## 4 Electronic Speckle Pattern Interferometry  
ESPI is a laser-based interferometric technique that measures, among others, the speckle behavior on the top plate surfaces of musical instruments. The ESPI setup is presented in Figure 2. A CW Laser/532 nm beam illuminated the top plate of the bouzouki, causing the speckle appearance on the top plate, while an internal beam of the setup was directed to a CCD camera as a reference beam. A loudspeaker driven by a frequency generator excited the bouzouki at specific frequencies. A loudspeaker driven by a frequency generator excited the bouzouki at specific frequencies. The loudspeaker was positioned 60 cm from the instrument. Apart from the excitation at different frequencies, the loudspeaker emitted a sound that was also varied. Two measurement sets at an 80 dB sound pressure level (SPL) and 90 dB SPL were measured. During the measurements, the stability of the SPL was monitored by a digital audio analyzer.  
The captured images from the camera of the setup were subtracted and processed using specially developed software. The intensity of each sequential image captured from the camera was \(I_{1}\) and \(I_{2}\), while their subtraction can be given by [10]:  
\[I=I_{1}-I_{2}=\frac{\sqrt{I_{1}I_{2}}}{2}\Big{|}(\cos\varphi)\Gamma^{2}(\Delta A )^{2}J_{0}(\Gamma A)\Big{|} \tag{1}\]  
where \(I_{1}\) and \(I_{2}\) are the intensity of each image, \(\varphi\) is the phase difference between the two beams, \(\Gamma=4\pi/\lambda\) with \(\lambda\) as the the laser wavelength; \(A\) is the vibration amplitude, \(\Delta A\) is the vibration amplitude difference between the two images, and \(J_{0}\) is the zero order of the Bessel function of the first kind.  
The vibrational modes that appeared where the top plate resonated were shaped by the Bessel function term \(|J_{0}(\Gamma A)|\). The dark and white fringes that appeared were equal  
Figure 2: Schematic of the ESPI setup at the Physical Acoustics and Optoacoustics Laboratory of HMU, with the bouzouki under study and the excitation source. CW Laser Source 532 nm, BS1—Main Beam Splitter, L1—Expanding Lens, VND—Variable Neutral Density Filter, BE—Beam Expander, CCD—Camera, BS2—Secondary Beam Splitter, L2—Objective Camera Lens, BZK—Bouzouki, PC—Computer, FREQ—Frequency Generator, LSPK—Loudspeaker.  
height curves of the same vibration amplitude, with the bright fringes corresponding to the maxima of \(|f_{0}(\Gamma A)|\).  
The resulting images contained both the spatial information of the vibrating surface and the information of its amplitude (perpendicular to the surface). Spatial information corresponds to the extent of the surface coverage by the fringes formed and by the different vibrational modes on the surface of the bouzouki. The amplitude information was extracted after measuring the number of bright fringes and by correlating each fringe to a vibration amplitude through the term \(|f_{0}(\Gamma A)|\). A detailed description may be found in [10].  
In the literature, the experimentally measured vibration modes for four-string [21,22] and three-string bouzoukis [21,22] with a large vibration amplitude extend to frequencies up to 1500 Hz. For this reason, it was chosen to perform experimental measurements using ESPI interferometry for the frequency range between 40 Hz and 1500 Hz.