Polarisation optics for biomedical and clinical applications: a review

Many polarisation techniques have been harnessed for decades in biological and clinical research, each based upon measurement of the vectorial properties of light or the vectorial transformations imposed on light by objects. Various advanced vector measurement/sensing techniques, physical interpretation methods, and approaches to analyse biomedically relevant information have been developed and harnessed. In this review, we focus mainly on summarising methodologies and applications related to tissue polarimetry, with an emphasis on the adoption of the Stokes–Mueller formalism. Several recent breakthroughs, development trends, and potential multimodal uses in conjunction with other techniques are also presented. The primary goal of the review is to give the reader a general overview in the use of vectorial information that can be obtained by polarisation optics for applications in biomedical and clinical research.


Introduction
Light, as an electromagnetic wave, possesses several fundamental properties, which include intensity, wavelength, phase and polarisation 1,2 (see Fig. 1a). While the former three are scalar quantities, polarisation has vectorial properties; its use has therefore required more advanced optical and computational approaches. Hence, studies of either the vector properties of light, described via the state of polarisation (SOP) or the full vectorial transformation properties of an object, have a shorter history in biomedical analysis compared with their scalar counterparts, and the extent of their application is still being explored [3][4][5] . So far, numerous intriguing areas of research have been enhanced through harnessing vectorial information acquired via polarisation optics; these range from fundamental research [6][7][8][9][10] , such as quantified polarisation entropy 11 , across quantum physics 12 , such as spin-orbital interaction of light 13,14 , to material characterisation (e.g. chiral characteristics 15 ) or for biomedical studies and clinical applications (e.g. characterisation of structural features in tissue [16][17][18][19][20][21] ).
Scattering, especially through multiple scattering processes, alters the degree of polarisation and SOP of the incident light beam 22 . While it is an insightful procedure for evaluating structural information of biomedical samples including tissues and cells 16 , it also introduces uncertainty in expected photon properties 22 . This characteristic largely hinders the development of modern tissue polarimetric techniques and related information analysis 20,22,23 . The turbidity of many tissue structures imposes randomness on the photons' interaction processes, which complicates the detection and analysis of vectorial information 20 . Such phenomena also distinguish tissue polarimetry from the traditional polarisation measurement technique of ellipsometry [22][23][24][25][26] . As summarized in Fig. 1b, their comparison shows several commonalities and differences. The Jones formalism is used for clear and non-depolarising media such as thin films; it consists of the Jones vector (describing the polarisation property of the light) and Jones matrix (describing the polarisation transformation properties of the object). They have been widely used in ellipsometry techniques 25,26 (see Fig. 1b; and summary in Ref 26 ). Another polarisation formalism is Stokes-Mueller, in which the Stokes vector and the Mueller matrix are used to describe the light beam and the object, respectively. Neither the Stokes vector nor the Mueller matrix maintain absolute phase information, but have the advantage of being able to represent depolarisation 27,28 . This is often essential in biomedical polarimetry, whose applications normally involve scattering induced light depolarisation [20][21][22][23] .
There exists an increasing trend in both modern ellipsometry and polarimetry to deal with increasingly complex media, moving from isotropic and homogeneous media towards anisotropic and inhomogeneous ones [20][21][22][23][24][25][26][27][28][29][30][31] . While modern ellipsometry is developing towards full polarisation measurement using the Stokes-Mueller formalism, advanced polarimetry is gradually changing from full vectorial measurement to partial detection, as some key features of biomedical specimens could possibly be revealed through partial, rather than complete, measurements of vectorial information 16,32,33 .
The structure of this review is given in Fig. 1c; it consists of introducing the basic polarisation optical tools, summarizing the current vectorial information detection, extraction, and analysis approaches, and pointing out the possibilities for future multi-modal synergy with other cutting-edge technologies. Although biomedical polarimetry is still developing towards various research fields and applications, largely unexplored spaces still exist. We also hope this review could stimulate new explorations or breakthroughs in such prospective fields.
