The flexing of an adaptive primary

The flexing required of an adaptive primary is slight. Though the primary in this video is going through its entire range of adaptation (from 0° solar zenith distance to 90° solar zenith distance) its bending is barely visible. POV-Ray source code here.

Adaptive primary: the movie

This is a POV-Ray ray-trace of an adaptive primary mirror for a telescopic heliostat. (Scene description file here.) The ray tracing was done in Mega POV on a MacBook, the movie frames were put together in Graphic Converter, sound was added with Audacity and iMovie, uploaded to Vine with Vinyet. [mini cooper model ccby gilles tran; music by longzijun]

The thin-shell mirror bends to adapt to different angles of solar elevation. For a sun near zenith, the mirror curvature is nearly spherical, the curvature becomes more toric as the sun sets. Physical bending is not simulated in the program, rather the ideal off-axis parabola is selected for each solar elevation angle. The primary shown is about 3.1 m in diameter.

Why does the photographer's image get reversed left-and-right but not up-and-down? When the mirror is adapted to a sun at zenith (the nominal condition) it's shape is nearly spherical. Standing just inside the center of curvature of this quasi-spherical mirror, the photographer sees his own reflection magnified and upright and undistorted just as in a shaving mirror. As the mirror adapts to lower sun angles, the lens becomes more toric. In particular, its radius of curvature in the sagittal plane gets shorter while the radius of curvature in the meridional plane gets longer. As the mirror flexes, as it does in the first few frames, the increased curvature in the sagittal plane is easily noticed from this vantage point. Towards the end of the film, when the photographer's reflected image is very distorted, the center of sagittal curvature is passing through his head (!), causing left and right to invert. At that same moment the center of meridional curvature has moved far behind the photographer—leaving no chance that up and down will also invert.

The trading off of sagittal and meridional curvature that occurs when a thin-shell mirror is bent is exactly what is required to maintain a constant distance between the focus and the center of the mirror as the sun moves.