# FPS and shutter effecting exposure time

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### #1 Jase Ryan

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Posted 28 June 2007 - 03:09 AM

Can someone help explain this to me? In another topic in this forum, David Mullen was talking about shooting at 6fps with a 180 degree shutter, making that 1/12th of a second per frame and shooting 6fps with a 45 degree shutter making it 1/48 of a second exposure time.

I?m having a hard time understanding how the shutter angle changes the exposure time. And what's the math to understand what shutter angle gives you how much exposure time?

Can anyone clarify this?

Thanks.
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### #2 David Mullen ASC

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Posted 28 June 2007 - 03:22 AM

The shutter is a spinning disk in a film camera, in front of the gate, with a pie slice hole cut out to allow light to pass through. Typical shutter is 180 degrees, or a half-circle (a full circle being 360 degrees.)

So if a half-circle is spinning in front of the gate, then the frame is being exposed for 50% of the time, or half the frame rate. So at 24 fps, the shutter is open for half of 1/24th of a second, so 1/48th of a second. If you close down that half-circle by half again, creating a 1/4 opening, then that's a 90 degree opening, half of a 180 degree opening, and you've cut the exposure down by half again, from 1/48 to 1/96 when shooting at 24 fps.

So I guess it's: 1/24 x 180/360 = 1/48

Or 1/fps x shutter angle/360 = shutter speed

So for 6 fps, that's:
1/6 x 180/360 = 1/12
1/6 x 90/360 = 1/24
1/6 x 45/360 = 1/48
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### #3 glen

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Posted 28 June 2007 - 06:41 AM

i've been getting to the nitty gritty of camera work and have found it easier to identify with engineering concepts, my background. here's how i work it out.

each full f-stop is a 3dB change in amount of light on sensor (film/ccd/cmos), but instead of log10 or ln (loge, log2.717...), they use log2, go figure..??

i think the lens mfg, should junk the f-stop and make it simple 0dB, 3dB, 6dB, 9dB....

anyway if want more light go down to
smaller f-stops, bigger aperture, shallow depth of field.

if you want less light,
larger f-stops, smaller aperture, deep depth of field (like video camera lens where everything is in focus from infinity to 10feet)

films are rated in how fast they will absorb light and make an image, ISO.

ccd/cmos are limited by the integration time and how fast they can get the charge or voltage off of the 'light bucket'.

two things control the image, fps and aperture, so two variables you can control. you can vary either one to get the same image or both, so reciprocity holds. if you keep the fps the same and change the f-stop is the same as keeping the same f-stop and changing the fps. this is probably not a good thing to do on the same roll of film, but i'm just guessing here.

if you want to get a mathematical handle on the aperture for abherations, comas, stygmatism, look at the bessel functions of J1(x)/x, or grab a copy of Born and Wolf.

just my .02

Edited by glen, 28 June 2007 - 06:45 AM.

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