Method for measuring a measurand of a light-scattering measuring object

Abstract

To measure a measurand of a light-scattering measurement object, coherent light (14) from a direction of illumination is focused into a focal plane (21) of an objective (20) such that the coherent light (14) has a phase singularity (5) with a phase jump of (2m+1)π, where m is an integer, in a transverse direction (x) running transversely to the direction of illumination in the focal plane (21), and a light intensity distribution that is symmetrical to the phase singularity (5). The measurement object is scanned in the transverse direction (x) with the phase singularity (5), wherein a portion (22) of the light (14) that is backscattered by the measurement object opposite to the direction of illumination is registered with a point or line detector (6) arranged confocally to the phase singularity (5).A curve (11, 12) of the intensity of the registered portion (22) of the backscattered light (14) over the positions of the phase singularity (5) in the transverse direction (x) is evaluated; and the value of the measured variable of the measurement object in the transverse direction (x) is inferred from the curve (11, 12).

Description

TECHNICAL FIELD OF THE INVENTION

[0001] The invention relates to a method for measuring a measurand of a light-scattering measurement object. The measurement object can be, for example, a nanoscale particle that is measured to determine an extension of the nanoscale particle, which is an indication of its mass. In another embodiment, the measurement object is a surface that is measured to determine a nanoscale structuring of the surface, for example, with regard to its spatial frequencies. STATE OF THE ART

[0002] WO 2015 / 097000 A1 discloses a method for determining the locations of individual molecules of a substance in a sample, wherein the individual molecules of the substance are in a fluorescent state in which they can be excited to emit fluorescent light using excitation light, and wherein the distances between the individual molecules of the substance in a region of interest in the sample maintain a minimum value. The individual molecules of the substance are excited to emit fluorescent light using the excitation light, with an intensity distribution of the excitation light exhibiting a local minimum. The fluorescent light from the excited individual molecules of the substance is recorded for various minimum positions in the region of interest in the sample; and the locations of the individual molecules of the substance are derived from the course of the intensity of the fluorescent light from the respective molecule over the minimum positions.Using this method, the locations of individual molecules can be resolved even when they are closer than λ / 2nsinα to each other, where λ is the wavelength of the fluorescent light, n is the refractive index of the optical material between a sample and an objective lens used to direct the excitation light onto the sample, and α is half the aperture angle of the objective lens. However, this known method can only determine the locations of molecules that are in a fluorescent state. Most molecules of interest in biological studies do not exhibit a fluorescent state by themselves. In order to determine their locations using this known method, they must therefore first be labeled with a fluorescent dye.

[0003] WO 2018 / 069283 A1 discloses methods for determining, with high spatial resolution, the location of an isolated molecule, which can be excited to emit luminescent light using excitation light, in one or more spatial directions in a sample. The excitation light is directed onto the sample with an intensity distribution that has a zero point and a region of intensity increase that border the zero point on both sides in each of the spatial directions. The luminescent light emitted by the molecule is recorded at each of the different positions of the zero point in the sample; and the location of the molecule in the sample is derived from the intensities of the luminescent light recorded at different positions of the zero point.These techniques, known as MINFLUX (minimal photon fluxes) microscopy, require only a few photons of luminescent light from the molecule of interest to determine its position with an accuracy better than λ / 2nsinα, where λ is the wavelength of the luminescent light, and the same definitions apply as above. However, the molecule must be excitable to emit luminescent light, which is not true for most molecules as such.

[0004] EP 3 347 711 B1 discloses a method for detecting particles. In a detection step, interferometric scattering detection of a series of individual light scattering events is performed. These events are generated by the individual particles in a detection volume. During the detection step, the particles are bound to a detection surface of the detection volume or moved through the detection volume. Scattered light signals obtained by interferometric scattering detection are analyzed to determine a particle mass or volume from a contrast of spots from scattering sources in the scattered light signals. Interferometric scattering detection can be performed using a technique called iSCAT (interferometric detection of scattering). Interferometric scattering detection utilizes the scattering of light by the particles, which always occurs, and therefore does not rely on luminescent or fluorescent particles.

