Passive imaging through the turbulent atmosphere: Fundamental limits on the spatial frequency resolution of a rotational shearing interferometer

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Abstract
We compute the signal-to-noise (S/N) ratio to be expected when our 180° rotationally shearing interferometer is used for image recovery at the diffraction limit of a large telescope. The variance and covariance of the irradiance fluctuations at the detector array are shown to yield measures of the high-frequency spatial spectrum of the source. We consider four fundamental sources of noise: temporal fluctuations of the source, space-time fluctuations of the atmosphere, shot noise in the detected photocurrents, and the effects of finite sampling. S/N is found to be directly proportional to the angular resolution of the telescope, the single-frame integration time, the square root of the number of frames, the cube of the operating wavelength, the quantum efficiency of the detector, and the average spectral irradiance from the source on the pupil. It is inversely proportional to the cube of the field angle subtended by the source (or part thereof) under study.