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The optical scattering property of a target is the essential signal for passive remote sensing. In this study, we performed the photopolarimetric measurements of a manmade target in the wavelength range of 400-1000 nm over the hemispherical directions using the Northeast Normal University Laboratory Goniospectrometer System (NENULGS). We discussed the influence of the absorption of a polarizer on the measured Stokes parameters, and used the BRF (bidirectional reflectance factor) and BPRF (bidirectional polarized reflectance factor) to characterize the scattering property of our sample at selected wavelengths. These measured BRFs and BPRFs were also compared with the modeled results using a semi-empirical photometric model and a semi-empirical polarimetric model, respectively. Subsequently, the modeled BRFs and BPRFs were used to simulate the degree of linear polarization (DoLP) of a man-made target, which provided a comparison with the measured DoLP. We found that (1) the I parameter reflectance factor (IpRF) can effectively represent the BRF if we considered the absorption of the polarizer, (2) the modeled photopolarimetric results of manmade target were in good agreement with the measurements, and (3) the simulated DoLP of manmade target also provided a good match with the measured DoLP, with an average relative difference of approximately 0.2 for all the selected wavelengths. Our results appeared very promising for proving that the polarimetric measurement is a very effective and useful method for remote sensing applications as well as deepening our understanding of the optical properties of reflected light from the manmade object as ours.
© 2017 Optical Society of America
1. Introduction
Light reflected by a target surface can be described in terms of its intensity and polarization. The intensity signal is usually measured in remote sensing applications [1,2], whereas the measurement of the polarization state of light can also provide useful information [3,4], which cannot be directly obtained from the intensity signal. Polarization is a property of light or electromagnetic radiation that refers to the orientation of the transverse electric field. Polarized light reflected from surfaces has been found to be useful and effective in several applications, such as material classification [5,6], shape extraction [7,8], and target detection or recognition [9,10]. These studies indicate that the photopolarimetric property of a target is important for remote sensing.
Scattering from a target surface can be represented using a bidirectional reflectance distribution function (BRDF) and a polarized bidirectional distribution function (pBPDF) [11]. A method of quantifying the BRDF or more generally, the pBRDF is required to measure the priori BRDF and pBRDF data set of target and background materials, which may subsequently be applied to algorithms. The most common and traditional measurement method is to use an illumination source and a detector system, which are the key elements, to measure the scattered radiance, such as the imaging and non-imaging measurements conducted in the laboratory and field [10,12–14]. In the ideal case, there should be enough measurements over the full hemispherical range of source and detector orientations to provide a full understanding of the scattering properties of the target. However, this goal is too difficult to achieve. In particular, an effective means of generating the data is through models, which may use physics-based principles to derive the directional reflectance and polarization. In addition, for practical purposes, measurements are required as inputs for most BRDF and pBRDF models.
BRDF and pBRDF models have been extensively studied and surveyed in many fields [15–19], and a popular model is the semi-empirical model, which can be used to simulate the reflectance [20–22], the Mueller matrix results [18,19,23], s- and p-polarized signals [24,25], and the DoLP of a target [19,26,27]. However, a few previous studies measured the bidirectional polarized reflectance factor (BPRF) of a target, which is derived from the Stokes parameters and can be used to represent the inherent polarization property of target [28]. Although both the BRF and BPRF have been used to describe natural surfaces [11], to date, there have been no studies that focus on combining these factors to quantify the reflection properties of manmade targets. In this paper, our primary focus is on measuring the Stokes parameters of a manmade target to enable the use of the BRF and BPRF to characterize the optical properties of light reflected from our sample. Moreover, we also explore if the simulated DoLP, which is obtained by BRF and BPRF, matches well with the measured DoLP of the manmade target.
To achieve this goal, we will (1) review the BRDF and pBRDF models in Section 2, (2) outline the set-up of the measurement system in Section 3, (3) present the sample and the angular reflectance and polarization distribution of the sample in Section 4, and (4) invert each model against the measurements and analyze the difference between the measurements and the model results with the best-fitting parameters in Section 5. In Section 6, we present the conclusions of this study.
