Digital Stroboscopic Holographic Interferometry for Power Flow Measurements in Acoustically Driven Membranes

Despite the importance of the eardrum and the ossicles in the hearing chain, it remains an open question how acoustical energy is transmitted between them. Identifying the transmission path at different frequencies could lead to valuable information for the domain of middle ear surgery. In this work a setup for stroboscopic holography is combined with an algorithm for power flow calculations. With our method we were able to accurately locate the power sources and sinks in a membrane. The setup enabled us to make amplitude maps of the out-of-plane displacement of a vibrating rubber membrane at subsequent instances of time within the vibration period. From these, the amplitude maps of the moments of force and velocities are calculated. The magnitude and phase maps are extracted from this amplitude data, and form the input for the power flow calculations. We present the algorithm used for the measurements and for the power flow calculations. Finite element models of a circular plate with a local energy source and sink allowed us to test and optimize this algorithm in a controlled way and without the present of noise, but will not be discussed below At the setup an earphone was connected with a thin tube which was placed very close to the membrane so that sound impinges locally on the membrane, hereby acting as a local energy source. The energy sink was a little piece of foam carefully placed against the membrane. The laser pulses are fired at selected instants within the vibration period using a 30 mW HeNe continuous wave laser (red light, 632.8 nm) in combination with an acousto-optic modulator. A function generator controls the phase of these illumination pulses and the holograms are recorded using a CCD camera. We present the magnitude and phase maps as well as the power flow measurements on the rubber membrane. Calculation of the divergence of this power flow map provides a simple and fast way of identifying and locating an energy source or sink. In conclusion possible future improvements to the setup and the power flow algorithm are discussed.