WO2025029181A1

WO2025029181A1 - A method of performing a fluorescence measurement, a controller and an apparatus

Info

Publication number: WO2025029181A1
Application number: PCT/SE2024/050704
Authority: WO
Inventors: Petter SÄTERSKOG
Original assignee: Ciprocity Ab
Priority date: 2023-07-28
Filing date: 2024-07-25
Publication date: 2025-02-06
Also published as: SE2350932A1

Abstract

A method of performing a fluorescence measurement comprising: exposing a sample to excitation light focussed to an excitation focus under illumination parameters wherein the sample comprises a fluorescent marker and the illumination parameters of the excitation light are configured to cause a non-linear fluorescence response measured by a detector focussed on a detection focus, where the non-linear fluorescence response is due to one or more of bleaching, saturation and stimulated emission; measuring a first response of the fluorescent marker to the exposure by the excitation light; measuring a second response to the exposure by the excitation light; wherein the method further comprises one or more of: modelling fluorescence saturation, bleaching and stimulated emission at the focus based on the measured first response and the measured second response; based on the one or more modelled non- linear effects, calculating a transmittance of excitation light through the sample to the focus.

Description

A METHOD OF PERFORMING A FLUORESCENCE MEASUREMENT, A CONTROLLER AND AN APPARATUS Field The present invention relates to the field of fluorescence measurements. More particularly, the present invention relates to a method for accounting for one or both of scattering and absorption of light by harnessing non-linearities of a fluorescence response. The invention also relates to a controller configured to cause an apparatus to carry out the method and a microscope configured to carry out the method. Background Fluorescence measurements, especially in microscopy, is a powerful tool for observing specific molecules. For example, fluorescence microscopy or a fluorometer can be used to observe target fluorescent samples or samples which have been stained with a fluorescent marker. For example, a fluorometer can be used to measure chlorophyll fluorescence in leaves of a plant. This can be performed by illuminating a fluorescent target with excitation light and then observing the fluorescent light re-emitted by the target. One limitation of fluorescence measurements, however, is that scattering and absorption of light between a focussing lens and a focus within the sample makes quantitative measurements of an observed fluorophore concentration impossible. The same scattering and absorption between the focussing lens and the focus makes it difficult to qualitatively understand microscopy images by eye, as images resulting from microscopy images are distorted by the scattering and absorption. Microscopy images, therefore, can often appear to not have the contrast that should be observed, making them difficult to interpret. Summary According to a first aspect of the present disclosure, there is provided a method of performing a fluorescence measurement comprising: exposing a sample to excitation light focussed to an excitation focus under illumination parameters wherein the sample comprises a fluorescent marker and the illumination parameters of the excitation light are configured to cause a non-linear fluorescence response measured by a detector focussed on a detection focus wherein the detection focus and the excitation focus are the same focus, where the non-linear fluorescence response is due to one or more of bleaching, saturation and stimulated emission of the fluorescent marker; measuring a first response of the fluorescent marker to the exposure by the excitation light; measuring a second response of the fluorescent marker to the exposure by the excitation light; wherein the method further comprises one or more of: modelling fluorescence saturation at the focus based on the measured first response and the measured second response; modelling bleaching of the fluorescent marker at the focus based on the measured first response and the measured second response; and modelling stimulated emission of the fluorescent marker at the focus based on the measured first response and the measured second response; based on the one or more modelled non-linear effects, calculating a transmittance of excitation light through the sample to the focus. In one or more embodiments, the method may also comprise: arranging excitation optics and detection optics such that the path of excitation light through the sample to the focus is substantially the same as the path of detection light from the focus through the sample wherein the excitation optics define the path of light through the sample to the focus and the detection optics define the light from the sample which the detector is able to detect; using the reciprocity of light to calculate the transmittance of detection light from the focus, through the sample, based on the calculated transmittance of excitation light through the sample, towards the focus. In one or more embodiments, the method may also comprise estimating a fluorescent marker concentration of the sample based on the measured responses and the calculated transmittances of detection light from the focus, through the sample. In one or more embodiments, the fluorescence measurement may be performed in a confocal microscope. In one or more embodiments, the second response may be measured at a time after the measurement of the first response. In one or more embodiments, the measured first response of the fluorescent marker to the exposure by the excitation light may be a measure of one of a first harmonic or a higher order harmonic of a modulated light source. In one or more embodiments, the measured second response of the fluorescent marker to the exposure by the excitation light may be a different harmonic to the harmonic measured for the first response. In one or more embodiments, the measured first response and the second response may be measured simultaneously. In one or more embodiments, exposing the sample to the excitation light under illumination parameters may comprise exposing the sample to the excitation light under a first set of illumination parameters and subsequently exposing the sample to the excitation light under a second set of illumination parameters. In one or more embodiments, the step of measuring the first response of the fluorescent marker to the exposure by the excitation light may occur simultaneously with initiation of exposure of the sample to the excitation light under the first set of illumination parameters but before the exposure by the excitation light under the second set of illumination parameters; and the step of measuring the second response of the fluorescent marker to the exposure by the excitation light may occur simultaneously with initiation of exposure of the sample to the excitation light under the second set of illumination parameters. In one or more embodiments, the illumination parameters of the first and second measurements may be chosen to result in different degrees of one or more of: fluorescence saturation at the focus; bleaching at the focus; and stimulated emission at the focus. In one or more embodiments, the excitation light and detection light may be focussed through a same focussing lens. In one or more embodiments, the excitation light and detection light may be combined using a beam splitter. According to a second aspect of the present disclosure, there is provided a controller for an apparatus in communication with the apparatus configured to cause the apparatus to perform the method of the first aspect. According to a third aspect of the present disclosure, there is provided a microscope comprising the controller of the second aspect. Brief Description of the Drawings One or more embodiments will now be described by way of example only with reference to the accompanying drawings in which: Figure 1 shows an example embodiment of a confocal microscope with the excitation light beam indicated according to one or more embodiments of the present disclosure; Figure 2 shows an example embodiment of a confocal microscope with the light rays reaching the