Diffraction by m-bonacci gratings

We present a simple diffraction experiment with m-bonacci gratings as a new interesting generalization of the Fibonacci ones. Diffraction by these nonconventional structures is proposed as a motivational strategy to introduce students to basic research activities. The Fraunhofer diffraction patterns are obtained with the standard equipment present in most undergraduate physics labs and are compared with those obtained with regular periodic gratings. We show that m-bonacci gratings produce discrete Fraunhofer patterns characterized by a set of diffraction peaks which positions are related to the concept of a generalized golden mean. A very good agreement is obtained between experimental and …

A computer-assisted experiment to study the influence of the point spread function in the image formation process

[EN] We present a new open experimental setup assisted with LabView to be used to teach the concept of the point spread function (PSF). The PSF describes the response of an image-forming system to a point object. The PSF concept is of fundamental importance in optics since the output of an image-forming system can be simulated as the convolution of the PSF with the input object. In this work, a new graphical user interface has been developed to obtain a real-time measure of the PSF and the corresponding images provided by different lenses and pupils with different sizes and shapes. From a didactical point of view, the proposed method allows students to interpret the results in a visual and …

Influence of different types of astigmatism on visual acuity

[EN] Purpose To investigate the change in visual acuity (VA) produced by different types of astigmatism (on the basis of the refractive power and position of the principal meridians) on normal accommodating eyes. Methods The lens induced method was employed to simulate a set of 28 astigmatic blur conditions on different healthy emmetropic eyes. Additionally, 24 values of spherical defocus were also simulated on the same eyes for comparison. VA was measured in each case and the results, expressed in logMAR units, were represented against of the modulus of the dioptric power vector (blur strength). Results LogMAR VA varies in a linear fashion with increasing astigmatic blur, being the slope o…

Generation of programmable 3D optical vortex structures through devil’s vortex-lens arrays

Different spatial distributions of optical vortices have been generated and characterized by implementing arrays of devil's vortex lenses in a reconfigurable spatial light modulator. A simple design procedure assigns the preferred position and topological charge value to each vortex in the structure, tuning the desired angular momentum. Distributions with charges and momenta of the opposite sign have been experimentally demonstrated. The angular velocity exhibited by the phase distribution around the focal plane has been visualized, showing an excellent agreement with the simulations. The practical limits of the method, with interest for applications involving particle transfer and manipula…

Self-similar focusing with generalized devil's lenses

[EN] 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. (C) 2011 Optical Society of America

Imaging quality of multifocal intraocular lenses: automated assessment setup

[EN] Purpose: A new technique for the assessment of the optical quality of multifocal intraocular lenses (MIOLs) under monochromatic and polychromatic illumination is presented. Methods: The system provides, in a totally automated procedure, the modulation transfer function (MTF) of the lens under test for different axial positions of the object. The artificial eye admits different artificial corneas, to optimise the axial resolution in the sampling of the MTF of the MIOL under test, and different pupils, to test the dependence of the optical performance of the MIOL on the eye pupil diameter. Results: The performance and sensitivity of the apparatus is tested with different commercial MIOLs…

Cantor-like fractal photonic crystal waveguides

Abstract We propose a new class of one-dimensional (1D) photonic waveguides: the fractal photonic crystal waveguides (FPCWs). These structures are photonic crystal waveguides (PCWs) etched with fratal distribution of grooves such as Cantor bars. The transmission properties of the FPCWs are investigated and compared with those of the conventional 1D PCWs. It is shown that the FPCW transmission spectrum has self-similarity properties associated with the fractal distribution of grooves. Furthermore, FPCWs exhibit sharp localized transmissions peaks that are approximately equidistant inside the photonic band gap.

The effect of fractal contact lenses on peripheral refraction in myopic model eyes.

