Amazon Kindle Unlimited Offer: 1-Month For FREE!

Crop factor and DOF


Krakman 14 3.6k Scotland
8 Apr 2007 8:26PM
Where was the hostility and unhelpfulness? I missed it!
Superficial 14 147
8 Apr 2007 8:26PM
So let me get this right:

Canon 30D (1.6 crop) + 20mm lens
Canon 1Ds MkII (Full Frame) + 32mm lens

Obviously these two setups would give a very similar angle of view/composition. But depth of field would be completely different (at a given aperture)?

That's really confusing? Is this important to anyone?
Krakman 14 3.6k Scotland
8 Apr 2007 8:27PM
No, depth of field will be the same. See the last link I gave!
theorderingone 17 2.4k
8 Apr 2007 8:31PM
DOF would be marginally shallower on the 1DS under those conditions, if the distance to subject was constant, yes.

It's important to me, I regularly shoot at f/2 and brighter. Knowing how things work helps me to gauge things when shooting.
Krakman 14 3.6k Scotland
8 Apr 2007 8:38PM
If you want a very detailed explanation of why focal length only appears to affect Dof, but doesn't optically, have a look at this link:

Scroll down to the para entitled DOF and focal length

Note: "It is well known that short focal length lenses have large apparent depths of field and long telephoto lenses have small apparent depths of field. There are some very practical reasons for this conception, but it isn't quite true. DOF is much more closely related to magnification and f-stop; DOF expressed in distance is nearly independent of focal length. It appears smaller with telephoto lenses because it is smaller when expressed as a fraction of the lens-to-subject distance, s"
theorderingone 17 2.4k
8 Apr 2007 8:43PM

Quote:No, depth of field will be the same. See the last link I gave!


Mr Croftsphoto Sir, did you read the article you linked to?

The distance to subject was changed to keep the subject the same size, hence the similar DOF. He didn't crop the images.

The reason the OP is confused, is because your conflicting arguement is flawed, you are changing two different variables. All three variables will change the outcome in the end, that's all I was saying.

EDIT - in your second link, he is also changing two variables, distance and focal length. I give up!

Strawman - I understand what you're saying, but my posts are an attempt to help answer the OP's question, correctly.
Krakman 14 3.6k Scotland
8 Apr 2007 8:45PM
Must admit it was slightly odd that the perspective changed in the images, as it shouldn't have done, and he repeats the other common misconception that perspective changes with a change of focal length. However, his basic premise about DoF and aperture is correct - see my second link! Smile
theorderingone 17 2.4k
8 Apr 2007 8:49PM
Sorry, sir, I edited my post after reading your second link.

Smile
Krakman 14 3.6k Scotland
8 Apr 2007 9:05PM

Quote:EDIT - in your second link, he is also changing two variables, distance and focal length. I give up!



The second link is just giving a mathematical formula - he isn't changing the distance to subject as it isn't been given a value in the formula, it's represented by a letter.

But he does then go on to quote the well known means of calculating acceptable depth of field for a print based on what appears acceptable in a print from a normal viewing distance. It's definitely the case that with a wider angle lens image that hasn't been cropped the DoF is less apparent (even though it's the same at a given aperture for different focal lengths). To put it another way, you can get away with less depth of field in a wide angle lens image. I'm not trying to dispute the fact that you can get away with less depth of field in a wide angle image without it being so noticeable!

Let me quote his full explanation, note especially the bits I've highlighted in bold:


Quote:It is well known that short focal length lenses have large apparent depths of field and long telephoto lenses have small apparent depths of field. There are some very practical reasons for this conception, but it isn't quite true. DOF is much more closely related to magnification and f-stop; DOF expressed in distance is nearly independent of focal length. It appears smaller with telephoto lenses because it is smaller when expressed as a fraction of the lens-to-subject distance, s.

Equations for Total Depth of Field
Combining the equations for Df and Dr from the first box of equations, we can obtain the total depth of field.
Total DOF = Df + Dr = sC(s-f )/( fa-C(s- f )) + sC(s- f )/( fa+C(s- f ))
= 2 fasC(s- f )/(( fa)2-C2(s-f )2)
Now, substitute magnification M into the equation using M = d/s = f / (s-f ); s-f = f / M.
Total DOF = 2 fasC( f /M )/(( fa)2-C2 f 2 / M2) = 2asCM / (M2a2 - C2)
Eliminate s using s = f + f / M = f (1 + 1/M) = Na (1 + 1/M), where N = f-stop = f / a.
Total DOF = 2Na2C (M+1)/ (M2a2 - C2) = 2NC (M+1)/ (M2 - (CN / f )2)
No approximations yet, but we haven't entirely eliminated the focal length f. Fortunately, the (CN / f )2 term is usually much smaller than M 2, except for very distant images (with very small magnification). As we point out below, c/f is a constant, independent of format, equal to about 1/1600 for a "normal" lens. For example, for the 35mm format with a standard 50 mm lens at f/8, cN / f = 0.03*8/50 = 0.0048 ~= 1/200. So the (cN / f )2 term can be eliminated from the equation (the error will be less than 1%) for magnifications M larger than 1/20 (a 20x30 inch or smaller field for 35mm format), which covers most portraits and still lives.
Total DOF ~= 2NC (M+1)/ M2
This approximation holds for large magnifications: portraits, still lives, etc. (M > 1/20 in the above example).


