Optical signal processing

Abstract

The disclosure relates to apparatus for spectrally characterising and differentiating optical signals, using a plurality of spectral modulation functions that are orthogonal or substantially orthogonal to each other, to enable representation and classification of the optical signals through the use of spectral modulation vectors that are sensitive to shapes of associated spectral intensity profiles, wherein the apparatus comprises a polarisation-resolved detection system, and wherein the polarisation-resolved detection system comprises: at least one polariser configured for polarising incident light to output polarised light, at least one optical retarder configured to receive the polarised light from the at least one polariser, and at least one detector for detecting light output from the optical retarder; wherein the at least one polariser, the at least one optical retarder and optionally the at least one detector are configured for providing the plurality of spectral modulation functions.

Description

[0001]OPTICAL SIGNAL PROCESSING Field of the InventionThe invention relates to the processing of optical signals, and more particularly tospectrally characterising and differentiating optical signals. Merely by way ofexample, the invention may be used for polarisation-based detection of opticalsignals for spectral classification. Associated apparatus and methods are provided.It will be appreciated that the term ‘optical signal’ as used herein should beinterpreted broadly to encompass any suitable range of wavelengths of light. Forexample, the optical signal could be in the visible region. Alternatively, for example, the optical signal could be in the infrared or ultraviolet region. Background to the InventionSpectrally-resolved imaging has many applications such as endoscopy, microscopyand tomography, and can be used to provide molecular (spectroscopic) contrast, forexample between different biological molecules for clinical diagnostics. As a furtherexample, spectrally-resolved imaging can be used to detect different colour labelsfor pathology, microscopy, or for remote sensing applications. Spectroscopicinformation can be combined with image information to identify and / or classifydifferent states of a sample. Increasingly, methods of spectrally resolved imagingare combined with machine learning algorithms, for example to automateidentification / classification tasks.In many optical instruments, including microscopes and telescopes, distinguishingbetween spectrally varying signals is conventionally realised by multispectraldetection in which incident light is divided between different spectral bins, eithersequentially using optical filters with the loss of out-of-band light, or in parallel using dichroic beamsplitters. These spectral bins, or “channels”, are often associated with specific chromophores (e.g. stains or fluorophores). Where more information is required, the signals can be resolved with respect to multiple adjacent narrowerspectral bins to acquire more densely sampled spectra. This information is typically acquired sequentially by scanning a narrow band optical filter in the wavelength (frequency) domain, or by acquiring all the information in parallel, e.g., by dispersing the incident light using a spectrograph. In imaging instruments, such as microscopesand telescopes, multispectral and hyperspectral imaging are used to produce maps(images) of samples with independent spectral information available for every pixel. Multispectral imaging refers to a case where the image (for example, transmitted / reflected / scattered light or fluorescence) is resolved with respect to a relatively small number of discrete spectral channels, where the goal may be tocompare spatial distributions of different chromophores or to map the ratio ofintensity from different chromophore (fluorophore) states and / or to unmix optical signals from several different entities (molecules, fluorophores) that overlap inspace. Hyperspectral imaging on the other hand refers to an imaging modality wherethe light from each pixel is resolved with respect to a larger number of contiguous spectral bins such that there is a relatively densely sampled spectrum associated with each image pixel. Multispectral imaging is most commonly implemented using a sequential acquisition of full-field images through a set of spectral filters. This can be implemented with anelectronically tunable (or ‘adjustable’) spectral filter such as a liquid crystal-basedfilter or an acousto-optic filter, and these can be switched rapidly to acquire images resolved (x, y, λ) with respect to a large number of spectral bins to produce a hyperspectral image data set. However, the use of spectral filters is inherently lossysince the out-of-band light is rejected. Alternatively, a (relatively small) number offull-field spectral images can be recorded simultaneously without filtering loss using a cascade of dichroic beamsplitters with a number of cameras or with image splitters acquiring multiple full-field images on a smaller number of camera sensors, frequently a single camera sensor.Hyperspectral image data can be acquired by obtaining a series of full-field imagesthrough a series of narrow band filters, such as those provided by an electronicallyscanned liquid crystal-based filter or an acousto-optic filter. However, this method isphoton-inefficient since the out of band light is lost, and this loss increases with thespectral precision required. For hyperspectral imaging with point scanning or line-scanning instruments, light can be directed to the entrance slit of a spectrograph and the full spectrum can be recorded to provide hyperspectral image data, as is represented in Figure 1. In principle this avoids out-of-band filtering loss but the need to scan the image slows down the image acquisition rate compared to full-field imaging techniques. Single-shot recording of hyperspectral image data, where all spectrally-resolved image data are acquired simultaneously with no sequential image acquisition, is not usually possible without some kind of compressive sensing(with information loss) – usually a reduction in spatial image information.Although increasingly popular, hyperspectral imaging frequently acquires more information than is required for the common applications of spectral analysis, including unmixing of different chromophores or classification of samples. Where information is discarded during subsequent analysis, the measurement is not optimally photon efficient. This is the case for spectral phasor analysis applied to conventionally acquired hyperspectral image data where computational Fourier transforms can be used to generate polar plots that enable different spectralsignatures distributed across a field of view to be visualised and unmixed [1, 2, 3,4]. These polar plots present a fraction of the information about the spectral intensity profiles that is present in the acquired hyperspectral image data. Recently, the direct generation of spectral phasor image data has been demonstrated by sequentially acquiring full-field images transmitted through optical filters with a sinusoidal and a cosinusoidal spectral transmission function, togetherwith a third image acquired without either filter being used [5]. These three imagesenabled the spectral phasors of the incident light to be calculated without the acquisition of a full hyperspectral image data set. However, this approach is lossy because the photons not transmitted through the sinusoidal filters are lost and the sequential acquisition of three images requires mechanical filter changes, limiting acquisition speed and requiring motorization of the microscope. In a further demonstration of the direct phasor approach where incident light is split and directed to both a cosinusoidally and a sinusoidally varying spectral filter, both the transmitted and reflected light images have been detected simultaneously byacquiring the four images simultaneously using four cameras [6]. This single-shotspectral phasor imaging approach is photon efficient but is cumbersome and expensive, requiring extensive modification of a (fluorescence) microscope toincorporate an image-splitter and optical component trains to four separate regionson a camera sensor. Furthermore, once implemented, the spectral range andresolution are fixed by the optical filters used. Changing these operational parameters, e.g., to work in different spectral ranges (e.g., with different fluorophores) or with higher resolution or to unmix more spectral components (using higher harmonic sinusoidal filters) would require changing the optical filters. The optical filters with (co)sinusoidal modulation functions are not standard opticalcomponents, and a new dielectric filter coating may need to be designed andfabricated for any change in operational parameters. It will be appreciated, therefore, that there is a need for improved apparatus and methods for more efficiently detecting and processing optical signals for spectral classification. For example, there is a need for improved apparatus and methods for more efficient classification of optical signals with respect to different spectralcharacteristics with reduced (or negligible) filtering losses to reduce data acquisitiontimes. There is also a need to reduce the cost of such instruments, and to improve the flexibility such that they can be easily reconfigured to work optimally with different spectral profiles, e.g. in terms of wavelength range, spectral width and the ability to unmix multiple spectral components. Summary of the Invention Aspects of the present invention are set out in the appended independent claims, while details of certain embodiments are set out in the appended dependent claims. According to a first aspect of the invention there is provided apparatus for characterising and differentiating optical signals using a plurality of spectral modulation functions to enable representation and classification of the optical signals through the use of spectral modulation vectors that are sensitive to shapesof associated spectral intensity profiles, as defined in claim 1 of the appendedclaims. It is noted that, unlike spectral phasors, the spectral modulation functions donot require the specific sine / cosine modulation functions associated with Fourier analysis. The sensitivity to the shapes of the associated spectral intensity profiles may be, for example, sensitivity to the spectral width and mean wavelength.Thus there is provided apparatus for spectrally characterising and differentiatingoptical signals, using a plurality of spectral modulation functions that are orthogonalor