Purpose: To test multizone contact lenses in model eyes: Fractal Contact Lenses (FCLs), designed to induce myopic peripheral refractive error (PRE). Methods: Zemax ray-tracing software was employed to simulate myopic and accommodation-dependent model eyes fitted with FCLs. PRE, defined in terms of mean sphere M and 90–180 astigmatism J180, was computed at different peripheral positions, ranging from 0 to 35 in steps of 5, and for different pupil diameters (PDs). Simulated visual performance and changes in the PRE were also analyzed for contact lens decentration and model eye accommodation. For comparison purposes, the same simulations were performed with another commercially available conta…

Optical performance of a new design of trifocal intraocular lens based on the Devil's diffractive lens

In this work, we propose a new diffractive trifocal intraocular lens design with focus extension, conceived to provide a high visual performance at intermediate distances. This design is based on a fractal structure known as the "Devil's staircase". To assess its optical performance, numerical simulations have been performed with a ray tracing program using the Liou-Brennan model eye under polychromatic illumination. The simulated through the focus visual acuity was the merit function employed to test its pupil-dependence and its behavior against decentering. A qualitative assessment of the multifocal intraocular lens (MIOL) was also performed experimentally with an adaptive optics visual s…

Axial behaviour of Cantor ring diffractals

Cantor ring diffractals describe rotationally symmetric pupils constructed from a one-dimensional polyadic Cantor set. The influence on the axial irradiance of several fractal descriptors of such pupils, including fractal dimension, number of gaps and lacunarity, are investigated. It is shown that, contrary to their transversal response, the axial behaviour of these pupils does not resemble the fractal structure of the aperture. The sensitivity of such pupils to the spherical aberration is also analysed.

Opto-digital tomographic reconstruction of the Wigner distribution function of complex fields.

An optical-digital method has been developed to obtain the Wigner distribution function of one-dimensional complex fields. In this technique an optical setup is employed to experimentally achieve the Radon-Wigner spectrum of the original signal through intensity measurements. Digital tomographic reconstruction is applied to the experimental spectrum to reconstruct the two-dimensional Wigner distribution function of the input. The validity of our proposal is demonstrated with experimental data, and the results are compared with computer simulations.

Analysis of the irradiance along different paths in the image space using the Wigner distribution function

Abstract The intensity distribution along different paths in the image space of an optical system is described in a two-dimensional phase-space domain in terms of the Wigner distribution function. This approach is useful for an efficient analysis of the performance of optical imaging systems suffering from spherical aberration. The good performance of the method is shown in some numerical simulations.

Encriptación óptica empleando llaves Weierstrass-Mandelbrot

[EN] This paper presents the generation of encryption keys using the local oscillating properties of the partial sums of Weierstrass-Mandelbrot fractal function. In this way, the security key can be replicated if the parameters used to obtain it are known. Therefore, these parameters can be sent instead of sending the key. This procedure reduces the amount of information to be sent and prevents possible interception of the key. Moreover, the key can not be affected by data loss or pollution. The effectiveness of the Weierstrass-Mandelbrot keys were demonstrated by computer simulation in a 4f optical encryption system and the double random phase encoding technique. These keys allow us to enc…

Devil’s vortex-lenses

In this paper we present a new kind of vortex lenses in which the radial phase distribution is characterized by the "devil's staircase" function. The focusing properties of these fractal DOEs coined Devil's vortex-lenses are analytically studied and the influence of the topological charge is investigated. It is shown that under monochromatic illumination a vortex devil's lens give rise a focal volume containing a delimited chain of vortices that are axially distributed according to the self-similarity of the lens.

A virtual laboratory designed for teaching diffractive lenses

[EN] We present a virtual laboratory generated in Matlab GuiQc (Graphical User Interface) for its use in Optics courses as an informatic tool for teaching the focusing properties of a diffractive lens. This Gui allows the students to learn easily and rapidly about the influence on the focal volume of the lens construction parameters. As an example in this work we analyze fractal diffractive lenses because we found that fractal geometry is a highly motivating topic for students since it is related to a wide range of scientific and technological phenomena.

Analysis of the imaging method for assessment of the smile of laser diode bars.

We study imaging systems designed to assess the smile of laser diode bars (LDBs). The magnification matrix is derived from the required sampling period and the geometries of the LDBs and the charge-coupled device (CCD) array. These image-forming systems present in-plane pure translation invariance, but in the case of anamorphic ones, lack in-plane rotation invariance. It is shown that the smile parameters of the image of the LDB are linked with the smile parameters of the LDB by simple mathematical expressions. The spatial resolution of such optical systems is estimated at approximately 1 microm for a mean wavelength of lambda approximately 800 nm. Our results suggest that, with the current…

Devil's lenses.

