Focusing Tilt Shift Lenses

This article is published coincident with this site's May, 2008 report on the new Nikon 24mm PC-E lens. It is intended to provide a more in-depth explanation of the principals involved in using this type of lens. Thanks to David Summerhayes for permission to reprint this tutorial here.
Introduction
With normal 35mm camera lenses, the axis of the lens is mounted in a fixed position at right angles to the film plane. The lens can move forward and backward creating a plane of sharp focus in front of it. A slice of focused space if you like, that also moves forward and backward, but always parallel to the film plane.
Tilt shift lenses are designed to emulate the camera movements found on larger monorail and technical field cameras. These cameras, with their fine mechanical controls, have the ability to move this slice of space to the left and right, up and down and most importantly tilt and swing it away from the perpendicular. For example, by tilting the lens forward by the right distanc...