substantially orthogonal to each other, to enable representation and classificationof the optical signals through the use of spectral modulation vectors that are sensitive to shapes of associated spectral intensity profiles, wherein the apparatuscomprises a polarisation-resolved detection system, and wherein the polarisation-resolved detection system comprises: at least one polariser configured for polarisingincident light to output polarised light, at least one optical retarder configured to receive the polarised light from the at least one polariser, and at least one detector for detecting light output from the optical retarder; wherein the at least one polariser,the at least one optical retarder and optionally the at least one detector areconfigured for providing the plurality of spectral modulation functions. The at least one detector may comprise at least two polarisation-resolved detectors. The at least two polarisation-resolved detectors may be configured for detecting all, or substantially all, of the light output from the at least one optical retarder. The at least one detector may comprise a polarisation-resolved detector. The apparatus may further comprise a further polariser arranged to receive light output from the at least one optical retarder, and wherein the at least one detector is arranged to detect light output from the further polariser; and wherein the at least one polariser, the at least one optical retarder and the further polariser are configured for providing the plurality of spectral modulation functions. The at least one detector may comprise a camera having a plurality of pixels; wherein the plurality of pixels comprises a first group of pixels having a firstpolarisation mask arranged at a first polarisation angle; wherein the plurality of pixelscomprises a second group of pixels having a second polarisation mask arranged ata second polarisation angle; wherein the plurality of pixels comprises a third groupof pixels having a third polarisation mask arranged at a third polarisation angle; wherein the plurality of pixels comprises a fourth group of pixels having a fourthpolarisation mask arranged at a fourth polarisation angle; wherein the firstpolarisation angle, the second polarisation angle, the third polarisation angle andthe fourth polarisation angle are different from each other; and wherein the at leastone polariser, the at least one optical retarder and the polarisation masks are configured for providing the plurality of spectral modulation functions. The at least one detector may comprise a detector configured to acquire sequential polarisation-resolved data, or configured to acquire image data of orthogonally polarised signals incident on different areas of the detector. By virtue of the use of the polariser and optical retarder, the apparatus advantageously enables the spectral intensity profiles of optical signals to becharacterised in terms of spectral modulation vectors using relatively inexpensivecomponents that provide more information than conventional multispectralmeasurements and are more compact and less complex than conventionalspectrograph-based apparatus for hyperspectral measurements of optical signals.Moreover, the spectral modulation vector measurements can be performed in alossless manner (or with reduced losses), avoiding the out-of-band filtering lossesthat occur when conventional filters are used and enabling more photon efficientmethods for classifying spectral signatures. The apparatus benefits from the wideavailability of polarisation optics, for example quarter and half wave plates available at a wide range of wavelengths, and low-cost components based on polymer sheetsto provide polarisation filters and retardance. The particularly compact size of someimplementations of the apparatus enables, for example, the apparatus to bemounted on a drone for aerial measurements. Alternatively, for example, thecompact size of the apparatus enables the apparatus to be provided as part of a handheld device for point of care diagnostics. The apparatus can advantageously be used to replace lossy spectrally resolveddetection based on spectral filters, or to replace expensive and complexmultispectral detection based on cascades of dichroic beamsplitters. The apparatusis particularly beneficial for (but not limited to) methods for multiphoton microscopyin which emission from multiple fluorophores is separated from excitation light, andthe apparatus can be configured to work with a range of different fluorophores without requiring the purchase and installation of additional components such asoptical filters. However, the apparatus can also be applied to a wide range ofspectroscopy or imaging modalities, including with transmitted light, scattered lightor fluorescence, for applications including unmixing of different spectral channelsand classification of samples based on spectral signatures. In general, thepolarisation-based optical spectral modulation approach can be more flexible, lowercost and more photon efficient than conventional implementations of multispectralor hyperspectral imaging or direct spectral phasor imaging.It is noted that combinations of polarising optical components and retarders can be configured to provide photon-efficient multispectral imaging instruments (i.e., dividing incident photons between discrete spectral bins), e.g., [7], but this approach entails increasing complexity as the number of spectral bins is increased and does not directly generate the signals required to calculate the spectral modulationvectors. It is further noted that combinations of polarising optical components andretarders can be configured to provide photon-efficient spectral filters that can be optimised to detect specific spectral features, e.g. gas absorption lines, e.g., [8]. However, in contrast to [7,8] where the optical configurations are optimised forpredetermined spectral properties, the spectral modulation vector approach of the present disclosure is spectrally agnostic, capturing information over a wide spectral range. The at least one optical retarder may comprise an adjustable optical retarder having an adjustable retardance. The adjustable retardance may be electronicallyadjustable. By virtue of the optical retarder being adjustable, adjustment of spectralrange and resolution of spectral modulation functions can be performed, e.g. tounmix an increased number of spectral components using more than two spectralmodulation functions. The spectral (range / resolution) performance of the apparatuscan beneficially be adjusted by adjusting the retarder, resulting in improved flexibilitycompared to a colour camera with a mosaic filter, for example. The adjustableretarder can effectively enable “colour imaging” with a single camera in spectralregions where no mosaic filter is available, for example in the near infrared.The adjustable optical retarder may comprise a liquid crystal retarder.Advantageously, since the liquid crystal retarder can switch retardance at >100 Hzrates, “real-time” multispectral (spectral modulation vector) imaging can be achieved(for example, imaging at a rate of 10s of frames per second).The at least one polariser may comprise a first polarising beam splitter. The first polarising beam splitter may be configured to polarise the incident light to output a first polarised beam and a second polarised beam; and the first polarised beam may be orthogonally polarised with respect to the second polarised beam. The apparatus may comprise a second polarising beam splitter, a first optical retarder, a third polarising beam splitter, a second optical retarder, a first detector, a second detector, a third detector and a fourth detector; wherein the apparatus isconfigured for output of the first polarised beam to the second polarising beamsplitter via the first optical retarder; wherein the apparatus is configured for outputof the second polarised beam to the third polarising beam splitter via the secondoptical retarder; wherein the second optical retarder has a retardance that is different to that of the first optical retarder, to provide a different and orthogonal spectral modulation function; wherein the second polarising beam splitter isconfigured to output a third polarised beam to the first detector and to output a fourthpolarised beam to the second detector; wherein the third polarised beam isorthogonally polarised with respect to the fourth polarised beam; wherein the thirdpolarising beam splitter is configured to output a fifth polarised beam to the thirddetector and to output a sixth polarised beam to the fourth detector; and wherein thefifth polarised beam is orthogonally polarised with respect to the sixth polarised beam. The apparatus may comprise a second polarising beam splitter, an adjustable retarder, a first detector and a second detector, wherein the first polarising beamsplitter is configured to polarise the incident light to output a first polarised beam tothe second polarising beam splitter via the adjustable retarder; and the secondpolarising beam splitter may be configured to output a second polarised beam to thefirst detector, and to output a third polarised beam to the second detector. Theadjustable retarder may be a liquid crystal retarder. The adjustable retarder may beconfigured to provide different orthogonal spectral modulation functions in sequential image acquisitions. The first polarising beam splitter may be further configured to polarise the incident light to output a fourth polarised beam to the second polarising beam splitter via theadjustable retarder; and the fourth polarised beam may be orthogonally polarisedwith respect to the first polarised beam; wherein the first polarised beam is incident upon a first face of the second polarising beam splitter; and wherein the fourth polarised beam is incident upon second face of the second polarising beam splitter that is different from the first face, for output of a fifth polarised beam to the first detector from the second polarising beam splitter, and for output of a sixth polarised beam to the second detector from the second polarising beam splitter. Advantageously, by virtue of the fourth polarised beam being incident upon second face of the polarising beam splitter that is different from the first face, the apparatusis insensitive to the original polarisation of the incident light. The apparatus maydetect all, or substantially all, of the incident photons. The apparatus may comprise a second polarising beam splitter, an optical retarder, a first detector, a second detector, a third polarising beam splitter, an achromatic quarter wave plate, a third detector, and a fourth detector; wherein the first