The circles might be due to the way you processed the shot. I’m not an expert in this type of thing but I’d guess it is due to mathematical rounding of numbers. It may alleviate the issue if you do all your processing at full resolution, eg in a 16bits per channel colour space, and only at the very end reduce the image to 8bits and lower resolution (if needed).
Also the order you do your processing might contribute to this effect but may not change the overall look, so changing the order of processing steps might help. In PS, for example, looking at how each processing step causes choppiness in your histogram(s) can give you an idea of what is going on.
If you manage to keep smooth tonal gradations, it would make a beautiful print. Very nice work!