Leaf chlorophyll content (LCC) and equivalent water thickness (EWT) are critical indicators of plant physiological state and photosynthetic capacity. Hyperspectral measurements provide technical support for the efficient estimation of these leaf biochemical parameters. However, most current studies ignored the influence of leaf surface specular reflection, which reduces estimation accuracy, in the multi-angular measurements. This study proposed the spectral angle cosine-band depth indices (SACIBD), a method that transforms additive specular reflection into multiplicative differences using band depth (BD) and eliminates them via spectral angle cosine (SAC). Based on a multi-angular calibration dataset, the optimal spectral intervals (OSI) for SACIBDwere identified. Then, SACIBDwas validated across five independent leaf datasets and canopy imaging datasets obtained through close-range camera and LESS simulated scene. Results demonstrated that SACIBDefficiently captured biochemical-sensitive spectral absorption shape features (OSILCC: 658-748 nm and OSIEWT: 1872-2026 nm) and eliminated the specular reflection influence on biochemical estimation. Strong linear relationships with both LCC (R2=0.9) and EWT (R2=0.94) as well as validation results of five leaf datasets (LCC: RMSE = 5.98 μg/cm2, n = 2143; EWT: RMSE = 0.0031 g/cm2, n = 1919) confirmed the applicability of SACIBDfor various measurement strategies and plant species in the estimation of leaf biochemical parameters. When the study was extended to the canopy level, SACIBDachieved similarly good accuracy (LCC: RMSE = 6.98 μg/cm², n = 104; EWT: RMSE = 0.0044 g/cm², n = 34). Thus, the novel combination of SAC and BD provides an effective tool for quantitative plant biochemistry research.

PROSPECT is an effective method to retrieve leaf biochemical constituents, such as chlorophyll (Cab), carotenoid (Cxc), water (Cw), and dry matter (Cm). Several published PROSPECT inversion approaches have been performed using spectral bidirectional reflectance factor (BRF) measured at fixed illumination-viewing geometry. However, considering random leaf orientation, varied solar illumination angles, and wide field of view of the sensor, angular reflection is actually used to retrieve leaf biochemical constituents, which may affect the performance of these inversion approaches. Based on multi-angular spectral BRFs of 497 leaves from 13 plant species in the hemispheric space or the principal plane, we evaluated the performance of seven PROSPECT inversion approaches, including PROSPECT, PROREF, sPROCOSINE, PROCWT-S4, PROCWT-S5, PROFED, and PROSED. Significant angular effects was found on the original PROSPECT inversion, which showed low and angle-dependent retrieval accuracy. PROREF, sPROCOSINE, PROCWT-S4, and PROSED improved certain leaf biochemical constituent retrievals compared with PROSPECT. Interestingly, PROCWT-S5 and PROFED improved the retrievals of Cab, Cxc, Cw, and Cm. Among seven inversion approaches, PROFED not only produced the best accuracy in retrieving Cab(R2= 0.92, RMSEadj= 5.92 μg/cm2), Cxc(R2= 0.46, RMSEadj= 2.86 μg/cm2), Cw(R2= 0.91, RMSEadj= 0.0031 g/cm2), and Cm(R2= 0.25, RMSEadj= 0.0017 g/cm2), but also was insensitive to viewing angles. These results suggest that PROFED could effectively retrieve leaf biochemical constituents across a wide range of plant species at random illumination-viewing geometry, which is beneficial for ecology and botany studies.

Anisotropy index (ANIX), which is defined as the ratio between the maximum and minimum reflectance factors in the principal plane, has been applied in characterizing the optical properties of vegetation. But it is seldom used to estimate the chlorophyll content in leaf level. In this study, we found the leaf spectral anisotropy index (ANIX) depended on the variation of leaf chlorophyll content (LCC). Newly proposed indices, (ASRI: A750/A720 and ANDI: (A750-A720)/(A750+A720), A is the modified ANIX (mANIX=ANIX-1)), were derived from the format of the existing reflectance-based vegetation indices: simple ratio (SR) and normalized difference (ND) indices. The diffuse reflection, closely related to LCC, can be extracted from the two new indices (or directly obtained as the minimum bidirectional reflectance factor). They have strong linear relationships with LCC (R2=0.88 and 0.89), and have good estimation accuracy using an independent dataset (RMSE=6.39 μg/cm2 and 6.10 μg/cm2). We also found the ASRI (ANDI) had similar LCC estimation accuracy as the range-ASRIs or range-ANDIs (RANDIs or RANDIs), which were calculated by the random combination of reflectance factors in the forward scattering directions (ranged from -30° to -50°) and near the backward scattering directions (ranged from 0° to 20°). The wide and effective ranges of viewing angles strengthen the usability of ASRI and ANDI to estimate LCC in the practical measurements.