detector indicated according to one or more embodiments of the present disclosure; Figure 3 shows a method according to the present disclosure; Figure 4 shows an uncorrected microscopy image; Figure 5 shows a corrected microscopy image which demonstrates the results of the disclosed method; and Figure 6 shows an example system comprising a controller and a microscope according to one or more embodiments of the present disclosure. Detailed Description The present disclosure provides a method of performing one or more fluorescence measurements which accounts for the scattering and absorption within the sample by harnessing the non-linearities of a fluorescence response. Such scattering and absorption are particular problems in confocal microscopy imaging of 3D samples where the target focus is not at the surface of the sample. In the present disclosure, the sample will generally be a 3D sample and the focus may be located at a position within the sample, rather than at the surface of the sample. The scattering and absorption may also be a problem in other types of fluorescence measurements other than only confocal microscopy. The detector response is typically linear in the excitation light intensity for short, low intensity, exposures. This means that exposing with the summed light intensities of several exposures should yield a detector response that is the sum of the detector responses that would be obtained by the individual exposures. This is not always true, however, due to fluorophore bleaching, fluorescence saturation, stimulated emission and other non-linear effects. In the present disclosure, bleaching, saturation and stimulated emission will be discussed as specific examples of non-linear effects, however, it will be appreciated that other mechanisms of non-linear fluorescence response may be induced, modelled and used in the calculation of a transmission of excitation light through the sample to the focus. By measuring non-linearities, it is possible to obtain additional information that is not accessible when measuring a linear response. Saturation, bleaching and other non- linear interactions between excitation light and a fluorescent marker depend on the local intensity of light at the fluorescent marker (such as a fluorophore). It has been found that by measuring the strength of these non-linear effects, and modelling the mechanism of the non-linear response, it is possible to model the light intensity at the focus. The strength of the non-linear effects is obtained by taking at least two detector readings, at e.g. two different exposure intensities, after different amounts of total exposure, with different exposure times, at different harmonics of a modulated excitation light. From the model of the light intensity at the focus, it is possible to obtain the transmittance of excitation light through the sample to the focus. This transmittance captures what fraction of excitation light makes it through the sample to the focus, i.e. is not lost due to scattering or absorption. It has also been found that, by arranging the detector to be focussed on the same focus as the exciting light source and arranging it so the excitation and detection light takes the same light paths through the sample at similar wavelengths (as is the case in confocal microscopy), we may use the reciprocity of light (a principle that states invariance under exchange of sources and detectors) to estimate the transmittance of emitted light from the focus to the detector given the transmittance from the excitation light to the focus. Knowing both transmittances allows for quantification of fluorescent marker concentrations from the linear part of the response despite absorption and scattering of excitation and emission light. Doing this for each pixel in microscopy images, for example, allows for the correction of transmittance variations across an image, between different depths of a 3D sample, and between different 3D samples. By performing these steps and proper calibration of all components, it is possible to obtain fluorescent marker concentrations in molecules/μm³, allowing for quantitative comparison of concentrations between different samples, objectives and microscopes. In the present disclosure, a cartesian co-ordinate system is used where z is a depth into the sample increasing along the excitation beam path towards the focus. x and y are two directions orthogonal to each other and z. It will be appreciated that these co- ordinate systems and assumptions are used for ease of reference but are in no way intended to limit the disclosure. The reader will appreciate that alternative co-ordinate systems, nomenclatures and assumptions can be made without departing from the scope of the disclosure. Figure 1 shows an example embodiment of a confocal microscope 100 with excitation light rays indicated. A confocal microscope will be used as an exemplary form of measurement apparatus in the present disclosure, however, it will be appreciated that other measurements of fluorescence may make use of the same method as disclosed herein in order to obtain one or more benefits described herein. For example, the method may be applied in one or more of light sheet microscopy, multi-photon microscopy, or another form of microscopy, or fluorescence sensors such as fluorometers, microfluorometers, spectrofluorometers, x-ray fluorescence spectrometer, or other devices that use confocal excitation and detection optics for measuring fluorescence. In microscopy or other fluorescence measurements, a sample 101 may be received at a sample stage. A stage may be a typical sample stage in a microscope 100. It will also be appreciated, however, that the term stage here is used to refer to the location at which the sample must be placed for measurements to be performed on it. As such, industrial-scale systems may use a conveyor belt which moves samples 101 into the correct location for measurement or other means for placing a sample 101 in a desired location may be used. Hand-held devices may require placing the device such that the stage is in front of the leaf of a plant. In any case, the location at which the sample 101 is located relative to the apparatus 100 for measurement is considered to be the stage for the purposes of the present disclosure. The apparatus may be, for example, a microscope such as a confocal microscope. In the case of 3D samples, the sample 101 may be, for example, spheroids made up of cells, organoids or another 3D tissues sample. In other examples, the samples 101 need not necessarily be tissue samples at all but a different type of sample such as a part of a living organism such as a leaf, a single cell, a mineral sample, an electronic device, a colony of bacteria or fungi. The sample comprises a fluorescent marker. In the present detailed description, the sample 101 may be referred to as being fluorescent itself, however, this does not necessarily need to be the case and is described in this way for easy of description. In other examples, the sample 101 itself may be fluorescent or have a fluorescent component to it. In other examples, the sample 101 may be stained with a fluorescent marker or may have a fluorescent marker applied to it in some other manner. The method according to the present disclosure may comprise a step of staining the sample 101 with a fluorescent marker prior to or after receiving the sample 101 at the sample stage. The method may further comprise one or more additional sample preparation steps such as clearing the sample with a clearing agent to make the sample transparent or substantially transparent. Prior to exposing a sample 101 to the excitation light source 102 in the microscope 100, the method of the present disclosure may require a step of setting one or more illumination parameters to appropriate parameters for exciting, bleaching or stimulating emission of the selected fluorescent marker. It should be recognised that light does not only refer to visible light but electromagnetic radiation in general. The present disclosure may be applied to, for example, infrared light, visible light, ultraviolet light or x-ray radiation. The excitation light source may be a laser, a light emitting diode, an X-ray tube, another generator of photons, or a combination of