Reflectances from a supercontinuum laser-based instrument: hyperspectral, polarimetric and angular measurements

Romain Ceolato; Nicolas Riviere; Laurent Hespel

doi:10.1364/OE.20.029413

1. Introduction

Hyperspectral sensors have been used intensively for years in the remote-sensing community [1–3]. Developments [4] in nanostructured fiber optics and compact pulsed lasers have resulted in the conception of supercontinuum laser sources. These sources are generated using a pulsed laser propagating through a non-linear medium. It results in a spectral broadening [5] and the creation of white directional coherent light. The combination of supercontinuum laser sources with hyperspectral sensors are of rising interest for civilian [6–8] and defense [9–11] applications.

Active hyperspectral systems, such as active hyperspectral imaging [12] or hyperspectral Light Detection And Ranging (LiDAR) [13], are based on these recent advances. These systems are used in rural and urban environments where natural materials (eg. agricultural fields or canopies) but also man-made materials (eg. ceramics, composites, metallic and plastic compounds or paint coatings) are involved. These latter materials are particularly known to scatter light not uniformly in space as they exhibit severe anisotropy reflection [14].

Current hyperspectral sensors present a high spectral resolution but often a low spatial resolution [15, 16]. However, sensors technology is improving fast enough (e.g lower signal-to-noise ratio and refresh rate) to use low beam divergence laser sources for active systems with low footprint size. As a consequence, the illuminated target surface decreases and a strong reflectance anisotropy is to be measured for man-made materials. Lambertian approximation may fail for such applications and accurate materials reflectances are needed.

Man-made materials have distinctive spectral, polarimetric and angular reflectances resulting from complex light scattering and absorption phenomema (i.e. surface or subsurface scattering [17]). Dedicated instruments [18–20] are used to evaluate at discrete wavelengths Bidirectional Reflectance Factor (BRF) or Bidirectional Reflectance Distribution Function (BRDF) but also Directional Hemispherical Reflectance (DHR). However, more accurate and comprehensive optical characterization (i.e. full spectral range, polarimetric and high angular resolution) is useful for new applications.

In this paper, we report an original and fast supercontinuum laser-based instrument to measure the hyperspectral, polarimetric and angular reflectances of materials with a high angular resolution. First, we introduce a tensorial framework derived from hyperspectral remote-sensing to describe the light scattered by a sample for a continuous spectrum. Our instrument is described and its calibration procedure is detailed. Then, hyperspectral polarimetric and angular reflectance measurements are carried out on reference materials and paint coatings with various optical characteristics. Man-made materials characterization is split in two parts. On the one hand, known optical properties of reference materials are retrieved and compared to identify measurement errors. On the other hand, we measure optical properties from unknown materials and discuss the results on limited domains. Lastly, results are checked to respect physical principles such as the energy conservation or the Helmholtz reciprocity.

2. Theory

In this section, the basic radiometric quantities adapted to hyperspectral polarimetric and angular reflectances are outlined.

Spectral radiometry is the science of measuring the spectral intensity of electromagnetic field vectors while polarimetry analyze the polarization state of an electromagnetic field. The terminology in this paper uses the definitions accepted by the International Standards Organizations (ISO) and the International Commission on Illumination (CIE). Morevover, the huge amount of data involved in hyperspectral measurements implies the use of tensorial quantities [21]. Notations of the hyperspectral tensors are listed in Table 1.

Table 1. Notations used in the hyperspectral polarimetric tensorial framework where m and n refer to the incident and reflected polarization states.

View Table | View all tables in this article

Hyperspectral measurements have been carried out in many scientific fields. For instance, hyperspectral remote-sensing data are stored in hypercubes [22] that contains both spatial and spectral information. We extend this method to store hyperspectral polarimetric and angular information. Figure 1 illustrates the geometry used in the framework in a spherical coordinate system.

Fig. 1 Definition of the hyperspectral tensors in a spherical coordinate system.

