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DoF for Smaller Surfaces


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#1 Chris Durham

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Posted 30 October 2009 - 06:06 PM

This is an elementary thing, I know, and I thought I had it figured out but there's so much muddled information on the topic. Someone says something contrary and it confuses the notion.

If I put a 35mm lens on a camera with a smaller capture plane, say 16mm, is my DoF based on a 35mm capture or 16mm?

I thought that because the 35mm lens was projecting for a 35mm plane, the DoF would be the same as if it were 35mm film. In other words the 16mm film just captures a smaller portion of what the lens projects, which incidentally narrows the field of view (i.e. crop factor).

Am I wrong in thinking this?
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#2 Chris Millar

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Posted 30 October 2009 - 07:22 PM

16mm

Not that I think it affects my answer but do you mean a 35mm focal length or all lenses with 35mm coverage ?
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#3 Chris Durham

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Posted 30 October 2009 - 07:26 PM

35mm coverage
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#4 Jonathan Bowerbank

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Posted 30 October 2009 - 08:48 PM

A 50mm focal length lens, is a 50mm lens is a 50mm lens...depth of field wise.

However, if it's a 35mm lens (meaning for a 35mm frame) on a 16mm camera, your biggest difference is in the field of view. Your depth of field may seem more shallow, but that's because effectively a 50mm seems like a 100mm when thrown on a 16mm camera.

You can really see the difference when you're on a RED and switching between 4k & 2k. Same DoF, more narrow FOV
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#5 Chris Durham

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Posted 30 October 2009 - 10:20 PM

This is what I thought, but then someone I respect said something otherwise and I had to do a sanity check. So theoretically (even though it's not out yet) when the Ikonoskop camera comes out, if I put Canon lenses on it, I should get the same DoF as if I were shooting on a 35mm (full frame) camera, right? Same thing if I had a PL mount and used, say, 35mm speed primes?
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#6 Chris Millar

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Posted 30 October 2009 - 11:01 PM

Its the play between blow up (or reduction) between formats to achieve the same FOV that causes the DoF change...

What was acceptably in focus in a smaller format - say an arbitrary plane just off the focal plane - will now be able to be differentiated as more out of focus compared to the actual focal plane ...
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#7 John Sprung

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Posted 31 October 2009 - 01:55 AM

A 50mm focal length lens, is a 50mm lens is a 50mm lens...depth of field wise.


Very true, but also surprisingly difficult to express clearly. Here's another try at saying the same thing:

Provided that the lens covers the format you're shooting, it doesn't matter what format it was designed for. The right DOF table to use is the one for the format and focal length you're using.



-- J.S.
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#8 Chris Keth

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Posted 31 October 2009 - 02:29 AM

.

Edited by Chris Keth, 31 October 2009 - 02:31 AM.

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#9 Chris Keth

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Posted 31 October 2009 - 02:39 AM

I dug up an old post of mine that explains simply and concisely the factors that determine depth of field:

The simplest way to state depth of field I have found is this:

Two things and only two things affect depth of field. (1.) Magnification, which is the product of focal length and subject distance. and (2.) f/stop of the lens.

There are even rules for the change in depth of field when one of these variables changes:

If you double focal length, the depth of field will be cut in half.

If you halve the subject distance, depth of field is halved.

For each f/stop that you open up, depth of field is divided by the square root of 2.


I will add that the circle of confusion has sort of an overarching effect on depth of field by helping to define what "in focus" means for the optical system. It changes what you calculate but not what you see. It doesn't normally change in the course of filming and a lot of people don't even know the concept, so I didn't include it in the old discussion for simplicity sake.
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#10 John Sprung

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Posted 31 October 2009 - 05:19 AM

Yes, in fact it would be a good idea to shoot some diagonal newspaper tests and use them to decide what you want to use for the circle of confusion. It's a subjective decision that should be made by the DP, not an engineering constant.




-- J.S.
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#11 David Mullen ASC

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Posted 31 October 2009 - 12:07 PM

Yes, while in theory, a 50mm is a 50mm on any format, different formats have different Circle of Confusion figures which do affect depth of field calculations. However, CoC is not really an exact science because it's based on the variable notion of degree of image enlargement -- i.e. it sort of assumes all formats will end up being displayed on the same sized screen with the same viewer distance to the screen.

If you look at a depth of field chart for a 50mm lens for the 35mm format and then figure that you'd switch to a 25mm lens for a format that is half as wide to get the same horizontal field of view... so you then look at the depth of field chart for a 25mm lens, you realize that you gain four stops more depth of field at the same f-stop as the 50mm, which isn't right -- because for the format that is half as wide, your CoC figure will be twice as critical if the final image size will be the same as the 35mm version, so a four stop difference becomes a two stop difference, which is about right in practical terms.
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#12 Chris Durham

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Posted 31 October 2009 - 04:30 PM

So let me make sure I understand this all correctly, because I've been seeing what is probably a very similar thing written in different ways. I want to put what I understand into my own words and see if I get it right.

