Bubble optics: Leonardo's cross revisited-Part 1, numerical methods

Around 1508, Leonardo DaVinci observed a curious image of the sun formed by a floating bubble. Now, some 500 years later, we give a full picture of the surprisingly rich phenomenology of the light pattern formed below surface bubbles. Under shallow illumination, and for shallow depths of water, the caustic deviates from the symmetrical astroid shape obtained for larger depths and/or near-vertical illumination. Whereas the astroid caustic involves refraction through the outer meniscus only, more complex ray paths explain the asymmetric, multicomponent (composite) light pattern.