[3.5.6]The luminance of a surface in a specified direction also has been expressed in terms of the luminous exitance the surface would have if the luminances in all directions,within the hemisphere on the side of the surface being considered, were the same as the luminance in the specified direction. In other words, luminance has been expressed as the luminous exitance of a lambertian surface (see Lambert’s cosine law) whose luminance equals the luminance of the surface in question and in the specified direction.

Lambertian                  Lambertian
Luminous                  Luminous              Equivalent
Unit                  Exitance              Luminance
1 asb =                1 lm/m^{2} =            (1/\pi )cd/m^{2}
1 fL =                1 lm/ft^{2} =            (1/\pi )cd/ft^{2}
=            (1/144\pi )cd/in^{2}
1 L =                1 lm/cm^{2} =            (1/\pi )cd/m^{2}


Note: The lambertian units of luminance are numerically equal to the corresponding units of luminous exitance.Thus, the luminance (in lambertian units) of a surface could be determined, and the numerical value could be directly used in the equation for a lambertian reflecting surface relating illuminance and luminous exitance, i.e., M = ρE, where ρ is the reflectance and M is the luminous exitance. In practice, no surface follows exactly the cosine formula of emission or reflection, and many do not even approximate it; hence, the luminance is not uniform but varies with the angle from which it is viewed. Since the raison d’être for this system was the use of a relationship of generally unknown and variable accuracy when applied to real surfaces, the use of lambertian units of luminance has not been acceptable since 1967.*


* Kaufman JE. Introducing SI units. Illuminating Engineering. Oct 1968;63(10):537.

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