# Signal Diversity for Laser-Doppler Vibrometers with Raw-Signal Combination
## 1 Introduction  
With the advancement of laser-Doppler vibrometers (LDVs), various additional applications are continuously made available in which contactless vibration measurement is possible [1, 2, 3]. These applications are difficult to implement with conventional methods of vibration measurement, impossible in the case of rotating or hot parts [4], or unwanted in medical applications [5].  
Throughout this article, we use laser-Doppler vibrometer (LDV) to refer to heterodyne LDVs, such as described in [6, 7]. One limitation in LDV measurements is the impact of the laser speckle effect [6, 7, 8, 9], which leads to so-called signal dropouts [7] on rough or fast-moving surfaces [10].  
In this case, no light reaches the photodetector at a certain point in time and consequently no information about the vibration can be obtained. The impact of this effect is the subject of several publications and has already been widely researched [11, 12, 10, 13, 9]. Even though the effect can be utilized for some specific measurement methods [14, 15], in most LDV applications, it reduces the signal quality and limits the minimally detectable amplitude of a vibration [7]. Therefore, a reduction of the impact of this effect is desirable.  
Various approaches using adaptive optics have been used to accomplish this [16, 17, 18]. For this purpose, however, commercial vibrometers must be modified to a large extent. Another method to achieve this is through signal diversity, which is widely used in radio communications [19, 20]. With signal diversity, the signal is detected from multiple channels. The fundamental idea of improving the signal quality through signal diversity is the assumption of stochastically independent signal dropouts of the individual channels, causedby the laser speckle effect. Therefore, the probability of a signal dropout occurring on all channels at a given time is exponentially lower with an increasing number of channels [7; 21].  
First results to improve the signal quality through signal diversity have been published by [PERSON] [18; 21]. In his publications, an algorithm for calculating a combined signal from two or more demodulated velocity signals was developed and subsequently tested in a practical experiment.  
This article first aims to confirm [PERSON]'s results by an experimental verification using four channels of a Multipoint Vibrometer (MPV). For our purposes, the individual measuring heads (channels) of the MPV can be seen as independent conventional LDVs and therefore all results can be achieved with several conventional LDVs in the same way.  
The limitations of the algorithm are shown by evaluating our measurements. Subsequently, we derive a modified algorithm, which generates a combined signal from the raw signals of the individual channels and compare the results of the algorithms. By this comparison we can show the improvement of the resulting combined signal with our modified algorithm.  
We would like to mention at this point that we do not require real-time performance if the result is obtained within a reasonable amount of time. We are focusing on investigating whether an improvement of the signal quality is possible, so a slightly increased processing time is not relevant at this time.