Download Full Size | PDF

Let’s define a 5-order hyperspectral tensor ℋ(i₁, i₂; r₁, r₂; l) ∈ ℝ^{I₁×I₂×R₁×R₂×L} where i₁, i₂ go from 0 to I₁, I₂ referring to numbers of angles of incidence, r₁, r₂ go from 0 to R₁, R₂ referring to numbers of reflected angles and l goes from 0 to L referring to the number of wavelengths. Basic tensors needed are the polarized irradiance tensor ℰ^m(i₁, i₂; r₁, r₂; l) and the polarized radiance tensor $ℒ_{r}^{n} (i_{1}, i_{2}; r_{1}, r_{2}; l)$ . The scripts m and n refer respectively to the incident and reflected polarization states. The term cosθ(r₁) · ΔA is used in the definitions of tensors and corresponds to the projected area varying with the observation angle and ΔΩ to the solid angle. It is called the cosine law or the Lambert law. These tensors can be retrieved from the power tensors 𝒫(i₁, i₂; r₁, r₂; l) directly measured from our instrument, i.e.,

ℰ^{m} (i_{1}, i_{2}; r_{1}, r_{2}; l) = \frac{𝒫_{i}^{m} (i_{1}, i_{2}; r_{1}, r_{2}; l)}{cos θ (r_{1}) \cdot △ A}

ℒ_{r}^{n} (i_{1}, i_{2}; r_{1}, r_{2}; l) = \frac{𝒫_{r}^{n} (i_{1}, i_{2}; r_{1}, r_{2}; l)}{cos θ (r_{1}) \cdot △ A \cdot △ Ω}

Let’s define the polarimetric bidirectional reflectance distribution function tensor as the ratio of the polarized reflected radiance tensor to the polarized incident irradiance tensor. It corresponds to the tensorial representation of the spectral polarimetric BRDF or BRF defined by Nicodemus [23] i.e.,

ℋ_{B R D F}^{m n} (i_{1}, i_{2}; r_{1}, r_{2}; l) = \frac{ℒ_{r}^{n} (i_{1}, i_{2}; r_{1}, r_{2}; l)}{ℰ^{m} (i_{1}, i_{2}; r_{1}, r_{2}; l)}

For reflectance measurements, BRF is used as exposed by G. Schaepman-Strub et al. [26]. Also, the BRDF can be computed from the BRF using a simple proportional relation for small solid angles and directional light sources [24]. Material appearance is described as “diffuse” or “specular” from its BRDF which results from different scattering processes. In this paper, we report spectral polarimetric BRDF as it is found in literature [25]. The commonly used BRDF.cosθ representation is preferred for experimental reasons.

For in-plane measurements, we define a 3-order principal-plane hyperspectral bidirectional reflectance tensor. The principal-plane (θ_i, ϕ_i = ϕ₀; θ_r, ϕ_r = ϕ₀) is defined by the incident laser source, the illuminated surface and the detector.

H_{B R D F, 0}^{m n} = \frac{ℒ_{r}^{n} (i_{1}, r_{1}; l)}{ℰ_{i}^{m} (i_{1}, r_{1}; l)}

We also define the principal-plane polarimetric directional hemispherical reflectance tensor as the ratio of the principal-plane polarized reflected power tensor to the principal-plane polarized incident power tensor, i.e.,

ℋ_{D H R, 0}^{m n} (l) = \frac{𝒫_{r}^{n} (l)}{𝒫_{i}^{m} (l)}

There are two ways to measure this quantity: either by measuring the power ratio (e.g. using an integrating sphere instrument), or by integrating the principal-plane BRDF over reflected angles under the assumption that the surface is a perfect Lambertian surface. The latter way is useful to verify to the energy conservation.

3. Instrument and technique

Onera develops a hyperspectral polarimetric reflectometer (Melopee) to measure reflectance properties of various types of materials in the visible and near infrared (VIS/NIR) from 480 nm to 1000 nm with a spectral resolution lower than 1 nm. From these measurements stored as hyperspectral tensors, one can retrieve the usual spectral polarimetric DHR, BRF or BRDF of materials. Specifications of the instrument are given in Table 2.

