# Signal Diversity for Laser-Doppler Vibrometers with Raw-Signal Combination
## 2 Materials and Methods  
To verify the results obtained by [PERSON] [18; 21], an experiment using four channels (measuring heads) of a MPV is conducted. The measuring heads are aimed at a shaker with a nearly identical angle of incidence. To verify the alignment of the measuring heads, the raw signals of the four channels are acquired and subsequently demodulated by an ATAN demodulation [22]. A correct alignment can be verified by a match of the four demodulated velocity signals. We aimed for a difference of less than 5% between the amplitudes of the four velocity signals.  
According to [PERSON]'s publication, the signal reliability can be improved by combining multiple demodulated velocity signals. Using Equation (1), the combined signal \(S\) is obtained using any number \(n\) of individual velocity signals \(X_{j}\)  
\[S=\sum_{j=1}^{n}w_{j}X_{j} \tag{1}\]  
with the weighting factors \(w_{j}\) calculated in Equation (2) [21] by the CNR (Carrier to Noise Ratio)  
\[w_{j}=\frac{1}{\sum_{l=1}^{n}\frac{\text{CNR}_{j}}{\text{CNR}_{j}}}. \tag{2}\]  
The CNR results from Equation (3) with the carrier power \(P_{c}\) and the noise power \(P_{n}\).  
\[\text{CNR}=10\,\log_{10}\frac{P_{c}}{P_{n}} \tag{3}\]  
The carrier and the noise power can be calculated with an estimation of the spectral power density with the MATLAB(tm) function _periodogram_. For calculating the carrier power \(P_{c}\), for short signal lengths of 1000 samples, we assume a bandwidth of 600 kHz around the carrier frequency of 2.5 MHz. The noise power \(P_{n}\) is calculated from the power of the remaining frequency band (bandwidth depending on the sampling rate Fs).  
The following experiment is intended to generate suitable velocity signals, for testing the algorithm based on Equations (1) and (2) [21]. Our goal is to generate an artificial and easy to replicate signal dropout by disrupting the beam paths to a shaker, which is used as a source for a known vibration. We achieve this with a rotating disc with holes for letting the beams pass through. Due to the rough surface of the disc and its placement out of focus of the laser beams, very little light is reflected, and a signal dropout is forced. This experimental setup, where the rotating disc is moved by a stepper motor, is shown in Figure 1.  
The four beams are aligned to ensure that at least one of the laser beams of the channels CH1-CH4 always passes through the holes and is positioned on the shaker. The results for this experiment are discussed in Section 3.  
Following the initial experiment with an artificial signal dropout, a more realistic experiment is performed. For this purpose, the four channels of the MPV are focused to the same spot on a test object. Unlike the previous experiment, only one of the measuring heads actively generates a laser beam (active channel), whereas the other three measuring heads only receive scattered light (passive channels). The experimental setup is shown in Figure 2.  
Figure 1: (a) Concept of the experiment to obtain velocity signals with signal dropouts; (b) Image of the actual test setup; laser beams go to the shaker in a straight line through the holes in the rotating disc.  
Figure 2: (a) Concept of the second experimental setup with one active measuring head (CH4) and three passive measuring heads (CH1–CH3); (b) Image of the actual test setup measuring on a speaker.  
For this experiment, the measuring heads are aligned on a vibrating speaker with a known frequency. Due to the angle of the laser beams and the vibration of the speaker, in-plane movement also occurs, resulting in noise caused by the laser speckle effect. With both experimental setups, several measurements are acquired and analyzed. The following section describes the results of our evaluation.