Working at the backdrop

picture

pixel

lens

focus

blur

Schedule

Focus drag the red line

General notes

1. A projector is a camera run backwards. The chip takes the place of the film, and the stage is where the image forms.
2. The lens brings one distance to a point. That distance is the focus, s, drawn in red.
3. Light from one pixel leaves through the whole lens opening, A. At the focus it lands as a point. Nearer or farther, it lands as a disc. The disc is b = A × |d − s| ÷ s.
4. You only see the disc once it is wider than one pixel, p. The sharp zone, drawn in blue, is every depth where the disc stays under one pixel.
5. The pixel grows with the picture. A wide throw gives big pixels and a deep zone. A long throw gives small pixels and a thin zone. The depth of the zone falls with the square of the throw ratio.
6. The lumens stay the same at any picture size. Double the width of the picture and each square metre gets a quarter of the light. The schedule gives full white in foot-lamberts. A cinema screen is set to about 14 fL, and dark paint sends back less.
7. Keystone tilts the whole projector. The top of the picture travels farther than the bottom, so the picture spreads into a trapezoid. Lens shift slides the chip and keeps the picture square. Fixing keystone in software spends pixels.
8. The rays are drawn to scale. Each fan is about 2 cm across at the lens. Opened up, the glass travel is drawn 100 times larger and the chip 6 times larger. The chip image is upside down and reversed.
9. The production table has a monitor for each piece. Click a piece of scenery to aim its monitor. Drag on a screen to pan it.
10. Every surface is worked out in cd/m² and shown through one exposure. Only lamps and lenses brighter than the brightest possible picture glow. The ghost light gives 8 lux. The haze is for looks.

Keys

Projector: 20,000 lm laser, 1 in class chip, 1920 × 1200 px, f/2 zoom, throw 1.2 to 2.4. Hung 3.5 m above the stage on the balcony rail, 10.5 to 15 m from the scenery. Depths are along the lens axis. Ideal thin lens. Not modelled: aberrations, field curvature, colour, contrast, stage light, bounce light. lux = lm ÷ m². cd/m² = lux × reflectance ÷ π. 1 fL = 3.4263 cd/m².