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The intersecting area can be calculated as the sum of the areas of two identical [[circular segment]]s: <math> \theta/2 - \sin(\theta)/2</math>, where <math>\theta</math> is the circle segment angle. By substituting <math>|\nu| = \cos(\theta/2)</math>, and using the equalities <math>\sin(\theta)/2 = \sin(\theta /2)\cos(\theta /2)</math> and <math>1 = \nu^2 + \sin(\arccos(|\nu|))^2</math>, the equation for the area can be rewritten as <math>\arccos(|\nu|) - |\nu|\sqrt{1 - \nu^2}</math>. Hence the normalized optical transfer function is given by:
: <math>\operatorname{OTF}(\nu) = \frac{2}{\pi} \left[\cos^{-1}(|\nu|)-|\nu|\sqrt{1-\nu^2}\right]
A more detailed discussion can be found in <ref name=Goodman2005/> and.<ref name=Williams2002/>{{rp|152–153}}
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