DOF optimization

[pesa]

I have tried to figure out the effect on DOF that sensor size has under a very specif set of circumstances.
The result seems odd so I thought somebody here might point out if I made any mistakes in my reasoning.

Of course a smaller sensor camera gives a larger DOF with equivalent lenses using the same fstop but since that will result in more diffraction on the cropped camera thats not very interesting.

The circumstanses are these: you are to take a picture of a specific view from a specific position (and hence with a specific angel) and make a print.
You want to find the camera/f-stop combination that gives you maximum dof while keeping diffraction minimal.
Assume the lenses are (close to at least) diffraction limited and only consider the print at the middle of the image.

Lets compare the result from a fullframe DSLR with a 1.5-crop one.
If both cameras have the same nr of pixels then the prints from a totally flat scene will have the same sharpness,right? (f-stop settings are assumed to not introduce diffraction)

Nikon D2X and Canon 5D have the same nr of pixels roughly.
Using http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm
I estimate that f-stop 11 would be the smallest aperture that doesnt introduce diffraction.
f-stop 8 looks very close to an equivalent for the Nikon D2X.
lets say the Canon has a 50mm lens and the nikon a 33mm lens

Using http://www.bobatkins.com/photography/technical/dofcalc.html I get theses results for the above setups and focus distance 5m:
Canon 5D 50mm 11.0   DOF=11.4m
Nikon D2X 33mm 8.0   DOF=15,6m

The difference is so big so I think its "true" even if I only estimated equivalent apertures for the D2X and 5D.
Is it?

What that would mean is that a garden photographer shold avoid medium format since reasonably they will offer even smaller DOF than a full frame DSLR.
Optimal should be a Canon 7D if you can find a (close to) diffraction limited lens for it.

[KeithB]

Your "garden photographer" probably does not have a lens good enough to make diffraction an issue.  I have always heard that f/8 was about the best spot where diffraction is minimized while lens performance is maximized.  While it should be sensitive to focal length, it should not relate to sensor size.  All the sensor can do is resolve fine enough details to see it.

[Bob Atkins]

Diffraction affects different sensor sizes differently because of the greater degree of enlargement required to get a print of a the same size.

You have to enlarge a 6mm x 9mm image a lot more than a 24mm x 36mm images to get, say, an 11x14 print. In fact you have to enlarge it 4x more. Therefore the 6mm x 9mm image needs to be 4x as sharp, which means that diffraction comes into play earlier since the diffraction limited spot size has to be 4x smaller.

When calculating DOF, the circle of confusion acts in a similar way. It has to be smaller for smaller sensors in order to maintain sharpness at a given print size.

While the numbers you have may be correct I don't think you have to restrict yourself to f11 on full frame of f8 on APS-C. You can go to f22 on full frame and f16 on APS-C without incurring too much of a penalty in sharpness due to diffraction. So in both cases in practice you can get more DOF than your numbers indicate without undue loss of sharpness due to diffraction.

[KeithB]

It has to do with the *resolution* of the sensor, not the *size* of the sensor.  What counts is the pixels being small enough to resolve the diffraction.  A 35mm 1 MP sensor is probably not diffraction limited, a 35 mm 25 MP sensor is.

[klindup]

I see this term difraction limited applied to sonsors. I am more used to it being applied to lenses and mirrors.  My question is how does the quality of the lens affect things?

Ken Lindup

[Bob Atkins]

I cover diffraction and it's relation to sensor size in this article:

http://www.bobatkins.com/photography/technical/diffraction.html

It's basically related to DOF insofar as DOF is defined by the size of the circle of confusion which will give acceptable sharpness. When looking at diffraction, there's a point at which the diffraction limited spot size is equal to the COF value, and at that point you're similarly at the limit of acceptable sharpness.

It's actually a bit more complex than that because DOF calculation assume geometric optics not wave a optics and so are only an appproximation and the intensity distribution in a diffraction limited spot isn't the same as that in a defocused spot, but there's a rough analogy between the two.

It's not really related to pixel count past some point because there's no sharpness advantage in sampling a blurred image at higher resolution than is needed and generally sensors do that. So a 24MP full frame sensor wouldn't give you any sharper images than a 10MP full frame sensor if you're shooting at f22 and the diffraction limited spot size is around 30 microns because both sensors would fully resolve the diffraction limited spot. However a 1MP full frame sensor would give you less sharpness since the pixel spacing in that case would be around 30 microns and would not be able to resolve the diffraction limited spot.

