Optical Design

Had a bit of a breakthrough this week on the optics front. Namely, after several months of work, I have succeeded in producing a design for the optical bits of an instrument that I'm working on which would not only perform approximately as we'd like, but which could actually be constructed. While this is by no means the final design, and we're not about to rush out and start fabrication, this nevertheless pleased me to no end.

This week Pharyngula spent some time talking about optical design as well. But that being a biologist's blog, it's not so much about designing telescopes and more about the oddly sophisticated eyes of the box jellyfish. They turn out to have several; most of them are simple light-sensing affairs (apparently), but two are equipped with a proper cornea, a nicely corrected lens, and sensitive retina. In fact, these organs would dish up vastly more data than a jellyfish's simple CNS could possibly process ... if only they were in focus. They've actually evolved sophisticated eyes that are extremely out-of-focus, but as the article points out, this makes sense when you think about how a jellyfish works.

Designing a telescope on a computer is conceptually entirely unlike watching one evolve in a line of organisms. Natural selection ensures that at every stage, the organ in question must work (this also implies the very basic requirement of "can exist") ... but there are no particular constraints on what it must do, so long as it provides its host organism with some net advantage. I, on the other hand, began with a tightly defined specification of what this instrument would have to accomplish, and to get there I went through all sorts of absurd unphysical permutations involving apertures fifty meters wide and lenses with negative thickness.

The thing is, working closer to the order that natural selection works is arguably the more manageable approach. My ideal workflow looks something like:

  1. Arrange some reflectors to produce a basic image.
  2. Put in some lenses to get the light to where I actually want the image to be.
  3. Tweak that to get something that fits our miscellaneous manufacturing and packaging constraints.
  4. Tweak that to make a decent image.

Sadly, the computer doesn't really allow working like that, primarily because the optimizer routines have a rather inflexible notion of which qualities to optimize for. As a result, it's quite easy to crank out an intermediate design with a lovely sharp image a mile across with ten-ton lenses. Leaving image quality to the last step is somewhat trickier. So instead, I wind up spending most of my time creating these wacky-but-nicely-focused systems, and then trying to massage them back towards the system we're actually trying to build.

This is a common problem with computer-based optimization problems, which is why genetic algorithms are constantly the cool thing on the horizon. In theory, I should be able to just specify what I think makes for a good system, and set the computer running. It would spit out a gazillion random systems, choose the least bad ones based on my specifications, and use those as a starting point for a new generation with random variations. And so on. It turns out, there are many simple problems for which this works quite well. So far as I know, my problem is not among them, because in practice it's usually just not possible* to specify what makes a solution "good" and get out an answer you can use, unless you pretty much know the answer already.

* By "just not possible", I naturally mean "nobody knows quite how."

In other words, evolving complex things on a computer has a nasty habit of running into Haggunennon behavoir:

THE BOOK:

The Haggunennons of Azizatus Three have the most impatient chromosomes of any life-forms in the galaxy. Where as most races are content to evolve slowly and carefully over thousands of generations - discarding a prehensile toe here, nervously hazarding another nostril there, the Haggunennons would do for Charles Darwin what a squadron of Arcturan Stunt-Apples would have done for Sir Isaac Newton. Their genetic structure, based on the quadruple-striated octo-helix, is so chronically unstable, that far from passing their basic shape onto their children, they will quite frequently evolve several times over lunch. But they do this with such reckless abandon that if, sitting at table, they are unable to reach a coffee spoon, they are liable without a moments consideration to mutate into something with far longer arms - but which is probably quite incapable of drinking the coffee.

-- The Hitch-hiker's Guide to the Galaxy radio play, by Douglas Adams, fit the sixth

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This page contains a single entry by Milligan published on May 20, 2005 8:58 PM.

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