Residual turbulent scintillation effect and impact of turbulence on the Fourier telescopy system

Abstract

The e ffects o f a tmospheric turbulence o n the g round—to-space p ropagation p ath a nd P oisson sh ot n oise o n a n a ctive laser-based imaging system for high-resolution imaging of Geosynchronous (GEO) satellites are investigated using a wave-optics simulation code. The phase and scintillation statistics in tilt corrected and uncorrected beams are examined at the top ofthe atmosphere and at the satellite. The effects of intensity and phase variations in the illuminating beams on the fringe visibility and spatial frequency of the interference pattern formed by the illuminating beams at the satellite are investigated. The Fourier phase variance caused by Poisson shot noise and turbulence on the uplink path is evaluated. We found that tilt correction reduces the scintillation in the laser beam at the satellite. In the Fourier telescopy system the scintillation variance at the edge of the beam is reduced by a factor of up to 3 for a tilt corrected beam. Long-range propagation in free space reduces scintillation in the illuminating beam. The scintillation variance in the Fourier telescopy system on the optical axis at the satellite is reduced by 26% to 36 %, as compared to that at the top of the atmosphere. The latter is due to diffraction of the laser beam in free space and enhancement of the spatial coherence of the beam described by the Van Cittert-Zernike theorem. The intensity spatial correlation scale in the scintillation pattern exceeds the satellite dimensions. This leads to a so-called residual turbulent scintillation effect, when the scintillation in the illuminating beam modulates the total reflected energy flux. As a result, an arbitrarily large receiver on the ground cannot average the received signal variations. This degrades the Fourier telescopy system performance. Also intensity and phase variations in the illuminating beams degrade the interference pattern formed at the satellite. The turbulence effect on the fringe visibility is stronger at high spatial frequencies. Intensity variations in the illuminating beams degrade the fringe visibility the most. Poisson shot noise and scintillation on the uplink path strongly impacts the Fourier phase of the object. In the turbulent atmosphere the Fourier phase variance increases by a factor of 1 .5-3, as compared to that in free space. The increase of the phase variance is caused by a non-linear interaction between the two statistically independent noise sources. For the nominal signal level and number of averaged pulses the Fourier phase variance is less than 0.1, or ()L I20)2 . This suggests that the Fourier telescopy method is feasible.