[0005] In iSCAT, see PILIARIK, Marek ; SHANDOGHDAR, Vahid: Direct optical sensing of single unlabled proteins and super-resolution imaging of their binding sides, Nature Communications, Vol. 5, 2014, Article-No.: 4495, the interference between a first portion of incident light reflected by a reference surface and a second portion of the incident light scattered by the respective particle is used to obtain a measurement signal whose intensity is greater than the intensity of the scattered portion relative to the intensity of the reflected portion. The intensity of the portion scattered by nanoscale particles is very small compared to the intensities of all reflected portions of the incident light.But even the measurement signal used in iSCAT only stands out compared to the high-intensity reflected portion of the incident light when the difference is formed between those intensity distributions of registered light that are not influenced by the respective particle and those intensity distributions of registered light that are influenced by the respective particle.

[0006] From KÜPPERS, Michelle [et al.]: Confocal interferometric scattering microscopy reveals 3D nanoscopic structure and dynamics in live cells, Nature Communications, Vol. 14, 2023, Article-No.: 1962, a confocal iSCAT variant is known in which, as in confocal scanning fluorescence light microscopy, light is focused onto the respective particle with an objective into a focal area. Light from the focal area is confocally registered, while a spatial region in which the particle is located is scanned with the focal area. A confocally arranged pinhole with an aperture of 0.3 AU (Airy Units) is used to separate the measurement signal from closely spaced particles, where 1 AU = 1.22 λ / NA with the numerical aperture NA of the objective. The use of this pinhole, which is described as almost closed, should be possible because the measurement signal is still above the detector noise.For confocal scanning fluorescence light microscopy, a typical size of the confocal pinhole is given as 1.2 AU due to the limited signal-to-noise ratio.

[0007] From SHAMIR, Joseph: Singular beams in metrology and nanotechnology, Opt. Eng. 51(7) 073605 (6 July 2012) the use of optical singularities to determine a measurand of a light-scattering object is known. Optical singularities are localized regions in a light field in which one or more field parameters, such as phase or polarization, become singular at a zero point, i.e. exhibit a singularity. If the light field is focused into a small spot, the electromagnetic field around the singularity exhibits interesting properties, particularly when it interacts with matter. The light scattered by a object in the strongly varying optical field around the singularity is said to be extremely sensitive to changes and can be used for high-sensitivity measurements and for studying physical processes on a nanometer scale.In so-called singular beam metrology (SBM), a measurement object is scanned with a singular beam. For this purpose, the phase fronts of an incident coherent light beam are modified with a phase mask exhibiting a phase shift of π, and the light beam is focused so that the singular beam used to scan the measurement object has a linear zero between two adjacent intensity maxima in a detection plane. A detector is arranged behind the measurement object in a transmission configuration. If a small detector is arranged in the dark region of the zero of the intensity distribution, a small measurement object scatters light into the detector, similar to dark-field microscopy. Due to the phase disturbance induced by the object, the detector is also sensitive to small shifts in the overall pattern.Two detectors positioned over the regions adjacent to the zero point with high light intensity gradients increase sensitivity to such changes. When the two detectors are differentially connected, the measurement order becomes largely immune to light intensity fluctuations and noise.

[0008] A method for particle size and concentration measurement using the SBM in transmission configuration using two differentially connected detectors is also known from US 2008 / 0037004 A1. OBJECT OF THE INVENTION

[0009] The invention is based on the object of demonstrating a method for measuring a measured variable of a light-scattering measurement object, in which the signal-to-noise ratio of the measurement signal is improved by significantly reducing the noise. SOLUTION

[0010] The object of the invention is achieved by a method having the features of independent patent claim 1. The dependent patent claims relate to preferred embodiments of the method according to the invention. DESCRIPTION OF THE INVENTION

[0011] In a method according to the invention for measuring a measurand of a light-scattering measurement object, coherent light from an illumination direction is focused into a focal plane of an objective such that the coherent light has a phase singularity with a phase jump of (2m+1)π, where m is an integer, in a transverse direction running transversely to the illumination direction in the focal plane, and a light intensity distribution symmetrical to the phase singularity. The measurement object is scanned in the transverse direction with the phase singularity. A portion of the light that is backscattered by the measurement object opposite to the illumination direction is registered with a point or line detector arranged confocally to the phase singularity. If the line detector is used, it is adapted to a shape and orientation of the phase singularity in the focal plane.A curve of the intensity of the recorded portion of the backscattered light over the positions of the phase singularity in the transverse direction is evaluated, and the value of the measured quantity of interest of the measurement object in the transverse direction is deduced from this curve. In particular, by comparing the curves for known values ​​of the measured quantity of comparison objects in the transverse direction, the value of interest of the measured quantity of the measurement object in the transverse direction can be deduced.

