### Depth of Field: Long focals versus tele lenses

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Would the theory confirm my observation that a long lens has more DOF than a tele lens of same power at same working aperture? My observation was with lenses of different focals so I'm not quite sure (450 long versus 600T). In other words, does the DOF depend of the lens design or of the angle of the lens? (In my comparison shots, the crop in the 450 shot corresponding to the 600 frame has MUCH more DOF than in the image from the 600T at same f-stop. Has someone tested lenses of same power for DOF?

-- Paul Schilliger (pschilliger@smile.ch), May 02, 2001

Hmm, interesting question.
My instinctive reaction is "of course there's no difference", but then all the formulae for DOF make the assumption that an approximation to a simple lens is 'near enough', and that the back focus and the EFL are one and the same.

I don't remember seeing any references to DOF changing with the telephoto ratio, so I'll have to draw myself a few diagrams and do a few calculations before jumping to any conclusion about this one.
DoF is the result of changes in subject distance causing the focal plane to shift, played off against depth of focus. If the projection angle of a lens is different from the theoretical angle relating to its EFL and aperture, then one might expect the depth of focus, and hence the depth of field, to differ as well.
The implications for a zoom lens with a fixed back focus are interesting as well.
I'll get back to you.

-- Pete Andrews (p.l.andrews@bham.ac.uk), May 02, 2001.

Paul,

I believe your intuition is correct. I did a similar comparison between an Apo-germinar 600 and a Nikkor 600T. Same subject, same aperture (F32), same film (Provia F). The results showed that the Apo-Germinar produced more DOF, from center to corners, than the Nikkor T. So I also reasoned whether a plasmat type lens would give more DOF than a tele type lens. In theory, if all assumptions hold true, as Pete said "of course there's no difference". However, in practice, the assumption(s) for a plasmat type lens might be slightly different from ones for a tele type, and maybe that's all the diference there is. The difference is munite, but noticeable. A dear friend told me that I should look into one of those SPIE series optics books to find math evidence. Unfortunately, I don't have the books, and probably wouldn't understand the math any more....

Pete, we are looking up to you for a confirmation.

PS How does lens quality contribute to DOF, if there is any? And in theory, how is this evaluated or assumed?

-- Geoffrey Chen (DB45TEK@AOL.COM), May 02, 2001.

Hi Geoffrey

Was it not only because of the better sharpness of the Germinar up to the corners? The Germinar is known as a deadly sharp lens! As far as I know the DOF should be only changing during different f stops and different angle of lenses! So your 450 should have more DOF Paul!

-- Armin Seeholzer (armin.seeholzer@smile.ch), May 02, 2001.

A telephoto lens in canonical form is a lens group with the desired focal length followed by another lens group to shorten the back focal distance and thus shorten the overall lens length. (Here's a link to a page with a diagram of a 500 mm tele lens: http://sr5.xoom.com/nathandayton/page25.html )

I'll assume the 1st lens group is on the left and the 2nd is on the right. You'll also have to menatlly add the light rays from a typical object coming to a focus on the right.

Removing the 2nd group for a moment, the light rays from the object pass thru the 1st element and converge in a cone with the apex at the focal plane. The angle of this cone determines the depth of field. A narrower light cone with a smaller angle corresponds to the lens being stopped down. This makes sense because as you move the object the focal plane moves and with a smaller aperture the light cone is narrower and therefore can tolerate more movement in the object for acceptably sharp focus. (Words fail me; does everybody follow this?)

Conversely, with a greater aperture, the cone has a greater angle and the object has a much smaller range of movement before it is out of acceptable focus.

OK, now add the 2nd lens group. To shorten the focal length the 2nd group causes the light rays to focus to a plane closer to the 1st lens. To do this, the angle of the light cone must increase. This then causes the depth of field to decrease because a smaller change in the position of the object is needed to cause the image to be out of focus.

I'd imagine that this effect would be much more pronounced at large apertures as the light cone angles would be greater.

Hmmm, given that a retrofocus lens as used on an SLR camera has a back focus longer than the focal length of the lens will it also have a greater depth of field than a standard lens?

Cheers,

Duane

-- Duane K (dkucheran@creo.com), May 02, 2001.

I suspect that things work as they really should (DOF for a given aperture and a given focal length is the same for a given circle of confusion), but that true long focals are likely to be better corrected than teles, so they appear to have more depth of field.

The original comparison isn't really fair, because it is the focal length and aperture that determines the DOF, not the angle of view on film. That is why photos made with Minox cameras and consumer digital cameras have so much DOF--the normal lens is around 15mm.

-- David Goldfarb (dgoldfarb@barnard.edu), May 02, 2001.

