# DOF and Sensor Size



## bdunbar79 (Jul 1, 2014)

Sorry guys, I tried to search for this topic on here and I couldn't really get exactly what I needed so I will post the question but if you know the link to another thread that already discussed this thoroughly I would really appreciate that too. 

I'm very familiar with the mathematics behind focal length, aperture, DOF, and CoC. However, I keep getting the question on whether sensor size really does affect DOF objectively. I don't think it does, in that I think it is a subjective matter, but I cannot answer them succinctly. 

I don't want to take up too much of anyone's time explaining this, but I would really love to hear someone else's technical explanation of this or at least be linked to one, preferably from this site since the knowledge on here is incredible. 

Thanks!


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## mackguyver (Jul 1, 2014)

bdunbar79 said:


> Sorry guys, I tried to search for this topic on here and I couldn't really get exactly what I needed so I will post the question but if you know the link to another thread that already discussed this thoroughly I would really appreciate that too.
> 
> I'm very familiar with the mathematics behind focal length, aperture, DOF, and CoC. However, I keep getting the question on whether sensor size really does affect DOF objectively. I don't think it does, in that I think it is a subjective matter, but I cannot answer them succinctly.
> 
> ...


I'll leave the technical details (and resulting arguments) to others, but I think the way to look at this is in practical terms, say shooting a portrait. If you have a crop sensor and use a roughly equivalent focal length (i.e. 50 f/1.4 @ f/1.4) from the same distance as someone shooting with a full frame and a 85mm (@f/1.4), the full frame will have shallower DOF. The crop would be equivalent to shooting at f/2[.24] instead of f/1.4. If you change any of those variables, obviously it would be different, but that's how I would explain it.


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## bdunbar79 (Jul 1, 2014)

One question and well-known example is the through DOF calculators online. If you select a subject distance say at 100 feet, 1Dx, 50mm lens, f/4, you get a DOF. You merely change cameras to the 7D, and get quite a different DOF. Everything else is the same, you haven't moved and your subject hasn't moved, lens hasn't changed, but you will most certainly get a different DOF calculation because the CoC is different. I guess that's conceptually where I am not great. Thanks.


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## Sporgon (Jul 1, 2014)

I think basically sensor size / format size only effects dof when you put a lens on


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## viggen61 (Jul 1, 2014)

This can be so confusing, but it really should not be.

For a given lens, subject and _distance to that subject_, the DoF is exactly the same whether your EF lens is mounted on a full frame camera, APS-H camera or APS-C camera. But because of the narrower angle of view of the APS sensor sizes (aka "crop factor"), you do not see the same framing in each camera. So with a full face portrait, the APS-H might cut off the ears, and the APS-C much more than that.

Where the DoF changes is when you want to achieve exactly the same _framing _between disparate sensor sizes. Since the APS-size sensor image looks like a "zoomed in" version of a full frame image (due to the narrower angle of view), to achieve the same image in both sensors corner to corner, you need to either back away from your subject with your APS camera (increasing the distance to the subject), or zoom out, shortening the focal length of your lens. Either one of these variables then changes the DoF result in the image and mathematically when changed in the formula.

But, as with most comparisons between full frame and crop, unless you carry both with you, and need to make a decision on which to use in a given situation, there's little reason for most of us to worry over it on a daily basis.


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## neuroanatomist (Jul 1, 2014)

viggen61 said:


> This can be so confusing, but it really should not be.
> 
> For a given lens, subject and _distance to that subject_, the DoF is exactly the same whether your EF lens is mounted on a full frame camera, APS-H camera or APS-C camera.



Unfortunately, it _is_ confusing, and you seem to have fallen victim to that (circle of) confusion. :-[

For a given lens, subject, distance, *and aperture*, the DoF is _not_ the same for different sensor sizes. In fact, in that case the DoF is actually deeper as sensor size increases (e.g., 100mm f/2.8 at 5 m, a FF sensor has deeper DoF than APS-C). If you match framing, changing the distance overcomes the effect of the circle of confusion (CoC), and you get shallower DoF with FF. 

Basically, DoF is determined by magnification and aperture. When comparing sensor sizes, we generally assume a fixed output size and a fixed viewing distance (both of which affect DoF). For a fixed output size (e.g., an 8x10" print), the image from the larger sensor requires less magnification, which means deeper DoF (all else being equal). The standard CoC values used in DoF calculators account for output size and viewing distance by holding them constant.


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## bdunbar79 (Jul 1, 2014)

Thanks neuro. I'm not a specialist in this area and I just couldn't come up with the relationship with output size. Thanks again!


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## jdramirez (Jul 1, 2014)

I want to stay far away from this one... it just give me a headache. 

I know the answer is yes sensor size does affect DOF... and not just when you are framing the image similarly... and I know magnification has something to do with the whole DOF issue... but by george... that is about where my pretty smart brain take a rain check.


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## Lee Jay (Jul 1, 2014)

Sensor size doesn't affect DOF, except for when it does. 

