Sensor size, reducers / teleconverters, and DOF

Question

I understand the basic concept that a larger sensor doesn't change DOF. The change only happens when you compensate by moving close to the subject or using a closer focal length. This video would seem to confirm that: https://m.youtube.com/watch?v=ZUbU6exONdU

And yet, every DOF calculator I can find changes the results when I change the sensor size. Why? Is it because sensor size is part of the CoC formula?

Furthermore, I've tried two calculators that support teleconverters and reducers. One of them shows no difference in DOF and the other one does. Which is correct? Is it an issue of assumptions, where one calc is assuming that I'm factoring in the TC and one isn't? E.g. with a 2x TC, my 50mm is really a 100mm-- is one calculator assuming that when I say "50" I mean "50" and one is assuming when I say "50" I mean "100"?

Answer 1

And yet, every DOF calculator I can find changes the results when I change the sensor size. Why? Is it because sensor size is part of the CoC formula?

Yes, sensor size is part of the Depth of Field formula... the output image size, viewing distance, and visual acuity are also part of the formula; but not what the image contains.

The reason sensor size changes the DoField (and the CoC limit) is because a smaller sensor (negative) area has to be enlarged/magnified more in order to create the same size output.

And anything that increases relative size/magnification makes errors (softness) more apparent/visible, which is a reduction in the DoField. That includes shorter subject distances, longer FL's (and TC's), crop factor/cropping, larger image display, and shorter image viewing distance.

Those last two are often left out as variables (and from people's understanding) because they are standardized in the DoField calculation; with the image being viewed from a distance ~ equal to the image diagonal (which keeps its' size relative to the viewer constant)... but if the viewing conditions are not standard then that also changes the applicable CoC limit.

DoField is a perceptual thing and it does not exist as a fixed aspect of an image... Take an image of questionable sharpness and make it small on your monitor, it will look better/sharper with more that is within acceptable focus/sharpness. Then make it larger (magnify it) so it looks kind of bad and things that are not sharp/in focus are quite apparent. Now get up and walk away until it looks good again... that is DoField in action.

Changing sensor size does not change the Depth of Focus; which is the relative focus/point sizes as recorded at the image plane (the focus tolerance).

Edit to add: that video is confusing Depth of Focus/Focus tolerance as recorded at the image plane with Depth of Field in the final image/viewing condition. They are intricately related, but they are not the same thing.

Or to put it another way, because he cropped the FF sensor much harder (much greater magnification) in order to get the same remaining image as the 4/3 image, he created the same DoField in the end results... in this case the original format CoC is not applicable because that relates to enlarging the whole image area; they would instead have the same CoC limit because they are the same portion of the image circle projected by the lens. Cropping in post has the same effect as cropping at the time the image is taken (using a crop mode/crop sensor).

As I said at the beginning, the DoField formula does not care what the final image contains (output field of view)... he did the opposite. But, TBF; quite often people are really talking about DoFocus as an inherent aspect of an image (which it is) when they talk about/say DoField... they just don't know it.

Answer 2

I understand the basic concept that a larger sensor doesn't change DOF.

Just because you understand a certain proposition does not make it a correct proposition. In this case, your understanding is incorrect, given some unspoken assumptions that almost all DoF calculators make:

Images taken with the

• same focal length with the
• same lens at the
• same aperture from the
• same shooting position will be
• enlarged to the same display size

every DOF calculator I can find changes the results when I change the sensor size. Why?

Because every one of them assumes you will display all images at the same display size, usually 8x10 inches or 8x12 inches from a distance of 10 inches.

To get to the same display size an image from a smaller sensor must be enlarged by a greater factor than an image from a larger sensor.

The more you enlarge, the larger you make the same blur measured as it was projected by the lens onto the sensor.

Furthermore, I've tried two calculators that support teleconverters and reducers. One of them shows no difference in DOF and the other one does. Which is correct?

The Purple one.

Seriously, until we know what all of the other assumptions are for both of them, we have no way to properly answer the question.

Update in response to a comment from the OP:

Assume that I insert a teleconverter between the lens and camera. I change nothing else. Does DOF change?

Yes, for three reasons.

• Focal length actually changed with the addition of additional refractive surfaces between the front of the lens and the sensor.
• Because focal length changed but the entrance pupil size did not change, the f-number is also changed. For a 1.4X TC the f-number is one stop higher with the same size e.p. For a 2X TC the f-number is two stops higher. For a 0.71X reducer, the f-number is one stop lower (0.71 is the reciprocal of the square root of 2).
• Unless you refocus your lens after changing the focal length, your focus distance has also changed and your subject is no longer in focus.

Answer 3

Sensor size does affect DOF. I started insect photography about 18 years ago with a Fuji Finepix S7000, which had a 6.3 megapixel sensor and 6x zoom. It was very easy to use for insect photography as the small (1/1.7”) sensor provided good depth of field. When I upgraded to a digital SLR with APC sensor and 90mm macro lense it was some time before I achieved results that equalled the S7000. Depth of field with the 90mm is 0.5mm at closest focusing (ie maximum magnification).