Leaf chlorophyll content (LCC) is a key indicator of plant photosynthesis and can be estimated by the optical properties of leaves. Due to the random distribution of leaf angles and the change of incident light angle, it is necessary to reduce the effects of specular reflection when estimating LCC under different measurement geometries. Because the polarized reflectance factor can account for specular reflection, which does not relate to LCC, it is possible to improve LCC estimation using spectral indices when the polarized reflectance is removed from the total reflectance. In this study, polarimetric measurements of leaves from three different plant species were performed with different measurement geometries in both laboratory and field conditions. We tested all possible waveband combinations in the 400–1000 nm range with two types of spectral indices: simple ratio (SR) ($R_{\lambda 1}/R_{\lambda 2})$and normalized difference vegetation index (NDVI) ($R_{\lambda \mathrm {i}} - R_{\lambda \mathrm {j}}$)/($R_{\lambda \mathrm {i}} + R_{\lambda \mathrm {j}}$), using both total intensity [defined as$I$parameter reflectance factor (IpRF)] and non-polarized [defined as non-polarized reflectance factor (NpRF)] information. By comparing the LCC estimation accuracy based on IpRF with that based on NpRF, we found that NpRF increased the number of bands that can estimate LCC with relatively high accuracy. These results indicate that the simple two-band indices based on the NpRF are robust and accurate for estimating LCC at leaf scale, and the broad effective wavelength range of NpRF may have the ability to overcome bandwidth limitations. The results of this study support future vegetation indices design and model development.

Optical remote sensing is one of the most popular methods for estimating leaf nitrogen concentration (LNC). This nondestructive approach based on reflected intensity measurements has been applied to estimate the variation and distribution of nitrogen concentration in leaf and canopy levels in numerous studies. However, both intensity and polarization are necessary to describe the optical properties of light reflected from leaves and to estimate LNC estimation. In this study, based on the Stokes parameters, the total reflectance, the polarized reflectance, and the nonpolarized reflectance factors (NpRFs) were simultaneously obtained through polarimetric hyperspectral measurements under varied source-viewing geometries in both laboratory and field conditions. Several published hyperspectral indices based on the NpRF showed much better LNC estimation accuracy than those using the total reflectance factor. A clear improvement was found in the viewing directions dominated by specular reflection. Thus, using multi-angular polarimetric hyperspectral measurements not only improves the accuracy of hyperspectral indices on LNC estimation using the NpRF, but also enables the hyperspectral indices to be effective for a wide range of viewing angles. Moreover, polarimetric measurements deepen the understanding of the optical properties of light reflected from leaves. These results indicate that the combination of multiangular, polarimetric, and hyperspectral measurements may play a key role in the estimation of LNC.

Plant leaf chlorophyll content (LCC) plays a key role in the assessment of plant stress and plant functioning. To date, accurate estimation of LCC over a wide range of plant species (trees, bushes, and lianas) under different measurement conditions is still challenging for nondestructive methods. Based on multiangular hyperspectral reflection of 706 leaves (ten plant species), several popular spectral indices were evaluated for a general estimation of LCC. The modified difference ratio index (MDRI) had the strongest linear relationship ($R^{2}=0.92$) to LCC among all the tested spectral indices. The regression algorithm was then used to estimate LCC in other datasets from different regions across the globe. Comparing with the machine learning techniques and PROSPECT model, validation results from 2024 leaves (114 plant species) confirmed that the linear algorithm derived from the MDRI was the most effective for estimating LCC (root-mean-square error (RMSE)$=6.72\,\,\mu \text{g}$/cm2) across a wide range of plant species under different measurement conditions. The MDRI does not require parameterization for each plant species and has the potential to estimate LCC from a simple handheld laboratory or field instrument at any arbitrary direction. The generality of the approach makes it convenient for botanical and ecological studies under different measurement conditions that need accurate LCC estimates.

