i did not FUCKING realize that there was a split diopter shot in DEEP SPACE NINE, fully NINETEEN YEARS after 1975, the last year anyone could get away with a split diopter shot. you will begin posting your favorite / most jarring split diopter shots at this time
on this and put my stagehand hat on. So the basic explanation: A split diopter lens is a special camera lens that's half convex.
Normally, when you're filming (anything) you set your depth of field for the shot (where the focus on the shot is, how long it is in terms of actual, physical length) with the aperture, lens and focus adjustment. Shallow focus is a short depth of field, where things in a particular narrow plane are in focus but nothing else is. It emphasizes whatever's in that focal plane over everything else the camera is picking up, which is blurred out.
A large or deep depth of field has a much wider focal plane, so you get much less blur. The famous Windows XP hills photo has a wide depth of field; everything in the picture is basically in focus. You'll see the same in other landscape photography.
So what if you want to have two narrow focal planes? Well, bring in the split-field diopter lens. The half-convex lens basically works like bifocals for your camera but moreso, with the result that one half (usually one-half horizontally, so the left or right side) is effectively nearsighted, and the other side is farsighted. You can then focus at two different planes to get the effect in that DS9 screenshot. As Gravis notes, it's a pretty oldschool effect and is sort of a hallmark of Extremely 70s Movies like Jaws and Carrie. These days people get a similar effect without the weird blurry vertical streak in the middle by using an extreme depth of field and a long-throw zoom lens, which puts the entire scene in focus and doesn't require some dude to squish his face up into the lens.
though I will say that the DS9 episode was much more subtle about it