It is worth noting that the use of biomedical polarimetry is expanding and has also been summarized in several recent reviews by Tuchin 22 , Ghosh & Vitkin 20 , Ramella-Roman et al. 23 24 , De Boer et al. 34 , He et al. 16 . They have demonstrated the fast progress of this technique in the biomedical and clinical fields. # , %# , )* , +)* are the projection intensities (different linear components in directions of 0°, 90°, 45°, -45° with respect to the local coordinate system) of a light beam, . andare components of left/right-handed circular polarised light, respectively. Note some other parameters can be defined with components of Stokes vector: degree of polarisation = 2 3 + 3 + 3 / degree of linear polarisation = 2 3 + 3 / and degree of circular polarisation of light 3-5 .

= 2 3 /
From the above expressions, we see that the Stokes vector can be calculated via intensity measurements that can be readily performed in an experiment 47,48 . The Jones vector, on the other hand, is defined by amplitude and phase that cannot be directly measured, which is another reason why the Jones approach is less well suited to biomedical polarimetry [20][21][22][23] . The intrinsic reason for the existence of depolarisation is due to temporal or spatial averaging 16,[20][21][22][23] . If an extremely fast and small detector could monitor the vector properties of the light, then it would only detect polarised light. Such averaging properties can also be found in the definition of the Stokes vector 47,48 . Note the definitions of righthanded circular polarised light (clockwise rotation) and left-handed circular polarised light (anticlockwise rotation) are different in optics books and academic communities. It depends on whether the observer 'sees' the light from the source (Convention I), or from the detector (Convention II). Institute of Electrical and Electronics Engineers (IEEE) uses Convention I, so it is also widely used in engineering fields; Quantum physicists also use Convention I, to be consistent with the conventions for representing particle spin states 49,50 . However, for numerous optics books such as Principles of Optics (Born & Wolf 48 ) and Handbook of Optics 51 , Convention II is used. In this review, we use Convention II in order to correspond to such scientific references.
The Jones vector has a graphical representation known as the polarisation ellipse 47,48 (if we add the parameter DOP, the polarisation ellipse can also represent the Stokes vector (see Fig. 2b (i))). While for Stokes vector visualization, the Poincaré sphere (PS) is commonly used 47,48 (see Fig. 2b (ii)). SOPs are represented via the PS, which is defined in a three-dimensional coordinate system, whose coordinates correspond to the eigenbasis formed by , and (each normalized by ). The PS is a unitary sphere that represents complete polarisation states on its surface and depolarised states inside the sphere. Any transformation of the SOP through a specimen is equivalent to manipulation of the original Stokes vector between different points on or inside the PS. Figure 2b (ii) gives a schematic demonstration of the PS. The length of the vector from the origin point to the SOP location denotes the DOP 47,48 . The letters , , , are specific polarisation states: horizontally polarised ( ), vertically polarised ( ), 45° polarised ( ) and -45° polarised ( ). The polarisation ellipse parameters (c and y) can be interpreted from the azimuth angle (and the polar angle) of the derived vector inside the PS.
Such a graphical representation excludes the absolute phase information, which is sometimes not addressed in typical vectorial beam analysis such as pure polarisation measurement or tissue polarimetry [20][21][22][23]47,48 . However, one type of the absolute phase variation that is referred to as geometric phase is related to the pathway of the SOP movement on the surface of the PS 47,48 , which features scope for the extension of the tissue polarimetric technique (also see Discussion).

