Fourier Acoustics: Uncovering the origins of sound

It was 25 years ago when the first experiment in nearfield acoustical holography (NAH) took place. Since the first paper appeared in 1980, published in Phys Rev Lett by Williams and Maynard[1], there has been a world wide explosion of research and development, with practical applications finding its way into may varied noise and vibration problems in both military and industry. An overview of the world wide development and morphing of NAH is discussed in this paper. What separates NAH from holography and a multitude of image reconstruction techniques as well as the popular time reversal approaches is the inclusion of evanescent waves in the reconstruction (formation of the image). These evanescent waves decay rapidly away from the surface of the vibrating structure of interest and can not be retrieved from measurements far away from its surface. They can only be retrieved from measurements up close to the structure. The resolution of the image reconstruction in this case is independent of the actual wavelength of the sound since the smaller-than-awavelength evanescent waves provide a resolution much less than the propagating wavelength. The primary objective is to recover the normal fluid velocity and the pressure very near or on the reconstruction surface, the combination of these two quantities allowing us to calculate the active intensity and thus obtain the total power radiated from the source. Mathematically speaking this represents an ill-posed inverse problem due to the fact that small perturbations in the measurement can lead to large perturbations in the reconstructed quantities. The reconstruction is stabilized by using a regularization procedure[2]. The velocity reconstruction is a more ill-posed problem than the pressure reconstruction and thus requires more regularization. Recent approaches have used velocity measurements for the hologram[3]. This approach has the advantage in encountering less errors in the velocity reconstruction than pressure measurement approaches although direct measurement velocity probes are quite a bit more expensive than microphones. SIGNAL PROCESSING FRONT END NAH requires a coherent sound field measured on an imaginary surface. To obtain this coherence it is necessary to measure at the same time a reference or set of references. The reference signals may come from accelerometers attached to the source