Editing Fractional Fourier transform (section)

===Fresnel and Fraunhofer diffraction===
The diffraction of light can be calculated using integral transforms. The [[Fresnel diffraction|Fresnel diffraction integral]] is used to find the near field diffraction pattern. In the far-field limit this equation becomes a Fourier transform to give the equation for [[Fraunhofer diffraction]].  The fractional Fourier transform is equivalent to the Fresnel diffraction equation.<ref>{{cite journal |last1= Pellat-Finet |first1= Pierre |date= 15 September 1994 |title= Fresnel diffraction and the fractional-order Fourier transform |journal= Optics Letters |volume= 19 |issue= 18 |pages= 1388–1390 |doi= 10.1364/OL.19.001388|pmid= 19855528 |bibcode= 1994OptL...19.1388P }}</ref><ref>{{cite journal |last1= Pellat-Finet |last2= Bonnet |first1= Pierre |first2= Georges |date= 15 September 1994 |title= Fractional order Fourier transform and Fourier optics |journal= Optics Communications |volume= 111 |issue= 1–2 |page= 141 |doi= 10.1016/0030-4018(94)90154-6|bibcode= 1994OptCo.111..141P }}</ref> When the angle <math>\alpha</math> becomes <math>\pi/2</math>, the fractional Fourier transform is the standard Fourier transform and gives the far-field diffraction pattern. The near-field diffraction maps to values of <math>\alpha</math> between 0 and <math>\pi/2</math>.