Technical Discussion about Depth of Field Tutorial

[anonymous]

I am finding a conflicting issue with the DOF tutorial and its probably my lack of knowledge.

https://www.cambridgeincolour.com/tu...h-of-field.htm

What I find odd, is that using the DOF calculator I get ....

DSLR with 1.6 crop, f/32, 200mm, 10 meter subject distance:

8.61m front focus
11.926 back focus
3.3 total DOF

Then when I change the focal length to 100mm, the DOF changes

6.05 front focus
28.78 back focus
22.73 total DOF

Then one paragraph later it says ...

"depth of field does not change with the focal length."

when clearly changing the focal length changed the above calculation.

[McQ]

The key is that DoF is virtually independent of focal length *for the same magnification*.

Specifically, with the 100 mm lens you would have to get closer to the subject to fill the frame in the same way you had with the 200 mm lens, which was not done in your calculation. Otherwise you are comparing apples and oranges since the 100mm and 200mm shots contain different subject matter.

Also, take a look at the table illustrating this calculation for several focal lengths (on the depth of field page you mentioned).

[anonymous]

I have some comments about the depth of field tutorial hosted on this website. The claim is made that at constant magnification, the total depth of field is virtually constant with focal length. A tabular, numeric example is given which supports the claim for a particular circumstance. However, the claim does not hold true in general.

It's easy to demonstrate a counterexample using the Depth of Field Calculator on the same Web page (keeping the assumption of unit pupil magnification). For example, consider a 1.6X DSLR with lenses set to f/8. Say you use a 20 mm lens focused at 2 meters and a 200 mm lens focused at 20 meters. The total depth of field is 9.754 m for the former but only 3.285 m for the latter --- that's nearly a ratio of 3 to 1.

Another counterexample is the following: Set both lenses to f/11. Focus the 20 mm lens at 3.53 meters and the 200 mm lens at 35.3 meters. The total depth of field is infinite for the former but only 14.616 m for the latter.

In essence, the claim is a good approximation when the total depth of field is shallow (e.g. with large apertures at close focus distances). On the other hand, when we focus the shorter lens at distances approaching or exceeding its hyperfocal distance, its total depth of field rapidly exceeds that of the longer lens working at the same magnification.

The referenced Luminous Landscape tutorial similarly overlooks the behavior in the region of the hyperfocal distance. In addition, it ignores the definition of depth of field. The tutorial states correctly:

"Depth of field is the range of distance around the focal plane which is acceptably sharp"

but the Luminous Landscape tutorial states:

"As you can see there is not enough depth of field at this aperture to have either the hand puppet or the tower in focus."

and:

"the degree of unsharpness is indeed the same as in all the other frames --- even the one taken with the 400mm lens. Thus the depth of field is the same."

The Luminous Landscape tutorial examines a phenomenon that is, by definition, outside the depth of field. Indeed, I believe that the phenomenon shown by Luminous Landscape does remain constant for given f-number and subject magnification, regardless of lens focal length. So, it would not be a proper indicator of total depth of field in general.

Let me know if you have any questions or comments in response.

[McQ]

You are indeed correct in that the depth of field is larger for a wide angle lens when comparing to another longer focal length lens, both at high magnification. I was careful to
always say "virtually constant," but I do think an additional sentence is warranted as this concept (of Focal Length vs DOF) appears to be the most misunderstood and most widely misquoted on the web.

It appears as though you are talking about two separate processes influencing different DOF between wide and telephoto lenses: high magnification and focal distance near the hyperfocal distance. I will try to address these separately below.

The main problem with comparing lenses at high magnifications is that a new effect begins to have a significant impact of DoF: pupil magnification. The other problem is that this topic is beyond the scope of that intro tutorial. Pupil magnification actually acts to at least partially offset the DoF advantage of wide angle lenses, although this also depends on the type of lens (and whether it has been designed for macro work or not).

The other problem with comparing simple DoF numbers is that the distribution of the DoF also changes, as shown on that same page. This means that the DoF can become exponentially sensitive to focal length for some focal distances very near the hyperfocal distance, where the wider angle lens has more of a "reach" behind the focal plane in terms of DoF. This can give a misleading result that one lens has 10X as much distance in focus, but a real-world look at the photo would show them as being very similar. Similarly, the DoF calculation for both a wide and telephoto lens which are focused near their hyperfocal distance becomes very sensitive to the arbitrary definition of the circle of confusion-- changing the definition of CoC even slightly can mean the difference between negligibly different DoF's, and those which appear to be vastly different. Again though, these would appear to have a very similar DoF in a real-world print, examined by a person instead of using a strictly numerical calculation.

