Digital light processing (DLP) uses millions of tiny mirrors to reflect light onto a microchip. The chip then processes these millions of reflections into a coherent image. The "rainbow effect" happens because all of this processing is handled by a single microchip, which rapidly switches the primary color from red to blue to green. Three-chip DLPs solve the problem, but they're still very new and very expensive.
Liquid-crystal displays (LCD) work by projecting light through crystal molecules that, to varying degrees, pass or block the light's path to each pixel. LCD screens use three microchips, so there's no rainbow effect. Light does leak through and between the pixels, though, causing the "screen-door effect."
LCoS (liquid-crystal-on-silicon) technology is similar to DLP, except that the light gets split not by millions of mirrors but by a prism and a solid-state filter. The light is then recombined into a coherent image by a three-chip processor. Compared with DLP, there's less space between them, meaning they absorb light more efficiently. Thus, no screen doors or rainbows.
