The "[ff35] equivalent f-number"

We are seeing frequently these days reference to the concept of the "equivalent f-number" of a certain aperture as found on a camera of a certain format size.

Briefly, that refers to the concept that, if we consider the use of a lens with a certain f-number on a camera with a certain format size, then the depth of field performance of that camera is comparable to the depth-of-field performance - conditioned on certain details of how we define "other factors being equal" - of a camera with a full-frame 35-mm format size using a lens of that "equivalent f-number".

If in fact we adopt this definition of "other factors being equal":

• focus of the camera at the same distance for both cameras

• focal length of the lens to give the same (angular) field of view with both cameras

• depth of field reckoning based on a criterion of "negligible blurring" based on a circle of confusion diameter limit (COCDL) that is the same fraction of the format size for both cameras


then:

For a camera with a format whose diagonal dimension (for example) is 1/1.5 that of the "full-frame 35-mm" format, the depth of field performance with an f/2.8 aperture will be very nearly the same as it would be on the full-frame 35-mm format size camera with an f/4.2 aperture.

Thus, in this situation, we might say that the f/2.8 lens on our assumed "small format camera" has an "equivalent f-number" [in the sense discussed here] of f/4.2.

I do not encourage this usage.

Best regards,

Doug

The matter of blur in the image of an object resulting from an object not being at the distance at which the camera is focused most often comes to our attention in one of these different contexts:

• Depth of field. Here, we ask the question: "For a camera focused at a certain distance, with a certain focal length lens and a certain aperture, over what range of subject distances is the blurring of the subject - because it is not at the focus distance - not over a certain amount?"


• Out-of-focus blur performance. Here we ask the question: "For a camera focused at a certain distance, with a certain focal length lens and a certain aperture, then for a (secondary) object at a certain distance (not the distance at which the camera is focused), what is the degree of blurring?


In the earlier article of this series, I discussed the concept (which use I disparage) of "[ff35] equivalent aperture". In the context I discussed there, this is the answer to this question: "What f-number aperture, used on a camera with a full-frame 35-mm size format, will give the same depth-of-field performance as will a certain f-number aperture used on a camera with a different (most often smaller) format size (all predicated on a certain definition of 'all other factors being equal')?"

Now we ask is there a corresponding concept that pertains to the matter not of depth-of-field performance but to out-of-focus-blur performance?

Yes there is, and it works the same way.

If the format of the camera of interest is 1/1.5 times the size of the ff35 format, and we consider an aperture of f/2.8 on that camera, then if, comparing the "smaller format" and "ff35 format" camera situations:

• the two cameras are focused at the same distance

• the focal length used in each case gives the same (angular) field of view

• the distance to the "out-of-focus object" of interest is the same

• we define the degree of blurring as the diameter of the circle of confusion created in the image from a point on the out-of-focus object, measured relative to the size of the format, then:

To get very nearly the same degree of blurring (as defined just above) we must use on the FF35-format-size camera an aperture of f/4.2.

Thus, in this sense, we can say that the "[ff35] effective aperture of the f/2.8 aperture on the smaller format camera is f/4.2".

Again, I discourage the use of this notation.

Conversely, were we to use an aperture of f/2.8 on the larger-format camera just as on the smaller-format camera, we would get blurring for which the diameter of the circle of confusion (measured relative to the format size) was about twice as great as on the smaller-format camera.

Best regards,

Doug