In this paper we present a new kind of kinoform lenses in which the phase distribution is characterized by the “devil’s staircase” function. The focusing properties of these fractal DOEs coined devil’s lenses (DLs) are analytically studied and compared with conventional Fresnel kinoform lenses. It is shown that under monochromatic illumination a DL give rise a single fractal focus that axially replicates the self-similarity of the lens. Under broadband illumination the superposition of the different monochromatic foci produces an increase in the depth of focus and also a strong reduction in the chromaticity variation along the optical axis.

Twin axial vortices generated by Fibonacci lenses.

Optical vortex beams, generated by Diffractive Optical Elements (DOEs), are capable of creating optical traps and other multifunctional micromanipulators for very specific tasks in the microscopic scale. Using the Fibonacci sequence, we have discovered a new family of DOEs that inherently behave as bifocal vortex lenses, and where the ratio of the two focal distances approaches the golden mean. The disctintive optical properties of these Fibonacci vortex lenses are experimentally demonstrated. We believe that the versatility and potential scalability of these lenses may allow for new applications in micro and nanophotonics.

WAVEFRONT TESTER: Un nuevo laboratorio virtual para el estudio de los sensores frente de onda.

[EN] We present a new virtual laboratory developed with MatlabcGUI (Graphical User Interface) used toteach di erent aberration eff ects in the "Tecnologi a de Sensores Optoelectr onicos" at "Escuela T ecnicaSuperior de Ingenier a del Diseño" of the Universitat Polit ecnica de Val encia. The objective of this lab is to provide a computer tool to study the working principle of a Shack Hartman sensor and the parameters that determine the dynamic range of the same. Some examples made with di fferent aberrations (defocus,astigmatism, coma) and for diff erent sensor con gurations are presented.

Synthesis of filters for specified axial irradiance by use of phase–space tomography

A procedure for designing pupil filters for applications where specified axial responses are required is developed. The method is based on the mathematical relationship between the axial impulse response of a system and the Wigner distribution function (WDF) associated to its pupil function. The desired axial irradiance, which can also have a predefined behavior depending on spherical aberration, is used to obtain this WDF by tomographic reconstruction. The synthetic pupil is retrieved from this distribution.

Undergraduate experiment with fractal diffraction gratings

We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics laboratories and compared with those obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. Good agreement is obtained between experimental and numerical results. © 2011 IOP Publishing Ltd.

Stereopsis assessment at multiple distances with an iPad application

[EN] We present a new application for iPad for screening stereopsis at multiple distances that allows testing up to ten levels of stereoacuity at each distance. Our approach is based on a random dot stereogram viewable with anaglyph spectacles. Sixty-five subjects with no ocular diseases, wearing their habitual correction were measured at 3 m and 0.5 m. Results were compared with a standard stereoscopic test (TNO). We found not statistically significant differences between both tests, but our method achieved higher reproducibility. Applications in visual screening programs and to design and use of 3D displays, are suggested. (C) 2017 Elsevier B.V. All rights reserved.

Subjective Refraction Techniques in the Frame of the Three-Dimensional Dioptric Space

A novel heuristic approach to the well-known representation of the dioptric power in a three-dimensional space is presented. It is shown how this theoretical framework is ideal for discussing the principles of several subjective refraction methods. In particular, this formalism is used to justify the stenopaic slit refraction, the Barnes subjective refraction technique, and the Jackson cross-cylinder procedure. In view of this analysis, some modifications to the traditional procedures are proposed.

Difract: Un nuevo laboratorio virtual para la modelización matemática de las propiedades de difracción de redes fractales

[EN] This work presents a new virtual laboratory, Difract, developed with Easy Java Simulations, for using in Optics courses as a computer tool for the mathematical modelling of the diffraction properties of 1D and 2D fractal gratings. This virtual laboratory enables students to quickly and easily analyze the influence on the Fraunhofer diffraction pattern of the different construction parameters of the fractal grating. As an application example, the Cantor fractal set has been considered.

