The Zamboniscope

It's a bad sign when you can make Roger Angel laugh out loud at your idea.

In a conversation with James Lloyd from Cornell at the Spirit of Lyot conference in 2007, he'd mentioned a novel way of making a space-based telescope using an old idea called a "luneberg lens". The lens is a sphere of matter, with a certain monotonic gradient of refractive index that varies only with radius, i.e. n=n(r). If you place a camera on the surface of the sphere and look back through the center of the bubble, you form an image that is free of spherical aberration and many other low order terms.

Lloyd's idea was with trying with a gaseous diffuser - initially, the gas flies off at the speed of sound determined by the temperature of the gas, but if you constantly replenish it from a compact source, maybe you could attain a steady state and have a large, very long focal length lens floating in space. Thinking further though, there is a simple case which shows that this doesn't work - when we look at distant stars passing behind the atmosphere of nearby planets, very little refraction of the the star is observed. So, even with approximately 1 STP of atmosphere, the focal length of such a system is ludicrously large.

Okay, so that doesn't work.

But.... what about a liquid or a solid?

I vaguely recalled that there is an under ice experiment in Antarctica that uses strings of photomultipliers, melted and subsequently refrozen into place in the antarctic ice many hundred of meters far below. Surely there was some measurement of the transmission coefficient of this ice?

Sure enough, there was! And the numbers in the paper blew me away - the mean free path for visible/blue light is about 200 meters - yes, that's right, the ice is so free of scattering microbubbles that you can see for two football pitch lengths.

Adding to this, it turns out that this is several times clearer than any ice made in a laboratory. The purest ice in the world appears to be about 1000m below the surface of Antarctica.

So, if you can manufacture a sphere of pure ice, which is then doped with a chemical that provides the index of refraction change in accordance with the Luneburg formula, you're good to go.

How big a lens can you build? Well, since we are in the realm of fantasy here, I thought I'd be conservative and go for 500m in diameter. After a quick bit of algebra demonstrated to me that the optimal size for an Ice lens is on the order of the absorption length (the exponent in the absorption quickly clobbers the effective surface area of the lens with increasing diameter), I also came up with a way to do the metrology. Get your sphere to within 1cm of the ideal sphere, and then use a reflective ball bearing in the center to act as a reference mirror, and then have machines that trundle along on the surface of the lens, peering down through a liquefied section of the ice that is melted by a surrounding hot plate.

Hmm, a machine that melts rough ice into a smooth surface. Where have I seen those before? Ah, at the ice hockey games!

Yes, I've invented the Zamboniscope.

No wonder Roger laughed at me.