks at hand. As a beneficial side effect, imperfections of the focusing that raise the center intensity of the donut above zero are concomitantly mitigated, since they manifest as an additional background contribution that predominantly depends on average emitter brightness and the laser power applied.

[0110] The above-described approach of using the position of the absolute maximum of a histogram HST.sub.k as the value EBG is a computationally inexpensive choice. It requires the histogram bin size to be chosen wide enough to allow the maximum to be formed, while narrow enough to prevent quantization effects from distorting the estimate. In practice, a bin size that corresponds to 5%-15% of the expected single emitter intensity represents a working tradeoff. For a higher precision of the estimate and/or less dependence on measurement parameters, methods that are more complex can be applied. For example, the bin size may be chosen to be smaller than 1% of the expected single emitter intensity. In this case, peak-detection algorithms may be applied to derive the value EBG. For example, the value EBG may be derived as the highest peak or as the first peak from a copy of the histogram after smoothing it with a Gaussian kernel. As an alternative, the value EBG may be derived from the position of the peak that contains the most entries in total, instead of most entries per bin. Of course, other density estimation methods may be used in place of histograms.

[0111] With regard to the effect and determination of the threshold TBG.sub.k, a simple situation with a histogram HST.sub.k built from SIPs that contain either background, or background plus signal from emitters of interest is assumed. The histogram HST.sub.k will exhibit two peaks, which are broadened due to Poisson noise of the detected signal and variation in emitter and background brightness. Under the measurement conditions stated above, the background peak will exhibit the global maximum and its position will be the value EBG. If the background peak is approximately symmetric and the threshold TBG.sub.k is set to zero, roughly half of pure-background SIPs measured would erroneously be treated as signal from a current emitter, i.e. the would constitute false positives. If the threshold TBG.sub.k is chosen larger, more and more area of the emitter-peak will eventually fall below the threshold given by the value EBG+TBG.sub.k, and the corresponding portion of measured emitter-SIPs would be discarded. Typically, the threshold TBG.sub.k can be set to 10%-50% of the expected single emitter intensity during a measurement, decreasing with iteration index. The higher threshold during the initial iteration k=0 prevents chasing background. Lower values of the threshold TBG.sub.k and, consequently, more false positives can be tolerated in higher iterations, since an emitter of interest has already been identified and the background compensation scheme mitigates the effect of false positive SIP classification with respect to mislocalization.

[0112] In practice, the usable field of view of a single MINFLUX localization step is usually limited to below half the wavelength of the excitation light that is used. To scan extended samples in a micrometer-sized region of interest, the microscope spans it with a hexagonal grid of scanning positions. The principle of an iterative MINFLUX localization is illustrated by the example shown in FIG. 8. In this example, the process starts with a pre-localization by pinhole orbit scanning, in which the pinhole is sequentially projected to the points of a hexagonal targeted coordinate pattern without a probe position at its center. Following the pre-localization by pinhole orbit scanning, the iterative procedure proceeds with three intermediate subsequent iterations and one final iteration. In the figure, the projection positions of the pinhole are indicated by the filled black circles. The black empty circles indicate the targeted coordinate pattern applied for the iterations, i.e. the donut center positions. The center position of the targeted coordinate pattern is also marked, though it is not used as a probe position. The star designates the position of the fluorophore. After each iteration, the targeted coordinate pattern is recentered according to the prior emitter position estimate from a calibrated least-mean-squared estimation based on the registered photon counts. The procedure thus quickly zooms in on the emitter, shrinking the targeted coordinate pattern to smaller dimensions of L. A precision of −2 nm is uniformly afforded. Subsequently emitted photons may be used to further refine the position estimate until the emitter ceases to fluoresce.

[0113] FIG. 9 shows targeted coordinate patterns applied in the MINFLUX localization process, with simulated mean position estimates and confidence intervals. The black solid circles indicate the simulated mean position estimates. The ellipsoids indicate the confidence intervals for spaced out emitter positions, which are indicated as black crosses. FIG. 9a) shows a pre-localization, FIG. 9b) an intermediate localization, and FIG. 9c) the final localization. The mutual distance d between the scanning positions preferably is between 10% and 50% of the excitation wavelength λ.sub.exc that is used, i.e. 0.1.Math.λ.sub.exc≤d≤0.5.Math.λ.sub.exc. These positions are repeatedly probed during a measurement and serve as starting points for the activation, search and localization of fluorescent markers. Since the field of view of a single MINFLUX localization step is generally limited to an area of about the size of the diffraction limit or even less, according to one aspect of the invention a lower-precision but further-reaching localization mode is implemented, named pinhole orbit scanning, which improves the efficiency of the search process. Contrary to such used in previous MINFLUX implementations, the pre-localization does not resort to a regularly focused beam. Instead, galvanometric and electro-optical scanners act in concert to keep the donut-shaped excitation beam stationary at a grid position, while the pinhole is sequentially projected to the points of a hexagonal targeted coordinate pattern, i.e. m=6, without a probe position at its center and with a beam separation of about L=300 nm. The position estimate is then obtained according to equation (4) as in the MINFLUX mode with matching P.sub.k for 40 photons in one or more steps. To prevent dark spots next to grid positions that potentially arise from the donut zero, the usable range for d is preferably capped at about λ.sub.exc/2. This arrangement provides a detection radius of about a full wavelength and significantly simplifies the setup, as it makes dedicated hardware for microsecond-scale switching between different focal intensity distributions, e.g. between a Gaussian shape and a donut shape, redundant.