Imaging Performance of a Diffractive Corneal Inlay for Presbyopia in a Model Eye

[EN] In this work we evaluated the imaging properties of the Diffractive Corneal Inlay (DCI), a novel type of corneal implant working by diffraction that we proposed for the treatment of presbyopia. ZEMAX OpticStudio software was employed for the numerical assessment, with simulations performed in a human-based eye model. In the ray tracing analysis, we used the Modulation Transfer Function (MTF), the Area under the MTF (AMTF), and the Point Spread Function (PSF). The theoretical performance of the DCI under different situations was evaluated in comparison with a commercially available pinhole based corneal inlay. Finally, real images were obtained experimentally in vitro in a model eye wit…

<p>Effect of cylinder power and axis changes on vision in astigmatic participants: a comment [Letter]</p>

Influencia de los diferentes tipos de astigmatismo en la agudeza visual

[EN] Purpose To investigate the change in visual acuity (VA) produced by different types of astigmatism (on the basis of the refractive power and position of the principal meridians) on normal accommodating eyes. Methods The lens induced method was employed to simulate a set of 28 astigmatic blur conditions on different healthy emmetropic eyes. Additionally, 24 values of spherical defocus were also simulated on the same eyes for comparison. VA was measured in each case and the results, expressed in logMAR units, were represented against of the modulus of the dioptric power vector (blur strength). Results LogMAR VA varies in a linear fashion with increasing astigmatic blur, being the slope o…

Influencia del modelo de ojo teórico en la evaluación numérica de lentes intraoculares fractales

In this work we present the numerical evaluation of a new design of fractal intraocular lens studied through a ray-tracing program. To determine the monochromatic and polychromatic performance of these lenses in different theoretical model eyes the Modulation Transfer Function (MTF) and the area above the MTF (AMTF) have been used. These merit functions show the same behavior for different values of asphericity (Q), independently from the theoretical model eye, even though there are differences due to the Spherical Aberration (SA) considered in each model.

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.

Cantor Dust Zone Plates

In this paper we use the Cantor Dust to design zone plates based on a two-dimensional fractal for the first time. The pupil function that defines the coined Cantor Dust Zone Plates (CDZPs) can be written as a combination of rectangle functions. Thus CDZPs can be considered as photon sieves with rectangular holes. The axial irradiances produced by CDZPs of different fractal orders are obtained analitically and experimentally, analyzing the influence of the fractality. The transverse irradiance patterns generated by this kind of zone plates has been also investigated.

Lacunar fractal photon sieves

We present a new family of diffractive lenses whose structure is based on the combination of two concepts: photon sieve and fractal zone plates with variable lacunarity. The focusing properties of different members of this family are examined. It is shown that the sieves provide a smoothing effect on the higher order foci of a conventional lacunar fractal zone plate. However, the characteristic self-similar axial response of the fractal zone plates is always preserved.

White-light optical implementation of the fractional fourier transform with adjustable order control.

An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.

Aperiodic Diffract: Study of diffraction gratings

[EN] In this work we introduce a virtual laboratory, APERIODIC DIFFRACT, developed in Matlab GUI (Graphical User Interface) as an informatics tool for teaching the diffractive properties of aperiodic gratings. This GUI allows the student to generate aperiodic sequences by iterating and lets to study the spectra for different iterating orders.

Fractal zone plates with variable lacunarity.

Fractal zone plates (FZPs), i.e., zone plates with fractal structure, have been recently introduced in optics. These zone plates are distinguished by the fractal focusing structure they provide along the optical axis. In this paper we study the effects on this axial response of an important descriptor of fractals: the lacunarity. It is shown that this parameter drastically affects the profile of the irradiance response along the optical axis. In spite of this fact, the axial behavior always has the self-similarity characteristics of the FZP itself.

Performance analysis of optical imaging systems based on the fractional fourier transform

Some image quality parameters, such as the Strehl ratio and the optical transfer function, are analysed in the generalized phase-space, or x-p domain, of the fractional Fourier transform associated with a modified one-dimensional pupil function. Some experimental results together with computer simulations are performed which illustrate the tolerance to defocus of different apertures.

Visual acuity with computer simulated and lens-induced astigmatism

[EN] The relationship between spherical and astigmatic refractive errors and their associated visual acuity is investigated in this work by means of two different approaches. In the first one, different refractive errors were induced in normal subjects by trial lenses. In the second one, defocused images were simulated numerically by the optical transfer function of a model eye and then judged by the same subjects. The amount of defocus (measured in terms of the modulus of the dioptric power vector) necessary to reduce the visual acuity to 0.1 logMAR and to 0.4 logMAR was computed with each method and then compared. We found that the visual system is clearly more tolerant to lens-induced de…

Fractal zone plates.