2. Theory
2.1 Definition
The polarization state of light reflected by natural surfaces can be described by the four Stokes parameters (I, Q, U and V); V, is ignored hereafter since it is negligible after reflection [4]:
where Lx is the polarized reflected radiance from a surface at different polarizer directions, the reference plane for the four polarizer directions (0°, 45°, 90° and 135°) is taken to be the meridional plane of the instrument, Ip is the polarized reflected radiance from a surface, and DoLP is the degree of linear polarization.Theoretically, the I parameter equals to the total reflected radiance from a target surface. In practical applications, without considering the polarization of the reflected light from the target surface, the bidirectional reflectance factor (BRF) of each sample, which is defined as the ratio of the reflected radiant flux (dLsample) from the sample surface area (dA) to the reflected radiant flux (dL) from an ideal and diffuse surface of the same area (dA) in the identical viewing geometry under single-direction illumination, was measured in the laboratory. This factor is defined as follows [29,30]:
where θs is the incident zenith angle, θv is the viewing zenith angle, φ is the relative azimuth angle, φs is the incident azimuth angle, and φv is the viewing azimuth angle. Strictly speaking, our measurements should be referred to as the bi-conical reflectance factor (BCRF), as shown in [29,30]. However, to maintain a definition of the reflectance that is identical to that used in previous studies [31–33], we assume here that the BRF is approximately equal to the BCRF.The bidirectional polarized reflectance factor (BPRF) is used to quantify the polarized reflected radiance [34,35]:
where E is the total irradiance illuminated vertically on the horizontal plane. A common method of obtaining an estimate of the total spectral irradiance (Ecos(θs)) is to measure the spectral radiance L from a horizontal reference panel of a known hemispherical spectral reflectance (ρλ) and assumed Lambertian properties [36]:We used the measured bidirectional polarized reflectance factor (BPRFm), which is defined as the ratio of the polarized reflected radiance dIp from the surface area dA to the reflected radiance dL from an ideal and diffuse surface of the same area dA under an identical viewing geometry and illumination direction:The Spectralon panel, which was provided by the manufacture, was used as a perfect Lambertian panel in this study. Based on Eqs. (6) and (9), if the I parameter equals to the total reflected radiance in one measurement direction, the expression of DoLP is as follows:We will discuss whether the I parameter can be used to represent the total reflected radiance in the next section.2.2 Models
In this paper, we use a BRDF model to simulate the BRFs and a BPDF model to simulate the BPRFs of a manmade target. We briefly review the two models. Based on the Torrance-Sparrow model [17], the BRDF model is proposed by Wu et al. [37], and it has been used to model the BRDF of manmade target [21]. This model can be described as:
where φ = φv-φs, kr2cosα/[1 + (kr2-1) cosα] is the distribution function of the sun-surface, exp[b(1-cosγ)a] is the approximation description of the Fresnel reflection function, and V (λ, θs, θv, φ) is the masking and shadowing function [21,37]. In the modified Torrance-Sparrow model by Wu et al. [37], there are five parameters kb, kd, kr, a and b that need to be inverted. kb is the mirror-direction component, kd is related to the diffuse component of reflectance, and kr is related to the distribution of the subsurface, the exponential function with two parameters is used to substitute the Fresnel reflectance function to void the calculation of many trigonometric functions [21,37].The BPDF model, which was established by Diner et al. [28], was represented as the sum of a depolarizing volumetric scattering term and a polarizing reflections term. The model at wavelength λ is written as follows:
where where η is the scattering angle. This model is written as the product of a function of only the wavelength and a function of only the illumination and viewing geometry and is described by the parameters aλ, k and g. The depolarization matrix D in Eq. (15) is a Mueller matrix with unity in the upper left-hand element and zeros everywhere else [28]. By generalizing the scalar BRDF, and using the polarized formulation by Priest and Meier [18], the second component of the model is given by the following:The function f(σ, β) describes the distribution of facets, the matrix P is defined in the local coordinate system of a facet, rotations between the global and facet coordinate systems are represented by the matrices M(m0) and M(–m), and the expression of these functions was detailed in [28]. A wavelength-independent scaling parameter ζ and σ are the free parameters. This polarized reflectance model has been used to predict the polarized reflection from two manmade targets (a parking lot and a truck roof). In this paper, we only use the two models to simulate the BRFs and BPRFs of the target based on our measurements; we do not discuss the theory of them.3. Measurement system
In this study, we used the Northeast Normal University Laboratory Goniospectrometer System (NENULGS) [38] to measure the reflectance and polarization of a manmade target in the laboratory. A detailed description of the laboratory measurement system was provided in our previous paper [38]. The basic NENULGS configuration consists of a goniometer, artificial illumination and an Analytical Spectral Devices FieldSpec 3 (ASD FS3, Colorado, USA) spectroradiometer.
