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Depth of field

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Ever wondered why consumer D-SLRs (with smaller sensors) have a greater DOF than full-frame cameras when the framing is the same?

True, but only at low magnifications and identical f-numbers!

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Right. I guess the tutorial didn't talk about that. Perhaps I should have been more specific... :unsure:

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I think the tutorial explains correctly what people experience with digital. The danger comes in extending that experience to macro and coming to the wrong conclusion. For wide angle it's on the money.

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Several things are different with macro. First, the rear DOF and front DOF are virtually the same. Second, you must use effective f-numbers which are magnification compensated (a lens geometry issue). Third, best DOF is accomplished at the smallest physical apertures. Because of the reduced COC, diffraction limited maximum aperture of a cropped sensor will be reduced by the crop factor.

 

Let's say we're comparing a 1Ds to a D100. For the 1Ds the diffraction-limited f-number is f/32. The equivalent for the D100 is f/22. In order to compare the macro capabilities properly we must use f/32 vs. f/22. Using the D100 at f/32 results in diffraction distortion greater than the COC. It doesn't really matter whether you accept f/32 or f/22 or f/16 as you smallest aperture for full frame so long as you divide it by the crop factor to get the equivalent.

 

Cutting to the chase, you can compare two cameras in macro mode using the following formula:

 

DOF2/DOF1 = (x + M1) / (x * (1 + M1))

 

where M1 is the magnification of camera 1 and x is the crop factor of camera 2 relative to camera 1.

 

At a magnification of 1:1 for the 1Ds, the D100 has only 5/6 the DOF. At 2:1 it is only 7/9. At very low magnifications the equation breaks down because the front and rear DOF's are no longer the same. This doesn't matter because you aren't using f/22 by then anyway. In the far field you're using identical f-numbers and the tutorial explanation holds.

 

The differences are modest for a 10D/D100/S2 compared to a 1Ds but they are much greater when you compare a 1Ds to a digital P&S. A 5050 is 5/8 at 1:1 effective and 1/2 at 2:1 (if it could do that at all). The common belief is that cameras like the 5050 have superior DOF but that's only true for wide angle. All this is for ideal lenses. Real lenses will probably further favor the SLR's over the P&S cameras.

 

Finally, you may wonder where this weird adjustment factor comes from. It has to do with the physical geometry of the lens, subject, imaging plane and pupil. This same issue is responsible for requiring bellows correction, and while I don't fully understand it, that's the cause of the gradual lessening of DOF for smaller sensors. I would welcome a better explanation of what's going on. I got all the information above from the photo.net lens tutorial website although I cranked a little algebra to get it in this form.

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Thanks, Craig!

 

My brain is heating up trying to understand this with my rudimentary knowledge of optics. I think I get part of it.

 

But my question is -- why is it valid to compare the same f-number in wide-angle, but not at macro range? The tutorial compares equivalent f-stop and focal length, but your macro comparison is comparing "best" DOF, given crop factor and associated diffraction-limited maximum aperture, correct?

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For wide angle you usually choose aperture and shutter settings for exposure only. If you are trying to control DOF it may be to limit it rather than increase it. Aperture settings are rarely set small in this case and if two cameras have matching ISO ratings they'll be used with the same aperture/shutter for a given shot.

 

In macro you are frequently trying to achieve large DOF so you'll stop down as much as you can (until you have enough). In this case a smaller sensor can't be stopped down as much because the COC is smaller. Anything that scales COC will scale acceptable diffraction likewise.

 

So, in other words, aperture is chosen for exposure in wide angle while it's chosen for DOF in macro. That's why you compare them differently.

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It makes sense that you are usually trying to maximize DOF in macro photography.

 

But I am wondering whether the tutorial's message holds when fixing the aperture to be the same f-stop for macro photography, in both cases.

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The tutorial compares equivalent f-stop and focal length, but your macro comparison is comparing "best" DOF, given crop factor and associated diffraction-limited maximum aperture, correct?

I forgot to answer this. Yes, that's correct. In macro you're not worried about balancing strobe with ambient light so you fix your shutter, set your aperture based on DOF and adjust your strobe power to get the exposure right. Best aperture will vary with the COC and therefore the imager size.

