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08-31-2009, 11:55 PM   #1
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DOF & Crop factor

Guys, this is bothering me for a long time. I don't get it!
How the hell is cropping going to change the DOF?
I use the same lens, same settings on the lens, same registration distance. This means in my mind the system is optically identical.
I change the sensor, how will this influence the bloody DOF?

It seems I'm not alone in this:

Full Frame vs Crop Sensor - Depth of Field Myth | Have Camera Will Travel | Gary Gray

I've read debates upon this: "reasonably sharp", "circle of confusion", "how large is your print", and so on.

My point is: if you take two pictures from the same point with two different cameras (APS-C and FF) using the same lens and settings, crop images to the same visible area and print crops to same size, you should get the same result.
Right?

09-01-2009, 12:22 AM   #2
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Indeed, DOF is always the same for the same lens, but what is of importance for the average shooter is the DOF changes between "equivalent" (same FOV) lenses (i.e. 50mm FF vs 35mm APS-C)...

For instance, I used my FA50/1.4 a lot on my MZ camera, so I was quite used to the focal length...

To find a similar FOV, I would now have to use a FA35/2... But with the crop factor, and for similar output formats, it will behave more or less like a 50mm set to f/2.8 or even f/3.5...

So, yes, available DOF will change for a similar FOV...

Fastest lens in this range is the Sigma 30mm f/1.4, but it will still behave like a 45mm f/2.8 in term of FOV/DOF couple.
09-01-2009, 01:18 AM   #3
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I once calculated, I think, that if you want the same fov and dof that you get with 50/2 on film, you'd need a 33/1.2 lens on digital.
09-01-2009, 02:23 AM   #4
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QuoteOriginally posted by dlacouture Quote
Indeed, DOF is always the same for the same lens,
Incorrect.
QuoteOriginally posted by octavmandru Quote
My point is: if you take two pictures from the same point with two different cameras (APS-C and FF) using the same lens and settings, crop images to the same visible area and print crops to same size, you should get the same result.
Right?
Correct but misleading.
Because prior to "crop images to the same visible area" you had different DoF which you made equal again by cropping.
QuoteOriginally posted by octavmandru Quote
How the hell is cropping going to change the DOF?
octavmandru, your question goes straight to the heart of confusion.

An answer as simple as possible but no simpler:
  1. A lens has a single plane of focus, hence the "DoF" of a lens alone would be zero.
  2. Therefore, 100 years ago, opticians defined DoF by answering the question what would still be perceived sharp by an average human eye looking at the entire image.
  3. So, DoF is a property of the entire optical system going from lens to human eye's retina (the final sensor), not just lens to sensor (an intermediate sensor)!
    Note that DoF is defined as well for systems w/o any intermediate sensor, like a telescope.
  4. So, e.g., if you change human to eagle, DoF changes just like it does when cropping or approaching a print.
    (change human to eagle: this is like changing the final sensor)
    (cropping or approaching a print: this is like zooming in the optical system from lens to retina)
  5. A commonly accepted part of the formula for DoF is that areas of confusions are perceived sharp if their diameter stays below 1/1730 of the image diagonal (Zeiss formula). This is the "circle of confusion". And this circle becomes smaller if you crop an image. Very simple, actually.
I have proposed to introduce a new term, PDoF for "pixel depth of field" which replaces the Zeiss formula's circle of confusion (0.016 mm for APS-C (*)) by the pixel size (0.005 mm for K-7/K20D). PDoF is unaltered by cropping.
___
(*) Most DoF-calculators use 0.020 mm. I recommend to use 0.013 mm for APS-C to maintain some headroom and to comply with the HDTV fullHD specification.


Note that DoF and PDoF answer two very distinct questions:
  • DoF: areas sharp for a human watching the image
  • PDoF: areas sharp on a 100% pixel peep computer screen crop
You could also say that DoF is PDoF when considering retina pixels (very hard to pixel peep on a computer screen)

Another way to look at it is this: DoF is PDoF after rescaling the image to 1.38 megapixel (3:2 ratio), because this is what the Zeiss formula computes to.

Before digital photography, DoF and PDoF couldn't be confused because PDoF simply didn't exist. Now, it is confused all the time and w/o a clear understanding of the distinction, most computer affine guys tend to believe PDoF is DoF. It is not.


Last edited by falconeye; 09-01-2009 at 03:12 AM.
09-01-2009, 05:08 AM   #5
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I liked the comparison with the human and eye of the eagle.
I think the eye of the falcon is more suitable.

