Linear predictive border-padding for PNAH: influence of aperture size and filter order

Linear Predictive Border Padding (LPBP) is a recently presented aperture extrapolation technique [1] to extend the applicability of PNAH to small spatial apertures (compared to the source size). Although Planar Near-field Acoustic Holography (PNAH) is recognized as a powerful and extremely fast acoustic imaging method, small measurement apertures over a portion of larger source structures lead to significant and often intolerable errors in the acoustic source images. The strategy presented in [1] to pre-process the spatial acoustic data before applying FFT is robust and minimizes leakage and distortion of the acoustic field. The filter order determines the wave-number content of the extrapolated data and affects the accuracy of the reconstruction. In this paper the influence of the aperture size and filter order on the accuracy of LPBP is studied based on numerical examples and measurements on a hard disk drive and a cooling fan. The reconstructed source information is compared to the reference source reconstruction obtained using a large aperture. The reconstructed sources are compared both qualitatively (visual comparison) and quantitatively (RMS reconstruction error). The results show that LPBP is a fast and efficient extrapolation method, which leads to accurate reconstructions even for very small aperture sizes. The optimal filter order is depends on the SNR and particular source measured, but in practical situations a filter order between 5-10 should lead to adequate reconstructions.