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PostPosted: Sat Nov 24, 2007 11:42 am 
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Here is a thing I don't understand:

Thom Hogan said with regard to depth of field (dof): "you need an equivalent f/2 lens on DX to match an f/2.8 lens on FX". Implying that dof in general is smaller on the FX-body than on the DX-body.

I have learned that dof depends on aperture and magnification of the displayed pic. So that would mean if you shoot a scene with 50mm/f4 on DX sensor or with 75mm/f4 from the same position on FX sensor you get the same fov and if you magnify both pics to the same print/display size you should have absolutely identical dof.

So who is right? And who can explain it to me??

Hint: perhaps Thom was thinking of using the same lens on both bodies, so has to change his position towards the subject (go closer with the FX-body) to frame the same pic. That in turn would also lead to a change in perspective so is not really comparing apples to apples...

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Last edited by Thomas on Sat Nov 24, 2007 9:09 pm, edited 1 time in total.

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PostPosted: Sat Nov 24, 2007 12:38 pm 
I suggest you read this and look for the "DOF vs. format size" section. :)


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PostPosted: Sat Nov 24, 2007 1:15 pm 
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Hi Thomas,

I have shared some of your confusion over this. :? There is a great description of DoF on this Cambridge in Colour page with the added benefit of a Depth of Field Calculator. Here are a couple of result from that calculator. Both results assume an f/2 lens with a focal length of 50mm and a distance to the subject of 4 metres.

For a DSLR with a 1.5x crop factor (such as the D80) the results are
    Closest distance of acceptable sharpness 3.74 m
    Furthest distance of acceptable sharpness 4.299 m
    Total Depth of Field 0.559 m
For a DSLR with a 1.0x crop factor (full-frame such as the D3) the results are
    Closest distance of acceptable sharpness 3.622 m
    Furthest distance of acceptable sharpness 4.466 m
    Total Depth of Field 0.843 m
On the face of it this is nonsense. Let's assume that the 1.5x crop camera has been placed on a tripod at such a distance that an object of interest is nicely framed when it is 4 metres away (50mm lens at f/2 as above). After we take the picture we put a D3 (full frame) on the tripod and use the same lens so we are still at 4 metres with f/2 and a 50mm lens. There is no way that the light falling on the central part of the sensor "knows" that there is more sensor at the periphery than before and so somehow magically increases it's depth of field.

The key to understanding this is the hidden assumption that the full-frame print will be the same size as the 1.5x crop print. So if, for the sake of argument, both prints were 30cm wide then objects from the full frame camera's print would be about 1.5x smaller than the same objects on the 1.5x crop camera's print. That also means that any blurring caused by objects being out of focus is also 1.5x smaller. Hence, perceptually, objects can be further from and closer to the point of optimum focus before blurring becomes obvious.

To re-phrase, our eyes don't have infinitely good resolving power :shock: . For each of us, when viewing an object like a print at a particular distance, there is a limit to how much fine detail we can see. If the out of focus blurring is smaller than this value we can't see it. Because the assumption was that the full-frame camera's print would be the same size as the cropped camera's print then the out of focus blurring drops below the eye's resolution limit more slowly as the distance of objects in the picture from the point of optimum focus increases.

Of course, if you can't get physically closer to an object when using a full-frame camera and so have to re-frame the picture by digitally zooming in post-processing then the full-frame depth of field reduces to the value calculated for the cropped sensor camera.

Right, I thought I had finished but there is one more thing to discuss. With the full-frame camera we can move closer to the subject so that the framing is the same as with the cropped sensor camera. So in the example above we can move in from 4 metres to about 2.7 metres with the 50mm lens. Still at f/2 we now have
    Closest distance of acceptable sharpness 2.523 m
    Furthest distance of acceptable sharpness 2.903 m
    Total Depth of Field 0.38 m
So the act of re-framing by moving the camera with the identical 50mm lens closer to the subject has actually resulted in a decreased depth of field. A similar result is seen if, instead of moving the camera closer to the subject, a 75mm lens is used at f/2 at the original 4 metres. Chances are though, that if you are using a 75mm lens you can only afford a similar lens diameter so you are more likely to be working at f/2.8 where, at 4 metres, the total depth of field is pretty similar to the cropped sensor camera at f/2.

So, controversially perhaps, I will assert that this depth of field argument comparing full-frame versus cropped sensors is sterile. With a fixed print size and the cropped sensor as our benchmark you can end up with a smaller DoF if you re-frame by moving the full-frame camera closer to the subject, you can end up with a greater depth of field if you don't re-frame with the full-frame camera (and so objects in the final print are smaller) or you can end up with the same DoF if you re-frame with the full-frame camera by changing lenses but are operating to the same lens budget (which means you can only afford a slower lens). :shock: :shock: :shock:

Bob.

P.S. Sorry the post was so long. :oops: I had the time today because I'm also watching the latest space walk from the Space Station using NASA TV's Internet broadcast. 8)

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PostPosted: Sat Nov 24, 2007 2:19 pm 
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Brilliant, Bob!
After you were halfway through I thought you just proved the opposite of what Thom (Hogan that is) and Wikipedia were asserting :wink:
But then came the "Right, I thought I had finished but..." with the other options (1. going closer, 2. zooming in).
Of that options I would not count the "going closer"-option because it shifts the perspective so you're not really getting an apples-by-apples comparison. So the only option left for producing identical pictures are:
2. zooming in
3. shooting from the same distance but croping the FX-pic by 0.7 and magnifying the remains by 1.5
As an aside: The ugly thing with option 3 is that the resolution of the cropped FX-shot is lower (namely 5MPix) than the res of the original DX-shot (10/12 MPix). This in itself has a "flooring-effect" on the size of the airy-disks that can be resolved with the FX-sensor. But let's ignore this fact fo rthe rest of the discussion.

Let's see if we can resolve option 3 quickly: If you take the same lens/aperture and distance with the FX-body and just crop the DX-part out of it, magnify that crop to the same print-size as with the DX-body, well :?: :roll: :idea: You will certainly get the same dof :P (because you in effect through away the borders of the FX-pic and use the D3 just a bulky DX-body. So this one was easy, phew!

Now on to option 2: using a 75mm on the FX-body instead of the 50mm on the DX-body, same distance same aperture. So fov and perspective of both pics are identical!

-----stay tuned, we'll be back after a short brake...

Well, at least the cambridgeincolour dof-calculator shows a dof of 37cm @ f2 and 52cm @ f2.8 (using the 75mm lens on a FX-body and 4m subject-distance). So this gives credit to Thom's assertion that you roughly need one stop greater aperture on a DX/APS-C-sensor than on a FX/FF-sensor to achieve the same dof.

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PostPosted: Sat Nov 24, 2007 9:06 pm 
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Good explanation Bob. I think the part where most people get confused is assuming a cropped sensor does more than its name suggests.

Whereas in fact all it is doing is cropping the edges of a full frame area. If you took a full frame photo and just chopped off the sides, you'd get the same result as a cropped sensor would have done form the same spot.

Where you see differences in DOF and perspective is when you adjust your distance so the framing between cropped and full frame are the same.

I realise this was taken with different lenses, but you can see some perspective and DOF differences in my comparison of the 5D plus 24-105 and the 350D plus 17-85mm here: (check out the portrait shots)

http://www.cameralabs.com/features/Cano ... age5.shtml

Gordon


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