Probably not what you want, but since brighter sources tend to be bluer in color, you could filter out some of the short wavelength light. Rich ________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] On Behalf Of James Propp [jpropp@cs.uml.edu] Sent: Friday, November 14, 2008 1:12 AM To: math-fun@mailman.xmission.com Subject: [math-fun] optics / materials science question While we're talking about optics, I was musing the other day about whether there's a way to make a windshield (or a pair of sunglasses) that will transmit less of the light emitted by really bright sources without transmitting less of the light emitted by dimmer sources. (I'm not talking about glare-reduction of the ordinary sort --- at least I don't think I am! --- since it's my impression that glare-reduction makes everything look dimmer.) It's not enough to make the windshield out of a substance that has non-constant transmittance (i.e., a substance for which the amount of transmitted light is some non-linear function of the amount of incident light), because every point on the windshield gets as many photons as every other; they're just travelling in different directions. We would need different transmittances in different directions. Are there materials that do this? Are such materials theoretically possible but not known? Or are there physical reasons why no such materials could exist? Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

I know it's not what you wanted, but _polarization_ can be different in different directions. There have been proposals since at least the 1940's that car windshields & car headlights should both be polarized, but in orthogonal axes, so that oncoming car headlights wouldn't blind drivers. --- What's wrong with electronics -- i.e., cameras/computers/display screens? Many vans now have such systems for their "rear view" capabilities, and several auto manufacturers have experimented with "heads up" displays with infrared-type capabilities to aid drivers at night. Assuming that the camera has enough dynamic range to begin with (a big assumption), the computer can process any amount of nonlinearity you would desire, prior to displaying the image. I believe that the newer military "night vision" goggles already have such processing to eliminate the temporary blindness that would otherwise occur if someone switched on a light. Nonlinear digital processing is already happening in Hollywood, which is pushing for as much dynamic range as possible--no matter what artifacts--because artifacts can be removed in "post processing". For example, if the lighting is slightly wrong when a scene is "filmed"/captured, this can always be "cleaned up in post", so long as the basic information is there in the form of dynamic range. Proposed Hollywood dynamic range is approx. 14 bits, which is pretty darn good, considering the fact that normal video hardware/software (e.g., professional MPEG) can handle only 10-12 bits. Where this dynamic range/nonlinearity issue shows up in video is in the form of "gamma", which is of the form of f(x)=c*x^gamma, which shows how much dim figures are accentuated or "compressed"/"crushed" (as in "the blacks seem really crushed in that scene", which should give you a lot of credibility at your next film opening). In order to increase the ability to encode dynamic range in cameras, there have been proposals to utilize _logarithmic_ functions. Unfortunately, logarithms don't work so well in the neighborhood of zero, so various proposals to switch to _linear_ functions in the neighborhood have been proposed. These proposals are essentially identical to the_audio_ "range compression" ("companding") telephony standards in use since ~1960, which are basically logarithmic, but with a linear piece around the origin. You can now guess where I'm going with this. As I have proposed a number of times before, _asinh(x)_ is a perfectly good companding function, as it is linear about the origin, and logarithmic away from the origin. At 12:12 AM 11/14/2008, James Propp wrote:

While we're talking about optics, I was musing the other day about whether there's a way to make a windshield (or a pair of sunglasses) that will transmit less of the light emitted by really bright sources without transmitting less of the light emitted by dimmer sources.

(I'm not talking about glare-reduction of the ordinary sort --- at least I don't think I am! --- since it's my impression that glare-reduction makes everything look dimmer.)

It's not enough to make the windshield out of a substance that has non-constant transmittance (i.e., a substance for which the amount of transmitted light is some non-linear function of the amount of incident light), because every point on the windshield gets as many photons as every other; they're just travelling in different directions. We would need different transmittances in different directions.

Are there materials that do this? Are such materials theoretically possible but not known? Or are there physical reasons why no such materials could exist?

Jim Propp