I have a Canon FD 28mm f/2.8 that I shoot on my entry-level Canon DSLR using an adapter. You have to set the aperture manually, but only every second aperture is marked: between ƒ/2.8 and ƒ/4, for example, there’s an unmarked stop on the aperture ring.
This got me curious: how can I determine the ƒ number of that middle stop? The obvious answer is that it’s ƒ/3.2, and of course the number doesn’t really matter; I should use that stop if it will allow me to make the photograph I’m trying to make.
For the sake of curiosity, though, is there a way to experimentally determine the ƒ number or aperture size when that stop is in use? (I’d prefer a software-based solution, not something that requires equipment beyond the camera and the lens.)
One method is to use the camera to make the measurement. This is actually surprisingly accurate, and is how most T stop measurements are done with a single reference measurement using a spectrophotometer.
- Take an exposure at a known (or even "known") aperture, like f/2.8
- Open the raw image in a software like RawDigger, or process it with DCRaw to get the unmanipulated image data. Find the intensity of the image in the center
- Stop the lens down and repeat, the ratio of the brightness of the two informs you about the aperture.
If you get e.g. 1024 at f/? and 2048 at f/2.8, you know you have exactly halved the exposure and f/? = f/4. The new aperture will be (old aperture) + log2(ratio of exposures).
You can also do this with Jpeg files, or images processed (opening counts as processing in this case) by e.g. Adobe Camera Raw. You just have to linearize them first, when the raw image is almost always already quite linear.
You could calculate it by hand. The ƒ# is actually a formula
N = ƒ/D where
N is is the ƒ#,
ƒ is the focal length and
D is the diameter of the entry pupil. So, if you take your focal length of 28mm and measure the diameter of the pupil,
D, you should get 8.75mm for ƒ/3.2.
The f/number (focal ratio) is derived by dividing the focal length by the working diameter of the aperture. The working diameter of a 28mm lens set to f/2.8 is 10mm. The working diameter of a 28mm lens set to f/4 is 7mm. The traditional ½ stop between the two is f/3.4. What will be the working diameter for this f/stop? Answer = 28mm ÷ 3.4 = 8.2mm Suppose the unmarked stop is one third f/stop smaller. This is f/3.2. The working diameter is thus 28mm ÷ 3.2 = 8.75mm Now the problem is this: how to find the actual working diameter? Not that easy but --- dismount the lens. Using a flashlight that is adjustable to a spot (parallel light rays exit). Shine the flashlight into the lens from the front. Hold a piece of paper about 25mm from the back of the lens. You will see a circle of light projected on the paper. This circle will be what is called the exit pupil. Measure the diameter of this circle and divide this value into the 28mm. You can check your work by setting the lens to some of the marked f/number settings.
You could also aim the camera at a uniform (mundane) target. At f/4 allow the camera automation to select an appropriate shutter speed. Now set the lens to the unmarked aperture setting. Did the shutter speed change? If so, what is the multiplying factor? Using this method you can figure out if the unmarked increment is 1/2 or 1/3 f/stop.