Bidirectional Reflectance Calibration of Spectrometer Data using Spectralon Reference Panels

April 27, 2001

​

Larry Biehl

Electrical & Computer Engineering

Purdue University

(biehl@purdue.edu)

ASPRS 2001 1

2001 ASPRS Annual Conference

April 23-27, St. Louis, Missouri

Acknowledgements

• This research was funded in part by NASA contracts in 1990 and 2000.

ASPRS 2001 2

Outline

• Purpose of study
• Background
• Approach and methodology used
• Results
• Analysis
• Summary
• References

ASPRS 2001 3

Objective

• Develop procedure to calibrate the spectrometer field data (such as that from a GER 2600) to bi-directional reflectance factor using R(8⁰/h) values supplied by Labsphere and measured angular properties of a Spectralon panel.

ASPRS 2001 4

Background

• In many cases, measurements of a reflectance reference surface such as a Spectralon panel (made by Labsphere) are used for field measurements to calibrate the data to bidirectional reflectance factor.

ASPRS 2001 5

Background (cont.)

• Reflectance factor is defined as the ratio of flux reflected by a sample surface to that which would be reflected into the same beam geometry by a lossless, perfectly diffuse (lambertian) surface that is identically radiated (Nicodemus et al., 1977)

ASPRS 2001 6

Background (cont.)

• Not possible to construct a perfectly lambertian surface.
• Need to take into account the angular (non-lambertian) properties of the reference surface during calibration, R_r(θ,λ).

ASPRS 2001 7

Background (cont.)

• Calibration measurements provided with spectralon reference panel are directional-hemispherical reflectance: �R(8⁰/h)
• The need for much field collected data is directional-directional reflectance: �R(0⁰/θ)

ASPRS 2001 8

Background (cont.)

• Jackson et al. (1997) adapted work by Hsia & Weidner (1981) and angular measurements of spectralon panels with a Barnes Modular Multiband Radiometer (MMR) to generate “general” equations that relate R(8⁰,h) and R(0⁰,θ) for TM Bands. Measurements were made with an outdoor apparatus.

ASPRS 2001 9

Background (cont.)

• The need is for similar procedure to calibrate spectrometer data with 100’s of wavelength measurements (bands).

ASPRS 2001 10

Background (cont.)

Relationship of directional-hemispherical and directional-directional measurements.

Or

When R(0^ο/θ) is approximated by a polynomial in θ (radians) of degree n. b_i are the coefficients of the polynomial and I_i are 0.50000, 0.39270, 0.36685, 0.37990, 0.42147 and 0.49129 for i=0-5).

ASPRS 2001 11

Background (cont.)

• Hsia & Weidner (1981) found that R(45^ο/0^ο)/ R(6^ο/ h) was 1.015 at 550 nm for polytetrafluoroethylene, the base material for Spectralon.

ASPRS 2001 12

Methodology

• Bidirectional reflectance factor measurements were made of 30x30 cm Spectralon plate at illumination zenith angles of:
• 3, 6, 10, 20, 30, 40, 50, 60, 70 and 80 degrees.
• Using LARS indoor reflectometer
• and Exotech 20C Spectroradiometer

ASPRS 2001 13

Methodology (cont.)

Picture of Indoor Reflectometer

Picture of Exotech 20C

Exotech 20C was mounted above reflectometer in a dark room to take measurements of spectralon plate.

ASPRS 2001 14

Methodology (cont.)

• Determine R(45^ο/0^ο)/ R(8^ο/ h) for the the measured data over the Spectralon panel and compare Shia & Weidner’s value at 550 nm.
• Compare the angular measurements in reflective Landsat TM bands to those made by Jackson et. al.(1992).

​

ASPRS 2001 15

Results

Labsphere’s Spectralon table was used for 10⁰ illumination data.

ASPRS 2001 16

Results (cont.)

ASPRS 2001 17

Results (cont.)

ASPRS 2001 18

Analysis

ASPRS 2001 19

Analysis (cont.)

ASPRS 2001 20

Analysis (cont.)

ASPRS 2001 21

Analysis(cont.)

• Reflectance of Spectralon is computed by:

ρ = R(8/h)*(a₀+a₁θ+a₂θ²+a₃θ³+a₄θ⁴+a₅θ⁵)

​

where:

ρ = bidirectional reflectance factor of scene

R(8/h) = directional-hemispherical reflectance for spectralon panel from Labsphere

θ = illumination zenith angle in radians

a_i = Fifth order polynomial coefficients

ASPRS 2001 22

Analysis (cont.)

