Closed-Form Analytical Formulation of Lighting Design Objectives Procedure in Rooms With an Isotropic Light Source

Mean room surface exitance (MRSE), which indicates the amount of ambient illuminance in a room, is an important parameter in contemporary lighting design objectives (LiDOs) procedures. However, the fundamental MRSE model does not provide explicit relations with the light source characteristics. For the case of an isotropic light source, whose luminous intensity is constant, it is hypothesised that the direct flux on each surface can be accurately computed by first determining the solid angle. This study aims to provide closed-form analytical formulation for computing MRSE using LiDOs procedure in rooms with an isotropic light source. Theoretical calculations are provided and verified to demonstrate the equality of specified and actual MRSE in various room scenarios. Monte Carlo simulations with 1000 random combinations are conducted to parametrically explore the design outcomes. Results suggest that the intended ambient illumination can always be achieved, indicated by the equality between the specified and actual MRSE, due to exact computation of the direct flux received by each surface within the room. This study proposes a new insight on lighting design objectives procedure under the design constraint of isotropic light source, and how MRSE can be related with the relevant input variables to achieve the design objectives.