DOF - OK, I'm confused!

tkamiya · Apr 24, 2011

I'm confused about DOF when different image size AND equivalent focal length is concerned. I'd like to confirm my understanding.

As a multi-format shooter, this is important to me.

Let's say I have a 35mm film format camera with 50mm lens.
Let's say I have a 645 film camera with 80mm lens.

They are said to be about the same when it comes to viewing angles - correct?

If I set an aperture to f/2.8 for example, I will have LESS DOF on 645 camera than 35mm camera. At least that's true according to online DOF calculator at www.dofmaster.com

So... to generalize this, for equivalent focal length lens between different image size cameras, larger the image size, tighter DOF for a given aperture size. I have MORE control over DOF (ie. being able to obtain narrower DOF) on MF cameras than 35mm cameras.

Going extreme, if I have a pocket digi cam (sorry guys) with a tiny sensor, even if I go down to f/2.8 (if I could), I have a huge DOF that it is virtually impossible to have anything defocused.

If I have a 8x10 for example, LF camera, if I wanted to keep everything in focus, I really have to stop down to f/64 or something.

Am I correct on this?

Please keep this discussion simple. Please try not to add to my confusion. I really want to understand this.... if someone wants to discuss fine details on this, please start your own thread.

Thanks!

guitstik · Apr 24, 2011

It all depends on how well you understand the "Circle of Confusion"

http://en.wikipedia.org/wiki/Circle_of_confusion

Nikanon · Apr 24, 2011

tkamiya said:
Please keep this discussion simple. Please try not to add to my confusion. I really want to understand this.... if someone wants to discuss fine details on this, please start your own thread.

Thanks!

I dont think circle of CONFUSION will confuse this guy any less

tkamiya · Apr 24, 2011

I actually understand CoC at some preliminary level. But I want to grasp this practical DOF issue before digging into details. That's why I asked for simplified discussions first. Thanks.

MattKing · Apr 24, 2011

Your understanding is reasonably correct, although there are a couple of wrinkles to be aware of.

1) The focal length equivalents are a bit of a problem, because the aspect ratios of the negatives/slides differ so much. A comparison between 2 1/4 x 1 5/8 vs. 4 x 5 would take that concern out of the question;
2) To measure the similarities or differences accurately, you need to go so far as to actually print the negatives (or project the slides). And the viewing distance can factor in as well; and
3) The tiny sensor on the digicam will involve you in a further set of complexities - the Bayer array on the sensor, and the equivalent array on the video monitor you use for display. If you don't use a video monitor to display the results, then you get into real concerns about print size if the digicam doesn't have a particularly high resolution sensor.

tkamiya · Apr 24, 2011

Matt,

Thanks.

1) yes, I know.... roughly equivalent is what I meant. I am aware of aspect ratio issue.
3) bad example. I should have said 110 film maybe.

Concerning 2.... My understanding is that definition of DOF itself relies on final print size and the viewing distance. So to aid my understanding, I was assuming one final print size and identical viewing distance. Why is it that bigger the film size, smaller the DOF? Why does this even matter when I'll be printing to the same size paper to compare? It became further confusing when I started to factor in equivalent focal length size adjusted to the film image size....

Can you help me explore the topic 2?

Paul Sorensen · Apr 24, 2011

The way I learned it, and this is very simple, is that the dof is pretty much dependent on the actual focal length of the lens rather than the format size. In other words, on a 28mm lens, you have generally pretty deep depth of field. If you are using a small format camera and that represents a normal or tele lens, you still have a deep depth of field. A 90mm lens will have generally a pretty shallow depth of field, if you are using a 4X5, that is a wide angle and you have a shallow depth of field, if you are using a 35mm, it is a portrait length and you have a fairly shallow depth of field. I am sure that it is more complicated than that, but it works for me to understand the general issue.

