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I have just basic understanding of Physics from elementary school. But I still wonder, why after 10 years of cameras in cellphones, there is no "small-pack" optical zoom.

I think there should be no problem to make small, but still precise lenses. It should not be a problem to make small light sensor, while keeping large resolution. It should not be a problem to make tiny electric motor or servomotor to move the lenses and pack all that into 1 cm x 1 cm x 0.5 cm packing.

So what is the problem? I think there may be 3 explanations:

  1. There is some limit in physics (nature), that does not allow to do that (which one?)

  2. There is some limit in engineering, which makes tiny optical zoom extremely expensive.

  3. It might work, but nobody came yet with the idea to make tiny optical zoom.

Can you validate or disprove any of 1/2/3?

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Purely an engineering question. – dmckee Jun 20 '13 at 19:15
@dmckee I actually think there is a good physics-related answer for this question and was just writing one down. Basically, there are fundamental limits to how small you can make camera optics and still get acceptable noise levels, due to light quantization. Would you consider reopening? – jkej Jun 20 '13 at 19:24
@jkej Frankly I think the on-the-ground answer is cost, but if you want argue the physics of the situation I will leave it to others to decide on a close. – dmckee Jun 20 '13 at 19:27
This is part of my field of research - there is a bit of both factors - cost and technological limitations. (But, I may be misinterpreting the question). – user24901 Jun 20 '13 at 19:30
I doubt this is photon noise - there are plenty of photons to be had entering a few mm aperture, at least if you have a good ccd. I bet this has more to do with short focal length optics being difficult to manufacture (you can only work with the materials given to you by nature). – Chris White Jun 20 '13 at 20:04

The fundamental reason for this is that light is quantized. If it wasn't for this, it would in theory be possible to scale down any camera to an arbitraily small size. However, as a camera is scaled down, less light will enter it and therefore fewer photons. As the number of photons hitting a pixel goes down, the shot noise goes up (the signal-to-noise-ratio goes as $\sqrt{N}$, where $N$ is the number of photons). This means there are fundamental limits to how small you can make the optics for a camera and still get acceptable noise levels. What these limits are exactly depends on a number of parameters, like light conditions, resolution, field of view (i.e. zoom level), quantum efficiency of the detector. The mobile cameras that exist tend to have fixed wide-angle optics (i.e. large fild of view = more light), because that reduces the noise problem. It might be possible to build tiny cameras with optical zoom, but they would probably produce very low quality images for the high zoom levels.

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Thanks! :) You say, that camera size limits depend on a number of parameters. But I think taht you can still catch enough photons with a 3 mm lense and narrow field of view. Do you know anything about current camera technology? What is current "critique parameter" for making a tiny optical zoom? – Ivan Kuckir Jun 20 '13 at 19:58
While this argument is basically correct, it would help if you exhibited some sample calculation to show that current performance parameters are withing, say, an order of magnitude of being noise limited. – dmckee Jun 20 '13 at 20:04
If you take the direct light from the sun, you get about $10^{13}$ photons in a 1 mm lens, for a 10 ms duration. This would focus to just 100 to 1000 pixels ideally, so no problem of noise here. Now, if you take the flux from an equivalent portion the atmosphere you quickly a factor $10^5$ as it is way dimmer. Add to that a given quantum efficiency, a 100 times dimmer room, and I would not be surprised we get to about 100 photons per pixels. – fffred Jun 20 '13 at 23:58

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