The goniometer has a 1.2-m long motor driven arm that can be tilted up to ± 90° from the zenith with a stepping motor; it allows for an accuracy of 0.1° in the viewing direction. The azimuth direction, which has an accuracy of 0.25°, can be rotated from 0° to 360° with a stepping motor. A tungsten halogen lamp, which was attached to a 90° arc with a 1.5-m radius, was used to mimic sunlight in these measurements. The zenith angle measurement for the source has an accuracy of 0.25°. The goniometer can place the fiber-optic cable of the ASD spectrometer at any point on the hemisphere above a sample with its oblique and vertical axes. Because of the limitations of our apparatus, 8° was the smallest phase-angle measurement that could be obtained when rotating the arm in the viewing direction.
When measuring the polarization in the laboratory, a calcite Glan-Thomson prism, which is effective from 350 nm to 2300 nm, was installed in a small device, and it allowed free rotation in front of the fiber-optic cable from 0° to 360° in 1° increments. A broadband depolarizer was added between the prism and the fiber-optic cable to counter the polarization sensitivity of the ASD FS3 spectroradiometer in the near infrared wavelengths, similar to what was performed by other researchers [31,32]. The average uncertainty in the linear polarization of our instrument was less than 5%, and the polarimetric accuracy of the instrument was less than 0.01, which was determined as the absolute value of the degree of linear polarization, and was established by measuring a Spectralon plane [38,39]. These parameters are appropriate for studying the polarization of natural surfaces [31–33,40]. In this paper, our main focus was on the reflectance and polarization of a manmade target from 400 to 1000 nm, because the polarization sensitivity of the ASD FS3 spectroradiometer could be excluded in this wavelength range. NENULGS has been used to detect phase and spectral reflectance curves and the linear polarization degree of snow [40], soil [41–43] and ice [44] when the incident light is unpolarized. The size of the field of view was 8° for both the BRF and BPRF measurements. The distance from the sensor to the sample’s surface was 0.2 m. The sensor, whose viewing zenith angle was changed from 0° to 60°, recorded data from its circular footprint with a diameter of 2.8 cm to its elliptical footprint with a major axis with a length of 5.7 cm. Because the diameter of the illuminated area, which was 10cm, was greater than the viewing footprint area at all times, we did not need to consider the effect of the surroundings on the reflectance beyond the target surface.
4. Measurement results
4.1 BRFs of the manmade target
The illumination zenith angles were 40° and 60° during the measurement process in the laboratory. The measurements were performed on the hemisphere above our painted plate. We assumed the sample surface was homogeneous and the reflectance was left-right symmetric with respect to light-source principal plane of painted plate. Thus, we measured the half-azimuth direction in this paper, the increment of the viewing zenith angle was 10° at all the azimuth angles (e.g. 0°, 10°, 20°…60°), the measurement interval of the azimuth direction was 15°, e.g., [0°, 15°,…75°, 90°] and [180°, 195°, …255°, 270°]. The solid lines represent the measured azimuth directions, and the solid points represent the viewing zenith positions, as shown in Fig. 1. There were 79 measurement directions were investigated in the laboratory measurements. To fill the gap of the polar plot, we replaced the reflectance and polarization value at a phase angle of 0° by the value at a phase angle of 8° in the principal plane (e.g. the reflectance and polarization value at the viewing angle of 32° was used when the illumination zenith angle was 40°). Figure 1 shows the measurement schematic diagram when the illumination zenith angle was 40°; the measurement at the viewing angle of 40° was absent in the backward scattering direction in the principal plane.
Fig. 1 Measurement schematic diagram when the incident zenith angle was 40°; 0° refers to the backward scattering direction, and 180° corresponds to the forward scattering direction. The solid lines represent the measured azimuth directions.
