Light is a type of transverse electromagnetic wave， and polarization is one of its most fundamental properties， which has been widely and deeply applied in many fields， such as imaging^［1-4］， communication^［5-10］， material analysis^［11］， and life sciences^［12-15］. Polarized light mainly includes linear polarized light and circular polarized light. Circular polarized light can be further divided into Left-handed Circularly Polarized （LCP）light and Right-handed Circularly Polarized （RCP）light. The Polarization Extinction Ratio （PER）is one of the most critical performance indicators in evaluating polarization detectors or polarization detection systems. The PER is defined as the ratio of the responsivity for the primary detection polarization state to that for the polarization state orthogonal to the primary detection polarization state^［16］. This indicator is used to characterize the polarization discrimination ability of the polarization detector. In practical applications， a commonly used method for measuring the polarization information of a target is the Stokes parameter method， which includes four Stokes parameters： S₀， S₁， S₂， and S₃^［17-19］. Here， S₀ represents the total intensity of the polarized light， S₁ indicates the difference in components of the polarized light along the 0° and 90° directions， S₂ represents the difference in components along the 45° and 135° directions， while S₃ denotes the intensity difference between right-handed circular polarized light and left-handed circular polarized light^［20］.

Traditional polarization detectors are divided into two categories： ‘division of time’ and ‘division of amplitude’ ^［21］. A division-of-time polarimeter measures the intensities of different polarization states sequentially over time by rotating a waveplate or polarizer， significantly restricting temporal resolution. In contrast， a division-of-amplitude polarimeter separates incident light into distinct photosensitive regions using a sophisticated optical system， leading to a large and complex structure. The demand for real-time polarization imaging and the miniaturization of polarimeters has driven extensive research into the development of integrated polarization detectors^{［16-17， 22-26］}. However， the ultra-compact structure， light diffraction， scattering， and near-field light absorption pose some challenges for the development of integrated polarization detectors： （1）the PERs of integrated polarization detectors are usually 2 to 3 orders of magnitude lower than that of a polarization detection system consisting of discrete polarization optics and a detector； （2）integrated polarization detectors are much less sensitive to changes in polarization state than their traditional counterparts； （3）most integrated polarization detectors can only discriminate a few polarization states， but cannot measure the full Stokes parameters. Furthermore， with the increasing demands for multi-dimensional information perception， integrated polarization detectors are desired to be able to simultaneously perceive other key properties of light along with polarization.

To address the challenges outlined above， researchers have proposed various new theories， methods， and structures， leading to integrated polarization detectors with innovative features and high performance. This review focuses on these innovative advancements， systematically presenting cutting-edge developments in integrated polarization detectors. Topics include integrated polarization detectors with ∞/-∞ PERs， those with ultra-high sensitivity to polarization state changes， those capable of one-shot full Stokes parameter measurement， and those capable of simultaneously sensing polarization along with other key optical properties. The reasons and solutions for these challenges are summarized in Table 1. Finally， the paper discusses future opportunities and challenges in the development of integrated polarization optoelectronic detectors.

Conventional polarization detection systems， typically equipped with high-quality polarization optical elements， can achieve linear PERs （LPERs）higher than 10⁴. In contrast， the LPERs of integrated polarization detectors are 2 to 3 orders of magnitude lower than that of a polarization detection system consisting of discrete polarization optics and a detector^［27-34］. The situation becomes even worse for integrated circular polarization detectors， whose circular polarization extinction ratios （CPERs）are typically lower than five^［16］. The insufficient PER of an integrated polarization detector is due to less efficient suppression of the photoresponse to the light in the polarization state orthogonal to the primary detection polarization state， the so-called residual photoresponse^［16］. Recently， new effects of polarization photoresponse^{［23-24， 35-36］}， novel polarization detection principles^{［16， 26］}， and innovative materials and device structures^［37-39］ have been proposed， leading to ∞/-∞ PER.

To achieve ∞/-∞ PER， the critical factor is to ensure that the residual photoresponse becomes zero. This task is very difficult to achieve by relying solely on the light field manipulation provided by the integrated polarization discriminative structure. The light diffraction， scattering， and near-field absorption at an integrated polarization detector would inevitably generate residual photoresponse. Recent studies reveal that light field-electric field joint manipulation becomes a promising route to achieve this task.

