Browsing by Author "Durand, P.E."
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Item Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms(Institute of Physics Publishing, 2011) Patiño Vanegas, Alberto; Durand, P.E.; Fogret, É.; Pellat-Finet, P.According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.Item Diffuser in Fractional Fourier Optics(OSA - The Optical Society, 2016) Patiño Vanegas, Alberto; Durand, P.E.; Pellat-Finet P.; Torres R.We propose a method for calculating a bandlimited diffuser with smooth spectrum in the Fresnel domain without any 2p phase ambiguities using the fractional Fourier transform. Such diffusers are necessary to avoid problems of speckles. © OSA 2016.Item α-bandlimited diffuser in fractional Fourier optics(SPIE, 2016) Patiño Vanegas, Alberto; Durand, P.E.; Torres R.; Pellat-Finet P.; Sheridan J.T.; Meuret Y.; Wyrowski F.We propose a method for calculating appropriate α-band limited diffusers using the fractional Fourier transform. In order to do this, we implement a method for performing a numerical interpolation in the fractional Fourier domain. Such diffusers with compact support in the Fresnel regime may be used in fractional Fourier optical systems where the use of diffusers produce speckles, e.g. digital holography or optical encryption. Numerical simulations are presented. © 2016 SPIE.