|SEA OF COREOPSIS, © Bill Brockmeier, all rights reserved|
I won't bore you with the details of these dozens of methods, but many of them were devised over the past few centuries as the globe became circumnavigated and every far-flung corner of it became a goal of human exploration. At that time, it became important to be able to precisely represent this three-dimensional sphere we call "earth" on a flat piece of paper, so it could be easily rolled up and carried in a captain's quarters on a ship, or in the saddlebag of a horse-borne explorer. The profession of a cartographer was an incredibly demanding and important job.
When photography came along, this ability to conflate a three-D world down onto a simple two-D representation became an incredibly "easy" transformation to accomplish– automatic, in fact. The photographer didn't even have to think about it, the camera just "did it." But what determined the actual geometric transformation was hidden in the details of the optical system: the precise optical makeup of the lens system and the geometric relationship of the lens to the photosensitive plate (and its shape).
The devising and engineering of optical/lens systems has been a rich field of innovation for the past century and a half. Some of the world's brightest technical minds have been devoted to this pursuit. Their efforts at devising new lens systems have been aimed at things like sharper image focus (better detail), improved light-gathering ability, and decreased geometric distortion– whatever that means.
Lens designers have a very limited definition of what "geometric distortion" (or "image distortion") means. I won't go into what that specific definition is here, but it has very limited significance for most of the photographs that most people take. For instance, if one was trying to exactly reproduce the type on a printed, flat sheet of paper, this narrow view of distortion might be important. But if someone's portrait, or a distant landscape are more likely the subject, it's not clear that this "distortion" is an important consideration.
Most people don't know, and even most photographers don't realize, that most photographic lenses are actually designed with a certain distortion built in. It's easy to demonstrate this with almost any camera, and the more "wide angle" that a lens is, the easier it is to see.
Look through a camera's viewfinder, or at its digital display, and look carefully at some scene before you. Then, start panning the camera to the right. As the camera is in motion you will notice that objects in view will change their shape and size somewhat as they move from the right edge of the frame, to the center, and finally to the left edge. The real objects are obviously NOT changing in shape just because the camera is moving, rather, their image is different because it is passing through the lens in a different direction, thus revealing the lens's built-in distortion.
In both of the photographs below, the camera was placed at a point precisely perpendicular out from the center of the clock. The only difference in the two photos is that in one of them the clock was placed at the right edge of the camera's field-of-view, in the other it was at the left. Notice how the square of tiles immediately surrounding the clock is not square but trapezoidal in nature, and that in one of them the top and bottom lines converge to the left and in the other they converge to the right— their shape has changed. Remember that the location of the camera for each photograph was identical, and that only its direction changed.
|clock at right edge of camera's field-of-view|
|clock at left edge of camera's field-of-view|
I'll leave the proof of this final assertion for my next entry.