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Corrective glasses are usually intended to help focus light on your retina. Supposing I had good vision already, but simply wanted more light, could I make glasses that would send more light into my eye without magnifying, focusing, or distorting the image? (Ignore chromatic aberration.)

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up vote 12 down vote accepted

First, let me try to clarify the question, because not everyone seems to get it ("where would the photons come from?"). If I'm buying binoculars, I might choose from 8x24, 8x36, or 8x50 binoculars. The first number is the magnification; 8x for all the examples. The second number is the size of the objective in millimeters, 24 to 50 millimeters in the example. All else being equal, the larger objectives will gather more light, and produce a brighter image. The 8x24 and 8x50 binoculars will deliver the same 8x magnification, but the 8x50 pair will be brighter.

So it's reasonable to ask if you could make 1x binoculars that have a big objective that brightens the scene in front of you. There's no conservation of energy issue here; the larger front objective would gather more light. The problem is that there's a relationship between the magnification and the sizes of the entrance and exit pupils:

magnification = entrance_pupil_size / exit_pupil_size

If you create a binocular with an entrance pupil (objective, basically) that's larger than your eye's pupil, so that it can gather more light than your eye's pupil, then at 1x magnification, the exit pupil is going to be just as big as the objective lens. And since that's bigger than your eye's pupil, the "extra" light is going to run into your iris instead of going through the pupil, and you will gain no advantage from it.

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Yes, exactly: make a huge aperture to gather lots of light, and then arrange the optics such that there is no apparent magnification. –  nibot Nov 12 '10 at 17:12
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Thanks! Can you expand a little on why that magnification law should always hold, or give a link? I would be interested in understanding that law through more basic optics. –  Mark Eichenlaub Nov 12 '10 at 17:46
    
But... you can never use a larger aperture to make the image brighter than it already would be if you looked at it without 1x binoculars. This is why everybody keeps asking where the extra photons come from. –  ptomato Nov 13 '10 at 17:30
    
@conesalyer: Ah, but the device mightn't necessarily take on the form of binoculars @ptomato: no, you can definitely gather more light from an object than reach your eyes. Whether you can redirect correctly it is another issue –  Casebash Feb 25 '11 at 12:10
    
You addressed conservation of energy, which is good, but I take issue with this answer, and any "simple yes" answer because of entropy. Couldn't I make an infinite number of these and thus passively obtain temperatures greater than the surrounding environment? How do you reconcile that? –  AlanSE Jun 5 '11 at 21:51
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The "speed" of a photographic lens, and the brightness of the image produced by any lens is determined by a single number - the focal ratio. That is the ratio of 1) the distance between the lens and the image (of an infinitely distant object) and 2) the diameter of the lens. It is basically the ratio of collecting area to image area. You can increase it by moving the image closer to the lens but only up to a point where you reach the lens itself. This principle is the reason that no concentrator lens can produce a spot of light on a surface and make that surface achieve a temperature greater than that of the visible surface of the sun.

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Expanding a bit on what ptomato said, I think there's a problem with the second law of thermodynamics regardless of any problems with the first law.

Suppose the universe consisted of two things: a black body the shape of eyeballs and the microwave background. Then the black body would come into thermal equilibrium with the microwave background.

Now we introduce these glasses that make things brighter, placing them in front of the black body. Suddenly the black body has more light coming on to it. It absorbs all this light, so it has to heat up. We made heat flow from a colder place (the microwave background) to a hotter place (the black body) by a passive optical phenomenon. That violates the second law.

EDIT: It turns out this principle is called "conservation of brightness" or "conservation of surface brightness" and is well-known in optics. See, for example, http://www.cv.nrao.edu/course/astr534/Brightness.html

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No, not using optics; you'd need some sort of active amplification. Without magnifying, focusing, or distorting the image, the glasses would need to be flat. But consider the energy in the light entering the front face and leaving the rear face of the lenses - what you want would require there to be more coming out than going in, which violates energy conservation. The extra energy has to come from somewhere.

