ProjectorsProjectors (beamers) allow an image to be produced of almost any size usually from 20" - 300". The differences between the different models are important in what you look for if you are trying to choose a certain projector:
Lumen Rating (Brightness):This rating tells how bright the projector will be. Most projectors are between 1000-3000 lumen. The larger the number the brighter the image will be. There are also settings on most projectors to turn the bulb on econo mode, which dims the brightness, but adds more life to the bulb, which need to be replaced when it reaches the end of its life. Pico projectors which are becoming popular now have very low lumen rating, usually a couple hundred lumen. This means that in a room that is not totally or nearly dark, the image will be hard to make out. The lumen rating is important when you are designing your table for certain environments, where the image will need to be brighter than the ambient light so that it can be well seen.
Throw Ratio:This number tells how well the optics inside the projector are at throwing an image at a certain distance. Useful tools to use with this are projection calculators and image-mirror tools which calculate the final image after the image from a projector is reflected or "bent" by mirrors. There are projectors known as Short Throw Projectors which are able to produce larger images at a closer distance which are popular in building smaller multi-touch setups, though usually more expensive.
Resolution:The resolution for projectors is just like TV and computer monitors. Standard Definition (SD) is the lowest resolution and is not HD. An example of SD resolution is 800x600. High Definition (HD) resolution is a much better image: 720p is anything that has a 720 or 768 in the last number. So for example, 1280x720, 1280x768, 1024x720, 1024x768 are all 720p HD resolution; 1080i (or 1080p) is anything that has a 1080 or higher as the last number. So for example, 1920x1080 and 1900x1200 are both capable of 1080 HD resolution.
There are two formats for resolution: they are 4:3 (which I call "square") and 16:9 (which I call "rectangle"). When deciding on a projector the native resolution is important because that is the resolution that will give you the truest quality. For instance if your native resolution is 800x600, but it has the ability to go up to 1280x768, you would be enlarging the pixels and creating a simulated HD image. Simulated since the pixels wont really be creating an HD image due to the enlarged pixels, and you may get noticable pixelation in fast video/animations. For most people working on multitouch tables, they usually get low-end 800x600 projectors since they are cheaper and easier to find. The low resolution is usually fine for most basic animations that are not coded for HD screens. The problem with the low resoltion projectors though is that the above categories like throw ratio and lumen aren't usually very good.
When buying a projector, I look at the spec sheets for the above things, and then I figure out the limitations in the image size due to the throw ratio on the projector by using a projection calculator. Then I go look at as many reviews as I can, noting little things like db rating (how loud the projector is when on) and over-all quality of the image.