Question about DOF/Circle of Confusion

I have question about what seems to have an obvious answer but thought I would ask anyway.

When I read discussions about DOF all explanations seems presented in terms of two dimensions only. Problem is we live in a 3D world. So is the "circle of confusion" better described as a "sphere of confusion"? And should we actually consider DOF spatially as a sphere also?

If the above is the case then I also assume axis-tilt on any given plane will influence the apparent DOF relative to each other. We would need to use the actual focal plane as our reference point so a slight tilt in any given plane will change the symmetry for the area in focus within that sphere of confusion.

Am I thinking about this correctly?

But a photo is a 2D product. Being that the circle of confusion is only present on the photo, it is only a two dimentional thing...not a sphere.

actually, a photo is a projection of a 3D object on to a 2D surface. So, yes, obviously a photograph is a 2D object...

What I am asking I suppose is how does this CofC project onto a 3D object. There must be a 3-dimensional component to the theory. I have not looked into the type of transforms (aka equations/functions) used in calculating the projection.

I would add in thinking about it, while it might not be a true sphere a more cylindrical shape might make more sense...I just have been too lazy to work thought the equations myself to see what is actually happening.

I suppose I will need to look at the theory more closely I suppose. My degrees are in pure mathematics not applied. The reason is I am awful at applied so, I can have problems with conceptualizing the theory in application...thanks for having patience with me here...hehehehe...I can't speel worth a sheet either...

It's not a sphere of comfusion, it's a cone that presents a circular cross section onto a flat sensor.

If you want to apply it, just buy a view camera or a Canon TS lens.

The image is always projected onto a flat surface, so we're always talking about the diameter of a 2D blur circle projected onto the surface. What we're really talking about, though, is the intersection of an imperfect cone by a plane.

In this case, the cone never comes to an apex of a single point, but if focus is as perfect as it can be, the plane (the sensor's surface) intersects the cone at its most narrow region.

When focus is not quite perfect, the plane intersects the cone farther from the apex, so the image on the sensor is a circle of varying diameter rather than a point. But a tiny circle looks like a point to the eye, as long as it's small enough. But we enlarge the image, so the circle has to start out small enough so that even enlarged it's still small enough to look like a point.

Camera manufacturers plan for an enlargement to 8x10 or about A4, and base the maximum permissible size of that circle on that enlargement. For Canon 24x36mm format, the maximum permissible circle is 0.035mm...that is the "circle of confusion."

krb wrote in post #7966255
It's not a sphere of comfusion, it's a cone that presents a circular cross section onto a flat sensor.

ahhhhh....ok, now that makes sense to me. I was just doing a sketch of the two (CofC and DOF) and it did looks as the projection is a slice from the interaction of the two...I kept seeing a section (slice) of a cylinder rather than a cone. What I neglected to consider is the actual lens effect...which creates the cone shape. THANKS...I get it now...

Like I mentioned I am just, well, not good at applied stuff. I can build all manner of things but for some reason, when looking at physics applications I am completely lost.

Your explanation is very appreciated.

RDKirk wrote in post #7966287
If you want to apply it, just buy a view camera or a Canon TS lens.

The image is always projected onto a flat surface, so we're always talking about the diameter of a 2D blur circle projected onto the surface. What we're really talking about, though, is the intersection of an imperfect cone by a plane.

In this case, the cone never comes to an apex of a single point, but if focus is as perfect as it can be, the plane (the sensor's surface) intersects the cone at its most narrow region.

When focus is not quite perfect, the plane intersects the cone farther from the apex, so the image on the sensor is a circle of varying diameter rather than a point. But a tiny circle looks like a point to the eye, as long as it's small enough. But we enlarge the image, so the circle has to start out small enough so that even enlarged it's still small enough to look like a point.

Camera manufacturers plan for an enlargement to 8x10 or about A4, and base the maximum permissible size of that circle on that enlargement. For Canon 24x36mm format, the maximum permissible circle is 0.035mm...that is the "circle of confusion."

Even clearer yet, thanks! If I am getting it, the apex of the cone is really beyond the sensor itself otherwise we would get no image at all on the film/sensor.

I suspect my understanding of the interaction between the definition of DOF and CofC was my stumbling block?

For a detailed explanation of what it is and how it works, look here: http://doug.kerr.home.​att.net/pumpkin/Depth_​of_Field.pdf

Hey all...I haven't posted back not because I gave up...rather you all got me to re-visit the whole CoC topic. And I really had it sort of mucked up in my head. I am not there yet...but, I am getting a grasp on the relationship between DOF & CoC...it is certainly NOT what I had in my head. I have that much sorted but will work on it over the long weekend.

Seriously, the patience of everyone is much appreciated. I have also gone ahead and really played with a few DOF Calculators in order to get a ball park idea of what focal length/distance combinations will give for a DOF.

I have been using the following resources:

First...I have to thank RODGER for the link to the Doug Kerr site. The wealth of info there is non-trivial which helps me a great deal. The sheer volume of tools, theory and application information will take me weeks to work through. I know I will be revisiting that site fora very long time. Here is a link to all of his calculators and papers: http://doug.kerr.home.​att.net …n/index.htm#DoF​Calculator

The PDF's alone might justify getting a epaper ebook reading device later this year. PDF's on my Nokia N800 (not a phone) or my old Sony Clie nx73v are just not that easy to deal with. More on that front once I decide how to proceed as the new devices come out later this year. I already have a Kindle, which I am just so-so about but I am going to have a couple PDF's converted to see what the give me in the short term. I might also be able to convert the PDFs to different formats my other devices can better manage.

The calculators I am using are:

• http://doug.kerr.home.​att.net …n/index.htm#DoF​Calculator
• The Excel spreadsheet here: https://photography-on-the.net …highlight=dof+s​preadsheet
• This is the one I use most and even downloaded a copy to my N800 so I can use it offline when away from connectivity options: http://www.dofmaster.c​om/dofjs.html
  It also has the benefit of more nice explanations of what I had actually glossed over in all my excitement to just get shooting.