Synthetic aperture imaging with arrays of arbitrary shape. Part I. General case

The problem of synthesizing full-aperture resolution with linear transmitting and receiving arrays of arbitrary shape is considered. The arrays are assumed to lie in the same plane and can be open (e.g., curved or straight line segments) or closed (e.g., circles). It is shown that a full (area) aperture can be synthesized by suitably weighting the transmitted and received signals. This weighting turns out to be the Jacobian of a transformation that yields uniform coverage in the spatial-frequency domain. If the Jacobian is factorable, then full-aperture resolution can be achieved in a single transmission. The theory is illustrated with two annular arrays of different diameter: one that transmits and one that receives. If the radii of the annular arrays are a and b, then the synthesized point-spread function (PSF) is shown to be equivalent to that of a filled circular aperture of radius a+b.