Mueller matrix
The Mueller matrix (MM) describes the vectorial transformation properties of an object 16,[20][21][22][23]  Several factors may contribute to depolarisation in experimental scenarios. We describe three main reasons here. a) The first reason relates to the time domain. In general, the Stokes vector polarimeter is based on intensity measurement 26 , so in practice the intensity recorded at the detector includes a time-integration process. If the SOP changes rapidly, possibly due to multi-scattering induced by complex bio-media, then depolarisation would be measured. b) This reason relates to the spatial domain. When imaging processes are involved, every point on the beam section is created through the integration of various sub-beams that could have different polarisation states. The superposition of these states leads to depolarisation. c) The final reason is given in the spectral domain. Many processes that affect polarisation, such as birefringence and scattering, are also dependent on wavelength. Hence for different wavelengths, variations in amplitude and phase may also lead to depolarisation.

Vectorial information measurement techniques for biomedical applications
Numerous vectorial information measurement methods have been put forward in the past decades 4,7,11,26,28,29,63 . In this section, we categorize the polarisation measurement techniques into two types: time-sequenced and snap-shot approaches 28,29,64-67 (see Fig. 3). For both cases, the preparation required before detection is similar and can be divided into three general steps: denoising, optimization and calibration 32,68-78 (see Fig. 4). The aim of those steps is to reduce the complex errors that would occur during the measurement process, hence obtaining imaging results with higher precision and accuracy 32,[69][70][71][72] . The technical aspects of such advanced polarimetry are summarized in the review papers by Both time-sequenced and snap-shot polarimetry techniques can be classified in two general ways: firstly, as either Stokes vector (light property) or MM (material property) measurement; and secondly, as partial or full vectorial measurement ( Fig. 3). We will classify different techniques using the second criteria in later sections of this review.

Time-sequenced techniques
Stokes polarimetry is clearly the basis for more advanced MM polarimetry. Both of their intrinsic mechanisms can be interpreted with respect to the instrument matrix (A) 68-72 (see Fig. 4). This matrix represents the settings of the polarisation state generator (PSG) and polarisation state analyser (PSA) in the various measurement steps: for MM measurement it represents the PSG and PSA, for Stokes vector measurement it represents one the PSA. Combinations of the rotating waveplate and/or polariser are widely adopted in such approaches [64][65][66] . The original proposal for a Stokes vector measurement scheme (that using SOPs of , , , , and ) was from Collett 87 in 1984. Later it was adopted for biomedical information extraction or phantom analysis with ability of the full depolarisation information characterisation 16,[20][21][22][23] .
The use of rotating components has disadvantages, such as increasing measurement time and introducing unexpected errors from mechanical movements. However, such systems are easy to construct. Hence, numerous commercialized polarimeters still use this approach. In order to make improvements, researchers have tried to reduce the number of the rotating components (such as the dual-rotating waveplate MM polarimeter with fixed polarisers that was proposed by Azzam 64 in 1978, which is widely used in tissue analysis 16,22 ) or use fast modulation devices (such as Stokes or MM polarimeters enabled via liquid crystal variable retarders (LCVR) 88 , spatial light modulators (SLM) 89  Although there are some applications that require high speed operation, such as detection in dynamic situations like in vivo sensing for clinical diagnosis 24 , time-sequenced polarimeters still play an important role in modern polarimetric research, due to their mature state of development and simple configuration. Such applications include characterisation of complex vector fields 6,7,9 , or providing ground truth validation in tissue research (e.g., differentiating human breast cancer [93][94][95] ).

Snap-shot techniques
Rapidly changing or dynamic objects need snap-shot detection, in order to correctly extract vectorial information that would be complicated by time-sequenced measurement. Snap-shot approaches are configured to take different measurements in parallel, as opposed to the serial measurement of sequential techniques. In general, snap-shot techniques must, to some degree, sacrifice alternative dimensions to enable simultaneous vector measurement 67,96 . Those methods include (see Fig. 3b): Stokes vector polarimeters with division-of-amplitude 97-99 , division-of-wavefront 71,[100][101][102][103][104][105] or division-of-focus-plane 106-122 -these fit in the category of spatial modulation with respect to different analysis channels (see Fig. 3b (iii)). Savart-plate-based polarimeters (Oka et al.) are in the category of Fourier frequency domain segmentation, which are interferometric systems where the polarisation information is encoded in the spatial carrier fringes 123 . If combined with the property of birefringence dispersion, spectroscopic polarimetry with channelled spectrum can also be presented 67,96 .
