A Compact Laboratory Spectro-Goniometer (CLabSpeG) to Assess the BRDF of Materials. Presentation, Calibration and Implementation on Fagus sylvatica L. Leaves
Abstract
:1. Introduction
- (i)
- Geometric stability of the apparatus, velocity of the components, and deviation of the sensor field-of-view across the target.
- (ii)
- Stability, homogeneity, and conical illumination of the light source, consistency and repeatability of measurements, and the deviation of Spectralon from an ideal Lambertian reference panel.
- (iii)
- Water stress induced to the samples due to heat from the light source, and the irregularity of sample sizes compared to the field of view of the spectroradiometer.
2. Theoretical background
- Lr = sensor radiance (W m-2 sr-1 nm-1),
- Ei = hemispherical irradiance (W m-2 nm-1),
- λ = wavelength (nm),
- θi,φi = source zenith and azimuth angles, respectively,
- θr,φr = view zenith and azimuth angles, respectively.
- fr values range theoretically from zero to infinity.
- ρ = hemispherical reflectance of sample.
- Rref = correction factor for the non-Lambertian reflection properties of the reference panel.
- Li = incoming radiance (W m-2 sr-1 nm-1),
- R = Bidirectional Reflectance Factor,
- μ = cosθ,
- rs= the distance between the location (x,y,0) and the position of the sensor,
- θ0,φ0 and θ,φ = nominal illumination and sensor angles, respectively.
3. System Set up and Technical specifications
- A horizontal, circular black anodized aluminum rail ring of 1.25 m diameter for the azimuthal movement of the light source.
- A vertical half-circular arc (diameter = 1.25 m) mounted on the horizontal rail, supporting the zenith movement of the light source.
- A vertical stationary half-circular arc (diameter = 1.05 m) mounted inside both previous arcs on a black wooden table to support the zenith movement of the spectroradiometer.
- A rotating stainless steel horizontal plate of 0.20 m diameter, placed in the centre of the apparatus, which enables the azimuthal movement of the sample holder.
4. Calibration
4.1 Geometric Calibration
4.1.1 Ground Instantaneous Field Of View
4.2 Radiometric Calibration
4.2.1 Stability and homogeneity of the light source
4.2.2 Temperature of the light source
4.2.3 Reproducibility of the measurements
5. BRDF data processing
5.1 Spectralon
5.1.1. The Spectralon, as non-Lambertian body
5.2. Correction of the biconical effect
5.3 Leaves
5.3.1 Leaf endurance under light source stress
5.3.2 Leaf BRF acquisition
6. Discussion and Conclusion
Acknowledgments
Appendix A.
λ (nm) | Coeff. α0 | Coeff. α1 | Coeff. α2 | RMSE (%) |
---|---|---|---|---|
350 | 1.074 | -1.5904e-007 | -2.275e-005 | 1.0821 |
400 | 1.066 | -1.4206e-007 | -3.374e-005 | 1.0824 |
450 | 1.066 | -1.4290e-007 | -3.280e-005 | 1.0819 |
500 | 1.065 | -1.4382e-007 | -3.245e-005 | 1.0820 |
550 | 1.064 | -1.4460e-007 | -3.191e-005 | 1.0818 |
600 | 1.064 | -1.4506e-007 | -3.169e-005 | 1.0818 |
650 | 1.063 | -1.4572e-007 | -3.135e-005 | 1.0818 |
700 | 1.064 | -1.4612e-007 | -3.115e-005 | 1.0818 |
750 | 1.064 | -1.4658e-007 | -3.089e-005 | 1.0818 |
800 | 1.061 | -1.4668e-007 | -3.058e-005 | 1.0816 |
850 | 1.058 | -1.4662e-007 | -3.053e-005 | 1.0815 |
900 | 1.062 | -1.4664e-007 | -3.066e-005 | 1.0816 |
950 | 1.061 | -1.4782e-007 | -3.000e-005 | 1.0816 |
1000 | 1.063 | -1.4098e-007 | -2.877e-005 | 1.0780 |
1050 | 1.064 | -1.4174e-007 | -2.826e-005 | 1.0779 |
1100 | 1.060 | -1.4080e-007 | -2.852e-005 | 1.0778 |
1150 | 1.059 | -1.4130e-007 | -2.800e-005 | 1.0776 |
1200 | 1.064 | -1.4184e-007 | -2.812e-005 | 1.0778 |
1250 | 1.058 | -1.4096e-007 | -2.821e-005 | 1.0776 |
1300 | 1.050 | -1.4050e-007 | -2.745e-005 | 1.0768 |
1350 | 1.061 | -1.4148e-007 | -2.803e-005 | 1.0776 |
1400 | 1.048 | -1.3984e-007 | -2.781e-005 | 1.0769 |
1450 | 1.041 | -1.3966e-007 | -2.733e-005 | 1.0764 |
1500 | 1.043 | -1.4032e-007 | -2.704e-005 | 1.0764 |
