Finite Lambertian source analysis of concentrators: application to solar reflectors

The maximum power cast on a collector from a source of finite angular extension by a concentrator of fixed position occurs when the collector sees the concentrator as a Lambertian source. Concentrators not fully meeting this requirement are evaluated using a parameter called the shape quality factor. Lambertian concentrators can be obtained with mirrors but not with lenses of finite n. In many cases they are not ideal, and some rays are cast outside the collector leading to an intercept factor below unity. Among those mirrors with the highest intercept factor, shape inaccuracies reduce this parameter and the shape quality factor to the extent which is analyzed. Rules for effective cost design are given leading to the conclusion that Lambertian concentrators must be used if the collector cost is high, while ideal concentrators should be used if the concentrator cost is high.