Abstract

A new instrument to measure the in situ bidirectional reflectance distribution function (BRDF) of surfaces is described. This instrument measures the BRDF for eight illumination angles from 0 to 65 deg, three colors (475, 570, and 658 nm), and at over 100 selected viewing angles. The viewing zenith angles range from 5 to 65 deg, and the azimuth angles, relative to the illumination direction, range from 0 to ±180 deg. Many tests of the system have been run and show that for flat surfaces the BRDF of a sample surface can be measured with a precision of 1–5% and an accuracy of 10% of the measured reflectance. The BRDF for a dry and wet sand sample is presented as a demonstration of the instrument.

© 2000 Optical Society of America

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References

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  1. B. Hapke, Theory of Reflectance and Emittance Spectroscopy, Vol. 3 of Topics in Remote Sensing (Cambridge U. Press, New York, 1993).
  2. R. A. Leathers, N. J. McCormick, “Algorithms for ocean-bottom albedo determination from in-water natural-light measurements,” Appl. Opt. 38, 3199–3205 (1999).
    [CrossRef]
  3. J. M. Chen, J. Cihlar, “A hotspot function in a simple bidirectional reflectance model for satellite applications,” J. Geophys. Res. 102, 25907–25913 (1997).
    [CrossRef]
  4. D. R. White, P. Saunders, S. J. Bonsey, J. van de Ven, H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt. 37, 3450–3454 (1998).
    [CrossRef]
  5. J. R. Zaworski, J. R. Welty, M. K. Drost, “Measurement and use of bi-directional reflectance,” Int. J. Heat Mass Transfer 39, 1149–1156 (1996).
    [CrossRef]
  6. J. W. Giles, K. J. Voss, “Submerged reflectance measurements as a function of visible wavelength,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 140–146 (1991).
    [CrossRef]
  7. B. T. McGuckin, D. A. Haner, R. T. Menzies, “Multiangle imaging spectroradiometer: optical characterization of the calibration panels,” Appl. Opt. 36, 7016–7022 (1997).
    [CrossRef]
  8. K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: instrumentation, calibration, and performance in coastal waters,” J. Atmos. Oceanic Technol. 15, 496–509 (1998).
    [CrossRef]
  9. W. C. Snyder, “Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 685–691 (1998).
    [CrossRef]
  10. R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
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1999 (1)

1998 (3)

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: instrumentation, calibration, and performance in coastal waters,” J. Atmos. Oceanic Technol. 15, 496–509 (1998).
[CrossRef]

W. C. Snyder, “Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 685–691 (1998).
[CrossRef]

D. R. White, P. Saunders, S. J. Bonsey, J. van de Ven, H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt. 37, 3450–3454 (1998).
[CrossRef]

1997 (3)

1996 (1)

J. R. Zaworski, J. R. Welty, M. K. Drost, “Measurement and use of bi-directional reflectance,” Int. J. Heat Mass Transfer 39, 1149–1156 (1996).
[CrossRef]

Bonsey, S. J.

Chen, J. M.

J. M. Chen, J. Cihlar, “A hotspot function in a simple bidirectional reflectance model for satellite applications,” J. Geophys. Res. 102, 25907–25913 (1997).
[CrossRef]

Cihlar, J.

J. M. Chen, J. Cihlar, “A hotspot function in a simple bidirectional reflectance model for satellite applications,” J. Geophys. Res. 102, 25907–25913 (1997).
[CrossRef]

Drost, M. K.

J. R. Zaworski, J. R. Welty, M. K. Drost, “Measurement and use of bi-directional reflectance,” Int. J. Heat Mass Transfer 39, 1149–1156 (1996).
[CrossRef]

Edgar, H.

Fry, E. S.

Giles, J. W.

J. W. Giles, K. J. Voss, “Submerged reflectance measurements as a function of visible wavelength,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 140–146 (1991).
[CrossRef]

Gordon, H. R.

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: instrumentation, calibration, and performance in coastal waters,” J. Atmos. Oceanic Technol. 15, 496–509 (1998).
[CrossRef]

Haner, D. A.

Hapke, B.

B. Hapke, Theory of Reflectance and Emittance Spectroscopy, Vol. 3 of Topics in Remote Sensing (Cambridge U. Press, New York, 1993).

Leathers, R. A.

McCormick, N. J.

McGuckin, B. T.

Menzies, R. T.

Moore, K. D.

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: instrumentation, calibration, and performance in coastal waters,” J. Atmos. Oceanic Technol. 15, 496–509 (1998).
[CrossRef]

Pope, R. M.

Saunders, P.

Snyder, W. C.

W. C. Snyder, “Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 685–691 (1998).
[CrossRef]

van de Ven, J.

Voss, K. J.