Similar to Stokes vector polarimeters, there exist concepts for snap-shot MM polarimeters, in which certain dimensions are sacrificed to enable simultaneous MM estimation (see 3b (iv)). Dubreuil et al. 67 and Hagen et al. 96   (iii) Full Stokes vector polarimetry; the PSA and PSG can both be a tuneable retarder (rotating quarter wave plate or SLM assembly) followed by a fixed polariser 28,63,79 . (iv) Full MM polarimetry; the PSG can be a fixed polariser followed by a tuneable retarder 28,63,79 (rotating quarter wave plate or LC components); the PSA can be a tuneable retarder (rotating quarter wave plate or LC components) followed by a fixed polariser 28
It also can be seen in the figure that three directions towards obtaining the correct vectorial measurements are still developing.
Note again that A is the instrument matrix for polarimetric measurement specifically, which is determined by the In order to reduce δA and δI 32,68-78 , a 'denoising process' is adopted. Figure 4 shows the approaches in time or spatial domain including time average and interpretation methods. To deal with the ΔA and ΔI, a 'calibration process' is required. Numerous polarimetric calibration methods have been proposed 23,29,63,71,130 ; these can be divided into global and local calibration approaches. Note that the calibration process itself also suffers from the error transfer process.
Hence, determining the SOPs for calibration, choosing the standard calibration samples, as well as designing specific calibration methods for different systems should be taken into consideration 131,132 .  [139][140][141] . Other useful criteria have also been proposed 142,143 . Such optimisation parameters can be used for evaluating the intrinsic error amplification of a polarimetry, which affect the accuracy and precision of the measurement 23,29,63,71,[130][131][132] . If we consider the CN, the minimum CN value for a matrix based Stokes polarimetry is √3 , which is the theoretical limit for systematic error amplification 68,70 , as opposed to the minimum possible CN value (CN = 1) for matrix inversion. A similar error amplification also exists in MM polarimetry 144 . The three above-mentioned processes (denoising, optimization, calibration) are vital for any biomedical polarimetry, as they determine the credibility of the information extraction and further analysis.
For the matrix based calculation of Stokes polarimetry (within the scope of above explanations), there exist two problems: first, the mathematical aspect of minimal error amplification through the matrix calculation; second, the practical aspect that the above-mentioned three separate procedures contribute to error accumulation separately, as they  68 . In essence, this approach means that the Stokes vector retrieval process changes from matrix-based calculation to information-based image processing.

Vectorial information extraction methods for biomedical applications
Information about the vectorial properties of a biological specimen can be derived partially from the polarisation properties of the light beam or, in a more complete fashion, from the polarisation properties of the tissue itself [20][21][22][23]153 . To extract information from the measured Stokes vector or MM (or part of them), different decomposition methods and parameters were proposed to represent meaningful physical processes, to extract information that could be used in subsequent analysis [52][53][54][55][56][57][58][59][60][61][62] .

Information extraction from the vector properties of the light beam
Several parameters can be calculated from the Stokes vector directly (see Fig. 5a (i) and previous section): such as the degree of polarisation (DOP), degree of linear polarisation (DOLP) and degree of circular polarisation (DOCP) of light.
