Large concentrating dishes generally have a reflecting surface made up of a number of individual mirror panels (facets). The surface geometry of each panel is a function of its mounting location, if we wish to create a paraboloidal dish. Conversely, if a single, identical, profile is used for all panels the dish is no longer truly paraboloidal. In this case there is a loss in optical quality, but this is offset by a reduction in manufacturing (and assembly) costs.
The optics of a dish with mirror panels of spherical profile and uniform radius of curvature (r.o.c.) have been analysed in a previous paper [1]. However the study neglected the fact that any point on the paraboloidal surface is characterised not by a single r.o.c. (i.e. that of a two-dimensional parabolic curve), but rather by two principal radii of curvature in orthogonal directions (tangential and sagittal). Once the second (sagittal) r.o.c. is taken into account the choice of the optimum panel r.o.c. changes significantly, and the concentration ratio is increased.
At any point on a paraboloid (other than the vertex) the tangential and sagittal curvatures are unequal, and as a consequence a spherical mirror panel would exhibit some amount of astigmatism. We discuss the use of uniform but asymmetric mirror panels, as a means of improving the overall optics of a dish.

[1] Glen Johnston, Keith Lovegrove and Andreas Luzzi. Optical performance of spherical reflecting elements for use with paraboloidal dish concentrators. Solar Energy, 74(2),2003,133-140.