polarisingbeam splitter is configured to polarise the incident light to output a first polarisedbeam to the second polarising beam splitter via the optical retarder; wherein thesecond polarising beam splitter is configured to output a second polarised beam tothe first detector, and to output a third polarised beam to the second detector;wherein the first polarising beam splitter is further configured to output a fourthpolarised beam to the third polarising beam splitter via the achromatic quarter waveplate and via the optical retarder, wherein the apparatus is configured so that the fourth polarised beam passes through the achromatic quarter wave plate before passing through the optical retarder; and wherein the third polarising beam splitteris configured to output a fifth polarised beam to the third detector, and to output asixth polarised beam to the fourth detector.The at least one polariser may comprise a linear polariser. The apparatus may comprise a first optical retarder, and a second optical retarder;wherein the linear polariser is configured for polarising the incident light to outputpolarised light to the second optical retarder via a first optical retarder; and the atleast one detector may be arranged for detecting light output from the second optical retarder. The apparatus may comprise an achromatic quarter wave plate and an opticalretarder; wherein the linear polariser is configured for polarising the incident light tooutput polarised light to the achromatic quarter wave plate via the optical retarder;and the at least one detector may be arranged for detecting light output from the achromatic quarter wave plate. The at least one detector may comprise a camera having a plurality of pixels; wherein the plurality of pixels comprises a first group of pixels having a first polarisation mask arranged at a first polarisation angle; wherein the plurality of pixels comprises a second group of pixels having a second polarisation mask arranged at a second polarisation angle; wherein the plurality of pixels comprises a third group of pixels having a third polarisation mask arranged at a third polarisation angle; wherein the plurality of pixels comprises a fourth group of pixels having a fourth polarisation mask arranged at a fourth polarisation angle; and wherein the first polarisation angle, the second polarisation angle, the third polarisation angle and the fourth polarisation angle are different from each other. The second polarisation angle may be offset by 45 degrees from the first polarisationangle; wherein the third polarisation angle is offset by 45 degrees from the secondpolarisation angle; and wherein the fourth polarisation angle is offset by 45 degrees from the third polarisation angle.Advantageously, by virtue of the provision of the camera and the four polarisationmasks, the apparatus can be used to simultaneously acquire four wide-field imagesused to calculate spectral modulation vectors for spectrally resolving optical signals.One or more of: the linear polariser, the first optical retarder and the second opticalretarder, may be mounted on the camera.One or more of: the linear polariser, the optical retarder and the achromatic quarterwave plate, may be mounted on the camera.The apparatus may further comprise a quarter wave plate (or a half wave plate)configured for polarising the light that is incident on the linear polariser. The quarterwave plate or half wave plate may be configured to adjust the polarisation of thelight that is incident on the linear polariser to maximise light transmitted through thelinear polariser. According to a second aspect of the invention there is provided an imaging system, such as a microscope system or camera system, comprising the apparatus according to the first aspect of the invention. According to a third aspect of the invention there is provided a method of spectrally resolving optical signals, the method comprising: receiving the incident light at apparatus according to the first aspect of the invention; and detecting light output from the optical retarder at the at least one detector. The incident light may be from a sample, and the method may further comprise classifying a spectral signature of the sample based on the light detected at the at least one detector.The method may comprise using a time-resolved detector for fluorescence lifetimeimaging. The method may further comprise generating a polarisation resolved image based on the light detected at the at least one detector. Brief Description of the Drawings Embodiments of the invention will now be described by way of example only with reference to the attached figures in which:Figure 1 schematically illustrates apparatus for illuminating a sample and acquiringa corresponding spectrum at each pixel in the field of view in a hyperspectralmicroscope;Figure 2a shows a schematic illustration of a generalised approach for representingspectral profiles as spectral modulation vectors that can be used for photon-efficient spectral analysis and classification of samples; Figure 2b illustrates the complementarity of the spatial image information and the spectral modulation vector plots and indicates some potential applications;Figure 3 illustrates a single-shot spectral classification (spectral modulation vectorimage data acquisition) set-up using polarisation optics to generate spectral modulation vectors corresponding to cos(Λν) / cos(2Λν) spectral modulationfunctions in a single-shot mode;Figure 4 illustrates a single shot approach for generating spectral modulation vectorimages corresponding to cos(Λν) / sin2(Λν) spectral modulation functions at a cameraframe rate using a polarisation-resolving camera;Figures 5 to 7b illustrate apparatus for spectral classification image data acquisition(spectral modulation vector image data acquisition) using polarisation optics togenerate spectral modulation vectors corresponding to cos(Λν) / cos(2Λν) spectralmodulation functions;Figure 8 illustrates apparatus for single-shot acquisition of spectral modulationvector signals or images corresponding to cos(Λν) / sin(Λν) spectral modulationfunctions that can be acquired using, for example, photomultipliers or cameras;Figure 9 illustrates apparatus for a single shot approach for generating spectralmodulation vector images corresponding to cos(Λν) / sin(Λν) spectral modulationfunctions at the camera frame rate using an achromatic quarter wave plate beforea polarisation-resolving camera;Figure 10 illustrates apparatus for a single shot approach for generating spectralmodulation vector images corresponding to cos(Λν) / sin(Λν)sin(Λν / Χ) spectralmodulation functions at the camera frame rate using a polarisation-resolvingcamera;Figure 11 illustrates the output of a single shot approach similar to that depicted inFigure 4 for generating spectral modulation vector images corresponding to cos(Λν) / sin2(Λν) spectral modulation functions of a colour display at the camera frame rateusing a polarisation-resolving camera with a linear polariser and two wave plates; Figure 12 shows the total intensity image obtained when imaging the colour image of Figure 11;Figure 13 shows images obtained when applying a spectral modulation vector redmask, spectral modulation vector green mask and spectral modulation vector blue mask to the measurements illustrated in Figure 11; Figure 14 shows the total intensity image, the spectral modulation vector plot and the spectrally classified red, green and blue masks of pollen grains imaged using the configuration of Figure 5 with the liquid crystal retarder used to provide twodifferent retardances for generating spectral modulation vectors corresponding tocos(Λν) and cos(2Λν) spectral modulation functions in two sequential image acquisition; and Figure 15 shows exemplary apparatus for performing methods of the present disclosure, for example to analyse the output of the one or more detectors to perform classification of a sample. In the figures, like elements are indicated by like reference numerals throughout. Detailed Description of Preferred Embodiments The present embodiments represent the best ways known to the Applicant of putting the invention into practice. However, they are not the only ways in which this can be achieved. This present disclosure is concerned with methods for distinguishing betweenspectrally varying signals using spectral modulation vectors. Methods of the presentdisclosure can be used to identify and / or classify a sample by illuminating thesample with light and detecting the corresponding light from the sample (e.g. thelight transmitted through, reflected from, scattered by, or emitted by the sample).The sample could be, for example: ^a tissue sample for diagnosis;^ a plant sample for determining crop health, ripeness, or impact of pollution;^ solar cells or displays, for quality assurance;^ a biochemical assay, for spatial proteomics, high throughput screening, ordetection of disease; ^any other suitable sample, for example for surveillance / classification.Methods of the present disclosure enable more efficient acquisition of informationusing generalised “spectral modulation vectors” to classify optical signals withrespect to different spectral channels with no out-of-band filtering loss (or reduced out-of-band filtering loss). This method can be used to assign photons to differentspectral channels – i.e., “multicolour imaging” – to distinguish light from differentchromophores and to provide ratios of signals in different spectral channels. Themethods are flexible and can advantageously be configured to be notionally losslessand to provide single-shot operation. Moreover, electronically tunable adjustment ofspectral range and resolution can be used to unmix an arbitrary number of spectralcomponents. Figure 1 schematically illustrates two examples of apparatus for illuminating a sample and acquiring a corresponding spectrum. In a first example 100a, incident light 100 illuminates a sample 102a, and the transmitted and / or reflected light 104 is detected using a spectrometer 106. An emission long pass (LP) filter is arranged before the detector 110 which detects the light from the sample 102a. In the second example 100b illustrated in Figure 1 the incident light 100 illuminates a sample 102b on a microscope slide of a hyperspectral microscope 114. As with the first example 100a, an LP filter 108 is arranged before the detector 111, but in the second example the spectrum is measured per pixel 116 of the hyperspectral microscope 114.A plot 113 of the spectral intensity data, I(^), against wavelength is also illustratedin Figure 1, illustrating the spectral bins between ^1and ^N. The wavelength ^LPcorresponding