Estimation of leaf chlorophyll content with polarization measurements: Degree of linear polarization

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Estimation of leaf chlorophyll content with polarization measurements: degree of linear polarization Ce Yao , Shan Lu , Zhongqiu Sun PII: DOI: Reference:

S0022-4073(19)30446-7 https://doi.org/10.1016/j.jqsrt.2019.106787 JQSRT 106787

To appear in:

Journal of Quantitative Spectroscopy & Radiative Transfer

Received date: Revised date: Accepted date:

27 June 2019 12 November 2019 3 December 2019

Please cite this article as: Ce Yao , Shan Lu , Zhongqiu Sun , Estimation of leaf chlorophyll content with polarization measurements: degree of linear polarization, Journal of Quantitative Spectroscopy & Radiative Transfer (2019), doi: https://doi.org/10.1016/j.jqsrt.2019.106787

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Highlights: 

Variation of chlorophyll content changed the spectral degree of linear polarization (DOLP) of leaves as the photometric measurements.



Spectral indices expressed in terms of DOLP were able to estimate leaf chlorophyll content at different directions dominated by specular reflection.



The spectral DOLP and BRF indices have the potential to be used for LCC estimation under laboratory and field conditions.

1

Estimation of leaf chlorophyll content with polarization measurements: degree of linear polarization Ce Yao, Shan Lu*, Zhongqiu Sun* Key Laboratory of Geographical Processes and Ecological Security in Changbai Mountains, Ministry of Education, School of Geographical Science, Northeast Normal University, Changchun, 130024, China

Corresponding authors: Shan Lu ([email protected]) and Zhongqiu Sun ([email protected])

Abstract: Leaf chlorophyll content (LCC) is an important indicator of plant physiological status, photosynthetic capacity, plant stress and senescence. Optical reflection measurements offer a nondestructive method for estimating LCC and have been widely used in plant science and ecological applications. Light reflected from leaves surfaces can be described by photometric and polarimetric measurements. In this study, previously introduced spectral indices based on photometric measurements did not yield highly accurate estimates of LCC using multi-angular measurement in the forward scattering directions. Subsequently, an index derived from photometric measurements, the bidirectional reflectance factor (BRF), and some previously introduced spectral indices based on the degree of linear polarization (DOLP) were used to estimate LCC. We found that a newly proposed spectral index based on BRF 2

and 1/DOLP allowed the convenient estimation of LCC with a high accuracy, explaining more than 90% of LCC variation. The method, which relates LCC to the BRF and 1/DOLP of leaves using multi-angular measurements, indicates that both photometric and polarimetric properties are effective for LCC estimation. This study opens the possibility for estimating LCC based on polarization reflected from leaves. One advantage of using polarization to remotely sense leaf biochemical parameter is that DOLP measurements do not need to be normalized by a reference panel as BRF measurements. Key words: Polarization; leaf chlorophyll content; DOLP; spectral indices

1. Introduction The accurate estimation of leaf chlorophyll content (LCC) is useful for understanding a plant’s physiological state and biological activity [1-3]. LCC varies between and within species, and quantifying LCC can give us important information on the relations between plants and environmental changes [4-6]. Mapping chlorophyll and its applications have been used to improve the estimation of carbon and water fluxes of forested ecosystems [7-9]. Moreover, chlorophylls are fundamental determinants of the utilization and capture of incident light. In the visible wavelengths, chlorophylls strongly absorb blue and red light [10, 11], and the absorption characteristics change with variations in chlorophyll contents [12, 13]. This allows to estimate LCC using spectral indices [4, 14-18]. Polarization, a primary physical property of light, can be obtained from spaceborne (Polarization and Directionality of Earth’s Reflectance instrument) [19], airborne (Research Scanning Polarimeter) [20] and ground measurements (Ground-based Multiangle 3

SpectroPolarimetric Imager) [21]. These polarimetric measurements have also been used to characterize the optical properties of leaves [22, 23]. Using polarimetric measurements, the total reflection of a leaf can be separated into polarized and non-polarized portions [23-25]. The former is caused by the quasi-specular reflection that occurs on the leaf surface, and the latter is derived by multiple scattering within the leaf [23, 25]. These findings provide a basis for understanding how incident light is reflected and polarized by leaves, and some studies have shown the potential of characterizing vegetation structure parameters (canopy roughness) using polarization data [26-28]. However, polarization measurements have not yet been used for estimating or retrieving biochemical properties of leaves because polarization data observed by most polarimetric sensors is designed to observe atmospheric properties, rather than earth surfaces properties [19, 20]. Moreover, previous studies found that the polarized reflectance factor is spectrally neutral [29, 30] and indicated that the polarization of leaf surfaces, between 500 nm and about 800 nm, contains no information about leaf biochemical properties [31]; these studies further confirm the results given by Vanderbilt et al. [23] and show the potential to characterize leaf internal properties using non-polarized measurements. Researchers have worked to deepen our understanding of the multi-angular and spectral polarization from leaves and vegetation covers [32-38]. The polarized reflectance factor and the degree of linear polarization (DOLP, the ratio of polarized to total reflection) are usually used to describe polarization properties [24, 25, 32, 33, 36, 39, 40]. While the polarized reflectance factor, which is derived from the leaf surface, does not relate to biochemical parameters in the leaf [24, 25, 28], the DOLP of leaves from different plant species can potentially be used to measure LCC since 1/DOLP has a direct and strong relationship with 4

leaf reflection [24, 25, 40]. Spectral indices, which are based on ratios and differences of reflectance, can be used to eliminate the sensitivity to surface properties [60]. In this paper, we used spectral index values from the bidirectional reflectance factor (BRF) and 1/DOLP of leaves to estimate LCC at some measurement directions that are mainly dominated by specular reflection. Then, we compared the LCC estimates using DOLP indices and BRF indices. If the spectral indices based on DOLP are as effective at accurately estimating LCC as indices based on BRF, it would indicate that the polarimetric characteristics of leaves can be exploited for estimating leaf properties using multi-angle optical measurements. The objective of this study was to explore whether of polarization measurements taken from different directions could be used to infer leaf biochemical properties, and therefore serve as a convenient method for tracking the physiological status and stress of plants.

