Tomographic reconstruction using a generalized regressive discrete Fourier series

When measuring three-dimensional phenomena such as flow fields or acoustic fields using an interferometric technique, one is proneto measure different angles of view to obtain a full three-dimensional representation of the phenomenon under investigation.This is due to the fact that an interferometric technique measures a line integral across the optical path. To obtain the full three-dimensional view the different angles of view are passed through a tomographic algorithm. The most widely used tomographic method is the so-called filtered back projection. However, this process suffers from a series of drawbacks, the most important one being the fact that substantial truncation errors occur in the back projection step. In this article a method is devised to eliminate these errors, based on a parametric frequency-domain approach called generalized regressive discrete Fourier series (GRDFS). The method will be applied both to simulated acoustic fields as to real acoustic fields measured using laser doppler vibrometry. The acoustic source will be rotated to obtain continuous angle views of the acoustic field, hence eliminating the tedious process of rotating the measurement setup.