Abstract
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.
Highlights
Acoustic focusing is widely employed to explore objects or biological tissues where optical techniques are not optimum due to scattering and absorption phenomena
The different Fresnel regions can be implemented by alternating either pressure blocking with transparent regions, which is known as a Soret zone plate (SZP), or by alternating phase-reversal with transparent regions, which results in a Phase-Reversal zone plate (PRZP)
We propose a simple design technique based on the fast Fourier transform (FFT) capable of providing zone plates (ZPs) with two equal-intensity foci located at arbitrary distances
Summary
Acoustic focusing is widely employed to explore objects or biological tissues where optical techniques are not optimum due to scattering and absorption phenomena. Fresnel Zone Plates (FZPs) are planar monofocal lenses that can achieve good focusing performance while keeping an easy design and manufacturing process This type of lenses has been widely employed in the past in various fields, including microwaves [12], optics [13,14], and acoustics [15,16,17]. Using a M-bonacci binary mask results in a bifocal profile with two equal-intensity foci [19,20,21], while using fractal Cantor sequences provides a focusing profile with interesting self-similarity multifocal properties [22,23,24,25]. Other alternative methods for providing bifocal profiles based on combining preexisting Fresnel ZPs have been proposed in [28], but they require a complex design process with an accurate control of the phase interference pattern. Not shown in the paper, the results can be extended to other domains such as optics and microwaves, because the relation between the binary sequence and the ZP focusing profile is the same with independence of the domain
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