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: instrumentation, calibration, and performance in coastal waters,” J. Atmos. Oceanic Technol. 15, 496–509 (1998).
[CrossRef]

J. W. Giles, K. J. Voss, “Submerged reflectance measurements as a function of visible wavelength,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 140–146 (1991).
[CrossRef]

Welty, J. R.

J. R. Zaworski, J. R. Welty, M. K. Drost, “Measurement and use of bi-directional reflectance,” Int. J. Heat Mass Transfer 39, 1149–1156 (1996).
[CrossRef]

White, D. R.

Zaworski, J. R.

J. R. Zaworski, J. R. Welty, M. K. Drost, “Measurement and use of bi-directional reflectance,” Int. J. Heat Mass Transfer 39, 1149–1156 (1996).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Geosci. Remote Sens. (1)

W. C. Snyder, “Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 685–691 (1998).
[CrossRef]

Int. J. Heat Mass Transfer (1)

J. R. Zaworski, J. R. Welty, M. K. Drost, “Measurement and use of bi-directional reflectance,” Int. J. Heat Mass Transfer 39, 1149–1156 (1996).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: instrumentation, calibration, and performance in coastal waters,” J. Atmos. Oceanic Technol. 15, 496–509 (1998).
[CrossRef]

J. Geophys. Res. (1)

J. M. Chen, J. Cihlar, “A hotspot function in a simple bidirectional reflectance model for satellite applications,” J. Geophys. Res. 102, 25907–25913 (1997).
[CrossRef]

Other (2)

B. Hapke, Theory of Reflectance and Emittance Spectroscopy, Vol. 3 of Topics in Remote Sensing (Cambridge U. Press, New York, 1993).

J. W. Giles, K. J. Voss, “Submerged reflectance measurements as a function of visible wavelength,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 140–146 (1991).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Diagram of measurement geometry for BRDF. Collimated irradiance E comes in at angle θ i . The reflected radiance is sampled at a polar angle θ v with azimuth ϕ.

Fig. 2
Fig. 2

Diagram of instrument design with major components listed.

Fig. 3
Fig. 3

Measured Spectralon BRDF values used in the calibration. Values are given for both air and water (submerged). The Spectralon plaques are the nominally 99% reflectance plaques. Curves are fits to the data described in the text.

Fig. 4
Fig. 4

Correction factor for sample depth as a function of θ v . This factor is predicted by the given sample depth and was applied to the data in Figs. 57.

Fig. 5
Fig. 5

Normalized BRDF and percent error in the BRDF as a function of sample depth and θ i for θ v = 5°.

Fig. 6
Fig. 6

Normalized BRDF and percent error in the BRDF as a function of sample depth and θ i for θ v = 35°.

Fig. 7
Fig. 7

Normalized BRDF and percent error in the BRDF as a function of sample depth and θ i for θ v = 65°.

Fig. 8
Fig. 8

(a) System linearity and (b) percent error from linearity. System is linear over 3 orders of magnitude of response. Multiple data points are the results from each of the fiber viewing spots.

Fig. 9
Fig. 9

Standard deviation of repetitive measurements of a Spectralon plaque. The plaque was measured nine times, with a rotation between each measurement. Data points are the average standard deviation for a whole image, θ v = 5° and θ v = 65°. Each set of vertical points is for a different illumination angle and LED color. Illumination angle sets are shown on the graph; colors for each set vary from red (R) to green (G) to blue (B) from left to right.

Fig. 10
Fig. 10

REFF polar plots of a mirror surface. (a) Polar plot illustrating the location of the view fibers. Each + corresponds to a view direction. The plot is orientated such that the middle (0,0) is looking normal to the surface. Descending along the y axis corresponds to the specular direction. Ascending along the y axis corresponds to the backscattering directions (toward the illumination beam). Note the increase of samples in the specular and backward directions. (b) Normal-incidence, red LED sample shows a large increase in reflectance directly upward. Peak value was 2600%. (c) θ i = 25°, red LED shows a large peak in the specular direction (1700%) and a small peak in the back direction (20%). (d) θ i = 65°, red LED also shows a large peak in the specular direction (4300%) and a relatively small peak in the back direction (100%).

Fig. 11
Fig. 11

REFF polar plots of dry and wet sand surfaces. (a) REFF (θ i = 0°, θ v , ϕ) at 658 nm for a dry sand surface. (b) REFF(θ i = 65°, θ v , ϕ) at 658 nm for a dry sand surface. (c) REFF(θ i = 0°, θ v , ϕ) at 658 nm for a wet sand surface. (d) REFF(θ i = 65°, θ v , ϕ) at 658 nm for a wet sand surface.

Equations (3)

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BRDFθi, θv, ϕ=Lθv, ϕ/E cosθi.
BRDFθi=0, θv=0.9686+0.001976θv- 6.470 × 10-5θv2,
BRDFθi=0, θv=0.9792+0.0012770θv- 7.430 × 10-5θv2.

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