5th Order Polynomial Coefficients Wavelength (Function of Illumination Zenith Angle in Radians)

(um) a0 a1 a2 a3 a4 a5

0.25 1.0784 -0.1007 0.2380 -0.6660 0.7336 -0.2934

0.30 1.0784 -0.1001 0.2325 -0.6560 0.7281 -0.2925

0.35 1.0784 -0.1003 0.2306 -0.6517 0.7258 -0.2922

0.40 1.0784 -0.0999 0.2275 -0.6466 0.7239 -0.2923

0.45 1.0786 -0.1019 0.2322 -0.6536 0.7302 -0.2943

0.50 1.0785 -0.1024 0.2340 -0.6583 0.7361 -0.2965

0.55 1.0786 -0.1029 0.2339 -0.6585 0.7383 -0.2978

0.60 1.0785 -0.1015 0.2259 -0.6450 0.7300 -0.2960

0.65 1.0786 -0.1029 0.2292 -0.6495 0.7348 -0.2978

0.70 1.0785 -0.1018 0.2220 -0.6375 0.7277 -0.2965

0.75 1.0787 -0.1047 0.2320 -0.6550 0.7431 -0.3013

0.80 1.0786 -0.1039 0.2284 -0.6507 0.7426 -0.3019

0.85 1.0788 -0.1053 0.2303 -0.6523 0.7447 -0.3028

0.90 1.0787 -0.1036 0.2198 -0.6323 0.7303 -0.2991

0.95 1.0788 -0.1047 0.2228 -0.6384 0.7370 -0.3016

1.00 1.0788 -0.1053 0.2238 -0.6405 0.7404 -0.3030

1.05 1.0788 -0.1061 0.2243 -0.6400 0.7410 -0.3035

1.10 1.0788 -0.1067 0.2259 -0.6440 0.7464 -0.3056

1.15 1.0790 -0.1080 0.2272 -0.6449 0.7482 -0.3066

1.20 1.0789 -0.1068 0.2219 -0.6384 0.7468 -0.3070

1.25 1.0790 -0.1085 0.2260 -0.6444 0.7525 -0.3090

1.30 1.0791 -0.1088 0.2248 -0.6420 0.7522 -0.3094

1.35 1.0792 -0.1099 0.2278 -0.6482 0.7590 -0.3118

1.40 1.0791 -0.1095 0.2235 -0.6395 0.7539 -0.3109

ASPRS 2001 23

Analysis (cont.)

5th Order Polynomial Coefficients

Wavelength (Function of Illumination Zenith Angle in Radians)

(um) a0 a1 a2 a3 a4 a5

1.45 1.0793 -0.1110 0.2274 -0.6470 0.7618 -0.3137

1.50 1.0792 -0.1107 0.2256 -0.6453 0.7627 -0.3145

1.55 1.0793 -0.1124 0.2297 -0.6513 0.7684 -0.3165

1.60 1.0793 -0.1118 0.2252 -0.6442 0.7655 -0.3164

1.65 1.0792 -0.1117 0.2226 -0.6395 0.7637 -0.3165

1.70 1.0793 -0.1120 0.2201 -0.6333 0.7594 -0.3155

1.75 1.0792 -0.1105 0.2131 -0.6232 0.7547 -0.3150

1.80 1.0793 -0.1125 0.2186 -0.6322 0.7633 -0.3179

1.85 1.0794 -0.1134 0.2199 -0.6330 0.7645 -0.3184

1.90 1.0795 -0.1147 0.2234 -0.6397 0.7718 -0.3211

1.95 1.0794 -0.1137 0.2167 -0.6281 0.7650 -0.3198

2.00 1.0795 -0.1145 0.2198 -0.6356 0.7735 -0.3228

2.05 1.0795 -0.1146 0.2156 -0.6252 0.7654 -0.3207

2.10 1.0795 -0.1139 0.2127 -0.6232 0.7676 -0.3222

2.15 1.0797 -0.1166 0.2203 -0.6353 0.7780 -0.3255

2.20 1.0796 -0.1159 0.2165 -0.6296 0.7759 -0.3256

2.25 1.0796 -0.1167 0.2180 -0.6322 0.7794 -0.3270

2.30 1.0796 -0.1164 0.2133 -0.6225 0.7730 -0.3256

2.35 1.0797 -0.1175 0.2147 -0.6234 0.7748 -0.3265

2.40 1.0797 -0.1176 0.2145 -0.6254 0.7794 -0.3286

2.45 1.0797 -0.1178 0.2144 -0.6266 0.7826 -0.3300

2.50 1.0798 -0.1189 0.2132 -0.6206 0.7781 -0.3290

​

ASPRS 2001 24

Summary/Conclusions

• R(45^ο/0^ο)/ R(8^ο/ h) ratio at 550 nm (1.016) was very near that published by Shia & Weidner (1.015); difference of 0.1%.
• However, the Purdue measurements indicate that this ratio is a function of wavelength which differs from the Jackson et al data. The ratio varied from 1.017 to 1.011.
• Not sure if reality or instrument related.

ASPRS 2001 25

Summary/Conclusions (cont.)

• The Purdue angular measurements (indoor) were very similar to those reported by Jackson et al. (outdoor) from 0 to 75 degrees.

ASPRS 2001 26

Summary/Conclusions (cont.)

• Algorithm has been implemented using Matlab to calibrate our spectrometer data. The steps are:
• Determine illumination zenith angle
• Determine R(0⁰/θ) for each .05 um
• Subsample the .05 um table to match wavelengths for spectrometer
• Apply the subsampled table to the data

ASPRS 2001 27

References

• Jack Hsia and Victor Weidner, “NBS 45⁰/Normal Reflectometer for Absolute Reflectance Factors”, Metrologia, Vol. 17, pp 97-102, 1981.
• Ray Jackson, Thomas Clarke and Susan Moran, “Bidirectional Calibration Results for 11 Spectralon and 16 BaSO4 Reference Reflectance Panels”, Remote Sensing of Environment, Vol. 40, pp 231-239, 1992.

ASPRS 2001 28