For a single uniform light beam, the DOP is 1 for fully polarised, 0 for unpolarised or completely depolarised, and between 0 and 1 for partially polarised. The DOP cannot be larger than 1. Despite containing four elements, a Stokes vector contains fewer than four degrees of freedom due to physical constraints. The Stokes vector can also be considered as an incoherent superposition of a completely polarised part and an unpolarised part 3 . Those parameters have been adopted in different polarimetric applications 16,20,22,23,32,80,81 . The polarisation angle (PA) and intensity of the linear SOP also can be defined, with respect to dipole orientation applications 154-156 (see Fig. 5a (iv)). For a beam generated via an incoherent light source (such as a LED), the Stokes vectors can be directly added by scalar calculation. Therefore, partially polarised light can be divided into two parts -fully polarised/depolarised components 3 , i.e., Stotal = Su + Sp; where Su and Sp represent fully depolarised and polarised components respectively.  Fig. 5a (ii)). Kunnen et al. employed Stokes vector detection with circular and elliptical incident SOPs for differentiation between healthy and cancerous lung tissues specifically using a Poincaré sphere illustration 160 (as Stokes vector locations shown in Fig. 5a (iii)). Note that the circular SOP illumination is especially useful for biomedical analysis, as its effects are independent of the orientation of the anisotropic components that widely exist in biomedical specimens [20][21][22][23][24]32 . What is more, its strong polarisation memory effect with respect to tissue-induced Mie-scattering has also gained attention 161 (here the memory effect 162 means that circular polarisation can survive many more scattering events than linear polarisation due to excessive forward scattering, hence it has higher probability to maintain the original information when passing through turbid tissue consisting of Mie scattering particles that are comparable in size to the wavelength).

Measurement of the full vector properties of biomedical targets requires illumination with multiple SOPs in combination
with multiple analyzing SOPs 20-24 . As we have mentioned above, the individual MM elements lack clear physical meanings, or explicit associations with microstructures [20][21][22][23][24] . That is to say, vectorial characteristics of the object, like diattenuation, retardance, and depolarisation are encoded within the MM elements. For a complex optical system (like tissue), each MM element is always associated with more than one polarisation property. Hence, numerous MM decomposition methods were proposed to quantitatively characterise the optical and structural properties of the object 52- 52 56 . Furthermore, other decomposition schemes were also developed, such as MM differential decomposition 55 , symmetric decomposition 60,61 and Cloude decomposition 62 . Among the various decomposition approaches, different mathematical assumptions need to be made for different applications [52][53][54][55][56][57][58][59][60][61][62] , such as assuming a determined layer sequence of different fundamental polarisation components for a complex object, which in effect simplifies the matrix reciprocity problem 52 . Recently, those methods and related parameters have also been compared quantitatively with each other for the purpose of structural characterisation [171][172][173] . We can summarise the parameters derived via the above methods:
The MM contains fundamental physical characters like polarisance, diattenuation, retardance and depolarisation (shown in Fig. 2c); however, some concepts like anisotropy can be a combination of several fundamental polarisation processes 16,57 . It is worth mentioning that the depolarisation property -which is used for evaluating a SOP's disorder, randomness, or uncertainty 3-5 -is also linked with the concept of entropy in polarimetric research 11,174  The MM decomposition methods all require different assumptions (strong or weak) such as matrix reciprocity, the order that polarisation effects happen in the media, or homogeneity for the tissue analysis 52,58,[177][178][179] . Therefore, their decomposed values are not strictly physically determined, if the assumptions do not hold in reality, which may well be the case, as biological tissue has high spatial complexity 58 Fig. 5b (iii)); 3) Breaking or restoring the symmetry (see Fig. 5b (iv)), based on analysis of different subregions of the MM, to extract determined information of the system is recently gaining interest 180 ; The information extraction process is gradually developing from an analytical mathematics approach (equation-based, forward problem), to fitting or observing vectorial semantics/metrics (data-based, or shape/form-based inverse problem).