The manmade target is a yellow painted plate, with a size of 15 cm*15 cm, as observed in Fig. 2(a). We also show the spectrum curves of the manmade target at different viewing zenith angles for an incident zenith angle of 40° in Fig. 2(b). Although the spectral reflectance of manmade target at the nadir direction is similar to that of desert sand [43,45], the distribution of the reflectance is different: there is a reflectance peak for manmade target in the forward scattering direction of the principal plane, while there is a minimum reflectance for desert sand in the same direction [41–43,45]. We have to confess that it is difficult to determine the contribution of paint and plate on the reflectance in the near infrared wavelengths, because we only have a single manmade target-a yellow painted plate in this paper. In order to simplify the reflection process, we assume the paint dominates the reflectance in near infrared. To further illustrate the distribution of the reflectance of manmade target, we show the BRF of our sample at 560, 670 and 865 nm in Fig. 3. We focused on these bands because the multi-angular reflectance and polarized reflectances of natural surfaces and manmade target can be obtained from the Research Scanning Polarimeter (RSP) [46] and the Ground-based Multiangle SpectroPolarimetric Imager (GroundMSPI) [28]. It is found that the manmade target produced a reflectance peak in the forward scattering direction when the viewing zenith angle was close to the incident zenith angle. This is a common phenomenon for a sample such as ours, and it has been observed in previous studies [10,20].
Fig. 2 The picture of the manmade target (a) and the spectrum curves of sample (b) at different viewing zenith angles in the forward scattering direction in the principal plane when the incident zenith angle was 40°.
Fig. 3 The distribution of the BRFs of the manmade target for all viewing zenith angles at 560, 670 and 865 nm; the incident angle was 40°.
4.2 The relation between I parameter reflectance factor (IpRF) and BRF of manmade target
During our measurement, we measured the BRF and the Stokes parameters using a small device without a prism and a small device with a prism, respectively, as our mentioned in Section 3. The two small devices had the same size. Subsequently, we compared the I parameter reflectance factor (IpRF) with the BRF of the manmade target, which was computed by Eq. (6), as shown in Fig. 4(a). In Fig. 4(a), it is clearly found that the BRF was larger than the IpRF of the manmade target in the range of 400-1000 nm. If this phenomenon is true, the I parameter cannot be used to represent the total reflectance during the measurement process. However, we neglected the absorption of the prism in our measurements (www.thorlabs.hk/newgrouppage9.cfm?objectgroup_id=5707), which would influence our measured Stokes parameters results and has not been reported by previous researchers. It is also found the difference between BRF and IpRF varied with viewing angles, for example, the difference at 40° seemed to be larger than the difference at 0°. This is due to the value of the absorption of prism is constant, the higher reflectance the relative large value of difference between BRF and IpRF of our sample can be found, such as at 0 degree and 40 degree in Fig. 4(a).Thus, determining the absorption of the prism in the range of 400-1000 nm is a key problem.
Fig. 4 The comparison between the BRF and IpRF of our manmade target in the forward scattering directions in the principal plane: (a) without considering the absorption of the prism, and (b) considering the absorption of the prism, the incident zenith angle was 40°.
In this paper, we used the Spectralon panel to ensure the absorption of the prism, because the DoLP of the Spectralon panel was not larger than 0.01 in the range of 400-1000 nm [38,39], as observed in Fig. 5(a). We used Lx,spectralon (with prim) and Lx,spectralon’ (without prism), which represent the polarized reflected radiance from the Spectralon panel at different polarizer directions (0°, 45°, 90° and 135°) at the nadir direction when the incident zenith angle was 20°, to compute the absorption of the prism abspx = (1-Lx,spectralon/Lx,spectralon’) at different polarizer directions, as shown in Fig. 5(b). In practice, the absorption of a polarizer is a fixed value, and the average value of the absorption of the polarizer at four directions is reasonable for determining the absorption of the polarizer, absp = (absp0° + absp45° + absp90° + absp135°)/4.Then, we divided the measured radiance Lx for all the viewing direction by (1-absp) at the polarizer directions of 0°, 45°, 90° and 135°, respectively, to recalculate the Stokes parameters in Eqs. (1)–(5). The comparison between the BRF and recalculated IpRF was shown in Fig. 4(b); it is clear that considering the absorption of the prism improves the match between the BRF and IpRF of the manmade target. This is because the absorption at each polarizer direction was similar, as observed in Fig. 5(b), and the recalculated I parameter was larger than the original value in the range of 400-100 nm when the absorption of the prism was considered.
Fig. 5 The DoLP of Spectral plane (a), and the absorption of the prism at different polarizer directions (b) at the nadir direction when the incident zenith angle was 20°.