EDIT

This question caused a lot more discussion than I expected. I would like to try to explain my answer a little further, because people seem to have misunderstood me.

Let me say first, I want to consider the case of using only lenses and similar devices. In j.c.'s answer we have already established that what you ask is possible using amplification, frequency conversion, or thermal imaging -- all of which are used in night vision / image intensification technology. Browsing Wikipedia I found out that some animals have a tapetum lucidum, a reflecting membrane behind the retina which turns around any light that made it through the retina without getting absorbed, allowing it to pass through the retinal cells once more and be absorbed on the rebound. This increases the efficiency of the retina, which is also a way to do what you ask, but I'm discounting it since it is not available to us humans without resorting to surgery.

Now down to business. We want to create corrective glasses that make your vision brighter, but with no

  • magnifying
  • focusing
  • or distortion.

This means, considering the following diagram:

a wavefront entering a mystery "?" box and emerging the same

The optical system we want to create is represented by the "?" box. The wavefront on the left has to be the same as the wavefront on the right, only brighter. (Except for the effects of propagation across the distance that the box occupies, but let's ignore that.) Notice that I have drawn the wavefronts as squiggly lines with arrows all over them. This is because the images that our eyes observe are not the same as the point sources we deal with in undergraduate optics, they are made up of many different rays traveling in different directions and with different phases (i.e. running a little ahead of or behind each other.) So it's not enough to just capture "more light" into the system, it has to be in the right place, traveling at the proper angle, with the right amount of delay compared to the other rays.

Now look at my crude drawing of an eye looking at a triangle:

an eye regarding a triangle, with some light rays from the triangle entering the eye and some missing it

I have drawn the outermost rays of the outermost points of the triangle that enter the eye. I have also drawn some rays that go off in different directions that don't enter the eye. To make the image brighter, you would have to ensure that more of the rays that diverge from a single point on the triangle, also converge on the same point on the retina. But how? If the eye's iris and lens were infinitely large, then they would naturally converge there. But we don't have huge eyes, so we would have to use external lenses to achieve that. There is no way, though, to build a system of lenses that does that, without changing the rays that are already on the right track. You can't refract some of the rays and not others.

So what I definitely want to make clear is that the idea of "if the glasses can capture more light, then it will brighten the image" is a partial misconception. I say 'partial' because what coneslayer says is true: binoculars with a bigger aperture will produce a brighter image. However, this is only true if the brightness was already reduced due to a smaller aperture! Think of it this way: the absence of binoculars is equivalent to 1x binoculars with an infinitely large aperture!

Ultimately, the brightness of the image on your retina is limited by the natural aperture of your eye: your pupil. This is why your pupils get bigger in the dark. And you can't make your pupils any bigger than you already do instinctively, at least not without resorting to surgery.

By the way, I would like to thank everyone who contributed here for making it such a lively discussion. This forced me to think more carefully about the problem than I did at first, and get all my arguments in order.

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Could you give a little more detail? Why couldn't I have a double lens? The first might have some combination of magnification and focusing, and the second would undo the magnification and focusing, but leave you with some extra light. Or does the energy argument simply hold more generally? –  Mark Eichenlaub Nov 12 '10 at 8:00
    
More light from the same scene won't make it brighter. You might have have to capture live photograph of the scene and use some image processing techniques e.g. gamma correction giassa.net/?page_id=475 –  Pratik Deoghare Nov 12 '10 at 8:53
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Even with a double lens, the question still holds - where does the extra light come from? –  ptomato Nov 12 '10 at 9:52
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@MSalters, But there's no magnification, so the extra light hits your retina elsewhere (or even doesn't enter your pupil), giving you a wider view but at the same brightness. –  ptomato Nov 12 '10 at 11:59
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Well, that's the real question: is is possible to create a lens arrangement such that the extra light hits the retina at the same point? I'm inclined to say no, but can't find the math to prove that. –  MSalters Nov 12 '10 at 12:32
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Suppose you just start with an enormous magnifying glass (convex lens) and project the (inverted?)image onto a very fine ground glass intermediate screen. That would be plenty bright and small. It Seems to work with my reading glasses projecting an image onto a piece of paper.

