Circle of Confusion featured image.

Circle of confusion or CoC is ironically one of the most confusing terms for beginners in photography.

And for good reason, it is a fairly tough concept to grasp. Most resources only grazed on the term as it relates to the depth of field.

The problem is, it requires a little more understanding of how your camera and lens works rather than just the DoF.

In this article, we’ll try to demystify this topic without going too technical.

What is the circle of confusion?

The circle of confusion (CoC) is the measurement of the optical blur circles created by the lens when light converges inside the camera.

Using the diameter of these circles will help us define the transition point between the “acceptably sharp” parts and out of focus elements in our printed or web-uploaded image. In other words, it will help us determine the depth of field.

Let me explain further.

When you focus on a subject, the light travels from your subject in a cone-like manner and converge at a certain point inside your camera. 

However, your camera can only resolve lights that converged at one distance, the focal plane.

Light convergence that doesn’t fall exactly on the focal plane creates a circle of light or blur spot. These blur spots become bigger as it converges further from the focal plane.

Circle of Confusion defined through graphics showing how light travels to the image sensor and pointing where the CoC is.

The measurement of these blur spot is the circle of confusion. Smaller circles mean it is more in-focus and sharp while bigger blur spots are less in-focus and unsharp.

Before we proceed, I just want to clarify something…

Circle of Confusion is not Bokeh:

Bokeh is just a result of light converging too far from the focal plane. And even then, It is not even the blur itself, but the quality of blur.

While the circle of confusion is used to define the “border” between the blurred and sharp portion of your image.

Here’s how bokeh is created:

As you change the plane of focus (by moving your lens’ focusing ring), you are also changing the trajectory of the lights going through your sensor. This will make some light that should’ve converged ON the focal plane, converge, OFF the focal plane.

In other words, if you move your focus point too far, your camera sensor would not be able to render some converging lights. This creates some indistinguishable portion of your image.

While you are not changing the actual amount of depth of field, you are moving the focus point further away from the focal point.

Thus creating the bokeh balls effect.

Bokeh Balls Effect

So to be clear, the blur spot itself is NOT the CoC, but the measurement of the diameter of those blur spot is.

TIP: If you can take a shot with a small enough aperture and far enough background lights, you can shoot an image with bokeh balls while still having some in-focus subject(s).

To better understand the concept, let me illustrate what happens when you focus your camera on a subject. It’s also a good way to bring in a few technical terms relating to how the light travels to the image sensor.

How light travels to your image sensor when you focus on a subject:

Technically, the only in-focus parts are the ones the fall on the focal plane. From there, the image loses its sharpness very gradually.

It is so subtle that our eyes can still perceive some parts as “in-focus” even though it is technically not.

This is where the circle of confusion comes in.

Basically, we can divide the light’s path into two sides. The object side depth(the actual scene you are shooting) and the image side depth (inside your camera).

How the Circle of Confusion is created.

Focus Point – This is part of the object side depth. It is where your focus is currently at. And the portion of your frame that will render at its sharpest. Everything not in this point will slowly lose its sharpness.

Lens Element – As light passes through the lens, it will be handled by an element in your lens responsible for projecting the light to your sensor.

Focal point – The light’s path to your sensor is like a cone. They will always intersect to a certain point. The point where the light intersects after it was projected by the lens is the focal point.

Focal Plane – This is your camera sensor. This is pretty much the focus point but in the image side depth (inside the camera).

Any point that doesn’t exactly fall to the focal plane will create a circle of confusion and will create bigger ones as it converges further from the focal plane.

This video from Richard Clabaugh is perhaps the most concise explanation I’ve found about this topic:

Here’s how it works:

  1. When you set your focus on a subject, the light reflected from the subject will be received by your lens. The subject will be your focus point.

    Anything that is not your focus point will still reflect light and will still be received by your lens.

  2. The lens element will then try to project the light from your focus point to your sensor.

    And once the light from your subject passes the lens element, it will converge on a single point(focal point).

  3. Any lights that fall on the focal plane will render very sharp.

  4. Everything else will create a blur spot that grows bigger as the distance increase from the focal plane. It will also gradually lose sharpness.

  5. But, if the light that falls outside of the focal plane is still within the circle of confusion diameter limit, that portion of the image will still be perceived as in-focused even though it is technically not.

Factors that affect the Circle of Confusion:

The main purpose of the circle of confusion is to somehow measure how big the blur spot needs to be before it is deemed out of focus. This, in turn, helps us determine the amount of depth of field.

Unfortunately, the depth of field is subjective and the “acceptable sharpness” varies based on different factors it was viewed.