[0012] The phase singularity with the phase jump of π or an odd multiple of π, which the coherent light exhibits in the transverse direction, results in the destructive superposition of components of the coherent light that are backscattered from both sides of the phase singularity on the point or line detector, which will be referred to as the "detector" without distinction between point and line detectors. The same applies to components of the coherent light reflected on both sides of the phase singularity. Furthermore, since the light intensity distribution of the coherent light is symmetrical to the phase singularity, if the corresponding scattering centers and reflectors on both sides of the phase singularity are homogeneous or at least equally distributed, the backscattered or reflected components of the coherent light originating from both sides of the phase singularity cancel each other out on the detector.In this way, the signal background, i.e. the intensity of the backscattered or reflected light on the detector, is ideally reduced to zero.

[0013] The light-scattering measurement object causes an uneven distribution of the light scattered from both sides of the phase singularity when scanning in the transverse direction. However, this uneven distribution does not occur when the phase singularity coincides with the centroid of the scattering cross section of the light-scattering measurement object or a light-scattering feature of the light-scattering measurement object, but rather when this centroid, and in particular when the entire light-scattering measurement object or the entire light-scattering feature of the light-scattering measurement object lies on one side of the phase singularity in the transverse direction. The light-scattering measurement object or the light-scattering feature of the light-scattering measurement object therefore leads to a measurement signal that temporarily becomes zero when the centroid of its scattering cross section and the phase singularity coincide in the transverse direction.

[0014] In practice, the course of the measurement signal over the positions of the phase singularity in the transverse direction can be overlaid with noise because the scattering centers and reflectors on either side of the phase singularity are not evenly distributed. However, this noise can be estimated based on the intensity of the light registered by the detector when the scattering cross section of the light-scattering measurement object and the phase singularity coincide. This allows a correction of the intensity of the registered light. Often, however, even without such a correction, the value of the measurement variable of the measurement object in the transverse direction can be successfully deduced from the course of the intensity of the registered portion of the backscattered light over the positions of the phase singularity in the transverse direction by comparing it with comparison curves for known values ​​of the measurement variable of comparison objects in the transverse direction.A corresponding evaluation routine can be trained using machine learning.

[0015] The phase singularity with the light intensity distribution symmetrical to the phase singularity can be realized in a fundamentally known manner by forming a light intensity distribution of the coherent light with a central zero in the focal plane. For this purpose, the phase fronts of the coherent light are provided with a corresponding phase shift before focusing. Specific examples of this are known to those skilled in the art from the field of STED fluorescence light microscopy for shaping the intensity distribution of the STED light or from MINFLUX fluorescence light microscopy for shaping the intensity distribution of the excitation light, each with a central zero. As a rule, the phase singularity therefore coincides with a central zero of the intensity distribution of the coherent light in the focal plane.

[0016] In the method according to the invention, a light-sensitive surface of the point or line detector has an extension in the transverse direction of no more than Mλ / 3NA. Here, M is a magnification factor between the focal plane of the objective and the point or line detector; λ is the wavelength of the coherent light; and NA is the numerical aperture of the objective. This numerical aperture NA is equal to nsinα, where n is the refractive index of the optical material between the measurement object and the objective and α is half the aperture angle of the objective. In Airy Units (AU), with 1 AU = 1.22 λ / NA, λ / 3NA is equal to 0.27 AU, i.e., less than 0.30 AU.This very small light-sensitive area of ​​the detector in the transverse direction ensures that the portions of coherent light reaching the detector from scattering centers or reflectors evenly distributed on both sides of the phase singularity are canceled out on the light-sensitive area of ​​the detector by destructive interference. Ideal conditions for this are achieved with an even smaller extension of the light-sensitive area of ​​the detector in the transverse direction of no more than Mλ / 4NA equal to 0.20 AU, no more than Mλ / 5NA equal to 0.16 AU, no more than Mλ / 6NA equal to 0.14 AU, no more than Mλ / 7NA equal to 0.12 AU, or no more than Mλ / 8NA equal to 0.10 AU. However, as the area of ​​the detector decreases, so does the number of registered photons. This effect can be compensated for by increasing the intensity of the coherent light over large intensity ranges.However, it is usually not practical to choose the extension of the light-sensitive area of ​​the detector in the transverse direction smaller than Mλ / 16NA, i.e. smaller than 0.05 AU, or even smaller than Mλ / 32NA, i.e. smaller than 0.025 AU.

[0017] In the method according to the invention, at least one additional portion of the light scattered counter to the illumination direction can be registered with at least one additional point or line detector arranged confocally to a region of the focal plane. This region of the focal plane can be the phase singularity.