Table 2. Specifications of the VIS/NIR hyperspectral version of Melopee instrument.

View Table | View all tables in this article

A multispectral version of the instrument was previously reported [27]. Multispectral and polarimetric measurements were carried out on paint coatings. A schematic of the hyperspectral version of instrument Melopee is presented in Fig. 2.

Fig. 2 Schematic of the VIS/NIR hyperspectral version of Melopee instrument. The incident lighting system is a supercontinuum laser coupled to wide-band polarizers. The sensing system is composed of a CCD sensor based spectrophotometer mounted on a goniometer platform.

Download Full Size | PDF

The incident lighting system consists in a supercontinuum laser used as a coherent collimated hyperspectral unpolarized light source. The laser source is fully unpolarized at full power and is coupled to wide-band polarizers (Codixx colorPol^® VISIR) to select incident polarization states. The variation of incident power is measured to ensure stable measurements. The polarizers efficiency was found higher than 98% on the whole spectral range using a VIS/NIR polarimeter. The sensing system measures the reflected power tensor 𝒫_r with an angular resolution of 0.1°. It provides highly resolved measurements and is composed of a grating CCD-based spectrophotometer mounted on a goniometer platform at 1 m from the sample. The noise-equivalent BRDF was measured lower than 10⁻⁷ sr⁻¹. A 5-axis fully automated sample holder facilitates the measurement procedure. A coarse alignment of the sample holder is done using a specular sample by measuring the specular reflection for various angles. A fine alignment is obtained by measuring the angular scattered light at various symmetric positions using a Lambertian sample. By repeating these alignment measurements, the procedure is complete when a root-mean-square error lower than 1% is obtained. All measurements are carried out in the principal-plane and are fully interfaced via GPIB and PCI cards to control step motors using homemade software.

Our measurement procedure is based on the Standard ASTM-E1392-96 [28]. Hyperspectral calibration is known to be quite complex as it involves huge amount of data due to the number of spectral bands [2]. A proper calibration process is needed to measure $ℋ_{B R D F, 0}^{m n}$ and to retrieve BRDF of reflectors. Each optical component in our instrument has its own spectral, radiometric and angular signature to be taken into account. The calibration procedure is based on a relative calibration extended to hyperspectral polarimetric measurements. It requires the determination of the instrument function using a standard Lambertian reference (LabSphere Spectralon^®). It is direct, fast and requires no external measurements. Verification is carried out on other reference samples in Section 4 and discussed in details in Section 5. We retrieve the main BRDF physical properties (i.e., positivity, energy conservation and Helmholtz reciprocity) to complete the validity of our calibration method.

4. Results

The need of Lambertian surfaces is crucial for imaging and non-imaging system calibration. White, grey or color Spectralon (PTFE) provided by LabSphere samples are used as references in remote sensing and active imaging for calibration. Spectralon samples are well documented [29, 30] for monochromatic and unpolarized illumination, but very few experiments were conducted to expose the Lambertian nature of such samples with a hyperspectral polarized coherent illumination.

We report here measurements from our calibrated instrument on Spectralon Reflectance Standard (SRS), Spectralon Diffuse Color Standards (SCS) and a glossy paint coating sample to demonstrate the capabilities of our instrument. The importance of hyperspectral polarimetric and angular optical studies for man-made materials is later discussed.

4.1. Spectralon Reflectance Standards (SRS)

We carry out measurements on spectrally neutral Spectralon SRS-99 (white) and SRS-20 (dark grey) with respective DHR = 0.99 and DHR = 0.20. The illumination is P-polarized and the detection unpolarized. Figure 3 shows the measured $ℋ_{B R D F, 0}^{m n}$ at normal angle of incidence for these samples.

Fig. 3 $ℋ_{B R D F, 0}^{p u}$ measurements for Lambertian materials : Spectralon SRS-99 and SRS-20. The illumination is P-polarized and the detection unpolarized..

