View Full Version : Another Depth of Field Question

Ken Lee
25-Jul-2004, 19:42
Let's say we are shooting a 3-dimensional subject like a flower, using 4x5 film, at close range, at exactly 1:1. Let's say we are using a camera with lots of bellows draw. To make a 1:1 image with a 150mm lens, we need 300mm bellows extension. To make a 1:1 image with a 300mm lens, we need 600mm bellows extension. I presume we can take the picture from twice as far away with the 300 mm lens, as we can with the 150mm lens.

Even though the 150mm lens gives greater depth of field (presumng the same f/tsop used in both cases), we have to get in 2x closer to fill the frame. The closer we get, the more critical becomes depth of field, because the distances between parts of the subject are relatively greater.

Does that closeness defray, proportionately, the depth of field gained by using the shorter lens ?

David A. Goldfarb
25-Jul-2004, 20:08
At macro distances, DOF is almost exactly the same (out to at least 4 significant figures) for any lens at a given magnification, aperture, and format, so at 1:1, a 150mm lens has almost the same DOF as a 75mm lens or a 300mm lens.

The advantage you get with a longer lens is more working distance, so the camera doesn't obstruct the light or otherwise get in the way.

The advantage you get with a shorter lens is less bellows required, so the camera will be easier to stabilize and can be lighter in weight.

Ken Lee
25-Jul-2004, 20:41
Thanks David, that helps a lot.

May I modify the question a little ? What if we are shooting a bunch of flowers instead, which I guess would be something like 1:3 or 1:4... In other words, no longer Macro distance, but still within the province of lenses designed for close work.

At these distances, is the increased depth of field from smaller lenses noticeable ?

Eric Wagner
25-Jul-2004, 21:19
I think I understand your question. If you focused a 150mm lens at 4 feet, the depth of field at f22 would extend from 3.6' to 4.5' using a circle of confusion of 1/250. If you backed up to 8 feet with a 300mm lens, the depth of field at f22 would extend from 7.6 feet to 8.5 feet. The formulas I used are in my old "Encylopedia of Photography."

Ralph Barker
25-Jul-2004, 22:57
I haven't done the math, Ken, but I think the scenario David describes is still generally applicable in the 1:2 - 1:4 or so range, too. While DOF is a major issue, so is the formulation of the lens. In some cases, you might get a better overall image with a lens that is optimized for close work, than you would with a lens that provides greater mathematical DOF, but is optimized for greater distances.

While I haven't done any scientific testing, one of my favorites for close-ups with either 4x5 or 8x10 is my 240mm G-Claron, for example. Here's a scan of an 8x10 Polaroid of some Asiatic Lillies shot with the 240 G-Claron. The open flowers measured about 3" across, so this is actually in the 1:1 - 1:2 range. I was shooting at f/45, with multiple pops of the strobes to achieve the proper exposure.


Dan Fromm
26-Jul-2004, 05:40
Funny you should ask.

Some years ago I shot the same deep subject on KM using flash at 1:4 at f/8 with 55/2.8 AIS, 105/2.8 AIS, 200/4 AIS MicroNikkors and a 700/8 Questar. The transparencies were indistinguishable; equally sharp in the plane of best focus, same DOF. The Questar 700 is a hell of a lens.



Edward (Halifax,NS)
26-Jul-2004, 05:49
Ralph, that picture is simply amazing. Thanks for posting it.

Ken Lee
26-Jul-2004, 07:24
Thanks a lot for all the info. I have both a Rodenstock 150 APO Sironar S and a Fujinon 180 A, which I got for close work. While the Rodenstock is outstanding at normal distances, the Fujinon definitely outperforms it when you get in close.

It helps to know that a shorter lens for close work will not "buy me anything" in terms of DOF... and that I can keep both of them :-)

Leonard Evens
26-Jul-2004, 07:25

For subjects at a moderately close distance, with rare exceptions, if the magnification is the same, you get the roughly the same depth of field independent of the focal length. This is usually true within the closeup range.

More precisely, both the near and far depth of field, at the same magnification and f-stop, will be roughly independent of the focal length as long as the ratio

R = (subject distance - focal length)/hyperfocal distance

is sufficiently small. The reason is that the formulas for these quantities involve a denominator of the form

one plus R (for near DOF) or one minus R (for rear DOF).

(Actually the rear DOF will be infinite if one minus R is zero or negative.)

The total depth of field involves dividing by

one minus (R squared)

The denominators tend to shorten the near DOF and lengthen the far DOF, so there is some cancellation which takes place in calculating the total DOF.

If R is small enough, the denominators are close to 1, particularly the one for the total DOF. If you approximate by ignoring R in the formula, you get something independent of focal length and depending only on f-number and magnification. For plausible f-numbers and normal or longer focal lengths the hyperfocal distance is likely to be pretty large. So it is only when you have a very short focal length lens and you are using a large f-number that the approximate formula breaks down. In that case you get more depth of field than the approximate formula would predict.

Let's consider your example. With a 150 mm lens at f/64, assuming a coc = 0.1 mm, the hyperfocal distance is about 3.156 meters. At a magnification of 1:4, the subject distance is 5 times the focal length and the numerator in the above ratio is 4 times the focal length or 0.6 meters. So the ratio is .6/3.156 = 0.19. Squaring this yields 0.03. The result is that if you ignore the factor R, you will be off by almost 20 percent in rear and far DOF, but in opposite directions. In the total DOF you will be off only by about 3 percent.

Note however that the pictures taken with different focal length lenses, although the DOF may be roughly the same, will still differ in other ways. For example, even if you adjust subject distance so that the magnification in the exact subject plane is the same, magnification elsewhere will be different for different focal length lenses. In the close-up situation, the DOF is pretty small, so the differences will be slight at the limits of DOF, but beyond that region, which of course will be out of focus, there will be significant differences.

The exact formulas, should you want to use them are

Near DOF = Nc (1+M)/M^2 divided by 1 + R

Far DOF = Nc(1 + M)/M^2 divided by 1 - R or infinity if R is greater than or equal to 1

Total DOF = 2Nc(1 + M)/M^2 divided by 1 - R^2 or infinity if R is greater than or equal to 1

The formula for the hyperfocal distance is f^2/Nc.