I can use a DoF calculator, or crunch the heavy math by hand if I really want to know exactly what my DoF is going to be... but most of the time knowing exactly is actually overkill, and taking the time to pull out a DoF calculator is impractical. I'm wondering if anyone knows of a 'rule of thumb' that is common for quickly figuring out a rough estimate of what my DoF will be when I'm in the field...
Answer
Depth of field formulas are indeed complex and nonlinear, but they still afford useful rules of thumb. For medium subject distances (not too close to the lens, compared to its focal length, and not so far away that the DoF extends to infinity), the DoF is approximately proportional to:
The f-stop.
The square of the distance.
The inverse square of the lens's focal length.
This assumes a given standard of blurriness (usually quantified as the diameter of the circle of confusion), which depends on your sensor, intended magnification of the ultimate images, your visual acuity, and many other things. For this reason I'm not going to recommend one rule for everyone, but rather will explain how to develop your own rule(s) for your own purposes.
To make this aproximation work, you only need to know the DoF for a standard f-stop, a standard distance, and a standard lens, chosen in advance by you. For instance, let's set the diameter of the circle of confusion to 0.02 mm (a fairly small size, but not uncommon). Then, using an online DoF calculator, we obtain a depth of field of 1.59 m = 5.2 feet for a subject at 10 meters from a 100 mm lens at f/4. Using only these data (10m, 100mm, f/4, 5.2 ft), we can now anticipate the DoF for any similar exposure combination by making a series of simple adjustments. For example,
Doubling the f-stop from f/4 to f/8 should double the DoF from 5.2 to 10.4 feet. (Actual value: 10.66 feet.) Halving the f-stop from f/4 to f/2 should halve the DoF from 5.2 to 2.6 feet. (Actual value: 2.59 feet.)
Now, continuing from f/2, halving the subject distance to 5 meters should divide the DoF by four, giving 2.6/4 = 0.65 feet. (Actual value: 0.66 feet.)
Halving the lens's focal length from 100 mm to 50 mm should quadruple the DoF. Continuing from the previous result, it should go from 0.65 ft back to 2.6 feet. (Actual value: 2.62 feet.)
In this example we have worked out the DoF at 5 meters for a 50 mm lens at f/2 using simple multiplications and divisions and we have made only an inconsequential error of less than 1% in our estimate.
Thus, if you choose a standard combination of focal length, f-stop, and subject distance close to those about which you are usually concerned, you need only memorize a single DoF value which you can rescale as appropriate in the field.
Typically, you might work out the DoF for a trial shot and then use this rule of thumb to anticipate the effects of proposed changes (of distance to subject, aperture, and even choice of lens) on the DoF. This needn't even involve a calculation. For example, after examining an initial shot closely, you might decide you need twice the depth of field (even though you don't know exactly, as a number, what the current DoF really is). Your options therefore include:
Double the f-stop. (Watch out, though, for diffraction blurring once the aperture gets smaller than a few millimeters!)
Move back from the subject to increase its distance to the lens by about 40% (1.4^2 = 2 more or less).
Use a lens of about 0.7 times the focal length (0.7^2 = 1/2 more or less). E.g., change from a 50 mm to a 35 mm lens.
Although the first option is so quick you might forgo any calculation and just try it, the next two could be sufficiently cumbersome or time-consuming that having this rule of thumb might just be useful ;-).
Note that the approximation breaks down for macro photography and landscape photography. In both cases one usually has more time to prepare and test shots so perhaps having a quick rule of thumb is less important in those situations.
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