Having done a few retrofits and following many discussion threads here, I wanted to better understand how projector optics work. It is worth mentioning some threads that seeded a lot of questions and thoughts for this thread, such as upashi's study of the contribution of different reflector bowl segments to the overall output (link here), and frederik's hypothetical mapping of beam as projected to the wall, to how it lights up the road (link here).

Since I don't work for a company that designs projectors, I'm going to start with the simplest model, a 2-dimensional version of a basic DE (diaxial ellipsoid) projector. I will assume an ideal point source of light, which might be ok for a halogen filament, but not for HID. I realize there are going to be assumptions I make that may be far from the latest state of the art. The derivations are from high school &/ undergraduate level trigonometry and optics, and I will only mention them whenever absolutely necessary. (Hopefully zero times)

This thread will be a work in progress. If you're an industry insider, I'd appreciate some insights.

I will start with the basic shapes.

Since I don't work for a company that designs projectors, I'm going to start with the simplest model, a 2-dimensional version of a basic DE (diaxial ellipsoid) projector. I will assume an ideal point source of light, which might be ok for a halogen filament, but not for HID. I realize there are going to be assumptions I make that may be far from the latest state of the art. The derivations are from high school &/ undergraduate level trigonometry and optics, and I will only mention them whenever absolutely necessary. (Hopefully zero times)

This thread will be a work in progress. If you're an industry insider, I'd appreciate some insights.

I will start with the basic shapes.

- To the left, is an ellipse where the reflector bowl will sit.
- It has two focal points, one marked with a yellow circle, and another marked with a square.
- A point source of light sits on the yellow circle.

- To the right, is a circle that represents the shape of the "round" part of the lens.
- The center of this circle is marked by a "+"
- The back of the lens is assumed to be completely flat, and the focal point of the lens is marked by an "x", which happens to coincide with the square. The blue arc plots a constant distance from this "x".

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