Fractal zone plates (FZPs), i.e., zone plates with a fractal structure, are described. The focusing properties of this new type of zone plate are compared with those of conventional Fresnel zone plates. It is shown that the axial irradiance exhibited by the FZP has self-similarity properties that can be correlated to those of the diffracting aperture.

Diffractive corneal inlay for presbyopia

[EN] A conceptually new type of corneal inlays for a customized treatment of presbyopia is presented. The diffractive inlay consists on a small aperture disc having an array of micro-holes distributed inside the open zones of a Fresnel zone plate. In this way, the central hole of the disc lets pass the zero order diffraction and produces an extension of the depth of far focus of the eye, while the diffracted light through the holes in the periphery produce the near focus. Additionally, the micro-holes in the inlay surface fulfill the essential requirement of allowing the flow of nutrients through it to the cells of the corneal stroma. Theoretical and optical-bench experimental results for t…

Optical Evaluation of New Designs of Multifocal Diffractive Corneal Inlays

[EN] Purpose. To assess the imaging properties of two different designs of a new concept of corneal inlays whose working principle is based on diffraction. Methods. The quality of the retinal images provided by Diffractive Corneal Inlays (DCIs) was evaluated theoretically in comparison with Small Aperture Corneal Inlay (SACI). ZEMAX OpticStudio software was employed for the simulations in an eye model with different pupil diameters (3.0 mm and 4.5 mm). The employed merit functions in the analysis were the Modulation Transfer Function (MTF), the area under the MTF (MTFa), and the Point Spread Function (PSF). Comparison was made with the SACI at different defocus conditions. Results. The bifo…

White-light Fourier transformer with low chromatic aberration.

A simple Fourier transformation system working with broadband parallel illumination is presented. The proposed setup, consisting of two on-axis zone plates and an achromatic objective, allows us to obtain the achromatic Fourier transform representation of the input at a finite distance with a low chromatic aberration. The discussion of the system, using the Fresnel diffraction theory, leads to an analytical expression to evaluate the transversal and longitudinal chromatic aberrations. It is shown that the resulting chromatic aberrations for typical values of the involved parameters are less than 1% over the entire visible spectrum.

Relative Peripheral Myopia Induced by Fractal Contact Lenses

[EN] Purpose: To assess the peripheral refraction induced by Fractal Contact Lenses (FCLs) in myopic eyes by means of a two-dimensional Relative Peripheral Refractive Error (RPRE) map. Materials and Methods: This study involved 26 myopic subjects ranging from -0.50 D to -7.00 D. FCLs prototypes were custom-manufactured and characterized. Corneal topographies were taken in order to assess correlations between corneal asphericity and lens decentration. Two-dimensional RPREs were measured with an open-field autorefractor at 67 points, covering the central 60 x 30 degrees of the visual field. The bidimensional RPRE vector components: M, J(0) and J(45) of the difference between the values obtain…

Aperiodic Diffract: Study of diffraction gratings

In this work we introduce a virtual laboratory, APERIODIC DIFFRACT, developed in Matlab GUI (Graphical User Interface) as an informatics tool for teaching the diffractive properties of aperiodic gratings. This GUI allows the student to  generate aperiodic sequences by iterating and lets to study the spectra for different iterating orders.<br /><br />

The Radon-Wigner Transform and Its Application to First-order Optical Systems

The Radon-Wigner transform is presented as a tool for the description of 1st-order optical systems. The input/output relationships for this phase-space representation are obtained and their application in analysis and design tasks is pointed out.

Diffractive m-bonacci lenses.

[EN] Fibonacci zone plates are proving to be promising candidates in image forming devices. In this letter we show that the set of Fibonacci zone plates are a particular member of a new family of diffractive lenses which can be designed on the basis of a given m-bonacci sequence. These lenses produce twin axial foci whose separation depends on the m-golden mean. Therefore, with this generalization, bifocal systems can be freely designed under the requirement at particular focal planes. Experimental results support our proposal. (C) 2017 Optical Society of America

Polyadic devil's lenses.

Devil’s lenses (DLs) were recently proposed as a new kind of kinoform lens in which the phase structure is characterized by the “devil’s staircase” function. DLs are considered fractal lenses because they are constructed following the geometry of the triadic Cantor set and because they provide self-similar foci along the optical axis. Here, DLs are generalized allowing the inclusion of polyadic Cantor distributions in their design. The lacunarity of the selected polyadic fractal distribution is an additional design parameter. The results are coined polyadic DLs. Construction requirements and interrelations among the different parameters of these new fractal lenses are also presented. It is …

Influence of the theoretical model eye on the numerical evaluation of fractal intraocular lenses

In this work we present the numerical evaluation of a new design of fractal intraocular lens studied through a ray-tracing program. To determine the monochromatic and polychromatic performance of these lenses in different theoretical model eyes the Modulation Transfer Function (MTF) and the area above the MTF (AMTF) have been used. These merit functions show the same behavior for different values of asphericity (Q), independently from the theoretical model eye, even though there are differences due to the Spherical Aberration (SA) considered in each model.

Volumetric multiple optical traps produced by Devil's lenses

We propose the use of a new diffractive optical element coined Devil's Vortex-Lens (DVL) to produce optical tweezers. In its more general form it results as the combination of a Devil’s lens and a helical vortex phase mask. It is shown that under monochromatic illumination a DVL generates a focal volume with several concatenated doughnut modes that are axially distributed according to the self-similarity of the lens. The orbital angular momentum associated to each link in the chain is investigated.

Corneal and Refractive Astigmatism in Adults: A Power Vectors Analysis

Purpose. In this article, we examine the relationship between corneal and refractive astigmatism (including with the rule, against-the-rule, and oblique astigmatism) in an adult population using power vectors. Methods. Refractive and keratometric measures of astigmatism were conducted on right eyes of 105 white subjects aged 18 to 59 years. We performed a linear regression of refractive astigmatic error on corneal astigmatism, using the J0 and J45 components of the astigmatism. Results. We obtained a statistically significant regression relationship between the corneal (C) and refractive (R) astigmatism for both J0 and J45 components, namely, RJ0 = 1.07 × CJ0 − 0.28; and RJ45 = 1.46 × CJ45 …

A new trifocal corneal inlay for presbyopia

[EN] Corneal inlays (CIs) are the most recent surgical procedure for the treatment of presbyopia in patients who want complete independence from the use of glasses or contact lenses. Although refractive surgery in presbyopic patients is mostly performed in combination with cataract surgery, when the implantation of an intraocular lens is not necessary, the option of CIs has the advantage of being minimally invasive. Current designs of CIs are, either: small aperture devices, or refractive devices, however, both methods do not have good performance simultaneously at intermediate and near distances in eyes that are unable to accommodate. In the present study, we propose the first design of a …

Hybrid optical-digital method for local-displacement analysis by use of a phase-space representation.

A method for evaluating the local deformation or displacement of an object in speckle metrology is described. The local displacements of the object in one direction are digitally coded in a one-dimensional specklegram. By optically performing the local spectrum of this pattern, one simultaneously achieves information about the local displacement and its spatial position. The good performance of this technique is demonstrated with computer-generated test signals.

Variable fractional Fourier processor: a simple implementation

A new set of optical implementations of the fractional Fourier transform (FRT) is developed by use of Wigner matrix algebra. The reinterpretation of some elementary operations that synthesize a rotation in the phase-space domain allows us to propose a lensless setup for obtaining the FRT. This compact configuration is also very flexible, because the fractional degree of the transformation can be varied continuously by shifting the input and the output planes along the optical axis by proper amounts. The above results permit one to build an optical FRT processor formed by two FRT systems in cascade, with a spatial filter between them. We present the design of such a variable FRT processor, w…

Fractal photon sieve

A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are analyzed. The good performance of our proposal is demonstrated experimentally with a series of images obtained under white light illumination. It is shown that compared with a conventional photon sieve, the fractal photon sieve exhibits an extended depth of field and a reduced chromatic aberration.

