Relating Peak Luminous Intensity and Luminous Flux
In general, the luminous intensity of a point on a surface varies by direction; for a Lambertian surface, that distribution is defined by the cosine law, with peak luminous intensity in the normal direction. Thus when the Lambertian assumption holds, we can calculate the total luminous flux, from the peak luminous intensity, by integrating the cosine law:
and so
where is the determinant of the Jacobian matrix for the unit sphere, and realizing that is luminous flux per steradian. Similarly, the peak intensity will be of the total radiated luminous flux. For Lambertian surfaces, the same factor of relates luminance to luminous emittance, radiant intensity to radiant flux, and radiance to radiant emittance. Radians and steradians are, of course, dimensionless and so "rad" and "sr" are included only for clarity.
Example: A surface with a luminance of say 100 cd/m2 (= 100 nits, typical PC monitor) will, if it is a perfect Lambert emitter, have a luminous emittance of 314 lm/m2. If its area is 0.1 m2 (~19" monitor) then the total light emitted, or luminous flux, would thus be 31.4 lm.
Read more about this topic: Lambert's Cosine Law
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