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The circle of confusion is one of the most scientific parts in the theoretical side of photography and many photographers are wondering what the deal is with it.
It's also known as the disk of confusion or the circle of indistinctness and besides photography, it is also an important factor in microscopy.
In our craft however, it is used to determine the all-important depth of field. There are certain factors that influence the size of the circle of confusion, including viewing distance, visual acuity and sensor format. To alter the size of the circle of confusion, all you have to do is change aperture. By that rule, a wide open aperture will result in a large circle of confusion, and ultimately into a shallow depth of field. To oversimplify, more blur in the picture.
Closing the aperture will have the opposite effect, reducing the size of the circle of confusion and putting more of the frame into focus.
With today's digital cameras, there are presets for the circle of confusion for each sensor format. Each pixel on the sensor makes a convenient focus point definition. Sharpness will be lost if the circle is larger than the size of the pixel and if it starts to affect pixels around it.
I'm not the best source for technical explanations, so I'm going to leave it to master photographer Mark Wallace to do the explaining in this video made by Adorama TV.