Vectorial information analysis for biomedical applications
Polarimetric techniques maintain unique advantages compared with other optical techniques: they can provide extra vectorial information through methods that are compatible with many existing optical systems, such as microscopes and endoscopes 16,24,32,33,92,181 . Much existing biomedical polarimetry research concerns sensing of bio-information in a labelfree way without extraneous dyes 16,22,24 . In other areas, polarimetry can be used to characterise the vectorial information of fluorescence dyes, as the dipole orientation of the fluorophore is encoded in the polarisation state of the emitted light 155,156 . The SOP of such emission is always in a linear state; hence the polarisation angle (PA) and intensity of the linear SOP are quantities that can be harnessed, such as in biomedical applications in super-resolution microscopy 154,182,183 . Here we briefly summarize common phantoms used for biomedical polarimetric techniques. These techniques include: polarised wide-field microscopy 16,24,184 , polarised light spatial frequency imaging 185 , polarimetric endoscopy [186][187][188][189][190][191] , spectral light scattering polarimetry 18,82,[192][193][194] , polarised fluorescence spectroscopy [195][196][197] , polarised confocal microscopy 198 , polarised Raman-spectroscopy 199,200 , polarised super-resolution microscopy 155,156 , polarisation sensitive optical coherence tomography 201-219 , non-diffraction beam polarimetry (such as Bessel beam based) 220 , polarisation-resolved nonlinear microscopy (including second/third harmonic generation) [221][222][223][224][225][226][227] , and polarised speckle imaging 214,228 (several techniques will be mentioned again in the Discussion). The relationship between incoherence and depolarisation of the light should be kept in mind when considering coherence based polarimetric techniques: they are different but related optical concepts. If a polarised coherent beam passing through a scattering medium becomes incoherent, it can result in either polarised light or depolarised light. If after such a medium a polarised coherent beam changes into depolarised, the coherence property may still be maintained. For more details see Ref 229 . Several of the above techniques have also been adopted in three-dimensional (3D) imaging with signal integrations or sample segmentations 230 . However, numerous existing polarimetry techniques (within the scope of this review) fall into twodimensional (2D) analysis [23][24][25][26][27][28][29] . With the completion of the cutting-edge mathematical interpretations and methodologies (see Discussion) there exists of course intriguing scope for further explorations.
In order to understand the interactions between polarised photons and biological specimens, and link the parameters obtained via the Stokes vector or MM with the biomedical microstructural information, a software phantom -Monte Carlo (MC) simulation -was proposed to give plausible explanations for the originality of the observed physical phenomena 45,46 . While biomedical samples are considered as turbid media with complex structures, different fundamental units to mimic the microstructural architecture have been employed: spherical scatterers 35,46 ; cylindrical scatterers 41,46 ; birefringent intermedia [37][38][39] , multi-layered geometry 45 and so on 46 . MC simulations have successfully reproduced most of the important polarimetric characteristic features for biomedical samples 16,231,232 .

Thin specimens
Specimens and their mimicking phantoms can be thin or bulky, which also in general determines the configurations of the biomedical polarimetry. A transmissive geometry is used for the thin cases (see Fig. 6) which are less scattering, thus most of the incident photons would be transmitted. A backscattering geometry (see Fig. 7) is preferred for the bulk cases (ex vivo and in vivo) which are highly scattering and depolarising, thus most of the incident photons would be backscattered. There is no clear boundary between what constitutes thin or bulk tissues. Indeed, intermediate or mixed states can exist, for which both the transmission and backscattering photons can be detected simultaneously 16,22,23,153 . In response to the beginning of this section, biomedical polarimetry can be used in labelled or label-free measurement; Figure 6 gives a summary for two types of the use of thin tissue polarimetry.
For label-based direction, polarimetry has found use in scientific applications, such as biomedical microscopy 16 . The vectorial information of the dipole emitters is encoded in the SOP of the detected light 154,155 . The dipole orientation (and the fluorescence intensity) polarimetric detection technique plays an important role in thin biomedical sample analysis: e.g., in fluorescence polarisation microscopy (FPM) 195,196,233,234 ; FPM can be used to study the nuclear pore complex subcomplexes and the relative orientations 235 , or be used to study different types of cytoskeleton such as actin, myosin, kinesin, microtubule and septin -those closely related with the performance of the dipole behaviours 236-240 -enabling research such as ATP and ADP binding 238 . Advanced research has been adopted in super-resolution imaging harnessing fluorescent dipoles via polarised illumination, with applications such as revealing heterogeneity and dynamics of subcellular lipid membranes 182,241,242 . These fluorescence anisotropy properties also belong to the fundamental polarisation properties that are encoded in the MM.