In Figs. 6 and 7, we presented the relative difference between the BRF and IpRF (without considering the absorption of the prism) and the relative difference between the BRF and IpRF (considering the absorption of the prism), respectively, of the manmade target at selected wavelength when the incident zenith angle was 40°. We found that the maximum relative difference was approximately 0.2 in Fig. 6, and approximately 0.05 in Fig. 7. It is also observed that the average relative difference over all the measurement directions decreased from 0.163 to 0.023 at 560 nm, from 0.089 to 0.015 at 670 nm and from 0.096 to 0.011 at 865 nm when the incident zenith angle was 40°. Moreover, the average relative difference over all the measurement directions decreased from 0.145 to 0.013 at 560 nm, from 0.701 to 0.018 at 670 nm and from 0.078 to 0.018 at 865 nm when the incident zenith angle was 60°. This means that the average relative difference between the BRF and IpRF (considering the absorption of the prism) at each selected wavelength over all the measured direction was not larger than 0.02. These results indicated that considering the absorption of the prism essentially improves the match between the BRF and IpRF of our sample for all the viewing directions and all the wavelengths. It is worth noting that the maximum relative difference is always observed in the forward scattering and backward scattering directions in Fig. 7. This phenomenon may be attributed to the domination by the specular reflectance on the reflectance values in the forward scattering direction and the location of the minimum reflectance value in the backward scattering direction; in the practical measurement process, we could not ensure that our measured areas were perfectly focused on the same position of the manmade target when two measurements (photometric and polarimetric measurements) were performed in one viewing direction; thus, a small change in the viewing angle would lead to a relatively large difference in the forward and backward scattering directions compared with other viewing directions. Furthermore, the BRF measurement of our system has an average uncertainty of 0.01 in the laboratory [38]. In summary, it is very safe to use the IpRF instead of the BRF of our sample when the absorption of the prism is considered.
Fig. 6 The relative difference between the BRF and IpRF (without considering the absorption of the prism) () at selected wavelengths, the incident zenith angle was 40°.
Fig. 7 The relative difference between the BRF and IpRF (considering the absorption of the prism) () at selected wavelengths, the incident zenith angle was 40°.
Following the method in which we consider the absorption of the prism, the recalculated Q, U and Ip values were larger than the original values, and the DoLP was smaller than the original value. In this paper, we do not discuss the change in these parameters, and all the polarization properties (BPDF and DoLP) of the manmade target were referred to the recalculated results in the following context.
4.3 The polarization property of the manmade target
A common phenomenon is that the DoLp of manmade targets provides essentially the same spectral information as the inverse of the BRF, as shown in Fig. 8(a) and Fig. 2(b). This is because the BPRF, which is generated by specular reflection, is spectrally neutral [34,35], see Fig. 8(b). In Fig. 9, we show the distribution of the DoLP and BPRF of our sample at 560 nm, the incident zenith angle was 40°. It is found that the maximum DoLP of our sample did not occurs in a small lobe in the specular plane (θs = θv = 40°), but it was spread out across the specular plane. This is due to the presence of a rough sample, surface roughness leads to two effects: the broadening of the specular lobe and the increase of the diffuse scattering [26], although the roughness of the manmade target was not quantified. On the other hand, the DoLP is the portion of the polarized reflectance within the total reflectance; it is not only dominated by the BPRF but also related to the BRF of the manmade target; therefore, the position with maximum BPRF does not necessarily have the maximum DoLP, as observed in Fig. 3(a) and Fig. 9(b). These photometric and polarimetric measurements of our sample, which have the similar distribution patterns compared to previous results [10,21,22,26], are accurate enough to be used in this study to invert the models.
Fig. 8 The (a) DoLP and (b) BPRF of the manmade target at different viewing zenith angles in the principal plane when the incident zenith angle was 40°.
Fig. 9 The distribution of the (a) DoLP and (b) BPRF of the manmade target at 560 nm when the incident zenith angle was 40°.
5. Comparison between model results and measurements
As mentioned above, fundamentally, the BRF can fundamentally be replaced by the IpRF, and then the DoLP can be computed by the BPRF and IpRF when only the Stokes parameters are measured. Therefore, accurately modeling the IpRF and BPRF is a key problem in this study.