to the characteristic wavelength of the LP filter 108 is also illustrated. For phasor analysis, the spectral profile from each pixel of the hyperspectral microscope 114 can be represented as a point on a polar plot.Figure 2a shows a schematic illustration of a generalised approach for photonefficient spectral classification as provided by the present work. Incident light 100illuminates an instrument comprising a modulator 202 that provides some spectralmodulation functions, e.g., P(ν), Q(ν), which are functions of the frequency ν andare orthogonal in this example. Determining both the transmitted light (P(ν), Q(ν))and non-transmitted light (1-P(ν), 1-Q(ν)) enables normalisation of the spectral modulation vectors and is 100% photon efficient. As will be described in more detaillater, the apparatus of the present disclosure is configurable for generating spectralmodulation functions using polarisation-based optics for which a generalisedanalysis using the spectral modulation vectors is illustrated in Figures 2a and 2b.A vector (V, H) can then be calculated, using the equations illustrated in the firstpart 204 and the second part 206 of Figure 2a, that represents the spectral profileof the incident light. Where multiple spectral profiles are present in the incidentsignal 100, the vectors representing each spectral profile add to produce theresulting spectral modulation vector. If the component spectral profiles are known,the resulting “reference spectral modulation vectors” can be unmixed. With twomodulation functions, P(ν), Q(ν), up to 3 spectral reference vectors can be linearlyunmixed. If the unmixing of more reference vectors is required, then moremodulation functions can be applied, enabling higher dimensional spectralmodulation vectors to be unmixed.In examples of the present disclosure, polarisation optics (e.g., polarisationfilters / beamsplitters and retarders) can be used to provide the spectral modulationfunctions P(ν), Q(ν), rather than using dielectric or absorption spectral filters. In thepresent disclosure this approach is referred to as a “PolSpec” approach, and isbased on the concept of a Lyot filter in which a retarder such as a birefringent crystal is placed between two parallel (or orthogonal) polarisers with its ordinary / extraordinary axes orientated at 45oto the input polarisation. Theretardance of the birefringent element is given by ^n L 2π / ^, where L is the physicalpath length and ^n is the refractive index difference between the ordinary andextraordinary axes of the birefringent element. In general, the birefringent element will rotate the polarisation of the input radiation leading to attenuation of the signal transmitted by a polariser with its axis aligned parallel to the input polarisation. However, at a specific wavelength, ^0, the retardance of the birefringent element can be set to an integer multiple of 2π and the input radiation at will be rotated by 360 degrees and will be transmitted through the second polariser without loss. The transmission function of this arrangement (Lyot filter) is proportional tosin2(^n L π / ^) with transmission peaks at ^n L = i^0 where i is an integer. If theoutput polariser of the Lyot filter is replaced by a polarising beam splitter (PBS), thenthe detectors will detect complementary signals proportional to sin2(^n L π / ^) andcos2(^n L π / ^), together detecting all the incident photons. Advantageously,acquiring both these complementary perpendicularly polarised outputs enables thespectral modulation vectors to be normalised. Since 2sin2^ = 1-cos2^, the Lyotfilter provides a cosinusoidal modulation of the intensity spectrum of the inputradiation proportional to 1- cos(^n L 2π / ^) = L 2πν / c) = 1-cos(Λν),where Λ = ^n L 2π / c. Variations of this cosinusoidal spectral transmission functioncan be used to provide the orthogonal spectral transmission functions P(ν), Q(ν)used to acquire spectrally classified image data. The two or more spectralmodulation functions used to generate the spectral modulation vectors may be (substantially) orthogonal such that the spectral modulation vectors for each image pixel can be decomposed into spectral components through conventional linear unmixing.Advantageously, methods of the present disclosure benefit from the wide availabilityof polarisation optics, including quarter and half wave plates available at a widerange of wavelengths, and low-cost polarisation filters and retarders fabricated frompolymer sheets. Methods of the present disclosure can also utilise electronically controlled liquid crystal retarders, which are cost-effective compared to scientific camera or custom dielectric coatings. Apparatus for characterising and differentiating optical signals using a plurality of spectral modulation functions to enable representation and classification of the optical signals through the use of vectors that are sensitive to shapes of associatedspectral intensity profiles will now be described with reference to Figures 3 to 10.An improved single-shot spectral classification instrument is illustrated in Figure 3,which shows a schematic illustration of single-shot spectral classification apparatus300 comprising polarisation optics for generating spectral modulation vectorscorresponding to cos(Λν) / cos(2Λν) spectral modulation functions in a single-shotmode. The incident light 100 from a sample is first divided into two orthogonallypolarised beams using a polarising beam splitter 302. In other words, the apparatus300 comprises a first polarising beam splitter 302 that is configured to polarise theincident light 100 to output a first polarised beam and a second polarised beam; andthe first polarised beam is orthogonally polarised with respect to the secondpolarised beam. The orthogonally polarised beams are then each transmittedthrough a respective birefringent optical retarder plate 306, 308 with their axesorientated at 45° to provide retardances of ^0 and 2^0, respectively. The transmittedbeams are then incident on further polarising beam splitters 310, 312 that eachprovide two complementary outputs, one with a modulation of cos(Λν) and one modulated at cos(2Λν). In other words, the apparatus 300 is configured for outputof the first polarised beam to a second polarising beam splitter 310 via a first opticalretarder 306, and the apparatus 300 is configured for output of the second polarisedbeam to a third polarising beam splitter 312 via a second optical retarder 308.The light output from the polarising beam splitters 310, 312 is detected using a set of detectors 314, 316, 318, 320. The second polarising beam splitter 310 isconfigured to output a third polarised beam to a first detector 314 and to output afourth polarised beam to a second detector 316, wherein the third polarised beamis orthogonally polarised with respect to the fourth polarised beam. The thirdpolarising beam splitter 312 is configured to output a fifth polarised beam to a thirddetector 318 and to output a sixth polarised beam to a fourth detector 320, whereinthe fifth polarised beam is orthogonally polarised with respect to the sixth polarised beam. The polarising beam splitters 302, 310, 312, the retarders 306, 308 and the detectors 314, 316, 318, 320 may be collectively referred to as a polarisation- resolved detection system.The signals at the detectors 314, 316, 318, 320 can be subtracted and normalisedto yield the spectral modulation vector elements corresponding to functions: which are orthogonal and can be used as the basis for spectral modulation vectoranalysis. In other words, the polarisers and retarders are arranged for providingspectral modulation functions that are orthogonal (but could alternatively besubstantially orthogonal, for example).Figure 4 schematically illustrates apparatus 400 for a single shot method forgenerating spectral modulation vector images corresponding to cos(Λν) / 0.5(1-cos(2Λν)) = cos(Λν) / sin2(Λν) spectral modulation functions at a camera frame rateusing a polarisation-resolving camera 408. The polarisation-resolving camera 408is operable to simultaneously acquire the four wide-field images used to calculatethe spectral modulation vectors indicated in Figure 4. The polarisation-resolvingcamera 408 is a camera with a pixel-wise polariser mask with axes pixels 410 ingroups of four orientated at 0, 45, 90 and 135 degrees, such that it effectively outputsfour polarisation resolved sub-images as if they had been imaged through linearpolarisers at these orientations. In other words, the detector is a polarisation-resolved detector comprising a camera 408 having a plurality of pixels 410, whereinthe plurality of pixels comprises a first group of pixels having a first polarisation mask arranged at a first polarisation angle, a second group of pixels having a second polarisation mask arranged at a second polarisation angle, a third group of pixels having a third polarisation mask arranged at a third polarisation angle, and a fourth group of pixels having a fourth polarisation mask arranged at a fourth polarisation angle, wherein the first polarisation angle, the second polarisation angle, the third polarisation angle and the fourth polarisation angle are different from each other. In this example, the second polarisation angle is offset by 45 degrees from the first polarisation angle, the third polarisation angle is offset by 45 degrees from the second polarisation angle, and the fourth polarisation angle is offset by 45 degrees from the third polarisation angle. The incident light 100 from the sample first passes through a linear polariser 402.After the incident light 100 has been linearly polarised by the linear polariser 402 itpasses through a first retarder 404 (e.g., wave plate at ^0) with its axis at 45degrees, followed by a second retarder 406 (e.g., wave plate at ^0) with its axisaligned parallel to the input linear polariser 402. In other words, the linear polarizer402 is configured for polarising the incident light to output polarised light to a second optical retarder 406 via a first optical retarder 404, and a detector 408 (in thisexample, the polarisation-resolving camera 408) is arranged for detecting lightoutput from the second optical retarder 406.The light detected at the polarisation-resolved pixels 410 of the polarisation-resolving camera will experience the spectral modulation functions indicated inFigure 4. Thus, the four sub-images provided by the polarisation-resolving camera408 enable the spectral modulation vectors to be calculated for each image pixel asdescribed above. Advantageously, the components used with the polarisation-resolving camera 408 in the example illustrated in Figure 4 comprise a linearpolariser 