A Technique of Holographic Projection from Far Field Pattern to an Unconstrained Planar Surface

Holographic back projection to a plane from spherical pattern data offers more details than from planar data because the image is derived from data over an entire hemisphere. A previous study introduced a back-projection method where the far field pattern can be projected to a plane which is orthogonal to the radial direction. With this arrangement, the projection is forced to be centered at the interception point between the plane and the radial line. This could force the desire image to be located away from the center where the best image resolution resides. In case of a large offset, it could even result in incorrect hologram. In this study, we propose a more robust back projection method. In this proposal, a translation and a series of rotation operations are applied on the far field pattern, after which the desired image area is centered and orthogonal to the propagation direction. The plane wave spectrum and hologram can then be calculated from the translated and rotated far field pattern. The propagation term ${e^{j\gamma d}}$ in the conventional back projection technique is no longer needed after the pre-process of the far field pattern because it is included in the translation operation. This method provides a high-resolution holographic projection onto any desired area. It is especially applicable for cases when Antenna Under Test (AUT) has an arbitrary orientation with an offset from the origin, or for cases where projections are needed onto several surfaces of a multifaceted AUT.