Understanding the optical properties of light reflected from snow surfaces is fundamental for remote sensing-based characterizations of snow properties and quantification of radiative transfer in the atmosphere–earth system. In theory, both intensity and polarization are required for describing the optical properties of light reflected from snow. However, thus far, a few studies have focused on the polarimetric properties of snow. In this study, we measured both multiangular photometric and polarimetric (based on the Stokes parameters) hyperspectral field results of snow with different properties (grain size, pollution levels, and microscopic surface roughness). By considering the absorption ratio of the polarizer, the intensity defined by photometric results [bidirectional reflectance factor (BRF) and hemispherical directional reflectance factor (HDRF)] was first confirmed to be similar to those derived from polarimetric measurements [$I$parameter reflectance factor ($I$pRF)] of snow surfaces. Then, the bidirectional polarized reflectance factor (BPRF) of snow, which is used to define the polarimetric properties of snow, was found to be useful for characterizing snow properties. Moreover, comparing ground measurements of snow BPRF with modeled results, we found that some existing BPRF models did not match well with the BPRF measured in the$2\pi $space. These results suggest that more attention should be paid to the combination of$I$pRF (BRF or HDRF) and BPRF because polarimetric measurements can be used both for describing the optical properties of light reflected from snow and for quantifying snow properties.

Leaf BRDF (bidirectional reflectance distribution function) is partly controlled by the specular reflection from the leaf surface, which does not convey information about leaf biochemical parameters. Therefore, vegetation remote sensing can benefit from understanding the effects of BRDF on leaf biochemical parameters estimation and attempting to reduce them. In this study, polarimetric measurements, which simultaneously derive intensity and polarization information, were taken on the leaves of four plant species in the hemispheric space. The results showed that there are distinct BRDF effects on leaf biochemical parameters (leaf chlorophyll content (LCC) and equivalent water thickness (EWT)) estimated using spectral indices based on the intensity (IpRF: I parameter reflectance factor) reflected from leaves. The relationships between four types of spectral indices (single reciprocal, difference between two wavelengths or two reciprocal, simple ratio, and normalized difference indices) and leaf biochemical parameters were found to be weak and dependent on the BRDF of leaves, especially in the forward scattering directions, which are dominated by the specular reflection. After separating the bidirectional polarized reflectance factor (BPRF) from the reflectance intensity (IpRF), the non-polarized reflectance factor (Rn-p) significantly reduces the BRDF effects on biochemical parameters estimation near the specular reflection directions, and a relatively improved estimation is found in either individual viewing directions or over all viewing directions. This study demonstrates that polarimetric measurements are able to reduce BRDF effects on leaf biochemical parameters estimation, and therefore are useful to improve the leaf biochemical parameters estimation using spectral indices in the hemispheric space.

The reflection property of targets is the fundamental signal for applications of optical remote sensing of the earth's surface. In this paper, we measured the photometric and polarimetric characteristics of 15 leaves with different properties from one plant species (i.e., Pachira aquatica) using a laboratory goniospectrometer system and used the bidirectional reflectance factor (BRF) and the bidirectional polarized reflectance factor (BPRF) to describe the reflection of these leaf samples. The results illustrated that the BRF can be replaced by the I parameter reflectance factor (IpRF) when the extinction of the polarizer is considered. Subsequently, the BRF model was fit to the IpRF measurements at selected wavelengths, and the inverted refractive index was used in a BPRF model, which has been proposed to simulate the polarization of surfaces. We found that the modeled photometric results of all the leaves matched well with our measurement results over all the measurement directions, while the modeled polarimetric results of the leaves gave a good agreement with the measurements at the forward scattering directions. Moreover, the degree of linear polarization (Dolp) of the leaf, which is derived from the ratio between BPRF and IpRF, can also be effectively computed by the combination of BPRF and BRF models in the forward scattering directions. These findings suggested that more attention should be dedicated to the combination of BRF and BPRF of leaves in the future because we can completely describe the essential optical properties of the light reflected by leaves via the polarimetric measurement. This paper indicates that the polarimetric measurement is a beneficial method for optical remote sensing applications and helps us deepen the understanding of the optical properties of leaves.