[0018] A light-sensitive area of ​​the at least one further point or line detector can have an extension in the transverse direction that is at least 1.5 times as large as the extension of the light-sensitive area of ​​the detector in the transverse direction. Preferably, the extension of the light-sensitive area of ​​the further detector in the transverse direction is at least 2 times as large, more preferably at least 3 times as large, and even more preferably at least 4 times as large, at least 5 times as large, or at least 6 times as large as the extension of the light-sensitive area of ​​the detector in the transverse direction. In absolute terms, the extension of the further point or line detector in the transverse direction is typically no more than 3 Mλ / NA and preferably no more than 2 Mλ / NA.The light-sensitive area thus has an extension in the transverse direction that corresponds to or is smaller than that of a typical confocally arranged pinhole in confocal scanning fluorescence light microscopy.

[0019] The additional detector detects more light from the regions of the light intensity distribution of the coherent light in the focal plane adjacent to the phase singularity on both sides. This light can contain additional information about the measurement parameter of interest on the measurement object. If the additional detector is arranged confocally to a sub-region of an intensity maximum of the intensity distribution of the coherent light adjacent to the phase singularity in the focal plane in the transverse direction, the additional detector can detect this light, in particular selectively, even if its light-sensitive area is no larger than the light-sensitive area of ​​the detector arranged confocally to the phase singularity. In a preferred embodiment, two additional detectors are arranged confocally to sub-regions of the focal plane on both sides of the phase singularity.

[0020] When inferring the value of the measured quantity, the intensity profile of the recorded component can be compared with the intensity profile of at least one other recorded component of the coherent light. Alternatively or additionally, the intensity profile of the at least one other recorded component can be taken into account when comparing with comparison profiles for known values ​​of the measured quantity of comparison objects. For this purpose, additional comparison profiles for the known values ​​of the measured quantity of the comparison objects are preferably stored.

[0021] In the method according to the invention, each point or line detector can be formed using a pinhole or slit aperture and / or with a small number of pixels of an image sensor array. The small number of pixels of the image sensor array preferably comprises no more than 21, and even more preferably no more than 7, nearest adjacent pixels for a point detector and pixels in no more than 5 nearest adjacent rows of pixels, preferably in no more than 3 nearest adjacent rows of pixels for a line detector. However, it is particularly preferred if the light-sensitive area of ​​the detector is defined by a pinhole or slit aperture.

[0022] In the method according to the invention, the light can be polarized before focusing; and the portion of the light scattered back against the direction of illumination can be recorded using polarization-selective methods. In this way, in a generally known manner, the light scattered by the measurement object can be separated from light that was not scattered at scattering centers in a polarization-preserving manner, but was reflected by reflectors with changes in polarization.

[0023] In one embodiment of the method according to the invention, the coherent light has at least a first component of a first wavelength and a second component of a second wavelength, wherein the second wavelength differs from the first wavelength such that the first component and the second component of the portion of the light scattered back against the direction of illumination can be recorded separately. Using the different components of the light, different values ​​of the measured variable of the measurement object can be determined for different wavelengths of the coherent light. For example, a chromaticity of the measured variable of interest of the measurement object can be determined.

[0024] In the method according to the invention, each wavelength of the coherent light can be selected such that it does not fall within an absorption band of the measurement object and / or does not correspond to a plasma frequency of the measurement object. In an absorption band and at the plasma frequency, the phase of the scattered light can be influenced by the measurement object in a way that impairs the method according to the invention. Two wavelengths of two components of the coherent light can be arranged, preferably at equal spacing, on either side of an absorption band or a plasma frequency of the measurement object.

[0025] In the method according to the invention, the phase singularity can be formed with a line shape running in the direction of illumination or with a sheet shape running in the direction of illumination and the transverse direction. Thus, the method according to the invention can have a considerable depth of field in the direction of illumination. To utilize the depth of field, it can be advantageous to detect the position of the respective measurement object in the direction of illumination using additional method steps that can be based on fundamentally known techniques. The position of the measurement object in the direction of illumination detected in this way can be taken into account when evaluating the curve of the intensity of the recorded portion of the backscattered light over the positions of the phase singularity in the transverse direction.

[0026] In the method according to the invention, the measurement object is preferably scanned at different orientations of the transverse direction with the phase singularity. In this way, the measured variable can be determined for the different spatial directions. Different values ​​of the measured variable in the different spatial directions occur for all measurement objects that are not rotationally symmetrical to a rotation axis running parallel to the illumination direction.

