D e


sin e

/ /

/ &e \



Fig. 1.5 The geometrical relations underlying the volume scattering function. (a) A parallel light beam of irradiance E and cross-sectional area dA passes through a thin layer of medium, thickness dr. The illuminated element of volume is dV. d/(8) is the radiant intensity due to light scattered at angle 8. (b) The point at which the light beam passes through the thin layer of medium can be imagined as being at the centre of a sphere of unit radius. The light scattered between 8 and 8 + D8 illuminates a circular strip, radius sin 8 and width D8, around the surface of the sphere. The area of the strip is 2p sin 8 D8, which is equivalent to the solid angle (in steradians) corresponding to the angular interval, D8.

all directions per unit pathlength - by definition, equal to the scattering coefficient - we must integrate over the angular range 0 = 0 ° to 0= 180°

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