Optical transfer function: Difference between revisions

Revision as of 20:33, 10 March 2020

Revision as of 20:56, 10 March 2020

Line 94:

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>\mathitoperatorname{OTF}(\nu) = \frac{2}{\pi} \left(\arccos(|\nu|)-|\nu|\sqrt{1-\nu^2}\right).</math>.

A more detailed discussion can be found in <ref name=Goodman2005/> and.<ref name=Williams2002/>{{rp|152–153}}