These factors are:

  • The viewing distance.
  • Enlargement from the original image
  • Visual acuity

Let’s have a closer look, shall we?

Viewing Distance:

The closer we are from the image we are viewing, the smaller CoC we need for an object to be perceived as sharp.

Conversely, you can say that as the distance of the object increases, the “tolerable” blurriness expands.

Viewing Distance.

Ideally, the image size should increase as the intended viewing distance increases. This way, the acceptable CoC diameter will remain the same.

Try putting your index finger near your eye and then focusing your gaze on it. Did you notice that everything else is blurry?

Now, try moving your index finger slowly away from your eye, while still focusing on your finger. Did you notice that the background becomes clearer?

As the distance becomes of the object we’re focusing on shrinks, the smaller CoC we need for it to render acceptably sharp.

But say for example you’d be printing a big billboard-sized image. Then you’d better make sure that your photo will be placed where big billboards are usually placed.

Otherwise, if you view it at a close distance, you’ll probably notice that the photo isn’t very sharp.

Both these examples are closely tied up to the next factor…

Enlargement from the original size:

All things being equal, the more we enlarge an image from its original size, the more it is likely that some portion of the image will become unsharp and blurry.

Let me give you an example. I kinda cheated a little bit just to show what could happen to your images if you enlarge your image too much.

How Enlargement Affects the Sharpness.

The first one was downsampled from 5184 x 3456 pixels (the original RAW size) to 800 x 533 pixels.

On the other hand, I first exported the second image from the original file to 100 x 67 pixels. Then enlarged it to 800×533.

Though this is an extreme example, enlarging your image too much can pretty much destroy it.

Visual acuity:

A person with a 20/20 vision will need a smaller circle than those with poorer eyesight. Therefore, people with better vision have smaller depth of field.

It sounds counter-intuitive at first, after all, a better vision means better clarity on everything right?

But hear me out on this… 

Old Man Eye

Just looking is not the same as looking at an image.

If two people with extremely polar visual acuity look at the same enlarged image on the same comfortable distance, the person with better vision will notice a drop in sharpness on some portion of the image than that person with poor eyesight.

This is because people with higher visual acuity have lesser “blur tolerance”

We, unfortunately, do not have much control over this factor.

Example of these factors together:

Let’s assume that the final image will be printed on an 8 x 10 inches print size, viewed at the distance of 10 inches and viewed by a person with normal visual acuity.

The sizes of your circles of confusion will kinda look like this:

Acceptable Circle of Confusion Diameter

But say, you want the final image to be printed on a very big canvas maybe, 80 by 100 inches which is ten times bigger than 8 by 10. Then you would need smaller circles to render a sharp image.

If you relate that to the image above, some “acceptably sharp” circle will now look unsharp. This is because the acceptable circle of confusion diameter is now smaller.

Same goes if the visual acuity and viewing distance variables change.

How to Determine the Maximum Allowable CoC Diameter (Circle of Confusion Formula):

Now that we’ve identified the parameters that affect the circle of confusion, we now have the means to calculate it.

The formula isn’t really that complicated but this is still a little too long for my Math-hating brain. It goes something like this:

CoC in mm = (viewing distance cm / 25 cm ) / (desired final-image resolution in lp/mm for a 25 cm viewing distance) / enlargement)

Thankfully, there are a lot of CoC calculators available today.

The real question is, what do we do with once we have this information?

Circle of Confusion Applications:

The concept of CoC is pretty useful when you put the print size into consideration. Especially for large prints, where the critical focus is important.

If you know the acceptable Circle of Confusion value for your desired print size, intended viewing distance and intended audience (for example, will they pixel peep or not?), you will be able to calculate certain aspects of the depth of field.

Examples are the hyperfocal distance, the near and far distances of acceptable sharpness, and even the approximate amount of depth of field.

Knowing these will help us pick the best focus distance for your current aperture and focal length.

For practicality and speed’s sake, it’s best to just use a depth of field calculator like this one to determine the depth of field for your image.

But if you’re really curious how all these are calculated, this video is perfect for you:

All this because what may have looked sharp to you now, may not look as sharp when printed.

Filmmakers, for example, are preparing something that will be viewed in a very large viewing medium. Can you imagine just how hardcore they are with focusing? This is also one of the reasons why cine lenses exist.

Conclusion:

The circle of confusion is a technical concept to better understand how the depth of field works. It can also be used for a more precise (although still an approximate) calculation of the hyperfocal distance and the DoF.

CoC is especially helpful for printing big photos where the critical focus is a priority.

Hope this article helps! If you have some concerns, feedback, corrections or just want to leave a simple thank you, please do not hesitate to leave a comment. 🙂

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