I will therefore add a caveat noting that the DoF calculator becomes less accurate for high magnification, and that for such circumstances a wider angle lens generally has a higher DoF. I will also note that for focal distances near the hyperfocal distance the results are extremely sensitive to the definition of CoC and focal distance, even though this may not make the photos look as if they were significantly more or less in focus. These will be added in the more detailed depth of field calculator.

Hopefully there is no strong disagreement to the above comments.

[anonymous]

Your are indeed correct in that the depth of field is larger for a wide angle lens when comparing to another longer focal length lens, both at high magnification.

Actually, I was looking at a low-magnification situation --- when at least one of the lenses is working near or beyond its hyperfocal distance. My examples involved focus distances that were greater than those in the table on the Depth of Field tutorial page.

This means that the DoF can become exponentially sensitive to focal length for some focal distances very near the hyperfocal distance, where the wider angle lens has more of a "reach" behind the focal plane in terms of DoF. This can give a misleading result that one lens has 10X as much distance in focus, but a real-world look at the photo would show them as being very similar.

I think you're saying that having a large portion of the total DOF beyond the focus distance does not contribute to a perception of great total DOF. I'm not sure I'd agree. Think of a photo that has a prominent foreground subject with a sweeping vista extending into the distant background. The typical way to produce such a photo would be to use a short lens, stopped down enough to bring the hyperfocal distance somewhat in front of the foreground subject, and focused at a distance somewhere near that of the foreground subject. Such a photo gives an impression of great total DOF.

[McQ]

So for the low magnification scenario near the hyperfocal distance, imagine this scenario:

For distances very close to the hyperfocal, changes of the CoC on the order of 1% can lead to a several times the DoF when comparing short and long focal length lenses, even though changes in the CoC on the order of 1% make no visual difference to the quality of the image-- regardless of the subject matter.

I agree with you that having a large portion of the DoF behind the focal distance can in fact make a big difference in the DoF; the emphasis is on the fact that a simple DoF number can be misleading, since the actual perception of depth depends on the spatial distribution of the subject matter. If most of the subject matter is in front of and near the focal plane, the DoF value for a wide angle lens can be misleading as its use may not improve the actual perception of sharpness throughout the DoF (unless of course the photographer uses knowledge of the DoF distribution to better allocate the DoF, as I talk about in the hyperfocal distance page). Similarly, a wide angle lens can create a greatly improved perception of depth if much of the subject matter lies beyond the focal plane (such as the best-suited use of landscape photography). Overall: both the total DoF *and* its distribution are important for maximizing sharpness, however a simple DoF number does not fully describe both these contributing factors.

Are we on agreement with this?

[anonymous]

Overall: both the total DoF *and* its distribution are important for maximizing sharpness, however a simple DoF number does not fully describe both these contributing factors.

Are we on agreement with this?

Sure, but the point being made on your Depth of Field Web page is "the
total depth of field is virtually constant with focal length."

For distances very close to the hyperfocal, changes of the CoC on the order of 1% can lead to a several times the DoF when comparing short and long focal length lenses, even though changes in the CoC on the order of 1% make no visual difference to the quality of the image-- regardless of the subject matter.

We have to be careful not to fall into a circular argument here. If we discount the significance of CoC, claiming that it's not a good or sensitive indicator of the appearance of DoF, then the whole basis of the Depth of Field Web page (the DoF equations) becomes irrelevant. So, if we believe in the CoC model of DoF, and it predicts that a small change in CoC results in a large change of total DoF, then we should accept that result --- or adopt a different model.

So again, for any choice of CoC (assuming same f-number, same pupil magnification, and same magnification at the plane of focus), it's easy to show practical situations in which the shorter lens has significantly greater total DoF than the longer lens does. If one uses the CoC model of DoF, then claiming that DoF is independent of focal length (under the above assumptions) is akin to claiming that "DoF is one-third in front and two-thirds behind the plane of focus" --- a too-sweeping simplification that you nicely refute on your
Hyperfocal Distance Web page.