2. Samples and Methods 2.1. Sampling leaves A total of 217 leaf samples were taken from three plant species, Schefflera microphylla Merr. (Sm, n=90), Juglans (Ju, n=55) and Pachira aquatica (Pa, n=72), and 55 samples were used to validate the relationship between spectral indices and LCC. The leaf surface characteristics of the three plant species differ: Sm leaves have a glabrous and smooth surface that is thick and leathery; Ju leaves have a surface with many veins and sparse and fine hairs; Pa leaves have glabrous and a relatively smooth and flat surface with veins. Theses variations in leaf surface properties will affect the BRF and polarization of our samples, which is useful for testing the capability of our new method for estimating LCC. 5

2.2. Reflection and DOLP measurements After the leaves were collected from trees, photometric and polarimetric measurements were immediately performed on the adaxial leaf surfaces using the Northeast Normal University Laboratory Goniospectrometer System (NENULGS) [41]. The system is comprised of three main parts: a spectroradiometer (Analytical Spectral Devices (ASD) FieldSpec 3, Colorado, USA), which is used to collect spectral reflection and polarization; a goniometer, which is used to control the measurement geometry; and artificial illumination. In all previous laboratory studies, the uncertainty of polarized radiance at each polarizer direction was within 5%, and the polarimetric accuracy of this instrument was below 0.01 in the form of absolute value of degree of linear polarization [41, 42]. Our experimental setup included: a 1.2 m long motor driven arm that could be changed from -90° to +90° with a stepping motor in the viewing zenith directions with an accuracy of 0.1°. In the azimuth direction, the arm could be rotated from 0° to 360° using a stepping motor, with an accuracy of 0.25°. A tungsten halogen lamp was used to mimic sunlight, it was attached to a 90° arc with a 1.5-m radius, the accuracy was 0.25° in the incident zenith direction. This goniometer could fix the fiber-optic cable of the ASD spectrometer, whose sampling interval was 1.4 nm from 350 to 1000 nm and 2 nm from 1000 to 2500 nm, at any position on the hemisphere of the leaf samples. Because of the limitation of the structure of our apparatus, we could obtain the spectral results at a smallest phase-angle of 8°. A calcite Glan-Thompson prism was in front of the fiber-optic cable and used in the polarization measurements, its effective wavelength range was from 350 nm to 2500 nm. Except in the 6

wavelength ranges from 350 to 400 nm and from 2300 to 2500 nm, the average uncertainty of the linear polarized radiance was less than 5%. In our photometric and polarimetric measurement process, we primarily focused on forward scattering directions in the principal plane (0°, 10°, 20°, 30°, 40°, 50° and 60°), because specular reflection dominates the total reflection, therefore, we can obtain polarized measurements of the leaf in these viewing directions [23, 25, 39, 43]. In order to validate the effectivity of spectral indices on other viewing zenith angles, measurements were also taken in the backward scattering direction in the principal plane (-10°, -20°, -30°, -40° and -50°). The incident zenith angles were 40° and 50°, the field of view of the sensor was 6° and the distance from the sensor to the leaf surface was 0.2 m. Changing the viewing directions from 0° to 60°, the footprint of the sensor varied from a circular area (2.1 cm diameter) to an elliptical area (4.2 cm length). Our illuminated area and leaf area were larger than the footprint of the sensor for all leaf samples. Black tape (with a reflection below 0.05 in the wavelength range from 400-1000 nm) covered the objective stage to remove the background influence on the leaf reflection. The bidirectional reflectance factor (BRF) was used to characterize the photometric properties of the leaf samples in laboratory measurements. The BRF is defined as the ratio of reflected radiance (dLsample) from the leaf surface to the reflected radiance (dL) from an ideal diffuse surface (with the same area as the leaf sample) in the same viewing directions under single-direction illumination. The BRF is calculated as [48]: BRF ( , s ,v , s , v ) 

dLsample ( , s ,v ;s , v ) dL( , s ,v ;s , v ) 7



(1)

where θs is the incident zenith angle of artificial illumination, θv is the viewing zenith angle, φs is the incident azimuth angle, φv is the viewing azimuth angle and λ is the wavelength. The Spectralon panel (with a hemispherical spectral reflectance ρλ) was considered to be a perfect Lambertian panel. The DOLP was defined as the ratio of the Stokes parameter Q to total intensity I [44, 45]:

DOLP  

Q L  L90   0 I L0 +L90

(2)

where Lx is the radiance reflected from the leaf surface at different polarizer directions, the subscript ―x‖ refers to 0° and 90°. Equation (2) is a simplification of the DOLP described in [46], in which the numerator is

Q 2 +U 2 . This simplification is justified because previous

theoretical [35] and experimental [33] studies have shown that the U parameter of a leaf has a weak contribution to polarized reflection in the principal plane. Based on equation (2), without a reference panel, it was easy to calculate the DOLP using the polarized radiance from two orthogonal polarization states, which simplified the measurement process. The sampling process and photopolarimetric measurements of one leaf required no more than 20 minutes, and we assumed that leaf property variations did not affect the BRF and DOLP during the measurements.

2.3. LCC measurements After the photopolarimetric measurement of a leaf, the measured area was immediately cut into three small pieces using a hole punch (6 mm in diameter). We used a pestle to grind the pieces in a clean mortar, and then placed the pigment mixture in a 25 ml volumetric flask 8

with 95% ethanol. Subsequently, a centrifuge with a rotational speed of 3200 r/min was used to obtain the supernatants of a mix of the solution and chlorophyll. The absorption of the supernatant was measured by a Lambda 900 spectrophotometer, and then, based on the method provided by Wintermans and De Mots [59], the LCC (μg/cm2) was calculated. Statistical results of all leaf sample chlorophyll contents are shown in Table 1.

Table 1. Statistical results of all leaf sample chlorophyll contents, 162 calibration samples were related to spectral indices, and 55 validation samples served for validation. The photometric and polarimetric measurements were performed at two incident zenith angles: 40° and 50°.

Calibration Sm Ju Pa Sm Pa Total Validation Sm Ju Pa Sm Pa Total

Incident angle (°)

Sample number

Max Chl (μg/cm2)

Min Chl (μg/cm2)

Means (μg/cm2)

40 40 40 50 50

40 40 50 27 5 162

73.42 50.29 40.45 81.73 47.07 81.73

1.11 13.88 6.10 16.47 9.69 1.11

42.18 28.58 22.14 46.73 28.74 32.98

40 40 40 50 50

15 15 15 8 2 55

71.83 48.81 45.85 79.70 36.26 79.70

7.26 15.69 7.57 21.63 10.10 7.26

34.70 31.53 26.34 46.39 23.18 32.84

2.4 Spectral indices In this study, 15 previously used spectral indices were used to estimate LCC based on our spectral BRF and DOLP measurements (Table 3). Several types of indices were used in this study: single wavelength or simple difference indices between two different wavelengths, 9

simple ratio indices, normalized difference indices, derivative indices and other forms of indices. In the estimation of LCC, leaf reflection can be separated into diffuse and specular reflection [15, 47]. The diffuse reflection contains information about internal leaf properties. The specular reflection is partly polarized, and therefore the polarization signal can be used for the partial correction of the specular part [23]. The DOLP explicitly equated Q and I in equation (2) to polarized (Rp, λ) and the sum of polarized and non-polarized (Rnon-p, λ) proportions, respectively,

DOLP 

R p , R p ,  Rnon  p ,

(3)

Because of the weak wavelength-dependence of polarized reflection [31, 33, 39], the spectral index derived from the ration of difference between the reciprocal of DOLP at two wavelengths (λ) will reduce the polarized reflection,