Snow has a very high reflection property when compared with all other natural surfaces on Earth; thus, a small amount of contamination (30 ng/g) can dramatically reduce the reflectance of snow. To quantify the effect of black carbon (BC) concentrations on the directional reflectance factors of snow, we deposited BC concentrations onto snow surfaces at natural levels (98-4095 ng/g) and compared the measurement results with those from a theoretical model. It was found that increasing BC concentrations decreased the reflectance factor of snow and changed its distribution pattern. Moreover, our data provided valuable verification of the snow reflection model, which has previously been used to characterize the reflectance of snow. The model did not well match our measurements; for example, the model found fewer anisotropic results than those from observations. Subsequently, a specular kernel combined with two free parameters was proposed to counter the forward and backward scattering of the optical property of snow. The improved model successfully characterized the observed variability in the reflection measurements of snow with different BC concentration levels under field conditions, and its inverted parameter (M) had the potential to estimate BC concentrations. The improved model also had the ability to simulate the spectral reflectance factor of snow with low BC concentrations (i.e., smaller than 118 ng/g) over a wide range of viewing zenith angles. This paper provides an additional and effective method for studying the angular and spectral reflection properties of snow.

Polarized light has been studied over the past four decades as a useful signal to enhance the information from a variety of remote sensing applications. In the measurement process, the Stokes parameters are usually used to describe the state of polarization of light reflected from target surfaces. However, there is no research concerning the influence of extinction of the polarizer on the polarization properties derived from the Stokes parameters when we perform the polarimetric measurements of target surfaces using a spectrometer. In this paper, we measured the Stokes parameters of six natural surfaces (two soil samples, three vegetation covers, and a single leaf) and two man-made targets over a wide range of viewing directions at different incident zenith angles in the laboratory under two measurement conditions: considering and without considering the extinction of the polarizer. The comparison of these measured results indicated that the extinction of the polarizer, which was taken from the Spectralon panel, decreased the I parameter and the bidirectional polarized reflectance factor of all the samples. Moreover, it is safe to use the I parameter to represent the total reflected intensity of all our samples when we considered the extinction of the polarizer. Thus, the polarimetric measurements of target surfaces can not only give us the polarization information but also provide a reliable intensity signal.

In this paper, we performed multiangular measurements spanning a wide viewing range in a hemisphere space for three types of vegetation cover and analyzed the bidirectional reflectance factor (BRF) measurements based on basic physical reflectance mechanisms to ensure the accuracy of the data. The measurements and the results with the best fitted model parameters were evaluated to determine whether the BRF models produce vegetation cover reflectance factor values that are qualitatively the same as the measured values. These models effectively characterized the BRF of the vegetation cover at most of the selected wavelengths (565, 670, and 865 nm). However, for planophile vegetation cover with smooth leaves, the current BRF models did not produce accurate values in the selected visible wavelength range; the average relative difference was approximately 0.3 at 670 nm. Subsequently, we subtracted the specular reflectance factor (calculated using the bidirectional polarized reflectance factors) from the total BRF and compared these data with the modeled results. The difference between the measured and modeled BRFs was notably decreased when we separated the specular reflectance factor at 670 nm for the planophile vegetation cover with smooth leaves. Moreover, there was a different degree of improvement in the agreement between the measured and modeled results, which depended on the wavelength and the type of vegetation cover. These results indicated that the subtraction of the specular reflectance factor effectively improved the capability of the BRF models to calculate the diffuse portion of the BRF of the vegetation cover.

As the knowledge of polarized reflection from ice may be important for understanding radiative transfer in ice and be of potential value in imaging applications, spectral reflectances and linear polarization of sea ice and lake ice have been measured in visible and near infrared (NIR) (350–2500 nm) at nadir and the specular direction, respectively. Results are presented for three ice types: 1) black lake ice (bubble-free ice); 2) lake ice with air bubbles; and 3) sea ice with brine pockets but no air bubbles. The effects of air bubbles and brine pockets on spectral reflectance and degree of linear polarization (DLP) are investigated in ice of 0.15 m thick at$-20\ ^{\circ}\hbox{C}$. Spectral reflectances are sensitive to ice condition, consistent with earlier studies of lake ice and sea ice. The DLP of ice in the specular reflection direction is found to be inversely but nonlinearly proportional to reflectance. The case of 1) polarized clearly more light than 2) or 3) in visible wavelength, but they were similar in NIR wavelength, implying the significant contribution of polarization derived from specular reflection. Apparent changes are predicted as volume scattering from air bubbles and brine pockets play an important role in decreasing the DLP of ice in the specular direction.