Maybe I’m confused about something but this does not seem conceptually difficult at all. It might require some funky meta-materials with weird refractive indexes to accomplish but there’s nothing intrinsically impossible about this idea.
I’ve mocked up a quick GIF to prove that such a lens system can work. I shows the unaided eye getting 3 light rays from an object and then a lens system that can provide 9 light rays without any apparent magnification. Can anyone tell me if I’m missing something here.
Maybe the .gif isn’t coming through correctly, but what I see is a still image of a square on with three light rays appearing to converge on a semi-circle.
You’ve got four rays from the top of the object converging on the same point on the small lens from different directions. Those should refract into four different directions to the left when they exit the small lens, but they are all following the same direction to the eye.
The diagram you drafted looks a bit inaccurate, but how is this making the refracted image more intense in luminance over what can be seen with the naked eye, if you’re merely canceling out the magnification?
If the .gif I am seeing is correct, all you are doing in your ray diagram is recovering the light rays that are diverged from the first optical element and collecting them in the second giant lens. ?
I had heard of etendue but wasn’t quite sure how it behaved. It makes sense. I suspect that it’s totally equivalent to the entropy of unabsorbed photons. It follows the Second Law of Thermodynamics, for a start (i.e., it can never decrease). And it seems to be responsible for the “enforcement” of the second law in other cases, like trying to use lenses to concentrate light for a heat engine. It also has the general feel of entropy: a perfectly collimated beam has zero etendue and seems very ordered; a perfectly diffuse area light has very large etendue, with photons going every which way.
So that’s the bit I’m not sure about and why I specified that strange metamaterials may be used. Obviously, two simple lenses could not do the job but it’s possible some more complex arrangement of lenses could mimic what I proposed.
This was meant to show that, conceptually, such a thing should be possible and I don’t think it’s valid to argue that you can prove it’s impossible from first principles.
Yes, which means you have a bigger collection area and thus, higher brightness. In the first image, 3 photons are impinging on the eye and in the second, 9 photons.
But not with a lens made of any known material or geometry. You have light rays from a number of different direction hitting exactly the same point on the second lens, thus they are making different angles with the surface of the lens. They cannot all be refracted in such a way that they all end up with the same angle leaving the lens. Simple application of Snell’s Law, for one, prevents this.
Another principle is that all optical system are reversible - you can turn the direction of the light beams around, and they must run through the optical system along exactly the same paths as they came in on. The multiple beams cannot do this - as there is no way determining which of the four possible paths they should go back on. Any sketch an optical system needs to ensure that reversibility is obeyed (and this is a trivial property from first principles of geometry.)
Actually you can, and people do, show that it is exactly possible to prove from first principles that this is the case.
The article on etendue does this. Meta-materials don’t help either. They obey all the same basic laws, they can be built so that they act in strange ways for a limited range of wavelengths, but even then, they can’t avoid the fundamentals, like the laws of thermodynamics.
As others have pointed out, etendue is, at best, conserved by any optical system. This is a well known theorem in optics, can be rigorously proven, and is equivalent to Liouville’s Theorem in classical mechanics. If you could violate it, you could focus sunlight to be brighter than the surface of the sun, which would allow you to reach a temperature greater than the surface temperature of the sun, which would violate the laws of thermodynamics.
use a long lens with an anti-teleconverter
22~35mm seems the going rate for the focal length of the central portion of the eye, so a 70mm at f/2 with a 0.5x teleconverter you have a 35mm lens at f/1, beating the eye’s 22-35 at f/2.1 (at brightest)
By violating it The principle only works when considering perfect reflectors and refracting surfaces. Indeed refracting interfaces are messier still, as they will partly reflect, with the amount of reflectance depending upon the refractive indecies involved, and the angle of incidence - and get involved with polarisation of light.
What you can do is to treat every surface as involving some reflecting and some refracting, and you end up with four lines, of which three describe the beam path depending upon direction. In this form a modified principle still holds - those lines are the same in each direction - but one of the partial reflection paths is not taken. (The lines are bound by the optical laws, for instance they are symmetric about the normal to the interface.)
Suppose we use three half-silvered mirrors to make your metamaterial. One splits your beam in two, and the other two split each of those. Starting from the eye, and following the path backwards, you get four beams that come out, each with 1/4 the energy. If the beam starting at the eye has amplitude 1, those beams will each have amplitude magnitude of 1/2 each. For simplicity, lets assume their amplitudes are all 1/2. We’ll represent this as [1/2, 1/2, 1/2, 1/2]. (*)
By symmetry of time reversal, if you have four beams going from the object through the lenses and to the eye, and they all have equal amplitude of 1/2, they will all focus into a sharp spot like you expect. But there are three other orthogonal possibilities for their amplitudes: [1/2, 1/2, -1/2, -1/2], [1/2, -1/2, 1/2, -1/2], and [1/2, -1/2, -1/2, 1/2]. (Any other set of amplitudes can be thought of as a superposition of these four amplitudes.) For each of those other three amplitudes, if they start at the object and go through your lenses towards the eye, they will have amplitude 0 at the eye, because they are orthogonal to the case your metamaterial/silver mirror setup is designed to collect.
For incoherent light, you’re going to have equal amounts of all four of those amplitudes (otherwise, it’s not incoherent), so only 1/4 of the energy will focus on they eye. The second law of thermodynamics is saved.
(*) ETA: The total energy of a beam with amplitudes A = [a,b,c,d] is |A dot A| = sum(|a|^2 + |b|^2 + |c|^2 + |d|^2)
Reversibility is still preserved even with things like half-silvered mirrors, but you need to look at the light in considerably greater detail to do it. Consider, for instance, a beam striking a half-silvered mirror and splitting into two beams. If you exactly reversed those two beams and sent them back, then you’d only get the one beam (the reverse of the original beam) coming out… But if you got the polarization or phase of those beams wrong, it wouldn’t work. On the macro scale, we often don’t care about polarization of visible light, and almost never care about its phase, so it might appear that reversibility is lost, but really it’s still there, hiding in the details.
Of course, it gets worse than that. What if you send through one photon at a time, so that you don’t have two beams to work with? It’s still reversible, but now you need quantum mechanics to understand the behavior. There are some very weird experiments involving beam splitters and quantum mechanics.
If you don’t restrict yourself to passive optics, then yes, such a device exists and is probably reasonably priced. The device I envision consists of a camera linked to a monitor. You control the brightness of the image by adjusting the brightness knob of the monitor.
Yeah, that can work just fine. For best results, you’d want a very large CCD in your camera, but even with a camera the same size as the eye, you could still gain benefits from the increased efficiency of a CCD compared to a retina.
The principle only works when considering perfect reflectors and refracting surfaces. Indeed refracting interfaces are messier still, as they will partly reflect, with the amount of reflectance depending upon the refractive indecies involved, and the angle of incidence - and get involved with polarisation of light.