generators of photons. It should also be recognized that while the light the sample is exposed to is referred to as excitation light herein, it may have purposes other than exciting the fluorescent marker, such as causing a non-linear response by way of bleaching or stimulating emission. In particular, as will be described further below, the illumination parameters are configured to cause the one or more of saturation, stimulated emission, and bleaching of the fluorescent marker. The method may further comprise setting one or more detection parameters of the detector 103. For example, a gain of the detector 103 may need to be set or an interval of wavelengths at which to perform detection. In one or more embodiments, it may be desirable to select a detection wavelength that is substantially similar to, but still distinct from, the excitation wavelength of the excitation light 102. In one or more embodiments, the detection wavelength may be within 1%, 5%, 10% or 20% of the wavelength of the excitation light. In one or more embodiments, the detection wavelength may be within 10, 50, 100 or 150 nanometres from the excitation wavelength. The detector 103 may be a photomultiplier tube or any other appropriate photon detector suitable for detecting the photons emitted by the fluorescent marker. Figures 1 and 2 provide a depiction of confocal microscopy by way of example and the following description introduces some of the concepts and assumptions according to the present disclosure in the context of confocal microscopy. Full details of the method according to the present disclosure will be provided after the following general introduction to confocal microscopy. As shown in figure 1, confocal microscopy begins with excitation of a fluorescent marker of the sample 101 by an excitation light source 102 using a set of illumination parameters of the light source. In one or more embodiments, the beam emitted by the excitation light source 102 is directed at a beam splitter 104 which directs the incident beam towards a focussing lens 105 configured to focus the light at a target region 106. The beam splitter 104, which may be, for example, a dichroic mirror or a semi- transparent mirror, may be configured to be able to selectively reflect incident photons within a predetermined wavelength range and to allow photons not within the predetermined wavelength range to be transmitted therethrough. In the case of a confocal microscope 100, this allows the excitation light to be reflected for direction towards the sample 101 while emitted fluorescent light from the sample 101 is able to pass through the beam splitter 104 towards the detector 103. It will be appreciated that a beam splitter 104 is not an essential element of all fluorescence measurement systems and alternative arrangements not utilising a beam splitter 104 are possible. The focussing lens 105 is used to focus the excitation light towards a focus 106. While the focussing lens 105 focusses the light beam on the focus 106, the focussing lens cannot focus the light beam onto an exact discrete point. Instead, it will be appreciated that the focus 106 may be defined as the volume around which the light beam is focussed over its narrowest area before the beam begins to diverge again. This may, for example, alternatively be referred to as a focal region or focal volume. This focus may extend, for example, one, two, five or ten wavelengths from an "idealised" or calculated focus position. Indeed, there cannot be a finite precise focus point because the diffraction limit requires, at absolute minimum, that the extent of the focus is defined by the wavelength of the excitation light. While the focussing lens 105 focusses excitation light towards the intended focus 106, excitation light may be aberrated by the sample before reaching the focus 106 which results in a larger volume where the beam reaches its narrowest area than if the beam were not aberrated by the sample. By the focus 106, we refer to the volume around the narrowest area of the unaberrated beam. The distribution of the excitation light intensity in the focus may be described by the excitation point spread function (PSF). The focussing lens 105 may be an excitation focussing lens and may form part of a larger set of focussing optics. The focus 106 to which the excitation focussing lens 105 focusses the excitation light may be referred to as the excitation focus. As the excitation light impacts the sample 101, several possible interactions occur. Scattering of incident photons by the sample 101 are possible, causing the scattered photons to be sent in a different direction at the same or substantially the same wavelength. Photons may also be lost due to absorption by the sample before reaching the focus. Scattering and absorption decreases the number of excitation photons that arrive at the focus. Figure 2 shows the path taken by detection photons received at the detector 100. Detection photons are defined herein as those photons which are emitted in a direction that the detection optics lead to the detector. These are a subset of all of the photons that are emitted by the fluorescent marker, as the fluorescent marker will emit photons equally in all directions for isotropic materials. The majority of fluorescence emission that contribute to a detector response, occurs in the focus. Fluorescence emission photons are emitted in random directions, however, the path taken by photons that can be detected by the detector 103 is shown in figure 2. These photons take substantially the reverse path taken by the excitation photons through the sample. In the case of confocal microscopy, the detection photons continue on the reverse path of the excitation photons up to the beam splitter 104 and are there able to pass through and into the detector 103. The detector has a response that is focussed to the same focus as the excitation light. That is, the detection optics of the system are arranged such that photons originating from the focus that impinge upon the detection optics are directed towards the detector. The focus of the detector is similarly not a single point but a volume and the sensitivities of the detector to different points in space may be described by a detection PSF. As in the case of the excitation photons, detection photons can also be scattered and absorbed through the bulk of a 3D sample. Extinction of excitation and fluorescence photons is one of the primary reasons why quantitative detection cannot be performed during microscopy and why images often end up distorted, particularly within the bulk of a 3D sample. The detection optics may comprise a detection focussing lens which receives the detection light from the focus and directs it towards the detector. In a reciprocal manner, the detector may equally be described as being focussed by the detection focussing lens on the focus within the sample. The volume or region at which the detector is focussed may be referred to as the detection focus. The detection focus coincides with the excitation focus and, in particular, the detection focus may be defined over substantially the same volume as the excitation focus. Figure 3 shows an example embodiment of a method 300 according to the present disclosure. The following description shall explain the method and provide examples in the context of the above-described confocal microscopy. The method 300 may comprise receiving a sample 101 comprising a fluorescent marker at a stage of the microscope, as described above. The method may further comprise setting one or more detection parameters of the detector 103. For example, a gain of the detector 103 may need to be set or an interval of wavelengths at which to perform detection. Prior to exposing the sample 101 to the excitation photons 102, illumination parameters of the excitation light may be set. The illumination parameters are configured to cause at least one non-linear response in the fluorescent marker by way of the selection of parameters appropriate for the sample. This means that at least one of the responses is affected by fluorescence saturation, bleaching or stimulated emission. The parameters will be any parameters that will induce one or more of bleaching, saturation or stimulated emission in the fluorescent marker