This led me to consider an offshoot of the skylight concept. Some of my neighbors have installed a "solar tube" which provides a skylight effect in a remote room by reflecting the sunlight down the shiny inner wall of a tube roughly one foot in diameter. The light emerges at the lower end of the tube. It emerges quite brightly, I might add.
I originally hoped I could install such a tube, mount a sundial beneath the lower end and watch the time go by from the comfort of my family room. I don't think it's that simple, though. If the sun's instant by instant azimuth and elevation in the sky is "information," then that information must get completely garbled up and lost as the rays bounce their way down the pipe.
You don't want a tube, but a box. If you set up a rectangular prism so that sunlight can get in the top and out the bottom in your living room, then the rays will exit at the same angle they entered. (The prism need not be vertical.) Well, actually only those rays that make an even number of reflections from each pair of parallel faces will emerge in the same direction they entered. If you want to eliminate the rays emerging in the three wrong directions, you will have to get clever.
The other solution is to use imaging optics. Put a small mirror near the "canyon rim" and another in your living room or just outside the window. Focus the image of the first mirror onto the second one with a lens or concave mirror. The first problem is that the f-number of the mirror must be small to catch the sun over most the day, so it will have to be very close to the first mirror. The angular deviations of the rays at the second mirror will then be very small, but you can either design the readout appropriately or re-expand them with another lens or spherical mirror. You must also be careful to keep the small mirrors near the axis of the focussing element to avoid distortion.
Fiber optics is certainly a way of preserving and transmitting the information for use at a remote location. But is there another way?
Could the incoming light be polarized -- maybe in four sectors for N, E, W, S information -- to preserve the azimuth and elevation in its travels down the tube?
Could some esoteric principles of radar be invoked to usefully tap into the information at various points along the tube, or at the end? (All I know about radar is that the microwave energy bounces around in hollow waveguides and the practitioners of the black art are able to somehow work magic with it.)
Fiber optics are the equivalent of radar waveguides for light. Both are usually, though not necessarily, operated in single-mode, in which case, as you say, the information they are capable of transmitting is limited. My first suggestion of a reflecting box can be considered a multi-mode waveguide that is capable of preserving some angular information.
Have fun,
Art Carlson
