Generalized Fibonacci photon sieves

Abstract

We successfully extend the standard Fibonacci zone plates with two on-axis foci to the generalized Fibonacci photon sieves (GFiPS) with multiple on-axis foci. We also propose the direct and inverse design methods based on the characteristic roots of the recursion relation of the generalized Fibonacci sequences. By switching the transparent and opaque zones, according to the generalized Fibonacci sequences, we not only realize adjustable multifocal distances but also fulfill the adjustable compression ratio of focal spots in different directions.

Diffractive m-bonacci lenses

“…It has been proved that DOEs with nearly 50% of degradation, can still be used in image-forming devices without loss of performance capabilities, allowing applications in harmful working conditions [22]. Fibonacci zone plates [23][24][25][26][27] stand out for producing two foci, that are located one in front and one behind the focus of an equivalent Fresnel zone plate of the same number of zones. The axial positions of these foci are given by the Fibonacci numbers, being the golden mean the ratio of the two focal distances.…”

Two pairs of twin foci with the golden mean generated by a modified Fibonacci zone plate

“…For example, FiZPs have twin foci with equal intensity and golden mean [1]; kinoform Fibonacci lenses can be used to create two clear images with the golden mean [5]; three-dimensional printed THz Fibonacci lenses constructed in polyamide material can be used to provide twin foci with the golden mean along the optic axis [23]; twin foci positioned with a ratio of the golden mean and other ratios can be obtained by generalized Fibonacci photon sieves [24]; Greek ladders zone plates have three-dimensional array foci located at the positions with the golden mean or other ratios [25]. However, these zone plates [1,5,[23][24][25] produce only a pair of twin foci with the golden mean, and are unable to produce two pairs of twin foci with the golden mean. Another interesting way to generate twin foci with the golden mean is to implement a zone plate constructed by an m-bonacci sequence, which can have two foci with a position ratio related to the m-golden mean including the golden mean [26].…”

Multiplanar Fourier-transform phase-shifting digital holography with a generalized Fibonacci lens

“…Compared to traditional holography, Fourier holography records the spatial frequency spectrum of the object, which can be realized via the focusing lens or lens-less Fourier recording method. Based on previous work on photon sieves [16][17][18], here we introduce the generalized Fibonacci lens into phase-shifting digital holography. As is different from traditional photon sieves [19][20][21][22], the Fibonacci photon sieves can generate more than one focus on the optical axis, showing that it can provide multiplanar Fourier-transform operation.…”