5.1 Model parameters inversion
Both the BRDF model (Eq. (11)) and the polarized reflectance model established by Diner et al (Eq. (14)) are non-linear and contain several model parameters. These characteristics make it difficult for the inversion procedure to determine unique useful solutions. Using our reasonable IpRF and BPRF measurements, without a priori information about the parameter values, the inverse problem typically consists of determining the optimal set of variables that minimizes the difference between the modeled and measured results through iterative numerical calculations. Following a method used in previous studies [47], a non-linear least-squares fitting procedure was applied to solve the inverse problem. The optimization performance was assessed based on the square root of the mean squared error (RMSE):
where Mm and M are the measured and modeled values, respectively, of a sample for the same illumination and observation conditions; n is the total number of observations; and Nf is the number of degrees of freedom, which is equal to the number of independently measured data points minus the number of parameters estimated in the procedure. This inverse modeling problem was coded in MATLAB using the “Isqnonlin” function.Tables 1-4 list the listed the best-fitting parameters of the BRDF and BPDF models for our sample at selected wavelengths. It is obvious that most of our best fitting parameters of the models were different from previous studies [21,28] but have the same order of magnitude. This may be because the model parameters are non-unique and the fitting procedure found local minima, which means that there were many different combinations of parameters that would yield a good fit for the same measured data. Therefore, the parameters should be interpreted as only one possible set that fit the measurements in this study [42,47]. Moreover, the main reason that ours best-fitting parameters are different from previous researchers’ [21,28] is the different samples we used and the different wavelengths we selected.
Table 1. The best-fitting model parameters of the BRDF model, which is inverted from the IpRF of the manmade target when the incident zenith angle was 40°. The ARD means the average relative difference over all the measured directions.
Table 2. The best-fitting model parameters of the BPDF model for the manmade target, the incident zenith angle was 40°.
Table 3. The best-fitting model parameters of the BRDF model, which is inverted from the IpRF of the manmade target when the incident zenith angle was 60°.
Table 4. The best-fitting model parameters of the BPDF model for the manmade target, the incident zenith angle was 60°.
5.2 Comparisons between measurements and modeled IpRF and BPRF results
We do not assess the theory of the existing polarimetric models in this paper; rather, we focus on the difference between the measurements and modeled results. It is clear that the modeled IpRFs are in very good agreement with the measurements of the manmade target, see the RSME and ARD values in Tables 1 and 3; in addition the modeled BPRFs are also in good agreement with measured results, see he RSME and ARD in Tables 2 and 4. To further illustrate the good match between the measured and modeled results, we show the comparison between the IpRF and BPRF results in Fig. 10. However, it is not obvious that the average relative difference (ARD) of the IpRF (with relative small RSME) is smaller than the average relative difference (ARD) of the BPRF (with a relative high RSME), see Tables 1-4. This is due to the small value of most of the BPRF, approximately 0.02 (as shown in Fig. 9(b)), and it is difficult to show the apparent difference, such as the results presented in Fig. 10(b). We also show the distribution of the relative difference between the modeled BPRF and measured BPRF of our sample in Fig. 11, which plots the results at 670 nm when the incident zenith angles were 40° and 60°. We found that a maximum relative difference as high as 0.77 was observed in the backward scattering direction in Fig. 11. This does not mean that we can evaluate the BPDF models based on the relative difference because the BPRF of manmade target in the backward scattering direction was small (10−3); a small change thus leads to a great difference. These results mentioned above indicate that the models with the best-fitting parameters exhibit similar reflectance and polarization as our measurements.
Fig. 10 The comparison between the measured and modeled (a) IpRFs and (b) BPRFs of the manmade target for all the selected wavelengths for the incident zenith angles of 40° and 60°.
Fig. 11 The relative difference between the measured BPRF and modeled BPRF at 670 nm, the incident zenith angle was (a) 40° and (b) 60°.
5.3 Comparisons between the measured and modeled DoLP results
Based on the results in 5.2, we find that the models can be used to simulate the IpRF and BPRF of our sample over all the measured directions. Thus, we compare the modeled DoLP, which is calculated by the modeled IpRF and BPRF, with the measured DoLP of the manmade target to demonstrate if the combination of BRDF and BPDF models is effective for determining the DoLP, which is valuable for dielectric/metal classification [10,26,27]. We present the distribution of the measured and modeled DoLP and the relative difference between them in Figs. 12 and 13 at 670 nm when the incident angle was 40° and 60°, respectively. It is clear that the distribution of the measured and modeled DoLP of our sample have similar patterns (see Figs. 12, 13(a) and 13(b)), and most of the values are within the same order (see the light blue and blue area in Figs. 12 and 13(c)). However, the values of the measured and modeled DoLP of our sample are not well matched in the backward scattering direction near the principal plane, such that the maximum difference is approximately 0.75. It is worth noting that the distribution of the relative difference between the measured and modeled DoLP is very similar to the distribution of the relative difference of BPRF (see Fig. 11). This is because the modeled IpRFs are in very good agreement with the measurements (as observed from the ARD in Tables 1 and 3) and the modeled BPRFs dominate the relative difference between the measured and DoLP of our sample.