Paul, There are some points to be positive about and one more question to add. Of course, a 450mm lens will show better DOF. And lenses design can make some indirect influence over perceived DOF, as the comparision within sharp and unsharpness can be confusing if the sharpness limits also varies. A bad lens may probably show great apparent DOF, as nowhere you'll find a sharp image to compare. Now, if telephoto design can change anything, I'd suggest (avoiding all the math involved) it may only deals with depth of focus. I guess Mr. Merklinger would be rather welcome here!

Cesar B.

-- Cesar Barreto (cesarb@infolink.com.br), May 02, 2001.

Armin,

You are absolutely right. DOF, for a given lens, depends on its focal length, aperture used, and the distance between the lens and the object. This is simply known as object-based depth of field (ODOF). I was under the impression that Paul was comparing the two shots made by two different lenses on film, like what I did, so we are actually looking at a different type of DOF, or it's commonly referred to as image-based depth of field (IDOF). IDOF is a bit more complicated than ODOF. Let's agree on that DOF, in general, is a zone of acceptable definition. On film, the limit of such a definition is the distinguishable distance between two tiny dots. We all know that, besides a lens' ODOF and Scheimpflug principle, its sharpness/resolution, contrast, and the film's resolution all contribute to a given IDOF. Since I used the same film, almost same focal lengths, same aperture, processing by the same lab and in the same developer, the variables become lens resolution and contrast for the least. I have not conducted any tests regarding their resolution and contrast, so I can not conclude that the comparison was valid at large. Since you know the Apo Germinar lens is sharper, and I know the Apo Germinar lens is contrastier (my particular example), then the apparent better DOF (IDOF) of Apo Germinar, I observed, over Nikkor T is still true. Furthermore, it's still reasonable to ask the question whether a plasmat type lens will have a better IDOF over a tele type lens, and whether there is any math model(s) to support such a claim. Hope Chris and Kerry would have some test data to show that a plasmat lens in the 600 mm range is generally sharper and contrastier than a tele type lens in the similar focal length range. Cheers,

Duane,

I'm trying to figure out what you are trying to tell me. Frankly, I have a difficulty following it. But don't worry, it's probably my fault. I believe it's a sign of aging :-) I need to study it more carefully.

-- Geoffrey Chen (DB45TEK@AOL.COM), May 02, 2001.

After I presses the "submit" key, I found two more posts. Thanks Cesar. That's the name I tried so hard to recall. Yes, Dr. Harold M Merklinger. Did he write a book about DOF for view camera?

-- Geoffrey Chen (DB45TEK@AOL.COM), May 02, 2001.

Well, I've had a good ponder and a sleep on this, and, from a purely geometric and theoretical point of view, I think my first instinct was correct. There should be no difference.
The projection cone of both a long focus and a telephoto lens with the same EFL, at the same aperture, should be exactly the same. In fact the angle of the cone is dictated purely by the numerical aperture of any lens.
It's well known, however, that spherical and chromatic aberrations, and astigmatism, can increase the apparent DOF, by 'stretching' the plane of focus, and this must be what you're seeing. If the effect is due to spherical aberration alone, then the difference between the two lens should diminish as the apertures are stopped down.

This effect shouldn't be confused with what happens in SLR camera lenses.
In many zoom and all internal focusing lenses, the focus is changed by shortening the EFL. This naturally increases the DOF at closer focusing distances over what would be expected from the marked focal length of the lens.
I'm not saying that this is the full story, all I'm saying is that DOF calculations, which make the assumption of a perfect thin lens, can't be used to explain any difference between a telephoto and a long focus lens.

-- Pete Andrews (p.l.andrews@bham.ac.uk), May 03, 2001.

Geoffrey:

Yes, Merklinger wrote two books, "The Ins and Outs of Focus" and "Focusing the View Camera". He also has an interesting website at http://fox.nstn.ca/~hmmerk/.

-- Ken Burns (kenburns@twave.net), May 03, 2001.

Ahem - you can scratch my cunning theory a few posts back. I consulted the books last nite (after posting I'm afraid) and my memory of how tele lenses work was wrong. The only thing I had right was that two lens groups were used. If my

A tele lens has two lens groups. The 1st is positive and has a focal length shorter than the overall desired focal length. The 2nd is negative (diverging) and is used to bring the focal length up to the desired value. In essence, it is a simple lens followed by a magnifier. The exact same principle is used with SLR lenses and 2x teleconverters (Imagine that!).

The cone of light from this aggregate assembly is then equivalent to that from a longer, simple lens and there should be no difference in the depths of field for the two lenses. However, when going away from focus, the various abberations from the 1st lens are magnified by the 2nd lens group in difficult to predict ways. My life in engineering (not optical unfortunately) has always taught me that complicated systems have strange interactions that don't often improve the situation.

Does this make any more sense? If not, I have an even more cunning theory...

Cheers,

Duane

-- Duane K (dkucheran@creo.com), May 03, 2001.