It does when you make the assumption that the final results will be viewed at the same final size. This means a smaller sensor needs a larger enlargement ratio, which makes CoC smaller, which makes DOF smaller. But it's the enlargement, not the sensor size, that changes the DOF.

Personally, I think the only way to compare is at constant final size, and thus smaller sensors have shallower DOF at the same f-stop, focal length, and subject distance.

I even created a sample just to demonstrate this point. It's all the same shot, just cropped differently.


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## Kit. (Jul 1, 2014)

bdunbar79 said:


> I'm very familiar with the mathematics behind focal length, aperture, DOF, and CoC. However, I keep getting the question on whether sensor size really does affect DOF objectively. I don't think it does, in that I think it is a subjective matter, but I cannot answer them succinctly.


If you know the math behind DoF, I will only address the physics.

DoF is a subjective parameter. It depends on the amount of loss of detail that people are willing to tolerate in the resulting picture.

If we disregard cropping and pixel quantization, the image that is rendered by the camera is determined by the absolute aperture and the distance to the subject.

Cropping decreases the angle of view, and thus the amount of _total_ detail present on the picture. The out-of-focus loss of detail that would otherwise be unnoticeable on more _detail-rich_ picture, starts to be apparent with cropping.


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## neuroanatomist (Jul 1, 2014)

@ Lee Jay – great explanation and example!


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## dougkerr (Jul 2, 2014)

The question really has to be, "What is the effect of sensor size on DoF *all other factors being equal*."

And we have to decide what "all other factors being equal" is to mean.

A reasonable set of definitions starts with:

• The focal lengths on the two cameras will give comparable field of view.

• The two cameras will be focused at the same distance.

But there is one further wrinkle. Depth of field isn't an actual optical phenomenon. It s how we choose to look at an optical phenomenon. The actual question is, "considering the setup, over what range of object distances will the image not be blurred by more than a certain amount". And we have to decode what that certain amount is.

We do that, numerically, by placing a limit on the diameter of the blur figure (circle of confusion) that is created on the focal plan by a point on the subject when the subject is not in perfect focus. I call that the circle of confusion diameter limit (COCDL). It often (but misleadingly) called the "circle of confusion". (That's like calling the largest tire size you care will accept the "tire".)

There are two approached we might use to pick a COCDL. We might pick the COCDL that is essentially the diameter of a blur figure that the eye can just recognize as blurred. This of course requires us to assume that the image is "printed" at a certain size and viewed from a certain distance.

Often this might lead us to choose a COCDL of perhaps 1/1400 of the diagonal size of the sensor.

Or we might say that the COCDL should be chosen as the diameter of the blur circle that will just degrade the resultion of the camera from its resolution for an in-focus subject.

This might, for example, cause us to choose a COCDL or perhaps twice the sensel pitch of the sensor.

In any case, as we visualize moving from one sensor size to another, we need to decide how we will change our COCDL to follow.

Now, having made all those preparations, we are prepared to calculate the "smaller sensor" and "larger sensor" DoF values and compare them.

But for either approach to choosing our COCDL, and if we use the"degradation of resolution" approach to choosing our COCDL there is no dramatic difference in sensel pitch between the two cameras, then the DoF will be less for the larger-sensor camera. How much less depends on exactly what we do about the COCDL.

Best regards,

Doug Kerr


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## funkboy (Jul 2, 2014)

These LL articles should help:

http://www.luminous-landscape.com/tutorials/understanding-series/dof.shtml
http://www.luminous-landscape.com/tutorials/understanding-series/dslr-mag.shtml

That's where I learned how this stuff works...


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## tdrive (Jul 2, 2014)

I had a lot of trouble wrapping my head around this too. I did read somewhere this explanation that made sense.
Cameras with smaller sensors have a larger DOF to a full frame because it is dictated by ACTUAL focal length, NOT EQUIVALENT. As an example on a compact @ F2.8 it's roughly equivalent to a full frame camera @ F11


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## jdramirez (Jul 2, 2014)

tdrive said:


> I had a lot of trouble wrapping my head around this too. I did read somewhere this explanation that made sense.
> Cameras with smaller sensors have a larger DOF to a full frame because it is dictated by ACTUAL focal length, NOT EQUIVALENT. As an example on a compact @ F2.8 it's roughly equivalent to a full frame camera @ F11


Aye... that be true matey... but at equal distances from ye subject, thar full frame hast mo dof.


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## weixing (Jul 2, 2014)

Hi,
I usually just remember this:
Same FoV(which mean same distance and different focal length(eg. 35mm on APS-C and 50mm on FF) or different distance (FF closer than APS-C) and same focal length) and same F-Stop, FF has shallower DoF than APS-C.

Have a nice day.


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## bdunbar79 (Jul 2, 2014)

Thank you to everyone who replied. Doug Kerr's and Lee Jay's explanations were awesome. I always appreciate when people take the time to help me.


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