Wind J.

In this paper we present a fast evaluation to the Rayleigh integral, which leads to fast and highly accurate solutions in inverse acoustics. The method commonly used to reconstruct acoustic sources on a plane in space is Planar Nearfield Acoustic Holography (PNAH). Some of the most important recent improvements in PNAH deal with the alleviation of spatial windowing effects that arise due to the application of a Fast Fourier Transform to a finite spatial measurement grid. Although these improvements have lead to an increase in the accuracy of the method, the application of the Fast Fourier Transform will inevitably lead to certain errors such as leakage and edge-degradation. Such errors do not occur when numerical models such as the Boundary Element Method (BEM) are used. Moreover, these models solve the forward problem exactly as the number of degrees of freedom tends to infinity, but the time and computer memory needed to solve these problems up to an acceptable accuracy is large. We present a fast (O(n log n) per iteration) and memory efficient O(n) solution to the planar acoustic problem by exploiting the fact that the transfer matrix associated with a numerical implementation of the Rayleigh integral is Toeplitz. Hence, we propose the method to be named TRIM (Toeplitz Rayleigh Integral Method). In this paper we will deal with both the fundamentals of the method and its application in inverse acoustics. Special attention will be given to comparison between experimental results from PNAH and TRIM. Due to the fact that TRIM is based on common methods in numerical analysis, many off-the-shelf numerical solutions can be applied to exploit the speed and accuracy of the model. An overview of possible future applications will be given.