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(This is an article about making panoramas. You can also see my panoramic photo galleries.)
Originally panoramic photography was done using special cameras that would actually turn slowly to reproduce a panorama on a long strip of film. That works well, but it's expensive. Today it can be done by having an ordinary camera take a whole series of overlapping shots, and software "stitch" together the digital images to produce one big long, tall, or just giant picture. I use different packages to do my stitching, including PhotoVista from MGA/LivePicture, Panorama Factory and AutoPanoPro.
(The "Panorama" mode on most film point and shoot cameras simply means they crop out the middle of an ordinary frame -- or at best a wide field ordinary frame on a dedicated panorama point and shoot -- and blow it up. It's not much use.)
Every photographer seeks to capture an image nobody else has captured before. Because digital panoramas are new, they have given me the chance to do that. But they also produce photos that are far more than just a wide angle view.
Several of my panoramas are indeed very wide angle, all the way to a full 360 degree wraparound. When viewed as a unit, they offer the ability to see things no conventional camera could have captured, and in these cases one section of the photo might be something that would be invisible behind you if you were standing in the camera's location. As such they go beyond what even the eye can see. 360s often look strange for this reason, and most shooting spots don't actually have a fully interesting 360degree panorama, so I only have a few of these. You also can't shoot them in sunlight when the sun is not high up in the sky, since it means shooting into the sun and a wrong exposure.
However, I often shoot 180 degree panoramas or 270 degree ones to good effect.
A narrower panorama, stitching just a few shots, simply lets you get a wide angle shot without a wide angle lens. It also means you can get more resolution than you could even if you did have a wide angle lens, because more film is used, though you lose some of that in the stitching. The software also corrects the bending at the edges found in wide-angle shots.
However, even the widest angle lenses, short of a fish-eye, tend to cover at most about 120 degrees (1/3 of the full circle). Even without moving your head the human eye can do better, and humans have the illusion, with a bit of head and eye movement, of being able to see much more.
As such the panoramic photo is the first photo to truly photograph some subjects in a manner that captures some of the experience of actually seeing them. When you stand in front of a beautiful vista, you may focus on one point, but your mind captures all your surroundings, and the true grandeur of most vistas can't be captured even in the widest field lens. Even the panorama can't capture the other senses, the sense of space from your ears and skin, the 3-dimensionality and the depth of focus and resolution of your eye. But it gets closer than just about anything. (Though IMAX film, because it captures the motion and sound, and because it can pan, is also a worthy contender here.)
To best be seen, a panorama has to be printed on a high-quality photo printer at full length. The screen, even at 1920x1200 or more, doesn't have the ability to show it. In addition, your eye can capture almost the whole computer screen at once. A printed panorama must be scanned by the eye, simulating the real experience. However, if you adjust your distance from it, you get to see perhaps even more than your eye could normally have seen at once, and thus see some sights in a new and better way that being there doesn't provide.
Even with narrower fields, panoramic photos also allow some subjects to be fully captured even when very close to them, just as a wide field lens does. However, with the distortion corrected, you get a photo more similar to a distant shot with a longer lens. However, in many cases such a distant shot might be impossible (because there are intervening objects or walls) or might not be as clear because of compounded haze in the air. Often I've seen something in the distance and photographed it, but then found the best shot comes from getting close and taking a panorama.
Digital panoramas, with a bit of careful manipulation, can also take shots of impossible exposure range. Good software is able to correct over a blending region for exposure differences, so that one portion of the shot can be in bright sunlight (with a short exposure) and another in shadow (with a long exposure) and the two can be blended to simulate what the eye does in looking at such a scene -- close up in iris in bright light, and open it in shadow. Normal film shots are limited to one exposure, though that has much more range than paper so clever printing techniques can also help.
Of course, doing this is not always easy. It requires a tripod, often lugged to hard to reach spots, good metering and tinkering with the software and images when done. Over time it will get easier, and I expect the software to let anybody do it, with handheld shots and even MxN grids instead of the current Mx1 strips.
It also helps to have a special camera mount that rotates the camera and lens around the "nodal point" where the light rays from the lens converge before diverging again to form the image on the film plane. That varies from lens to lens and among focal lengths in a zoom.
Read my article on panorama tripod heads for more details.