Originally Posted by durack
OK, couldn't resist so I played with it a bit more, just out of curiosity (yeah, watching test pattern instead of movies like I should).
Interestingly, if you go into options and decrease the aperture of the lens, the unfocused corner becomes more and more focused, at the very end the picture is obviously quite darker but the focus is near perfect.
Anyone who knows optics care to comment?
Yes, by closing the aperture, you are increasing the depth of focus (depth of field on a camera). Basically you are limiting the light rays that are leaving the projector to only the ones that do not have steep exit angles from the projector (hence using more of the center of the lens surface than the outer portions). Very oblique light rays that would otherwise travel through the outer edges of your lens are now being blocked by the aperture. Therefore, certain (outer) portions of your lens aren't being used as muchn for image-forming light. It's possible that those portions of your lens have defects; what is also possible is that your lens has a high degree of spherical aberration. The latter is an aberration that results in the outer portions of your lens having a different effective focal length compared to the center; hence, it's like there's a range of focal planes created by your lens. By stopping down the lens, you're limiting the depth of this range of focal planes (in the ideal scenario, your focal plane would have infinitesimally small depth, where you'd place your screen... but this is impossible... you can't keep closing the aperture at will because at one point it'll get so small that diffraction will soften your image). As a lens maker you're trying to create an infinite series of prisms by grinding the surface of the glass so that, for example, all light rays from infinity, which can be approximated as being parallel, entering the lens from any point along its surface, converge to a single point. That requires a very evenly curved surface where parallel light rays normal to the surface of the lens entering the center don't get bent at all, but where rays entering the outer edges of the lens get bent the most. (and at every spot in between center to outer edge, the bending angles should progress evenly from 0 to whatever the final bend angle at the outer edge is for parallel rays; poor grinding or surface imperfections will muck this up). Furthermore, multiple elements can be used in a lens to control spherical aberration. So your final image depends upon a number of these factors. But all you need to know is that by stopping down you're limiting the use of outer edges (or 'rings') of the lens as well as
decreasing the effects of spherical aberration.
Here's a schematic that shows the different points at which rays from the same point being imaged are focused, based on where the rays entered the lens (projection is kind of the opposite of this, where you're taking the light from one focal plane -- the chip -- and focusing it on an outer focal plane -- the screen), from Wikipedia:
Ideally you'd want all those light rays converging to a single point. But at least by putting an aperture behind the lens, you cut out the outer oblique light rays, limiting your points of focus (for various light rays) to a smaller range. Remember: all those light rays that make it through the lens/aperture are image-forming light. So if some of them focus at a different plane, then those rays are serving to soften your image (b/c past the point at which they focus, those light rays get larger and larger... technically speaking: their circles of confusion get larger, and they blur/spread out whatever image detail they were carrying across neighboring pixels, causing a drop in MTF). Your cost, of course, is light... hence you increase the exposure on the camera (shutter speed), or go to high power on your projector and/or get a higher gain screen.
We see this problem all the time in photography. By stopping down, however, less of the image forming light passes through the outer edges of the lens surface. That doesn't mean *all* light passing through the outer edges of the lens are rejected; many of those still make it through and are image-forming. However, the ratio of those rays vs. rays passing through the center of the lens drops as you close the aperture, hence you get a sharper image.
Note: don't confuse this explanation with why a corner is more out of focus than the center; that's another story...
P.S. Kudos to you for playing around with test images
Music to my ears, haha.