Optical Image Formation

An optical image forms when multiple light rays from the same point converge elsewhere, creating contrast against the background. The object either emits light directly or reflects light from another source. How bright the image appears depends on two things: how much light the object reflects, and how large the lens opening is.

Lens equation

Here:

• $f$: focal distance of the lens
• $u$: distance to the object
• $v$: distance to the image

A lens is a curved section of glass, and the tightness of that curve determines $f$. For any given focal length, only one distance from the lens produces a perfectly focused image. In practice, most images form somewhere between the optical center and the focal point. More light reaches the image when the lens is larger, but shorter focal lengths require tighter curves, which means less surface area to work with.

Depth of field

Depth of field is the range of distances from the lens where objects appear in focus. Technically, only one plane is perfectly sharp according to the lens equation. Objects closer or farther than that plane are actually out of focus, but the sensor blurs them together and we don’t notice until the blur gets large enough to span an entire pixel. This tolerance for blur is what creates the appearance of a sharp zone that extends beyond the single focused plane.

Circle of confusion

When light from a point doesn’t converge exactly onto the image plane, it spreads out into a small blur spot called the circle of confusion. If that blur is smaller than a single pixel, our eye can’t see it. It looks sharp. But once the blur spot grows large enough to cover multiple pixels, we notice the fuzziness.