[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
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
On Fri, Nov 14, 2008 at 12:12 AM, James Propp <jpropp@cs.uml.edu> 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.
This is nonlinear optics, so you probably won't get it in a pair of sunglasses any time soon. The implementations I've seen use rubidium gas; the transparency of the cell depends critically on how many photons the gas has absorbed. This is useful for certain quantum algorithms where you have a photon in a superposition of paths, one leading into the chamber and one not; then a second photon fired at the chamber will be absorbed or reflect depending on the first, which entangles the two. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
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
________________________________ From: James Propp <jpropp@cs.uml.edu> To: math-fun@mailman.xmission.com Sent: Friday, November 14, 2008 12:12:19 AM 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 _______________________________________________ There are optical structures called photonic crystals. They have an internal structure whose optical properties vary periodically on a scale of the wavelength of light. Imagine, for example, a 3D checkerboard made of micrometer-sized cubes in which the red and black cubes are made of materials having two different refractive indices. Light transmission in a photonic crystal varies with wavelength, direction and polarization, possessing pass bands where the light is transmitted, ideally 100%, and stop bands where no light is transmitted, ideally 0%. It's plausible that someone could design a photonic crystal that would block light within a certain wavelength range and also within a certain solid angle of directions, and for any piolarization. The stop band directions are however fixed with respect to the photonic crystal, so this device will only block light in a fixed direction. It is not inconceivable that one might build a photonic crystal whose band structure could be modulated, electrically, optically, or acoustically. Then a camera and software could determine the direction of a bright source, and control the photonic crystal to block light from that direction. Gene
participants (5)
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Eugene Salamin -
Henry Baker -
James Propp -
Mike Stay -
Schroeppel, Richard