Modeling parabolic primary mirrors in Povray

Simulation of a bendable parabolic primary mirror in Povray.

This povray file ray-traces the sunlight reflected from a bendable parabolic primary at any chosen time and latitude. Actual bending of the mirror is not simulated, but the focal length of the parabola adjusts to the sun's zenith distance.

I am rather uncertain of the ray-trace (photons) settings in the .pov file, but it works. 

Modeling telescopic heliostat arrays with Povray

Computer-generated view of a telescopic heliostat array with the secondary mirrors represented by spheres.

I am starting on 3D modeling telescopic heliostat arrays using the povray software. This is an early result with the locations of the secondary mirrors represented by spheres. The heliostats are 6x and f-3.0; the sun is at 45° elevation.

A telephoto view of the same array from the direction of the sun, but a mere 50 primary focal lengths away. From the sun the entire field would look like the dark center of this view.

View from under the gimbaled primaries of a telescopic heliostat field. Sun is at zenith. These primaries are mirrored on their reverse side as well.

Two-mirror heliostats

Optical diagram of a two-mirror, or telescopic, heliostat. All profiles are parabolic and confocal. The primary mirror is gimbaled and bendable to accommodate the changing angles of the sun. The secondary mirror is fixed.

Definition: In solar engineering, a two-mirror heliostat, or telescopic heliostat, is a heliostat composed of two off-axis, parabolic mirrors, arranged in the configuration of a Mersenne telescope.

The larger primary mirror of a two-mirror heliostat is gimbaled and thin-shell bendable to accommodate the apparent movement of the sun. The small secondary mirror, which redirects concentrated sunlight toward the target, is rigid and fixed. The advantage of two-mirror heliostats over conventional one-mirror heliostats is that they can be packed closely together without incurring blocking losses—even when aiming at a target of low angular elevation. The optics and tracking motions of two-mirror heliostats are identical over the entire field.

Telescopic heliostats: designing heliostats as if thermodynamics mattered

Sunlight falls to the ground in an array of conventional heliostats—and the central tower is unnecessarily tall—because thermodynamics is ignored in the optical design. Since any optical system could be handling thermal radiation, all optical design is constrained by the Second Law of Thermodynamics.

It's not nice to fool Mother Nature. Redirecting sunlight toward a lower angular elevation is a sneaky way to increase its flux—therefore the Second Law of Thermodynamics demands that the light's divergence increase as well. In plain terms, thermodynamics permits us to make the sun look closer, but not hotter.  A high-performance heliostat must be an optical device that increases the flux and divergence of sunlight while keeping parallel rays parallel, in other words, a telescope.

The twin beams of light emerging from these 7x binoculars focussed at infinity and pointed at the sun are quite collimated, even though the solar flux has been increased about 49 times. Calculations indicate that 6x magnification would be optimal for a telescopic heliostat.

The Cassegrain configuration as it is usually described—a parabolic primary with a hyperbolic secondary—is not actually a telescope until an eyepiece is added. A secondary mirror having instead a parabolic profile would move the focal point to infinity, and thus serve as the eyepiece.