Depth of focus with close subjects

[bglick]

rob, i tried downloading that program, Win XP pro, but it doesn't install, error message = THREED32.OCX is missing? Did this happen when you installed it?

[robc]

go here

double click on VBUSC.exe and save file somewhere.

then double click it to install old(discontinued) visual basic runtime files.

then try install of pre-desgner again.

if that doesn't work then I can't help

let us know what happens because others might have same problem

[robc]

oops,

I think the file you need is here

[Witold Grabiec]

Here is what S. Ray has to say:

t=doFocus

T=doField

v=image focus distance (bellows extension)

u=object distance (plane of sharp focus)

f=focal length

t=(v*f*T)/u^2

It simplifies to

t≈T*m^2

(where m is magnification factor) this one becomes an approximation the closer you focus

While the "T" gets smaller with closer focusing, "m" becomes significantly larger, which ultimately leads to having a greater doFocus with very close objects. Again, this increased doFocus does NOT necessarily mean an easier focusing, because in close-ups focus is the most critical and the greater doFocus makes you guess more than with further objects. I can certainly attest to the fact that in focusing on far objects, detail seems to snap into focus rather quickly, while in close-ups it does not.

I realize your initial post was only talking about portraits, not exactly a close-up shot, but the increase in doFocus may be noticeable at such range, although the whole issue really seems to come to light for large magnifications, where most general assumptions hit the fan.

[robc]

oops I did it again,

it seems the vb runtime pack didn't do it either

this time I have validated what happens:

if you don't already have the threed32.ocx file installed or any other files the install claims are missing then do the following:

download and install from the rodenstock/linos site the winlens software. This software definitely has the files which the pre-designer software requires.

winlens

[Jerry Fusselman]

My original question concerned general photography (and macro photography), not just portraits. I will attempt to summarize where we are now with the math...

We assume no lens aberrations, no diffraction, and no swings or tilts. Let

T = depth of field;
t = depth of focus;
e = effective f-number;
r = relative (marked) f-number;
m = magnification;
c = circle of confusion;
P = pupillary magnification factor,

P is the ratio of the exit pupil diameter (as seen from the rear) to the
entrance pupil diameter (as seen from the front).

The formula Leonard cited is

t = 2ce,

and my guess is that this works for all P, and I think it is exact given our assumptions. This constitutes the main answer to my original question, because it works for all focal lengths, all magnifications, and I think it works even for asymmetric lenses (i.e., P not 1). There is certainly no better formula for depth of focus than this!

But the trick is how to accurately compute e, for the usual formula for e is valid only when P = 1. The best formula we have for computing the effective f-number is

e = r(1 + (m/P))

if the lens is front forward, but if the lens is reversed, the formula is

e = r(m + (1/P)).

When P is not 1, these formulas are much better than e = r(1+m), but are they exact?

Lefkowitz's formula for depth of field is

T = 2ce/(m*m),

but this formula is only intended for close-up work (perhaps primarily for m > 0.1 or so); it is obviously a bad approximation when m is very small---Consider focusing at the hyperfocal distance, which should have resulted in T = infinity.

The formulas Witold quoted are also approximations, but his second formula for t in terms of T matches the equations I just gave for t and T, because t = 2ce implies

T = t/(m*m).

The first formula for t he quoted is surely also intended primarily for macro photography, because T = infinity when we focus at the hyperfocal distance.

[Emmanuel BIGLER]

Dear Mr Fusselman
Thank you for pointing us to a reference textbook where general formulae for non-symmetrical lenses are given. This is something I had been looking for, for so long, that eventually I had to re-compute those formulae from scratch. So did Jeff Conrad, another reader/contributor of this forum. We have double checked our independant calculations but I think we would like to compare our results with Lefkowitz's or any other reference. But I agree that "t=2ce" is valid in the most general case if "e" is computed properly. What is not really obvious is how the effective f-number relates to the entrance pupil diameter, but this is another story.
So if the book by Lefkowitz is still available, I'd be glad to get the full bibliographical reference and eventually get a copy, if available.

A few remarks about depth of field and depth of focus for asymmetrical lenses with a pupillar magnification factor P substantially different from unity.

It happens that for far distant objects, the hyperfocal distance is independant from the pupillar magnification ratio P, so landscape view camera users usually do not care.

retro-focus wide angle lenses are not in use on LFcameras (except may be some extreme wide angle lenses, being slightly retro-focus but not that much), standard lenses are quasi-symmetrical, only view camera telephotos have a non-unit P-factor. I'm interested to learn that the Telomar has a P-factor close to 0.5. I do not think that many modern telephotos have such an extreme P-factor.

For example the modern Schneider apo-tele-xenar 400 mm exhibit a P-factor equal to 0.75 which does not depart that much, in practical use, from the usual DOF formulae with P=1.