[KeithB]

I see this term difraction limited applied to sonsors. I am more used to it being applied to lenses and mirrors.  My question is how does the quality of the lens affect things?

Ken Lindup

At smaller apertures, diffraction is a physical hard stop for sharpness.  The physics dictates that a certain sized aperture will have a certain amount of diffraction.  A poor lens might lack sharpness for other reasons and never reach the diffraction limitation.  So, you need good glass to be "diffraction limited" over a wide range of apertures. 

The sensor only comes into it because at large pixel sizes the diffraction "blur" gets swallowed up by the large pixel, you simply don't have the resolution to see the diffraction effects.  At some point, the pixels are small enough to resolve the diffraction which pushes the problem out to the lens.

[pesa]

Thanks for all input, I appreciate you all taking time to respond.
However I dont see any argument that faults my result that a d2x would create the same sharpness in a print for in-focus objects but would render out of focus objects sharper than the 5D.
True, my choices for equivalent f-stops was to conservative but if you  change them to 16 for the D2X and 22 for the 5D the DOF for the D2X's DOF still is larger.
And if that is true, reasonably also this is true: If a 7D produces good enough (in focus) sharpness for a print you WILL get a better result (DOF wise) with that then with however fance medium format camera+back. Again given the same camera position and equivalent lenses.

Not that I would change my 5Dmk2 for any cropped sensor camera, I dont trust the lenses to be as good as "fx" lenses.
And remember, this was only ment to be a theoretical question,as bob atkins said 22 on a 5D will produce a DOF thats very good.

[Bob Atkins]

Lets compare the result from a fullframe DSLR with a 1.5-crop one.
If both cameras have the same nr of pixels then the prints from a totally flat scene will have the same sharpness,right?

Actually no. The reasoning behind this is that somewhat complex, but it is based on the fact that you have to enlarge the crop image more. Pixel count is only one factor. You have to also take into account where on the lens' MTF curve you are operating. Basically for the smaller sensor you are asking the lens to work harder because it's required to give higher resolution in order to compensate for the increased magnification. Another way of looking at it is that you are asking the lens to work in a region where its MTF is lower. There's a graph at http://www.bobatkins.com/photography/technical/mtf/mtf4.html which sort of explains this (though in a different context).

If you take this argument to its logical conclusion you'd come to the observation that a 14MP digicam would give you greater DOF and equal sharpness to a 14Mp crop sensor camera, a 14MP full frame camera and a 14 MP medium format camera. While the digicam will give you more DOF, it won't give you the sharpest images if all are used to make prints of the same size (assuming a reasonable size print, say 11x14" or larger).

[pesa]

>If you take this argument to its logical conclusion you'd come to the observation that a 14MP digicam would give you greater DOF and equal sharpness to a 14Mp crop sensor camera, a 14MP full frame camera and a 14 MP medium format camera.

Sure, as I stated from the beginning my conclusion is assuming that the lenses are (close to) diffraction limited (for its sensor).
I agree that that is very far fetched when i comes to digicams but that it's at least possible to make a diffraction limited lens for a cropped sensor (like 7D).

I would have preferred it if someone had presented something wrong with my reasoning, as a physicist with a lot of mathematics I'm accustomed to natural laws being size-independent. Possibly not so in this case

[Bob Atkins]

You still run up against the problem that with smaller sensors you are operating in higher spatial frequency regions of the MTF curve, and so MTF  drops (i.e. contrast drops and sharpness along with it).

Since the image sharpness (or SQF if you like) depends on enlargement and lens MTF, bigger is better.

This applies even in the case of a diffraction limited lens.

So the larger format image will be sharper in the in focus regions (less enlargement, higher SQF/MTF), but will have a smaller DOF.


In practice whether or not you see the increased image quality from the larger sensor depends on (a) how much larger it is (b) what the print size is and (c) which lenses are involved (since different lenses of zoom settings will be required to give the same FOV).

However all else being equal (which it rarely is), the larger sensor will produce the higher image quality in the areas in which the subject is in focus.