402 and two retarders (waveplates) 404, 406, which are available as low-cost polymer sheets. Thin film polarisers and retarders could also be directly appliedto a camera chip. The linear polariser 402 and the retarders 404, 406 may be, forexample, less than 1 mm thick and can optionally be mounted directly on thepolarisation-resolving camera 408. This apparatus 400 illustrated in Figure 4 isrelatively inexpensive and beneficially provides a particularly compact configuration.This compact size enables, for example, the apparatus 400 to be mounted on a drone for aerial measurements. Such drone-mounted apparatus can be used tosurvey crops, or to survey for environmental pollutants using multispectralmodulation vector analysis. Alternatively, for example, the apparatus 400 could beprovided as a handheld device for point of care diagnostics.Due to the mask of linear polarisation transmission filters provided by thepolarisation-resolving camera 408, rather than the use of a polarising beam splitter(e.g. as illustrated in Figure 3), half of the incident light will be blocked by these filtersand so the photon efficiency will be reduced by 50%. The input linear polariser 402may also reduce the detection efficiency unless the incident light 100 is polarisedalong the axis of the input polariser 402. In a case where the incident light 100 isunpolarised light (e.g., fluorescence), this would correspond to an attenuation of50%. However, this sensitivity to the polarisation of the incident light 100 can beminimised by the use of an (achromatic) quarter wave plate provided before theinput linear polariser 402 and aligned to convert the most unfavourable incidentorthogonal linear polarisation to circular polarisation. It is noted that the conventionalapproach using spectral filters for multichannel imaging is also lossy since the outof band signal in each channel is rejected. For example, a conventional RGB colourcamera has three colour filters and so is limited to 33% light efficiency. Unlike aconventional RGB colour camera, the spectral (range / resolution) performance of the single-shot PolSpec approach can be adjusted by only changing the first retarder404, making it more flexible than a colour camera with a mosaic filter. For example,it would be possible to create a “colour camera” in spectral regions where no mosaic filter is available, e.g., in the near infrared. To implement PolSpec with cos(Λν) / cos(2Λν) spectral modulation functions,complementary polarisation-resolved images through ^0 and 2^0 retardance can beacquired sequentially to generate the two spectral modulation functions using anelectronically controlled adjustable retarder. Figure 5 illustrates apparatus forimplementing spectral modulation functions using an adjustable retarder. In thisexample, the adjustable retarder is an electronically controlled liquid crystal retarder(LCR) to generate spectral modulation vectors corresponding to cos(Λν) / cos(2Λν)spectral modulation functions (but any other suitable type of adjustable retardercould alternatively be used). The incident light 100 first passes through a PBS 502.An LCR 504 receives the light output from the PBS and enables two sequentialimages with the two retardance settings to be acquired. The light output from theLCR 504 then passes to a further PBS 506, and the light output from the furtherPBS 506 is detected at two detectors 508, 510. In other words, the apparatus 500comprises a first polarising beam splitter 502 that is configured to polarise the incident light 100 to output a first polarised beam to a second polarising beam splitter506 via an adjustable retarder 504 (in this example, via a liquid crystal retarder). Thesecond polarising beam splitter 506 is configured to output a second polarised beam to a first detector 508, and to output a third polarised beam to a second detector 510.It is noted that, unlike sequential spectral sampling using, for example, a filter wheelor liquid crystal tunable filter, this PolSpec approach can advantageously belossless. Figure 5 illustrates a configuration that would present a 50% loss tounpolarised incident light (e.g. from fluorescence). Figures 6, 7a and 7bschematically illustrate further examples of PolSpec apparatus for spectrallymodulated image data acquisition using polarisation optics to generate the spectralmodulation vectors corresponding to cos(Λν) / cos(2Λν) spectral modulationfunctions. Advantageously, the apparatus 600, 700a, 700b illustrated in Figures 6,7a and 7b are lossless. In the examples illustrated in Figures 6 and 7a, the firstpolarising beam splitter 502 is further configured to polarise the incident light to output a fourth polarised beam to the second polarising beam splitter 506 via the adjustable retarder 504, wherein the fourth polarised beam is orthogonally polarised with respect to the first polarised beam. The first polarised beam is incident upon a first face of the second polarising beam splitter 506, and the fourth polarised beam is incident upon second face of the polarising beam splitter 506 that is different from the first face. Figure 7b shows a modification of the apparatus of Figure 7a, in which the first polarising beam splitter 502 is replaced by a polarization beam displacer (a Savart prism).The configuration of Figure 5 could be modified by adding a second LCR to the inputsuch that the polarisation of the incident light is rotated before the first PBS 502.Advantageously, since the LCR 504 can switch retardance at >100 Hz rates, theimplementations using two detectors 508, 510 acquiring data simultaneously canprovide “real-time” multispectral (modulation vector) imaging.The detectors and cameras illustrated in Figure 3 and in Figures 5 to 8 may be singlepixel detectors such as photomultipliers, wide-field imaging detectors such as cameras, or line-detectors such as linear charge-coupled device CCD arrays. Forexample, the method depicted in Figure 6 could be implemented using a laserscanning microscope to provide lossless multispectral imaging with multiplearbitrary “colour” channels using only two photomultipliers. The methods of thepresent disclosure can replace lossy spectrally resolved detection based on spectralfilters or expensive (lossless) multispectral detection based on cascades of dichroicbeamsplitters. This is particularly beneficial for multiphoton microscopy where asingle fixed dichroic beamsplitter is used to separate the excitation light from allfluorescence. Advantageously, the PolSpec approach of the present disclosureenables the spectral performance to be easily turned by adjusting the liquid crystalretarder 504. In other words, the apparatus advantageously comprises anadjustable optical retarder having an adjustable retardance. Figure 14 shows thetotal intensity image, the spectral modulation vector plot and the spectrally classified red, green and blue masks of pollen grains imaged using the configuration of Figure5, with the liquid crystal retarder used to provide two different retardances forgenerating spectral modulation vectors corresponding to cos(Λν) and cos(2Λν)spectral modulation functions in two sequential image acquisitions.When used for spectral classification of wide-field images, the PolSpec method canbe implemented with two cameras and the polarisation optics can be combined withappropriate image relay optics 702, 704, 706 indicated schematically in theexemplary apparatus 700a, 700b shown in Figure 7a and Figure 7b.The output polarising beam splitter 506 and two cameras 708, 710 could bereplaced by a polarisation image splitter that delivers two orthogonally polarisation filtered images on a single detector (e.g. single camera). This would be particularly straightforward for the configuration of Figure 5.Spectral phasor analysis can also be achieved using the PolSpec method by usinga sinusoidal spectral modulation function that is orthogonal to cos(^n L 2πν / c). Togenerate sin(Λν) it is necessary to add a π / 2 phase change without changing Λ,which cannot be achieved conveniently, for example by adjusting ^n L. However, itcan be implemented by adding an achromatic quarter wave plate (AQWP) that provides a π / 2 phase change for all incident wavelengths. Figure 8 illustratesapparatus 800 for single-shot acquisition of spectral modulation vectors that can beacquired using, for example, photomultipliers or cameras. In the example of Figure 8, the first polarising beam splitter 502 is configured to polarise the incident light to output a first polarised beam to a second polarising beam splitter 806 via an optical retarder 804. The second polarising beam splitter 806 is configured to output a second polarised beam to a first detector 810, and to output a third polarised beam to a second detector 812. The first polarising beam splitter 502 is further configured to output a fourth polarised beam to a third polarising beam splitter 808 via an achromatic quarter wave plate 802 and via the optical retarder 804, wherein the apparatus 800 is configured so that the fourth polarised beam passes through the achromatic quarter wave plate 802 before passing through the optical retarder 804. The third polarising beam splitter 808 is configured to output a fifth polarised beam to a third detector 814, and to output a sixth polarised beam to a fourth detector 816.The retarder 804 may be, for example, a widely available halfwave plate, or seriesof half-wave plates. The AQWP 802 is also commercially available. The apparatus800 illustrated in Figure 8 has the important advantage that the operationalparameters (spectral range, resolution, additional modulation functions) can be conveniently tuned by (e.g. electronically) adjusting only the properties of theretarder 804.Figure 9 illustrates apparatus 900 for a single shot method for generating spectralmodulation vector images corresponding to cos(Λν) / sin(Λν) spectral modulationfunctions at the camera frame rate using a polarisation-resolving camera 408. In theexample of Figure 9, the linear polariser 402 is configured for polarising the incident light to output polarised light to an achromatic quarter wave plate 902 via an opticalretarder 404; and a polarisation-resolving detector (in this example, the polarisation-resolving camera 408) is arranged for detecting light output from the achromatic quarter wave plate 902. Advantageously, the apparatus 900 illustrated in Figure 9provides a particularly compact and low cost arrangement for spectral phasoranalysis using the polarisation-resolving camera 408.In addition to spectral modulation vector analysis based on cos(Λν) / sin(Λν) andcos(Λν) / cos(2Λν) spectral modulation functions, a range of other spectral functions could be