1 March 1996 ABCD matrix formalism of fractional Fourier optics
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The use of the ABCD matrix formalism to study fractional Fourier transforms (FRFTs) opens new perspectives on the optical implementation of the FRFTs and on the analysis and synthesis of optical systems. ABCD matrices of basic geometries implementing perfect and imperfect FRFTs are presented. The ABCD matrix method is used to demonstrate the cascading performances of FRFT elementary units and to support the established cascading rules. The matrix formalism is used to show that real and complex optical systems realize FRFTs of complex order.
Luis Miguel Bernardo, Luis Miguel Bernardo, } "ABCD matrix formalism of fractional Fourier optics," Optical Engineering 35(3), (1 March 1996). https://doi.org/10.1117/1.600641 . Submission:

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