Download Full Size | PDF

Table 3 presents averaged angular, radiometric, spectral and total spectrally averaged root-mean-square (RMS) errors from data provided by LabSphere [31].

Table 3. RMS Errors for Spectralon SRS.

View Table | View all tables in this article

The retrieved BRDF of SRS samples are found to behave closely as a Lambertian surface at normal angle of incidence from 480 nm to 1000 nm. The angular and radiometric RMS errors are lower than 1% whereas the spectral RMS error is close to 0% due to the spectrally independent nature of the samples. The angular RMS error is almost 10 times higher for SRS-20 sample. The total RMS error is found between 1% and 2% for SRS samples. We explain the large angular RMS error by the possible unperfect Lambertian nature of the SRS-20 sample. This explanation is supported by similar errors previously reported for SRS-20 [31]. The low RMS errors (less than 2%) found for reference samples confirm the good reliability of our instrument.

4.2. Spectralon Diffuse Color Standards (SCS)

One advantage of the hyperspectral measurements is to analyze the spectral dependence of the materials reflectances. It is usually due to complex absorption phenomena inside the materials and is related to their visual colors [27].

We perform similar measurements under the same experimental conditions on spectrally dependent Spectralon SCS-CY (cyan), SCS-GN (green), SCS-VI (violet) and SCS-YW (yellow). The illumination is P-polarized and the detection unpolarized. Figure 4 shows the measured $ℋ_{B R D F, 0}^{m n}$ at normal angle of incidence for these samples.

Fig. 4 $ℋ_{B R D F, 0}^{p u}$ measurements for color Lambertian materials : Spectralon SCS-CY, SCS-GN, SCS-VI and SCS-YW. The illumination is P-polarized and the detection unpolarized.

Download Full Size | PDF

Angular, radiometric, spectral and total spectrally averaged RMS errors are computed in Table 4 from data provided by LabSphere [31].

Table 4. RMS Errors for Spectralon SCS.

View Table | View all tables in this article

As reported for Spectralon SRS, the BRDF of Spectralon SCS are found to behave closely as a Lambertian surface at normal angle of incidence from 480 nm to 1000 nm. The angular and radiometric RMS errors are close to 1% whereas the spectral RMS error is lower than 0.5%. These errors are much higher for SCS samples compared with SRS samples. The total RMS error is found close to 2.5%. We explain larger RMS errors by the unperfect Lambertian nature of the SCS samples. The colored pigments used during the manufacturing process might have altered the Lambertian nature of the sample. This deviation from a perfect ideal Lambertian surface can explain errors found in the DHR computation as explained in Section 2.

4.3. Commercial paint coatings measurements

BRDF of man-made materials such as paint coatings are often separated [17,32] into two main components: directional and diffuse. The directional one is symmetric to the incident direction and the diffuse one is related to multiple scattering within the material. Measurements are carried out on a commercial urban glossy paint coating. Figure 5 shows the measured $ℋ_{B R D F, 0}^{p u}$ at 40° angle of incidence for a P-polarized illumination on the left and for a S-polarized illumination on the right. Detection is unpolarized. It illustrates the influence of the illumination wavelengths and polarization states on the measured BRDF for a man-made material.

Fig. 5 $ℋ_{B R D F, 0}^{p u}$ measurements for a commercial urban glossy paint coating for an incident P-polarized (left) and S-polarized illumination (right). Detection is unpolarized.

Download Full Size | PDF

For ideal specular materials, it is assumed from physical considerations [17] that the directional component remains unchanged for all wavelengths and polarization states. We report a similar behaviour for a glossy paint coating material with a noticeable spectral and polarimetric variation. Different levels of the directional and diffuse components for a P and S-polarized illumination appears in Fig. 5. Such spectral and polarimetric behavior could be explained (1) by a spectral dependance of the sub-surface directional component (i.e geometry, orientation and refractive index of the pigments) and (2) by a spectral and polarimetric dependence of the Fresnel coefficients of the coating. These phenomena were partially investigated with multispectral models and measurements in previous works [27, 32].

