Lensless microwave imaging using the Hartley transform

Abstract

We recently reported a method of optical phase measurement¹ that involves the creation of a Hartley transform² plane, which is constructed by the superposition of two Fourier transforms³, one of which was rotated spatially by 180^° and shifted in phase by 90^°. Because the Hartley transform, unlike the Fourier transform, is entirely real, it is able to extract more information when a phase-insensitive detector (for example, an optical detector) is used. In particular, the Hartley intensity encodes the location of the centroid of a source, whereas the intensity distribution of a Fraunhofer diffraction pattern does not change when the source shifts because source location is hidden in the phase information. Through the Hartley transform one gains access to the Fourier phase by amplitude measurements only. We have now extended this technique to the microwave range, and have also demonstrated how to obtain an image of an isophase source without using a phase-sensitive detector.