Optimal waveform design for array imaging

We introduce and analyze several algorithms for optimal illumination in array imaging. We consider time reversal and Kirchhoff migration imaging in homogeneous media, in regimes where the signal-to-noise ratio is high (infinite). Extensions to coherent interferometric imaging in clutter are described briefly. We show with numerical simulations that the optimal illumination algorithms image selectively closely spaced point scatterers and extended scatterers with considerably better resolution than without the optimization. We analyze the imaging algorithms in the Fraunhofer diffraction regime for small and extended scatterers. Using the prolate spheroidal wavefunctions we also derive analytic expressions of optimal illuminations for imaging strips. (Some figures in this article are in colour only in the electronic version)