Our measurements provide an illustration of the importance of hyperspectral polarimetric and angular optical studies of man-materials for active hyperspectral systems. Results presented for this sample cannot be extended for all type of materials and specific studies must be undertaken for other materials.

5. Discussion

We verify in this section the three principal properties (i.e. positivity, energy conservation and Helmholtz reciprocity) of the BRDF from Nicodemus [23] to validate the hyperspectral polarimetric reflectances measurements from our instrument.

Positivity. The BRDF is a positive function. All the retrieved spectral polarimetric BRDF and their tensorial representations $ℋ_{B R D F, 0}^{m n}$ are measured positive in the instrument operation range.
Energy conservation. The BRDF respects the energy conservation. In other words, the reflected energy leaving a material surface with no energy generation must be less than or equal to the incident energy. Figure 6 shows the DHR comparison between the one computed from our measurements and the one provided by LabSphere.
The reflected energy can be directly related to the DHR of materials. We compute the $ℋ_{D H R, 0}^{m n}$ of SRS and SCS samples from the measured $ℋ_{B R D F, 0}^{m n}$ at normal incidence. The straightforward relation $ℋ_{D H R, 0}^{m n} (i_{1}; l) = \sum_{r_{1}} ℋ_{B R D F, 0}^{m n} (i_{1}; r_{1}; l) \cdot △ Ω$ was derived from [23] assuming the Lambertian nature of the materials. The DHR retrieved from our measurements is plotted in Fig. 6. Energy conservation is verified with an averaged error lower than 2% for the all wavelengths.
Helmholtz reciprocity. The BRDF is a reciprocal function. Helmholtz and later Clarke and Parry [33] provided the statement of reciprocity asserting that there is an equal reflected flux density for an incident flux density when the propagation is reversed. The Helmholtz reciprocity principle was originally applied to optical components and later extended for scattering materials. It is one of the fundamental property of the BRDF and has been questioned in theoretical and experimental [34] works over the last decades. First considered as a postulate, it was later derived from first principles by Greffet et al. [35] for any type of surface using the framework of statistical optics to take into account coherence effects. However, sources in the literature reported experimental violations of the reciprocity [36]. A long-standing debate goes on about the causes of the measured violations. It appears reciprocity violation occurs when experimental errors are important [37, 38].

The reciprocity principle is verified if BRDF(θ_i;θ_f ;λ) = BRDF(θ_r;θ_i;λ) or ℋ_BRDF,0 (i₁; r₁; l) = ℋ_BRDF,0 (r₁; i₁; l) in our tensorial framework. The plot of this equation is a straight line passing through the origin. Measurements for a glossy paint coating are used to verify the reciprocity principle for the BRDF. Figure 7 plots the BRDF(θ_i;θ_r) vs BRDF(θ_r;θ_i) for different wavelengths VIS/NIR.

Fig. 6 Energy conservation for Spectralon SRS and SCS. Comparison between computed DHR from $ℋ_{B R D F, 0}^{m n}$ measurements (Melopee) and DHR provided by LabSphere.

Download Full Size | PDF

Fig. 7 Helmholtz reciprocity. BRDF reciprocity validation for ten VIS/NIR wavelengths on a glossy paint coating from ℋ_BRDF,₀ measurements. Incident P-polarized (on the left) and S-polarized (on the right) light are considered.

Download Full Size | PDF

Minimal RMS errors (close to 0%) corresponds to small incident angles (θ_i < 50°) and maximal RMS errors (5.5%) for large incident angles (θ_i > 50°) for P and S incident polarized light. The BRDF itself is known to be reciprocal whereas its tensorial representation is found fairly reciprocal giving systematic instrument errors.

The verification of the BRDF physical properties shows the accuracy and the validity of our hyperspectral polarimetric and angular measurements.

6. Conclusion

The growing interest for hyperspectral sensors and supercontinuum laser sources brings new challenges for calibration and material optical characterization. Hyperspectral polarimetric and angular reflectances are more and more needed for the development of future active hyperspectral systems.

