In this paper, a novel transformation connecting an arbitrary Planar Array to a virtual Uniform Linear Array (ULA) with a larger number of sensors is proposed. The array orientation, number of sensors and phase characteristics of the virtual array are a function of the array shape of the planar array. The two parameter manifold (azimuth,elevation) of a planar array of N sensors is a conoid surface embedded into an N -dimensional complex space which can be described by two families of curves (θ-curves and φ-curves). While the family of φ-curves have hyperhelical shape, the family of θcurves do not. The proposed transformation will allow the θcurves to be transformed to the manifold of a virtual ULA that has hyperhelical shape. This will allow a planar array system to be analysed or designed by analysing or designing simple hyperhelical curves associated with the virtual linear array.
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