# DoF and Circle of Confusion

The definition of Depth of Field (DoF) from Wikipedia says that it is “the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image“. It relies on the notion of “acceptable sharpness” which is based on a criteria called the ”Circle of Confusion” (CoC). This article explains the essential about the criteria of sharpness and DoF.

A photograph is exactly sharp only on the focus plane, and more or less blur around it. The transition between little blur and definitely blur is gradual, so where do we determine the limit of acceptable sharpness that defines the Depth of Field (DoF)?

In the context of DoF applied to photography, it makes sense to consider that sharpness is “as sharp as what the human eye can perceive”, but the visual acuity of human eye is subject to debate… It varies from one person to another, depends on the contrast and viewing conditions, and for instance we can distinguish lines better than dots. That’s a complex topic in itself and I do not discuss it here,  but if you want to learn more about it I recommend this article : http://www.luminous-landscape.com/tutorials/resolution.shtml

Despite the debate, there is a standard in the photography industry : when looking at a print of 17cm*25cm at an optimum viewing distance of 25cm,  a blur circle of less than 0.2mm diameter is seen as a dot and not a circle anymore. This is the diameter of the Circle of Confusion, the largest circle still perceived as a sharp point by the human eye. By default, the DoF is defined relatively to this degree of sharpness. When a different image format or viewing conditions implies a different degree of sharpness, the CoC has a different size, which of course impacts the DoF.

A object outside of the focus plane produces a blur circle on the sensor

Now let’s look in details at how the image format and viewing distance affects the CoC and therefore the DoF.

Have you ever looked at a sharp picture on the screen of your camera, and realized it is blur when you see it later on the larger screen of your computer ? Then you have already noticed that sharpness depends on the size of the picture, and that’s why the DoF also depends on it. On a large print/display, many details appear unsharp because they are larger than the CoC, those details are not inside the limits the DoF. When the image gets smaller, the DoF extends to the details that  become smaller than the CoC, this is why the DoF is shorter on a large print/display than on a small one. To talk in Math, the DoF is inversely proportional to the size of a print/display for the same viewing distance.

A picture has a larger DoF when viewed on a small print/display

A similar principle applies with different viewing distances. If the human eye perceives a circle of 0.2mm as being a dot from a distance of 25cm, he also perceives a circle of 2mm as being a dot from a distance of 250cm. In other words the DoF at 25cm encompasses the details smaller than a CoC of 0.2mm, and the DoF at 250cm encompasses the details smaller than a CoC of 2mm. To summarize the DoF is proportional to the distance from which you look at given the same print/display size.

A last remark to conclude on this topic : the CoC is often referred to the sensor size. The standard CoC of 0.2mm on a print of 17cm*25cm is equivalent to 0.0288mm on a full frame sensor of 24mm*36mm, or equivalent to 0.0192mm on a cropped sensor of 16mm*24mm. This is simply proportional. In terms of pixels, if you take a sensor of 24Mpix (4000pix*6000pix), the standard CoC corresponds to a circle of of 3.3pixels of diameter.

To summarize about the Circle of Confusion :

• The CoC is the largest blur circle perceived as a dot by a human being.
• The CoC is the criteria of acceptable sharpness used to define the DoF.
• To shrink a photograph augments the amount of details finer than the CoC.
• The CoC is proportional to the distance between the observer and the photograph.
• The DoF is proportional to the CoC.