# Focusing at infinity for a camera and circles of confusion

1. Dec 14, 2012

### fisico30

Hello Forum,

when a camera is focused at "infinity", everything from infinity on is in focus (acceptable).

How is that possible? Every plane that is not in perfect focus has a certain circle of confusion that gets larger (more blurring) as we move away from the best focus plane....

Also, what happens to the aperture stop when the camera setting is "infinity"?

thanks
fisico30

2. Dec 14, 2012

### schip666!

Depth of field is both closer and beyond the focus setting, where the main focus is sorta-kinda-handwaving about 1/3 of the distance into the "good" DOF range.

If you focus at infinity you basically throw away the depth beyond infinity and just get the 1/3 distance closer to you "in focus", meaning within your selected circle of confusion. To maximize your depth of field in long shots, the Hyperfocal Distance is what you want. Of course that distance changes with the f-stop as well. He's a website with a bunch of charts and information that may (or not) help: http://dofmaster.com/charts.html

I don't understand what you mean by "what happens to the aperture stop..." so I can't help there...

3. Dec 14, 2012

### fisico30

Thanks schip666!

I think I need a little more help but I will get it.

Let's say we have converging lens of focal length f= 1 cm.
An object is placed at distance d_o. The image is located at distance d_i (calculated using the lens equation). The images at all other planes are blurred (circle of confusion for each image point).

The depth of field DOF depends on the distance d_o. I understand what they conceptually are: axial distance over which the circle of confusion size is small enough to make the images acceptable.

Now, "optical infinity" starts where? At roughly 20, 30 times the focal lengths (I hear). So infinity could be 100 cm away. Everything farther than that considered to be at infinity....

What is the DOF if the object is at infinity? Is it small or large?

The hyperfocal length that distance H. If we focus at H, everything from H/2 to infinity will be in (acceptable focus). Perfect focus will be at H. All the other image planes will be slightly blurred.
Focusing at H give twice the DOF than focusing at infinity.

But regardless of where we focus, of where the object is, the circle of confusion size grows as we move away from the perfect focus plane. If we focus at H, how can things that are way far from H, at infinity, still be in acceptable focus? Wouldn't the size of hte circle of confusion be so large at that distance?

thanks
fisico30

4. Dec 14, 2012

### schip666!

"Optical infinity" starts at, well, infinity -- think the Andromeda galaxy for instance. But practically it's anything near to that, like those mountains 20 miles away across the valley. Unless you are using a _super_ long lens, then maybe the moon is a good practical limit on infinity.

It's pretty pointless to focus on things that are _beyond_ infinity, so using the Hyperfocal point gives you the best DOF. As I said it's more like 1/3 in front and 2/3 behind (rather than 1/2 each way) -- but you'd have to actually work the equations or charts to get the exact distances.

The "circles-of-confusion" are symmetrical around the image plane. If you do a ray trace of your lens system, with focus at different points you will get "cones" of different angles which intersect the image plane. Some of the cones' apexes will be at the image. Others will be in-front or in-back of the image plane (where they focus). The size of the circle on the image plane is the CC. When that is indistinguishable to our eyes at whatever resolution we want, then we think it's in focus.

I searched ray trace and found this, which may be clearer then me:
http://www.lhup.edu/~dsimanek/scenario/raytrace.htm
Otherwise I can't really explain it without scribbling with pencils on paper...

5. Dec 15, 2012

### fisico30

Thank you.

So, the farther the object is, the larger the depth of field, because the CC size gets smaller and smaller as the cones angles get smaller?

thanks
fisico30

6. Dec 15, 2012

### schip666!

The CC stays the same size but the angles get more acute, and thus take "longer" to fill the CC. I think that's probably what you meant....

7. Dec 15, 2012

### fisico30

Almost.

take a lens with f=+1 vm and an object located at d_0=1000 cm

the perfect focus image plane is at d_0=1/ [1-(1/1000)]=1.001 cm

Any other plane will have an image that is slightly blurred with each point having a CC with nonzero size.....

at that specific image plane, other objects that are located at other object distances d_0 will be imaged but they will be blurred, because of the circles of confusion associated to each image point....

Does the depth of field, which depends on d_0, get larger and larger as d_0 get larger?

thanks
fisico30

8. Dec 16, 2012

### schip666!

Yes, the absolute DOF distance gets larger as you focus further away, although I would make a small bet that the percentage (depth/distance) is either the same or at least non-linearly related.

For (what may be a good) explanation of the CC thing see figure 5 on this page:
http://www.galerie-photo.com/profondeur-de-champ-scheimpflug-english.html

And for extra credit, can you prove to me that the DOF is "deeper" when using a wide-angle versus a telephoto lens --with the caveat that we enlarge the resulting images such that objects from each shot are the same size? It's a trick question. The DOF is (very close to) identical, as is the perspective. The only thing that changes when you change lenses is the amount of space you capture on the film...