[0027] As already mentioned, the measurement object can be a nanoscale particle, where the measurand is the extension of the nanoscale particle in the transverse direction. In this case, a center of gravity position of the nanoscale particle in the transverse direction can be determined as the position at which the intensity profile of the recorded portion of the backscattered light exhibits a local minimum and, preferably, a zero. The local minimum occurs precisely when the scattered light originates equally from both sides of the phase singularity.

[0028] Specifically, the nanoscale particle can be arranged on a surface that has a lower refractive index than the nanoscale particle, or the nanoscale particle can be dispersed in a liquid that has a lower refractive index than the nanoscale particle. The smaller refractive index of the surface or the liquid creates a refractive index difference between the nanoscale particle and its surroundings, which is a prerequisite for the scattering of light. In the method according to the invention, the particle is nanoscale in the sense that it actually scatters the coherent light, i.e., so small that Rayleigh scattering occurs. For this to happen, the nanoscale particle must be small compared to the wavelength λ of the coherent light.

[0029] In an alternative embodiment of the method according to the invention, the measurement object is a surface, and the measured variable is a nanoscale structuring of the surface in the transverse direction. Values ​​of interest for this measured variable can be spatial frequencies of the structuring in the transverse direction.

[0030] Advantageous further developments of the invention emerge from the patent claims, the description and the drawings.

[0031] The advantages of features and combinations of several features mentioned in the description are merely exemplary and can be used alternatively or cumulatively without the advantages necessarily having to be achieved by embodiments according to the invention.

[0032] With regard to the disclosure content – ​​not the scope of protection – of the original application documents and the patent, the following applies: Further features can be found in the drawings – in particular the illustrated geometries and the relative dimensions of several components to one another, as well as their relative arrangement and operative connection. The combination of features of different embodiments of the invention or features of different patent claims is also possible, deviating from the selected references of the patent claims, and is hereby suggested. This also applies to features that are illustrated in separate drawings or mentioned in their description. These features can also be combined with features of different patent claims.Likewise, features listed in the patent claims may be omitted for further embodiments of the invention, but this does not apply to the independent patent claims of the granted patent.

[0033] The number of features mentioned in the patent claims and the description is to be understood as meaning that exactly this number or a greater number than the stated number is present, without the need for the explicit use of the adverb "at least." Thus, for example, if reference is made to one detector, this is to be understood as meaning that exactly one detector, two detectors, or more detectors are present. The features mentioned in the patent claims may be supplemented by further features or may be the only features present in the subject matter of the respective patent claim.

[0034] The reference signs contained in the patent claims do not represent a limitation of the scope of the subject-matter protected by the patent claims. They serve only the purpose of making the patent claims easier to understand. BRIEF DESCRIPTION OF THE CHARACTERS

[0035] In the following, the invention is further explained and described with reference to preferred embodiments shown in the figures. Fig. 1 shows various plots of an interference pattern of coherent light generated in a focal plane of an objective when carrying out the method according to the invention. Fig. 1A shows, looking towards the focal plane, a linear zero point and, in a transverse direction, first-order intensity maxima adjacent to it on both sides and second-order intensity maxima following on both sides. Fig. Figure 1B shows the distribution of the intensity of the coherent light in a section through the focal plane along the transverse direction. Fig. 1C shows the intensity distribution according to Fig. 1B corresponding amplitude distribution of the electric field of the coherent light and Fig. 1D the corresponding phases. Fig. Figure 1E shows the relative position of a confocal detector to a central phase singularity in the transverse direction. Fig. 2 shows two curves of intensities of coherent light components according to Fig. 1, which is scattered back by two differently sized light-scattering particles and detected by the confocal detector according to Fig. 1 when scanning the respective light-scattering particle with the phase singularity according to Fig. 1 must be registered. Fig. 3 shows schematically the structure of a confocal scanning light microscope for carrying out the method according to the invention. Fig. 4 shows details of another embodiment of the method according to the invention. Fig. Figure 4A shows two partial beams of coherent light directed side by side into an entrance pupil of the objective and having a phase shift of π. Fig. Figure 4B shows the resulting distribution of the amplitude of the coherent light in the focal plane of the lens along the transverse direction, this distribution Fig. 1C; and Fig. Figure 4C shows the relative arrangement of three confocal detectors to the distribution according to Fig. 4B. FIGURE DESCRIPTION