Integration of artificial optical nanoantennas on photosensitive materials is a common method to endow or change their polarization-sensitive properties^{［17， 25-26， 35， 40-41］}. Additionally， artificial optical nanoantennas can effectively enhance the absorption rate of photosensitive materials， thereby improving the photoresponsivity or specific detectivity of photodetectors^{［16， 26， 40， 42-45］}. The in-sensor superposition of nanoantenna induced vectorial non-local photoresponses can achieve zero residual photoresponse and thus ∞/-∞ PER.

In 2021， Wei et al.^［23］ proposed a mid-infrared semimetal polarization detector with configurable polarity transition and （-1 to ∞/-∞ to 1）PER based on manipulation of vectorial non-local photoresponse （Fig. 1（a））. Both the intensity and direction of the non-local vectorial photocurrent is modulated by the polarization state of the incident light， and the total photocurrent is the superposition of all the vectorial non-local photocurrents. This principle is known as the artificial bulk photovoltaic effect （BPVE）. By adjusting the angle of the tapered nanoantenna or choosing different metals to make up the nanoantennas， the PER can be configured to be all possible numbers in the range （-1 to ∞/-∞ to 1）.

In 2022， Dai et al.^［25］ proposed an infrared detector with ultra-high polarization sensitivity （Fig. 1（b））. By leveraging the strong anisotropic absorption of the perfect plasmonic absorber in the infrared region and the localized heating induced by finite-size effects， the detector exhibits polarization-dependent， self-driven photoresponse based on the photothermoelectric effect （PTE）. The operating wavelength is 8 μm. When the polarization direction of the incident light is perpendicular to the resonance direction of the perfect plasmonic absorber， the incident light is reflected. As a result， the Te nanoribbon have no temperature difference throughout the channel， the optical response generated by the PTE is zero， and the PER of the device achieves ∞/-∞.

In 2024， Dai et al.^［26］ proposed a dynamically reconfigurable polarimetry based on in-sensor differentiation of two self-powered photoresponses with orthogonal polarization dependence and tunable responsivities （Fig. 1（c））. Such a device can be electrostatically configured in an ultrahigh PER mode， where the PER tends to ∞/-∞. Moreover， the device achieves a polarization angle sensitivity of 0.51 mA·W^-1·degree^-1 and a specific polarization angle detectivity of 2.8×10⁵ cm·Hz^1/2·W^-1·degree^-1. This scheme is demonstrated throughout the near-to-long-wavelength infrared range.

In addition to integrated linear polarization detectors with ∞/-∞ LPERs， integrated linear polarization detectors with ∞/-∞ CPERs have also been invented. In 2023， Bu et al. ^［16］ reported a configurable integrated circular polarization detector based on the optoelectronic silent state， and operating in the NIR region， as shown in Fig. 1（d）. By adjusting the ratio of the optical power received by the two chiral plasmonic nanocavities， the total photoresponse of the device is configured to be zero when the incident light is LCP or RCP， thereby the CPER tends to ∞/-∞. Bu et al. ^{［16， 26］} proposed the concept of the optoelectronic silent state. In this state， the detector generates not only zero photoresponse but also significantly suppressed noise. The detector can be optoelectronic silent for different polarization states of the incident light， including the randomly polarized state. When the detector is set to be optoelectronic silent for the randomly polarized state of the incident light， a high infrared background is eliminated during the detection and a target in a different polarization state is significantly highlighted compared to the suppressed background.

After inventing these （∞/-∞）-PER detectors， people realize that the PER is no longer an effective indicator to characterize the polarization discrimination performance of polarization detectors. In this context， Bu et al. define a new PER by taking into account the noise of the detector when the residual photoresponse become zero. As shown in the following equation， the new PER is defined as the ratio of the photoresponse of the detector when illuminated by light in the primary detection polarization state to the noise of the detector when illuminated by light in the polarization state orthogonal to the primary detection polarization state.

where PDPS is the acronym of “primary detection polarization state”， and ⊥PDPS denotes the polarization state orthogonal to the primary detection polarization state. Since the detector in the optoelectronic silent state has a significantly suppressed noise， the PER_new still exceeds the PERs of conventional integrated polarization detectors by more than 4 orders of magnitude （Fig. 1（d））.

