A Numerical Describing Solution of the Integral Equation a Photometric Integrating Sphere

The integrating sphere is used in photometry to h.measure total luminous flux. In a sphere with a diffusely reflecting coating, the illuminance by reflected > light is approximately the same at all points on the sphere surface and is proportional to the total flux emitted by the lamp. This reflected light is measured at a point on the sphere surface which is shielded from the direct rays of the lamp by a baffle. Its intensity depends somewhat on the geometry and reflectance of the objects inside the sphere and on the angular intensity distribution of the light from the lamp. Unless this dependence is known, errors will occur 7 in measuring the luminous flux from different types of lamps. It is possible to describe the nonempty integrating sphere by an integral equation [1),1 whose solution i gives the illuminance by reflected light at every point ~ on all the surfaces inside the sphere: The present paper describes a numerical solution of this equation for a sphere containing a point source with an arbitrary angular intensity distribution and a disk-shaped baffle located perpendicular to the polar axis of the sphere. The existence of an oo-fold axis of symmetry simplified the work considerably by making it possible to do the azimuthal integrations analytically. The illuminance of the surface inside the sphere was calculated for several values of the baffle radius and its position along the polar axis. Although hemispherical source distributions were used for most of the calculations, the results are applicable to any small lamp whose intensity distribution is known. The extension of the technique to