Confusion Circles in Digital Photography

We can represent the trajectory of a light beam that makes up the image of a point as a series of cones. From the light rays a point emits in all directions, the ones captured by the lens form a cone with a base in the lens and vertex on the point. Because of the curvature and refraction index of the used optic glass, the lenses modify the trajectory of the light and also make the rays converge towards a same point (image). Beyond this point, the rays are diverged again. The converging rays form a cone with a base in the posterior lens and with a vertex in the image; this, at the same time, is the vertex of the cone that form the diverging rays behind an image. Seen this way, we can observe all the variable that surround the formation of the image on the focal plane.

Focus consists on situating the plane of the film, or the cameras sensor exactly on the plane were the image of the object we want to register is formed with maximum sharpness. We can consider the focus mechanism as a plane with which we cut the cones that form the image. If the plane of the sensor don't coincide with the vertex of the cone, the point doesn't appear as such, but as a confusion circle . This circle is exactly the section of the cone on the plane were the film is effectively placed. The greater the distance between the focal plane and the cone's vertex, the greater the confusion circle.

On the other hand, the human eye has limited resolution power . At large distances the eye has difficulty to distinguish details because the size of the image is too small and the points are confused. For this reason, the eye is incapable of distinguishing a point from a circle when they are small enough. For the human eye, al the circles have a diameter with a diameter inferior to .25 mm are points.

This constitutes for us a “unnoticeable out of focus” margin, marked by the maximum size with which we can represent a point. Because the size of the confusion circles depend in last instance on the image's enlargement factor , it's immediate that a slight out of focus can go by unnoticed in a small enlargement factor, but will make the image unacceptable from a certain point on. The minimal tolerance is given in movie images, were it is amplified hundreds of times.