sensor 
  
  
  
  
  
Figure 1: Definition of the angles 
A denotes the surface of the sample 
sensor can be found in [Bartsch, 1994]. Each spectrum is 
recorded simultaneously for all wavelength bands by means 
of a CCD-Array. We used 61 spectral bands in the range 
A = 600 — 900nm (AA = 5 nm), with a distance between 
sensor and samples of 1 m. The area on the sample covered 
by the instantaneous field of view (IFOV) of the sensor is 
about 10 cm?. 
A goniometer was constructed to hold the samples for all pos- 
sible combinations of incidence and reflection angles. The go- 
niometer allows to place the surface with arbitrary inclination 
towards sensor and light source (see [Meister, 1996]). 
The samples were selected with respect to azimuthal symme- 
try, so that the BRDF's of the samples depend only on the 
azimuth difference angle v = |®; — ®,|. We determined the 
BRDF of six samples: aluminum sprayed with red paint, a 
sheet of white smooth plastic, a concrete-type sidewalk cover 
block and three roof coverings (a red roofing tile, a slate-type 
tile and sprinkled roof paper). The values of the BRDF were 
measured at grid points of 0?,25?,50?,75? for the zenith 
angles 0; and 0, respectively, and at 0°,90°, 180° for the az- 
imuth difference angle v = |; — b,|,(see figure 1), making 
up a total of ca. 35 measured spectra for each sample. 
As a reference target we used a commercially available 
Spectralon panel (Labsphere Inc., Boulder, Colorado) with 
an albedo of p = 0.5 . Since we were not satisfied with 
the simplifying assumption of Lambertian behavior of 
the Spectralon panel, we adopted the following two step 
procedure (the second step was proposed by [Jackson, 1993]): 
2.1 Step 1: Laboratory Measurement of the BRDF of 
the Spectralon Target ; 
In the laboratory measurements, we used a 100 W halogene 
bulb as light source. We measured the reflected radiance 
L, [W m7?sr7*nm7*] from the Spectralon panel at the com- 
binations of angles described above. Integrating L, over the 
projected solid angle 2 as defined by [Nicodemus, 1970] and 
494 
dividing the result by the albedo of the Spectralon yields the 
incident irradiance E; [W m^?nm^!]: 
Eod JE 
1 v=m 0,=5 
2 / / 2: L«(0i,v,0.) cos, sin 0,d0,dy (1) 
P Jv=0 „=0 
These quantities allow to calculate the BRDF of the Spec- 
tralon : 
Speciralonyy, V, 0.) = PS (2) 
For small aperture solid angles, the BRDF can be approxi- 
mated by 
Spectralon (9. es Ly (6s, V, 0,) 
r (8; v, 0.) z ES s (3) 
The results agree qualitatively very well with earlier measure- 
ments of the BRDF of Spectralon panels with an albedo of 
1.0 by [Flasse, 1993] and [Jackson, 1992]. The BRDF values 
decrease with large zenith angles. The Spectralon panels with 
an albedo of 0.5 have a specular peak, that does not exist for 
the Spectralon panels with an albedo of 1.0 . The intensity 
of the specular peak increases rapidly with large zenith angles 
(see figures 3 and 4). 
Our measurements suggest, that the BRDF of Spectralon 
obeys Helmholtz's theorem of reciprocity, i. e. , exchanging 
incidence and reflection angles does not change the BRDF 
value: 
f» (0i, v,0.) — f.(0-,v,0i) (4) 
This equation was confirmed by the measurement of the 
BRDF at 2 x 11 different combinations of angles (0i, v,6,). 
The BRDF of the Spectralon panel is presented in figures 3 
and 4. 
The wavelength dependence of the diffuse component and the 
specular component of the BRDF of the Spectralon panel is 
linear, see [Meister, 1996]. 
2.2 Step 2: Outdoor Measurement of the BRDF's of 
the selected surfaces 
Four measurements of the reflected radiance L,()) are nec 
essary in order to obtain the Bidirectional Reflectance Factors 
(BRF) of the samples for each combination of angles : 
1. L, of the Spectralon panel illuminated by the sun and 
skylight 
2. L, of the Spectralon panel illuminated by skylight only. 
To this aim, the Spectralon panel was cast in shadow. 
The contribution of diffuse skylight to the global ir 
radiance was 2096 on average, obviously depending 
strongly on the angle of incidence 6;. 
The difference between these two measurements yields 
the radiance AL, reflected by the Spectralon panel 
which can be attributed to direct sunlight only. The in- 
coming radiance E?'"" from the sun can be calculated 
from the BRDF of the Spectralon panel, determined in 
step 1: 
fSpectraton (8; y, 0) (5) 
Ej (0;) — AL. Gi, ” 6.) 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996 
  
"o f" en.