A mask is made from variably transparent material, and illuminated with monochromatic plane wave radiation of wavelength 1 at normal incidence, propagating along the z-direction. The mask consists of four "windows and has approximate transmission function T(x) = exp x -2 a2 1: (* + 6(+) +86-)+66] where a is small compared to d and the operator * denotes convolution. Find an expression for the intensity of the Fraunhofer diffraction pattern produced by the mask as a function of the angle of deflection, assuming that this angle is small. Explain your working carefully. A mask is made from variably transparent material, and illuminated with monochromatic plane wave radiation of wavelength 1 at normal incidence, propagating along the z-direction. The mask consists of four "windows and has approximate transmission function T(x) = exp x -2 a2 1: (* + 6(+) +86-)+66] where a is small compared to d and the operator * denotes convolution. Find an expression for the intensity of the Fraunhofer diffraction pattern produced by the mask as a function of the angle of deflection, assuming that this angle is small. Explain your working carefully