such as, a first laser intensity, wavelength, or exposure time. The selected parameters may be sample specific and selected by a user or by the measurement apparatus (which may be a confocal microscope in some examples) itself based on automated detection of the type of fluorescent marker or based on a received input indicative of the type of fluorescent marker. In the case of automated selection, the apparatus may comprise a sample-type detector configured to detect the type of sample located at the sample stage. In one or more embodiments, a plurality of different parameters may be tested prior to acquiring a desired set of parameters that cause the desired non-linear response. It will be appreciated that, in one or more embodiments, it may not be necessary to perform a step of setting the illumination parameters, because these parameters may be pre-programmed or set as default parameters in the microscope or controller that controls the microscope. The illumination parameters of the excitation light 102 prior to taking the first measurement may be a first set of illumination parameters. The method 300 comprises exposing 301 the sample 101 to an excitation light 102 under illumination parameters. At least one set of illumination parameters is configured to cause a non-linear response due to one or more of bleaching, saturation and stimulated emission of the fluorescent marker, as described above. The set of illumination parameters which causes the non-linear response may be the first set of illumination parameters or a second set of illumination parameters. The method may comprise a step of arranging excitation optics and detection optics such that the path of excitation light through the sample to the focus is substantially the same as the path of detection light from the focus through the sample wherein the excitation optics are configured to define the path of light through the sample to the focus and the detection optics are configured to define the light from the sample which the detector is able to detect. The method 300 further comprises measuring 302 a first response of the fluorescent marker to the exposure by the excitation light 102. The method 300 also comprises measuring a second response of the fluorescent marker to the exposure by the excitation light 102. In one or more embodiments, the second response may be measured at a point in time after the first response. For example, the sample 101 will be exposed to the excitation light 102 and either substantially simultaneously with the exposure of the sample to the excitation light 102 or after a delay, the first response may be measured. The second response may be measured either substantially simultaneously with the exposure of the sample to the excitation light 102 or after a second delay from the first response measurement. The first delay and the second delay may be the same or different. In one or more embodiments, the method 300 may comprise a step of exposing the sample to the excitation light under a second set of illumination parameters after measuring the first response of the fluorescent marker to the exposure by the excitation light 102 but before or while measuring the second response of the fluorescent marker to the exposure by the excitation light. The first set of illumination parameters and the second set of illumination parameters may be different (if there is a second set), for example, in the intensity of the excitation light 102. In other examples, the exposure time may be different, the repetition rate of the excitation light, the wavelength, or any other parameter may be different. In one or more examples, the first set of illumination parameters and the second set of illumination parameters may be the same. Using like parameters may be particularly effective for separating out the impact of saturation of the sample compared to bleaching of the sample, as saturation may be expected to be the same across the first measurement and the second measurement whereas bleaching caused by the first, the second, or any additional exposures of the sample 101 to the excitation light, continue to impact the second measurement with the second exposure of the sample to the excitation light 102 compounding the impact of bleaching. Using different excitation wavelengths to selectively excite and stimulate emission allows for measuring the efficiency of stimulation. In one or more alternative embodiments, the first response and the second response may be measured simultaneously and without the exposure of the sample 101 to the excitation light 102 under a second set of illumination parameters. For example, different harmonic components of the response may be measured simultaneously when exposing the samples to a harmonically modulated light source. For example, the fundamental frequency (the first harmonic) may be measured simultaneously with the second or third harmonic. One way to achieve this may be to use a lock-in amplifier, however, alternative implementations may be used to achieve simultaneous measurement of the first response and the second response of the fluorescent marker of the sample to the excitation light. In one or more embodiments, the method may comprise measuring more than two responses of the fluorescent marker to the exposure by the excitation light. For example, the method may comprise measuring at least 3, 5, 10 or 20 responses of the fluorescent marker to the exposure by the excitation light. The additional measurements may provide additional data points which can be used to subsequently obtain more accurate models of the saturation, bleaching or stimulated emission and account for error sources like noise and background signals. Taking multiple measurements of the response of the fluorescent marker to the exposure by the excitation light may make use of a corresponding number of light exposures, as described above with relation to the use of a second exposure of the sample to the excitation light. In other embodiments, more than two different harmonics may be measured simultaneously. In one or more embodiments, more than one wavelength of fluorescence light may be measured simultaneously to separate stimulated and spontaneous emissions. In one or more embodiments, a combination of different harmonic measurements and time-spaced measurements may be performed. The method further comprises one or more of: modelling 304a saturation of the fluorescent marker at a focus of the excitation light 102 based on the measured first response and the measured second response; modelling 304b bleaching of the fluorescent marker at the focus, based on the measured first response and the measured second response; and modelling 304c stimulated emission of the fluorescent marker at the focus, based on the measured first response and the measured second response. It will be appreciated here that the focus of the excitation light will generally be considered to be the focus described above. There may be a plurality of approaches available to model saturation at the focus of the excitation light. For example: saturation may be modelled with a measured or estimated excitation PSF together with a model of the saturation of individual fluorescent marker molecules; saturation may be modelled with an empirically motivated parameterisation of the focus emission rate as a function of the excitation intensity at the focus with parameters found through calibration measurements; or a machine learning model may be trained on known reference samples to output the transmittance given the measured first and second response. Similarly, there may be a plurality of approaches available to model bleaching at the focus of the excitation light. For example, the amount of bleaching may be modelled as being different in different parts of the focus when e.g. imaging a single z-slice in confocal microscopy with well separated foci or when not imaging at all but instead measuring a single fluorescent marker concentration at a single focus. Then a measured or approximated excitation PSF can be used to model the amount of bleaching in the focus, and its effect on the measurements determined using a measured or approximated detection PSF. In another approach, many z slices and overlapping pixels may be imaged repeatedly such that