The final determination of the exitance on each subsurface requires knowing the total initial or direct flux onto each subsurface. These fluxes are determined in a two-step process: the unoccluded flux from a source onto a subsurface is determined and then modified by the occlusion factor for the source-subsurface pair.
The numerical double contour integration process described above is used to determine the unoccluded flux and the result multiplied by the appropriate occlusion factor. For flux accounting purposes, the flux arriving to each subsurface from each source in the system is recorded. If it is determined that a source is completely surrounded by subsurfaces, it is possible to check that the total flux involved for the source is correct. The total flux to all surfaces from that source should equal the known total emitted by the source (luminaire lumens). Any imbalance is corrected on each surface, the correction being weighted by the amount of flux onto the surface. In this way and in most cases, the flux from each source distributed to all subsurfaces exactly equals the total source emitted flux.
Using the initial flux and the subsurface area, the initial illuminance on each subsurface can be determined.