DOLP11  DOLP21 DOLP11  DOLP31

 Rnon -p , 1   Rnon -p , 2   1+    1+  R R p , 2  Rnon -p , 1  Rnon -p , 2 p , 1       Rnon -p , 1   Rnon -p , 3  Rnon -p , 1  Rnon -p , 3  1+    1+  R p , 1   R p , 3  

(4)

Thus, the spectral DOLP indices in the form of equation (4) actually use the non-polarized reflection to relate to LCC. This is a fundamental principle pioneered by Vanderbilt et al. [23]: the non-polarized reflection conveys information about leaf absorbing constituents. In Table 3, the wavelengths and the forms of the original spectral indices are maintained. In this study, the spectral indices based on the BRF were first related to LCC, and then the spectral DOLP indices were related to LCC. The coefficient of determination (R2) was used to explain the relationship between spectral 10

indices (spectral DOLP indices) and LCC. The root means square error (RMSE) was used to calculate the fitness between measured LCC and estimated LCC by indices.

3. Results and discussion 3.1 Spectral DOLP of leaves with different LCC Because the polarized reflection is a part of the specular reflection, which makes the polarized reflection have a weak dependence of wavelength (Figure 1 (m-r)), and the DOLP is approximately inverse to the BRF. However, the polarized reflection of Sm leaves (Figure 1(r)) represents an exception in that it is wavelength-dependence when the viewing zenith angle equals to the incident zenith angle (40°). This polarization is due to the surface structure of Sm leaves with high LCC, which, unlike other leaves [60], may generate different polarized reflection under some special viewing geometries [24, 25, 32].

Figure 1. Bidirectional reflectance factor (BRF) (a-f), DOLP (g-l) and polarized reflection 11

(m-r) of leaves (g-l) from 0° to 60°, in the principal plane; the incident zenith angle was 40°. BRF is the ratio of reflected radiance from the leaf surface to the reflected radiance from an ideal and diffuse surface in the same measurement condition [48]. Polarized reflection is the ratio of reflected radiance from the leaf surface to the reflected radiance from an ideal and diffuse surface in the same measurement condition [32, 33]. The increasing trend in BRF with viewing angle is from Ju (Juglans) to Pa (Pachira aquatica) to Sm (Schefflera microphylla Merr.). Within each plant species, chlorophyll content increased from left to right.

In Figure 1, the maximum DOLP of some leaves does not show a small lobe in the specular plane when the incident zenith angle is equal to the viewing zenith angle. This is because the polarized component is caused by the quasi-specular reflection at the leaf surface, which is controlled by the leaf surface structure. The rough leaf surfaces of Ju and Pa leads to the broadening of the specular lobe and the increase of diffuse scattering [49]. Sm leaves with low LCC, which are less waxy, show lower spectral reflection than Sm leaves with high LCC at 30°-50° viewing zenith angles (Fig. 1 (e) and (f)). On the other hand, because the DOLP is derived from the ratio between Q and I, it is not only affected by the polarized reflection, but it is also related to total reflection. Thus, the distribution of the spectral DOLP does not necessarily have a similar pattern to the change in BRF with viewing angle [22, 24, 33], such as the DOLP curves flip in Sm leaves in Fig. 1 (k) and (l). In fact, the shape of the DOLP curves is roughly inverse to the BRF. The regions of the spectrum absorbed by pigments, such as the wavelengths around 400 nm and 670 nm, generally correspond to peaks in DOLP, 12

but are low in the BRF. Similar results were also found in previous studies of leaves with flat and smooth surfaces [22, 33]. The variation in spectral reflection with the change in chlorophyll content is the foundation for estimating LCC using spectral indices. In Figure 2, we show the spectral DOLP of leaves with different LCC at different viewing zenith angles. It is clear that with increasing LCC, the spectral DOLP in the visible wavelengths increased for all plant species. This result occurred because leaves samples with high chlorophyll content have a low total reflection in the visible wavelengths. Surface reflection (generates the polarized reflection) dominates the total reflection, which leads to relatively high DOLP. For leaf samples with low chlorophyll content, the proportion of polarized reflection in the total reflection decreases, generating relatively low DOLP values [23, 24, 31, 36, 42, 44]. Based on the results shown in Figure 2, it is possible to relate the spectral DOLP with LCC at different viewing zenith angles.

13

Figure 2. Spectral DOLP of leaves with different LCC at different viewing zenith angles (top, 30°; middle, 40°; and bottom, 50°) in the principal plane, the incident zenith angle was 40°. For all three types of plants, leaves with a high chlorophyll content have a high DOLP, and leaves with a low chlorophyll content have a low DOLP in the visible bands.

3.2. Relationship of LCC with spectral indices based on BRF and DOLP Based on the angular spectral BRF and DOLP of our leaf samples (n=162) from three plant species, 15 spectral indices based on BRF were firstly related to LCC, and then compared 14

with the results from spectral 1/DOLP at each viewing zenith angle. The R2 values from BRF are shown in Table 2 and values from 1/DOLP are shown in Table 3. Because the polarization near the nadir direction is weak for individual leaves [22, 24], the spectral DOLP of leaf samples at 0° and 10° viewing zenith angles were not included in our data to relate to LCC. In Table 2, the relationship between most spectral indices in terms of BRF and LCC strongly depends on the viewing angle, because leaf surface reflection, which is not related to LCC, dominates the total reflection in the forward scattering direction. Thus, the spectral indices that cannot reduce surface reflection, which are in the specular directions (40° and 50°), are insensitive to LCC and have the lowest R2 values in Table 2 [15, 47, 60]. A similar angular dependence is found for the spectral indices based on 1/DOLP (Table 3). This is attributed to the fact that DOLP is the ratio of polarized reflection to total reflection of the leaf, and the polarized reflection does not have a relationship with LCC. Thus, the relationships between spectral indices and LCC based on BRF and 1/DOLP are similar for several indices. However, the R2 are different between BRF and 1/DOLP, especially for two derivative indices, D730 and D740, for which the values notably decrease when the spectral 1/DOLP is used in the indices at each angle. The differences in R2 are attributed to the different values of spectral curves between BRF and 1/DOLP of leaves at different viewing angles. These results in Table 3 indicate that the spectral DOLP can not only be used to characterize the polarization properties of leaves [23, 33, 34], but also have a strong relationship with LCC based on spectral indices expressed as in Equation (4), which eliminates the dependence on polarized reflection.

