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Lecture26 - Fourier Optics Fourier optics methods can be...

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Lecture 26 Diffraction Fourier Optics Fourier Optics Fourier optics methods can be visualized by considering the Fraunhofer diffraction pattern of a single slit. The diffraction process transforms the slit in the object plane to a diffraction pattern in the distant image plane. This diffraction pattern contains information about the slit in a form in which smaller spatial details (narrower slits) are transformed into larger spatial displacement in the image plane (broader diffraction patterns). Smaller spatial detail can be referred to as a higher "spatial frequency", and the diffraction pattern produces a plot in which greater distance from the optic axis implies greater spatial frequency. This kind of transformation, where a plot of light distribution is transformed into plot of spatial frequency is an example of a Fourier transformation and is a conceptual starting point for Fourier optics. Fourier Transformation f x ( ) = 1 2 " F k ( ) e # ikx dk #$ $ % F k ( ) = f x ( ) e ikx "# # $ dx h x ( ) = f x ( ) + g ( x ) = 1 2 " F k ( ) + G ( k ) ( ) e # ikx dk #$ $ % 1-dimension
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