implemented using the PolSpec approach with different configurations ofpolarisation optics. For example, the arrangement shown in Figure 10 produces datato be represented on a spectral modulation vector plot corresponding to spectralmodulation functions of cos(Λν) / sin(Λν)sin(Λν / Χ), where Χ is a positive integerconstant. With Χ = 3 or 4, this spectral modulation vector plot is similar to theconventional cos(Λν) / sin(Λν) phasor plot within a limited wavelength range but doesnot require an achromatic quarter wave plate.Figure 11 illustrates the results of a single shot approach for generating spectralmodulation vector images corresponding to cos(Λν) / sin2(Λν) spectral modulationfunctions of a colour sample at the camera frame rate using a polarisation-resolvingcamera with a linear polariser and two half wave plates. In this example a linearpolariser and two low-cost halfwave plates cut from low-cost polymer sheets havebeen used following the configuration illustrated in Figure 4. This arrangement isparticularly compact and inexpensive. In the example of Figure 11, the apparatusreceives light from a colour plate 1100. The total intensity image 1200 of the colourplate is shown in Figure 12. The colour plate 1100 comprises regions of red 1100,green 1102 and blue 1104. As shown in the plot on the right-hand side of Figure 11,these red 1100, green 1102 and blue 1104 regions each correspond to well- separated respective groups of data points 1106, 1108, 1110 on the spectral modulation vector plot corresponding to spectral modulation functionssin2(Λν) / cos(Λν). The lower-left group of data points 1106 corresponds to red light,the upper right group of data points 1110 corresponds to blue light, and theremaining group of data points 1108 corresponds to green light. The spectralmodulation vector plot can therefore be used to identify regions corresponding to different colours. By selecting a group of points on the spectral modulation plot acolour mask can be generated. Figure 13 shows examples of the results of red 1302,green 1304 and blue 1306 colour masks (or ‘spectral modulation vector masks’)applied to the plot of Figure 11. In other words the red mask 1302 corresponds to the lower-left group of data points 1106, the blue mask 1306 corresponds to the upper right group of data points 1110, and the green mask 1304 corresponds to theremaining group of data points 1108. Whilst regions of red, green and blue areclassified in the example of Figure 11, more complex spectral signatures can alsobe classified or unmixed.Illustrative ApplicationsBy virtue of the PolSpec methods of the present disclosure requiring many fewerimage acquisitions than typically needed in hyperspectral imaging approaches, andnot having the out-of-band losses of many multispectral imaging approaches, themethods and apparatus of the present disclosure provide a more photon efficientmeans for mapping spectral characteristic. The improved methods and apparatuscan be applied to a wide range of applications including unmixing of different spectral channels and classification of samples based on spectral signatures. It can provide the functionality of spectral phasor analysis but with extended capabilities.The polarisation-based optical approach is more flexible, lower cost and / or morephoton efficient than previous implementations of spectral phasor imaging. PolSpecspectral classification of image and other data can also be combined with machinelearning to enhance both spectral unmixing and classification applications. PolSpec can be implemented in almost any optical instrument using any detector where there are polarisation optics (e.g., polarisers and retarders) available in the appropriate spectral region. This could include wide-field, light-sheet, line-scanning and confocal / multiphoton laser scanning microscopes, endoscopes, telescopes,remote sensing systems and even mobile phone cameras if the polarisationcomponents can be miniaturised. PolSpec spectral modulation vector imaging maybe combined with fluorescence lifetime imaging (FLIM). This enables unmixing ofmore channels using both spectral and lifetime signatures, for example for highly multiplexed readouts of fluorescence labels as desired for some spatial proteomics applications. When applied to the common technique of Forster resonance energy transfer (FRET) measurements, the methods and apparatus of the presentdisclosure enable the recording and unmixing of signals from both donor andacceptor fluorophores, including with FLIM, offering opportunities for more sophisticated and robust analysis for FRET experiments. PolSpec spectral modulation vector imaging may also be used with imaging and spectroscopic measurement modalities based on spectrally resolved scattered light. PolSpec can also be combined with other modalities such as polarisation resolved measurement / imaging, e.g., to map fluorescence anisotropy or FRET. The configurations of Figures 3 and 6 inherently provide this polarisation information. PolSpec could also be used for spectral characterisation of scattered light, which can provide information about the subwavelength structure of samples, e.g., using partial wave spectroscopic microscopy. Applications of PolSpec spectral (modulation vector) analysis include biomedical and physical sciences research, pathology, in vivo diagnostics (e.g., screening forabnormal tissue potentially indicating cancer), forensics, and multiplexedfluorescence readouts (e.g., for sequencing, spatial proteomics,immunofluorescence, and so on). It could also be applied to remote sensing forenvironmental monitoring, surveillance of plants and crops (including from drones), and other sensing applications. Modifications and Alternatives Detailed embodiments and some possible alternatives have been described above. As those skilled in the art will appreciate, a number of modifications and further alternatives can be made to the above embodiments whilst still benefiting from the inventions embodied therein. It will therefore be understood that the invention is not limited to the described embodiments and encompasses modifications apparent to those skilled in the art lying within the scope of the claims appended hereto. The spectral resolution (discrimination) of a PolSpec based instrument will dependon the period Λ of the spectral modulation function and the signal to noise ratio ofthe detected signals. The period can be decreased to provide higher spectralresolution by using birefringent elements with larger retardance (e.g., ^n L = i^0where i > 1), although this will decrease the spectral range proportional to 1 / Λ. Thismay be desirable, for example for Raman spectroscopic applications. Higherresolution PolSpec systems could be combined with other spectral filters to limit signals to specific spectral ranges, or the PolSpec concept could be cascaded using stages with different retardances and therefore different spectral modulation periods. The liquid crystal retarder approach enables convenient tuning of the period of the spectral modulation functions, which can improve the ability to unmix multiple spectral components. This is analogous to using higher harmonics in conventional spectral phasor analysis. Various other modifications will be apparent to those skilled in the art and will not be described in further detail here. Exemplary ApparatusFigure 15 shows a simplified schematic illustration of exemplary apparatus 1700 forperforming methods of the present disclosure, for example to analyse the output of the one or more detectors to perform classification of a sample.It will be appreciated that the apparatus 1700 may comprise any suitable computeror server, for example. As shown, the apparatus 1700 includes a communicationinterface 1705 which is operable to transmit signals to and receive signals from otherdevices via a network 1706. For example, the apparatus 1700 may receive an outputfrom the one or more detectors via the network 1706 Alternatively, the output fromthe one or more detectors may be loaded from a removable data storage device(RMD), for example. It will be appreciated that when the apparatus 1700 isconnected to a network 1706, the apparatus 1700 need not necessarily be co-located with the detector(s).The apparatus 1700 also comprises a user interface 1707. The user interface 1707may comprise a display, or any other suitable form of user interface. The userinterface 1707 may be configured for outputting an image or classification derivedusing the output of the one or more detectors, for example.A controller 1701 controls the overall operation of the apparatus 1700 in accordancewith software stored in a memory 1702, for example to perform any of the methodsdescribed above. The software may be pre-installed in the memory 1702 and / or maybe downloaded via the network 1706 or from a removable data storage device(RMD), for example. The software includes, among other things, an operatingsystem 1703 and a data analysis module 1704. The data analysis module 1704 isoperable to perform any of the methods described above, and to analyse the outputof the one or more detectors, for example for outputting an image and / or classification. The apparatus 1700 has been described for ease of understanding as having a number of discrete modules. Whilst these modules may be provided in this way for certain applications, for example where an existing system has been modified to implement the invention, in other applications, for example in systems designed with the inventive features in mind from the outset, these modules may be built into the overall operating system or code and so these modules may not be discernible as discrete entities. These modules may also be implemented in software, hardware, firmware, or a mix of these. As those skilled in the art will appreciate, the software modules may be provided in compiled or un-compiled form and may be supplied to the apparatus 1700 as a signal over a computer network, or on a recording medium. Further, the functionality performed by part or all of this software may be performed using one or more dedicated hardware circuits. However, the use of software modules is preferred as it facilitates the updating of the apparatus 1700 in order to update the functionalities.The controller 1701 may comprise any suitable form of processing circuitry including(but not limited to), for example: one or more hardware implemented computer processors; microprocessors; central processing units (CPUs); graphics processing units (GPUs); arithmetic logic units (ALUs); input / output (IO) circuits; internal memories / caches (program and / or data); processing registers; communication buses (e.g. control, data and / or address buses); direct memory access (DMA) functions; hardware or software implemented counters, pointers and / or timers; and / or the like. References[1] Fereidouni, F., Bader, A.N. & Gerritsen, H.C. Opt. Express 20, (2012) 12729–12741.