What are the physics of DOF?

[fuzzybabybunny]

What causes DOF? Why does increasing aperture decrease the DOF and why does stopping down increase it? What are the actual optical physics behind it?

I was thinking about how point and shoots have massive DOF because their sensors are so small and their apertures are so small compared to SLRs, but don't our human eyes have just as small apertures and "sensors?" Yet we have very limited DOF. The only reason we seem to have very wide DOF is because we focus on objects so fast, making it appear to us as if we have wide DOF. But if we consciously focus on something with our eyes, we'll notice that everything else is out of focus, meaning our eyes have a very limited DOF.

[gjl711]

Way too much to explain in one post, but if your really interested, here is a web site that dives deep into many optical properties including DOF. Enjoy.
http://www.minoxlab.com/Don_Krehbiel/mpl/dkdof.htm

[BillsBayou]

Interesting. I'd like to see someone explain that one nicely as well.

You may be looking at the wrong characteristics of P&S cameras. It's not that their sensors and apertures are so small, it's the f/number of the camera.

Hmmm... what's the f/stop range of the human eye? Does our DOF deepen in brighter light?

[fuzzybabybunny]

Interesting. I'd like to see someone explain that one nicely as well.

You may be looking at the wrong characteristics of P&S cameras. It's not that their sensors and apertures are so small, it's the f/number of the camera.

Hmmm... what's the f/stop range of the human eye? Does our DOF deepen in brighter light?

The f/number is simply the focal length divided by the number.

So a 50mm lens at f/2 would have an aperture diameter of 50mm / 2 = 25mm. The f/number IS the magnitude of the aperture size.

[gjl711]

...Hmmm... what's the f/stop range of the human eye? Does our DOF deepen in brighter light?
Lots of good reading on the human eye and photography. :)
http://www.clarkvision.com/imagedetail/eye-resolution.html

[fuzzybabybunny]

Way too much to explain in one post, but if your really interested, here is a web site that dives deep into many optical properties including DOF. Enjoy.
http://www.minoxlab.com/Don_Krehbiel/mpl/dkdof.htm

Eh... this hit on all of the most common optical phenomena like diffraction, Airy discs, and circles of confusion, but did not explain why decreasing the physical size of the aperture increases DOF. All it says is this:

If the size of the opening (aperture) is reduced, narrowing the light passage, the size of the CIRCLES OF CONFUSION are reduced on the negative.


1. Why are the circles of confusion reduced when you narrow the light passage?

2. Can we draw this light passage?

[BillsBayou]

The f/number is simply the focal length divided by the number.

So a 50mm lens at f/2 would have an aperture diameter of 50mm / 2 = 25mm. The f/number IS the magnitude of the aperture size.

I was addressing this comment of yours:

I was thinking about how point and shoots have massive DOF because their sensors are so small and their apertures are so small compared to SLRs...

"Small sensors and aperture compared to SLR" is not why P&S cameras have massive DOF.

Focal length of the P&S lens compared to its small aperture is where you should be looking. That is why I brought up the f/stop of the lens. Your initial post was off the mark and I was offering some guidance.

[Curtis N]

I was thinking about how point and shoots have massive DOF because their sensors are so small and their apertures are so small compared to SLRs,I can't explain the phenomenon optically, and I'm hoping someone can provide a link to a drawing that will ullustrate the concept.

In mathematical terms, the focal length is squared in the calculation of hyperfocal distance. This means that changing the focal length will affect the HFD dramatically, even if the sensor size (which relates to CoC diameter) changes proportionally. What gives P&S cameras their inherent DOF is their short focal lengths, even though they tend to use relatively large apertures (small f/ numbers).

[fuzzybabybunny]

I was addressing this comment of yours:

"Small sensors and aperture compared to SLR" is not why P&S cameras have massive DOF.

Focal length of the P&S lens compared to its small aperture is where you should be looking. That is why I brought up the f/stop of the lens. Your initial post was off the mark and I was offering some guidance.


We are both on the mark.

DOF is massive on P&S cameras because their sensors are so small, which necessitates shorter focal lengths which limits how big the diameter of the aperture can be which results in massive DOF.

[BillsBayou]

THAT'S IT! :D

[20droger]

Try this article for a good technical explanation of depth of field:

http://doug.kerr.home.att.net/pumpkin/Depth_of_Field.pdf

[fuzzybabybunny]

Try this article for a good technical explanation of depth of field:

http://doug.kerr.home.att.net/pumpkin/Depth_of_Field.pdf

Unfortunately, nothing in there explains physically why a smaller aperture opening will increase DOF. :(

I'm not looking for mathematical equations of DOF with aperture values as just an unexplained variable. I want to know the physics of the interactions between the aperture and the depth of field.

For example, diffraction is caused because light waves bend away from their original path when they pass close to an object, such as the inner edge of an aperture opening.

Above is a real, physical explanation of diffraction. Such an explanation is what I'm trying to find for why smaller apertures increase DOF.