For label-free biomedical polarimetric research, especially in clinical/pathological related topics, cancerous tissues detection is an important application [22][23][24] . In the past decades, such polarimetric techniques have assisted the diagnosis of various cancerous tissues, such as human skin cancer 243 , cervical cancer [244][245][246][247] , colon cancer 167,[248][249][250][251] , liver cancer 164,252 , breast cancer and gastrointestinal cancer [93][94][95]253 . A typical bio-information analysis of polarimetric data is for quantitative evaluation of the fibrosis process among different stages of cancer development 94,164 . Beside the degree of fibrosis that can be quantified via biomedical polarimetry, the distribution of features in the fibrous regions also can serve as another characteristic parameter to assist the pathological diagnosis; this distribution can be readily extracted via polarisation information 165,166,172 . Intuitively, such structures contribute intrinsic birefringence mainly affecting the fourth row and fourth column of the target MM 16 . A good demonstration in Ref 165 shows how polarimetric textural mapping of retardance properties can distinguish between the Crohn's disease and gastrointestinal luminal tuberculosis tissues (see Fig. 6b). Some thin specimen phantoms, as found in Ref 153 , target the fundamental understanding of the constitution of certain biomedical specimens, such as using nano-particles or microspheres. Moreover, polarimetry has recently been applied to other diseases detections including Alzheimer's disease and bladder outlet obstruction 24,254,255 .

Bulk specimens
Polarisation techniques can help improve the image contrast of the superficial layers of tissues by eliminating multiply scattered photons from the deep layers [20][21][22][23][24] . The previous literature shows that more than 85% of cancers originate from the superficial epithelium, which means that polarisation imaging methods have great potential in screening and identifying cancer at an early stage 257 . This would be specifically useful for in vivo clinical diagnosis, such as for minimally invasive surgery (MIS) 24 . Measurements in ex vivo thin tissue can use a transmissive geometry, whereas ex/in vivo bulk tissue detection would need backscattering configurations. Figure 7 gives a brief demonstration of certain current research topics related to bulk tissue polarimetry.
For polarimetric bulk tissue research, ex vivo detection plays an important role [22][23][24] . For example, collagen fibres, which widely exist in tissues and organs such as tendons, skin and bladder (from porcine, swine, lobster, calf or other animals 157,258-261 ), skeletal and myocardial muscle fibres 262-264 , and elastin fibres are widely-used due to their linear birefringence properties [20][21][22][23]165 . The alignment directions of all such fibrous structures are also linked with the fast axis orientation of the generated linear birefringence 16,166,172 . Furthermore, the scattering of bulk media is also studied via the extracted depolarisation 16,168,265 . The retardance and depolarisation related properties are the dominant parts of the vectorial properties of bulk tissues, as the magnitude of diattenuation for majority of tissue is typically very small 159 , with several exceptions like skeletal and myocardial muscles 168 (see Fig. 7a (i)). Previous research analysing muscle tissue 266 showed lower retardance compared with tendon tissue, owing to the cellularity of these tissues. Sections of the bulk myocardial fibre tissues showed two circularly aligned ring-shaped fibrous structures (see Fig. 7a (i)), revealing their anisotropic properties 168 . The different anisotropic vectorial information obtained from polarimetric measurements can be very helpful for the discrimination and identification of different fibrous structures in tissues 165,166,168 .