Changing the format (capture plane size) without changing the coverage (diameter of lens projection) does not change DoF.

Changing the format without changing the coverage does change AoV, which perceptually increases focal length (zoom, blow-up, crop factor).

Changing the AoV, perceptually zooming in, results in perceptually larger circles of confusion.

These "larger" CoC's, taken with the perceptually increased focal length result in a perceptual DoF which matches the format at the adjusted (perceptual) focal length.

I'm not sure that seems right to me. These circles are very confusing.
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#13 Chris Keth

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Posted 31 October 2009 - 05:23 PM

Changing the AoV, perceptually zooming in, results in perceptually larger circles of confusion.

These "larger" CoC's, taken with the perceptually increased focal length result in a perceptual DoF which matches the format at the adjusted (perceptual) focal length.

I'm not sure that seems right to me. These circles are very confusing.


All a circle of confusion does is define what is "in focus" and what is not. It says, "Once this footage makes it on screen, a circle X or smaller will appear as a point." That allows us to track that circle back through the system and define an equivalent circle on the film. The circle of confusion will not change once you have assigned it for the imaging system. Generally, standard circles of confusion are used and it's good enough.


For the most part, it's good enough to know that smaller formats will have smaller working circles of confusion because they will generally be enlarged more by the time they get to the movie screen.

You can see this in practice if you think of a movie that mixes 16mm and 35mm for theatrical projection. Without even worrying about the exact numbers, you just know that the 16mm will be enlarged 2x more than the 35mm because it is half the size and needs to become the same final size on the screen.

We can use the same example and involve real-life numbers. The standard CoC I (and a lot of others) use for super 16mm is .0005". The standard for 35mm is .001"- twice the size. Because 16mm is half the size of 35mm, it requires half the CoC to remain equally in focus. This sets up a ratio of CoC to frame size that remains pretty constant for materials meant for the screen. It gets trickier when we talk about shooting for print because various prints will be viewed at different distances, but that's a tangent I won't enter since this is not a still photography discussion.
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#14 David Mullen ASC

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Posted 31 October 2009 - 06:52 PM

Changing the format (capture plane size) without changing the coverage (diameter of lens projection) does not change DoF.


Except that different sized formats use different Circle of Confusion figures, which does affect Depth of Field figures.

Changing the format without changing the coverage does change AoV, which perceptually increases focal length (zoom, blow-up, crop factor).


It doesn't "perceptually" increase or decrease the focal length, the focal length is a fixed number for that lens (50mm, let's say) -- what it changes is the Field of View, making it either narrower or wider because of the cropping of the lens coverage. The mental trick here is to stop associating a focal length with a particular field of view, except for a specific format, i.e. stop thinking that when you move a 50mm lens from a 35mm camera to a 16mm camera, it becomes a longer focal length... it doesn't, it's still a 50mm lens, it's just that on a 16mm camera, it has a more telephoto view.

Changing the AoV, perceptually zooming in, results in perceptually larger circles of confusion.


If you mean that using smaller formats will crop the lens coverage, you generally have to use smaller, more critical, circle of confusion figures due to the increased degree of final image enlargment, assuming the same size for the final image as something shot on a larger format.
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#15 John Sprung

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Posted 01 November 2009 - 06:03 AM

A point at any distance other than the distance you're focused on is rendered as a circle on the film or chip. This is a circle of confusion. The farther from the plane of critical focus, the bigger the circle. In order to compute DOF tables, we have to pick a size for the circle to use as the boundary between OK and too soft. Typically, 0.001" is used for 35mm, and 0.0005" for 16mm. But now that we have computers, there's no reason you couldn't do some tests and pick your own circle of confusion size. I did a spreadsheet for this that's available on Dave Auner's web site.




-- J.S.
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#16 Chris Durham

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Posted 02 November 2009 - 01:07 PM

Thanks everybody. I think I have a better grasp of all the concepts involved here now. Accounting for smaller CoC's was the thing I hadn't really considered. I think I have a good idea of the basics of how these play together, and if I go do some math now it will help me internalize it all.
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#17 Chris Durham

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Posted 02 November 2009 - 02:53 PM

Nope, I'm still missing something. I went and did some math using some DoF formulas from wikipedia - basically I used Chris's suggested CoC figures for 35mm and 16mm formats, and did calculations for a subject at 2 different distances. Focal length and aperture remain the same.

The problem is according to these numbers 16mm yields a NARROWER DoF, all other things being equal, which is exactly opposite of how things are supposed to work. What am I missing?

50mm lens f/4.0 CoC .0254mm (.001", 35mm film) Subject Distance 2m

Hyperfocal = 2500mm / .1016 = ~24,606mm = ~24.6m

Near Limit = 49.2 / 26.6 = ~1.85m

Far Limit = 49.2 / 22.6 = ~2.18m

DoF = ~2.18 - ~1.85 = .33m

----------------------------

50mm lens f/4.0 CoC .0127mm (.0005", 16mm film) Subject Distance 2m

Hyperfocal = 2500mm / .0508 = ~49,213mm = ~49.2m

Near Limit = 98.4 / 51.2 = ~1.92m

Far Limit = 98.4 / 47.2 = ~2.08m

D0F = ~2.08m - ~1.02m = .16m

****************************

50mm lens f/4.0 CoC .0254mm (.001", 35mm film) Subject Distance 10m

Hyperfocal = 2500mm / .1016 = ~24,606mm = ~24.6m

Near Limit = 246 / 34.6 = ~7.11m

Far Limit = 246 / 14.6 = ~16.85m

DoF = ~16.85 - ~7.11 = 9.74m

----------------------------

50mm lens f/4.0 CoC .0127mm (.0005", 16mm film) Subject Distance 10m

Hyperfocal = 2500mm / .0508 = ~49,213mm = ~49.2m

Near Limit = 492 / 59.2 = ~8.31m

Far Limit = 492 / 39.2 = ~12.55m

D0F = ~12.55m - ~8.31m = 4.24m
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#18 John Sprung

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Posted 02 November 2009 - 03:00 PM

The problem is according to these numbers 16mm yields a NARROWER DoF, all other things being equal, which is exactly opposite of how things are supposed to work. What am I missing?


You have the same 50mm lens for both 16 and 35 film. You need to run the numbers with a 25 mm lens on the 16 mm camera to get the same field of view, and the greater DOF. The idea is that for matching shots, the smaller format has more DOF.

If you want to use the spreadsheet for this, here's the link:

http://www.auner.net/misc/DOF/DOF.xls




-- J.S.
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#19 Chris Durham

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Posted 02 November 2009 - 04:42 PM

Thanks John, that helps. What was confusing is the "50mm lens is a 50mm lens is a 50mm lens..." thing because it doesn't take into account AoV; but when you state it like that - DoF is deeper in a smaller format at the same AoV - it all comes together. What I was trying to reconcile is the notion that 50mm is 50mm is 50mm, but at half the format size is effectively double - it's a little confusing.

Thanks for the link to the spreadsheet - was looking for it earlier. I did my own math again though because it helps me learn:

50mm lens f/4.0 CoC .0254mm (.001", 35mm film) Subject Distance 10m

Hyperfocal = 2500mm / .1016 = ~24,606mm = ~24.6m

Near Limit = 246 / 34.6 = ~7.11m

Far Limit = 246 / 14.6 = ~16.85m

DoF = ~16.85 - ~7.11 = 9.74m

----------------------------

25mm lens f/4.0 CoC .0127mm (.0005", 16mm film) Subject Distance 10m

Hyperfocal = 625mm / .0508 = ~12,303mm = ~12.3m

Near Limit = 123 / 22.3 = ~5.52m

Far Limit = 123 / 3.2 = ~38.44m

D0F = ~38.44 - ~5.52m = 32.92m



So, it all makes sense now. It made sense before, then a discussion I thought I understood made sense in another way, then someone told me otherwise and muddied the issue again. Now I have it, with numbers. Thanks everybody.
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#20 Ruby Quincunx

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Posted 06 November 2009 - 06:27 PM

Forgive me for jumping in on this thread, but my question is right in line with this.

Regarding choosing a practical standard CoC for the sake of convenience (e.g., 0.025mm for 35mm, 0.0127mm for 16mm), what would be a sound choice for a 2/3" sensor at 16:9 HD or 1.89:1 2k, under similar intended viewing circumstances? Is it safe to calculate a CoC using the d/1500 or d/1730 formulae one sees online (where d = size of diagonal of sensor)? So, 2/3" sensor at 9.6mm x 5.4mm has a diagonal of 11mm, yielding a CoC of 0.007mm by the first formula & 0.006 by the second. Or would something else be more appropriate?

By the way, f/Calc at http://fcalc.net/ seems like a pretty good DoF, Hyperfocal, f-stop difference, etc. calculator. Have a look.

Edited by Ruby Quincunx, 06 November 2009 - 06:28 PM.

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