15

Table 2. Coefficient of determination (R2) between spectral indices based on BRF and LCC for the 162 calibration leaf samples at different viewing zenith angles. In the last column, the R2 values were computed by data over all the viewing zenith angles. P value is used to represent the statistical significance. Small P value refers to obvious significance. P>0.05 is not denoted; 0.001≤ P < 0.01 is denoted by * and P < 0.001 is denoted by **. The incident zenith angles were 40° and 50°. D740 (7) and D730 (8) are the derivative indices at 740 and 730 nm. Spectral indices

Number

References

60°

50°

40°

30°

20°

Total

R680

(1)

[50]

0.023

0.256**

0.180**

0.019

0.154**

0.080**

1/R700

(2)

[51]

0.042*

0.020

0.014

0.068*

0.586**

0.015*

1/R550-1/R750

(3)

[12]

0.035

0.008

0.005

0.066*

0.494**

0.017**

**

**

0.050**

**

0.001

0.000

0.123

1/R700-1/R750

(4)

[12]

0.095

R750/R705

(5)

[15]

0.258**

0.031

0.037

0.356**

0.802**

0.176**

R750/R710

(6)

[52]

0.351**

0.078**

0.091**

0.479**

0.853**

0.258**

D740

(7)

[53]

0.827**

0.648**

0.404**

0.624**

0.821**

0.609**

D730

(8)

[4]

0.831**

0.867**

0.835**

0.844**

0.824**

0.827**

(R800-R635)/(R800+R635)

(9)

[54]

0.019

0.027

0.020

0.058*

0.481**

0.004

0.035

0.043

*

**

**

0.174**

**

(R750-R705)/(R750+R705)

(10)

[2]

0.256

R705/(R717+R491)

(11)

[55]

0.715**

0.533**

0.508**

0.681**

0.792**

0.615**

(R734-R747)/(R715+R726)

(12)

[56]

0.542**

0.245**

0.185**

0.453**

0.756**

0.362**

(13)

[15]

0.843**

0.616**

0.622**

0.839**

0.876**

0.735**

(R850-R710)/(R850-R680)

(14)

[47]

0.735**

0.741**

0.789**

0.818**

0.789**

0.771**

(R750-R445)/(R705-R445)

(15)

[15]

0.778**

0.600**

0.594**

0.838**

0.901**

0.679**

(R710-R760)/(R710-R670)

(16)

0.905**

0.881**

0.920**

0.929**

0.912**

0.901**

(R750-R705)/(R750+R705-2 *R445)

Proposed in this paper

0.382

0.638

0.784

Table 3. Coefficient of determination (R2) between spectral DOLP indices and LCC for the 162 calibration leaf samples at different viewing zenith angles. The original spectral indices can be found in the references reported between brackets. The R2 values in the last column were computed over all viewing zenith angles. Significance, P>0.05 is not denoted; 0.001≤ P < 0.01 is denoted by * and P < 0.001 is denoted by **. The incident zenith angles were 40° and 50°. D740 (7) and D730 (8) are the derivative indices at 740 and 730 nm, respectively. Spectral indices

Number

References 16

60°

50°

40°

30°

20°

Total

DOLP680-1 [R680] 1/DOLP700-1 [1/R700] 1/DOLP550-1-1/DOLP750-1 [1/R550-1/R750] 1/DOLP700-1-1/DOLP750-1 [1/R700-1/R750] DOLP750-1/DOLP705-1 [R750/R705] DOLP750-1/DOLP710-1 [R750/R710] DOLP741-1-DOLP740-1 [D740] DOLP731-1-DOLP730-1 [D730] (DOLP800-1-DOLP635-1)/(DOLP800-1+DOLP635-1) [(R800-R635)/(R800+R635)] (DOLP750-1-DOLP705-1)/(DOLP750-1+DOLP705-1) [(R750-R705)/(R750+R705)] DOLP705-1/(DOLP717-1 +DOLP491-1) [R705/(R717+R491)] (DOLP734-1-DOLP747-1)/(DOLP715-1+DOLP726-1) [(R734-R747)/(R715+R726)]

(1)

[50]

0.259**

0.291**

0.333**

0.370**

0.305**

0.086**

(2)

[51]

0.377**

0.431**

0.450**

0.464**

0.386**

0.239**

(3)

[12]

0.423**

0.232**

0.262**

0.529**

0.476**

0.245**

(4)

[12]

0.654**

0.489**

0.526**

0.753**

0.738**

0.437**

(5)

[15]

0.253**

0.022

0.016

0.290**

0.783**

0.143**

(6)

[52]

0.339**

0.064*

0.057*

0.441**

0.845**

0.229**

(7)

[53]

0.035

0.005

0.028

0.004

0.042

0.000

(8)

[4]

0.188**

0.046*

0.054*

0.107**

0.155**

0.058**

(9)

[54]

0.036

0.025

0.026

0.031

0.387**

0.004

(10)

[2]

0.238**

0.021

0.017

0.311**

0.746**

0.130**

(11)

[55]

0.640**

0.569**

0.559**

0.643**

0.729**

0.581**

(12)

[56]

0.385**

0.137**

0.173**

0.602**

0.547**

0.232**

(13)

[15]

0.846**

0.844**

0.840**

0.842**

0.832**

0.833**

(14)

[47]

0.826**

0.827**

0.800**

0.793**

0.776**

0.798**

(15)

[15]

0.924**

0.922**

0.916**

0.923**

0.908**

0.909**

0.926**

0.932**

0.931**

0.929**

0.910**

0.924**

(DOLP750-1-DOLP705-1)/(DOLP750-1+DOLP705-1-2* DOLP445-1) [(R750-R705)/(R750+R705-2*R445)] (DOLP850-1-DOLP710-1)/ (DOLP850-1-DOLP680-1) [(R850-R710)/(R850-R680)] (DOLP750-1-DOLP445-1)/(DOLP705-1-DOLP445-1) [(R750-R445)/(R705-R445)] (DOLP710-1-DOLP760-1)/(DOLP710-1-DOLP670-1) [(R710-R760)/(R710-R670)]

(16)

Proposed in this paper

In fact, the three DOLP spectral indices (13), (14) and (15) based on Equation (4) used unpolarized reflection to relate to LCC. The dependence of the relationship between spectral indices and LCC on viewing zenith angle then is reduced in the forward scattering directions. Theoretically, spectral indices (13), (14) and (15), which are derived from the ratio of 17

difference between different wavelengths, based on the BRF will have a similar relationship with LCC as the spectral indices based on 1/DOLP. This is because the ratio of the difference between the reflections at different wavelengths will reduce the influence of specular reflection, so that the diffuse portion is used to relate to LCC. This form of index has been used to remove surface reflection [15, 47] and also reduced the dependence on viewing zenith angle (indices (13), (14) and (15) in Table 2) when compared to the other indicex. However, our

results

indicate

that

the

two

spectral

indices

((R750-R445)/(R705-R445)

and

(R750-R705)/(R750+R705-2*R445)) expressed in terms of 1/DOLP had a better relationship with LCC

than

the

spectral

indices

calculated

in

terms

of

BRF.