the exposure may be assumed to be uniform, apart from transmittance variations, and any spatial variations in the amount of bleaching are then due to differences in transmittance. Similarly, there may be a plurality of approaches available to model stimulated emission at the focus of the excitation light. For example, the amount of stimulated emission may be modelled as being different in different parts of the focus. Then a measured or approximated excitation PSF can be used to model the amount of stimulated emission in the focus, and its effect on the measurements determined using a measured or approximated detection PSF. By exposing the sample a plurality of times to identical amounts of excitation light but different amounts of stimulation light, the amount of stimulation light that arrives at the focus may be estimated from the different amounts of spontaneous and stimulated fluorescent light that arrives at the detector. The estimated amount of stimulation light arriving at the focus may be used to determine a transmittance through the sample. In an embodiment where several of saturation, bleaching and stimulated emission affect the responses, several of these effects may have to be modelled simultaneously. In modelling either of saturation, bleaching or stimulated emission, it should be recognised that many details of a model may become unimportant once the model is used to fit to detector responses. For example, the shape of the PSF may not be important for calculating expected measurements and a function summarizing the intensity distribution of the PSF may be used instead, as is done in the example embodiment below. A complete example of one approach of how to model saturation and bleaching in order to estimate the transmittance will be provided later in the present disclosure for illustrative purposes. Based on the modelling of one or more of the saturation, the bleaching and the stimulated emission, the method 300 further comprises calculating 305 a transmittance from an objective of the microscope (the focussing lens of the apparatus) to the focus. That is, one or more of the saturation model, the bleaching model and the stimulated emission model, can be used to estimate how many photons are transmitted from the focussing lens of the apparatus to the focus and how many are lost to one or both of scattering and absorption. It should be recognised that some parts of modelling may contain undetermined constants that result in transmittances being undetermined up to an overall constant. The method 300 subsequently comprises, based on the one or more modelled non- linear effects, calculating 306 a transmittance of fluorescence light through the sample from the objective. This may comprise using the reciprocity of light to calculate the transmittance of fluorescence light from the focus to the objective based on the calculated transmittance from the objective to the focus. Reciprocity of light means that light, with a certain wavelength and polarisation state, behaves the same when exchanging sources and detectors. Excitation and fluorescence light have similar but not exactly the same wavelengths which makes the reciprocity approximate. The method may comprise adjusting for this by estimating the error given characteristics of the wavelength dependence of light absorption and scattering in the sample. The method may also comprise using filters on one or both of the excitation light source and the detector to bring the excitation wavelength and the detection wavelength closer to each other to make the approximation of reciprocity more accurate. The filters may comprise part of one or both of the excitation optics and the detection optics. Additionally, the method may comprise one or both of arranging the excitation optics and the detection optics such that the excitation light beams and the detection light are reversed, but similar, in the part of the light paths that go through the sample. This is to allow for using the reciprocity of light to estimate the transmittance of detection light from the transmittance of excitation light. In general, the excitation optics and detection optics may be configured and arranged to ensure that one or more of: the correct light paths are defined for the excitation and detection light; the predefined wavelengths are selected for the excitation and detection light; and predefined polarisations are selected for the excitation and detection light. The light may be unpolarised or polarised, depending on the needs of the measurement in question. A complete example of how to calculate the transmittance from the focus to the detector based on the transmittance from the excitation light to the focus will be provided later in the present disclosure. The method 300 may finally comprise, using the estimated transmittance from the focus (the focal region) to the objective, estimating 307 a concentration of the fluorescent marker at the focus. In other embodiments, the method may alternatively comprise, based on the estimated transmittance from the focus to the objective, estimating and correcting the intensity of a fluorescence image to correct for the effect of scattering and absorption of excitation and detection light through the sample. The method may comprise repeating the steps of the above-described method a plurality of times at a plurality of different positions (x, y, z) through the sample. Repeating the method a plurality of times may allow for an image to be built-up from the individual measurements. The image may be provided as a 2D image if each of the pixels are measured in an (x, y) plane using the same depth, z. In other examples, a 3D image may be determined using different depths, z. In one or more alternative embodiments, the method 300 may not comprise the step of estimating a fluorescent marker concentration. In such embodiments, the method 300 may instead comprise a step of estimating a corrected intensity of an image pixel associated with the position in the sample. This method may then be repeated for a plurality of points throughout the sample in order to build-up a corrected image within the sample. In yet other embodiments, both fluorescent marker concentration estimation and estimating a corrected intensity of an image pixel may be performed. Figure 4 shows an example uncorrected image 400. As can be seen, the interior of the sample appears to be dark because of the increased number of scattering and absorption events that occur for light rays reaching the bulk of the sample. Figure 5 shows an example corrected image 500 which has been corrected using the method of the present disclosure. As can be seen, the interior of the sample does not suffer from the same artificial darkening caused by the scattering and absorption and, instead, provides a more accurate representation of the sample. Figure 6 shows an example controller 601 in communication with a microscope 602. The controller 601 is configured to cause the microscope 602 to perform each of the steps of the method 300. In one or more embodiments, the controller 601 may be remote from the microscope 602 and in one or more alternative embodiments, the controller 601 may form part of the microscope 602. For example, the controller 601 may form part of, or be, a connected computer configured to control the microscope 602. In other examples, the microscope 602 may not require external-control and, instead, may be configured to operate independently and so may comprise the controller 601. Example of an embodiment Without wishing to be bound by theory, the following section provides details relating to an academically more rigorous description of one or more embodiments of the present disclosure. It will be appreciated that, as outlined above, one or more steps of the following derivation may not be necessary in all embodiments but are provided in this description by way of example. The scope of protection is defined by the appended claims. We consider the case of a confocal microscope where a sample is imaged repeatedly at the same z slice, at several different intensities ^_^ of an exciting laser where k labels the different exposures in the order they are taken, k=1,2,3,…. Each detector reading (image) is represented as a count of detected photons at each pixel

