A numerical algorithm for 2-D wavefront reconstruction from intensity measurements in a single plane

Computer experiments were performed to determine the effects of photon noise on reconstructing images from stellar speckle interferometer data. Estimates of the modulus of the Fourier transform of an extended space object were computed using the method of Labeyrie on degraded images simulated to include the effects of atmospheric turbulence and photon noise (Poisson statistics). Several Fourier modulus estimates with different signal-to-noise ratios were computed by assuming different brightness levels (photons per pixel) for the object in each case. Images were reconstructed from the Fourier modulus estimates using an iterative method based on the nonnegativity of the object. It was found that the rms error of a reconstructed image is roughly equal to the square root of the rms error of the Fourier modulus estimate.