For

example,

(DOLP750-1-DOLP445-1)/(DOLP705-1-DOLP445-1) has the best relationship with LCC, with R2 is 0.909; while (R750-R445)/(R705-R445), the R2 is 0.679. A similar result is also found in the spectral

indices,

using

the

wavelength

at

445

nm,

such

as,

for

(DOLP750-1-DOLP705-1)/(DOLP750-1+DOLP705-1-2*DOLP445-1), the R2 is 0.833, while for (R750-R705)/(R750+R705-2*R445), R2 is 0.735. These differences arise from the fact that the relationships between spectral indices ((13) and (15)) based on 1/DOLP and LCC are stronger than those based on BRF for Sm leaves with high LCC (see the comparison between Fig. 3 (b)-(c) with Fig. 4 (b)-(c)). That spectral indices using the wavelength at 445 nm based on 1/DOLP are better than those based on BRF cannot be explained in the study. We assume that Sm leaves with high LCC have different leaf surface structures (more wax or much thicker) compared with others leaves. These surface properties may have a greater influence on the relationship with LCC using BRF than using DOLP, which leads to higher R2 for spectral DOLP indices. This assumption will be confirmed using the photometric and 18

polarimetric measurements of more leaf samples combining with surface structure analysis results in future studies. A complete description of the optical properties of a leaf includes intensity, polarization, angular and spectral information [23, 45]. In terms of both photometric and polarimetric results, spectral indices can be used to accurately estimate LCC at different viewing zenith angles. In the last column of Tables 2 and 3, the relationships between spectral indices based on BRF and 1/DOLP and LCC over all five viewing directions (from 20° to 60°) with LCC are shown. As expected, the three more angle-insensitive spectral indices (13), (14) and (15) have a relatively higher relationship with LCC over the five measurement directions. Based on the R2 shown in Table 2, the spectral indices (13), (14) and (15), which are the ratio of the difference between two different wavelengths, appear to be useful for estimating LCC. Our proposed spectral index based on the BRF (index (16), which has the highest R2 (0.901) in Table 2) was optimized using three wavelengths in the region of 670-885 nm. Following equation (4), the format of a new spectral index based on BRF can be described as (R710-R760)/(R710-R670) or 1-(R760-R670)/(R710-R670). All the three wavelengths of our new spectral index are within the range of wavelengths identified by previous studies, such as, λ1 is an index wavelength (typically between 670 and 720 nm, where the red and red edge wavelengths have a strong relationship with LCC [11, 12]), λ2 is a reference wavelength, typically between 740 nm and 900 nm [15], λ3 is as a measurement of surface reflection, which can remove the surface (specular) reflection [14, 15, 47]. We found that this new index based on 1/DOLP was also independent of the viewing zenith angles and had a very high relationship with LCC over all five viewing angles, R2=0.924, as shown in the last line in 19

Table 3.

Figure 3. Relationships between spectral indices (based on BRF measured at different incident zenith angles: 40° and 50°) and LCC for all measurements from 20° to 60° in the forward scattering direction in the principal plane (n=162), (a) our proposed index (16), (b) index (15) and (c) index (13) are from Sims and Gamon [15], (d) index (14) is from Datta [47]. The selected spectral indices have a strong relationship (R2> 0.65) with LCC at different viewing zenith angles. Index (15) and index (13) based on BRF have a weaker relationship with LCC than the indices expressed in terms of 1/DOLP (Fig. 4).

20

Figure 4. Relationships between the spectral DOLP indices and LCC for all measurements from 20° to 60° in the forward scattering direction in the principal plane (n=162), (a) our proposed index (16), (b) index (15) and (c) index (13) are from Sims and Gamon [15], (d) index (14) is from Datta [47]. From linear and non-linear fits, it is found that the linear relationship between spectral DOLP indices and LCC is the strongest. The selected spectral DOLP indices have strong correlations with LCC at different viewing zenith angles, which has the potential of estimating LCC using polarimetric measurements.

The relationships between the four spectral indices and LCC for all the measurements from 20° to 60° in the forward scattering direction in the principal plane based on BRF and 1/DOLP are shown in Figure 3 and Figure 4, respectively. It is clear that our proposed spectral index has a very strong and similar relationship with LCC for both BRF and DOLP. 21

In the nadir and backward scattering directions, the specular reflection is low and the total reflection of the leaves does not have an obvious anisotropy [33, 43], thus leading to a strong relationship between spectral indices and LCC (Table 4). The relationships also have a weak dependence with the viewing zenith angle in the nadir and backward scattering directions (Table 4). Because the polarization of the leaves is small in the backward scattering and nadir directions, the spectral indices based on DOLP in these scattering directions cannot yield useful information regarding LCC (Table 5).

Table 4. Coefficient of determination (R2) between spectral indices based on BRF and LCC for the 162 calibration leaf samples at different viewing zenith angles in nadir and backward scattering directions. Significance, P < 0.001 is denoted by **. The incident zenith angles were 40° and 50°. The negative angle signs correspond to backward scattering directions. Spectral indices R750/R705

Number

(5)

References

0°

[15]

-50°

-10°

-20°

-30°

-40°

0.943**

0.937**

0.931**

0.956**

0.958**

0.969**

**

**

**

**

**

0.909**

D740

(7)

[53]

0.917

R705/(R717+R491)

(11)

[55]

0.832**

0.823**

0.822**

0.875**

0.934**

0.876**

(R734-R747)/(R715+R726)

(12)

[56]

0.915**

0.916**

0.917**

0.934**

0.962**

0.949**

(R750-R445)/(R705-R445)

(15)

[15]

0.929**

0.927**

0.925**

0.951**

0.952**

0.953**

(R710-R760)/(R710-R670)

(16)

0.923**

0.922**

0.920**

0.957**

0.960**

0.963**

Proposed in this paper

0.906

0.917

0.927

0.956

Table 5. Coefficient of determination (R2) between spectral DOLP indices and LCC for the 162 calibration leaf samples at different viewing zenith angles in nadir and backward scattering directions. The original spectral indices are referenced in brackets, and the spectral DOLP indices are in table. Significance, P>0.05 is not denoted, means that the relationships are not significant. The incident zenith angles were 40° and 50°. The negative angle signs correspond to backward scattering directions. Spectral indices DOLP750-1/DOLP705-1

Number

References

0°

-10°

-20°

-30°

-40°

[15]

0.004

0.002

0.004

0.014

0.118

(5) 22

-50°

0.036

[R750/R705] DOLP741-1-DOLP740-1 [D740] DOLP705-1/(DOLP717-1 +DOLP491-1) [R705/(R717+R491)] (DOLP734-1-DOLP747-1)/(DOLP715-1+DOLP726-1) [(R734-R747)/(R715+R726)] (DOLP750-1-DOLP445-1)/(DOLP705-1-DOLP445-1) [(R750-R445)/(R705-R445)] (DOLP710-1-DOLP760-1)/(DOLP710-1-DOLP670-1) [(R710-R760)/(R710-R670)]

(7)

[53]

