Beam-down optics designed with coextensive penumbras

Design for the optics at the center of a field of telescopic heliostats. Beam from farthest heliostat (blue) and nearest heliostat (yellow.) Lamp walls with elliptical profile (red,) thermal cap (yellow,) thermal wall (orange.) Penumbras of the field and of the thermal cap and thermal wall are adjusted to be coextensive.

Cross-section of the entire heliostat field (green) with lamp (red) and target point (yellow.)

Following the advice of the previous post, this design has coextensive penumbras. That is, the penumbra of the thermal cap (the upper portion of the radiant field lying between black and the sharp bends in the fringes) is coextensive along the surface of the lamp (red) with the upper penumbra of the field (the region between the blue rays coming from the farthest heliostat;) and the penumbra of the thermal wall (the lower portion of the radiant field between black and the sharp bends in the fringes) is coextensive along the surface of the lamp with the lower penumbra of the field (the region between the yellow rays coming from the nearest heliostat.)

This design has:

field radius = 1
inner field radius = 0.2
telescopic heliostat power = 6x
oculus radius = 0.0058
thermal cap radius = 2.1 * oculus radius
zenith distance to edge of cap = pi/3.6
thermal wall radius =2.7 * oculus radius
zenith distance to top of wall = pi/2.33
lamp height = 0.060