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Format size and bokeh

Doug Kerr

Well-known member
In a recent musing here, I called attention to some empirical observations on the matter of the influence of sensor size on "image quality", without adopting any specific quantitative metric for "image quality".

James Lemon joined the discussion and aptly pointed out that there can be another, perhaps quite separate, motivation for the use of a larger sensor: its beneficial effect on the attainment of a desired bokeh effect.

To put a finer point on it, the use of a larger sensor facilitates the attainment of a larger blur circle diameter (compared to the overall frame size) for consistent distances and so forth. This is of course only one parameter of the bokeh, but usually an important one.

How does that happen, technically? At first glance that relationship seems counter-intuitive. If we increase the size of the sensor, then "all other things being equal", the diameter (on the sensor) of the blur circle from a certain out-of-focus object point keeps the same diameter. But on a fixed-size print (for example), the diameter of that blur circle becomes less, not more (because of the lesser sensor-to-print magnification needed for that situation).

The secret ingredient here is that, to attain the same framing, and thus the same field of view, we must, with a larger sensor, use a greater focal length. With "all other things kept equal", the diameter of the blur circle (on the sensor) varies as roughly the square of the focal length.

So if we double the sensor size, and double the focal length as required to maintain a constant field of view, then:

• The diameter of the blur circle on the sensor increases to about 4 times its size in the original smaller-sensor case (because of the change in focal length).

• The sensor-to-print magnification has to become about 1/2 what it was for the original smaller-sensor case (to get the same print size).

Thus, the diameter, on the print, of the blur circle is about 2 times what it was for the original smaller-sensor case.

Now, let's consider the matter of attaining a desired blur circle diameter on the print.

With everything else kept the same, if we double the f-number, the diameter of the blur circle goes to about half of what it was.

Thus, to attain a certain diameter of the blur circle on the print, if we have twice the sensor size, we can have twice the f-number that would be required in the original smaller-sensor case.

So, for example, an f/4 lens can give us, with the larger sensor size, the same blur circle diameter on the print that we would have to use an f/2 lens to get on the print with the smaller sensor.

All roughly, of course.

Best regards,