The Circle of Confusion Doesn't Deserve That Name
There's a specific term used in photography that causes a great deal of confusion. Photographers young and old run in fear when they hear its name. Oh, did I forget to mention? That term is none other than the "circle of confusion."
Somewhere along the way, most photographers have heard of the circle of confusion. They were forced to because it was somehow important. It's just that they'd rather not talk about it for fear of letting on that they still don't understand what it is. The first rule of the circle of confusion seems to be not mentioning the circle of confusion.
But the circle of confusion doesn't really need to be confusing. This circle thing is actually a lot simpler than its confusing moniker implies. The truth is, the circle of confusion doesn't deserve such a bad rap.
By way of explanation, allow me to start with a consideration of the night sky. Specifically, the appearance of stars in the night sky. As is our own sun, each star is quite large but since it's also quite far away, it appears to us here on earth as a pinpoint of light. Some stars are bright and some more dim, but they all look basically as dots in a sea of black.
If we now take a photo of the sky, we would expect to see those same points of white in a sea of black. If instead, we see a photo with nothing but fuzzy blobs and splotches in place of stars, we know that we goofed and forgot to focus our camera before firing the shutter release. Hey, it can happen. Oops, those look more like fuzzy discs instead of sharp points. Like it's never happened.
Now let's instead suppose we take a look at our results and find it hard to make a judgement. Somewhere between the extremes of sharp points of light and blurred, out of focus blobs of light it stands to reason there must be some point where we really can't say if things look sharp to us or not. A little bit further one way and we're certain our results look sharp. A little bit further the other way and we're equally certain it's a blob. But there's no clear-cut dividing line between sharp and unsharp. Somewhere in the middle, try as we might, we simply find ourselves unable to say one way or the other as to sharpness or lack thereof. Somewhere between the two ends of certainty lies uncertainty. Or to put another way, at the cross-over between certain sharpness and certain blur we pass through a stage of confusion.
At one extreme, we see tiny points. At the opposite extreme, we see fuzzy discs that are clearly larger than points. The diameter of disc at which we can't help but be confused as to whether we see sharp points or not is the circle of confusion, often abbreviated as CoC. A circle with a diameter smaller than this will still look like a point. A circle with a large diameter won't. Somewhere in between, well, we'd have to admit to being confused on the matter.
Any given lens can achieve exact focus at only a single distance at a time. You can focus closer (up to a certain point) or further away (to the horizon also known as infinity focus), but whatever distance you choose will be the only distance that is technically one hundred percent in focus. But objects at distances close to that focus point will appear sharp because they aren't sufficiently blurred to cause any confusion. Any distinct points on that object will still appear sharp so long as they fall within a range of distances near the actual focus point, thanks to our friend, the circle of confusion. Anything that lies within this depth of field will still appear to us as sharp. Things beyond this range will increasingly look blurry.
When you look at something right at the limit of acceptable sharpness for the current depth of field, you'll be a bit confused, unable to say whether they are sharp or not. If you just look casually or from a distance, you might be willing to say something looks sharp. If you examine it close up though, you may be more apt to say it doesn't. And this is the thing with the circle of confusion. It depends on how close you look and how picky you want to be as to what you would consider sharp, blurry, or confusing. And it's for this reason that you will see some disagreement (dare I say "confusion?") as to what value is acceptable to use for the circle of confusion when creating all those depth of field and focus calculators all over the internet. That is to say, some people feel a need to hold sharpness to a closer standard than do others. When it comes right down to it, it depends on how large the final viewed print will be, and from what distance will people be looking at it. An image for a billboard can be surprisingly soft if viewed up close. Luckily for the advertiser (and photographer) billboards are generally viewed from distances sufficient to make many such issues irrelevant. There's no need to hold them to the same standard as a magazine cover or typical print hung on the wall that has different viewing expectations and circumstances.
From all this it should be clear that any depth-of-field or sharpness calculation is predicated on the assumptions made in the choice of circle of confusion. But there's more. Circle of confusion values are generally quoted in terms of sizes on the recording sensor or medium. And since an image shot on a smaller sensor will require a greater degree of enlargement to reach any given final print size than would one shot on a larger sensor, a different standard for CoC will be called for in one expects the resulting images to be equally sharp, regardless of sensor. For sensors somewhere around the 35mm "full frame" format, typical CoC values will be somewhere around 0.025mm, give or take. It's a little confusing.
If at this point, you're starting to wonder if you understand this whole "circle of confusion" confusion but aren't really quite sure one way or the other, congratulations. Welcome to the circle of confusion – that place where you just can't tell if you understand the "circle of confusion" or not. Maybe we'd better just agree not talk about it.