# Relationship Between Ball Speed and Spin in Elite Youth Table Tennis Players Using Optical Sensors
## 2 Materials and Methods
### Ball Spin Measurement  
We also developed a rotation meter for spin measurement (rad/s), an optical system based on a patent of [PERSON] et al. [15], which is shown in Figure 3A, and an inner view in Figure 3B. This system was originally designed to observe the periodic light reflection effect produced by an insect's wings. This effect was identified as a discriminant factor for insect classification, called the frequency of wing beat [16; 17]. Although this approach may not be novel, it appears effective for frequency determination in our case study. This rotation meter has been duplicated to cover both parts of the table, so we had information on rotation before and after the net. Based on a large photodiode (model _S1227_ from _Hamamatsu_) as a receiver (Figure 3B), we observed the scattered light reflected from spinning balls (Figure 3C). We used a slightly modified version of [PERSON] et al. 's [15] system by using 2 external white LEDs from High-Speed Vision (40 W/80,000 lux) instead of an internal light source to illuminate the area of interest. In addition, bicolored balls (black and white) were used to accentuate the light reflection on the spinning surface, as the simple brand of the ball was not sufficient by itself (white/black balls are used). The balls were 3 stars NITTAKU NSD 40 +. Figure 2: Maximal angle error (\(\alpha_{max}\)) for linear speed measurement with player, target, and served ball placement. This creates a controlled environment to measure ball rotation, especially to limit the effect of natural light or insufficient switching rotation between black-and-white patterns. We added a stretched black sheet on the background to accentuate the light contrast between the black-and-white patterns of the ball. Both rotation meters were placed 3 m to the side table. The area of interest was defined by adjusting optical parameters and covers the first half of the table. The field of view height is set at approximately 15 cm, corresponding to the net height, to maximize signal strength in the area of interest. The position of all measurement systems is given in Figure 4.  
Rotation meter 1 (RM1) was assigned to the half-table on the player's side, and RM2 to the opposite half-table (on the ball launcher's side). A complete example of the signals of the rotation measurement system and their chronology is presented in Figure 5.  
Figure 4: Experimental setup used to measure ball speed and spin. The game area is composed of a pair of detectors for linear speed, two rotation-meters (RM1 and RM2), and a ball launcher. Figure 3: Rotation meter overview. (**A**) Dimension of the rotation meter. (**B**) Breakdown of the measurement system behind the optic, one large central photodiode and two arrays of peripheral photodiodes. (**C**) Acquisition system principle. Time markers T1 and T2 indicate the entry and exit of the ball on the player-side half-table, respectively. The green signal is the rotation measured before the ball crosses the net between T1 and T2. The red signal is the rotation measured after the net has been crossed on the opponent's half-table. This configuration enables the observation of the ball's kinetic parameters at one specific point of its trajectory. Rotation signals over time are similar to a sine wave due to the alternate light reflection over the black and white surfaces; some of them are shown in Figure 6. We choose to use the rotation after the net because it is more representative of a ball that the player will have to return. (Figure 6B-D), especially because it is just before bouncing. It is possible to retrieve the ball's spin in the time domain by determining the inverse of the oscillation period between two consecutive spikes, but also in the frequency domain using the numerical Welch power spectrum density (PSD) [18]. The light-reflected signal is assumed to be stationary and of length \(N\). The length varies between 200 and 500 sample data points recorded at a 2 kHz sampling rate. The signal is divided into segments of duration \(\sim\)50 ms with 50% overlapping.