Thanks for the replies so far and for the brainstorming! I admit my question was not scientifically elaborate and was based on simple assumptions, comparing what was not comparable. I still would be interested in having practical evidences of if hyperfocal varies or not from one lens design to another, but actually I have found some theoretical elements that explain why my two shots showed such a difference in DOF. It would be interesting if someone could provide a scale in percentage of how DOF varies from one focal length to another or a formula (Pete, do you have that?). What I have seen from a few DOF tables is that DOF is non-linear compared to the focal length difference. For example a 150mm at f22 focussed at ten meters has a DOF from 5m to infinity. I would have thought that a 300mm had half that ammount but it's DOF is from 8m to 13m. Only 5 meters! That explains why I saw such a difference from the two lenses used in my comparison. They were only 1/3 apart but the DOF (focussed at 50m and closed at f32) was more than100 meters for the 450 when it was merely 15 meters for the 600 (these numbers are just what I can figure me by looking at the slides). Thus, the practical evidence is that very long focals are of limited use in landscape photography, the shot from the 450 (on 4x5) once cropped produces a good image, very sharp, when the shot from the 600 is desperately shallow. So you saved me the disappointing experience of changing my 600T for a 600C. Anyone interested in a cheap Fujinon 600T out there?

-- Paul Schilliger (pschilliger@smile.ch), May 03, 2001.

I just checked from Nikon's technical info's, as I had in mind that lense's DOF is cut by half when the focal is doubled, and found indications that a 1,4 x teleconverter preserves 70% of the original lense's DOF and a 2 x converter 50%. So obviously, a 100mm lens with 2 x converter should have much more DOF than a 200mm lens. Am I getting it right or am I missing something? If it is so, shoulden't the DOF vary with the lens formula?

-- Paul Schilliger (pschilliger@smile.ch), May 04, 2001.

For a given aperture and circle-of-confusion the DOF varies proportionally to the inverse of the square of the focal length.
DOF can be worked out accurately by going back to first principles, in the form of the conjugate focii formula: 1/F= 1/v + 1/u, and the fact that the tangent of the angle of the cone of light projected onto any point on the focal plane is easily calculated from the reciprocal of the numerical aperture.
Got that? Good. Now we can move on.
The change of focus which will result in a certain diameter of circle-of-confusion is calculated by didviding it (the CoC) by the aforementioned tangent. In other words, since the tangent is the reciprocal of the numerical aperure, the CoC multiplied by the F number gives the change of focal distance which will result in that CoC. This can be summed up as [ N*C = delta F ], where N = the aperture of the lens, C = the diameter of the circle of confusion, and delta F is the change of focal distance.
Still with me? Excellent!
Having first calculated the nominal focal distance from the subject distance and the lens focal length, using the formula for conjucate focii, we can then proceed to modify the lens to film plane distance by adding or subtracting the amount we previously calculated by multiplying the CoC by the f number. (Apologies if I confused you with my poor punctuation of that last sentence)
Putting those two new values of image distance back into the conjugate focii equation, we finally arrive at the two subject distances which correspond with the shift(s) in focus needed for a given circle of confusion.
There, that wasn't too hard was it? Geometry 101.
It's also easy to see that the double use of the conjugate focii equation, to arrive at the final answer, results in some of the terms in that equation being squared. Thus we can deduce that depth-of-field is inversely proportional to the squares of both a change in image distance and in focal length. Transparently obvious now, isn't it?

In case you're wondering. Yes, I did mean all that as a bit of a leg pull, but the information is correct, if you care to work your way through it.
As an example of the above in action, I've done the figuring for you on a few different focal lengths.
All the examples use the same parameters of f/22, and a CoC of 0.1 mm.
300mm lens focused on infinty: nearest focus point = 41 metres
300mm lens focused @ 10m: Nearest focus = 8.14 m, furthest focus = 13 m

450mm lens @ infinity: nearest focus point = 92.5 m
450mm lens @ 10m: nearest focus = 9.1 m, furthest focus = 11.1 m

600mm lens @ infinity: nearest focus point = 164 m
600mm lens @ 10m: near focus = 9.5m, furthest focus = 10.57 m
So you can see that the depth of field is reduced to a quarter for a doubling of focal length, and that comparatively small changes of focused distance can have a significant effect on DOF.
Boy I need a drink after that!

-- Pete Andrews (p.l.andrews@bham.ac.uk), May 04, 2001.