While ex vivo studies are mainly oriented towards fundamental research 24,153,172 (e.g., understanding the vectorial properties characterisation; see Fig. 7a (i), 7a (ii), 7b (i)), in vivo bulk tissue polarimetry is geared towards applications 24,258,267 . Typical backscattering mode polarimetry includes polarisation endoscopy 24 , reflection MM microscopy 16,268 , MM colposcopy 181,269 , wide-field handheld polarimetry 16 , and PS-OCT 270 (see Fig. 7a (iii), 7b (ii)), targeted to clinical diagnosis in vivo. As a promising in vivo, label-free diagnostic tool, polarisation endoscopic imaging has been implemented inside rat abdomen, revealing the small bowel, stomach, liver and fat with different polarisation characters 92 . Recent work also includes development of several different types of MM endoscope [189][190][191]258 , and extension into the spectral domain (with certain fixed wavelengths) 92 (see Fig. 7a (iii)). PS-OCT 201-219 is specifically used for in vivo ophthalmic imaging, where polarimetric data accompanied with clinical analysis has been demonstrated, for retinal imaging 270 (see Fig. 7b (ii)). Other types of bulk tissue analysis, such as human lung cancerous tissue 160 and skin tissue 271 , show good prospects for future clinical diagnosis 16,[22][23][24] .
While thin samples can feature multiple scattering process, such processes are of course more significant in bulk samples [20][21][22] . Considering the intriguing scope of the polarimetric technique for in vivo clinical diagnosis, beside the simulations, there is a need for complex phantoms, such as those exhibiting birefringence (see Fig. 7b (iii)) or depolarisation, to establish reliable processes for investigation of complex scattering mechanisms 272,273 . A recent review has summarised various phantoms for both thin and bulk samples 153 . Micro-spheres, silicon-based phantoms, nanoparticles, cylindrical scatterers, and birefringent/dichroism films 35,159,272,274 have all been employed in various validations. In vivo biomedical polarimetry and its related applications clearly offer a large space for future exploration. Biomedical applications of polarimetry have attracted substantial attention. We hope this short review paper gives readers a general overview from fundamental polarisation concepts, through polarimetric techniques, to recent biomedical and clinical applications 7,16,[20][21][22][23][24]29,34,63,79,153 . In addition to the summaries of recent research trends explained above, we provide here some further perspective on prospects in this application area, considering the use of polarimetry in a multimodal combination with other advanced technologies (see Fig. 8 for a summary).
Firstly, the fast development of the machine learning (ML) is clearly going to have an impact on this field 95,275,276 . Such data-driven techniques may pave new directions for biomedical polarimetry, either through improving the quality of polarimetry (such as overcoming the numerous sources of error) or through enhanced information extraction 68,95 . One possibility is to use low resolution information to reconstruct high resolution patterns (following the spirit of works such as Ref 277,278 ). Secondly, while ML is geared towards improving the information processing aspects of polarimetry, new adaptive optics techniques can be used to extend the capabilities of polarimetry through full vectorial beam control. This could enable enhanced polarisation imaging resolution physically via beam shaping and compensation of polarisation errors [279][280][281][282] . Thirdly, the emerging techniques based on metasurfaces -subwavelength arrays of nano-scatterers that can modify polarisation -have been adopted for polarimetry 283 , as well as for 3D polarisation control 284 . Such developments may bring new opportunities for advanced biomedical polarimetry, such as forming compact vectorial sensors 24,285 for deep tissue information extraction. Fourthly, second harmonic generation (SHG) and third harmonic generation (THG) based 3D MM techniques have been proposed [286][287][288][289] . These are described by extended MMs that are more complicated than 4 ´ 4 MMs used for linear scattering (4 ´ 9 and 4 ´ 16 elements, respectively, for SHG and THG) 286,287 . For these methods, further advanced information extraction and analysis approaches are of course intriguing. Finally, the intensity and wavelength have been utilized together with polarisation in polarimetry for a long time. However, the absolute phase information -especially geometric phase-related techniques 8,10 -may again open windows for new biomedical polarimetry approaches with multi-modal performance.