Started Jul 9, 2013 | Questions thread

Jeff wrote:

Pyramids, Hats, and Coffee Filters, flux capacitors ... we can call it the pointy head approach to exposure, lol.

Rereading what I wrote above, I realize now that my terminology was a bit confusing. So here's another cut at it, hopefully a bit clearer and using somewhat more standard terminology ...

Use B to refer to the scene brightness. Think of it as the light incident on the scene. Using N for f-number, t for shutter duration, and S for the sensitivity of the camera to light (a function of the sensor, camera electronics, and camera settings), then

B = N^2/(t*S)

The idea here is that to achieve a properly exposed image. A more brightly lit scene (larger B) requires a larger f-number (i.e., smaller f-ratio), a shorter shutter duration, or lower S.

For this to work as an honest engineering equation, B, N, t, and S need consistent units. If you want to use SI units to measure luminance and ISO to measure S, then you'd throw in a conversion factor, but that's not necessary for what we're doing. Just accept B as scene brightness measured in weird but consistent units.

The next step is logarithms. Why logarithms? We talk about logarithms all the time in photography by referring to N, t, or S in terms of equivalent 'f-stops'. That's the same as measuring these quantities in base 2 logarithms.

So fooling around a bit with high school algebra,

log2(B) + log2(S) = log2(N^2) + log2(1/t)

On the left side are scene brightness and ISO. On the right are f-number and shutter speed (1/t being shutter speed, the inverse of shutter duration). Using log2 means that we're measuring these quantities in terms of 'f-stops'.

The right side is the Exposure Value (EV).

The equation is a like a titter-totter. Changes on the left have to be matched by changes in exposure value on the right. One stop more brightness or a one-stop increase in S on the left has to be balanced on the right by a one stop increase in f-number or a one-stop increase in the shutter speed.

The exposure titter-totter

Another way of writing this is

Bv + Sv = Av + Tv

where Bv is the 'scene brightness value', Sv is 'Sensitivity value' of ISO, Av is 'Aperture Value', and Tv is 'Shutter Speed Value'. All measured 'f-stops'.

Creatively, you make the left side larger by using more real light. Or if that's not possible, artificially boost what light you do have by increasing Sv (ISO) in the camera. Unfortunately, Sv comes with noise.

On the right side, you can use that 'light' to increase depth of field by making Av larger, or freezing motion by increasing Tv.

You're free to make creative tradeoffs so long as the titter-totter is kept in balance.

Very nice Jeff and a good explanation of why the use of logarithms, especially binary logarithms are important. Photography has always and necessarily made use of this, though your simplified Bv + Sv = Av + Tv might not be the best way to close those expressions, it does work in a certain bizarre way I suppose. I love it for its simplicity. Moreover Titter-totters are more rhythmic than conic sections, the latter being better suited for sailing vessels.

(n2log n) is way less cumbersome than n^2. Everyone knows that. Next someone will toss in an N^n problem and we will really be in trouble in an NP Complete world. LOL

Just  having a little fun. .. 8=)

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Cheers, Craig
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