You made a very good point here. In fact, for me it's clear you have a better and more objective understanding of this optical phenomenon.

If I remember right the Zeiss formula was developed for engineers to know how good the lenses should be. It is useless to develop a lens more sharp then the sensor used (of film grain). That's why the medium format lenses are not necessarily better than the FF lenses, when used on FF, or 35 mm.

Thing is, I usually crop my pictures, and have the bad tendency to focus on details and loose the general picture. As one friend used to say: when you notice you are to deep buried in things, take a step back and relax. Seems to be a good advice for pixel peepers.

Anyway, I didn't realize that by cropping my pictures I'm actually changing the DoF. OK, that's a good lesson.
OK, I feel my rant is bigger then I wanted to be, but it's touching some items I've been thinking about for a while.

Last edited by octavmandru; 09-01-2009 at 06:00 AM.
09-01-2009, 05:13 AM   #6
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QuoteOriginally posted by octavmandru Quote
Guys, this is bothering me for a long time. I don't get it!
How the hell is cropping going to change the DOF?
I use the same lens, same settings on the lens, same registration distance. This means in my mind the system is optically identical.
I change the sensor, how will this influence the bloody DOF?

It seems I'm not alone in this:

Full Frame vs Crop Sensor - Depth of Field Myth | Have Camera Will Travel | Gary Gray

I've read debates upon this: "reasonably sharp", "circle of confusion", "how large is your print", and so on.

My point is: if you take two pictures from the same point with two different cameras (APS-C and FF) using the same lens and settings, crop images to the same visible area and print crops to same size, you should get the same result.
Right?
with your example, you are correct. If you crop a full frame image taken from the same point (and with same aperature and focal length) as an ASP-C image, to the ASP view, then DOF has remained unchanged.

But.......

if you take the same field of view with an ASP-C sensor camera (although this requires a shorter lens) and a FF camera, the DOF in the two images is different (assuming again the same aperture)
09-01-2009, 06:17 AM   #7
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This was very confusing to me as well, until I realized that after you crop the image, you have to enlarge that crop to the same size as the FF image in order to make a valid comparison.

When you do that, you are effectively enlarging all the circles, and so some of the areas that looked "in focus" (i.e., "sharp enough") in the FF image will begin to look "out of focus". Since the actual, physical distances represented in the two images are the same, therefore, the DoF actually becomes shallower in the cropped image.
09-01-2009, 06:19 AM   #8
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QuoteOriginally posted by Lowell Goudge Quote
if you take the same field of view with an ASP-C sensor camera and a FF camera, the DOF in the two images is different (assuming again the same aperture)
This is a true statement if aperture denotes an f-stop number, and a false statement if aperture denotes a diameter.

Not being precise here is the root of many rants
Note that aperture w/o qualification normally means the latter to opticiens and the former to photographers
QuoteOriginally posted by octavmandru Quote
If I remember right the Zeiss formula was developed for engineers to know how good the lenses should be.
[...]
That's why the medium format lenses are not necessarily better than the FF lenses, when used on FF, or 35 mm.
[...]
Take K20 & 5D. Canon has a bigger CoC, but a smaller PDoF, since it has a lower pixel density, right? If you take the same picture with both cameras, and print both images on max. resolution (equal printed pixel size), the reasonable clear depth on Pentax is narrower than Canon's?
The Zeiss formula was reverse-engineered by early web sites from the DoF scale on Zeiss lenses. Obviously, Zeiss uses a tighter CoC when what is commonly used by DoF calculators (which is 1/1500).

The resolution of lenses is determined by ambition.
- Zeiss 35mm rangefinder: 400 lp/mm
- Zeiss 35mm SLR: 300 lp/mm
- Zeiss for Hasselblad: 280 lp/mm (Superachromat 5,6/250)
- Zeiss Large Frame: 160 lp/mm (Biogon 4,5/75)

So, at least for Zeiss, the resolution of larger frame lenses decreases more slowly than their image circle increases:
The latter (8x10") renders 5300 million pixels (1 shot Gigapixel ) where 35mm SLR is limited to 300 million pixels (divide all numbers by 5 or so for comparison at higher contrast).

Your question about K20D vs. 5D is ill posed. You must clearly state what parameters you keep constant. Canon has a bigger CoC (1.5x) and bigger pixel size (1.3x). One really should only compare PDoF for some given constant number of pixels (same goes for noise and dynamic range btw).


