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Today we see ~100,000 fps cameras for hyper slo-mo.

Is there a physical limit for frames per second for a camera? Speed of light maybe? How?

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2 Answers 2

I used a 8 million fps camera 25years ago - and the technology was old even then. I think purely electronic cameras can beat this by a factor of 10x today.

Those cameras used a rotating hexagonal mirror and an arc of film, each frame behind an individual lens. As the mirror rotated it reflected the incoming rays onto each lens, and so each frame of film in turn. The only moving part was the mirror and that ran on helium bearings at something like 10,000 rps. IIRC 200 frames filled 90deg of the arc.

So in 0.25 * 1/10,000 of a second the camera generated 200 individual frames, (might have another factor of 2x because the reflection angle is twice the rotation angle)

The main difficulty with these cameras was that one revolution (0.1ms) later the images would be overwritten by the mirror again. Designing a shutter that closed in that time was interesting.

This is the same principle as the ligthhouse paradox. So if you were to make the arc of the camera large enough (say on the moon) and had a fast enough rotating mirror (and enough light!) you can get essentially unlimited frames per second.

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Here is some footage at $10^{12}$ fps, fast enough to show the movement of a pulse of light. It's actually a bit of a cheat, since they're actually using lots of puslses of light (one per frame) rather than just one, but still it's incredibly impressive, and amazing to watch. –  Nathaniel Oct 9 '13 at 5:57
    
Doing very short exposures is (relatively) easy - using short pulses of right down to the point where the uncertainty principle wins. –  Martin Beckett Oct 9 '13 at 15:49

Martin Beckett is correct that frame rates can be much higher than 100,000 fps. In this supplement to his perfectly good answer, I want to point out that principle there is a fundamental limit to the number of frames per second that can be captured. It's just that the limit is incredibly high.

The limit is due to the fact that a higher frame rate means that the shutter has to be open for a shorter period of time for each frame, which means that less light hits the photosensor array. You can counter this by making the sensors more sensitive, but eventually you'll get to the point where only a few photons make it through the aperture before the shutter closes on each frame.

In this case, you wouldn't see a scene, but just a few bright dots where the photons hit the detector. Of course you can combine many such images to produce a full picture, but then that defeats the point of having such a high frame rate in the first place. The uncertainty principle also comes into play at this point - if you want to know exactly when the photon arrived, it becomes impossible to know its energy (i.e. its frequency), so there's a point at which colour photography would be become impossible.

The only way to solve this fundamental problem would be to light the scene more brightly, so that there are more photons around to build up an image with. But sooner or later you'll get to the point where the light has to be so bright that it destroys whatever you're trying to film. You can also use a larger aperture, but that makes it hard to keep things in focus, and there's a limit to how much it will help you, since any given scene only gives off so many photons to be captured.

A perfectly efficient $100\:\mathrm{W}$ light bulb would give off $100\:\mathrm{J}$ per second of light, made of photons in the visible range. Each photon has an energy given by $hf \approx 6\times 10^{-34} \times 5 \times 10^{14} Hz \sim 10^{-21}\:\mathrm{J}$. ($h$ is Planck's constant and $f$ is the frequency of the light.) This means that the bulb gives off about $100/10^{-21} = 10^{23}$ photons per second. So if the camera was pointing directly at the bulb you would still see a grainy low-res image with a frame rate of up to, say $10^{17}$ fps, which gives you a million photons to build an image out of on every frame. This is an incredibly fast frame rate, much faster than has been achieved with present technology. Even light moves sluggishly at this frame rate. If you point the camera directly at the sun, with a $\sim 1\:\mathrm{m^2}$ aperture, you could go 1000 times faster than this. But to get much faster than that there's no choice other than using brighter and brighter lights.

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Usually ultra high speed is of high energy events or you can use laser pulses to provide quite a lot of light in a billionth of second –  Martin Beckett Oct 9 '13 at 15:52
    
@MartinBeckett sure - I just wanted to make the point that there is a fundamental limit to how short an exposure can be, even if it's probably shorter than anyone might have a practical reason to use. –  Nathaniel Oct 10 '13 at 1:14

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