Depth of field - rule of thumb?

[hm]

The Luminous Landscape site simply demonstrates that there is no
difference in blurriness relative to the size of the object . It
is correct - if you crop the 17mm's background and blow it up, it
looks just as blurry as it does in the 20mm shot.

The LL article text says:
"As you can see, the degree to which the tower and the hand puppet are out of

focus is essentially identical in each frame regardless of focal length. To be sure,
perspective changes dramatically, but not depth of field."

He's taking the position that depth of field doesn't change with focal length, provided you increase your distance from the subject as you switch to longer focal lengths to compensate for the narrower field of view, but maintain the relative positions of everything else in the shot.

What I've been saying is that relative to the size of the
picture , the background looks blurrier with a longer focal length
lens. The longer focal length magnifies the background more,
resulting in a blurrier looking background.

If you're pointing out that longer focal length lenses provide a "smaller" background which can eliminate clutter and allow you to 'select' a background that might be uniform, then, yes, that's obvious, though this has nothing to do with depth of field, of course, but is purely about perspective. This isn't what the Luminous Landscape article is talking about (it's about depth of field).

If this is what you're referring to, then I mistook it for a statement about depth of field and I think we're talking about different topics.

The Luminous Landscape article is trying to demonstrate that the tower in the distance is equally "out of focus" in each of the shots, an assertion that's somewhat difficult to eyeball as the tower is obviously different sizes in the different photos and blurriness due to lack of focus isn't that easy to compare in two dissimilar images This assertion is, however, easily verified or disputed mathematically. I think the answer is that the math demonstrates that it's not mathematically equal, though whether it's "close enough that you can't tell the difference" might still hold in many cases, particularly as it isn't clear (to me) what differences in blurriness are noticeable.
-harry

 

[dimage]

I would like to re-enforce what John has said and that he is not contradicting the post by Karl, but making sure people understand other factors.

One has to understand that the DoF equation gives the range of acceptable focus, but says nothing (directly) about how blurry something far away in the background will be.

One caveat on my work below: I work this up myself and did not read it in any book. So I could have totally misapplied the hyperfocal equation (but I think I did it right or I would not have posted it). If I have gotten this wrong, I would welcome somebody giving us the correct equation to use.

If we go to the “Hyperfocal Equation” we learn that h=f* 2/Ac where h is the hyperfocal distance, f 2 is the focal length squared, c= circle of confusion (and thus the diameter of the blur), and A is the (Aperture Ratio which F-number).

If we solve for the blur diameter (if I am doing this right)
c=f* 2/Ah.

Now lets say we stand with 50mm lens at 10 meters from the subject with the background 100 feet away at F8. The blur diameter (of a point of light) at the distance of 100 meters away will be:

c=50mm* 2/(8*100m) = .003125mm

Now lets use a 100mm lens (2x 50mm)and step back 10 feet so the subject will be the same size (and thus 100 + 10 meters = 110m) :

c=100mm* 2/(8*110m)=.01136mm or about 3.6 times the diameter of the blur.

I find that the following post can be quite helpful:

http://www.dpreview.com/forums/read.asp?forum=1019&message=2824952

Good post by Karl.

It is true that DoF roughly goes up by the Square of the Distance
to the focus point, Down by the square of the Focal length, and Up
linearly with the F-number. Thus while the Distance and Focal
length have the "largest effect" (square law) they cancel each
other out if you keep the subject the same size by changing the
distance AND the focal length at the same time and thus the
F-number gives you the DoF control.

A lot of times, people equate DoF with blur (less DoF = more blur).
While this is the trend, it is not strictly true. With DoF, if you
keep the subject the same size in the image by changing the
distance and focal length, the two will cancel out. However, the
amount of blur in an out-of-focus object will depend on the
magnification, of which the longer focal length will have more. So
if you take two shots, one at 100mm f/2.8 and another 200mm f/2.8
and keep the subject the same size in both images, the DoF will be
the same, but the 200mm's background will look blurrier simply
because it's magnified more. Hence one of the reasons longer focal
lengths are preferred for portraits.

 

[DavidP #28649]

I don't care WHAT the article says (and I'd read it before), nor what the math says. To me, the tower LOOKS much more blurry in the photo taken with the telephoto lens. I think most would agree with that assessment.

Call it an optical illusion if you wish, but it's really the final perception that counts, is it not?

The LL article text says:
"As you can see, the degree to which the tower and the hand puppet
are out of
focus is essentially identical in each frame regardless of focal
length. To be sure,
perspective changes dramatically, but not depth of field."

The Luminous Landscape article is trying to demonstrate that the
tower in the distance is equally "out of focus" in each of the
shots, an assertion that's somewhat difficult to eyeball as the
tower is obviously different sizes in the different photos and
blurriness due to lack of focus isn't that easy to compare in two
dissimilar images This assertion is, however, easily verified or
disputed mathematically. I think the answer is that the math
demonstrates that it's not mathematically equal, though whether
it's "close enough that you can't tell the difference" might still
hold in many cases, particularly as it isn't clear (to me) what
differences in blurriness are noticeable.

