Okay well first you need to slap down a white circle with like an opacity of 80 or 70 or something.
Do pretty much the same thing with a black circle, but position it slightly above the white circle.
Replace the bit where the two circles overlap with a slightly darker version of the background, then add anti-aliasing, maybe a hint of blur, and adjust any colors until results are optimal.
Here's what the original looked like for reference: