Depth of focus (NOT field) calculation query

Hoping the LF subforum to be the most appropriate for this question ...

Do please note this is NOT a question about depth of field!

I am a very inadequate mathematician indeed, and thus I am struggling to determine the depth of focus for a given focal length, aperture and format. (I am trying to establish the room for error I might have if I wanted to construct a fixed-focus LF "box" camera.)

The parameters are:

Lens focal length: 150mm
Aperture: f/45
Format: 10"x8"
Assumed Circle of Confusion: 0.2mm
Object distance: 1000m (i.e. for all intents and purposes, ∞)

The Blessed Wikipedia offers the following equations:
t=2Nc(v/f)
where t=depth of focus, N=f/stop, c=circle of confusion, v=image distance and f=lens focal length.

as well as t≈2Nc for all but large magnifications

My Focal/Ilford Manual also offers t=2Nc(v/f), but also

t=(2f^2)/h, where h=hyperfocal distance (presumably for a given focal length and f/stop?)

I had assumed that the depth of focus would be in the order of a perhaps only 2 or 3 millimetres at most, but however I plug numbers into the equations I get a range of answers from 17mm up to the quite absurd 120m!

I presume I am misunderstanding something rather basic, to say the least.

SO ... how should one use these equations to correctly calculate depth of focus? (or is there a simpler way?)

I can't help with the math, at all.
There isn't much room for error though and that's why it's the most important measurement when building a camera. Why do you want to know and what are you going to do with these numbers when you come up with them?

Use a software DoF tool. I use Dead Link Removed. You'll have to define the 8x10 format in the database which is easy. The putting in your numbers for focal length and aperture and CoC gives me a depth of focus of 18.3 mm. I used a 35mm CoC of 0.027 mm in Barnack which equates to 0.203 mm on 8x10 inch.

18mm is right unless you are doing macrophoto with your LF(!!). BUT, that is total range of allowable error. Margin of error either side of the "perfect" position is half that.

Plus, if you plan on a fixed-focus camera, you need as much margin as you can get for depth of field. If you start eating into that margin with errors of positioning the lens, so much lost in quality or flexibility...

Finally, I find it strange to scale the acceptable CoC proportional to the size of the negative. It means you have no better expectations for sharpness (relative to image size) in LF compared to miniature format.

wildbill: I explained my reasons for wanting the numbers in the 4th sentence of my OP.

spijker: thanks

bernard_L: Thanks. No, there won't be any macro going on! and yes, I realise the need for DOF, and I do realise the need for minimising error. However, this is a "fun foamcore" project, as I have no workshop, woodworking tools or indeed skills, and thus none of the things of most of the LF community take for granted. I really just want to know how much wiggle room I have, if any. I'm not sure whether your final remark is for me or for spijker - for my part, I simply used a CoC number that seems commonly used for calculating DOF on 10x8 (at Dofmaster.com for instance).

Try this ( based on Hansma):

N = D / (2 * c)

N = f stop
D = depth at film plane; (mm)
c = circle of confusion size (mm)

Hi, I sort of dislike using formulas that I don't understand, so my first approach is to consider how things work. You've stated both the lens' focal length and aperture (150mm and f/45). So we can act as though any given image point on the film originates from a disc of 3.3mm diameter (150mm/45) at the lens, which is 150mm away from the film. In other words, imagine a cone of light coming to a point at the film. If there were no film in place, then the cone would continue to expand on the other side.

The diameter of the light cone at any position limits the finest detail. For example, if the cone had a diameter of 1 mm, it would not be possible to resolve any finer, for example, a one-half mm image point could not be resolved. (Diffraction will further degrade the image, but nothing will make finer detail than the cone of light allows.)

If you sketch this out, you can see that this cone's diameter expands at a rate of 3.3 mm per 150mm = 0.022 mm per mm. In other words, for each 1 mm error you have in locating your image plane, the cone-of-light's diameter increases by 0.022mm. So your specific question is, "How much locating error is allowed before the cone of light reaches a diameter of 2mm?" The answer is 2/0.22 = 9mm.

In other words, your allowable error in locating the film plane would be a maximum of +/- 9 mm. The total range of possible error is from -9 to +9 = 18mm, roughly the same as a couple other people (especially bernard_L) have mentioned.

Sorry if I made it sound complicated, but the concept is actually pretty simple. Once one understands the concept of the cone, it's probably quicker to calculate by hand than it is to use an on-line calculator.

Personally, I would try to build the camera more precisely, something like the +/- 2 or 3mm you originally thought, in order to improve the focus. If you make your lens mount so that it screws onto a stack of shims, this would let you have any arbitrary amount of precision that you desire. Good luck on the project.

pdeeh said:

Do please note this is NOT a question about depth of field!

Click to expand...

My understanding is that depth of focus and depth of field mean the same.

(My photographic encyclopediae and dictionaries confirm this.)

ic-racer: thanks

Mr Bill: That is one of the most beautiful explanations - I want to say visualisations - I have ever seen of this issue, and one which moreover makes it pellucidly clear how theory and application mesh. Thank you!
I'm certainly going to try and make it as tight in tolerance as possible, and even with my limited skills 2 or 3mm is achievable. I'd even thought about shims

AgX: Field and focus are distinguished in both my Focal/Ilford Manual (6th ed) and Focal Encyclopedia (3rd ed) with the latter devoting several pages to each concept

AgX said:

My understanding is that depth of focus and depth of field mean the same.

(My photographic encyclopediae and dictionaries confirm this.)

Click to expand...

As far as I know, depth of field is related to the subject while depth of focus relates to the film plane. See image below.

So if the subject is a plane, say a brick wall, parallel to the film plane, then the film plane can move within the depth of focus area and the subject is still perceived as in-focus.

AgX said:

My understanding is that depth of focus and depth of field mean the same.

(My photographic encyclopediae and dictionaries confirm this.)

Click to expand...

In English depth of field refers to the distance between the nearest and farthest points around the subject that are acceptably sharp.

In English depth of focus refers to the distance between the nearest and farthest points around the film plane that are acceptably sharp.

The two are not at all the same.

FWIW, the depth of focus formula given in S. F. Ray's Applied Photographic Optics, 3d edition, is (approximation for small magnification, p. 221) is 2CN where C is the diameter of the Circle of Confusion and N is the relative aperture, i.e., the f/ number).
In the OP's situation, depth of focus at f/45 with a CoC of 0.2 mm will be 9 mm. I note that Ray recommends a CoC of 0.2 mm for 8x10; this will allow contact printing, is too large for sharp enlargements.

and indeed, contact printing (of paper negatives) is exactly the aim!

This is just my recent experience building a fixed focus box camera. Yours might be different if you are a more careful builder than I am. I first built a test camera in a cardboard box, like the one you recently built but open on one side. Inside was a movable film plane, with a piece of white paper on it. ( In other words I stuck a piece of cardboard in to be the "back" of the box ) I adjusted the position until the projected image was perfectly in focus, then measured and built my fixed box based on that measurement.

The camera was meant to use only the rear element of a rapid rectilinear lens. In a comedy of errors, I kept forgetting to take the front element off, and ended up over at f295.org asking the same questions you are about depth of focus. I even speculated that my images were blurry because of chemical actinic focus.

It turned out that the focus was just fine at f/45 and f/64.

But here's the part of the story I wanted to get to: after using and being happy with the camera for a while, I tried to make some photos with the lens opened up a little bit more. It was clear that my focus was off just a hair. So I ended up cutting a hole in the back of the camera and inserting a frame identical to what holds the paper negatives, but with some scotch tape stretched across an opening where the paper would have been.

It turned out that the focal length needed to be a bit longer. Shorter would have been easier because I could have added some shims in the back of the box. But I was able to move the lens out the required amount without too much trouble. The adjustment was small, maybe only 1/16th of an inch, but it made a huge difference. It might be my imagination but I think the negatives at f/45 and f/64 are also improved. Now the camera is easy to use and reliable... aim ( with viewing dots ), calculate exposure, and make a picture.

You can see a picture of the camera in (there was a url link here which no longer exists) ( the 1st picture of a camera after "photo details" ) and you can see the tape on the back of the camera where I patched the hole I'd cut to adjust the focus.

I think building with foamcore or matboard is not such a bad way to start... it's easy to fix things with tape and you can learn what works and what doesn't without much expense or time.

Also the film plane has to be flat and parallel to the lens mount to maintain even sharpness on the 4 corners.

Here are the final errors on a medium format metal camera I built, measured as shown.
https://app.box.com/s/96ap1stgz0e489vvtl27

TIR of parallel register was about (50 micron), 2 thou inch after a hand lap

Change in register of the aluminum body from minus 10 Celsius to 35 C was calculated to be 65 micron (2.5 thou inch)

Here are some measurements on rollfilm backs for Graflex 4 x5 to get an idea of typical tolerances for well worn components.
For Rollfilm backs, the height of the 4 roller ends with respect to the face was
(in thou inch)
A Singer RH10 206, 197, 202, 202 ( that is within a TIR of about 9 thou inch)
A newer RH10 195, 195, 195, 198
An older RH/8 190, 202, 200, 200

The ground glass, was difficult to measure but I concluded it was around 220 thou inch which puts it about 20 thou inch behind the roller plane of the rollfilm backs.


I expect a fixed focus Large Format camera build would be more of a challenge to get accurate especially if wood is used. The removable shims mentioned by Ned sound like a good idea in the initial design. Shim it longer then home in by removing shims.

Ned: Thanks. As you know I'm planning a sliding-box camera for the 213mm lens I also have. When I get bored with the heavy vignette and falloff I'll get from the 150mm on 10x8, I can then take the lens end out and use the box as the back half of the new camera ...

wombat2go said:

Also the film plane has to be flat and parallel to the lens mount to maintain even sharpness on the 4 corners.

I expect a fixed focus Large Format camera build would be more of a challenge to get accurate especially if wood is used. The removable shims mentioned by Ned sound like a good idea in the initial design. Shim it longer then home in by removing shims.

Click to expand...

Yep, but bear in mind that this is really a bit of fun as part of a longer term project, and I won't be expecting deadly accuracy at any stage. As I said in my OP, my craft skills are minimal, and even if I had the sort of kit you clearly have the use of, I'd have no idea where to start!

pdeeh said:

this is really a bit of fun as part of a longer term project, and I won't be expecting deadly accuracy at any stage.

Click to expand...

Yes, I really enjoy building bits and pieces for cameras and I learned a from it too.
If you start with tools the first 2 recommended would be a 300mm stainless rule and a 150 mm dial or vernier caliper of reasonable quality.
The caliper and the vacuum cleaner are the most used items in my little workshop.

pdeeh said:

wildbill: I explained my reasons for wanting the numbers in the 4th sentence of my OP.

spijker: thanks

bernard_L: Thanks. No, there won't be any macro going on! and yes, I realise the need for DOF, and I do realise the need for minimising error. However, this is a "fun foamcore" project, as I have no workshop, woodworking tools or indeed skills, and thus none of the things of most of the LF community take for granted. I really just want to know how much wiggle room I have, if any. I'm not sure whether your final remark is for me or for spijker - for my part, I simply used a CoC number that seems commonly used for calculating DOF on 10x8 (at Dofmaster.com for instance).

Click to expand...

gotcha, somehow I missed that. if you can get gatorboard instead of foamcore, it's much easier to cut accurately and is very rigid. I built a 4x5 fixed camera out of it.

That's an amazingly simple equation: d of focus= 2xcxN.nothing to it.

bernard_L said:

18mm is right unless you are doing macrophoto with your LF(!!). BUT, that is total range of allowable error. Margin of error either side of the "perfect" position is half that.

Plus, if you plan on a fixed-focus camera, you need as much margin as you can get for depth of field. If you start eating into that margin with errors of positioning the lens, so much lost in quality or flexibility...

Finally, I find it strange to scale the acceptable CoC proportional to the size of the negative. It means you have no better expectations for sharpness (relative to image size) in LF compared to miniature format.

Click to expand...

and that is true because you enlarge it less.35mm is most critical due to the relatively high magnification

AgX said:

My understanding is that depth of focus and depth of field mean the same.

(My photographic encyclopediae and dictionaries confirm this.)

Click to expand...

Sorry,utthey are not.The former is in front of the lens surrounding the subjectplane.Tthe latter is behind the lens surrounding the film plane.;very similar and proportional to each other but not the same; or are you thinking Tiefenschaerfe vs Schaerfentiefe?