--
The Unofficial Photographer of The Wilkinsons
http://thewilkinsons.crosswinds.net
Photography -- just another word for compromise

 

[dimage]

I think John Kim is right per my math in the post below:

http://forums.dpreview.com/forums/read.asp?forum=1019&message=4105631

There is a difference between DoF and how much the background will be blurred.

Call it an optical illusion if you wish, but it's really the final
perception that counts, is it not?

The LL article text says:
"As you can see, the degree to which the tower and the hand puppet
are out of
focus is essentially identical in each frame regardless of focal
length. To be sure,
perspective changes dramatically, but not depth of field."

The Luminous Landscape article is trying to demonstrate that the
tower in the distance is equally "out of focus" in each of the
shots, an assertion that's somewhat difficult to eyeball as the
tower is obviously different sizes in the different photos and
blurriness due to lack of focus isn't that easy to compare in two
dissimilar images This assertion is, however, easily verified or
disputed mathematically. I think the answer is that the math
demonstrates that it's not mathematically equal, though whether
it's "close enough that you can't tell the difference" might still
hold in many cases, particularly as it isn't clear (to me) what
differences in blurriness are noticeable.

--
The Unofficial Photographer of The Wilkinsons
http://thewilkinsons.crosswinds.net
Photography -- just another word for compromise

 

[hm]

Now lets say we stand with 50mm lens at 10 meters from the subject
with the background 100 feet away at F8. The blur diameter (of a
point of light) at the distance of 100 meters away will be:

c=50mm* 2/(8*100m) = .003125mm

Assuming I understand your point, then I believe that using the hyperfocal distance equation won't tell the CoC at any arbitrary point, any such equation would have to be based on 4 factors: distance to focus plane, distance to background "point", focal length, and aperture.

For instance, the plot I attached to an earlier post was based on taking the last equation on this page:
http://www.dof.pcraft.com/dof.cgi

and solving for 'c'. This allows you to figure out the CoC for a background at any distance behind the focus plane.

What you can calculate from the hyperfocal distance equation, I suppose, is what the CoC will be at infinity, which isn't synonymous with background, of course, but can serve, at least, as an existence proof with one possible background at infinity.

But to use it in this manner, you want to plug in the hyperfocal distance as the distance to the focus plane. So in your example the two calculations would be:

c=(50mm*50mm) (8*10m) = .03125

and

c=(100mm*100mm) (8*20m) = .0625

In other words, if I use a 50mm lens and focus 10m away, the CoC at infinity is .03125. If I use a 100mm lens and focus 20m away, the CoC at infinity is .0625 . That's enough to demonstrate right there that doubling the focal length and doubling the distance to the subject has the ability to increase blurriness of the background (at inifinity at least).

There are a few lessons here. First is that the idea that doubling the focal length and doubling the distance to the subject has no effect on depth of field is just an approximation, one which is only "close" under a certain set of assumptions. It's easy to provide examples where this approximation is way off.

The other is that we shouldn't equate depth of field directly with blurriness of background, as two shots with different focal lengths from different distances might have nearby depth of field distances, while still having significant differences in the out of focus blur in the background. In other words, a pair of shots might hit the rear depth of field threshold at nearly similar distances, yet have CoC growing beyond that point at very different rates.
-harry

 

[dimage]

Now lets say we stand with 50mm lens at 10 meters from the subject
with the background 100 feet away at F8. The blur diameter (of a
point of light) at the distance of 100 meters away will be:

c=50mm* 2/(8*100m) = .003125mm

What you can calculate from the hyperfocal distance equation, I
suppose, is what the CoC will be at infinity, which isn't
synonymous with background, of course, but can serve, at least, as
an existence proof with one possible background at infinity.

Yes, and something I did not get quite right. But as I think you correctly point out, if the background is very far away, it would seem to be a good approximation.

But to use it in this manner, you want to plug in the hyperfocal
distance as the distance to the focus plane. So in your example the
two calculations would be:

c=(50mm*50mm) (8*10m) = .03125

and

c=(100mm*100mm) (8*20m) = .0625

In other words, if I use a 50mm lens and focus 10m away, the CoC at
infinity is .03125. If I use a 100mm lens and focus 20m away, the
CoC at infinity is .0625 . That's enough to demonstrate right there
that doubling the focal length and doubling the distance to the
subject has the ability to increase blurriness of the background
(at inifinity at least).

Right, so we have "proved something" and as you pointed out if the background is sufficiently far away this should be reasonable approximation.

There are a few lessons here. First is that the idea that doubling
the focal length and doubling the distance to the subject has no
effect on depth of field is just an approximation, one which is
only "close" under a certain set of assumptions. It's easy to
provide examples where this approximation is way off.

This is true, but it is a pretty good approximation most of the time. It falls apart as the subject distance gets near the Hyperfocal distance for example.

The other is that we shouldn't equate depth of field directly with
blurriness of background, as two shots with different focal lengths
from different distances might have nearby depth of field
distances, while still having significant differences in the out of
focus blur in the background. In other words, a pair of shots might
hit the rear depth of field threshold at nearly similar distances,
yet have CoC growing beyond that point at very different rates.

I think this is the point that John Kim was trying to make. So hopefully we have closure and general agreement ( a rarity on the subject of DoF and definitions of blur).