哈工大信息光学Chapter4-2.pdf

幻 灯 片 Chapter 4 1 Fresnel and Fraunhofer Diffraction Weimin Sun College of Science Harbin Engineering University 幻 灯 片 4.7 2 n Assuming unit -amplitude, normally incident plane -wave illumination: n (a) Find the intensity distribution in the Fraunhofer diffraction pattern of the double-slit aperture shown in figure above. n (b) Sketch normalized cross sections of this pattern that appear along the x and y axes in the observation plane, assume X/lz = 10/m, Y/lz = 1/m, and /lz = 1.5/m, z being the observation distance and l the wavelength. 幻 灯 片 Solution: 3 n (a) The amplitude transmittance of this aperture can be written x y / 2 y / 2 tA (x ,h) rect ( )[rect( ) rect ( )] X Y Y n The Fourier transform of this function is F {t (x ,h)} 2XY sinc(Xf )sinc (Yf ) cos(pf ) A X Y Y n The Fraunhofer diffraction pattern is therefore 2XY 2 2 Xx 2 Yy 2 py I (x,y ) ( ) sinc ( )sinc ( ) cos ( ) lz lz lz lz 幻 灯 片 4 n (b) The required sketch is shown below 幻 灯 片 4-8 5 n (a) Sketch the aperture described by the amplitude transmittance function