900 research outputs found

    Filter-generating system of Zernike polynomials

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    This work proposes a new approach to find the generating function (GF) of the Zernike polynomials in two dimensional form. Combining the methods of GFs and discrete-time systems, we can develop two dimensional digital systems for systematic generation of entire orders of Zernike polynomials. We establish two different formulas for the GF of the radial Zernike polynomials based on both the degree and the azimuthal order of the radial polynomials. In this paper, we use four terms recurrence relation instead of the ordinary three terms recursion to calculate the radial Zernike polynomials and their GFs using unilateral 2D Z-transform. A spatio-temporal implementation scheme is developed for generation of the radial Zernike polynomials. The case study shows a reliable way to evaluate Zernike polynomials with arbitrary degrees and azimuthal orders

    Robust control of a bimorph mirror for adaptive optics system

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    We apply robust control technics to an adaptive optics system including a dynamic model of the deformable mirror. The dynamic model of the mirror is a modification of the usual plate equation. We propose also a state-space approach to model the turbulent phase. A continuous time control of our model is suggested taking into account the frequential behavior of the turbulent phase. An H_\infty controller is designed in an infinite dimensional setting. Due to the multivariable nature of the control problem involved in adaptive optics systems, a significant improvement is obtained with respect to traditional single input single output methods

    Polar Phase Screens: A Comparison with Other Methods of Random Phase Screen Generation

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    This research provides the first organized comparison of random phase screen generation methods, including logarithmic polar Fourier series, using structure functions. Random phase screens are essential elements of simulating light propagation through turbulent media. In order to be effective, they must accurately reflect theory and be practical to implement. This research explains and evaluates three methods of generating random phase screens: using a Fourier series upon a polar frequency grid with logarithmic spacing; using the fast Fourier transform, with its Cartesian frequency grid; and using Zernike polynomials. It provides a comparison of the Polar Fourier Series technique with the two more common techniques (Fast Fourier Transform and Zernike), with the end result of giving the users enough information to choose which method best fits their needs. The evaluation criteria used are generation time (usability) and phase structure function (accuracy)

    Image Reconstruction with Analytical Point Spread Functions

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    The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto image reconstruction techniques, even when observing with adaptive optics systems. These techniques rely on the development of the wavefront using Zernike functions and the non-linear optimization of a certain metric. The resulting optimization procedure is computationally heavy. Our aim is to alleviate this computationally burden. To this aim, we generalize the recently developed extended Zernike-Nijboer theory to carry out the analytical integration of the Fresnel integral and present a natural basis set for the development of the point spread function in case the wavefront is described using Zernike functions. We present a linear expansion of the point spread function in terms of analytic functions which, additionally, takes defocusing into account in a natural way. This expansion is used to develop a very fast phase-diversity reconstruction technique which is demonstrated through some applications. This suggest that the linear expansion of the point spread function can be applied to accelerate other reconstruction techniques in use presently and based on blind deconvolution.Comment: 10 pages, 4 figures, accepted for publication in Astronomy & Astrophysic

    Zernike Piston Statistics in Turbulent Multi-Aperture Optical Systems

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    There is currently a lack of research into how the atmosphere effects Zernike piston. This Zernike piston is a coefficient related to the average phase delay of a wave. Usually Zernike piston can be ignored over a single aperture because it is merely a delay added to the entire wavefront. For multi-aperture interferometers though piston cannot be ignored. The statistics of Zernike piston could supplement and improve atmospheric monitoring, adaptive optics, stellar interferometers, and fringe tracking. This research will focus on developing a statistical model for Zernike piston introduced by atmospheric turbulence
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