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
Famous quotes containing the words relating, peak, luminous, intensity and/or flux:
“Family lore can be a bore, but only when you are hearing it, never when you are relating it to the ones who will be carrying it on for you. A family without a storyteller or two has no way to make sense out of their past and no way to get a sense of themselves.”
—Frank Pittman (20th century)
“You know, I often thought that the gangster and the artist are the same in the eyes of the masses. They’re admired and hero-worshipped but there is always present underlying desire to see them destroyed at the peak of their glory.”
—Stanley Kubrick (b. 1928)
“A quibble is to Shakespeare what luminous vapours are to the traveller: he follows it at all adventures; it is sure to lead him out of his way and sure to engulf him in the mire.”
—Samuel Johnson (1709–1784)
“The bourgeois treasures nothing more highly than the self.... And so at the cost of intensity he achieves his own preservation and security. His harvest is a quiet mind which he prefers to being possessed by God, as he prefers comfort to pleasure, convenience to liberty, and a pleasant temperature to that deathly inner consuming fire.”
—Hermann Hesse (1877–1962)
“Death not merely ends life, it also bestows upon it a silent completeness, snatched from the hazardous flux to which all things human are subject.”
—Hannah Arendt (1906–1975)