An explanation of the number of peaks and symmetries of starbursts

Starbursts are the light-intensity patterns seen when small bright sources are observed at low illumination levels, typically stars at night. Starburst patterns are formed because the eye’s wave aberrations generate caustics at the retina. However, a fascinating yet unexplained fact about starbursts is that they usually exhibit p -fold symmetry. Moreover, the number of peaks, related to the symmetry perceived by the subject, is not always the same. The main aim of this study is to explain these visual optics phenomena. For this purpose, we provide a theoretical framework based on the geometric and algebraic properties of the wave aberration function expressed as a Zernike polynomial expansion. Specifically, we investigated the number and distribution of the fertile cusps of Gauss of the wave aberration function. We also established the connections between these points with the symmetries and the number of starburst peaks. We found that starbursts are likely generated by wave aberrations dominated by axially symmetric polynomials combined with a certain amount of non-axially symmetric ones. For instance, whereas a wave aberration with a dominant spherical aberration (Zernike polynomial Z₄⁰ ) plus Z₃³ may induce a 3-peaks starburst with a 3-fold symmetry, a wave aberration combining Z₄⁰ and Z₄⁴ may induce a 4-fold symmetry starburst with four or eight peaks. In addition to providing a comprehensive explanation of starburst symmetries, our theory has other promising applications; for instance, we could infer some basic properties of an eye’s wave aberration function from a measurement (subjective or objective) of the starburst pattern.