[2] Cutrale, F., Salih, A. & Gratton, E. Methods Appl. Fluoresc. 1 (2013) 035001.[3] Cutrale et al, Nat. Meth., 14 (2017) 149[4] WO2020160485A1[5] A. Dvornikov and E. Gratton, Biomed. Opt. Express 9 (2018) 3503[6] Wang et al, Cell Reports Methods 3 (2023) 100441[7] A. R. Harvey et al, “Spectral imaging in a snapshot”, Proc. of SPIE. Vol.5694 (2005) [8] F. Snik and C. U. Keller, US 2021 / 0131950 A1 Examples Examples of the present disclosure are also described in the following numbered clauses:1. Apparatus for spectrally characterising and differentiating optical signalsusing a plurality of spectral modulation functions to enable representation and classification of the optical signals through the use of vectors that are sensitive to shapes of associated spectral intensity profiles, wherein the apparatus comprises a polarisation-resolved detection system, and wherein the polarisation-resolved detection system comprises: at least one polariser configured for polarising incident light to output polarised light, and at least one optical retarder configured to receive the polarised light from the at least one polariser, wherein the at least one polariser and the at least one optical retarder are configured for providing the plurality of spectral modulation functions; and at least one detector for detecting light output from the optical retarder.2. The apparatus according to clause 1, wherein the at least one polariser andthe at least one optical retarder are configured for providing spectral modulation functions that are orthogonal or substantially orthogonal.3. The apparatus according to clause 1 or 2, wherein the at least one opticalretarder comprises an adjustable optical retarder having an adjustable retardance.4. The apparatus according to clause 3, wherein the adjustable retardance iselectronically adjustable.5. The apparatus according to clause 3 or 4, wherein the adjustable opticalretarder comprises a liquid crystal retarder.6. The apparatus according to any preceding clause, wherein the at least onepolariser comprises a first polarising beam splitter.7. The apparatus according to clause 6,wherein the first polarising beam splitter is configured to polarise the incident light to output a first polarised beam and a second polarised beam; and wherein the first polarised beam is orthogonally polarised with respect to the second polarised beam.8. The apparatus according to clause 7, wherein the apparatus is configured for output of the first polarised beam to a second polarising beam splitter via a first optical retarder; wherein the apparatus is configured for output of the second polarised beam to a third polarising beam splitter via a second optical retarder; wherein the second polarising beam splitter is configured to output a third polarised beam to a first detector and to output a fourth polarised beam to a second detector; wherein the third polarised beam is orthogonally polarised with respect to the fourth polarised beam; wherein the third polarising beam splitter is configured to output a fifth polarised beam to a third detector and to output a sixth polarised beam to a fourth detector; and wherein the fifth polarised beam is orthogonally polarised with respect to the sixth polarised beam.The apparatus according to clause 6,wherein the first polarising beam splitter is configured to polarise the incident light to output a first polarised beam to a second polarising beam splitter via an adjustable retarder; and wherein the second polarising beam splitter is configured to output a second polarised beam to a first detector, and to output a third polarised beam to a second detector.The apparatus according to clause 9, wherein the adjustable retarder is aliquid crystal retarder.The apparatus according to clause 9 or 10,wherein the first polarising beam splitter is further configured to polarise the incident light to output a fourth polarised beam to the second polarising beam splitter via the adjustable retarder; wherein the fourth polarised beam is orthogonally polarised with respect to the first polarised beam; wherein the first polarised beam is incident upon a first face of the second polarising beam splitter; and wherein the fourth polarised beam is incident upon second face of the second polarising beam splitter, that is different from the first face, for output of a fifth polarised beam to the first detector from the second polarising beam splitter, and for output of a sixth polarised beam to the second detector from the second polarising beam splitter.12. The apparatus according to clause 6,wherein the first polarising beam splitter is configured to polarise the incident light to output a first polarised beam to a second polarising beam splitter via an optical retarder; wherein the second polarising beam splitter is configured to output a second polarised beam to a first detector, and to output a third polarised beam to a second detector; wherein the first polarising beam splitter is further configured to output a fourth polarised beam to a third polarising beam splitter via an achromatic quarter wave plate and via the optical retarder, wherein the apparatus is configured so that the fourth polarised beam passes through the achromatic quarter wave plate before passing through the optical retarder; and wherein the third polarising beam splitter is configured to output a fifth polarised beam to a third detector, and to output a sixth polarised beam to a fourth detector.13. The apparatus according to any one of clauses 1 to 5, wherein the at leastone polariser comprises a linear polariser.14. The apparatus according to clause 13,wherein the linear polariser is configured for polarising the incident light to output polarised light to a second optical retarder via a first optical retarder; and wherein the at least one detector is arranged for detecting light output from the second optical retarder.The apparatus according to clause 13,wherein the linear polariser is configured for polarising the incident light to output polarised light to an achromatic quarter wave plate via an optical retarder; and wherein the at least one detector is arranged for detecting light output from the achromatic quarter wave plate.The apparatus according to clause 14 or 15,wherein the at least one detector comprises a camera having a plurality of pixels; wherein the plurality of pixels comprises a first group of pixels having a first polarisation mask arranged at a first polarisation angle; wherein the plurality of pixels comprises a second group of pixels having a second polarisation mask arranged at a second polarisation angle; wherein the plurality of pixels comprises a third group of pixels having a third polarisation mask arranged at a third polarisation angle; wherein the plurality of pixels comprises a fourth group of pixels having a fourth polarisation mask arranged at a fourth polarisation angle; and wherein the first polarisation angle, the second polarisation angle, the third polarisation angle and the fourth polarisation angle are different from each other.The apparatus according to clause 16,wherein the second polarisation angle is offset by 45 degrees from the first polarisation angle; wherein the third polarisation angle is offset by 45 degrees from the second polarisation angle; and wherein the fourth polarisation angle is offset by 45 degrees from the third polarisation angle.18. The apparatus according to clause 16 or 17 when dependent on clause 14,wherein one or more of the linear polariser, the first optical retarder and the second optical retarder are mounted on the camera.19. The apparatus according to clause 16 or 17 when dependent on clause 15,wherein one or more of the linear polariser, the optical retarder and the achromatic quarter wave plate are mounted on the camera.20. The apparatus according to any one of clauses 13 to 19, wherein theapparatus further comprises a quarter wave plate configured for polarising the light that is incident on the linear polariser.21. An imaging system, such as a microscope system or camera system,comprising the apparatus according to any preceding clause.22. A method of spectrally resolving optical signals, the method comprising:receiving the incident light at apparatus according to any one of clauses 1 to 20; and detecting light output from the optical retarder at the at least one detector.23. The method according to clause 22, wherein the incident light is from asample, and the method further comprises classifying a spectral signature of the sample based on the light detected at the at least one detector.24. The method according to clause 22 or 23, wherein the method comprisesusing a time-resolved detector for fluorescence lifetime imaging.25. The method according to any one of clauses 22 to 24, wherein the methodfurther comprises generating a polarisation resolved image based on the light detected at the at least one detector.26. Apparatus for spectrally characterising and differentiating optical signalsusing a plurality of spectral modulation functions to enable representation and classification of the optical signals through the use of spectral modulation vectors that are sensitive to shapes of associated spectral intensity profiles, wherein the apparatus comprises a polarisation-resolved detection system, and wherein the polarisation-resolved detection system comprises: at least one polariser configured for polarising incident light to output polarised light, and at least one optical retarder configured to receive the polarised light from the at least one polariser, wherein the at least one polariser and the atleast one optical retarder are configured for providing the plurality of spectralmodulation functions in conjunction with at least two polarisation-resolved detectors that detect all, or substantially all, of the light output from the at least one optical retarder.27. The apparatus according to clause 26, wherein the at least one polariser andthe at least one optical retarder are configured for providing spectral modulation functions that are orthogonal or substantially orthogonal in order to facilitate linear unmixing of the spectral modulation vectors.28. The apparatus according to clause 26 or 27, wherein the at least twopolarisation resolved detectors comprise a detector configured to acquire sequential polarisation-resolved data or acquiring image data of orthogonally polarised signals incident on different areas of the detector.

