References per coherence length: A figure of merit for multireference acoustical holography

Abstract

Multireference partial field decomposition (PFD) can be used to generate coherent holograms for scan-based near-field acoustical holography measurements. PFD is successful when the reference array completely senses all independent subsources, but meeting this requirement is not straightforward when the number of subsources and their locations are ambiguous (such as in aeroacoustic sources). A figure of merit based on spatial coherence lengths, called references per coherence length (RPLc), is a useful metric to guide inter-reference spacing in the array design so that the source is spanned. Coherence length is defined as the axial distance over which the ordinary coherence drops from unity to some desired value. Numerical experiments involving an extended, partially correlated source show that sufficiency of the reference array for different source conditions may be simply expressed in terms of RPLc. For sources of varying spatial coherence and over a large range of frequencies, one reference per coherence length is equivalent to sensing all independent subsources.