Heterojunctions with special band structures are also an effective way to achieve ∞/-∞ PERs. In 2024， Li et al.^［37］ proposed a polarization photodetector based on the CdSb₂Se₃Br₂/WSe₂ heterojunction （Fig. 2（a））. In the CdSb₂Se₃Br₂/WSe₂ heterostructure， gate voltage variations control the anisotropic band alignment. This leads to a polarization-dependent shift in the photo-induced threshold voltage （V_th）， caused by the anisotropic carrier transition. The significant V_th shift reverses the polarization photovoltaic current， allowing the PER to switch from positive （unipolar regime）to negative （bipolar regime）， covering the entire range of values （1→∞/-∞→-1）.

In the same year， Wang et al.^［38］ discovered a polarization- and gate-tunable optoelectronic reverse in 2D semimetal/semiconductor photovoltaic heterostructure （Fig. 2（b））. By adjusting the gate voltage， the Fermi level in ambipolar WSe₂ can be tuned between the conduction band （CB）and valence band （VB）. This enables easy control and inversion of the built-in electric field， resulting in sign reversal of polarization-sensitive photocurrent. With the in-plane anisotropic structure of 1T′-MoTe₂， the device demonstrates highly efficient polarimetric detection， achieving a PER value of up to ∞/-∞.

Combining ferroelectric materials with 2D vdW materials can significantly enhance the performance of polarization detectors^{［39， 46］}. In 2024， Wu et al.^［39］ proposed a polarization photodetector based on black phosphorus. As shown in Fig. 2（c）， the authors found that "T"-shaped ferroelectric domain array broke the intrinsic C₃v symmetry of MoTe₂ and induced an asymmetric carrier distribution in MoTe₂. By applying different bias voltages， the photoresponse corresponding to different polarization states can be eliminated （Fig. 2（c）（ii））， leading to ∞/-∞ PER.

Noise-equivalent polarization angle difference （NEΔχ， unit： degree·Hz^-1/2）is a parameter used to assess the sensitivity of a polarization detector to changes in the polarization state of the incident light. It is related to noise （I_noise， unit： A Hz^-1/2）and polarization-angle sensitivity （PAS， unit： A degree^-1）. The calculation formula is：

NEΔχ refers to the minimum fluctuation in the photoresponse caused by changes in the incident light's polarization state that the polarization detector can resolve. The lower the value， the stronger the capability of the device to sense changes in the polarization state^［23］.

For ordinary polarization photodetectors， due to their extinction ratio is not high enough to achieve complete shielding of the photocurrent， there is always a current flowing in the device. As a result， the device is often accompanied by substantial noise， such as 1/f noise， shot noise， thermal noise， etc^{［16， 26］}. Excessive noise reduces the noise-equivalent polarization-angle rotation performance of the device. In contrast， for polarization detectors with infinite PER， their photocurrent minima can be reduced to zero， and the optoelectronic silent state helps maintain noise at a low level. However， at this point， the polarization-angle sensitivity of the device tends to be zero， and so the noise-equivalent polarization-angle reaches infinity， which prevents the detector from sensing small changes in the polarization angle of the incident light. As a result， the minima of noise-equivalent polarization-angle rotation tends to occur in polarization-dependent balanced detectors， which are characterized by a PER equal to -1^{［24， 35］}. In this type of polarization detector， at the point of photocurrent polarity reversal， the polarization-angle sensitivity reaches maximum while the noise intensity remains at the lowest level.

In 2020， Wei et al.^［35］ proposed a zero-bias mid-infrared graphene photodetector with bulk photoresponse and calibration-free polarization detection， which exhibits cascaded polarization-sensitive photoresponse under uniform illumination， simulating the BPVE. The device's responsivity is three orders of magnitude higher than that of photodetectors based on traditional bulk photovoltaic effects， with a noise-equivalent power of 0.12 nW Hz^-1/2. As shown in Fig. 3（a）， the authors fabricated a metal nanoantenna device with threefold rotation symmetry. The responsivities of the three sets of detection units are the same， with a phase difference of 60° between each set， and the PER of each set of devices is -1.