Onera has designed and developed an original supercontinuum laser-based instrument to measure hyperspectral polarimetric and angular reflectances. The instrument allows measurements from 480 nm to 1000 nm with a spectral resolution of 1 nm and a high angular resolution (less than 1°). Different polarization configurations are made possible. A great of advantage of the instrument is the ability to provide fast (less than 30 s) and comprehensive reflectances as BRF, BRDF or DHR. A dedicated calibration procedure was detailed and applied to Lambertian reference samples. The averaged measurement error was found lower than 2%. Reflectances of man-made materials are presented to illustrate the capacities of our instrument. Specular material such as a commercial glossy paint coating is studied to expose the instrument capabilities. Moreover, we retrieved and verified from our measurements the fundamental properties of the BRDF (positivity, energy conservation and Helmholtz reciprocity).

Measuring hyperspectral polarimetric and angular reflectances is one step in the route of future active hyperspectral systems. The evaluation of performances for these systems requires a solid knowledge of the optical properties of materials. The instrument and the measurements presented in this paper are to give the ability of a better, faster and more accurate calibration of systems in rural or urban environment.

Acknowledgments

This work was funded by the Onera, The French Aerospace Lab, and the Region Midi-Pyrenees. The authors are thankful for advices and helpful discussions with Pr. B. Biscans, B. Guillame and B. Tanguy, and for comments provided by anonymous reviewers.

References

1. G. Shaw and H. K. Burke, “Spectral imaging for remote sensing,” Lincoln Laboratory Journal 14, 3–28 (2003).

2. D. Manolakis and D. Marden, “Hyperspectral image processing for automatic target detection applications,” Lincoln Laboratory Journal 14, 79–116 (2003).

3. E. Ientilucci and M. Gartley, “Impact of BRDF on physics-based modeling as applied to target detection in hyperspectral imagery,” Proc. SPIE 7334, 73340T1 (2009).

4. R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 A via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970). [CrossRef]

5. J. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

6. Y. Peng and R. Lu, “Analysis of spatially resolved hyperspectral scattering images for assessing apple fruit firmness and soluble solids content,” Postharvest Biol. Tec. 48, 52–62 (2008). [CrossRef]

7. C. Zakian, I. Pretty, and R. Ellwood, “Near-infrared hyperspectral imaging of teeth for dental caries detection,” J. Biomed. Opt. 14, 14, 64047 (2009). [CrossRef]

8. F. Larusson, S. Fantini, and E. Miller, “Hyperspectral image reconstruction for diffuse optical tomography,” Biomed. Opt. Express 2, 946–965 (2011). [CrossRef] [PubMed]

9. B. Johnson, R. Joseph, M. Nischan, A. Newbury, J. Kerekes, H. Barclay, B. Willard, and J. Zayhowski, “A compact, active hyperspectral imaging system for the detection of concealed targets,” Proc. SPIE 3710, 144–157 (1999). [CrossRef]

10. L. Farr, “Active Spectral Imaging for Target Detection,” EMRS DTC Technical Conference 4, 1–8 (2007).

11. T. Hakala, J. Suomalainen, S. Kaasalainen, and Y. Chen, “Full waveform hyperspectral LiDAR for terrestrial laser scanning,” Opt. Express 20, 7119–7127 (2012). [CrossRef] [PubMed]

12. M. L. Nischan, R. M. Joseph, J. C. Libby, and J. P. Kerekes, “Active spectral Imaging,” Lincoln Laboratory Journal 14, 131–144 (2003).

13. Y. Chen, E. Raikkonen, S. Kaasalainen, J. Suomalainen, T. Hakala, J. Hyyppa, and R. Chen, “Two-channel Hyperspectral LiDAR with a Supercontinuum laser source,” Sensors 10, 7057–7066 (2010). [CrossRef] [PubMed]

14. B. Mc Guckin, D. Haner, and R. Menzies, “Multiangle imaging spectroradiometer: optical characterization of the calibration panels,” J. Quant. Spectros. Radiat. Transfer. 15, 281–290 (2007).