1550 | 1.052 | -1.4142e-007 | -2.735e-005 | 1.0771 |
1600 | 1.054 | -1.4142e-007 | -2.772e-005 | 1.0774 |
1650 | 1.059 | -1.4224e-007 | -2.791e-005 | 1.0778 |
1700 | 1.064 | -1.4360e-007 | -2.775e-005 | 1.0782 |
1750 | 1.064 | -1.4358e-007 | -2.778e-005 | 1.0782 |
1800 | 1.064 | -1.5060e-007 | -2.829e-005 | 1.0811 |
1850 | 1.072 | -1.5006e-007 | -2.947e-005 | 1.0819 |
1900 | 1.073 | -1.5086e-007 | -2.936e-005 | 1.0821 |
1950 | 1.073 | -1.5116e-007 | -2.889e-005 | 1.0818 |
2000 | 1.078 | -1.5198e-007 | -2.899e-005 | 1.0822 |
2050 | 1.090 | -1.5324e-007 | -2.941e-005 | 1.0829 |
2100 | 1.098 | -1.5436e-007 | -2.981e-005 | 1.0837 |
2150 | 1.106 | -1.5582e-007 | -2.947e-005 | 1.0839 |
2200 | 1.089 | -1.5224e-007 | -2.994e-005 | 1.0830 |
2250 | 1.087 | -1.5258e-007 | -2.950e-005 | 1.0827 |
2300 | 1.098 | -1.5460e-007 | -2.920e-005 | 1.0832 |
2350 | 1.110 | -1.5624e-007 | -2.933e-005 | 1.0840 |
2400 | 1.116 | -1.5304e-007 | -3.266e-005 | 1.0855 |
2450 | 1.115 | -1.5862e-007 | -2.904e-005 | 1.0847 |
2500 | 1.105 | -1.5832e-007 | -2.804e-005 | 1.0840 |
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SENSOR Zenith | ||||||
---|---|---|---|---|---|---|
LIGHT SOURCE Zenith | 0° | 15° | 30° | 45° | 60° | 75° |
15° | 3.94 ± 1.73 | 5.84 ± 4.85 | 3.79 ± 2.84 | 5.98 ± 5.06 | 5.44 ± 3.63 | 11.64 ± 8.80 |
30° | 17.68 ± 3.40 | 12.91 ± 5.86 | 16.04 ± 7.26 | 10.23 ± 5.03 | 10.36 ± 5.84 | 12.76 ± 8.31 |
45° | 37.84 ± 4.28 | 33.59 ± 7.20 | 34.83 ± 5.45 | 27.56 ± 9.88 | 27.40 ± 8.52 | 18.57 ± 12.77 |
60° | 64.38 ± 2.98 | 61.18 ± 4.96 | 61.79 ± 4.04 | 56.36 ± 5.85 | 53.42 ± 7.37 | 30.83 ± 20.50 |
75° | 83.25 ± 1.21 | 82.04 ±1.84 | 81.64 ± 1.43 | 79.03 ± 2.51 | 75.02 ± 4.18 | 51.29 ± 25.52 |
Light Azimuth | Light (L) over sensor (S) Zenith positions |
---|---|
0° | 0°L/0°S |
30° | 0°L/0°S |
60° | 15°L/75°S, -15°L/60°S, 15°L/45°S, -15°L/30°S, -15°L/15°S, and 0°L/0°S |
90° | -75°L/75°S, -60°L/60°S, -45°L/45°S, -30°L/30°S, -15°L/15°S, and 0°L/0°S |
120° | 15°L/60°S, -15°L/45°S, 15°L/30°S, -15°L/15°S, and 0°L/0°S |
150° | 0°L/45°S, 0°L/30°S, 0°L/15°S, and 0°L/0°S |
Wavelength (nm) | 450 | 500 | 550 | 600 | 650 | 700 | 750 | 800 | 850 | 900 | 950 | 1000 |
Difference (%) | 1.69 | 1.44 | 0.95 | 0.75 | 0.51 | 0.21 | 0.53 | 1.06 | 1.54 | 1.39 | 1.92 | 3.23 |
Wavelength (nm) and Light Source Zenith (°) | ||||||
---|---|---|---|---|---|---|
STD (%) | 550 (30°) | 550 (60°) | 850 (30°) | 850 (60°) | 1650 (30°) | 1650 (60°) |
MIN | 5.39 | 2.9 | 3.87 | 4.21 | 2.78 | 3.75 |
MAX | 17.38 | 17.73 | 10.36 | 10.11 | 8.30 | 9.49 |
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Biliouris, D.; Verstraeten, W.W.; Dutré, P.; Van Aardt, J.A.N.; Muys, B.; Coppin, P. A Compact Laboratory Spectro-Goniometer (CLabSpeG) to Assess the BRDF of Materials. Presentation, Calibration and Implementation on Fagus sylvatica L. Leaves. Sensors 2007, 7, 1846-1870. https://doi.org/10.3390/s7091846
Biliouris D, Verstraeten WW, Dutré P, Van Aardt JAN, Muys B, Coppin P. A Compact Laboratory Spectro-Goniometer (CLabSpeG) to Assess the BRDF of Materials. Presentation, Calibration and Implementation on Fagus sylvatica L. Leaves. Sensors. 2007; 7(9):1846-1870. https://doi.org/10.3390/s7091846
Chicago/Turabian StyleBiliouris, Dimitrios, Willem W. Verstraeten, Phillip Dutré, Jan A.N. Van Aardt, Bart Muys, and Pol Coppin. 2007. "A Compact Laboratory Spectro-Goniometer (CLabSpeG) to Assess the BRDF of Materials. Presentation, Calibration and Implementation on Fagus sylvatica L. Leaves" Sensors 7, no. 9: 1846-1870. https://doi.org/10.3390/s7091846
APA StyleBiliouris, D., Verstraeten, W. W., Dutré, P., Van Aardt, J. A. N., Muys, B., & Coppin, P. (2007). A Compact Laboratory Spectro-Goniometer (CLabSpeG) to Assess the BRDF of Materials. Presentation, Calibration and Implementation on Fagus sylvatica L. Leaves. Sensors, 7(9), 1846-1870. https://doi.org/10.3390/s7091846