Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials
نویسندگان
چکیده
منابع مشابه
Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils.
Zernike polynomials and their associated coefficients are commonly used to quantify the wavefront aberrations of the eye. When the aberrations of different eyes, pupil sizes, or corrections are compared or averaged, it is important that the Zernike coefficients have been calculated for the correct size, position, orientation, and shape of the pupil. We present the first complete theory to trans...
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Recently, we have demonstrated a new and efficient method to simultaneously reconstruct two unknown interfering wavefronts. A three-dimensional interference pattern was analyzed and then Zernike polynomials and the stochastic parallel gradient descent algorithm were used to expand and calculate wavefronts. In this paper, as one of the applications of this method, the reflected wavefronts from t...
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Zernike circle polynomials, their numbering scheme, and relationship to balanced optical aberrations of systems with circular pupils are discussed.
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Zernike polynomials are an orthogonal set over a unit circle and are often used to represent surface distortions from FEA analyses. There are several reasons why these coefficients may lose their orthogonality in an FEA analysis. The effects, their importance, and techniques for identifying and improving orthogonality are discussed. Alternative representations are presented.
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Abstract. Over the past few years considerable attention has been given to the role played by the Zernike polynomials (ZPs) in many di↵erent fields of geometrical optics, optical engineering, and astronomy. The ZPs and their applications to corneal surface modeling played a key role in this development. These polynomials are a complete set of orthogonal functions over the unit circle and are co...
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ژورنال
عنوان ژورنال: Journal of Optometry
سال: 2011
ISSN: 1888-4296
DOI: 10.1016/s1888-4296(11)70040-1