I've tried lots of searches, but any and all articles I find, even the technical ones, simply tell how aperture effects DOF (aperture smaller, DOF larger), and don't explain why it effects DOF.

[20droger]

It has to do with the physical size of the circle of confusion on the film/sensor. The larger the aperture, the greater the amount of light passing through the lens, and the larger the circle of confusion. A larger circle of confusion results in a smaller depth of field.

This site explains it a little better:

http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/950/depth-of-field.html

Hope that helps.

Roger

[fuzzybabybunny]

It has to do with the physical size of the circle of confusion on the film/sensor. The larger the aperture, the greater the amount of light passing through the lens, and the larger the circle of confusion. A larger circle of confusion results in a smaller depth of field.

This site explains it a little better:

http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/950/depth-of-field.html (http://www.cs.mtu.edu/%7Eshene/DigiCam/User-Guide/950/depth-of-field.html)

Hope that helps.

Roger

Since circles of confusion are formed by light rays passing through the lens tube, the size of a circle of confusion is proportional to the amount of light that can pass through the lens tube.

The size of circles of confusion may be proportional to the amount of light that can pass through the lens tube, but this is hardly an explanation for why it's proportional. It's like saying the number of car accidents is directly proportional to the number of cars on the road. This statement in itself may be true, but if you're trying to figure out the cause of car accidents, "because there are more cars on the road" is hardly an explanation.

I've been sitting here staring at a simple lens and light path diagram and I think I'm close to figuring our a hypothesis. Impossible to say if I'm right though. I think it has to do with the angle of intersection of the light rays that come from the subject. A smaller aperture makes this intersection more acute, thereby making the circles of confusion smaller. I'm gonna go into Paint and see if I can figure this out.

[Naturalist]

Check this out for those pesky questions on everything photo related and then some!

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

[20droger]

I'll try to explain....

I have included a quick and crude sketch of two diagrams. The upper one has a larger aperture (A), and the lower one a smaller.

In each diagram, the green dot is focused on the film plane (FP). The red dot is farther from the lens, and therefore focuses ahead of the film plane. This causes it to produce the circle of confusion (CoC) indicated. Similarly, the blue dot is closer to the lens, focuses behind the film plane, and produces a circle of confusion.

Now, the upper diagram has a larger aperture, and the lower a smaller aperture. The aperture of a lens defines its effective optical diameter. That is to say, a lens with an aperture is effectively an "aperture-less" lens having the diameter of the aperture. Therefore, reducing the aperture effectively reduces the lens diameter. This reduces the circles of confusion, as shown in the two diagrams.

Is this clear enough?

[fuzzybabybunny]

I figured it out. I think.

Basically the CoC is smaller when stopped down because stopping down results in a smaller angle between the intersecting light paths right in front of the film plane, which results in a narrower circle of confusion that falls on the film plane.

Some properties as a result of this:

1. Changing the diameter of the aperture changes this angle.
2. Moving the subject towards or away from the focus plane does not change this angle.
3. Moving the subject towards or away from the focus plane DOES change the location of the intersection of the light paths directly in front of the film plane, resulting in changes in the CoC, and thus, the sharpness of the image.


http://fuzzybabybunny.smugmug.com/photos/181575794-O.jpg

[poloman]

Check out this link...you may need your calculator. :)
http://www.normankoren.com/Tutorials/MTF6.html

[droiby]

I'll see if I can use my background in optics to explain it without lots of greek symbols...

Firstly, the first concept you need to understand is what's termed "circle of confusion". When a point of light is focused by the lens, it forms a "circle" at the focal plane. If this circle is smaller than the CoC, it is deemed to be in focus. Otherwise, it is considered to be out of focus.

Note that the CoC is not dependent on the aperture.

Now, if this point of light is on the plane of focus, then theoretically it will be a dot on the focal plane (but it never is in reality -- just a very small circle). As this point of light moves away from the plane of focus, then the dot will grow bigger, until it gets so big that the dot is larger than the CoC. The DoF is determined by the closest/furthest you can move this point of light and still maintain a dot on the focal plane that is smaller than the CoC.

When the aperture is stopped down to something small, light rays converge to the focal plane at a shallower angle. This means that for any given distance, the dot at the focal plane is smaller with a small aperture than the dot produced at a larger aperture. The effect of this is that you can move the point of light a greater distance before the dot gets larger than the CoC, and this directly means larger DoF.

[fuzzybabybunny]

I'll see if I can use my background in optics to explain it without lots of greek symbols...

Firstly, the first concept you need to understand is what's termed "circle of confusion". When a point of light is focused by the lens, it forms a "circle" at the focal plane. If this circle is smaller than the CoC, it is deemed to be in focus. Otherwise, it is considered to be out of focus.

Note that the CoC is not dependent on the aperture.