0.003

0.000

0.002

0.000

0.090

0.017

(11)

[55]

0.000

0.000

0.006

0.009

0.028

0.001

(12)

[56]

0.004

0.002

0.000

0.004

0.108

0.000

(15)

[15]

0.000

0.002

0.011

0.013

0.008

0.015

0.011

0.000

0.001

0.002

0.060

0.031

(16)

Proposed in this paper

3.3 Estimating LCC using BRF and DOLP spectral indices in different directions Fifty-five leaves (Table 1) from the three plant species were used to test against the modeled LCC using the calibration formulas in Figures 3 and 4 based on BRF and 1/DOLP, respectively. First, we combined the BRF and the 1/DOLP of the leaves over all five directions to estimate LCC. The results of this estimation are denoted as ―total‖, and the R2 and RMSE of the calibration formulas are shown in Figures 5 and 6. Our proposed index based on the BRF and 1/DOLP had a high LCC estimation accuracy over all measurement directions, with RMSE of 4.90 μg/cm2 and 4.29 μg/cm2, respectively. The calibration formulas shown in Figures 3 and 4 were used to estimate LCC at each viewing angle for BRF (Figure 5 and Table 6) and DOLP (Figure 6 and Table 7). The LCC estimation results of spectral indices (14) and (16) based on BRF were independent of viewing angles, while spectral indices (13) and (15) were dependent of viewing angle at 40° and 50° (Table 6). The four spectral DOLP indices were independent of the viewing angles, and our proposed index (16) and index (15), with relatively small RMSE, also had a stable and great ability at estimating LCC based on multi-angular polarimetric measurements (Table 7). Theoretically, 23

spectral indices based on BRF and on 1/DOLP expressed as in Equation (4), should be independent of viewing angle in the LCC estimation, but the BRF spectral indices (13) and (15), which contain 445 nm, are viewing angle-dependent (Table 6). The angular dependence in the specular directions (40° and 50° viewing angles in Table 6) when using spectral BRF indices (13) and (15), which may be determined by the specular reflection of Sm leaves with high LCC content at 445 nm, 705 nm and 750 nm are different. This assumption is supported by the polarized reflection of Sm leaf with high LCC in Figure 1 (r) has a dependence of wavelength, because specular reflection dominates the polarized reflection [24, 25].

Figure 5. R2 and root mean square error (RMSE) of validation samples from four different BRF spectral indices using the combination of five angles in the forward scattering directions 24

in the principal plane (n=55), (a) our proposed index (16), (b) index (15) and (c) index (13) are from Sims and Gamon [15], (d) index (14) is from Datta [47]. The measured LCC at each angle is denoted in different colors.

Figure 6. R2 and root mean square error (RMSE) of validation samples from four different spectral DOLP indices using the combination of five angles in the forward scattering directions in the principal plane (n=55), (a) our proposed index (16), (b) index (15) and (c) index (13) are from Sims and Gamon [15], (d) index (14) is from Datta [47]. The measured LCC at each angle is denoted as different colors.

Based on the LCC estimation results comparison between spectral DOLP indices (Table 7 and Figure 6) and spectral BRF indices (Table 6 and Figure 5), one advantage of our study 25

is that spectral indices (13) and (15) based on 1/DOLP do not depend on the viewing angle and generate accurate LCC estimation results (Table 7). However, the phenomenon that using 1/DOLP has a better LCC estimation than using BRF for spectral indices (13) and (15) also cannot be explained in this study.

Table 6. RMSE (μg/cm2) of validation samples calculated using BRF at each viewing zenith angle and over all of them in the principal plane, n=55. The incident zenith angles were 40° and 50°. BRF Spectral indices

Number

(R750-R705)/(R750+R705-2*R445)

Total

60°

50°

40°

30°

20°

(13)

6.98

10.87

10.52

6.89

6.43

8.63

(R850-R710)/(R850-R680)

(14)

9.97

9.16

7.99

7.39

6.90

8.41

(R750-R445)/(R705-R445)

(15)

7.11

11.55

11.52

5.87

5.01

8.78

(R710-R760)/(R710-R670)

(16)

4.77

6.24

4.68

4.22

4.17

4.90

Table 7. RMSE (μg/cm2) of validation samples calculated using DOLP at each viewing zenith angle and over all of them in the principal plane, n=55. The incident zenith angles were 40° and 50°. Spectral DOLP indices

Number

(DOLP750-1-DOLP705-1)/(DOLP750-1+DOLP705-1-2*DOLP445-1) (DOLP850-1-DOLP710-1)/ (DOLP850-1-DOLP680-1) (DOLP750-1-DOLP445-1)/ (DOLP710-1-DOLP760-1)/

Total

60°

50°

40°

30°

20°

(13)

7.39

7.42

7.48

7.24

6.66

7.27

(14)

8.05

7.86

8.58

8.68

8.26

8.29

(DOLP705-1-DOLP445-1)

(15)

5.13

5.23

5.48

5.04

4.81

5.16

(DOLP710-1-DOLP670-1)

(16)

5.18

4.45

4.34

4.04

3.97

4.44

Studies have typically used the existing reflection-based spectral indices to estimate LCC by performing measurements near the nadir direction or with an integrating sphere, which can reduce the leaf surface reflection and angular reflection. In this study, we do not try to replace the BRF by the DOLP, and just indicate that spectral DOLP indices are also effective for 26

estimating leaf properties using multi-angular optical measurements. Although using the BRF and DOLP will obtain similar results for some spectral indices following the format in Equation (4), the use of 1/DOLP is still effective for estimating LCC for leaves from different plant species. This is because the DOLP can be derived from only two orthogonal polarization states using a polarizer and a spectrometer, without the need to be normalized by a white reference panel as the BRF, making ground studies of plant LCC possible under both laboratory and field conditions. Previous studies have demonstrated the potential of relating DOLP to architectural conditions of vegetation covers [26, 27], our study expand the use of DOLP to biochemical parameter (leaf chlorophyll content) of plant leaves.

4. Conclusion We found that some existing spectral indices expressed either in terms of the BRF or the reciprocal of DOLP, can be applied to different plant species for the nondestructive estimation of LCC using multi-angle measurements. Moreover, we proposed a spectral index based on both the BRF and 1/DOLP, which is very sensitive to the LCC of the three studied plant species, is independent of the viewing zenith angle, and has a coefficient of determination with LCC larger than 0.9. This method can not only estimate LCC with a high accuracy from each single measurement direction in the forward direction in the principal plane, but also has the ability to estimate LCC across all directions that are dominated by specular reflection. Our study indicates that the polarimetric reflection of leaves is as effective as the photometric reflection for predicting chlorophyll content using multi-angle measurements, 27

especially in the directions that are dominated by specular reflection. The advantages of this study are that our proposed index based on 1/DOLP is not only convenient for accurately estimating LCC without the need to normalize by a reference panel, but also gives a similar estimation accuracy for an arbitrary direction (larger than 20°) in the forward scattering directions in the principal plane. Changes in LCC have been related to plant growth and senescence, photosynthetic capacity, and effects of disease and environmental stresses [5, 11, 47, 57, 58]. Our findings make it possible to rapidly estimate LCC over a wide range of intact leaves using spectral indices expressed in terms of 1/DOLP and BRF. This optical measurement method is non-destructive, and allows to repeatedly sample leaf reflection during different developmental and senescing stages or under plant stress. In this way, fundamental leaf properties revealed by leaf-level polarimetric and photometric measurements can be examined for their contribution to larger scale physiological and ecological processes.

