## 2 Materials and Methods
### Data Processing  
Kinovea was used to digitalize the different phases of upper- and lower-limb movements. The instantaneous kicking position was processed via the Hilbert transform using the method by [PERSON] [3], where NumPy (NumPy v1.21.6) and SciPy (SciPy v1.8.1) were used to transform the vertical position to the phase angle. In a kicking cycle, for example, the foot at the \"lowest\" position, namely at the end of the downbeat or the beginning of the upbeat, is defined as 0\({}^{\circ}\) for the phase angle. When upbeating to the \"middle\" position (horizontal), the foot position is defined as 90\({}^{\circ}\). Upbeating to the \"lowest\" position is defined as 180\({}^{\circ}\). When downbeating, the foot passes the \"middle\" position again, defined as 270\({}^{\circ}\). Finally, as the foot continues downbeating to its \"lowest\" position again, it is defined as the end of this cycle with a phase angle of 360\({}^{\circ}\), or 0\({}^{\circ}\), considered as the beginning of the next kick cycle. Thus, a complete kick cycle can be transformed into a continuous time series curve characterizing the continuous lower-limb movement using phase angle. As arm movement is on the same time series, the stroke cycle can be positioned to its relative foot position [28]. During the successive arm stroke phase, phase A is defined as entry and catch phase (from the hand's entry into the water to the beginning of its backwards movement); phase B is defined as the pull phase (from the beginning of the hand's backwards movement to the hand's arrival in the vertical plane to the shoulder); phase C is defined as the push  
Figure 1: Selection of Participants with Minor Visual Impairment (S12) and Limb Impairment (S10). phase (from the hand's position below the shoulder to its release from the water); and phase D is defined as the recovery phase (from the hand's release from the water to its following entry into the water) [1]. The index of coordination (IdC) [1,6] is the proportion of non-propulsion phase (lag time) between two consecutive strokes (two arms) over a swimming cycle time (T). The lag time is calculated:  
\[\text{Lag time}=t_{end}^{i}-t_{start}^{i+1} \tag{1}\]  
where \(i\) represents the \(i\)th stroke, so \(i+1\) means the next stroke on the other side arm; \(t_{start}\) represents the chronological time point of the start of the propulsive phase (phase B); and \(t_{end}\) represents the end of the propulsive phase (phase D, i.e., the beginning of the recovery phase), measured in the underwater video respectively. \[\text{IdC}=\frac{t_{end}^{i}-t_{start}^{i+1}}{T} \tag{2}\]  
IdC (Equation (2)), according its value, can be defined as three modes [1]: IdC \(<\) 0 means catch-up mode, where the lag time is negative; IdC = 0, i.e., opposition mode, where the lag time is zero; and IdC \(>\) 0, i.e., superposition, where the lag time is overlapped because the start of next propulsive phase (\(t_{start}^{i+1}\)) on other side is earlier than the end of current propulsive phase (\(t_{end}^{i}\)). The index of synchronization (IdS) assesses coordination between the upper and lower limbs in swimming [3]. It calculates the phase shift between stroke phases and kick phase (Equation (3)):  
\[\text{IdS}=\frac{[(KR+0.55R)modSR]}{SR}-0.5 \tag{3}\]  
where KR is the kicking rate and SR is the stroke rate. The numerical value of IdS ranges from \(-0.5\) to \(0.5\), and IdS values within \(\pm 0.1\) are considered the synchronized coordination mode. In contrast, the values closer to \(\pm 0.5\) suggest inconsistent coordination mode, where a large phase shift happens between the stoke and kick phases according to the equation. The index of inter-limb coordination (IdIC) is used to assess the coordination between the upper and lower limbs [3].