 

In wide angle you set aperture based on ISO and ambient light strength so imager size doesn't matter. The tutorial makes perfectly valid assumptions---just not useful for macro.

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It makes sense that you are usually trying to maximize DOF in macro photography.

 

But I am wondering whether the tutorial's message holds when fixing the aperture to be the same f-stop for macro photography, in both cases.

It does hold ignoring the effective f-number errors that adjust the outcome somewhat.

 

If we compare the 5050 and the 1Ds in macro and fix both apertures at f/8 then the 5050 will have a big DOF advantage. The problem is that you're penalizing the 1Ds by not using the range of apertures appropriate for that system. The 5050 cannot go any higher than f/8 because f/8 is equivalent to f/32 for its sensor size. If you could stop the 5050 down to f/32 it would have huge DOF but the diffraction effects would be 4 times larger than the COC.

 

The reason we use f-numbers is that it's easy to do exposure calculations. We forget, though, that the f-number is not the same as the physical aperture and it's the physical size of the opening that determines DOF. When we compare the 5050 at f/8 to the equivalent 1Ds lens at f/32, the physical apertures are identical and the DOF is largely identical, too. When we compare both at f/8, we're burdening the 1Ds with an aperture 4 times larger.

 

For macro we have to think in terms of physical aperture. For wide we think in terms of f-number. All this was functionally the same back when all the cameras were 35mm full frame. Now we have to be more careful.

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With a dome port for wide angle UW photography you will be focusing on the virtual image made by the dome port. How does this affect depth of field calculations? Hyperfocal distances and their usage? and actual distance you have to focus the lens at??

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For wide angle you usually choose aperture and shutter settings for exposure only. If you are trying to control DOF it may be to limit it rather than increase it.

 

Not true.

 

DOF can be a critical choice in setting aperture in wide angle. I use hyperfocal distances when shooting wide angle landscape, trying to keep foreground in focus and getting as much background in focus as possible, offset (or limited) against the overall sharpness of the lens at various f/stops.

 

For an even better explanation of DSLR DOF check out

 

Bob Atkins article

 

No discussion of DOF would be complete without a discussion of circles of confusion. Using the Zeiss formula, the diagonal of the frame is a factor in determining the circle of confusion. I think one of the reasons we "see" greater DOF with smaller sensor cameras is that we are often looking at a 640x480 image on our computer screen, rather than the standard print size originally specified for determining the circle of confusion. We have lost the EF (enlargement factor).

 

Gee, Craig, I think we had this discussion before. Deja vu?

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Yeah...

 

So the original link that spawned this entire thread was the "Dummy's Guide to Why It's Hard to Blur the Background with Your Consumer Digicam."

 

But this is fascinating stuff. ;)

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For wide angle you usually choose aperture and shutter settings for exposure only. If you are trying to control DOF it may be to limit it rather than increase it.

 

Not true.

 

DOF can be a critical choice in setting aperture in wide angle. I use hyperfocal distances when shooting wide angle landscape, trying to keep foreground in focus and getting as much background in focus as possible, offset (or limited) against the overall sharpness of the lens at various f/stops.

 

For an even better explanation of DSLR DOF check out

 

Bob Atkins article

 

No discussion of DOF would be complete without a discussion of circles of confusion. Using the Zeiss formula, the diagonal of the frame is a factor in determining the circle of confusion. I think one of the reasons we "see" greater DOF with smaller sensor cameras is that we are often looking at a 640x480 image on our computer screen, rather than the standard print size originally specified for determining the circle of confusion. We have lost the EF (enlargement factor).

 

Gee, Craig, I think we had this discussion before. Deja vu?

I agree. I meant that in wide angle you aren't necessarily always going for big DOF. Much of the time you are, though.

 

I like the photo.net optics articles found here: http://www.photo.net/learn/optics/

 

They include scorpio's link plus the sources that I used for the equation I provided.

 

When I was at a photo contest I overheard some local pros saying they wanted Nikon 5000's because the DOF was way superior to film for macro work. I've been traumatized ever since.

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