A Phaseless Near-Field to Far-Field Transformation With Planar Wide-Mesh Scanning Accounting for Planar Probe Positioning Errors

Abstract

This paper proposes a method to correct severe, but known, probe positioning errors affecting a phaseless Planar Wide-Mesh Scanning (PWMS) Near-Field to Far-Field (NFFF) transformation technique and shows its numerical assessment. The involved technique exploits a scanning strategy by applying the non-redundant sampling representation of the squared amplitude of the electromagnetic field and by considering the source as surrounded by an oblate spheroid. In this way, the acquired NF samples are drastically reduced as compared to the classical phaseless NFFF transformation techniques. For the considered technique, the phaseless problem is addressed as a quadratic inverse one by exploiting the squared amplitude of the data gathered on two separate scanning planes and by devising a proper representation of the searched for unknowns. By assuming the planar positioning errors as known, the squared amplitude of the NF samples, at the nominal sampling points of the non-redundant representation, are recovered, from the positioning errors corrupted ones, by a Singular Value Decomposition based approach. After the compensation error step, an optimal sampling interpolation algorithm allows one to get, from the so obtained correctly positioned PWMS squared amplitude NF data, those on the classical plane-rectangular grid necessary to apply the phase retrieval procedure. The effectiveness of the proposed compensation approach is here shown by numerical results.

Keywords

• Phase retrieval
• phaseless NFFF transformations
• positioning errors compensation
• prolate spheroidal wave functions
• PWMS
• non-redundant sampling