[0036] The Fig. 1A to Fig. The interference pattern 10 of coherent light in a focal plane of a lens focusing the coherent light, illustrated in different aspects in Figure 1D, is also called the “bun mode” due to the shape of its intensity maxima 2 that border a line-shaped zero point 1 on both sides. Fig. 1A and Fig. 1B, which describe the intensity distribution of the coherent light in the focal plane and along the transverse direction x to the line-shaped zero point 1, unlike the representation of the amplitude A of the electric field of the light according to Fig. 1C that the sign of the amplitude, "-" or "+", is reversed in zero 1, which is a zero-order zero, and also in zero 2 between the first-order maxima 2 and the second-order maxima 4 following in the transverse direction x. This results in the phase distribution according to Fig. 1D with a phase singularity 5 in the form of a phase jump of π or an odd multiple of π in the zero 1. For this phase singularity 5, the light intensity distribution is according to Fig. 1A and Fig. 1B in the transverse direction x, symmetrical. Light scattered back from the focal plane from both sides of the phase singularity 5 is superimposed due to the phase jump on a Fig. 1E destructively interferes with the detector 6 arranged confocally to the phase singularity 5. The same applies to light reflected back from the focal plane from both sides of the phase singularity 5. If the corresponding scattering centers that backscatter the light, or reflectors that backreflect the light, are equally distributed on both sides of the phase singularity 5 in the focal plane, this destructive superposition leads to an extinction of the scattered light and the reflected light on the detector 6. However, if the uniform distribution of the scattering or reflection is disturbed by a light-scattering particle in the region of the interference pattern of the coherent light, the detector 6 registers a measurement signal in the form of the intensity of the non-extinguished light.If the light-scattering particle with the phase singularity 5 is scanned in the transverse direction x, the resulting course of the intensity of the backscattered portion of the light registered by the detector 6 depends on the extension of the particle in the transverse direction x. In . Fig. 1E, the detector 6 is illustrated as a photon multiplier tube (PMT) 7 with a pinhole 8 having an aperture 9 in front of it. The aperture 9 is arranged confocally to the phase singularity 5, and its size determines the light-sensitive area of ​​the detector 6. The extent of this light-sensitive area 6 in the transverse direction x is comparatively small, at no more than Mλ / 4NA and preferably no more than Mλ / 6NA, in order to effect the explained extinction of backscattering of light evenly distributed around the phase singularity 5. M is the magnification between the focal plane of the objective and the detector 6, λ is the wavelength of the light, and NA is the numerical aperture of the objective.

[0037] Fig. 2 shows two curves 11 and 12 of the intensity I registered by the detector 6 Regof the portion of light scattered back by two differently sized light-scattering particles when they are each scanned by the phase singularity 5 in the transverse direction x. If the phase singularity 5 coincides with a center of gravity position P of the respective particle, the respective curve 11 or 12 has a zero point, because the light scattered back by the respective particle 11 and incident on the detector 6 then originates equally from both sides of the phase singularity 5 and is thus canceled out on the detector 6. However, as soon as the respective particle is located predominantly or entirely on one side of the singularity 5 in the transverse direction x, this cancellation does not occur, and with the detector 6, an increasing intensity I Regwhich then drops again when the respective light-scattering particle reaches the area of ​​one of the first-order zeros 3. From the respective curves 11 and 12, conclusions can be drawn about the size of the respective light-scattering particle from which the light is scattered. These conclusions can be drawn practically by comparing curves 11 and 12 with reference curves that were recorded for particles of known size. The assignment of the size to the respective curves 11 and 12 can be carried out by a Kl algorithm that was trained with the help of the reference curves within the framework of so-called machine learning. Fig. The curves 11 and 12 shown in Figure 2 are to be understood schematically and do not have to correspond in every detail to the real curves of the intensities I recorded by the detector 6 Reg are equivalent to.