Ordinary circularly polarization detectors with integrated chiral nanostructures often fail to avoid the response caused by linear polarized light. To address this issue， in 2022， Wei et al.^［24］ proposed a geometric filterless photodetectors for mid-infrared spin light. As shown in Fig. 3（b）， the polarization-dependent photocurrent demonstrates that the detector is also a circular polarization-balanced detector， capable of blocking responses to S₁ and S₂ parameters. A self-powered optical response rate of 392 V W⁻¹. At a small incident power of 1.8 μW， an optical ellipticity detectivity as low as 0.03 degree Hz^-1/2 at room temperature.

In 2023， Xie et al.^［47］ proposed a zero-bias long-wave infrared nanoantenna-mediated graphene photodetector for polarimetric and spectroscopic sensing （Fig. 3（c））. The PER of the detector is -1. By adjusting the near-field distribution of the nanoantenna， the absorption rate of the detector was improved. The noise-equivalent polarization-angle rotation of approximately 0.05° Hz^-1/2 at the power of 26.6  μW. In addition to the use of metals to fabricate nanoantennas， the idea of preparing polarization detectors by directly processing photosensitive materials has also gained much attention in recent years. In 2024， Zhang et al.^［36］ reported a high-discrimination， broadband circular polarization photodetector using dielectric achiral nanostructures. As shown in Fig. 3（d）， the authors directly etched achiral nanostructures on Te nanosheets. The noise equivalent light ellipticity difference reaches a minimum of 0.03° Hz^-1/2 at the cut-off frequency.

In addition to the artificial BPVE， polarization-dependent balanced detection can also be achieved using a pair of orthogonal or chiral light-coupling structures^{［44， 48-49］}. In 2015， Lu et al.^［48］ proposed a thermopile detector of the light ellipticity （Fig. 4（a））. By constructing a square array， the photoresponses generated by the Stokes parameters S₁ and S₂ are canceled out， enabling the detector to directly output a bipolar photovoltage proportional to the Stokes parameter S₃.

In 2019， Peng et al.^［44］ proposed a chiral graphene-based mid-infrared photodetector. As shown in Fig. 4（b）， the device integrates nanoantennas with opposite chirality on source and drain electrodes. Surface plasmon resonance enhances the absorption rate of graphene by 17 times， and the device exhibits equal but opposite photoresponses to left- and right-handed circular polarized light. In the same year， Thomaschewski et al.^［49］ reported a study on circularly polarized light detection using plasmonic nanocircuits. As shown in Fig. 4（c）， the authors utilized plasmonic achiral nanocouplers to separate left- and right-handed circularly polarized light and couple them into two plasmonic waveguides. The photocurrents generated by two germanium （Ge）detectors were then processed externally using differential calculations， achieving high-precision resolution of circularly polarized light.

The demand for real-time full Stokes polarimetric imaging has attracted a lot of research interest. To address this demand， researchers have tried to combine multiple independently polarization detection pixels into a superpixel^［50-53］ and reconstruct the Stokes parameters of the incident light based on the photoresponses of the subpixels and a specific algorithm. This method would reduce the imaging resolution of the detector since many of the pixels originally used for imaging are used to probe the polarization state. Thus， the main challenge lies in designing the polarization dependent optoelectronic properties of the individual pixels to achieve the most accurate acquisition of full Stokes parameters while minimizing the number of the pixels.

For the fabrication of superpixel detectors， integrating different polarization-sensitive structures in different regions of one detection material is a convenient and common approach. In 2020， Li et al.^［18］ reported the monolithic full-stokes near-infrared polarimetry with a chiral plasmonic metasurface integrated graphene-silicon photodetector. The working wavelength is 1 550 nm. As shown in Fig. 5（a）， the same metasurface， arranged in different orientations and handednesses， is integrated with each of the four pixels. The four pixels share a common ground terminal， i.e. the Si substrate. Based on the photocurrent values of the four pixels and an empirical algorithm， the full Stokes parameters are reconstructed in one shot. However， the root mean square errors （RMSEs）of the reconstructed S₁， S₂ and S₃， which are 13%， 17% and 17%， respectively， are not sufficiently low for practical applications. In 2022， Dai et al.^［41］ proposed an on-chip mid-infrared photothermoelectric detector with PdSe₂ as the channel material. As shown in Fig. 5（b）， the device integrates four metasurfaces with different polarization dependent optoelectronic properties. In the experiment， the average measurement errors for Stokes parameters S₁， S₂， and S₃ were 14.2%， 15.2%， and 5.4%， respectively.