Now let's look at Depth of Field for M ~= 1/20 at f/8 for several focal lengths, using Jonathan Sachs' Depth of Field Calculator set for 30 lp/mm resolution (the default).


DOF for f/8, M ~= 1/20, 35mm format Focal length
f mm Distance
S mm Near DOF
limit mm Far DOF
limit mm Total
DOF mm Total
DOF/S %
20 mm 400 319 536 217 54.2
50 mm 1000 908 1113 205 20.5
100 mm 2000 1904 2107 203 10.1
200 mm 4000 3901 4104 203 5.1
1000 mm 20000 19899 20102 203 1.0

For a specific format, depth of field, expressed as distance, is independent of focal length. But depth of field, expressed as a percentage of the distance to the subject (Total DOF/s %), is inversely proportional to focal length. It can be very small for long telephoto lenses.
Using a long telephoto lens is an effective way of isolating a subject from busy, uncontrolled backgrounds without sacrificing actual depth of field.

Carabosse 18 41.5k 270 England
8 Apr 2007 9:16PM
Visual acuity and viewing distance are other factors which come into it as well.

Just to complicate things! ;-D
theorderingone 17 2.4k
8 Apr 2007 9:19PM

Quote:But depth of field, expressed as a percentage of the distance to the subject (Total DOF/s %), is inversely proportional to focal length. It can be very small for long telephoto lenses.


Indeed, the distance used in the calculation for a 20mm lens is 400mm, the distance used for a 1000mm lens is 20,000mm. That's why the total DOF is roughly the same.

If both distances were the same, the DOF would be wildly different.

In science, if you want to test a theory, you change one variable only, to prove it. As a result of changing focal length, with your subject being at the same distance, the DOF will be shallower as a result of the greater magnification, which agrees with his theory. So, in practical terms, changing focal length does alter the DOF.

If however, you take a step back so that your subject is magnified exactly the same, the DOF will be very similar.

Anyway, I'm off to the pub to numb this wasp sting! It's actually been an interesting discussion. You had me doubting myself for a moment then. :-P
ian walker 16 717 United Kingdom
8 Apr 2007 9:22PM
this discussion always gets ugly Smile

go take photos, its for the bestSmile
Krakman 14 3.6k Scotland
8 Apr 2007 9:29PM

Quote:Visual acuity and viewing distance are other factors which come into it as well.

Just to complicate things!


Agreed, but that's when viewing the print, which is a slightly different matter!


Quote:Indeed, the distance used in the calculation for a 20mm lens is 400mm, the distance used for a 1000mm lens is 20,000mm

The 20mm lens/400mm and 1000mm lens/20,000mm is only brought in where he's quoting Jonathan Sachs' Depth of Field Calculator - it's not in the author's formula at all. The Sach's depth of field calculator is used for the purpose of determining what's acceptable resolution of lines per millimetre taking into account the final viewing distance of print etc. That's different from the issue of what the optical depth of field of the lens is. For that - see the author's own formula set out above that!

To put it another way, with a wide angle lens you would need a much higher resolution of lines per millimetre on the sensor/film to be able to detect the fact that the DoF in that part of the subject is the same as in the telephoto lens, which has 'magnified' that area.

Have a good drink Smile
certx 14 415 1 United States
8 Apr 2007 10:59PM
wow... I thought that was a relatively simple question. Obviously I was mistaken. But, to take all the above, and compress it into a single sentence or two, would it be fair to say it this way (to myself)?

Aperture, focal length, distance-to-subject, and subject to background, all have an effect on "apparent" DOF, which I suppose is what really matters, how the DOF appears?

Since crop factor effectively increases a given focal length, and f/stop is the ratio of aperture diameter, which directly effects DOF, to focal length, then crop factor also effectively increases DOF.

Is that fair in layman's terms? Greatly oversimplified I realize after reading all the responses.
User_Removed 16 4.9k England
8 Apr 2007 11:17PM
All I know is that there ain't much DoF in macro or telephoto......but there is in wide angle. Does it for me.Smile

Sign In

You must be a member to leave a comment.

ePHOTOzine, the web's friendliest photography community.

Join For Free

Upload photos, chat with photographers, win prizes and much more.