how does the autofocus work in a DSLR camera?

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I know it’s something related to the camera changing the focal length until it obtains the sharpest image but does it know which one is the sharpest image?

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It evaluates the sharpness by edge detection. It finds the line that divides the highest brightness and color change, then changes the focus to create the sharpest, most abrupt change across the line. They get more sophisticated by testing several areas and more recently, prioritizing face detection.

> I know it’s something related to the camera changing the focal length until it obtains the sharpest image

Wrong; that’s the cheap way. It’s slow too because you don’t know whether to try focusing nearer or farther and the camera often has to try both ways and then overshoot before settling on a sharp focus. Working out how sharp an image is is simple: sharper images have a bigger average difference between adjacent pixels.

DSLRs use phase-based auto-focus. Effectively they can compare the image seen by the right-hand side of the lens with that seen by the left. This used to require extra image sensors but now a version of the system can be built in to the main image sensor. It has the advantage of being able to tell which way you’re out of focus and by how far, so the lens can quickly adjust correctly. They can even work out if the subject is moving nearer or farther, like in sports photography, and continuously predict the best focus.