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Session III.7 - Special Functions and Orthogonal Polynomials


Symmetry structure of starbursts

Antonia M. Delgado

Universidad de Granada, Spain   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

When looking at a star under low-light conditions, most people perceive some structured symmetric patterns, which have been called starbursts. Starburst patterns can be very diverse but some typical ones are those in which a bright central area is surrounded by clearly marked intensity spikes (star points) [2, 3]. These light patterns are formed due to the imperfections in the optical elements of the human eye, which are mathematically described by a bivariate orthogonal Zernike expansion. Based on the deep relation between wavefront aberration and caustic patterns symmetry-preserving and the properties of some singular points of curvature functions of the classical Zernike polynomials [1], in this work we investigate a theoretical explanation of the types of symmetries and the number of points of starbursts.


[1] S. Barbero, A. Bradley, N. López-Gil, J. Rubinstein, L. Thibos, Catastrophe optics theory unveils the localised wave aberration features that generate ghost images, Ophthalmic Physiol Opt. 2022; 42: 1074-1091.

[2] J. Rubinstein, On the geometry of visual starbursts, J. Opt. Soc. Am. A 36(4), B58-B64 (2019).

[3] R. Xu, L. N. Thibos, N. López-Gil, P. Kollbaum, A. Bradley, Psychophysical study of the optical origin of starbursts, J. Opt. Soc. Am. A 36(4), B97-B102 (2019).

Joint work with Sergio Barbero (CSIC - Instituto de Óptica Daza de Valdés, España), Lidia Fernández (Universidad de Granada, España) and Teresa E. Pérez (Universidad de Granada, España).

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