In order to enhance the accuracy of full Stokes parameters detection， a proper formalism describing the polarization-dependent photoresponses of metasurface-integrated photodetectors is required. In 2024， Deng et al.^［17］ proposed the concept of an optoelectronic polarization eigenvector （OPEV）The OPEV， which is a 1×4 vector， expresses the linear relationship between the incident Stokes vector and the photocurrent of a detector. As shown in Fig. 5（c）， each subpixel contains an in-situ integrated plasmonic metasurface and corresponds to a distinct OPEV. Combined with a machine learning algorithm， this polarimeter achieves full Stokes parameters reconstruction over the entire polarization state range at any light intensity， with a root mean square error less than 1% for each Stokes parameter.

Using only anisotropic or chiral materials to form full-Stokes polarimeters is an effective way to further simplify the device structure （Fig. 5（d））. In 2021， Chen et al.^［19］ proposed a self-powered， filterless on-chip full Stokes polarimeter based on a monolayer MoS₂/few-layer MoS₂ homojunction. This design allows a full-Stokes polarimeter without an additional filter layer. The RMSEs of the reconstructed Stokes parameters S₁， S₂， and S₃ are >5%， >4.8%， and >6.7%， respectively. It should be noted that this device is not a one-shot polarimeter， and it needs to be rotated around the center axis of the sample holder during operation. In the same year， Ma et al.^［54］ reported a full-Stokes polarimeter based on chiral Perovskite single crystal （（S- and R-MBA）₂PbI₄， where MBA = C₆H₅C₂H₄NH₃）. It is important to note that， in order to detect all the linear polarization parameters （S₁ and S₂）， the incident light's tilt angle needs to be continuously adjusted during testing. The average error of the reconstructed Stokes parameters from this detector ranges from 7.5% to 26%.

Polarization detectors are primarily used to sense the polarization state of light， often overlooking other fundamental properties of light such as wavelength and phase. Expanding the information dimension that polarization detectors can perceive is an important development direction.

In 2022， Ma et al.^［55］ first observed the bulk photovoltaic effect in twisted double bilayer graphene （TDBG）， which is induced by the moiré-induced strong symmetry breaking and quantum geometric contribution. With the help of artificial neural networks， the authors analyzed and reconstructed the photocurrent， achieving simultaneous detection of the wavelength， polarization， and power of light （Fig. 6（a））.

In 2024， Jiang et al.^［56］ proposed a broadband multidimensional optoelectronic detector based on metasurfaces. As shown in Fig. 6（b）， the authors designed a three-port device with differently structured metasurfaces integrated into the graphene photodetector at each port. By combining machine learning and the Adam optimization algorithm， the detector successfully achieved the resolution of circularly polarized light in the wavelength range of 1-8 μm. In the same year， Wang et al.^［57］ used two twisted black arsenic–phosphorus （b-AsP）homojunction to achieve polarization and wavelength detection （Fig. 6（c））. The responsivity of the device is influenced by both wavelength and polarization state. The authors demonstrated simultaneous detection of both polarization and wavelength by plotting the dependence of responsivity on wavelength and polarization state. Zhang et al.^［58］ developed a multidimensional optical information acquisition device based on a misaligned unipolar barrier photodetector， consisting of a b-AsP/MoS₂/BP stacked structure （Fig. 6（d））. The b-AsP/MoS₂ and BP/MoS₂ heterojunctions can be adjusted by a bias voltage， enabling the sensing of both polarization and spectral information.

Integrating metasurfaces with commercial cameras combines the focal plane array technology with the advanced optical properties of metasurfaces， providing a new solution for high-precision detection of multidimensional optical information.

In 2022， Fan et al.^［59］ introduced an innovative nanophotonic light-field camera inspired by the optical structure of Trilobite eyes （Fig. 7（a））. This camera incorporates a spin-multiplexed bifocal metalens array， capable of capturing high-resolution light-field images with an unprecedented depth-of-field range， spanning from centimeters to kilometers. The metalens array operates efficiently across a wide wavelength range from 460 nm to 700 nm， achieving broadband photonic spin-multiplexing in the visible spectrum.