[0038] Fig. Figure 3 shows a confocal scanning light microscope 13 with which the method according to the invention can be carried out. The coherent light 14 is provided by a laser 15 and expanded into an expanded, collimated beam 17 by an only partially illustrated expansion optics 16. The phase fronts of the expanded, collimated beam 17 are modulated by a phase plate 18, which imposes a phase shift of π on the phase fronts, halving the beam cross-section. The light enters an entrance pupil of the objective 20 through a beam splitter 19, which focuses the light in one illumination direction into its focal plane 21. The interference pattern 10 with the central phase singularity 5 is formed in the focal plane 21. Fig. 3 is according to Fig. 1C, the amplitude A of the light in the focal plane 21 is plotted over the transverse direction x. A portion 22 of the light scattered back against the direction of illumination passes through the lens 20, via the beam splitter 19 and through a focusing optics 23 on the detector 6 with the pinhole 8, whose aperture 9 is arranged confocally to the phase singularity 5 in the focal plane 21. In Fig. 3, a scanner of the scanning light microscope, with which a light-scattering particle with the phase singularity 5 is scanned in the transverse direction x, is not shown. Such a scanner can be an optical scanner arranged in the beam path between the beam splitter 19 and the objective 20, thus also descanning the backscattered light. Alternatively or additionally, the scanner can be a mechanical scanner that moves a sample with the particle relative to the objective 20. Furthermore, the beam splitter can be a polarization beam splitter, or the light focused into the focal plane 21 by the objective 20 can be polarized in another way, with the backscattered portion 22 of the light being registered in a polarization-selective manner.A polarization beam splitter can be combined in a generally known manner with a λ / 4 plate in the beam path between the polarization beam splitter and the objective 20, wherein the λ / 4 plate is preferably rotatable about the beam axis. By polarized coherent light 14 and polarization-selective registration of its backscattered portion 22, the light backscattered by the particle of interest can be separated from light reflected from the particle's surroundings if the latter undergoes a polarization change upon reflection.

[0039] Fig. Figure 4A shows the entrance pupil 24 of the objective 20, into which two partial beams 25 and 26 of the coherent light 14 are directed, which have a phase shift of π from each other. This also results in an interference pattern with a central intensity zero 1, at which the phase singularity 5 with the phase jump of π occurs, and with adjacent first-order intensity maxima 2, as well as following first-order intensity zeros 3 and second-order intensity maxima 4. Fig. Figure 4B shows the corresponding distribution of the amplitude A of the electric field of the light 14 plotted against the transverse direction x. Fig.4C shows, in addition to detector 6, whose pinhole 8 has the aperture 9 arranged confocally to the phase singularity 5, two further detectors 27 with photon multiplier tubes 28 and pinhole diaphragms 29, whose apertures 30 are each arranged confocally to a partial region of one of the first-order intensity maxima 2. Furthermore, the apertures 30 are significantly larger than the aperture 9. The further detectors 27 register additional portions of the light backscattered by a light-scattering particle when scanning the particle with the phase singularity 5. This results in additional information for determining the size of the particle. The light-scattering particles, whose size can be determined using the method according to the invention, are small particles that backscatter the light 14 through Rayleigh scattering, or correspondingly small light-scattering features of a light-scattering surface.In the latter case, the method according to the invention can be used to determine a structuring of the light-scattering surface in the transverse direction, for example with regard to the spatial frequencies of the structuring. LIST OF REFERENCE SYMBOLS 1 Zero-order intensity zero 2 First-order intensity maximum 3 First-order intensity zero 4 Second-order intensity maximum 5 Phase singularity 6 Detector 7 photon multiplier tubes 8 pinhole aperture 9 aperture 10 interference patterns 11 History 12 History 13 confocal scanning light microscope 14 coherent light 15 lasers 16 Expanding optics 17 expanded collimated beam 18 Phase plate 19 beam splitters 20 lens 21 Focal plane 22 backscattered portion 23 Focusing optics 24 Entrance pupil 25 partial beams 26 partial beams 27 additional detectors 28 photon multiplier tubes 29 pinhole 30 aperture I Intensity A Amplitude φ phase angle x transverse direction P Center of gravity position

