Effect of turbulence on downlink and horizontal path on high-order coherence moments in Fourier telescopy system

Fourier Telescopy is an active laser-based imaging method for high-resolution imaging of dim objects in Geosynchronous (GEO) orbit. The Geo Light Imaging National Testbed will be buit to demonstrate new powerful imaging capability. Several processes including laser speckle, atmospheric turbulence on the downlink and 1-km horizontal path, as well as Poisson shot noise can contribute to the measurement error of the Fourier phase of the object and thus degrade the reconstructed image. We investigated the impact of three processes including laser speckle, turbulence, and Poisson shot noise on the measurement error of the Fourier phase. We introduced the concept of power-in-the-bucket receiver and applied this concept to the receiver in the Fourier telescopy system. We found that the power-in-the-bucket receiver cancels the effects of turbulence on the horizontal path on the Fourier telescopy system. We evaluated variance of the real and imaginary parts of the triple product, as well as variance of the Fourier phase of the object by using a numercal simulation code. The twelfth moment of the optcal filed was calculated in the resenceof laser speckle, atmospheric turbulence, and Poisson shot noise. Simulation results confirmed that Fourier telescopy system is immune to the efects of turbulence on the horizontal path. It also showed that the effect of turbulence on the downlink path on the triple product is small. Laser speckle contributes strongly to the variations of the real part of the triple product and weakly to the imaginary part. Statistical properties of the triple product depend on the noise source. Poisson shot noise and laser speckle poduce the main contribution to the variance of the triple product and measurement error of the object Fourier pase. Phase variance reduces with increasing the number of heliostats, number of pulses, fringe visibility, and fringe signal-to-noise ratio. For 40 heliostat receivers, 100 averaged pulses, and all considered fringe SNRs and fringe visibilities the phase variance caused by Poisson noise, laser speckle, and turbulence on the downlink path is significantly less than 0.36, which corresponds to the phase measurement accuracy of 1/10 of the wave.