Minimum Physical Frames for Smooth Motion

Motivation

At the Exploratorium in San Francisco, there’s an exhibit (refer to the figure below) where a horse gallops across etched glass panels, animated by strobing LEDs.

To make a digital GIF of a horse galloping at 60 fps for one second, you need 60 frames. Each frame costs essentially nothing—it’s just bytes. But in a physical zoetrope (what this is), each frame is a hand-etched mirror or a sculpted object. The cost per frame is presumably enormous.

Formal challenge

Are there configurations of geometry, lighting, or optics that let you achieve $k$ fps perceived motion with fewer than $k$ physical frames? What’s the theoretical minimum? What does it depend on—the symmetry of the motion, the number of light sources, the observer’s perceptual system, some combination?