A Reference on DOF?

[Don Merz]

Can someone point me to a good reference source to understand the pure physics of DOF? I think I am just easily confused and my photographic education is lacking... but I just don't get it. Why does DOF increase when the lens is stopped down? Because the hole gets smaller? The part that really bothers me is that DOF apparently has nothing to do with reducing the amount of light coming through the aperture. Otherwsie DOF would increase when we put ND filters in front of the lens. Is it the position of the aperture within the lens structure? Or can the aperture be located anywhere? Behind the lens? In front? Can the aperture be off-center and still have the same increase in DOF when stopped down?

Corollary questions: So a hypothetically perfect pinhole camera would have perfect depth of field from 1mm to infinity? How small would that pinhole have to be?

Anyway, I am sure there is some great referecne source out there somewhere that makes all of this as clear as a bell and I would appreciate it if someone would point me in that direction.

Thanks.
--Don Merz

[Jeff Conrad]

For a given format and final-image size, DoF depends on the lens focal length, the subject distance, and the lens f-number--it has nothing to do with the amount of light entering the lens. You indeed get the same effect when the aperture is off center, and almost the same effect if the lens is tilted.

There are innumerable web resources for DoF, ranging from excellent to utter nonsense. You might try the Wikipedia article, and you also might want to look at Paul van Walree's web site for a comprehensive yet accessible discussion. I have a paper (PDF) posted on this site that covers the topic quite extensively, but may go into more detail than you want.

[Don Merz]

Thanks for your kind reply. I will look those references up.

Your list of DOF factors does not mention the final image size which is a factor in DOF that I don't understand. For instance, I have a 4x5 camera with a macro lens on it and I am shooting a 4x5 image at a given f-number, with a given lens and subject distance. Now I pull out my film holder, slap in a 6x7 roll film back--and my DOF changes (increases!) because the final image format is smaller? That is not intuitive to me. I am missing it.

[jim kitchen]

Dear Don,

Tough question...

There are many mathematical sources available that explain the simple math behind the depth of field question, and if you would like the quick and dirty answer it can be found here: http://en.wikipedia.org/wiki/Depth_of_Field

In a nutshell, the simple answer can be described as follows, without getting too technical, and without introducing other influencing factors such as the lens focal length, lens design, object's distance from the lens vertical axis, et al...

1. simply stated, you focus on an object at a specific distance with the lens aperture wide open, such as f-2.8, where the diameter of the aperture opening might be 1.0 inches;

2. an object measured just behind this focal point, and an object measured just in front of this focal point are blurry because each object's "circle of confusion" upon the film's surface happens to be larger than the fine focus point's circle of confusion, located upon the film's surface. The measured circle of confusion is measured at film's surface, which happens to be the same focal point location for the focused object...;

3. that said, the most simplistic view regarding depth of field and its relationship to apertures, again excluding all other influencing factors, can be best described by stating that the non focused object's circle of confusion shall be divided by the current aperture, generating a resultant depth of field value, measured in inches;

4. so, when one divides the object's circle of confusion, measured in inches, by a smaller aperture measured in inches, such as f-16 which has an aperture opening of 0.0625 inches, the resultant depth of field answer, measured in inches, obviously becomes larger.


For example, excluding all other required information:

1. Measured circle of confusion (c) equals 0.5 inches; <=== measured object in front of and, or behind the original focal point...

2. current aperture f-2.8 (d) equals 1.0 inches;

3. since simplistic view for DOF equals (c) divided by (d);

4. then the DOF (0.5) / (1.0) equals 0.5 inches... <=== calculated DOF for a lens with a wide open aperture, measured at f-2.8...

5. making the aperture smaller we set it to f-16, which is measured at 0.0625 inches;

6. therefore the resultant DOF is (0.5) / (0.0625) which equals 8.0 inches.


Again, many good technical solutions and better simplistic solutions are available, both graphically and mathematically on the internet, which lead to other questions and solutions, such as hyper focal distances for various focal length lenses, and their associated apertures. If you had the technical information for a lens, you could calculate the DOF for any aperture, when you know the object's measured focal distance from the vertical axis of the lens.

