Changing from floats to doubles

In an attempt to remove some of the banding I'm seeing, I've changed from floats to doubles:

Index of refraction 1.33, double precision floating point:


Index of refraction 1.33, single precision floating point:


Difference image of the two:


The banding is gone, but now I'm seeing some ellipse shaped dark spots that I didn't expect to see.

The next three images use an index of refraction of 2.69.

Double precision:


Single precision:


Difference: