Conjecture on necessary caustic structures for perceiving star-like starburst points

Establish whether visual perception of star-like starburst points occurs only under the presence of either a cusp caustic or two fold caustics that are sufficiently close to each other, and provided these caustic features are sufficiently separated from the central bright spot to be resolved by the human visual system.

Background

The paper models starbursts as caustic patterns at the retina generated by the eye’s wave aberration and analyzes the geometry via the Hessian determinant of the wave aberration function expressed in Zernike polynomials. Catastrophe optics indicates that light concentration is particularly intense at cusp caustics or where fold caustics are sufficiently close, suggesting these structures are visually salient.

Motivated by these considerations, the authors conjecture that perceiving star-like starburst points requires the presence of either a cusp caustic or two very close fold caustics, and that these must be sufficiently separated from the central bright spot to be visually resolved. This conjecture serves as a guiding hypothesis for their analysis linking fertile cusps of Gauss and starburst symmetries.