The Finite-Width Single Slit lambda=.633 %Wavelength of laser (micron) =meshgrid((-MeshSize/2:MeshSpacing:MeshSize/2),(-MeshSize/2:MeshSpacing:MeshSize/2)) Ī=RSZ/2)=FGridX_Shift(FGridX_Shift>SZ/2)-SZ įGridY_Shift(FGridY_Shift>SZ/2)=FGridY_Shift(FGridY_Shift>SZ/2)-SZ MeshSize=200 %Size of Screen (micron) %Calculate and show the Amplitude across the aperture. MeshSpacing=1 %Sampling across aperture (micron) Z=Z_Meters*10^6 %Screen distance in microns Lambda=.633 %Wavelength of laser (micron) Figure 2: Examples of the non-uniform quadtree subdivision: sub- tractive superposition (a) and non-square rectangles (b). Let's revisit diffraction from a circular aperture. lambda=10 %Try adjusting and look at the result.įigure imshow(abs(F_Wave),) title( '2D FFT of Wave')įigure imshow(abs(F_Wave_Shift),) title( '2D FFT of Wave, DC at Center.') Let's try a simple example to demonstrate the 2D FT. The two dimensional fourier transform is computed using 'fft2'. A Fourier transform of the coordinatespace wave function yields the momentum wave function and the momentum distribution function, which is the diffraction pattern. The complex amplitude at each position can be seen as the 2D Fourier coefficient calculated for the frequency. The complex amplitude of a diffracted wave far from an aperture can be calculated using the Fraunhofer diffraction integral:Īre the coordinates across the aperture, is the complex amplitude across the aperture, and are the coordinates at the screen.
Fraunhofer Diffraction and the 2D Fourier Transformįraunhofer Diffraction and the 2D Fourier Transform.
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