Again, I hope this simple answer will suffice for the moment...

jim k

[Jeff Conrad]

Everything that is acceptably sharp in the final image is within the DoF; what is "acceptably sharp" depends on visual acuity, viewing distance, and the enlargement of the initial image to the final image. The common assumption is an 8x10 image viewed at 250 mm; the usual assumption for visual acuity at 250 mm is that any blur spot smaller than 0.2 mm is indistinguishable from a point. Consequently, any object point that has a blur spot smaller than 0.2 mm in the final image is within the DoF.

The acceptable blur in the initial image is smaller than 0.2 mm by the enlargement; for example, if a 4x5 initial image is enlarged 2x to make an 8x10 final image, the acceptable blur in the initial image is 0.1 mm, the common value of the acceptable circle of confusion for 4x5. If a 16x20 final image is to be viewed at 250 mm, the visual acuity does not change but the enlargement is 4x, so the acceptable CoC in the initial image is 0.05 mm; consequently, if the subject distance, lens, and f-number are not changed, the DoF is halved.

For the 8x10 final image, again with subject distance, lens, and f-number the same, a 6x7 initial image requires greater enlargement, so it has less DoF. On the other hand, if the focal length is adjusted so the the angle of view is the same for the 6x7 image (the "same picture" in both formats), the 6x7 initial image has greater DoF.

There are many possible combinations of the relevant factors, far too many to discuss here. The topic is covered in detail in the Wikipedia article under DOF vs. format size.

To my mind, most discussions of DoF quickly become pointlessly academic. The camera format, final-image size, subject distance, and lens are largely dictated by aesthetic considerations (the format and lens are also constrained by the photographer's equipment). Consequently, the only real remaining control is the lens aperture: when the aperture diameter is reduced, the blur spots from near and far object points are smaller; conversely, near and far objects at greater distances from the subject will give the same size blur spots, increasing the DoF.

[Brian Ellis]

The simplest way to think of it for me is this: there can be only one plane in a scene that's in focus. Everything on that plane will be represented by a point on the film. Everything in front of and behind that plane will be represented by a circle. The closer to the plane the circles are, the smaller they'll be and so the more they'll look like points. The more they look like points the more they'll appear to be in focus even though they really aren't (this area in front of and behind the plane of focus that appears to be in focus represents the depth of field). And vice versa, i.e. as the distance of the circles in front of and behind the plane of focus increases the bigger the circles get and the less they'll look like points. At some point they'll be so large that they won't appear as points and so they'll obviously be out of focus (i.e. they'll be outside the depth of field).

If the print is small enough all the circles in front of and behind the plane of focus may look like points and and so everything in the photograph will appear to be in focus from front to back. As the print is enlarged more and more the circles get bigger and more and more of the circles cease to look like points so that more and more of the areas in front of and behind the plane of focus will be obviously out of focus.

You speculated that the reason depth of field increases when the lens is stopped down is because the "hole" gets smaller. That's correct. The smaller the hole the smaller the circles in front of and behind the plane of focus will be. If the other two factors affecting depth of field (camera-to-subject distance and focal length of lens) remain the same, the smaller aperture will produce greater depth of field.

All of this could be expressed better and more accurately in scientific and mathematical terms. But I think this is sufficiently accurate to get an idea of what's going on with depth of field. Hopefully it isn't too confusing.

[Emmanuel BIGLER]

To the list of references provided by Jeff, we could add a recent white paper by Dr. Nasse from Carl Zeiss.
http://www.zeiss.com/C12567A8003B8B6...5_Bokeh_en.pdf
Jeff will probably agree that "inifinity plus one metre is still infinity", so "an innumerable number of web resources plus one is still innumerable"

On pages 21 and 22 of Dr. Nasse's paper, section "Depth of field and modulation transfer MTF", there is an interesting discussion explaining how conventional DOF is altered by digital pre-processing of images in consumer cameras, aimed at pre-sharpening the image to deliver it under a more flattering aspect.
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Regarding DOF in a pinhole camera :
Corollary questions: So a hypothetically perfect pinhole camera would have perfect depth of field from 1mm to infinity? How small would that pinhole have to be?

