It seems to me that there are a lot of terms that are poorly understood, or which will make the process of describing a problem or solution easier. I (Or any of the mod team) may add to or clarify any of the definitions here.
Here are some terms and definitions, which I think will help.
Objective Lens: This is usually the triplet, and is responsible for focusing the image onto the screen.
Collimator lens: The "first fresnel." This is the fresnel lens that bends the light from the lamp and makes it parallel (Or at least as close to parallel as it will be.)
Collector lens: This is the fresnel that bends the light back towards the objective lens.
Primary Optics: These is the optics involved in the projection of the image. Basically, the LCD (image source), the objective lens, and the screen.
Secondary Optics: These are the lamp, and the collimator and collector fresnel lenses. These lenses together should focus an image of the lamp at the objective lens.
Keystone: This is the phenomenon where the projected image is skewed or distorted in shape due to the principal axis of the projector not being perpendicular to the screen.
Lens shift: This is a method of correcting keystone by shifting the principal axis (therefore the objective lens placement) so that the principal axis of the projector can still be perpendicular to the screen. It is actually easier to think of this as placing the LCD so that it is not centered on the principal axis of the projector.
Throw: This is simply the ratio of how large the projected image is compared to the distance from the projector to the screen. 'short throw' means that the projector is close to the screen, while 'long throw' means that the projector is further back.
Precondenser: This is a lens that sits beween the lamp and the collimator fresnel. This lens' purpose is the allow the lamp to be closer to the collimator fresnel than would usually be possible. Because light from a radiated source dissipates in intensity proportionate to the square of the distance, this has large implications to the overall brightness of the setup. Also, an aspheric lens can be made to allow the corners to be "brighter" than the center, which results in more even lighting.
Square Law: Not really a projector term, but you'll see it come up a lot. This is basically the mathematical concept that the relative brightness of a light source diminishes with the square of the distance.
lux: This is a unit of brightness, not to be confused with the amount of light. As per the square law, the same light will produce 4 times the lux at 1/2 the distance, or conversely 1/4 the lux at 2 times the distance.
lumen: This is a unit of light. 1 lumen = 1 lux covering 1 square meter.
Colour Temperature: This is in degrees kelvin, hence the k suffic commonly used. This is the colour that a theoretical "black body" would emit light if it were heated to the specifiec temperature. FOr projectors the lighting should be at least 4000k up to 6500k. Generally higher is better. (Note that a "warm" light is actually a lower colour temperature than a "cool" light. Go figure.)
Vigneting: This is a term for how much brighter an image is at it's center, as compared to how bright it is at the corners. Member Rox has set forth a standard by which we can measure this. His idea is to take the lux reading at the center of the screen, and compare it to the average of the 4 'corner' readings, if you are measuring the 9 points which are standard for determining ANSI lumens. The result is expressed as a percentage. 100 means that the corner measurements are 100% of the value of the center, and 0 would mean that the corners are BLACK. We sometimes refer to the unit of measure as 'ROX' in honour of the member who proposed this standard.
Some Abbreviations and acronyms:
FFC: Flat Flexible Cable. If an LCD monitor has circuit boards attached to the side as well as the bottom, there will generally be an FFC connector between them. They are made up of thin rectangular copper conductors laminated between two layers of polyester insulation. They are fragile and usually need to be extended to move the circuit boards out of the light path
HID: High Intensity Discharge. This is used to describe lighting that uses an arc discharge tube to produce light instead of a filament. Electricity arcs between two electrodes, and the content of the tube (Usually metal salts, but it can also be inert gasses) heats and produces light.
HQI: Hydrargyrum quartz iodide. Hydrargyrum quartz iodide (HQI) is a special type of high-intensity discharge (or HID) lighting, where the light is produced using a very high voltage electrical arc through a gas The "H" in "HQI" comes from hydrargyrum, the Latin name for the element mercury.
MH: Metal Halide. Covers practically all HID lighting, but is usually used to refer to the 'white' lamps of 4000k colour temperature and higher.
OHP: OverHead Projector. These are the things they use in schools with transparncies so teachers don't have to write big on the chalkboard.
CRI: Colour Rendering Index. This is a number from 1 to 100 which indicates how well a light will show colours as compared to noonday sunlight. a low number is poor, while a high number is better. This number should never be lower than about 65 for a projector, but will rarely be higher than 85.
Any questions, suggestions or additions, please let me know!