Fig. 12 The distribution of (a) the measured DoLP, (b) the modeled DoLP and (c) the relative difference between the measured and modeled DoLP of the manmade target at 670 nm when the incident zenith angle was 40°.
Fig. 13 The distribution of (a) the measured DoLP, (b) the modeled DoLP and (c) the relative difference between the measured and modeled DoLP of the manmade target at 670 nm when the incident zenith angle was 60°.
Moreover, we list the ARD between the modeled DoLP and measured DoLP of our sample and show the comparison between them at all selected wavelength over all the measured directions in the and show the comparison when the incident zenith angle are 40° and 60° in Table 5 and Fig. 14, respectively. It is found that the ARD between the modeled and measured DoLP of our sample is approximately 0.2 for all the selected wavelengths over all the measurement directions. As reported by Goel [48], if a model gives modeled values that are qualitatively the same as the measured values (i.e., have an average relative difference within 0.2), the model is valid. Our results show that combining the photometric and polarimetric model is a feasible method for simulating the DoLP of a manmade target. In particular, the ARD of DoLP is dominated by the BPRFs of our sample, which decrease with the phase angle. Thus, we use the modeled BRPFs in the forward scattering direction, in which the relative high BPRFs will decrease the relative difference between the modeled and measured results, to compute the DoLP of our sample. It is found that there is an improvement of the ARD from approximately 0.2 to approximately 0.15 when we only consider half the measurement directions (in the forward scattering direction), as shown in Table 5, the models parameters inverted by half measurements are absent in this paper. In summary, the DoLP of our manmade target can be effectively simulated by combining the photometric and polarimetric models.
Table 5. The average relative difference (ARD) between the modeled DoLP and measured DoLP of our sample at all selected wavelength over all the measured directions and half measured directions (in the forward scattering direction), when the incident angle are 40° and 60°.
Fig. 14 The comparison between the measured and modeled DoLP of the manmade target for all the selected wavelengths over all the measurement directions in the incident zenith angle of (a) 40° and (b) 60°.
6. Conclusion
This paper reports the BRFs and BPRFs from a manmade target over a wide range of viewing directions under laboratory condition. We find that the BRF can be replaced by the IpRF of our sample when we consider the absorption of the prism during the measurement of the Stokes parameters. Subsequently, all the reflectance and polarization measurements of the manmade target are used to invert the parameters of one BRDF model and one BPDF model. As expected, our IpRF and BPRF measurements can be effectively computed using existing models at all the selected wavelengths. These modeled DoLP values, obtained using photometric and polarimetric reflectances are also in good agreement with the measurements. These results demonstrate that the optical properties of light reflected from a manmade target can be effectively characterized by the photometric and polarimetric measurements, which are well matched with model results.
It is also worth noting that we can accurately obtain both of the intensity and polarization properties of a manmade target (similar to the target used in this paper) from the Stokes parameters when the absorption of the prism is considered in the laboratory measurements with a spectrometer. Although the polarimetric measurements will take more time than the photometric measurements, we can obtain the IpBRF (equals to BRF), BPRF and DoLP of a target simultaneously, and all these useful information can be directly or indirectly simulated using the proper models. Thus, if the polarimetric measurements, in which the absorption of the prism is considered, are performed for the study of a target, we will obtain not only accurate intensity reflectance signals, but also polarization signals; these results will deepen our understanding of the optical properties of light reflected from manmade objects and will be valuable for the detection and identification of man-made targets. However, our study considers only one manmade target and the measurements of manmade target should be performed under a wide range of illumination zenith angles to follow the natural conditions and we should also intend to conduct more measurements of manmade targets (with different surface properties) to prove the repeatability and reliability of our results in future studies, these studies would investigate properties such as the following: the relation between IpRF and BRF, and the relation between the measured DoLP and modeled DoLP, which is derived from the BRDF and BPRF models. Moreover, a comparison of the polarimetric properties of a manmade target and the nature background is also necessary, because there is a difference between their properties [3], and this difference can potentially be used for target detection in nature background.
Funding
National Natural Science Foundation of China (NSFC) (41401379, 41571078, 41571343, 41671347).
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