15. M. Eismann and R. Hardie, “Hyperspectral resolution enhancement using high-resolution multispectral imagery with arbitrary response functions,” in Proceedings of IEEE Transactions on Geoscience and Remote Sensing 43, 455–465 (2005). [CrossRef]

16. J. Bieniarz, D. Cerra, J. Avbelj, and P. Reinartz, “Resolution enhancement of hyperspectral imagery through spatial-spectral data fusion,” in Proceedings of ISPRS Hannover Workshop 2011: High-Resolution Earth Imaging for Geospatial Information 33–37 (2011).

17. K. Ellis, “Polarimetric bidirectional reflectance distribution function of glossy coatings,” J. Opt. Soc. Am. A 13, 1758–1762 (1996). [CrossRef]

18. S. Nevas, F. Manoocheri, and E. Ikonen, “Gonioreflectometer for measuring spectral diffuse reflectance,” Appl. Opt. 43, 6391–6399 (2004). [CrossRef] [PubMed]

19. J. Liu, M. Noel, and J. Zwinkels, “Design and characterization of a versatile reference instrument for rapid, reproducible specular gloss measurements,” Appl. Opt. 44, 4631–4638 (2005). [CrossRef] [PubMed]

20. H. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications,” Opt. Eng. 45, 043605 (2005). [CrossRef]

21. R. Ceolato, N. Riviere, L. Hespel, and B. Biscans, “Probing optical properties of nanomaterials,” SPIE Newsroom (January 12, 2012). doi: [CrossRef] .

22. N. Renard and S. Bourennane, “Improvement of target detection methods by multiway filtering,” in Proceedings of IEEE Transactions on Geoscience and Remote Sensing 46, 2407–2417 (2008). [CrossRef]

23. F. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4, 767–773 (1965). [CrossRef]

24. J. V. Martonchik, C. J. Bruegge, and A. Strahler, “A review of reflectance nomenclature used in remote sensing,” Remote Sens. Rev. 19, 9–20 (2000). [CrossRef]

25. A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corrons, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011). [CrossRef] [PubMed]

26. G. Schaepman-Strub, M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik, “Reflectance quantities in optical remote sensing - definitions and case studies,” Remote Sens. Environ. 103, 27–42 (2006). [CrossRef]

27. N. Riviere, R. Ceolato, and L. Hespel, “Multispectral polarized BRDF: design of a highly resolved reflectometer and development of a data inversion technique,” Opt. Appl. 42, 7–22 (2012).

28. “Standard practice for angle resolved optical scatter measurements on specular or diffuse surfaces,” Am. Soc. Test Mater Standard E1392–96 (1997).

29. C. L. Betty, “The measured polarized bidirectional reflectance distribution function of a Spectralon calibration target,” in Proceedings of IEEE Transactions on Geoscience and Remote Sensing 4, 2183–2185 (1996).

30. G. T. Georgiev and J. J. Butler, “BRDF study of gray-scale Spectralon,” Proc. SPIE 7081, 71–79 (2008).

31. Labsphere, “A guide to diffuse reflectance coatings and materials,” http://www.prolite.co.uk/File/coatingsmaterialsdocumentation.php.

32. H. Li and K. E. Torrance, “A practical comprehensive light reflection model,” Technical Report PCG-05-03, Cornell Univeristy (2005).

33. F. J. J. Clarke and D. J. Parry, “Helmholtz reciprocity: Its validity and application to reflectometry,” Ltg. Res. Technol. 17, 1–11 (1985). [CrossRef]

34. H. J. Eom, “Energy conservation and reciprocity of random rough surface scattering,” Appl. Opt. 24, 1730–1732 (1985). [CrossRef] [PubMed]

35. J. Greffet and M. Nieto-Vesperinas, “Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law,” J. Opt. Soc. Am. A 15, 2735–2744 (1998). [CrossRef]

36. H. Okayama and I. Ogura, “Experimental verification of nonreciprocal response in light scattering from rough surfaces,” Appl. Opt. 23, 3349–3352 (1984). [CrossRef] [PubMed]

