Longitudinal spatial coherence of computational ghost imaging through atmospheric turbulence

The resolution and imaging quality of ghost imaging is determined by the longitudinal spatial coherence (LSC) of speckle beams on the signal and reference arms. Based on the cross-correlation function, long-exposure and short-exposure computational ghost imaging through turbulent atmosphere is investigated analytically and numerically in the framework of the traditional imaging theory. According to the point spread function (PSF), the modulation transfer function (MTF) is derived, both of which are utilized to evaluate imaging resolution and imaging quality of computational ghost imaging (CGI), respectively. By simulating long-exposure and short-exposure ghost imaging through atmospheric turbulence, the comprehensive effects of atmospheric turbulence and beam initial parameters on the complex degree of coherence (CDC), PSF, and MTF are studied, respectively. It is found that the degradation of LSC between the two planes on the reference and signal path implies a narrower PSF and increased MTF values, which represent the better resolution and imaging quality. Thus, reducing the atmospheric turbulence strength, the speckle particle size, the wavelength and the propagation distance, and increasing the source size contribute to improving resolution and image quality of CGI because of the degradation of LSC. Furthermore, short-exposure CGI can provide imaging performance superior to long-exposure CGI in terms of resolution and imaging quality due to the decrease of LSC.