How can a subject stay in focus if the shot is recomposed afterwards?

Question

I have a doubt about a procedure that I see many photographers continuously apply and they taught me. I see that, when they want to take a picture with their reflex, they do this sequence of steps:

1) point the subject so that it is in the center of the frame (since they keep the center of focus at the center of the view).

2) move the reflex in order to put the subject on one side (in order to apply the rule of thirds). They often call this step "composition".

3) take the picture.

Steps 1) and 2) allow them to focus the subject and to put it in the "correct" third without moving the focus center from the center of the view (which would be a slow operation).

My question is about the focus: how can the reflex keep the focus on the subject if they move it? I do not understand how this is physically possible.

Answer 1

What you describe is often called the "focus and recompose" technique. It was first used back in the days of manual focus with a single focusing aid, usually a split prism, in the center of the camera's viewfinder.

Autofocus systems focus the lens at a specific distance from the camera, not at a set of coordinates in Cartesian space. As long as the distance from the camera to the subject is the same when the camera was pointed directly at it as it is when the camera is moved to reframe the subject, then the subject will still be in focus.

One thing to keep in mind is that when panning the camera to change the composition, the camera should be rotated around the optical center of the lens, also known as the "no parallax point" and sometimes incorrectly referred to as the "nodal point."

Most folks who aren't actively thinking about it tend to rotate the camera around the center of their own body, rather than rotating their body around the optical center of the lens. This changes the optical distance between the camera and the subject. Sometimes the difference is less than the depth of field resulting from the selected aperture, focal length, shooting distance, and intended display size and the subject still appears to be in focus. With wider apertures and short subject distances, though, the depth of field is fairly shallow and it is often the case that the subject will no longer appear to be acceptably sharp when using the "focus and recompose" technique.

Related: What is the advantage of a lens with a curved focal plane?

Answer 2

What is missing in your recipe is 2a) half-press the shutter button or use a focus lock button in order to fix what the autofocus comes up with, or focus manually.

That is what lets the camera retain the achieved focus.

It is worth noting that this stops working if the depth of focus is too shallow and/or the focal length makes for a rather wide angle. The reason is that there is a focusing plane (rather than a focusing sphere) in parallel with the sensor plane, so when you focus on an object in the middle of the frame and then move that object to the side of the frame, your focus falls short.

As an extreme example, if the focus in the middle of the frame is at 4m distance at 18mm effective focal length, the in-focus distance at the side of the frame is at almost 6m.

So particularly when working with shallow depth of focus, the abilities of newer cameras to focus to locations other than the center of the screen may be preferable to the focus-reframe-shoot recipe.