April 21, 2006 at 4 PM

Camera Dorkness

This is incredibly nerdy, but I just discovered something about the way digital cameras record exposure information which explains the confusing information you see in Flickr when you read the exposure details about a photo.

Flickr happily tells you the important stuff at the top (although the focal length is kind of meaningless if you don’t know how your camera’s sensor compares to “normal” 35mm film standards). But if you read lower down, it reports something called “Shutter Speed” as a fractional value. On the example, the shutter speed was recorded as 223/32, or 6.96875 in decimal form. It turns out this is how the camera records shutter speed, and the “real” shutter speed — 1/125 (or 0.008 seconds) — is mathematically calculated from this value. So what’s the actual relationship?

Well you’ll need your scientific calculators for this one: the number is the exponent of base 2 that equals the denominator of the shutter speed as a fraction.

In non-math-geek talk using the example of 1/125, you need to raise 2 to the power of 6.96875 to equal 125. (Well, almost — apparently my camera actually took the photo in 0.00798357147386 seconds, not 0.008.)

What the heck does 2 have to do with it anyway? Well, those of you who have used manual cameras will recall that one way you adjust the exposure on a camera is to double or halve the shutter speed. Using exponents of base 2 is the computer’s easy way of making this calculation.

So it’s fairly easy to translate these numbers (which are apex values) to the normal shutter speeds we’re used to. You might run across the untranslated number here and there, though most applications tell you the “exposure time”, which, ultimately, is the same thing.

The next question is: the aperture value is also shown as a similar number or fraction, rather than a standard f-stop like 2.8, 4 or 5.6. This time, the camera is actually recording the raw diameter of the lens pupil. You can calculate the f-stop by dividing the focal length by this diameter.

In fact, that’s all f-stop is: the ratio of the focal length to the size of the hole which lets light into the camera. This is why a higher f-stop means less light: because the opening is smaller relative to the focal length of the lens.

Why don’t f-stops get doubled or halved like shutter speeds? Well, because the diameter of the pupil is multiplied or divided by the square root of 2 (about 1.4), rather than being doubled or halved. That’s why the standard f-stop values on cameras are always the same: they are approximations of the exponents of the square root of 2 (1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22). These ratios are what allow double or half the amount of light to enter the camera.

It also explains an important principle behind crappy zoom lenses. The reason a cheap zoom lens can’t offer the same f-stop at 200 mm as it can at 20 mm is that it requires a diaphragm 10 times the size! That is, increasing the focal length by a factor of 10 lets in 1/10 as much light if the diameter of the opening stays the same. A 200 mm lens with an f-stop of 2.8 would be a real beast: it would have to have a diameter that opened to 71.4 mm.

Thus concludes your optics lesson for the day! Have I taken all the fun out of shooting photos yet?

Previously: Email Attachments in Mail

Subsequently: On Reviewing for Pleasure

April 2006
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