Last edited by falconeye; 09-01-2009 at 06:25 AM.
09-01-2009, 06:33 AM   #9
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Wow, Falk.
Your incredible DoK (depth of knowledge) on this field is remarkable.
Thanks for sharing this goldmine of info with us.

Though practically, I take it as Lowell says there is no discernible difference in DoF for the same lens between an APS-C and FF camera. I find trying to compare equivalent FoV (eg 35mm on APS-C vs 50mm on FF) like comparing apples and oranges - the two lenses produce different perspectives, let alone DoF.

edit - I didn't quite get that right... correction noted below.

Last edited by Ash; 09-01-2009 at 08:42 AM. Reason: incorrect assumption
09-01-2009, 06:55 AM   #10
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Different perspectives??? How so? I thought FoV and perspective were the same thing... (or, to be clearer, that two cameras with different sensor formats but with the same FoV will produce similar pics, in term of perspective).
09-01-2009, 06:56 AM   #11
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QuoteOriginally posted by falconeye Quote
This is a true statement if aperture denotes an f-stop number, and a false statement if aperture denotes a diameter.

Not being precise here is the root of many rants
Note that aperture w/o qualification normally means the latter to opticiens and the former to photographers

The Zeiss formula was reverse-engineered by early web sites from the DoF scale on Zeiss lenses. Obviously, Zeiss uses a tighter CoC when what is commonly used by DoF calculators (which is 1/1500).

The resolution of lenses is determined by ambition.
- Zeiss 35mm rangefinder: 400 lp/mm
- Zeiss 35mm SLR: 300 lp/mm
- Zeiss for Hasselblad: 280 lp/mm (Superachromat 5,6/250)
- Zeiss Large Frame: 160 lp/mm (Biogon 4,5/75)

So, at least for Zeiss, the resolution of larger frame lenses decreases more slowly than their image circle increases:
The latter (8x10") renders 5300 million pixels (1 shot Gigapixel ) where 35mm SLR is limited to 300 million pixels (divide all numbers by 5 or so for comparison at higher contrast).

Your question about K20D vs. 5D is ill posed. You must clearly state what parameters you keep constant. Canon has a bigger CoC (1.5x) and bigger pixel size (1.3x). One really should only compare PDoF for some given constant number of pixels (same goes for noise and dynamic range btw).
Actually, I deleted the 5D/K20 question shortly after posting because I felt it was misleading and not relevant.

I agree with Ash, Falk your knowledge is a goldmine.
Thanks for sharing.
09-01-2009, 07:14 AM   #12
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QuoteOriginally posted by Ash Quote
Though practically, I take it as Lowell says there is no discernible difference in DoF for the same lens between an APS-C and FF camera. I find trying to compare equivalent FoV (eg 35mm on APS-C vs 50mm on FF) like comparing apples and oranges - the two lenses produce different perspectives, let alone DoF.
Lowell compared equivalent FoV.

"Your" two lenses don't produce different perspectives. FoV and distance to the subject are the only factors which determine perspective.

So, if you like it or not, you better compare apples and oranges.

And last but not least, DoF for an identical lens on APS-C and FF is different. The APS-C sensor crops into the FF image leading to less DoF. Which is counter-intuitive for sure. But only as long as you ignore that the two images have an entirely different composition.


I think I said enough on topic. For some reason, these threads never die.

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09-01-2009, 07:22 AM   #13
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QuoteOriginally posted by falconeye Quote

I think I said enough on topic. For some reason, these threads never die.
...Why I did not chime in...

Thanks Falk for your contribution.

Steve
09-01-2009, 08:40 AM   #14
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QuoteOriginally posted by dlacouture Quote
Different perspectives??? How so? I thought FoV and perspective were the same thing... (or, to be clearer, that two cameras with different sensor formats but with the same FoV will produce similar pics, in term of perspective).
Falk is, of course, right - though what I should have said about the different perspectives is that for a 50mm lens on a FF cam produces a different perspective than a 35mm on the same FF camera, but requiring a closer subject-distance. I stand corrected that the image result is not different perspective-wise between 50mm FF and 35mm APS-C crop captures.
09-01-2009, 08:44 AM   #15
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QuoteOriginally posted by falconeye Quote
This is a true statement if aperture denotes an f-stop number, and a false statement if aperture denotes a diameter.

Not being precise here is the root of many rants
Note that aperture w/o qualification normally means the latter to opticiens and the former to photographers
Yeah, I thought about this as I wrote it, i really should have stated F stop.
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