Binocular ultra-high-speed photography for measuring tennis ball speed and spin at impact

Ball speed and spin at impact characterize tennis stroke quality, yet measuring both on an unmodified ball has required costly trackers or instrumented balls. We developed a synchronized binocular ultra-high-speed photography system recording at 2000 frames per second that reconstructs three-dimensional ball-center trajectories stereoscopically and recovers rotation from the natural seam texture by closed-form quaternion attitude estimation. Across 178 valid strokes from 15 provincial-level players, reconstruction was independently validated to 1.83 mm (static) and 2.34 mm (dynamic) position error, ball speed agreed with radar within 2.02 km/h, and rotational angular velocity matched a gyroscope-instrumented ball (2.87%) and a blinded human-annotation reference (3.05%). Flat, topspin and slice strokes showed distinct speed-spin coupling on the same trials. Costing about RMB 128,000 (≈USD 18,000) and deployable in 4 h, the system offers accessible marker-free stroke diagnosis for research, education, and grassroots coaching, complementing rather than replacing full-court commercial platforms.