Application of Fractional Fourier Transform to Hologram Formation of a Moving Acoustic Source

This paper examines how the fractional Fourier transform (FrFT) can be used to form and analyze acoustic holograms produced by a moving, linear, frequency-modulated (LFM) source in a shallow water waveguide. In these environments, the source sound field creates an interference pattern, referred to as a two-dimensional interferogram, which represents the distribution of acoustic intensity in the frequency–time domain. This interferogram consists of parallel interference fringes. Consequently, focal points are formed and aligned along a straight line in the source hologram, which is represented by the two-dimensional Fourier transform of the interferogram. We have developed a holographic method for constructing the interferogram of an LFM source signal and transforming it into a Fourier hologram based on FrFT in the presence of strong noise. A key finding of this study is that the FrFT-based holographic method enables localized focal regions to emerge from modal interference even under high-intensity noise conditions. The positions of these focal spots are directly related to the source parameters, enabling the estimation of key characteristics such as the distance and velocity of the LFM source. We analyzed the effectiveness of the FrFT-based holographic method through numerical experiments in the 100–150 Hz frequency band. The results demonstrate the method’s high noise immunity for source localization in realistic shallow water environments under strong noise.