I'll take a crack at that.
Let's say that you have a projector with a 4:3 element. If you want to display widescreen content on this projector, then there are two approaches:
1) You can use a strip across the middle of the element (exactly like watching a program "letterboxed" on a TV).
2) Or, you can display using the entire panel, with the 16:9 picture "squeeed" horizontally to fit. Then, you put an anamorphic lens on the front of the projector, and this lens stretches the picture back out to 16:9.
The advantages of approach #2 are:
1) You are able to use the full light output of the projector. If you use the letterbox approach, then some of the light from the lamp is hitting a portion of the element that's just displaying "black" the whole time and not contributing to the picture at all.
2) You take advantage of the full resolution of the panel. If you display a 16x9 picture on a 1024x768 panel, then your picture has 1024 pixels of horizontal resolution, and 576 pixels of vertical resolution, with the remaining 192 pixels "wasted" in the letterbox.
If, on the other hand, you use the anamorphic technique, then you still have 1024 lines of horizontal resolution, but you have 768 lines of vertical resolution. Your pixels aren't square -- they're rectangular -- but the extra vertical resolution should make for a sharper picture.
Now, if you want to display 4:3 material on a 4:3 projector with an anamorphic lens, you have two choices:
1) Take the lens off and use the whole panel.
2) Leave the lens on and use a processor to "squeeze" the 4:3 picture horizontally, allowing the lens to stretch it back out.
I hope this was helpful. Please correct me if I got any of this screwed up.
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Mike Kobb
(Formerly "ReplayMike", but no longer affiliated with the company; these opinions are mine alone.)