Another remark for telecentric lenses used in profile projectors and other measuring instruments (where P increases to infinity, m/P = 0) is that their effective f-stop is independant of the magnification ratio and their depth of focus is also independant from the magnification ratio.

A "strange" situation with respect to ordinary lenses where depth of focus is roughly doubled at 1:1.. but in exact proportion with the effective f-number as mentioned.

Even if is has been mentioned in the Press and in discussion groups that extremely asymmetrical retrofocus-type lenses can be interesting used with a silion sensor, I have doubts that true telecentric lenses will ever make
their way to LF users... simply because in a true telecentric lens, the exit lens element should be as big as the image diameter itself !! So I'm happy with our small & compact quasi-symmetrical wide-angle lenses, but, true I have no plans to switch to LF-digital soon ;-);-)

Now, a last remark. The model for depth-of focus contained in the formula 't=2ce' can be extended readily to a slighty slanted film plane. The diagram can be found in a well-known document by Leonard Evens. The two limit planes on each side of the desired focusing plane are in correspondence with slanted input planes that can plotted by a vistual ray tracing, following the path of a ray propagating along those planes. Thus the '2ce' formula holds, although the position of depth-of-field input planes cannot be expressed with a compact formula.

[Jerry Fusselman]

Thanks Emmanuel! Several used copies of Lefkowitz's book are available at Amazon.

You made an interesting point about modern telephoto lenses. By my measurements, the Nikon T 600mm f/9, 800mm f/12, and 1200mm f/18 lenses have P values equal to approximately 0.72, 0.69, and 0.675 respectively. These values are about the same as the P = 0.75 you found for a Schneider apo-tele-xenar 400mm.

When shooting at 1:1, these four telephoto lenses should be opened up about 1/2 stop more than implied by the usual formula for effective f-number. That seems worth knowing for those who shoot with slide film.

In addition to telephoto and retrofocus designs, Lefkowitz gives another category where P usually differs from unity: Fast lenses. That is why I checked my Xenotar's P value as well.

Two questions: Can telecentric lenses make sharp images at high magnifications? What happens when you reverse a telecentric lens---is your ground glass black?

[Dan Fromm]

Folks, the idea that effective aperture closeup had to account for pupillary magnification was current and out front in the early '70s. I bought a Nikon PB-4 bellows and SB-4 slide holder in 1971; a data sheet that presented and explained the formula and had graphs of exposure correction factor vs. magnification for at least a dozen Nikkors came with them. In addition, the writing factory that published numerous books on SLR systems, also at least one on closeup photography, under the name Carl Shipman presented the formula in the closeup chapter of the SLR systems books. The SLR systems books were for the most part highly specific to the equipment, but the closeup chapter was pretty much the same in all.

I can only surmise that the ideas were lost, or perhaps misplaced, as TTL metering systems for 35 mm SLRs matured and people got the idea that TTL metering would solve all problems.

[Emmanuel BIGLER]

Thanks do Jerry F. and dan F. for the references to interesting books. they are already on their way to my home ;-)

Regarding telecentric lenses..

Can telecentric lenses make sharp images at high magnifications?

Non-contact optical measurement systems rely on high performance telecentric lenses similar to microscope lenses in their use, although being quite different in their design. 5x and 10x do exist and up to 100x working magnification is available. I do not know whether 5x or 10x qualifies as 'high magnification' but 100X is not so bad ;-)
Some telecentric zoom lenses exist as well for measuring systems.

Those lenses are not used by photographers but are quite an old technology.
You'd be surprised to count the number independant manufacturers of telecentric lenses. Including Nikon and Carl Zeiss.

What happens when you reverse a telecentric lens---is your ground glass black?

Well I do not know. Not black but with a limited field.

Remember that the entrance or exit lens element should be as big in diameter as the object of the image field, according to the location of the entrance or exit pupil. For a given telecentric lens that has a focal length, It seems impossible that both pupils are at infinity, since pupils are conjugate of each others. So either the entrance or the exit pupil is at infinity, but not both, for a regular, "non-afocal" telecentric lens. The lens is certainly designed for a limited range of magnifications. This is not a general-purpose lens !

So if you use a telecentric lens in the wrong direction, first you'll probably get a terrible image quality and the available field might be limited to the diameter of the entrance or exit lens element.

If you look at what Internet resources about telecentric lenses, you'll find some Nikon-Photo advertising pages mentioning that their digital lenses "use a telecentric design". To me this does not mean aything as long as you do not know the pupillar magnification ratio. A pupillar magnification ratio of 2 is quite common in classical retrofocus lenses. Including the Nikon TSE-24 mm (P=2.6 for this lens) now used by many architecture photographer with a digital 35mm camera.