37. W. H. Venable, “Comments on reciprocity failure,” Appl. Opt. 24, 3943 (1985). [CrossRef] [PubMed]

38. W. C. Snyder, “Reciprocity of the BRDF in measurements and models of structured surfaces,” in Proceedings of IEEE Transactions on Geoscience and Remote Sensing 36, 685–691 (1998). [CrossRef]

ℰ^m	Polarized Irradiance tensor [W.m⁻²]
$ℒ_{r}^{n}$	Polarized Reflected Radiance tensor [W.m⁻².sr⁻¹]
$P_{i}^{m}$	Incident Power tensor [W]
$P_{r}^{n}$	Reflected Power tensor [W]
$ℋ_{B R D F}^{m n}$	Bidirectional Reflectance Distribution Function tensor [sr⁻¹]
$ℋ_{B R D F, 0}^{m n}$	Principal-plane Bidirectional Reflectance Distribution Function tensor [sr⁻¹]
$ℋ_{D H R}^{m n}$	Directional Hemispherical Reflectance tensor [unitless]
$ℋ_{D H R, 0}^{m n}$	Principal-plane Directional Hemispherical Reflectance tensor [unitless]

Source		Sensor
Laser type	Supercontinuum	Spectrometer type	Grating CCD
Wavelengths	480 nm–2000 nm	Wavelengths	400 nm–1000 nm
Output power	1.20 W	Spectral resolution	< 1nm
Spectral output power	0.8–50 mW/nm	Dynamic range	7 dB
Power stability	±1.0%	Integration time	100 ms
Pump pulse width	40 ps
Repetition rate	80 MHz	Goniometer
Beam divergence	< 5 mrad	Solid angle	10⁻⁵ − 10⁻² sr
M²	1.1	Angular resolution	< 0.1 °
Polarizers	Wide-band linear	Noise-equivalent BRDF	< 10⁻⁷ sr⁻¹

	Angular Error	Radiometric Error	Spectral Error	Total Error
SRS-99	≤ 0.12	≤ 0.84	≤ 0.05	≤ 1.01
SRS-20	≤ 1.01	≤ 0.88	≤ 0.05	≤1.94

	Angular Error	Radiometric Error	Spectral Error	Total Error
SCS-CY	≤ 0.78	≤ 1.04	≤ 0.45	≤ 2.27
SCS-GN	≤ 0.80	≤ 1.21	≤ 0.45	≤ 2.46
SCS-VI	≤ 0.85	≤ 1.33	≤ 0.35	≤2.13
SCS-YW	≤ 0.77	≤ 1.02	≤ 0.15	≤ 1.79

ℰ^m	Polarized Irradiance tensor [W.m⁻²]
$ℒ_{r}^{n}$	Polarized Reflected Radiance tensor [W.m⁻².sr⁻¹]
$P_{i}^{m}$	Incident Power tensor [W]
$P_{r}^{n}$	Reflected Power tensor [W]
$ℋ_{B R D F}^{m n}$	Bidirectional Reflectance Distribution Function tensor [sr⁻¹]
$ℋ_{B R D F, 0}^{m n}$	Principal-plane Bidirectional Reflectance Distribution Function tensor [sr⁻¹]
$ℋ_{D H R}^{m n}$	Directional Hemispherical Reflectance tensor [unitless]
$ℋ_{D H R, 0}^{m n}$	Principal-plane Directional Hemispherical Reflectance tensor [unitless]

Reflectances from a supercontinuum laser-based instrument: hyperspectral, polarimetric and angular measurements

Abstract

1. Introduction

2. Theory

3. Instrument and technique

4. Results

4.1. Spectralon Reflectance Standards (SRS)

4.2. Spectralon Diffuse Color Standards (SCS)

4.3. Commercial paint coatings measurements

5. Discussion

6. Conclusion

Acknowledgments

References

Cited By

Figures (7)

Tables (4)

Equations (5)

Optics Express