I think something like this (with complex lenses separated by a ground glass screen) is sometimes used in the motion picture industry.

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I'm skeptical of this solution being able to increase the brightness without distorting the image. Can you elaborate? –  ptomato Nov 13 '10 at 22:12
    
If the flat projection screen is parallel to the midplane of the lens as usual, i.e. is perpendicular to the axis of symmetry of the lens, then there is no distortion, except maybe some minimal chromatic aberration, I suppose. The difference is the decoherence induced by the projection screen. The brightness is definitely increased; think of using a lens to start a fire. The lens will definitely image. On the other hand, this is only my own intuition. –  sigoldberg1 Nov 15 '10 at 6:17
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Others have discussed things around this, but doesn't night vision qualify as an answer to "glasses that make everything brighter" ?

There are 3 main categories discussed. Most likely you're only interested in the first category.

Image intensification

Image intensification technologies work on the principle of magnifying the amount of received photons from various natural sources such as starlight or moonlight. Examples of such technologies include night glasses and low light cameras.

Active illumination

Active illumination technologies work on the principle of coupling imaging intensification technology with an active source of illumination in the near infrared (NIR) or shortwave infrared (SWIR) band. Examples of such technologies include low light cameras.

Thermal imaging

Thermal imaging technologies work by detecting the temperature difference between the background and the foreground objects.

For more info on the first category, the article on Night vision device discusses current technologies. The article image intensifier goes even further. Apparently these primarily use photocathodes to intensify images. They are a bit different from the optical amplifiers discussed by Bernardo Kyotoku in that they rely on the photoelectric effect.

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+1 for listing photocathods. I was trying to remember the name of that. –  Bernardo Kyotoku Nov 12 '10 at 14:09
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It looks like passive devices work by taking non-visible light and making it visible, so I guess they don't make more light enter the eye, but they do certainly make things appear brighter. –  Mark Eichenlaub Nov 12 '10 at 17:55
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""Apparently these primarily use photocathodes to intensify images. "" This is typical misunderstanding of "youngers" in classic electronics. A photocathode is 1st not a device, and 2nd it does not "intensify". A photocathode produces free electrons into vacuum, but there is no gain with that. The process will be energy neutral at best. The electron picture is "intensified" by amplification . –  Georg Jun 6 '11 at 4:45
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You want an optical amplifier. It uses stimulated emission to amplify the light, like in laser, but without the feedback loop. Generally used for amplifying fiber optics signal to greater than 200 km. Making wearable glasses with this wouldn't be easy. Inverting electron population of a piece of glass with enough gain to be useful. As ptomato noted it is an active device, therefore in needs a power source to feed it. But I don't think your are concerned about this.

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Can the down voter justify his vote? –  Bernardo Kyotoku Nov 12 '10 at 17:30
    
I was actually interested in a passive device, but I found your response very interesting nonetheless. I'm not sure why someone downvoted it. –  Mark Eichenlaub Nov 12 '10 at 17:59
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I'm assuming that brighter means more light power hitting your retina. Focusing light increases the Intensity of light (Power per unit area), but there is no passive way to increase the light power that hits your retina passively.

I want to avoid an appeal to thermodynamics and instead try to reason this to you somewhat intuitively. The light power that hits your eyes, is essentially the amount of photons that are hit your retina. There are ways to increase the energy of each individual photon (there are special crystals that can double or even triple the frequency of light), but always at the expense of the number of photons (i.e. the power stays at most the same as it was before doubling). You are essentially asking for a way to passively increase the number of photons hitting your eye. The simplest way is to merely turn up the brightness of the light in the room. There is no magic trick you can do with a piece of glass that will spit out more photons than you originally had. Let alone one that will increase the amount of information that you have available to you.

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But I could make more photons hit my eye easily! I just have to make sure less photons hit someone else's eyes. –  Mark Eichenlaub Nov 12 '10 at 9:46
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