Rolling Shutter Propeller

Two clocks, two effects

Each sensor row r (0 = top, 1 = bottom) collects light from start to end.

• Rolling: start = r × readout, end = start + exposure.
• Global: start = 0, end = exposure for every row; the stored charge is read out row by row afterwards, so readout time cannot bend the image.
• Blade angle θ(t) = θ₀ + ωt, ω = 2π × rpm / 60. Turn during a duration: rpm × 6 × ms / 1000 degrees (1500 rpm × 20 ms = 180°).
• Bend = turn between the top row's start and the bottom row's start (readout; zero for global). Blur = turn while one row is open (exposure; the same for both shutters).

How the photo is computed

Every photo pixel is the time-average of the scene over its own row's window. Because the blade turns uniformly, that average equals an angular box filter of the blade's polar profile. The profile is supersampled 4× per 0.25° bin and stored as prefix sums per radius, so each pixel's integral is exact and constant-time, even for windows longer than a full turn. Finished photos are cached per frame; while a frame is "developing", only rows still collecting light are recomputed, and pixels brighten in proportion to the light gathered so far.

The card thumbnails isolate one cause each: bend uses your readout with an instant exposure; blur uses your exposure with every row starting together.

Assumptions & honest limits

• Uniform rotation, linear row timing, equal exposure for every row, ideal optics.
• Brightness is normalised as if gain/ISO compensates exposure; a real short exposure is darker unless the camera amplifies it.
• The photo has 200–400 rows on screen, not the thousands in a real sensor; the timing law is the same.
• Not modelled: mechanical curtain shutters, camera shake ("jello"), flicker, sensor noise statistics (the grain is decorative), lens distortion, blade flex, global-shutter parasitic light.
• illustrative Preset timings (20 ms readout, 1/4000 s and 1/125 s) are typical-looking values, not measurements of a specific camera; readout times vary widely by device and mode.
• On screen, readout + exposure is slowed so every scan lasts 2.4 s, then the finished photo holds for 1.6 s. The slow-motion factor is printed beside the views and returned by demo.getState(). Bend and blur numbers are model outputs computed from your settings.

Sources

• Basler · Electronic shutter types — rolling rows start with a per-row offset and identical exposure; global rows start and stop together, then read out.
• Teledyne Vision Solutions · Rolling vs global shutter — row-by-row timing offsets skew fast subjects; long exposures add motion blur.
• Oxford Instruments Andor · FAQs on rolling and global exposure — staggered starts and ends per row, with a rotating-fan example.

Keyboard

All controls are native sliders and buttons. Press Space (outside a control) to pause or play.

Original code and art by explainer tools. Schematic teaching model.