Immersive Wave Propagation Experimentation: Physical Implementation and One-Dimensional Acoustic Results

Abstract

We present a fundamentally new approach to laboratory acoustic and seismic wave experimentation that enables full immersion of a physical wave propagation experiment within a virtual numerical environment. Using a recent theory of immersive boundary conditions that relies on measurements made on an inner closed surface of sensors, the output of numerous closely spaced sources around the physical domain is continuously varied in time and space. This allows waves to seamlessly propagate back and forth between both domains, without being affected by reflections at the boundaries between both domains, which enables us to virtually expand the size of the physical laboratory and operate at much lower frequencies than previously possible (sonic frequencies as low as 1 kHz). While immersive boundary conditions have been rigorously tested numerically, here we present the first proof of concept for their physical implementation with experimental results from a one-dimensional sound wave tube. These experiments demonstrate the performance and capabilities of immersive boundary conditions in canceling boundary reflections and accounting for long-range interactions with a virtual domain outside the physical experiment. Moreover, we introduce a unique high-performance acquisition, computation, and control system that will enable the real-time implementation of immersive boundary conditions in three dimensions. The system is capable of extrapolating wave fields recorded on 800 simultaneous inputs to 800 simultaneous outputs, through arbitrarily complex virtual background media with an extremely low total system latency of 200 μs. The laboratory allows studying a variety of long-standing problems and poorly understood aspects of wave physics and imaging. Moreover, such real-time immersive experimentation opens up exciting possibilities for the future of laboratory acoustic and seismic experiments and for fields such as active acoustic cloaking and holography.

Cloaking and Holography Experiments Using Immersive Boundary Conditions

“…The remaining energy is mainly due to the imperfect correction for the frequency-dependent loudspeaker transfer function. The correction is implemented as a deconvolution of the measured transfer function (in the frequency range of our experiment) from the Green's functions, which can be carried out prior to the experiment [33]. Note that further improvements in the correction come at the expense of increasing the latency to compute the extrapolation step, therefore increasing the separation between S and R.…”

“…The data-acquisition and control system is not shown here but is discussed in detail in Ref. [33]. functions appropriately [33].…”

“…In addition to the system latency, corrections minimizing undesired hardware effects contribute significantly to the total latency. These undesired effects include the frequency-dependent loudspeaker transfer function and the fact that the emitting surfaces (the loudspeakers) are not perfectly rigid [33]. The total latency dictates the separation distance between R and S. Here, a distance of 0.45 m is needed to allow for an extrapolation time of 1.31 ms, including all hardware corrections.…”

“…Precomputed GFs IBCs Free-field wave propagation facilitate the numerical implementation of the extrapolation in real time, the temporal convolution in Eq. (2) is discretized in a time-recursive fashion and the surface integral is expressed as a matrix-vector multiplication such that the calculation can be performed recursively at each time step [31,33].…”

“…The first IBC experiment verifying the successful real-time extension of a physical-experimentation domain has been presented in Ref. [33] and, even more remarkably, has shown that long-range interactions between the physical and virtual domain can be accounted for. On the other hand, immersion also allows acoustic cloaking and holography [34].…”