Fractal generalized zone plates

Design of Acoustic Bifocal Lenses Using a Fourier-Based Algorithm

In this work, we develop a new design method based on fast Fourier transform (FFT) for implementing zone plates (ZPs) with bifocal focusing profiles. We show that the FFT of the governing binary sequence provides a discrete sequence of the same length, which indicates the location of the main foci at the ZP focusing profile. Then, using reverse engineering and establishing a target focusing profile, we are capable of generating a binary sequence that provides a ZP with the desired focusing profile. We show that this design method, based on the inverse fast Fourier transform (IFFT), is very flexible and powerful and allows to tailor the design of bifocal ZPs to achieve focusing profiles with the desired foci locations and resolutions. The key advantage of our design algorithm, compared to other alternatives presented in previous works, is that our method provides bifocal focusing profiles with an absolute control of the foci locations. Moreover, although we analyze the performance of this novel design algorithm for underwater ultrasonics, it can also be successfully extended to different fields of physics, such as optics or microwaves, where ZPs are widely employed.

On the Design of Soret Zone Plates Based on Binary Sequences Using Directional Transducers

In this work, we analyze the effect of the distribution of transparent Fresnel regions over the focusing profile of Soret Zone Plates (SZP) based on binary sequences. It is shown that this effect becomes very significant in those fields where directional transducers are employed, such as microwaves or acoustics. A thorough analysis of both the SZP transmission efficiency and the focusing enhancement factor is presented. Moreover, experimental measurements are also carried out for a particular type of binary sequence, the Cantor ternary set, validating the theoretical model and demonstrating that the distribution of transparent Fresnel regions becomes a critical parameter in applications requiring directional emitters.

Analysis of Predistortion Techniques on Fresnel Zone Plates in Ultrasound Applications

In this work, we analyze the effect of predistortion techniques on the focusing profile of Fresnel Zone Plates (FZPs) in ultrasound applications. This novel predistortion method is based on either increasing or decreasing the width of some of the FZP Fresnel rings by a certain amount. We investigate how the magnitude of the predistortion, as well as the number and location of the predistorted rings, influences the lens focusing profile. This focusing profile can be affected in different ways depending on the area of the lens where the predistortion is applied. It is shown that when the inner area of the lens, closer to its center, is predistorted, this technique allows the control of the focal depth at the main focus. However, when the predistortion is applied to an area farther from the center of the lens, the acoustic intensity distribution among the main focus and the closest adjacent secondary foci can be tailored at a certain degree. This predistortion technique shows great potential and can be used to control, modify and shape the FZP focusing profile in both industrial and therapeutic applications.

Fractal lenses based on Cantor binary sequences for ultrasound focusing applications

In this work, we demonstrate the application of Cantor fractal lenses in acoustics. The Cantor Zone Plate (CZP), previously introduced in optics, is designed from a conventional Fresnel Zone Plate (FZP) using a binary sequence governed by the distribution of a generalized Cantor set. The CZP maintains its main focus at the same focal distance than its associated FZP, providing a softer multi-foci focusing profile which is very useful in certain ultrasound therapeutic applications. Experimental measurements are in good agreement with the theoretical model, demonstrating that CZPs are suitable for the ultrasound field.

M-Bonacci Zone Plates for Ultrasound Focusing

In this work, we present a thorough analysis on M-bonacci zone plates for ultrasound focusing applications. These planar lenses are capable of providing bifocal focusing profiles with equal intensity in both foci and become very appealing for a wide range of scenarios including medical and industrial applications. We show that in high-wavelength domains, such as acoustics or microwaves, the separation between both foci can be finely adjusted at the expense of slightly increasing the distortion of the focusing profile, and we introduce a design parameter to deal with this issue and simplify the design process of these lenses. Experimental measurements are in good agreement with numerical simulations and demonstrate the potential of M-bonacci lenses in ultrasound focusing applications.

Depth of focus enhancement of a modified imaging quasi-fractal zone plate

We propose a new parameter w for optimization of foci distribution of conventional fractal zone plates (FZPs) with a greater depth of focus (DOF) in imaging. Numerical simulations of DOF distribution on axis directions indicate that the values of DOF can be extended by a factor of 1.5 or more by a modified quasi-FZP. In experiments, we employ a simple object-lens-image-plane arrangement to pick up images at various positions within the DOF of a conventional FZP and a quasi-FZP, respectively. Experimental results show that the parameter w improves foci distribution of FZPs in good agreement with theoretical predictions.

Synthesis of fractal light pulses by quasi-direct space-to-time pulse shaping

We demonstrated a simple diffractive method to map the self-similar structure shown in squared radial coordinate of any set of circularly symmetric fractal plates into self-similar light pulses in the corresponding temporal domain. The space-to-time mapping of the plates was carried out by means of a kinoform diffractive lens under femtosecond illumination. The spatio-temporal characteristics of the fractal pulses obtained in this way were measured by means of a spectral interferometry technique assisted by a fiber optics coupler (STARFISH). Our proposal allows synthesizing suited sequences of focused fractal femtosecond pulses potentially useful for several current applications, such as femtosecond material processing, atomic, and molecular control of chemical processes or generation of nonlinear effects.

A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography

In optical coherence tomography (OCT) systems, there is a trade-off between the depth of focus (DOF) and lateral resolution when conventional lenses are used. We propose a new method that employs a modified fractal generalized zone plate (MFraGZP) combined with a conventional lens to improve the trade-off effect, with an extended DOF of about 2.5 mm (14 times larger) while the lateral resolution is maintained at ~9.5 μm. As an example, images of the calibration microspheres are obtained and demonstrated with the extended DOF in a spectral domain OCT system.

Self-similar focusing with generalized devil's lenses

We introduce the generalized devil's lenses (GDLs) as a new family of diffractive kinoform lenses whose structure is based on the generalized Cantor set. The focusing properties of different members of this family are analyzed. It is shown that under plane wave illumination the GDLs give a single main focus surrounded by many subsidiary foci. It is shown that the total number of subsidiary foci is higher than the number of foci corresponding to conventional devil's lenses; however, the self-similar behavior of the axial irradiance is preserved to some extent.

Multifractal zone plates

We present multifractal zone plates (MFZPs) as what is to our knowledge a new family of diffractive lenses whose structure is based on the combination of fractal zone plates (FZPs) of different orders. The typical result is a composite of two FZPs with the central one having a first-order focal length f surrounded by outer zones with a third-order focal length f. The focusing properties of different members of this family are examined and compared with conventional composite Fresnel zone plates. It is shown that MFZPs improve the axial resolution and also give better performance under polychromatic illumination.