# How does Depth of Field change when changing distance to account for cropped sensor?

I know that if I take my full frame lens (for example 50mm/1.4) and put it on an APS-C sensor, the field of view (FOV) changes. So what I will do is move back to retain the same subject magnification. However by doing so the depth of field changes. But by how much? Would the DOF be increased by a factor of 1.5 as well?

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cue @mattdm in 3..2...1 ;) - I think this is answered here? - photo.stackexchange.com/questions/10079/… – MikeW Mar 19 '13 at 4:46
But that answer is slightly different. It assumes you use a different lens and the math works out that you have to multiply both the focal length and the aperture. But the question here is, if you use the same lens and moved backwards. – erotsppa Mar 19 '13 at 5:08
How about this then? - photo.stackexchange.com/questions/15569/… - using the same lens on micro 4/3 vs full frame camera? – MikeW Mar 19 '13 at 5:32
And this one - photo.stackexchange.com/questions/10079/… – MikeW Mar 19 '13 at 9:31
Yes, it depends on how you ask the question. If you take the smaller sensor pane only and don't change anything else, then the DoF will even be reduced. (Per definition you measure DoF on the print.) But that is not the real thing. You don't want to compare that. You want to compare a certain image that is taken with small film (24x36) with the same image taken with crop. That means the same position (for the same perspective), same distance to the sujets and adjustments to the focal length. The different (shorter) focal length (lens) will cause an increas of the DoF. – Hermann Klecker Mar 19 '13 at 9:31

The DOF will increase, but not entirely with the crop factor, however, I just learned that it converges to that in certain cases.

Your distance increases by the crop factor, but the DOF doesn't follow a linear curve, which means that the increase on DOF as a factor depends on the distance you start at. An important factor is Circle of Confusion which is the real world "blur" that is projected on the sensor plane. How you view this will affect your aim for it.

When viewing in pixel space, you need to worry about the CoC relative to pixel cell size multiplied by magnification (viewing "fit to screen e.g. at M=0.25, your CoC may be 4x4 pixels). Ie. din't worry about sensor size. But if you view on a print in real world, you need to worry about the magnification given by print size/sensor size, and in this case you magnify crop factor more. So you work out the CoC as a function of print size and view distance, and divide by Magnification , where Mcrop = Mff*1.6. Thus CoCcrop = CoCff/1.6. So the figure below is for the print situation where you use the crop factor on CoC.

Here is the complex nature of how the DOF evolves with distance:

With dof master you can do some numbers on crop and fullframe camera. If you start from close range,10cm, the Dof factor is 3.5 if you keep the same CoC, 2.5 if you pick a Canon FF vs a Canon 1.6x crop, with 50mm 1.8. As you increase the distance, the numbers evolve like this:

``````10cm FF vs 16cm Crop: 2.5
1m FF vs 1.6m Crop: 1.75
10m FF vs 16m Crop: 1.63
50m FF vs 80m Crop: 1.66
``````

(These numbers normalize the CoC to the sensor.)

So it seems even though the formula is not linear, it converges to a linear segment at higher distances, with the crop factor (assuming it is correct to normalize the CoC). Definition of high is distance >> focal length.

You learn something every day..

I looked further into it, and I used the formula for DOF with distance >> focal length. I insert CoC (c) and distance (s) for crop sensro with the same lens, and in the case of print size based CoC, where crop CoC = FF coc / 1.6 and crop distance = ff distance *1.6:

And for Nikon replacex1.6 with x1.5.

I am amazed. But remember the formula is for the special case of s >> f. And the CoC factor for screen size is not the crop factor, unless you compare a FF and Crop sensor with equal resolution.

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Basically it's 1.5 factor as well as it seems from the graph. – Robert Koritnik Mar 19 '13 at 7:30
to get that approximate factor they normalize the CoC - if you keep the same CoC and just change the distance by factor 1.5, it changes. Im not convinced that it should - I have to investigate a bit more. – Michael Nielsen Mar 19 '13 at 8:00
ok , I worked it out on my bike, haha. When viewing in pixel space, you need to worry about the CoC relative to pixel cell size multiplied by magnification (viewing "fit to screen e.g. at M=0.25, your CoC may be 4x4 pixels). Ie. din't worry about sensor size. But if you view on a print in real world, you need to worry about the magnification given by print size/sensor size, and in this case you magnify crop factor more. So you work out the CoC as a function of print size and view distance, and divide by Magnification , where Mcrop = Mff*1.6. Thus CoCcrop = CoCff/1.6. – Michael Nielsen Mar 19 '13 at 9:17
So for us dummy out there, we can safely say that for cases where distance is > FL, the DOF is increased by the crop factor? – erotsppa Mar 19 '13 at 18:14
when it is "a lot bigger" and less than hyperfocal distance, yes :) – Michael Nielsen Mar 19 '13 at 18:32