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30 December 1994 Concurrent computation of Zernike coefficients used in a phase diversity algorithm for optical aberration correction
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Abstract
This paper describes a method to compute the optical transfer function, in terms of Zernike polynomials, one coefficient at a time using a neural network and gradiant decent. Neural networks, which are a class of self-tutored non-linear transfer functions, are shown to be appropriate for this problem as a closed form solution does not exist. A neural network provides an approximation to the optical transfer function computed from examples using gradient descent methods. Orthogonality of the Zernike polynomials allow image wavefront aberrations to be described as an ortho-normal set of coefficients. Atmospheric and system distortion of astronomical observations can introduce an unknown phase error with the observed image. This phase distortion can be described by a set of coefficients of the Zernike polynomials. This orthogonality is shown to contribute to the simplicity of the neural network method of computation. Two paradigms are used to determine the coefficient description of the wave front error to provide to a compensation system. The first uses a phase diverse image as input to a feedforward backpropagation network for generation of a single coefficient. The second method requires the transfer function to be computed in the Fourier domain. Architecture requirements are investigated and reported together with saliency determination of each input the the network to optimize computation and system requirements.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Richard A. Carreras, Gregory L. Tarr, Sergio R. Restaino, Gary C. Loos, and Meledath Damodaran "Concurrent computation of Zernike coefficients used in a phase diversity algorithm for optical aberration correction", Proc. SPIE 2315, Image and Signal Processing for Remote Sensing, (30 December 1994); https://doi.org/10.1117/12.196735
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