cylindrical irradiance (at a point, for a given direction of incidence) [*E*_{e,z}]

1. mean irradiance on the outer surface of a very small cylinder that is put vertically at a point in space, to obtain composite irradiance produced by incident radiation from various directions

2. equivalent definition: arithmetic mean of the vertical irradiance *E*_{e,v} at a point

where

*L*_{e} is the radiance in the direction (*ε*,*φ*);

d*Ω* is the element of solid angle in direction (*ε*,*φ*));

*ε* is the angle of incidence measured with respect to the axis of the cylinder;

*E*_{e,v} is the vertical irradiance for an area element with its normal in the direction *φ*);

*φ* is the angle in the plane perpendicular to the axis of the cylinder

Unit: W·m^{-2}

NOTE The analogous quantities "cylindrical illuminance", *E*_{v,z}, and "photon cylindrical irradiance", *E*_{p,z}, are defined in a similar way, replacing radiance, *L*_{e}, by luminance, *L*_{v}, or photon radiance, *L*_{p}.

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