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Fundamental assumptions : Lambertian reflection from the surface. The stereoscopic approach: . The difference between measured radiances at two view-angles can be used as a proxy for relative surface roughness. (1). (3). Fundamentals: .

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slide1

Fundamental assumptions: Lambertian reflection from the surface

The stereoscopic approach:

The difference between measured radiances at two view-angles can be used as a proxy for relative surface roughness

slide2

(1)

(3)

Fundamentals:

  • For a given pixel, surface-reflected solar irradiance L (Wm-2sr-1) at a given view angle  can be approximated as:
  • The ratio between L at 1 and L at 2 is then:

(2)

Isol – incident solar irradiation (Wm-2) Re- surface reflectivity

S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction

slide3

Can be removed using ‘dark object subtract’

Becomes a multiplicative scaling actor

Assuming a laterally ~homogeneous atmosphere at the image scale t(a1) / t(a2) can be regarded as constant for the whole image.

(5)

Atmospheric effects:

  • Per pixel, the ratio between at-sensor surface-reflected solar irradiance values L(Wm-2sr-1) at view angles 1 and 2 can be approximated as:

(4)

Isol – incident solar irradiation (Wm-2) Re- surface reflectivity S- path radiance (Wm-2sr-1)

S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction t(a) – atmospheric transmissivity

slide4

- can be regarded as a proxy for relative surface roughness between similarly sloping pixels within a single image.

    • incorporates roughness variations at all sub-pixel scales
      • is independent of surface composition
        • fairly insensitive to atmospheric effects

30°

Atmospheric transmissivity is a function of path length

atmosphere

surface

Atmospheric effects:

Isol – incident solar irradiation (Wm-2) Re- surface reflectivity S- path radiance (Wm-2sr-1)

S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction t(a) – atmospheric transmissivity