The circle of equal area now looks bigger than the square. And what if the colors were reversed? Light on black always looks thicker than black on white for ex

The circle of equal area now looks bigger than the square. And what if the colors were reversed? Light on black always looks thicker than black on white for example. I'm sure there are some formulas to deal with all this, but I don't think these are them; the 'real' ones are possibly quite complex. This must surely have been studied in some depth, are there any references?