Now, if this point of light is on the plane of focus, then theoretically it will be a dot on the focal plane (but it never is in reality -- just a very small circle). As this point of light moves away from the plane of focus, then the dot will grow bigger, until it gets so big that the dot is larger than the CoC. The DoF is determined by the closest/furthest you can move this point of light and still maintain a dot on the focal plane that is smaller than the CoC.

When the aperture is stopped down to something small, light rays converge to the focal plane at a shallower angle. This means that for any given distance, the dot at the focal plane is smaller with a small aperture than the dot produced at a larger aperture. The effect of this is that you can move the point of light a greater distance before the dot gets larger than the CoC, and this directly means larger DoF.


Thanks. Exactly what I was looking for. So the picture that I drew above is correct?

[droiby]

Thanks. Exactly what I was looking for. So the picture that I drew above is correct?

More or less correct. The main idea is there (shallower angle and hence smaller blur circle at focal plane), but I think you got the terminology a bit confused (your "CoC" is actually the "blur circle" - remember that the CoC is not dependent on aperture).

The EF Lens book has some good diagrams explaining this as well.

[StewartR]

I'll try to explain.... I have included a quick and crude sketch of two diagrams.I figured it out. I think.Looks like these two were more-or-less simultaneous posts.

20droger's diagram is correct. Spot on.

fuzzybabybunny's diagram isn't correct. The subject is situated off the axis of the lens, but the rays of light between the lens and the aperture diaphragm are shown as symmetrical about the axis. That just isn't possible, and therefore the fact that his diagram leads him to the correct conclusions is just a coincidence.

[Glenn NK]

What causes DOF? Why does increasing aperture decrease the DOF and why does stopping down increase it? What are the actual optical physics behind it?

I was thinking about how point and shoots have massive DOF because their sensors are so small and their apertures are so small compared to SLRs, but don't our human eyes have just as small apertures and "sensors?" Yet we have very limited DOF. The only reason we seem to have very wide DOF is because we focus on objects so fast, making it appear to us as if we have wide DOF. But if we consciously focus on something with our eyes, we'll notice that everything else is out of focus, meaning our eyes have a very limited DOF.

Actually your eyes work the same way; the DOF changes, but as you noted, "your" eyes focus on whatever "you" are looking at.

However this is going to change as you get older. Ever wonder why older people have bi-focal or tri-focal spectacles? It's because at about the age of 50 (usually younger) the lens in the human eye hardens and the muscles around the lens cannot change its shape any longer to achieve focus. Don't worry too much about it because it's inevitable, and will happen to you too.:D

There are other people (like myself) that have had cataract surgery and our lenses were removed and replaced with plastic lenses (both eyes for me). Actually these work very well. By the time I developed cataracts, my original ones had hardened, and I was wearing bi-focals anyway.

Now for depth of field; as it happens, my eyes are very well focused at about arm's length - good for the computer, but not too good for reading a book up close. When the light is bright, I can read something that's 12 inches away, but when the light gets poor, I can't. The reason is simple; my pupils get very small when the light is bright and this increases my DOF so I can read up close; in dim light, my pupils open up to about f/1.0 and my DOF disappears.

The camera was modelled after the human eye.

For now you have AF, but by the time you're in your late fifties, you won't even have MF.;) You will have to keep changes lenses.:lol:

And for a real explanation of DOF, you'll have to read the reference links - it's all about optics.

[20droger]

Actually your eyes work the same way; the DOF changes, but as you noted, "your" eyes focus on whatever "you" are looking at.

However this is going to change as you get older. Ever wonder why older people have bi-focal or tri-focal spectacles? It's because at about the age of 50 (usually younger) the lens in the human eye hardens and the muscles around the lens cannot change its shape any longer to achieve focus. Don't worry too much about it because it's inevitable, and will happen to you too.:D
...
For now you have AF, but by the time you're in your late fifties, you won't even have MF.;) You will have to keep changes lenses.:lol:
I resent this posting!!! My eyes, though well over 50, are perfect! It's the rest of the world that has become fuzzy.

Quadrifocals, anyone?

[Curtis N]

I don't think the definition of "Circle of Confusion" has been properly clarified in this thread yet.

For the purpose of calculating hyperfocal distance and depth of field, the circle of confusion diameter is defined as the largest blur circle that will still be perceived by the human eye as a point. Of course, this is dependent on viewing distance, and how much the image is magnified to produce a print.

A circle of confusion diameter of 30 microns has been typically used for DOF calculations using 35mm film and 8 x 10 prints at a fairly close viewing distance. Smaller CoC values are typically used for smaller format cameras (including 1.6x DSLRs and P&S digital cameras). If you change any of those variables (print size, viewing distance or sensor size), technically you should be using a different CoC value. Also note that cropping a digital image has the same affect as changing the sensor size. The resulting image is magnified more to make a print.

[droiby]

The "Circle of Confusion" is what you get when a bunch of photographers stand around trying to nut out the physics behind their equipment :P

[gjl711]

The "Circle of Confusion" is what you get when a bunch of photographers stand around trying to nut out the physics behind their equipment :PBest definition I have seen yet. :)