MattKing · Apr 25, 2011

The reason that viewing distance and the nature of the printing process matters is that, the entire process itself must be taken into account when you are examining whether something is "sharp". This includes the camera lens, film flatness, the resolution, contrast and acutance capacities of the film (and development) itself, and the qualities of the enlargement equipment. In the case of smaller formats like 35mm, there is a much greater chance of running up against a limiting factor like film grain.

If your viewing distance is limited to a distance that doesn't reveal grain on an enlargement from 35mm, you may be too far away to detect a lack of sharpness that would otherwise reveal itself.

wiltw · Apr 25, 2011

From Wikipedia, http://en.wikipedia.org/wiki/Depth_of_field:

Same picture for both formatsFor the common same picture comparison, i.e., the same camera position and angle of view, DOF is, to a first approximation, inversely proportional to format size (Stroebel 1976, 139). More precisely, if photographs with the same final-image size are taken in two different camera formats at the same subject distance with the same angle of view and f-number, the DOF is, to a first approximation, inversely proportional to the format size. Though commonly used when comparing formats, the approximation is valid only when the subject distance is large in comparison with the focal length of the larger format and small in comparison with the hyperfocal distance of the smaller format.

"To maintain the same angle of view, the lens focal lengths must be in proportion to the format sizes. Assuming, for purposes of comparison, that the 4×5 format is four times the size of 35 mm format, if a 4×5 camera used a 300 mm lens, a 35 mm camera would need a 75 mm lens for the same field of view. For the same f-number, the image made with the 35 mm camera would have four times the DOF of the image made with the 4×5 camera."

RalphLambrecht · Apr 25, 2011

Simply speaking: you are correct in all points.

A bit more complicated: The equation for DoF has four variables (subject distance u, focal length f, circle of confusion c, and aperture setting N). Only c is format dependent, and all but f are linear (see attached equation).

The picture comparison illustrates the increase in DoF with smaller formats.
Picture 1 shows that a 24mm lens has the same viewing angle with a small format as an 85mm lens with a larger format. Picture 2 shows that, if enlarged to the same image size, the smaller format has a DoF advantage at the same aperture setting, due to the shorter focal length.

Hope this helps.

tkamiya · Apr 25, 2011

Thank you Ralph...

Working on combining formulas for df and dr into dF=f(u,f,c,n)
Looks like a lot is going to cancel each other....

RalphLambrecht · Apr 26, 2011

I like to see your results, but you'll find that DoF always depends on those four variables in one way or another, unless some kind of assumption was made. For example, some people combine f and N to the true aperture dimension or use the magnification factor instead of u and f. But none of that makes DoF equations easier or more practical, in my opinion. Still, like to see your results.

tkamiya · Apr 26, 2011

I've been at this for two nights now and results aren't good. I got it down to:

2cnuf^2(u-f)
---------------------------
{f^2-cn(u-f)}{f^2+cn(u-f)}

I see a common term "cn(u-f)" but can't do anything from here...

So much for wanting a simple explanation!

2F/2F · Apr 26, 2011

IMO, it is best not to think about AOV as if it has a direct affect on D of F; it does not directly affect D of F. Think of D of F in terms of magnification and f stop, and it is more simple to understand. Anything that changes magnification will change D of F. Once you understand this, you can think of AOV in terms of how it affects magnification, and it will make more sense.

This means same format, same f stop, same location, different lens, and you will have different D of F. Longer lenses shot from the same distance as shorter lenses make things larger in the viewfinder, meaning more magnification. Therefore, less D of F.

Also, same AOV, same f stop, but different formats, and the larger format will have less D of F because it has higher magnification (image is larger on the film simply because the format is larger, even though the spatial relationships are the same with the equivalent FL on the smaller format).

And, of course, same format, same lens, move camera closer. Subject gets bigger, meaning more magnification. Thus, less D of F.

At a given f stop, you can figure out whether you will be getting more of less D of F by making any change if you simply reason out how that change will affect magnification.

And you can definitely get shallow D of F with subminiature cameras such as 110 format or APS-C/H. You just get more D of F at a given f stop and identical composition than you do with 35mm or larger formats.

The cameras that are hard to get shallow D of F with are the ones that have even tinier sensors or film frames than APS-C.

tkamiya · Apr 26, 2011

lxdude · Apr 26, 2011

Angle of view.

tkamiya · Apr 26, 2011

oh...

RalphLambrecht · Apr 27, 2011

tkamiya said:
I've been at this for two nights now and results aren't good. I got it down to:

2cnuf^2(u-f)
---------------------------
{f^2-cn(u-f)}{f^2+cn(u-f)}

I see a common term "cn(u-f)" but can't do anything from here...

So much for wanting a simple explanation!

In my opinion, thinking about DoF in terms of magnification is not any simpler than thinking about it in terms of distance and focal length, but in case the subject magnification is already known or calculated, the equation to determine the depth of field (dF) simplifies to (see attached), where c is the circle of confusion, N is the lens aperture in f/stops, and m is the subject magnification. This equation is adequately accurate for subject magnifications larger than 0.1, which means it can be used for close-up but not landscape photography.

markbarendt · Apr 27, 2011

You are correct.

For a moment and think about it one piece at a time.

Assume you have a camera where you can change anything you please. For large format cameras this is actually the norm.

If you have a given subject say a person and you want them to be a certain size in the frame, your camera is on a tripod and all you change is the format what happens?

The subject doesn't fit the same way anymore.

To fix that you can;

Move the camera. Getting closer while using the same lens and aperture reduces our DOF and vice versa.

Change the lens. Here longer lenses have shorter DOF at any given aperture and vice versa.

Once you fix the issue above then you adjust aperture.

rjbuzzclick · Apr 27, 2011

RalphLambrecht said:
Simply speaking: you are correct in all points.

Hope this helps.

Wow, a Fiesta! I had one of those in the mid 1980's!

(Sorry...way, way, way, OT...)

RalphLambrecht · Apr 27, 2011

rjbuzzclick said:
Wow, a Fiesta! I had one of those in the mid 1980's!

(Sorry...way, way, way, OT...)

No, you did not have one like this in the 1980s, but you can see and get one like this at a Ford dealer near you right now!

http://www.ford.com/cars/fiesta/

rjbuzzclick · Apr 27, 2011

RalphLambrecht said:
No, you did not have one like this in the 1980s, but you can see and get one like this at a Ford dealer near you right now!

http://www.ford.com/cars/fiesta/

I had heard a while ago that they were starting to build them again, but yeah, I suspect they're a bit different now. It was kind of a fun little car, but it really needed a 5th gear, it was really straining at 65 mph.

tkamiya · Apr 27, 2011

I used to drive a VW bug back then.... It didn't even get to 60mph... it was struggling to reach 55mph even...

Hey, I can hijack my own thread!

RalphLambrecht · Apr 28, 2011

rjbuzzclick said:
I had heard a while ago that they were starting to build them again, but yeah, I suspect they're a bit different now. It was kind of a fun little car, but it really needed a 5th gear, it was really straining at 65 mph.

Ford never stopped making them, just stopped selling them in the US. However, the current Fiesta is no comparison to the old one and goes well over 100 mph without any vibration in the steering as one would expect from >100 hp. 40 mpg are a good selling point too.

Enough OT, let's go back to DoF, or is everyone satisfied so far?

fdisilvestro · Apr 28, 2011

Another way to see it (keeping it simple) is that when comparing two different formats and same AOV (angle of view), then the DOF is approximately the same for a given aperture diameter (not the aperture ratio).

Example:

4x5 using a 105mm at f/8 will have approximately the same DOF as 8x10 using a 210mm at f/16, since the aperture diameters for 105mm at f/8 and 210/mm at f/16 are the same

DOF - OK, I'm confused!

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