where i and j are indices labelling the pixels. We show how the resulting images can be used to calculate a new image that is corrected for scattering and absorption of the excitation light and the fluorescence light. We consider that the sample is stained with a simple fluorophore (or another fluorescent marker) that can be in one of two states, relaxed or excited. When in the relaxed state, it is excited by incoming photons with extinction coefficient ^, i.e. the rate of excitations is ^^ where ^ is the local intensity of excitation light. When in the excited state, it is relaxed at rate ɒ^{ି^} and each relaxation emits a photon with probability ^, the quantum yield. Additionally, we consider that the fluorophore is bleached at rate ^^ regardless of its excitation state. This is an approximation, but it is good enough for low levels of saturation.^Initially, we do not consider bleaching but consider the effects of it in the end. In this example, there is no stimulated emission.^ When illuminated with local intensity ^ we have that the probability ^ that a fluorophore is in the excited state evolves as:

and the expected emission rate per fluorophore ^_^, is given by:

In the setting considered here, the time that a single pixel is exposed to the excitation light is of the order 1 ρ^, while the lifetime ɒ of the fluorophore is of the order 1 ns. A good approximation is thus that the system has reached equilibrium and the emission rate is given by the steady-state value:

where:

. Now consider a confocal microscope arranged as in Fig. 1. We have defined a plane 107A after the dichroic mirror but before the sample, and a plane 107B right before the region the fluorescence response originates from. The exciting laser emits light at intensity ^_^. This light travels through the microscope optics, through the plane 107A, and into the sample, through the plane 107B, and into the focus. The excitation point spread function (PSF) describes the intensity distribution of the exciting light in the focus. Similarly, there is a detection PSF that indicates the detector sensitivity to a fluorescence emission at different points in space. The exact 3D shape of the PSFs depend on the microscope optics (e.g. the excitation and detector pinhole sizes), the objective, and the transmittance of each possible beam path going from the objective to the focus. However, we have found that for the purposes described here, a reasonable approximation is that the shape of the excitation and detection PSFs are independent of the transmittances of individual light rays between the objective and the focus, and only a multiplicative factor is changed as the average transmittance over all light-rays is changed. We label this average transmittance as ^^{^՜^} and write the local intensity around a focus as:

where ɗ_^^^ǡ ^ǡ ^^ is the transmittance independent excitation PSF, ^_^ǡ ^_^ are coordinates of the focus when imaging a pixel at ^ǡ ^. ^_^ is the depth of the focal plane and ^_^ is a constant that depends on the microscope optics but is independent of ^ǡ ^ and the transmittance of the sample. We have put pixel indices on the transmittance as this varies between foci corresponding to different pixels. ^_^ is the intensity of the exciting laser for the excitation ^. Similarly, the density of light that makes it into the detector for a pixel ^ǡ ^ from a single point in space ^ǡ ^ǡ ^ is given by:

where ɗ_ଶ^^ǡ ^ǡ ^^ is the transmittance independent detection PSF and

is the average transmittance from the plane 107B to 107A and ^_ଶ is a constant that depends on the microscope optics but is independent of the pixel indices and the sample transmittance. The local rate of relaxations ^_^^^ǡ ^ǡ ^^ is given by the product of the concentration of fluorophores and their individual emission rates:

where ^^{^}^ǡ ^ǡ ^^{^} is the fluorophore concentration and ^^^ǡ ^ǡ ^^ is the local excitation light intensity. The total amount of light

that makes it into the detector for pixel ^ǡ ^ is obtained by integrating the contributions from the whole sample volume:

Here we have formally integrated over all of 3D space, however, we only need to know the shape of the PSFs near the focus because that is where the dominant contribution to this integral comes from. We will now make another simplifying assumption; we assume the fluorophore concentration to be uniform within each focus. This is generally a bad approximation, but for our purpose of measuring transmittance it turns out to be good enough. The reason is that while concentration varies within the focus, the transmittance variations due to scattering and absorption within a single focus are negligible. The concentration variations are still an issue for the expression here, but once we average over many pixels (by e.g. downscaling the images for transmittance calculations) this error averages out to 0 as the average concentration distribution in several foci is uniform. We thus make the approximation ^^{^}^ǡ ^ǡ ^^{^} ൌ ^_^ǡ^. Note that we still have a dependence on the pixel indices as the concentration may be different at foci corresponding to different pixels. We can now write

as

where:

