newton's rings

i'm getting Newton's rings on long exposures with 6 and 9 stop ND filters on my 16-35 f/4L when stopping down. no sign of them at f/5.6, noticeable at f/8, really bad at f/11. doesn't happen at all with my 3 stop ND or polarizer.

i've ordered some heavier duty cleaning solution, in case there is any residual oil on the filters. is there anything else i can do to fix this? i've had these filters for a while (too long to send back).
 
update:

further reading and testing has narrowed this down a little.

it doesn't happen in natural light (which is lucky for me, as that is my primary use case for long exposures). it also doesn't happen under incandescent lights. it does happen (for me) under energy saving led lights, and there are lots of reports by other people of it happening when photographing the northern lights, which are in a narrow band, using a clear filter, and focused at infinity.

what seems to be happening is that the anti-reflective coatings on the lens and/or filters are less efficient at some wavelengths than others, and certain light sources may show the phenomenon, while most do not.

does that make sense?
 
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