Luminous Flux Computation and the Use of Hybrid Symbolic Integration - Spline Interpolation Method

Lighting calculations are commonly done to evaluate the efficiency of a lighting system. One of the important parameters in establishing a luminaire’s efficiency is the total flux emitted from a luminaire or light source. The luminous flux of a light source can be calculated from readily available data of the measurements of its Luminous Intensity Distribution Function, in the form of table of values function. The method currently used in the lighting industry is by means of a semimanual method of computation and summation of flux at discrete angular steps of luminous intensity under measurement and the use of zonal constants. In this paper we explore the use of mathematical techniques through software to generate a scheme that provides a more automated and more accurate way of computing the luminous flux. We explore the use of cubic spline interpolation and of symbolic mathematics in a hybrid numericanalytic integration method, implemented in MATLAB environment. We also conduct some numerical experiments to verify the efficiency and accuracy of the new method for different simulated light intensity distribution function and compare it to results based on current practices.