6 January 2015 Focusing properties of diffractive lenses constructed with the aperiodic m-bonacci sequence
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Proceedings Volume 9450, Photonics, Devices, and Systems VI; 945014 (2015) https://doi.org/10.1117/12.2070434
Event: Photonics Prague 2014, 2014, Prague, Czech Republic
In this contribution we present a new family of diffractive lenses which are designed using the m-bonacci sequence. These lenses are a generalization of the Fibonacci Zone Plates previously reported. Diffractive elements of this type are called aperiodic zone plates because they are characterized by a radial profile that follows a given deterministic aperiodic sequence (Cantor set, Thue-Morse, Fibonacci...). Aperiodic lenses have demonstrated new interesting focusing and imaging properties that have found applications in different fields such as soft X-ray microscopy and spectral domain optical coherence tomography. Here, we show that m-bonacci zone plates are inherently bifocal lenses. We demonstrate that the relative separation of their foci depends on the m-value of the sequence and also can be correlated with the generalized golden ratio. As a particular case, the properties of the m-bonacci sequence with m=2 and m=3, called Fibonacci and Tribonacci Zone Plates respectively are discussed.
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Walter D. Furlan, Walter D. Furlan, Vicente Ferrando, Vicente Ferrando, Juan A. Monsoriu, Juan A. Monsoriu, } "Focusing properties of diffractive lenses constructed with the aperiodic m-bonacci sequence", Proc. SPIE 9450, Photonics, Devices, and Systems VI, 945014 (6 January 2015); doi: 10.1117/12.2070434; https://doi.org/10.1117/12.2070434

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