Spectral theory of microwave holographic image formation

The capabilities of subsurface microwave holography are limited by mutually contradicting factors, such as penetration depth, surface reflection, and spatial resolution. As a result of the trade-off, the wavelength at the operating frequency is comparable to the typical target sizes and is not small compared with the antenna array dimensions and probing range. In order to comprehend microwave image formation by a planar holographic antenna array we apply Fresnel-Kirchhoff diffraction theory uniformly treating target illumination, incident wave scattering, holographic data acquisition, and object reconstruction by means of numerical wave front conversion. Within the framework of narrow-angle diffraction model we derive an integral operator directly transforming the planar test object into its diffraction-limited image. The action of this operator is readily revealed by applying Fourier transform with respect to the transversal coordinates: it cuts from the target spatial spectrum a rectangular segment centered according to the illumination angle. The theory shows that for a successful object reconstruction the acquired rectangle must cover the significant part of the target spatial spectrum. If the antenna aperture is too small to meet this condition, synthetic aperture approach can be successfully used. Such a multiview-multistatic measurement scheme realized by moving the radiator around the fixed receiver antenna array may considerably improve the radar imaging performance - cf. [1]. This conclusion was confirmed by numerical simulation and physical experiment.