In this work we introduce a new category of diffractive lenses called multifocal binary Gabor zone plates (MGZP). These lenses are designed by integrating in a single plate multiple binary Gabor zone plates with distinct harmonic terms. We demonstrate how this binding allows the creation of a desired multifocal distribution that can be customized in the lens design to generate multiple focal points with adjustable focal distances of variable intensity. Numerical examples are presented of a bifocal and to a trifocal lenses with equi-energetic foci.
We present the multiple trapping of microspheres using structured diffractive lenses in a setup of optical tweezers. Diffractive lenses are experiencing a wide development due to their successful implementation in areas such as ophthalmology or biophysics. The implementation of multifocal diffractive lenses in an experimental arrangement of optical tweezers affords the generation of multiple traps in a stable and controlled manner. We carried out the multiple trapping of polystyrene microspheres of radius ∼ 2 − 2.4 μm immersed in distilled water. An infrared laser and a multifocal diffractive lens enabled a set of axial foci. The structured lens is generated in a spatial light modulator (SLM) calibrated for a 2π phase shift at λ = 1064 nm and the tailored beam is focused by a high numerical aperture objective. Each focal point generated by the lens acts as a separate optical trap, whereby the confinement of an individual microsphere is possible. The versatility provided by structured diffractive lenses allows increasing the number of optical traps by modifying the lens profile. In addition, such strategy increases the flexibility in the experimental arrangement of optical tweezers.
In this work, we report the achievement of images obtained with radial Walsh filters. Derived from Walsh functions, radial Walsh filters are phase binary diffractive optical elements characterized by a set of equal-area concentric rings that take the phase values 0 or π, corresponding to +1 or -1 transmittance values of the corresponding Walsh function. Then, a radial Walsh filter can be re-interpreted as an aperiodic zone plate with self-similar multi-focusing properties under monochromatic illumination and, therefore, multi-imaging capabilities. We have implemented these unconventional lenses with a spatial light modulator and the first images obtained with this type of lenses are presented and evaluated.
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.
Optical vortices are employed in optical trapping applications for their ability to set microparticles into rotation. Devil’s Vortex Lenses have high diffraction efficiency and it is possible to take advantage of their particular volumetric focal structure to design versatile and efficient optical tweezers. In this communication, we report a simple design procedure, involving arrays of Devil’s Vortex-Lenses implemented in a programmable Spatial Light Modulator, for generating spatial distributions of optical vortices. In our approach, the preferred position and topological charge value can be assigned to each vortex in the structure, tuning the desired angular momentum. We have demonstrated the generation of 3D optical vortex distributions through arrays of Devil’s Vortex-Lenses, including configurations with charges and momenta of opposite sign. Our experimental results present an excellent agreement with the simulations we have developed.
Fresnel zone plates are conventional focusing and imaging elements used for X-ray and extreme ultraviolet radiation. The distribution of the transmissive and opaque circular rings in a Fresnel zone plate is periodic along the squared radial coordinate. In this communication we present a novel family of zone plates in which this periodicity is broken. These aperiodic zone plates present interesting focusing properties. We found two different kinds of designs. One of them produces a bifocal device with predictable separation between the foci. The other one produces a focal distribution along the optical axis with a fractal structure which is governed by the lacunarity of the zone plate. Different parameters allow a flexible design of both kinds of zone plates.
Cantor ring diffractals describe rotationally symmetric pupils based on a polyadic Cantor set. The influence on the axial irradiance of several fractal descriptors including fractal dimension, number of gaps and stage of growth of such pupils are investigated. The analysis is performed through a new method for the computation of axial PSF's that uses a Wigner distribution function obtained from the pupil.
A new method for the computation of the tristimuli values that correspond to the impulse response along the optical axis provided by an imaging optical system working under polychromatic illumination is evaluated. A comparison between this method and the classical one of Hopkins and Yzuel shows that for systems with pupil functions of general profile it needs less computation time to obtain the same degree of accuracy.
It is presented a quite simple procedure for measuring the astigmatism aberration of lenses by using an optometric and ophthalmic instrument, the retinoscope, as a focimeter.
The optical implementation of the Radon-Wigner display for 1D objects is used in two different applications. First, it is used in the study of some properties of the wave field diffracted by unidimensional fractal gratings in the Fresnel region. Second, this optical representation is profited to perform a parallel space-variant optical correlation. Computer simulations and experimental results are presented.
We obtain that the irradiance impulse response along certain axes of an optical imaging system, that suffers from primary spherical aberration and longitudinal chromatic aberration, can be calculated from 1D integrations in a single 2D phase- space representation, the Wigner distribution function associated with a certain azimuthally-averaged version of the pupil of the system. This result is applied to study the response along the optical axis of unstable laser resonators and optical systems working under polychromatic illumination.
A method for the calculation of the axial illuminance and chromaticity as polychromatic merit functions of optical imaging systems is presented. We show that the Wigner distribution function of the pupil of the system allows us to obtain all the monochromatic components needed for the calculation of these parameters. From this single phase-space representation, the merit functions can be obtained in a polar fashion for a variable spherical and longitudinal chromatic aberrations. Numerical examples for an axially apodizing filter are shown.
We explore the features of a family of nonlinear filters called the fractional order mean. The median, the mode, and other statistical characteristics belong to this family as particular integer orders. The behavior of these filters in noise suppression in images is investigated. An improved version of these filters, which we call the 8-pixel window mean filter is also explored. In this case, the filtered value of the pixel is compared with its experimental value in the presence of a preset threshold. Noise suppression performance is tested with the usual mean square error (MSE) criterion, with a correlation criterion, and with a new criterion, the mean relative error (MRE). Evidence is found that the MRE correlates better than the MSE with the perceived visual quality of the processed image.
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