In 2023， Zuo et al.^［50］ introduced a chip-integrated metasurface-based Full Stokes Polarimetric Imaging sensor （MetaPolarIm）， which combines an ultrathin （~600 nm）Metasurface Polarization Filter array （MPFA）with a visible imaging sensor （Fig. 7（b））. This sensor was fabricated using CMOS-compatible processes， making it highly scalable for mass production. The MPFA features a hybrid dielectric-metal chiral metasurface design along with double-layer nanograting polarizers， providing high polarization sensitivity and accuracy. In practical experiments， the MetaPolarIm sensor achieved measurement errors of less than 2% for all Stokes parameters in red and green colors under normal incidence.

In 2024， Fan et al.^［60］ proposed an innovative concept that leverages spatial and frequency dispersion at optical interfaces to control polarization and spectral responses in the wavevector domain， combined with deep learning methods to decode polarization and spectral information. They introduced a dispersion-assisted multidimensional detector that enables the detection of high-dimensional optical field information in a single measurement using a single device （Fig. 7（c））. This system does not rely on complex designs or fabricated metasurfaces， yet its performance matches or even exceeds that of advanced commercial polarimeters or spectrometers. This research paves the way for the practical application of high-dimensional optoelectronic detectors.

Integrated polarization detectors have achieved notable progress， offering significant benefits in applications like improving image contrast and providing additional information about targets. However， their development encounters several challenges. For detectors integrated with photonic structures， the reliance on resonance restricts their operational wavelength range. Similarly， polarization detectors based on heterojunctions face limited material choices and persistent inaccuracies in Stokes parameter reconstruction.

The emergence of polarization detectors with innovative features has addressed several challenges across different fields. In Table 2， we compare representative high-performance integrated polarization detectors with commercial counterparts. The results indicate that in certain application scenarios， these high-performance integrated detectors can outperform commercial devices， demonstrating significant application potential. In terms of response speed， the graphene-based polarization detector utilizing the artificial bulk photovoltaic effect is at least as fast as commercial polarimeters and can theoretically achieve an ultra-fast mid-infrared response of 500 GHz. Its optical responsivity of 27 V W^-1 surpasses that of some high-speed commercial photodetectors （e.g.， the Thorlabs DXM20AF 20 GHz photodetector ， which has a responsivity of 0.9 A W^-1）. Meanwhile， the MoS₂ polarimeter， based on optoelectronic polarization eigenvectors， achieves a Stokes parameter reconstruction accuracy of less than 1%， whereas the polarization accuracy of commercial polarimeters is typically around 1% （e.g.， PAX1000， Thorlabs）.

In the infrared range， a major limitation of reported polarization detectors with PER values of ∞/-∞ or -1 is the lack of characterization using blackbody sources； instead， characterizations are typically conducted with high-performance lasers to assess optoelectronic properties. While lasers allow precise control over light source attributes （such as wavelength， power， spot size， and high-frequency modulation）in a laboratory setting， the resulting performance metrics are primarily suited for applications like spectral measurement， optical communication， or lidar. However， in imaging applications， the main challenge is detecting broad-spectrum， low-energy infrared radiation. The ability to respond to blackbody radiation is a key indicator of an infrared detector’s practical application potential， and thus future research efforts should continue in this direction.

Future advancements in device fabrication could involve novel large-area， narrow-linewidth patterning techniques， such as deep ultraviolet lithography and nanoimprint technology， which could enhance the efficiency of metasurface integration on detectors. On the data processing side， the emergence of more sophisticated artificial intelligence algorithms holds promise for improving the efficiency of multi-Stokes parameter reconstruction and high-dimensional optical information processing. These advancements could significantly reduce computation time and improve reconstruction accuracy， paving the way for broader practical applications.

With the increasing demand for miniaturization and intelligence， integrated polarization detectors have become the primary focus of future polarization detection technologies. The development of these detectors focuses on two main objectives： enhancing polarization detection performance and incorporating new optical dimensional sensing capabilities. Integrated polarization detectors have achieved extinction ratios as high as infinity， while polarization-dependent balanced detectors enable highly sensitive detection of the changes in the polarization state. These advancements allow for the sensing of additional Stokes parameters and even other dimensions of information from the incident light. Despite significant progress， challenges persist in device design principles and fabrication techniques. Moving forward， the adoption of innovative fabrication methods and materials will further elevate detector performance. Additionally， integrating artificial intelligence algorithms is expected to substantially enhance the efficiency and accuracy of multi-Stokes parameter reconstruction and the interpretation of high-dimensional optical information.