Conflict of Interest None. Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant No. 41771362, 41971290 and 41671347), Jilin Provincial Science and Technology Development Project (Grant No. 20180519021JH and 20180101313JC), and the Fundamental Research Funds for the Central Universities (130014925). All data supporting the results and analyses of this study are presented in the figures, tables of this manuscript. All the polarization data of leaves has also been uploaded to the figshare repository at https://doi.org/10.6084/m9.figshare.8179286.v1.

References: 28

[1] Asner G, Martin R. Spectral and chemical analysis of tropical forests: Scaling from leaf to canopy levels. Remote Sensing of Environment. 2008;112:3958-70. [2] Gitelson A, Merzlyak MN. Spectral reflectance changes associated with autumn senescence of aesculus hippocastanum L. and Acer platanoides L. seaves. spectral features and relation to chlorophyll estimation. J Plant Physiol. 1994;143:286-92. [3] Hallik L, Kazantsev T, Kuusk A, Galmés J, Tomás M, Niinemets Ü. Generality of relationships between leaf pigment contents and spectral vegetation indices in Mallorca (Spain). Regional Environmental Change. 2017;17:2097-109. [4] Richardson AD, Duigan SP, Berlyn G. An evaluation of noninvasive methods to estimate foliar chlorophyll content. New Phytol. 2002;153:185-94. [5] Penuelas J, Gamon JA, Griffin KL, Field CB. Assessing community type, plant biomass, pigment composition and photosynthetic efficiency of aquatic vegetation from spectral reflectance. Remote Sensing of Environment. 1993;46:110-8. [6] Penuelas J, Munne-Bosch S, Llusia J, Filella I. Leaf reflectance and photo- and antioxidant protection in field-grown summer stressed Phillyrea angustifolia. Optical signals of oxidative stress? New Phytol. 2004;162:115-24. [7] Croft H, Chen JM, Zhang Y, Simic A, Noland TL, Nesbitt N, et al. Evaluating leaf chlorophyll content prediction from multispectral remote sensing data within a physically-based modelling framework. ISPRS J Photogramm Remote Sens. 2015;102:85-95. [8] Croft H, Chen JM, Luo X, Bartlett P, Chen B, Staebler RM. Leaf chlorophyll content as a proxy for leaf photosynthetic capacity. Global Change Biol. 2017;23:3513-24. [9] Luo X, Croft H, Chen JM, Bartlett P, Staebler R, Froelich N. Incorporating leaf chlorophyll content into a two-leaf terrestrial biosphere model for estimating carbon and water fluxes at a forest site. Agricultural and Forest Meteorology. 2018;248:156-68. [10] Tucker CJ. Red and photographic infrared linear combinations for monitoring vegetation. Remote Sensing of Environment. 1979;8:127-50. [11] Curran PJ. Multispectral remote sensing of vegetation amount. Progress in Physical Geography. 1980;4:315-41. [12] Gitelson AA, Gritz Y, Merzlyak MN. Relationships between leaf chlorophyll content and spectral reflectance and algorithms for non-destructive chlorophyll assessment in higher plant leaves. J Plant Physiol. 2003;160:271-82. [13] Penuelas J, Baret F, Filella I. Semi-empirical indices to assess carotenoids/chlorophyll a ratio from leaf spectral reflectance. Psyn. 1995;31:221-30. [14] Gitelson AA, Keydan GP, Merzlyak MN. Three-band model for noninvasive estimation of chlorophyll, carotenoids, and anthocyanin contents in higher plant leaves. Geophys Res Lett. 2006;33. [15] Sims DA, Gamon JA. Relationships between leaf pigment content and spectral reflectance across a wide range of species, leaf structures and developmental stages. Remote Sensing of Environment. 2002;81:337-54. [16] Lu S, Lu X, Zhao W, Liu Y, Wang Z, Omasa K. Comparing vegetation indices for remote chlorophyll measurement of white poplar and Chinese elm leaves with different adaxial and abaxial surfaces. J Exp Bot. 2015;66:5625-37. [17] Gara TW, Skidmore AK, Darvishzadeh R, Wang T. Leaf to canopy upscaling approach affects the estimation of canopy traits. GIScience & Remote Sensing. 2018:1-22. [18] Lu S, Lu F, You W, Wang Z, Liu Y, Omasa K. A robust vegetation index for remotely assessing 29

chlorophyll content of dorsiventral leaves across several species in different seasons. Plant methods. 2018;14:15. [19] Deschamps P-Y, Bréon FM, Leroy M, Podaire A, Bricaud A, Burize J-C, et al. The POLDER mission: instrument characteristics and scientific objectives. IEEE Transactions of Geoscience and Remote Sensing. 1994;32:598-615. [20] Cairns B, Russell EE, Travis LD. The Research Scanning Polarimeter: calibraton and ground-based measurements. Proceeding of SPIE. 1999;3754. [21] Diner D, Xu F, Martonchik J, Rheingans B, Geier S, Jovanovic V, et al. Exploration of a polarized surface bidirectional reflectance model using the ground-based multiangle spectropolarimetric imager. Atmos. 2012;3:591-619. [22] Woolley JT. Reflectance and transmittance of light by leaves. Plant Physiol. 1971;47:656-62. [23] Vanderbilt VC, Grant L, Daughtry CST. Polarization of light scattered by vegetation. Proc IEEE. 1985;73:1012-24. [24] Grant L, Daughtry CST, Vanderbilt VC. Polarized and non-polarized leaf reflectances of coleus blumei. Environ Exp Bot. 1987;24:139-45. [25] Grant L. Diffuse and specular characteristics of leaf reflectance. Remote Sensing of Environment. 1987;22:309-22. [26] Rondeaux G, Herman M. Polarization of light reflected by crop canopies. Remote Sensing of Environment. 1991;38:63-75. [27] Curran PJ. The relationship between polarized visible light and vegetation amount. Remote Sensing of Environment. 1981;11:87-92. [28] Vanderbilt VC, Grant L, Biehl LL, Robinson BF. Specular, diffuse, and polarized light scattered by two wheat canopies. Appl Opt. 1985;24:2408-18. [29] Maignan F, Bréon F-M, Fédèle E, Bouvier M. Polarized reflectances of natural surfaces: Spaceborne measurements and analytical modeling. Remote Sensing of Environment. 2009;113:2642-50. [30] Waquet F, Leon J-F, Cairns B, Goloub P, Deuzé JL, Auriol F. Analysis of the spectral and angular response of the vegetated surface polarization for the purpose of aerosol remote sensing over land. Appl Opt. 2009;48:1228-36. [31] Yang B, Knyazikhin Y, Lin Y, Yan K, Chen C, Park T, et al. Analyses of Impact of Needle Surface Properties on Estimation of Needle Absorption Spectrum: Case Study with Coniferous Needle and Shoot Samples. Remote Sensing. 2016;8:563. [32] Sun Z, Wu D, Lv Y, Zhao Y. Polarized reflectance factors of vegetation covers from laboratory and field: A comparison with modeled results. Journal of Geophysical Research: Atmospheres. 2017;122:1042-65. [33] Sun Z, Peng Z, Wu D, Lv Y. Photopolarimetric properties of leaf and vegetation covers over a wide range of measurement directions. Journal of Quantitative Spectroscopy and Radiative Transfer. 2018;206:273-85. [34] Martin WE, Hesse E, Hough JH, Sparks WB, Cockell CS, Ulanowski Z, et al. Polarized optical scattering signatures from biological materials. Journal of Quantitative Spectroscopy and Radiative Transfer. 2010;111:2444-59. [35] Kallel A, Gastellu-Etchegorry JP. Canopy polarized BRDF simulation based on non-stationary Monte Carlo 3-D vector RT modeling. Journal of Quantitative Spectroscopy and Radiative Transfer. 2017;189:149-67. [36] Suomalainen J, Hakala T, Puttonen E, Peltoniemi J. Polarised bidirectional reflectance factor 30

