A Basic Study on the Prediction of Luminous Intensity Distribution Curves of the Light Source Using the Floor Illuminance Distribution in a Room

Abstract

We have already published several papers describing application of an approximate calculation method for calculating interreflection in a room with fixtures. As a result, it is clarified that the illuminance ratio (illuminance ratio =the floor illuminance in a room with fixtures / the floor illuminance in a room where fixtures do not exist) distribution on the floor does not depend to the luminous intensity distribution curves of the light source. The method is presented for predicting the floor illuminance in a room (we called this the real space) with fixtures and a non-uniform diffuse light source from the floor illuminance in a room (we called this the virtual space) with no fixtures. In the previous paper, we presented that the luminous intensity distribution curves of light source of the narrow angle type and wide angle type can be represented as a polynomial expression with the components of cosine to the kth power and angle ακ of maximum luminous intensity. This paper proposed a method for predicting luminous intensity distribution curves of the light source when desired floor illuminance distributions is given. (we called this the inverse problem) This inverse problem of lighting design is useful for designing practical rooms, and ito procedures are as follows. First, the floor illuminance distribution of real space is replaced with floor illuminance distribution of virtual pace. Next, the relationship between position of the floor and floor illuminance distribution in a virtual room is expressed by the sixth equation. Finally, the relationship between the coefficient of the sixth polynomical with degree κ and the angle ακ of maximum luminous intensity of the light source is discussed. As a result, it is clarified that the luminous intensity distribution curves of the light source could be predicted from the coefficient of the equation, which has relation to floor illuminance distribution.