CIE x050-PO009

The limiting photometric distance (LPD) demarcates the boundary between the far-field and near-field regions of a light source, where the validity of the point source approximation and the application of the inverse square law can be upheld. Traditionally, this distance is determined along the optical axis and is considered universally applicable to all emission angles. However, for cosⁿ-distributed, rotationally symmetric light sources, an angular dependence is observed contingent on the beam width. Beyond a certain angle, the LPD for narrow beam light sources surpasses that along the optical axis in off-axis directions, indicating the invalidity of the point source approximation as defined on-axis. Therefore, an angular range is derived wherein the illuminance can be computed utilising the inverse square law, with errors of 1 % or less compared to exact solutions. This range is defined for square and round emitters based on their full-width at half-maximum angles.