Paul WRT the question about teleconverters (which you sneaked in while I was composing my treatise on DOF). I believe that Nikon thinks its customers are too dumb to realise that the effective aperture is altered by the use of a converter. A 2x converter doubles the numerical aperture, and a 1.4x converter multiplies the aperture number by 1.4.
If you take the aperture marked on the prime lens, then yes, the DOF is only halved when you use a 2x converter, but if you work it out properly, then you're doubling the focal length, and closing the aperture down by two stops simultaneously.
The two stop difference in aperture approximately doubles the DOF, but at the same time, the doubling of focal length reduces DOF to a quarter. Double one-quarter equals one-half, equals the figure that Nikon give (while neglecting to mention that you've effectively closed down two stops!).

-- Pete Andrews (p.l.andrews@bham.ac.uk), May 04, 2001.

Wow Pete, that sure deserves a drink! Forgive me if I pass above the formulas, (I might explode my neurones should I try hard enough), but knowing that the DOF is reduced to one quarter when the focal is doubled is a good base and should be helpful. By the way, I knew the answer was the additional f-stops but as soon as I had pressed the submit button on the converter addition! The practical side of all this is that some takings cannot be achieved on large format. For example, I had made some years ago a good image with a Pentax 67 with a 400mm closed at f32. The shot is a terrific compression of plans distant of say ~ 200 m from front to back, where everything is in sharp focus. I always wanted to achieve the same shot on 4x5 with the equivalent lens of 600mm. But this will be technically impossible, unless using perhaps apertures where the degradation is such that it might be worse than the 6x7 quality. This makes me wonder how 8x10 users manage to get sharp shots with medium and long lenses for the format!

-- Paul Schilliger (pschilliger@smile.ch), May 04, 2001.

If you go up in format, the acceptible circle of confusion gets larger, because you're not enlarging as much. In any case, with long lenses and 8x10", things like camera movement with all that bellows become bigger issues than diffraction at f:64.

-- David Goldfarb (dgoldfarb@barnard.edu), May 04, 2001.

It is worth pointing out that the conventional definition of DOF is carefully constructed so as to be invariant with the lens type, and even the projection (rectilinear, fisheye, telecentric etc). I therefore suspect that any difference between a tele and a non-tele of the same focal length lies in uncontrolled aberrations in the more complex tele lens. Also, in a world of linear tolerances, a tele will have a greater susceptibility to vibrations of the camera's structure because the reduced flange-to-film distance acts as a lever arm when converting linear vibrations into angular ones.

There is one way that apparent DOF can be affected, even in a world of perfect optics. The conventional derivation of DOF looks at the cone of light projected by the lens, with its base on the rear principle plane and its point at the film position. Defining a circle of confusion allows one to conceptually vary the film position between two limits, which are converted via the lens equation to distances out in front of the camera.

The problem is that this is not what photographers actually want to know. In the real world you focus on one distance and accept as acceptably sharp all those objects which are blurred by less than the circle of confusion at the film position. The difference is obvious if you think about it:

The conventional derivation is shown first. Note that although light from the far DOF plane (green) does have a light cone with a diameter equal to the COF at the required posiion, it has an even larger light spot at the film position. Conversely, the light from the near DOF plane (red) forms a spot at the film position which is smaller than the COF. In Real Life (TM) the near limit is too conservative, and the far limit too optimistic.

The STRUANDOF is shown second, and represents what photographers actually do. Now the diagram has been adjusted so that light from both the far DOF and the near DOF planes forms a circle on the film with a diameter equal to the COF. The result is to move the ideal focussing point within the DOF limits, and to change the total DOF for any given aperture

Calculating the new DOF limits I leave as an excercise for the reader.

-- Struan Gray (struan.gray@sljus.lu.se), May 08, 2001.

Note that although light from the far DOF plane (green) does have a light cone with a diameter equal to the COF at the required posiion, it has an even larger light spot at the film position.

Oj vey! I meant of course: Note that although light from the far DOF plane is focussed at a position where the diameter of the object's light cone is equal to the COF, it creates a spot at the film position which is larger than the COF.

-- Struan Gray (struan.gray@sljus.lu.se), May 08, 2001.

Well explained. It's very impressive. Thanks a lot!

-- Geoffrey Chen (DB45TEK@AOL.COM), May 09, 2001.

Gentlemen, I have just run across this discussion group while looking for depth of field information, and one of you may have an answer to my question. I was discussing dof with an aquaintance, and I made the point that dof is dependent only on the object size/image size ratio, but he countered my argument by saying that that the enlargement factor has to be taken into account. For example, if two negatives are made with two lenses, one of which is twice the focal length of the other, then the dof in two equal-sized prints from the whole negatives would be different. His point was that if negative made with the shorter lens was cropped to reduce the view to that of the negative from the longer lens, and then enlarged to the same size as the first two prints, the dof would be the same as that from the longer lens. Tis idea has never occurred to me, and to my knowledge is not mentioned or allowed for in standard formulae ond descriptions of dof. Does anyone have a comment on this? TIA, Colin

-- Colin Donoghue (cjdonoghue@xtra.co.nz), May 29, 2001.