Signal-to-noise ratio characterization

Understanding the noise or signal-to-noise ratio (SNR) is one of the most fundamental considerations in constructing an artificial sensory system. In REAL, the noise of the system comes from several sources, namely target movement noise ( \(σ_m\) ), electronic noise ( \(σ_e\) ), laser fluctuation noise ( \(σ_l\) ) and shot noise ( \(σ_s\) ). Since the total noise is the geometric mean of all these independent noises, the largest noise source dominates. The target movement noise is due to the body movement during speech and usually has a smaller magnitude in the audio frequency band compared to   \(σ_l\) and   \(σ_s\)  (see Methods for SNR analysis of REAL). Electronic noises including the Johnson–Nyquist noise depend on temperature and fabrication of the chips. They are independent of the laser power. Laser fluctuation can play a role and in our case. Our laser fluctuation is also an important factor to consider. In our case, laser power fluctuation within the audio band is measured to be ~0.005%. Since the APD signal is proportional to the collected laser power, this noise power is approximately proportional to square of laser power ( \(σ_l^2\sim P^2\) ). Additionally, shot noise should be considered which stems from the particle nature of photon and electron detection; the noise power is proportional to laser power (  \(σ_s^2\sim P\) ) with a gain. Because the shot noise is the ultimate noise of a given signal, the gain of the APD should be properly set so that the shot noise dominate the system noises for an optimal SNR performance. In Figure 2e, the noise power ( \(σ_{total}^2\) ) in this REAL system is measured as a function of the laser power. A noise model considering the respective noises (see Methods for SNR analysis of REAL) was used to fit the experimentally measured total noise. The close-to-linear relationship between the noise power and the laser power is an indication that the shot noise indeed dominates. With this noise model, a fixed amplitude vibration (11.6 mm) from a mask excited at 500 Hz by a loudspeaker (Figure 2d) is used to examine the signal model, i.e. vibration modulated intensity change, and hence the signal to noise ratio. The experimental SNRs detected at different distances are plotted in Figure 2f and our proposed SNR model could well fit the experimental data based on the theory of spherical wave propagation (see Methods for SNR analysis of REAL). Additionally, based on the proposed model, a few other parameter configurations (laser power and vibration amplitude) are calculated in Figure 2f as a guide to help design similar systems. If we set SNR = 0 dB as the detection limit, our current configuration would allow a remote detection range of 17 meters.