Claims

[1] Method for measuring a measurand of a light-scattering measuring object, - wherein coherent light (14) from an illumination direction is focused into a focal plane (21) of an objective (20), - that the coherent light (14) is directed in a transverse direction (x) which is transverse to the direction of illumination in the focal plane (21), - a phase singularity (5) with a phase jump of (2m+1)π, where m is an integer, and - has a light intensity distribution symmetrical to the phase singularity (5), - wherein the measurement object is scanned in the transverse direction (x) with the phase singularity (5), - wherein a portion (22) of the light (14) scattered by the measurement object is registered with a point or line detector (6) arranged confocally to the phase singularity (5), wherein the line detector, if present, is adapted to a shape and an orientation of the phase singularity (5) in the focal plane (21), - wherein a curve (11, 12) of the intensity of the registered portion (22) of the backscattered light (14) is evaluated over the positions of the phase singularity (5) in the transverse direction (x), and - whereby the value of the measured variable of the measuring object in the transverse direction (x) is inferred from the course (11, 12) characterized by , - that the portion (22) of the light (14) which is registered by the point or line detector (6) arranged confocally to the phase singularity (5) is scattered back by the measurement object in the opposite direction to the illumination direction, and - that a light-sensitive surface of the point or line detector (6) has an extension in the transverse direction (x) of not more than Mλ / 3NA, where M is a magnification factor between the focal plane (21) of the objective (20) and the point or line detector (6), λ is the wavelength of the light (14) and NA is the numerical aperture of the objective (20). [2] Method according to claim 1, wherein the value of the measured variable of the measurement object in the transverse direction (x) is inferred from the curve (11, 12) by comparison with comparison curves for known values ​​of the measured variable of comparison objects in the transverse direction (x). [3] Method according to one of the preceding claims, wherein the light-sensitive surface of the point or line detector (6) has an extension in the transverse direction (x) of not more than Mλ / 4NA, preferably not more than Mλ / 5NA, more preferably not more than Mλ / 6NA, even more preferably not more than Mλ / 7NA and most preferably not more than Mλ / 8NA. [4] Method according to one of the preceding claims, wherein at least one further portion of the light (14) scattered counter to the illumination direction is registered with at least one further point or line detector (27) arranged confocally to a region of the focal plane (21), wherein a light-sensitive surface of the at least one further point or line detector (27) in the transverse direction (x) has an extent that is at least 1.5 times as large, preferably at least 2 times as large, more preferably at least 3 times as large, even more preferably at least 4 times as large, even more preferably at least 5 times as large, and most preferably at least 6 times as large as the extent of the light-sensitive surface of the point or line detector (6) in the transverse direction (x), and wherein the extent of the further point or line detector (27) in the transverse direction (x) is not more than 3Mλ / NA and preferably not more than 2Mλ / NA,where M is a magnification factor between the focal plane (21) of the objective (20) and the further point or line detector (27), λ is the wavelength of the light (14) and NA is the numerical aperture of the objective (20), wherein the at least one further line detector, if present, is adapted to a shape and an orientation of the phase singularity (5) in the focal plane (21). [5] Method according to one of the preceding claims, wherein at least one further portion of the light (14) scattered counter to the illumination direction is registered with at least one further point or line detector (27) which is arranged confocally to a partial region of an intensity maximum (2) adjacent to the phase singularity (5) in the focal plane (21) in the transverse direction (x), wherein the at least one further line detector, if present, is adapted to a shape and an orientation of the phase singularity (5) in the focal plane (21). [6] Method according to claim 4 or 5, wherein the profile (11, 12) of the intensity of the registered portion is compared with a profile of an intensity of the at least one further registered portion. [7] Method according to one of the preceding claims, wherein each point or line detector (6, 27) with a pinhole (8, 29) or slit diaphragm and / or with a small number of pixels of an image sensor array of preferably no more than 21 nearest neighboring pixels for a point detector and in preferably no more than five nearest adjacent rows of pixels in a line detector. [8] Method according to one of the preceding claims, wherein the light (14) is polarized before focusing and the portion (22) of the light (14) scattered back against the direction of illumination is registered in a polarization-selective manner. [9] Method according to one of the preceding claims, wherein the light (14) has at least a first component of a first wavelength and a second component of a second wavelength, wherein the first component and the second component of the portion (22) of the light (14) scattered back against the direction of illumination are registered separately. [10] Method according to one of the preceding claims, wherein the phase singularity (5) is formed with a line shape running in the illumination direction or a sheet shape running in the illumination direction and the transverse direction (x). [11] Method according to one of the preceding claims, wherein the measurement object is scanned under different orientations of the transverse direction (x) in different spatial directions with the phase singularity (5). [12] Method according to one of the preceding claims, wherein the measurement object is a nanoscale particle and the measurement variable is an extension of the nanoscale particle in the transverse direction (x). [13] Method according to one of the preceding claims, wherein a center of gravity position (P) of the nanoscale particle in the transverse direction (x) is determined as the position at which the profile (11, 12) of the intensity of the registered portion (22) of the backscattered light (14) has a local minimum and preferably a zero point. [14] Method according to claim 12 or 13, wherein the nanoscale particle - is arranged on a surface that has a smaller refractive index than the nanoscale particle, or - is dispersed in a liquid that has a smaller refractive index than the nanoscale particle. [15] Method according to one of claims 1 to 11, wherein the measurement object is a surface and the measurement variable is a nanoscale structuring of the surface in the transverse direction (x).

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