I wanted to photograph a building facade which, from the available vantage point, is much too wide for my 75 mm lens to encompass. It is possible to do this using a panoramic head and stitching software, but I decided to try something simpler. I set up the camera to be as level as I could get it and square on the subject. I shifted to the right, made an exposure, and then shifted to the left and made a second exposure. This covered the subject with quite a bit of overlap. My plan was to merge the scanned images in my photoeditor (which happens to be Gimp). But I encountered problems getting the two images to register properly. After some thought, I conjectured that the problem might result from a slight shift of the lens axis between exposures. I then did a careful mathematical analysis which yielded some interesting results.

Suppose you shift the lens axis from the perpendicular by a small angle delta, which is measured in radians. I found that the total change in the length of the image is very slight---approximately proportional to the square of delta. But the change on each side, while small, is larger---approximately proportional to delta. One side gets smaller roughly by this amount and the other side gets larger. When you add the two, they cancer except for a residual term which, as I noted, is proportional roughly to delta squared.

Since when you merge images you try to register opposite sides of the two images, if there is a slight rotation between exposures, you can encounter a significant shift. In my case is amounted to about 80 pixels in 5000 or 1..6 percent. That could be produced by a delta of about one degree.

Note that this sort of problem is unlikely to arise with smaller formats involving lower pixel resolutions, so it seems characteristic, for now at least, of large format photography. I have to think some of possible ways to avoid such slight shifts! If that proves impractical, one way around the merging problem might be to use primarily one image and then merge it with a truncated version of the other, so there is little or no overlap, but I have to think of how best to accomplish that.