a simple introduction of bidirectional reflectance distribution function.

1. Definition, Significance,
Measurement and Modelling
of BRDF
Linyuan Li
School of Geography, Beijing Normal University
21/10/2016

2. Part I. Definition of BRDF
• Reflectance
• Spectral
• directional
• Reflectivity
• Reflectance factor
• Albedo
• Viewing geometry
• BRDF
• ANIF/ANIX

3. What sensors acquire?
• Spectral Radiance
• radiant flux in a beam per unit wavelength and
per unit area and projected solid angle of that
beam. SI units [W m−2 sr−1 nm−1].
• Radiant flux( )

4. Common symbols & sub-superscripts
Symbols
A Surface area [𝑚2
]
θ Zenith angle, in a spherical coordinate system [rad]
ϕ Azimuth angle, in a spherical coordinate system [rad]
ω Solid angle; ≡ ∫dω≡∫∫sinθ·dθ·dϕ [sr]
Ω Projected solid angle; ≡ ∫cosθ·dω≡∫∫cosθ· sinθ·dθ·dϕ [sr]
L Radiance; ≡ d2Φ/(dA· cosθ·dω) [W m−2 sr−1]
E Irradiance, incident flux density; ≡ dΦ/dA [W m−2]
M Radiant exitance, exitent flux density; ≡ dΦ/dA [W m−2]
ρ Reflectance; ≡ dΦr/dΦi [dimensionless]
R Reflectance factor; ≡ dΦr/dΦrid [dimensionless]
sub-
superscripts
i incident
r reflected

5. Key to Quantitative Remote Sensing
 Reflectance
The ratio of the radiant exitance (M [W m−2]) with the
irradiance (E [W m−2]) [dimensionless]
Reflectanc
e
Spectral Directional
, ,; ;
/
( )
/
r
i ri r
i
d dA dM
d dA dE
     


6. Spectral Reflectance

7. Spectral Reflectance Measurement
 Field:
• ASD, DECAGON, SVC
 Satellite:
• Landsat, SPOT, Terra/Auqa, Suomi-NPP, Sentinel
From RADI From USGS

8. Reflectance VS Reflectivity
 Reflectance
• The property of a particular sample of that material or
a particular surface
 Reflectivity
• The property of a material
• a value that applies to thick reflecting objects
• When reflection occurs from thin layers of material,
internal reflection effects can cause the reflectance to
vary with surface thickness.
http://ricmorte.com/index.php/light-a-colour/optics/reflectance-a-reflectivity

9. Reflectance VS Reflectance factor
Reflectance factor
• radiant flux reflected by a sample surface / radiant flux
reflected by an ideal (lossless) and diffuse (Lambertian)
• the identical beam geometry
• irradiated and viewed under the same conditions as the
sample surface
• reflectance factor can reach values beyond 1
, ,; ;
/
( )
/
r
i ri r
i
d dA dM
d dA dE
     

Born for measurement
, ,; ;
cos( )/
( )
/ cos( )
rr r r r r
i ri r
rid rid rid ridr r
dd d
R
d d d
LA L
A L L
     
 
  
 



10. Reflectance VS Albedo
• Key point: hemispherical exitance
Black-sky albedo Blue-sky albedo
,
/
( )
/
r
i i
i
d dA dM
d dA dE
   

White-sky albedo
, ,; ;
/
( )
/
r r
i ri r
i i
d d
d d
A
A
     


11. Directional Reflectance
From: The Notebooks of Leonardo Da VinciRoosjen, 2012
davinci’s consideration

12. Sun – Object – Sensor
Nicodemus, F. E., et al. (1977)

13. BRDF(Bidirectional Reflectance Distribution Function)
Nicodemus, F. E., et al. (1977) Non-measurable
• No absolutely direct light in nature
• Every sensor has finite FOV
Relationship between BRDF and BRF
Describes the scattering of a parallel beam of incident light
from one direction in the hemisphere into another direction in
the hemisphere

14. Characterization of surface BRDF
 Spectral Variability
• spectral dependency depends on optical properties
of components(leaf, stem, trunk, soil) and multiple
scatters(3D structure or arrangement)
• anisotropy factor and index
 Spatial Variability
• continuous heterogeneity
Angular Variability

