Using a ray trace, a suitable surface can be approximated by breaking it up into small facets where the position and orientation of one after the other can be sequentially optimised to achieve uniform illumination. Fig 2 shows this design process in which several facets are sequentially optimised. First the distance of a horizontal facet on the axis of symmetry is varied until the ray trace program calculates the wanted concentration or illumination on the surface within a given tolerance. Instead of optimising the position of the first facet for a given illumination or concentration, a position and orientation of the first facet can be chosen which defines the illumination and concentration for the whole uniformly illuminated surface.

Next, another facet is attached to the first facet with an arbitrary orientation. Now the orientation of the second facet is varied by turning it around the point in which it touches the first facet. For each variation a ray trace program calculates the average concentration or illumination on this facet. The facet is varied until the wanted value is

achieved within the given tolerance. Next another facet is optimised by turning it around the point where it touches the second facet. This procedure is continued until for a facet the maximum concentration is less than the wanted concentration and therefore no orientation can be found anymore for which the concentration or illumination is within the given tolerance. This defines the rim of the receiver.

The result strongly depends on the starting point. In principle it is possible to start at any point within the suitable region. For a symmetrical system it is reasonable to start along the symmetrical axis as shown in the example above to achieve a symmetrical result.

It is feasible to approximate the surface by small facets since a real photovoltaic receiver will be put together out of small flat solar cells too. It is sufficient to calculate the average irradiation on these facets since each cell produces electricity, which as well depends on the average irradiation over the surface of the cell.

Many ray trace programs using different principles are available or can be programmed which can be used for such an optimisation process. In a companion paper (Buie et al., 2004) another procedure for generating regions of uniform illumination is described.