The Hot Spot Effect in Plant Canopy Reflectance

  • A. Kuusk


The diffuse reflection of radiation from different media has a sharp maximum in the backward direction. This phenomenon is known as heiligenschein in meteorology, the opposition effect in astronomy, and the hot spot effect in aerial photography and optical remote sensing. These three effects are caused by the same physical mechanisms, and hence are essentially equivalent. If the particles of the reflecting/scattering medium cast shadows, then the shadows cannot be seen looking along the incident rays since they are screened by the particles themselves. With a change in the view direction we can see some of the shadows. Therefore, the mean radiance of reflection decreases. Generally, the radiance of the reflecting medium will decrease with increasing angle α between the view direction and incident rays because of the decreased probability of seeing illuminated particles.


Plant Canopy Vegetation Canopy Principal Plane Leaf Canopy Canopy Reflectance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


a(z, Ω̱)

gap probability (penetration function)


BiDirectional Gap Probability


radiance in the direction Ω̱

CHS(z, α)

hot spot factor


leaf diameter


distribution density of leaf normals


Ross-Nilson G-function (the mean projection of a unit foliage area)


canopy height


flux density of direct solar radiation


leaf hair index


Leaf Area Index


leaf area index (LAI)


refraction index

p(z, Ω̱0, Ω̱)

bidirectional gap probability (BDGP)


aureole radius


reflection coefficient of leaves

R(θ, φ)

canopy bidirectional reflectance factor


mean chord length of leaves


transmission coefficient of leaves


leaf area density


angle between vectors − Ω̱0 and Ω̱

Γ(Ω̱0 → Ω̱)

area scattering phase function

ξ(x, y, z)

leaf indicator function

Ω̱(θ, φ)

unit vector directed to the observer

Ω̱00, 0)

unit vector directed to the Sun


polar angle of the observation direction


polar angle of the Sun


azimuth angle relative to the Sun’s azimuth

Yξ(Ω̱0), ξ(Ω̱)(S)

cross-correlation coefficient of ξ(Ω̱0) and ξ(Ω̱)


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© Springer-Verlag Berlin Heidelberg 1991

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  • A. Kuusk

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