An Investigation of E-M1 Focus Bracketing

In keeping with their usual practice, Olympus tells us absolutely nothing about how the focus bracketing function recently added to the E-M1 actually works. It would be useful to know how to adjust the focus bracketing parameters to obtain a specific depth of focus. I have now done some tests with the E-M1 and the mZD 60 mm f/2.8 macro lens to determine how the camera settings affect the range of the focus bracketing function.

There are four factors that determine the size of the focus bracket:

1. Set number of shots in the Focus BKT menu. Within a sequence the focus moves in equal size steps from near to far focus, so the size of the focus bracket is linearly proportional to Set number of shots.
2. Set focus differential in the Focus BKT menu. The size of the focus bracket is also linearly proportional to this parameter.
3. The lens aperture. This plot shows how the focus step size varies with lens aperture, expressed in internal Focus Count units (EXIF tag 0x0301), with the lens focused at infinity.. The size of the focus bracket in counts is linearly proportional to the lens f-Number.

4. The Focus Distance, defined by Olympus as the distance from subject to sensor. The distance from the front of the 60 mm lens to the sensor is specified as 82+19.25 = 101.25 mm (3.99 in). This is not a nice linear function like the other three. Focus Bracketing sequences were shot for a range of distances from the focusing target. For each frame the Focus Count was read from the EXIF data, producing the following two graphs:

For both cases a curve of the form

count = a (D + FL) / D² + b

was fitted to the measured data, where D is the Focus Distance, FL is the lens focal length (60 mm), and a and b are constants. Combining these two to eliminate the intermediate count variable produces the following result:

Or for those who prefer, here is the same plot in inches.

Except for short distances, the focus step is very nearly proportional to the square of the focus distance. Unfortunately, neither of these graphs is very readable. A reasonable approximation is given by the expressions

Focus Step (metres) = f-Number x (Focus Distance (metres) / 21.4)²

or, in inches

Focus Step (inches) = f-Number x (Focus Distance (inches) / 133)²

The total size of the focus bracket is equal to the focus step for the appropriate distance and aperture, multiplied by the Set number of shots and Set focus differential parameters.

To confirm that all the mathematical curve fitting has maintained its link to reality, the accuracy of the focus step prediction was spot checked at three focus distances (only three because it is a lot of work). A 10-frame focus bracketing sequence of a linear scale was shot at a 45 degree angle and the point of best focus in each frame was estimated by eye. The estimated distances were fitted to a straight line with the following results

Focus Distance  Predicted Focus Step  Measured Focus Step  Error
0.5 m                  1.57 mm                        1.54 mm                        -1.9%
1.0 m                  7.26 mm                        7.55 mm                         4.0%
1.5m                   17.1 mm                        16.6 mm                        -2.9%

Everything so far has been about the change in focus. The other factor that needs to be considered is the variation of depth of field with distance and aperture.

Searching for "depth of field calculation" brings up a number of DoF formulae and DoF calculators. Comparing a few of them showed that they produce slightly different results for the same inputs! This plot was produced using the formulae from Wikipedia and the commonly accepted Circle of Confusion for Four-Thirds of 0.015 mm.

More interesting is this plot showing the ratio of DoF to Focus Step for a focus differential of 1.

It appears that Olympus intended the depth of field to be 3 times the minimum focus step. I don't know if the rise in DoF at the ends of the curve is real or a consequence of the approximations made in the analysis. In any case, it is safe to assume that the depth of field is at least 3 times the step size divided by the focus differential.

Here is an example showing how the focus differential affects the image. These are 100% crops of some plant thing, all made from the same 16-frame focus bracketing sequence shot with a focus differential of 1. They were assembled using Zerene Stacker, taking every frame, every second frame, every third frame, and every fourth frame respectively.

To my (not very good) eyes there is a barely perceptible loss of quality as the focus differential goes from 1 to 3, but a more noticeable difference between 3 and 4.