Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks

The navigational tasks of computing time to impact and controlling movements in specific range are addressed here. We show how time to impact can be obtained via the Mellin-based correlator, and we introduce the concept of fractional based correlators. The fractional Fourier/Mellin based correlators can be used in detecting or controlling specific range of movements. Also, both the conventional and the fractional-based correlators can be easily implemented optically in lenses, thus providing correlation images directly at image acquisition time. Lenses are considered cost-effective and therefore, the optical correlators are optimal in both senses, speed and cost.