Low Budget stage lighting:
The purpose of this system is to provide a cheap but versatile lighting method to small or mobile theater companies.
Claims:
1 - An infinite amount of light transitions without a computer program or switchboard
2 - Dimmable lights without dimmers
3 - Infinite color space - limited only by the spectrum of your light
4 - a simple control system that a child could operate
5 - As cheap as the world economy will allow for.

Materials- Please read the simplified version first - I wrote the universal section as this concept can be extensively expanded.
(simplified language // universal)
1 - A lightboard  //  A light source
2a - A video Projector // A system of projecting light
2b - A camera (adapted to connect live with the projector)
3 - Two polarizers // a system of cross polarization
4 - Transparency paper // Birefringent materials

Procedure -
Part 1 - Transmit your light through the projection system across your complete stage.
Simplified example:
A - Turn on your lightboard
B - Direct your camera towards the lightboard so the entire frame is full of light. (This is your controlled working space)
C - Connect your camera to a digital projector.
D - Turn on your digital projector and position it to cover your playing area. (This is also your expanded working space)

Part 2 - Polarize your light source.
Simplified example:
A - Add a sheet of polarizer to the surface of your lightboard.
B - Secure it with some acrylic sheeting or glass to prevent scratching. (Note - glass and acrylic are isotropic and transparent materials)
Part 3 - Cross polarize your projection system.
Simplified example:
A - Add a polarizing filter to your camera. Rotate the filter until the light appears black in the camera. Either tape a polarized filter sheet to your lens or you can buy a special polarized filter for cameras. The effect is the same, commercial polarizer filters are easier to turn and are more secure than tape. 

Part 4 - Add Birefringent materials between the polarizers.
Simplified Example:
A - Start with a sheet of transparency paper, cut a circle and place it on your lightboard.
B - Observe the circle appear as a beam of light on stage.
C - Rotate the circle. 
D - Observe the beam of light fading dimmer and brighter
E - Lift the circle towards the camera, out of focus...
F - Observe the light expanding, and the edge softening.

Conclusion - 
The above is a broad overview of a very effective system of governing light. Start simply, the behavior of polarized light is undertaught. Note an overhead projector uses the same technique but without the latency of a video projection system. Even candle light projected with two lenses will work as a system. 

Here is a list of fun birefringent materials to try:
Regenerated Cellulose (Cellophane)
Packing tape
Mica
Sugar
Epson salt crystals
Materials at different levels of birefringence produce different colors. These colors interact with each other in a precise and predictable way outside of the additive and subtractive color wheels. Michel Levy has a guide, Michael Vandergard and the Drolly Theater have a theatrically oriented guide they use for puppetry. 
For lighting cues - mount birefringent materials onto cellulose acetate, acrylic or glass. Pull them on and off your lightboard.
Helpful hint - draw your stage on your lightboard with dry erase markers. 

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