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 I 20)2 . This suggests that the Fourier telescopy method is feasible.

Fourier Telescopy is an imaging method that can form images of very dim objects with angular resolution of a few nanoradians, attained by means of a synthetic aperture that overcomes the effects of intervening aberrations using mathematical algorithms akin to that of long-baseline radio astronomy. The algorithm makes use of phase closure and advanced wavefront reconstruction techniques from adaptive optics and Knox-Thompson image reconstruction. The imaging technique is active and so can be used even with faint objects. The imaging technique is active and encodes the information in the temporal instead of spatial domain, allowing imaging of faint objects with extremely large, low-cost receivers. An implementation for deep space imaging is shown; it uses large-area solar collectors for the receiver, yielding a low-cost, highperformance design. Simulated images are shown for a potential realization ofthe 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 (GLINT) will be build 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 powerin-the-bucket receiver and applied this concept to the receiver in the Fourier telescopy system. We found that the powerin-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 numerical simulation code. The twelfth moment of the optical filed was calculated in the presence of laser speckle, atmospheric turbulence, and Poisson shot noise. Simulation results confirmed that Fourier telescopy system is immune to the effects 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 produce the main contribution to the variance of the triple product and measurement error of the object Fourier phase. 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 Ill 0 of the wave.

The upgraded 6.5 mMMT in Arizona will use an adaptive secondary to optimize performance in the near infrared spectral region. The secondary mirror is a 2 mm thick, 640 mm diameter Zerodur shell suspended only by a flexible center hub. Three hundred voice coil actuators installed in an aluminum reference surface deform the shell according to commands from a wavefront sensor. Capacitor position sensors surrounding each actuator provide feedback in an inner servo loop, much faster than the exterior wavefront sensor control bandwidth.A 60 actuator prototype, nearly identical to the final adaptive secondary size, has been built and is currently being tested.

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