Fig. 2: Knot survival for small apertures.

The figure shows different singular skeletons obtained for aperture values slightly below the critical aperture Ac and for strengths γ < 1 such that the topology is conserved. The examples shown are for 3-rd and 4-th order aberrations, namely (a) trefoil, (b) quadrafoil, (c) coma, and (d) secondary astigmatism. The first column shows a three-dimensional plot of the aberrations with a texture given by the cinquefoil phase pattern to highlight how the different Zernike polynomials affect the wavefront near the phase singularities.