There is a very provocative way to answer this question.
If we take a sharpness criterion that was in use at the beginning of the XX-st century, i.e. considering a circle of least confusion for acceptable sharpness equal to the diagonal "L" of the image divided by 1000, even an optimum pinhole camera for any given format fails to satisfy this criterion.
Hence, according to this criterion of L/1000, depth of of field in a pinhole camera is never infinite, but always : nil

Regarding image quality in a pinhole camera and optimum pinhole size, only 2-3 simple formulae explain almost everything.
- for a given projection distance "D" between pinhole and film, the optimum pinhole aperture "a" is about

a (in mm) = (square root of D(in mm) ) / 28

See the reference book by Leslie D. Stroebel, ``View Camera Technique'', 7-th Ed., ISBN 0240803450, Focal Press, 1999, with nice examples of images taken with an optimum and non-optimum pinhole in 8x10" format. Strobel's images are the very few I know where a side-by-side comparison of image quliaty is done with a pinhole size equal to 1/1, 1 a,d 2x the optumum value. Hence I tend to prefer Stroebel's formula (square root of D(in mm) ) / 28 to any other formula, since it is backed by a serious, experimental comparison.

- the smallest spot size in the image delivered by an optimum pinhole of diameter "a" cannot be smaller than the aperture size itself, it is something like 1.4 times the optimum aperture a.

Hence for the 4x5" format, diagonal of about 150 mm, the classical "vintage" circle of east confusion L/1000 yields someting in the range of 150 microns, and this is not very stringent ; modern lenses can of course deliver images much much sharper than that... but not al over the range of the subject, this is the basic DOF compromise.
Regarding the best optimum pinhole for a projection distance of 90 mm (a wide-angle covering the 4x5" format), it is about 0.34 mm, 340 microns, the minimum spot size in the image being bigger, may be .4 mm but this does not change the conclusion : no point of the image delivered by an optimum pinhole can satisfy the classical sharpness criterion demanded by photographers in 1900...
You could argue that a pinhole could cover up to 120 degrees, and consider a projection distance of 60 mm : even doing so, the minimum projected spot size cannot be smaller than the optimum diameter of 0.28mm @60mm projection distance (square root of 60)/28 = 0,28

So we could re-formulate the question
So a hypothetically perfect pinhole camera would have perfect depth of field from 1mm to infinity?
In a perfect, optimum pinhole camera, you can, if you wish, consider that the depth of field covers the whole range from 1 mm to infinity.
But your sharpness criteria in this regime are definitely much, much, less stringent than for any modest, vintage, photographic lens...

[Jeff Conrad]

I would agree that "an innumerable number of web resources plus one is still innumerable." We'd probably be much better off concentrating on the worthwhile resources, which are considerably fewer than innumerable, and would definitely include Dr. Nasse's article. For what it's worth, the Wikipedia article has quite a list of resources, under both References and External links. Dr. Nasse's article is included in the latter section.

[Ash]

I couldn't get my head around it for a while either. It's the diameter of the iris that provides the size of the out of focus blobs of light. They're sometimes called 'circles of confusion'.

The smaller the aperture (iris), the smaller the blobs of light til they look like dots. The smaller the dots, the more resolution in the out of focus areas, which in turn look apparently sharp.

Aperture is related to focal length, so when you have a big lens on a big camera, the depth of field is more obvious, because the aperture is bigger.

[Jack Dahlgren]

Thanks for your kind reply. I will look those references up.

Your list of DOF factors does not mention the final image size which is a factor in DOF that I don't understand. For instance, I have a 4x5 camera with a macro lens on it and I am shooting a 4x5 image at a given f-number, with a given lens and subject distance. Now I pull out my film holder, slap in a 6x7 roll film back--and my DOF changes (increases!) because the final image format is smaller? That is not intuitive to me. I am missing it.

The DOF is based on how big the blurry circle is. If you contact print both pieces of film the DOF would be the same. If you enlarge one by 5 times and another by 10 then the blurry circle with be twice the size on the one enlarged more. Your DOF does not increase by changing film.