This can be thought of as a generalization of the function ^^^^ to a whole focus. Given a normalized amount of light ^ incident on the focus, it says how much excitation light is emitted that may be detected by the detector. The function ^^^^ does not capture the transmittances of rays reaching between the objective and the focus, it only captures the nonlinearity of the response of light that already made it to the focus. As we later will see, it will be important to optimize excitation and detection wavelengths to be close to each other and to optimize the beam shapes for excitation and detection to be similar. Because of this, we can approximate the excitation and detection PSF to _{be the same,}

_{^ ɗ} ^{^} _^ ^{^} _{. We note that the integrand in the definition}

only depends on the position through the value of the PSFs. We can thus change variable to integrate over the value of the PSF instead. We label this variable ɗ^ᇱ:

where:

and ^ is the Dirac ^-function. ^^{^}ɗ^{ᇱ^} is independent of the shape of the PSF, it is a measure of the volumetric amount of each value of the PSF and we may thus get away with a rather coarse approximation of the PSF. Instead of measuring the PSF we use an idealised Gaussian PSF (here in cylindrical coordinates ^^ଶ ൌ ^^ଶ ^ ^^ଶ): Here ɐ_^ sets the width of the waist of the PSF (limited by the wavelength) and ɐ_^Ȁ^_^ is the beam divergence, proportional to the numerical aperture of the objective. This PSF is normalized so that the integral over an ^ǡ ^ plane is 1. An overall factor can simply be absorbed in the constants ^_^ and ^_ଶ. We can perform the integral in the definition

. From this we calculate

, _{where the dimensionless saturation function}

_{is defined as:}

Finally, we have that

. For now, we have assumed no bleaching and a constant fluorophore concentration. However, the fluorophore concentration decays as fluorophores are bleached by excitation light. Bleaching is often caused by fluorophore oxidation when they are in the excited state, which means that the bleaching rate also saturates with increasing intensity. However, we neglect this effect, which is only relevant for bleaching in the focal plane at high excitation intensities, for simplicity and assume a linear bleaching rate:

where ^ is a parameter indicating how rapidly the fluorophores bleach. We have added the, until now implicit, time dependence of concentration and intensity. We can write the solution to this differential equation as

We make a further assumption that the exciting laser is swept uniformly over the whole focal plane and bleaching is thus uniform. This is a good approximation out of the focal plane, but right at the focal plane bleaching will happen a bit heterogeneously depending on the pixel spacing compared to the PSF waist size. Note that both of our assumptions regarding bleaching become very good approximations out of the focal plane, and thus work well if bleaching is predominantly due to scanning multiple ^- stacks. We also note that the angular distribution of light rays does not change within the sample as light rays are straight. This means that the amount of light that makes it to a certain fluorophore is always the same (apart from some edge-effects) when a whole image is scanned, independent of the focal plane, given that the same laser intensity was used. This means that, again apart from edge-effects, the bleaching at a certain fluorophore is proportional to the integrated laser intensity multiplied by the local transmittance ^^{^՜^}, independent of which focal plane we are scanning. Considering now that we have several exposures of equal time ^_^௫^ but different laser intensity settings ^_^. The number of photons

detected in the detector for a certain pixel is Poisson distributed (we assume the signal comes from many individual fluorophores) with a mean given by the integrated intensity during the exposure time. Consider an exposure from

to ^_ଶ:

The average concentration at a certain pixel at the beginning of the ^-th exposure is given by:

We integrate the concentration over the ^-th exposure to obtain:

We note that ^_^ǡ ^_ଶǡ ɐ_^ǡ ^_^ may be unknown. ɒǡ ^ǡ ^ǡ ^ are fluorophore parameters that similarly may be unknown. However, we do not require all these factors as they show up in specific combinations only. We define and this simplifies to:

where

. ^_^ is known and ^ can be measured or fit separately. We have two unknowns per pixel:

By taking two or more images ^_^ǡ^ǡ^ǡ ^_^ǡ^ǡଶǡ ǥ we may use the result to solve for both of these unknowns. As these are random due to shot noise, we may get a better estimate of these unknowns by taking further images. Since the normalized concentration _^ ǁ^_ǡ^ and focus to objective transmittance ^{^^} _^ ^{^} ǡ_^ ^{՜^} always show up as a product here, we cannot solve for them separately. To find the concentration, we arrange the excitation and detection beam paths to be as similar as possible. This way, we may use the reciprocity of light to ensure that the objective to focus, and focus to objective, transmittances are the same, independently of what sample is placed in the microscope. This is similar to how confocal microscopes are already constructed. The geometry of the excitation light rays and detection light rays are the same. We label each ray by the point it intersects the plane 107A with and write the total transmittances as weighted sums of the transmittances of the individual light rays they are composed of:

. Here ^_^ ^{^՜^} భ ^^^ and ^_^ ^{^՜^} మ ^^^ label the transmittances of individual light rays from the point ^ in the plane 107A to the focus at wavelength

and the other way around at wavelength ^_ଶ. ^_^௫^^^^ and ^_ௗ^௧^^^ are weights that depend both on the contribution to the multiplicative factor of the PSFs each ray has, and the light sources intensity distribution across the plane A and the detectors sensitivity to different light rays across the plane 107A, respectively. Note that both ^_^௫^^^^ and ^_ௗ^௧^^^ can be engineered separately by using an apodization filter on either the excitation light or the detector so we can make them the same:

