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.

Reshaping divergence with lenslet arrays

Two lenslet arrays, separated by one mutual focal length, can be used to reshape the divergence of a light beam.

Optics near the central focus of a solar plant operates at high energy flux, for example, at the beam-down optics of a glass-making solar furnace the flux will be on the order of 100 suns. This creates both the need to operate at high optical efficiency, and the opportunity to employ more expensive optical solutions than are possible on surfaces of larger area.

Each point on the beam-down optics of a solar furnace will see the circular opening of the furnace (because it is distorted by perspective) as approximately an ellipse. The beam-down optics needs to redirect approximately horizontal radiation coming from the field of telescopic heliostats downward toward the furnace opening. It also needs to reshape the divergence of the radiation to fit inside the approximately elliptical angular extent of the furnace opening.

A simple way to reshape divergence is with two lenslet arrays of the same focal length, separated by one focal length. In effect, each array acts as a field lens for the other. As the figure above illustrates, the lenslets in the two arrays do not have to have the same shape (though they must have the same area) in order to be in perfect correspondence with the lenslets in the other array. For example, in the figure above, circularly divergent light entering through the elliptical lenslets, would exit the round lenslets with elliptical divergence.