Claims

CLAIMS1. Apparatus for spectrally characterising and differentiating optical signals,using a plurality of spectral modulation functions that are orthogonal orsubstantially orthogonal to each other, to enable representation andclassification of the optical signals through the use of spectral modulation vectors that are sensitive to shapes of associated spectral intensity profiles,wherein the apparatus comprises a polarisation-resolved detection system,and wherein the polarisation-resolved detection system comprises: at least one polariser configured for polarising incident light tooutput polarised light, at least one optical retarder configured toreceive the polarised light from the at least one polariser, and at leastone detector for detecting light output from the optical retarder; wherein the at least one polariser, the at least one opticalretarder and optionally the at least one detector are configured forproviding the plurality of spectral modulation functions.

2. The apparatus according to claim 1, wherein the at least one detectorcomprises at least two polarisation-resolved detectors.

3. The apparatus according to claim 2, wherein the at least two polarisation-resolved detectors are configured for detecting all, or substantially all, of the light output from the at least one optical retarder.

4. The apparatus according to any preceding claim, wherein the apparatusfurther comprises a further polariser arranged to receive light output fromthe at least one optical retarder, and wherein the at least one detector is arranged to detect light output from the further polariser; and wherein the at least one polariser, the at least one optical retarder and the further polariser are configured for providing the plurality of spectral modulation functions.

5. The apparatus according to any of claims 1 to 3, wherein the at least onedetector comprises a camera having a plurality of pixels; wherein the plurality of pixels comprises a first group of pixels having a first polarisation mask arranged at a first polarisation angle; wherein the plurality of pixels comprises a second group of pixels having a second polarisation mask arranged at a second polarisation angle; wherein the plurality of pixels comprises a third group of pixels having a third polarisation mask arranged at a third polarisation angle; wherein the plurality of pixels comprises a fourth group of pixels having a fourth polarisation mask arranged at a fourth polarisation angle; wherein the first polarisation angle, the second polarisation angle, the third polarisation angle and the fourth polarisation angle are different from each other; and wherein the at least one polariser, the at least one optical retarder and the polarisation masks are configured for providing the plurality of spectral modulation functions.

6. The apparatus according to any preceding claim, wherein the at least onedetector comprises a detector configured to acquire sequential polarisation- resolved data, or configured to acquire image data of orthogonally polarisedsignals incident on different areas of the detector.

7. The apparatus according to any preceding claim, wherein the at least oneoptical retarder comprises an adjustable optical retarder having anadjustable retardance.

8. The apparatus according to claim 7, wherein the adjustable retardance iselectronically adjustable.

9. The apparatus according to claim 7 or 8, wherein the adjustable opticalretarder comprises a liquid crystal retarder.

10. The apparatus according to any preceding claim, wherein the at least onepolariser comprises a first polarising beam splitter.

11. The apparatus according to claim 10,wherein the first polarising beam splitter is configured to polarise the incident light to output a first polarised beam and a second polarised beam; and wherein the first polarised beam is orthogonally polarised with respect to the second polarised beam.

12. The apparatus according to claim 11,wherein the apparatus comprises a second polarising beam splitter, a first optical retarder, a third polarising beam splitter, a second optical retarder, a first detector, a second detector, a third detector and a fourth detector; wherein the apparatus is configured for output of the first polarisedbeam to the second polarising beam splitter via the first optical retarder;wherein the apparatus is configured for output of the second polarised beam to the third polarising beam splitter via the second optical retarder;wherein the second optical retarder has a retardance that is different to that of the first optical retarder, to provide a different and orthogonalspectral modulation function; wherein the second polarising beam splitter is configured to output a third polarised beam to the first detector and to output a fourth polarisedbeam to the second detector;wherein the third polarised beam is orthogonally polarised with respect to the fourth polarised beam; wherein the third polarising beam splitter is configured to output a fifth polarised beam to the third detector and to output a sixth polarised beam tothe fourth detector; andwherein the fifth polarised beam is orthogonally polarised with respect to the sixth polarised beam.

13. The apparatus according to claim 10,wherein the apparatus comprises a second polarising beam splitter, an adjustable retarder, a first detector and a second detector; wherein the first polarising beam splitter is configured to polarise the incident light to output a first polarised beam to the second polarising beamsplitter via the adjustable retarder; andwherein the second polarising beam splitter is configured to output asecond polarised beam to the first detector, and to output a third polarisedbeam to the second detector.

14. The apparatus according to claim 13, wherein the adjustable retarder is aliquid crystal retarder.

15. The apparatus according to claim 13 or 14,wherein the first polarising beam splitter is further configured to polarise the incident light to output a fourth polarised beam to the second polarising beam splitter via the adjustable retarder;wherein the fourth polarised beam is orthogonally polarised with respect to the first polarised beam; wherein the first polarised beam is incident upon a first face of the second polarising beam splitter; andwherein the fourth polarised beam is incident upon second face of thesecond polarising beam splitter, that is different from the first face, for outputof a fifth polarised beam to the first detector from the second polarisingbeam splitter, and for output of a sixth polarised beam to the seconddetector from the second polarising beam splitter.

16. The apparatus according to claim 10,wherein the apparatus comprises a second polarising beam splitter, an optical retarder, a first detector, a second detector, a third polarisingbeam splitter, an achromatic quarter wave plate, a third detector, and a fourth detector; wherein the first polarising beam splitter is configured to polarise the incident light to output a first polarised beam to the second polarising beamsplitter via the optical retarder;wherein the second polarising beam splitter is configured to output a second polarised beam to the first detector, and to output a third polarisedbeam to the second detector;wherein the first polarising beam splitter is further configured to output afourth polarised beam to the third polarising beam splitter via theachromatic quarter wave plate and via the optical retarder, wherein the apparatus is configured so that the fourth polarised beam passes through the achromatic quarter wave plate before passing through the optical retarder; and wherein the third polarising beam splitter is configured to output a fifth polarised beam to the third detector, and to output a sixth polarised beamto the fourth detector.

17. The apparatus according to any one of claims 1 to 9, wherein the at leastone polariser comprises a linear polariser.

18. The apparatus according to claim 17,wherein the apparatus comprises a first optical retarder, and a secondoptical retarder; wherein the linear polariser is configured for polarising the incident light to output polarised light to the second optical retarder via a first opticalretarder; and wherein the at least one detector is arranged for detecting light outputfrom the second optical retarder.

19. The apparatus according to claim 17,wherein the apparatus comprises an achromatic quarter wave plate and an optical retarder; wherein the linear polariser is configured for polarising the incident light to output polarised light to the achromatic quarter wave plate via theoptical retarder; and wherein the at least one detector is arranged for detecting light output from the achromatic quarter wave plate.

20. The apparatus according to claim 18 or 19,wherein the at least one detector comprises a camera having a plurality of pixels; wherein the plurality of pixels comprises a first group of pixels having a first polarisation mask arranged at a first polarisation angle; wherein the plurality of pixels comprises a second group of pixels having a second polarisation mask arranged at a second polarisation angle; wherein the plurality of pixels comprises a third group of pixels having a third polarisation mask arranged at a third polarisation angle; wherein the plurality of pixels comprises a fourth group of pixels having a fourth polarisation mask arranged at a fourth polarisation angle; and wherein the first polarisation angle, the second polarisation angle, the third polarisation angle and the fourth polarisation angle are different fromeach other.

21. The apparatus according to claim 20,wherein the second polarisation angle is offset by 45 degrees from the first polarisation angle; wherein the third polarisation angle is offset by 45 degrees from the second polarisation angle; and wherein the fourth polarisation angle is offset by 45 degrees from the third polarisation angle.

22. The apparatus according to claim 20 or 21 when dependent on claim 18,wherein one or more of: the linear polariser, the first optical retarder and thesecond optical retarder, are mounted on the camera.

23. The apparatus according to claim 20 or 21 when dependent on claim 19,wherein one or more of: the linear polariser, the optical retarder and theachromatic quarter wave plate, are mounted on the camera.

24. The apparatus according to any one of claims 17 to 23, wherein theapparatus further comprises a quarter wave plate or half wave plateconfigured for polarising the light that is incident on the linear polariser.

25. An imaging system, such as a microscope system or camera system,comprising the apparatus according to any preceding claim.

26. A method of spectrally resolving optical signals, the method comprising:receiving the incident light at apparatus according to any one of claims1 to 24; and detecting light output from the optical retarder at the at least one detector.

27. The method according to claim 26, wherein the incident light is from asample, and the method further comprises classifying a spectral signature of thesample based on the light detected at the at least one detector.

28. The method according to claim 26 or 27, wherein the method comprisesusing a time-resolved detector for fluorescence lifetime imaging.

29. The method according to any one of claims 26 to 28, wherein the methodfurther comprises generating a polarisation resolved image based on the lightdetected at the at least one detector.

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