. We may additionally bring the excitation and detection wavelengths close to each other by e.g. choices of fluorescent marker and detector filters. If these are brought close enough, we may use the Stokes-Helmholtz reversal reciprocity principle. It tells us that the fraction of a light ray emitted with polarisation ^_^ from point U arriving with polarisation ^_^ at point V is the same if we switch the light source and the detector, i.e. the same as the fraction of a light ray emitted with polarisation ^_^ from point V arriving with polarisation ^_^ at point U. In our case, where U is a point in the plane 107A and V is a corresponding point in the plane 107B, this means that:

, and we have that:

, independently of the transmittances of individual rays, through the sample, between _{plane 107A and 107B. With such a setup, we may now find} ^{^^} _^ ^{^} ǡ_^ ^{՜^} _from ^{^^} _^ ^{^} ǡ_^ ^{՜^} _{and finally} _{calculate ^ ǁ^ǡ^ from the obtained value of} ^{^^} _^ǡ^. The absolute concentration

is related to

by a constant, that may be determined using the above formulas and measurements of the quantities therein, or simply through a calibration measurement. Otherwise, _^ ǁ^_ǡ^ may be used directly to create an image that is corrected for transmittance variations, but displayed with an arbitrary unit. Another nonlinear fluorescence effect that can be harnessed for transmittance calculation is stimulated emission. As is done in stimulated emission depletion microscopy (STED), it is possible to expose a fluorescent sample both to excitation and emission stimulation light, and to measure a response that only includes the spontaneously emitted (not stimulated) photons. Selectively measuring spontaneous emission can be done for example by filtering for differences in wavelength, or by gating the response based on the timing of the excitation and stimulation measurements. By measuring a first response that includes spontaneous and stimulated emission, and a second response that only contains spontaneous emission, one may obtain the ratio of spontaneous to stimulated emission. The ratio of stimulated to spontaneous emission depends on the intensity of stimulation light arriving at the focus. Most emissions may be stimulated for a high intensity of stimulation light as is the case in the depletion zone of STED. All emissions will be spontaneous when no stimulation light arrives at the focus. We may thus use this ratio as a measure of the intensity of stimulation light at the focus and use this intensity to calculate a transmittance from the objective to the focus.

Claims

CLAIMS 1. A method of performing a fluorescence measurement comprising: exposing a sample to excitation light focussed to an excitation focus under illumination parameters wherein the sample comprises a fluorescent marker and the illumination parameters of the excitation light are configured to cause a non-linear fluorescence response measured by a detector focussed on a detection focus wherein the detection focus and the excitation focus are the same focus, where the non-linear fluorescence response is due to one or more of bleaching, saturation and stimulated emission of the fluorescent marker; measuring a first response of the fluorescent marker to the exposure by the excitation light; measuring a second response of the fluorescent marker to the exposure by the excitation light; wherein the method further comprises one or more of: modelling fluorescence saturation at the focus based on the measured first response and the measured second response; modelling bleaching of the fluorescent marker at the focus based on the measured first response and the measured second response; and modelling stimulated emission of the fluorescent marker at the focus based on the measured first response and the measured second response; based on the one or more modelled non-linear effects, calculating a transmittance of excitation light through the sample to the focus. 2. The method of claim 1 wherein the method also comprises: arranging excitation optics and detection optics such that the path of excitation light through the sample to the focus is substantially the same as the path of detection light from the focus through the sample wherein the excitation optics define the path of light through the sample to the focus and the detection optics define the light from the sample which the detector is able to detect; using the reciprocity of light to calculate the transmittance of detection light from the focus, through the sample, based on the calculated transmittance of excitation light through the sample, towards the focus. 3. The method of claim 2 wherein the method also comprises estimating a fluorescent marker concentration of the sample based on the measured responses and the calculated transmittance of detection light from the focus, through the sample. 4. The method of any preceding claim wherein the fluorescence measurement is performed in a confocal microscope. 5. The method of any preceding claim wherein the second response is measured at a time after the measurement of the first response. 6. The method of any preceding claim wherein the measured first response of the fluorescent marker to the exposure by the excitation light is a measure of one of a first harmonic or a higher order harmonic of a modulated light source. 7. The method of claim 4 wherein the measured second response of the fluorescent marker to the exposure by the excitation light is a different harmonic to the harmonic measured for the first response. 8. The method of claim 5 except when dependent on claim 3, wherein the measured first response and the second response are measured simultaneously. 9. The method of any preceding claim wherein exposing the sample to the excitation light under illumination parameters comprises exposing the sample to the excitation light under a first set of illumination parameters and subsequently exposing the sample to the excitation light under a second set of illumination parameters. 10. The method of claim 9 wherein: the step of measuring the first response of the fluorescent marker to the exposure by the excitation light occurs simultaneously with initiation of exposure of the sample to the excitation light under the first set of illumination parameters but before the exposure by the excitation light under the second set of illumination parameters; and the step of measuring the second response of the fluorescent marker to the exposure by the excitation light occurs simultaneously with initiation of exposure of the sample to the excitation light under the second set of illumination parameters. 11. The method of any preceding claim wherein: the illumination parameters of the first and second measurements are chosen to result in different degrees of one or more of: fluorescence saturation at the focus; bleaching at the focus; and stimulated emission at the focus. 12. The method of any preceding claim wherein the excitation light and detection light are focussed through a same focussing lens. 13. The method of any preceding claim wherein the excitation light and detection light are combined using a beam splitter. 14. A controller for an apparatus in communication with the apparatus configured to cause the device to perform the method of any of claims 1 - 13. 15. A microscope comprising the controller of claim 14.