It’s a good point. Leaving image shape aside to keep things simple, tilts/swings are used to more closely align the plane of sharp focus with the object space one wants to keep in focus. At the same time, DOF is often more closely aligned with the object space one wants to keep in acceptable focus (although there are some gotchas to watch out for). Therefore when discussing tilts/swings in relation to focus, people sometimes say the movements are increasing DOF. If everything happens to fit, this might be effectively true, but strictly speaking is not correct, since any “de-squaring” of the lens and film plane decreases DOF.
Said another way, tilting/swinging decreases DOF about the plane of sharp focus, but might “better” orient the plane of sharp focus and DOF in relation to the object space. The simplest case is obviously forward front tilt for a receding subject that is more or less flat. One can quickly get into trouble with DOF if that receding object space includes things with significant vertical size relatively close to the camera. This is why in practice, rarely do tilts/swings allow you to use large apertures.
Bookmarks