15. Anisotropy factor and index
 Anisotropy factor(ANIF)
 allow separation of spectral BRDF effects from the
spectral signature of a target.
 normalization eliminates the impact of phenology
and depends less on the growing state.
 normalized BRF exhibits more the typical behavior
 Anisotropy index(ANIX)
 an overall estimate for reflectance anisotropy
 useful for comparing spectral BRDF effects of
different surfaces.
BRFANIF

16. Measurable
Measurable
Conceptual
Conceptual
Conceptual Conceptual
Conceptual
ConceptualConceptual
Reflectance Quantities

17. Part II. Significance of BRDF
BRDF reflects biophysical information
Play a role for:
Angular correction of reflectance
Correction of time series
Composition of images taken under different lighting conditions
Vicarious Calibration (calibration on geophysical object)
Calculation of surface albedo
classification
Deriving biophysical parameters from remote sensing data
Discharge of military recognition tasks

18. Example - NDVI correction

19. Part III. Measurement of BRDF
 Sampling strategies
 Platforms（view mode）
 Atmospheric correction
 Considerations

20. Observation Plane
Orthogonal Plane

21. Sampling Strategies
 Nadir method
• sensor is pointed vertically down at the surface to be
measured and the solar position during each
measurement is recorded.
 Solar principal plane(SPP) method
• the BRF of some surfaces show no preferred azimuthal
orientation.
 SPP & OP(Orthogonal plane) method

22. Sampling Strategies
Twin azimuthal plane method
• two azimuthal planes at 45° to the solar SPP (Kimes)
Hot-Spot method
• the angular width of the hot spot is related to plant canopy
architecture. Range ±10°, interval 2°
 Solar almucantar method
• sensor set at the solar zenith angle to scan through 360°
in azimuth in order to capture the extremes of off-nadir
reflectance
Schwarzbach, GRADIS, 2012

23. Observation Pattern
 Fixed Target Mode
• Sensor moves within hemisphere space, view
object with a particular distance
• Footprint varies with view zenith angle
 Fixed Sensor Mode
• Sensor rotates along azimuth.
• Assuming homogenous surface

24. Platform - Laboratory Goniometer
DCaF (NASA, 2006)
ClabSpeG (Biliouris, 2007)
WURrobot (Roosjen, 2012)

25. Platform - Field Goniometer
 FIGOS&SFG (Sandmeier,1998)
 Dual FOV FIGOS (Schopfer,2008)
ULGS II (Coburn, 2016)
 FIFFIGO (Suomalainen,2009)
 MAOS (Yan, 2012)
 PARABOLA (Deering,1986)
 GRADIS (Schwarzbach,2009)

26. Platform - Multiangular Observation by UAV
 Cross-line pattern
• MASA_ASASairb (Ranson,1994)
 Hemispherical pattern
• Chiba_GTMS (Hongoh, 2001)
• IBG_UAVG (Burkart, 2015)
• Rostock_FourVison (Grenzdörffer, 2011)
 Tilted Sensor
• NASA_MALIBU (Román, 2015)
• WUR _HYMSY (Roosjen, 2015)
• RADI_UAVTherm (Cao, 2016)
 Multi-view sensors

27. Platform - Satellite Multiangular Sensor
 Multi-view sensors
• ATSR-2(0°, 56°)
• MISR (9)
• PROBACHRIS (5)
 Wide-angle area array sensor
• POLDER(Up to 14)
 Wide-angle sensor scaning
• MODIS
• AVHRR
• VEGETATION
• FY-2MERSI

28. How to obtain absolutely accurate BRF?
• Impossible because of atmosphere scatter effect
• How to Correct?
• total – scatter = direct (opaque circular disk occlude sun)
No Aerosol Rural 23 Rural 11
Lambertian
Robinson & Biehl, 1979

29. Considerations
• Duration of whole measurements
• Impact on solar angle
• Solar move
• Impact on intensity of irradiance
• kept within ∓1° SZA to obtain homologous BRDF data
• Positioning and orientation accuracy
• Angular sampling resolution(sandmeier,1998)
• Sampling interval of 15°in zenith, 30°in azimuth, is
adequate to capture the general BRDF characteristics
of most natural and man-made

30. Part IV. Modelling of BRDF
• Minnaert function
• Lommel-Seeliger function
• Walthall function
• Rahman function
• Kernel function