Fourier transform method for imaging atmospheric Cherenkov telescopes

We propose Fourier transform (hereafter FT) method for processing the images of extensive air showers (EAS) detected by imaging atmospheric Cherenkov telescopes (IACT) used in the very high energy (VHE) gamma-ray astronomy. The method uses a special type of discrete Fourier transforms (DFT) based on orbit functions of compact Lie groups, and the use of continuous extension of the inverse transform to approximate the discrete images by continuous EAS brightness distribution functions. Here we present the FT-method for SU(3) group which provides a practicable technique for realization of the DFT approach for functions sampled on hexagonal symmetry grids implemented in the current IACT cameras. We note that the proposed FT-method can also be implemented for the rectangular grids using the DFT on SU(2) × SU(2) group. w the viability of the FT-method, here we apply it to Monte-Carlo simulated bank of TeV proton and gamma-ray EAS images only for the case of a stand-alone telescope and use a simple single-parameter (ALPHA) analysis. Comparing between the FT-method and the currently used ‘standard’ method for signal enhancement shows that a straightforward use of FT technique within standard parameterization scheme allows a better and systematic enhancement of the gamma-ray signal. The relative difference between these two methods becomes more profound especially for ‘photon poor’ images, for which the standard method significantly deteriorates. It suggests that the effective EAS detection thresholds could be reduced with implementation of the FT technique for IACTs. This prediction is further supported by a significant noise suppression capability of the method after using simple ‘low-pass’ filters in the image frequency domain. This new approach allows very deep ‘tail’ (and ‘height’) image cuts, differentiation of images, provides frequency spectra, etc., which could be used for development of new effective parameters for the EAS image processing.