Topics in Particle and Dispersion Science

Problem: Distribution of irradiance in an image of a uniform lambertian sphere

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Consider a spherical radiation source with a lambertian surface and assume that each equal-area element of the sphere surface radiates outward the same power. Given that the sphere surface is lambertian, each element of that surface emits a constant radiance in all directions of the outward hemipshere. Irradiance in an image of such a sphere generated by an imaging system working in the paraxial regime is independent of position within that image. As usually, the paraxial regime applies when sin(θ) ≈ tan(θ) ≈ θ, where θ is the projection angle. Hence, the lambertian sphere is seen by a far-away observer as a flat disk. Prove this assertion.

CITATION: Jonasz M. 2009. Problem: Distribution of irradiance in an image of an uniform lambertian sphere (www.tpdsci.com/Tpc/RdmLambSrcSph_P.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 05-Jan-2009 Modified: 22-Jun-2009 Peer-reviewed: 12-Feb-2009

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