measurements from vegetated land surfaces. Journal of Quantitative Spectroscopy and Radiative Transfer. 2009;110:1044-56. [37] Raven PN, Jordan DL, Smith CE. Polarized directional reflectance from laurel and mullein leaves. OptEn. 2002;41:1002-12. [38] Savenkov SN, Muttiah RS, Oberemok YA. Transmitted and reflected scattering matrices from an English oak leaf. Appl Opt. 2003;42:4955-62. [39] Grant L, Daughtry CST, Vanderbilt VC. Variations in the polarized leaf reflectance of Sorghum bicolor. Remote Sensing of Environment. 1987;21:333-9. [40] Peltoniemi JI, Gritsevich M, Puttonen E. Reflectance and polarization characteristics of various vegetation types. Light scattering reviews 9: light scattering and radiative transfer Berlin, Heidelberg: Springer. 2015:257-94. [41] Sun Z, Wu Z, Zhao Y. Semi-automatic laboratory goniospectrometer system for performing multi-angular reflectance and polarization measurements for natural surfaces. Rev Sci Instrum. 2014;85:014503. [42] Sun Z, Huang Y, Bao Y, Wu D. Polarized remote sensing: A note on the Stokes parameters measurements from natural and manmade targets using a spectrometer. IEEE Transactions on Geoscience and Remote Sensing. 2017;55:4008-21. [43] Bousquet L, Lachérade S, Jacquemoud S, Moya I. Leaf BRDF measurements and model for specular and diffuse components differentiation. Remote Sensing of Environment. 2005;98:201-11. [44] Tyo JS, Goldstein DL, Chenault DB, Shaw JA. Review of passive imaging polarimetry for remote sensing applications. Appl Opt. 2006;45:5453-69. [45] Talmage DA, Curran PJ. Remote sensing using partially polarized light. Internal Journal of Remote Sensing. 1986;7:47-64. [46] Diner DJ, Xu F, Garay MJ, Martonchik JV, Rheingans BE, Geier S, et al. The Airborne Multiangle SpectroPolarimetric Imager (AirMSPI): a new tool for aerosol and cloud remote sensing. Atmospheric Measurement Techniques. 2013;6:2007-25. [47] Datt B. A New Reflectance Index for Remote Sensing of Chlorophyll Content in Higher Plants: Tests using Eucalyptus Leaves. J Plant Physiol. 1999;154:30-6. [48] Schaepman-Strub G, Schaepman ME, Painter TH, Dangel S, Martonchik JV. Reflectance quantities in optical remote sensing—definitions and case studies. Remote Sensing of Environment. 2006;103:27-42. [49] Hyde MW, Cain SC, Schmidt JD, Havrilla MJ. Material classification of an unknown object using turbulence-degraded polarimetric imagery. IEEE Transactions on Geoscience and Remote Sensing. 2011;49:264-76. [50] Blackburn GA. Spectral indices for estimating photosynthetic pigment concentrations: A test using senescent tree leaves. IJRS. 1998;19:657-75. [51] Gitelson AA, Merzlyak MN. Signature analysis of leaf reflectance spectra: algorithm development for remote sensing of chlorophyll. J Plant Physiol. 1996;148:494-500. [52] Zarco-Tejada P, Miller J, Noland TL, Mohammed GH, Sampson PH. Scaling-up and model inversion methods with narrowband optical indices for chlorophyll content estimation in closed Forest canopies with hyperspectral data. IEEE Transactions of Geoscience and Remote Sensing. 2001;39:1491-507. [53] Mutanga O, Skidmore AK. Red edge shift and biochemical content in grass canopies. ISPRS J Photogramm Remote Sens. 2007;62:34-42. [54] Blackburn GA. Quantifying cllorophylls and caroteniods at leaf and canopy scales: an evaluation of some hyperspectral approaches. Remote Sensing of Environment. 1998;66:273-85. 31

[55] Tian YC, Yao X, Yang J, Cao WX, Hannaway DB, Zhu Y. Assessing newly developed and published vegetation indices for estimating rice leaf nitrogen concentration with ground- and space-based hyperspectral reflectance. Field Crops Res. 2011;120:299-310. [56] Vogelmann JE, Rock BN, Moss DM. Red edge spectral measurements from sugar maple leaves. IJRS. 1993;14:1563-75. [57] Gamon JA, Surfus JS. Assessing leaf pigment content and activity with a reflectometer. New Phytol. 1999;143:105-17. [58] Inoue Y, Guerif M, Baret F, Skidmore A, Gitelson A, Schlerf M, et al. Simple and robust methods for remote sensing of canopy chlorophyll content: a comparative analysis of hyperspectral data for different types of vegetation. Plant Cell and Environment. 2016;39:2609-23. [59] Wintermans, J. F. G.M., and A. De Mots. Spectrophotometric characteristics of chlorophylls a and b and their phenophytins in ethanol. Biochimica et Biophysica Acta (BBA)—Biophysics including Photosynthesis. 1965, 109, 448–453. [60] Li W., Sun Z., Lu S., Omasa K. Estimation of the leaf chlorophyll content using multi-angular spectral reflectance factor. Plant Cell and Environment, 2019, 42, 3152-3165.

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