Proposal of a new diffractive corneal inlay to improve near vision in a presbyopic eye

[EN] A new class of diffraction-based corneal inlays for treatment of presbyopia is described. The inlay is intended to achieve an improvement of the near focus quality over previous designs. Our proposal is a two-zone hybrid device with separated amplitude and phase areas having a central aperture and no refractive power. An array of micro-holes is distributed on the surface of the inlay conforming a binary photon sieve. In this way, the central hole of the disk contributes to the zero order of diffraction, and the light diffracted by the micro-holes in the peripheral photon sieve produces a real focus for near vision. We employed ray-tracing software to study the performance of the new in…

Fractal square zone plates

[EN] In this paper we present a novel family of zone plates with a fractal distribution of square zones. The focusing properties of these fractal diffractive lenses coined fractal square zone plates are analytically studied and the influence of the fractality is investigated. It is shown that under monochromatic illumination a fractal square zone plate gives rise a focal volume containing a delimited sequence of two-arms-cross pattern that are axially distributed according to the self-similarity of the lens.

Visual Acuity in Simple Myopic Astigmatism: Influence of Cylinder Axis

Purpose. The relationship between astigmatic refractive errors and their associated visual acuity has been studied in recent years in the context of refractive power space. The influence of the axis of astigmatism remains a matter of controversy. Our goal in this study is to provide additional experimental evidence to clarify this subject. The influence of the simulated axis orientation was compared with other factors that affect visual acuity such as the particular design of the test and the differences between eyes. Methods. Simple myopic astigmatism from 0 to 3.00 D, in steps of 0.25 D, and with five different axes between 0° and 90°, were simulated on four healthy eyes of young observer…

Diffraction by fractal metallic supergratings.

The reflectance of corrugated surfaces with a fractal distribution of grooves is investigated. Triadic and polyadic Cantor fractal distributions are considered, and the reflected intensity is compared with that of the corresponding periodic structure. The self-similarity property of the response is analyzed when varying the depth of the grooves and the lacunarity parameter. The results confirm that the response is self-similar for the whole range of depths considered, and this property is also maintained for all values of the lacunarity parameter. © 2007 Optical Society of America. Fil: Skigin, Diana Carina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación…

Diseño de una nueva prueba para medir la función de sensibilidad al contraste con iPad

[EN] Purpose: To introduce a new application (ClinicCSF) to measure Contrast Sensitivity Function (CSF) with tablet devices, and to compare it against the Functional Acuity Contrast Test (FACT). Methods: A total of 42 subjects were arranged in two groups of 21 individuals. Different versions of the ClinicCSF (.v1 and .v2) were used to measure the CSF of each group with the same iPad and the results were compared with those measured with the FACT. The agreements between ClinicCSF and FACT for spatial frequencies of 3, 6, 12 and 18 cycles per degree (cpd) were represented by Bland---Altman plots. Results: Statistically significant differences in CSF of both groups were found due to the change…

Diseño físico-matemático de un espectrómetro óptico

[EN] This work presents the design and construction of a spectrometer made in the laboratory and the development of mathematical models needed to process and analyze the acquired spectrum. For modeling functions it has been used LabVIEW program. The aim is to bring this type of instrumentation to engineering students from both, physical and mathematical point of view. The application has been successfully integrated in the learning strategies of the course Sensores Fisicos, Master Universitario en Sensores Para Aplicaciones Industriales at the Universitat Politecnica de Valencia. As an example, we have characterized different light sources emitting in different regions of the electromagneti…

3D printed diffractive terahertz lenses

[EN] A 3D printer was used to realize custom-made diffractive THz lenses. After testing several materials, phase binary lenses with periodic and aperiodic radial profiles were designed and constructed in polyamide material to work at 0.625 THz. The nonconventional focusing properties of such lenses were assessed by computing and measuring their axial point spread function (PSF). Our results demonstrate that inexpensive 3D printed THz diffractive lenses can be reliably used in focusing and imaging THz systems. Diffractive THz lenses with unprecedented features, such as extended depth of focus or bifocalization, have been demonstrated.

Optical-data storage-readout technique based on fractal encrypting masks

We propose the use of fractal structured diffractive masks as keys in secure storage-readout systems. A joint transform correlator based on a photorefractive crystal in the Fourier domain is implemented to perform encryption and decryption. We discuss the advantages of encrypting information using this kind of deterministic keys in comparison to conventional random phase masks. Preliminary experimental results are presented to demonstrate the effectiveness of the proposed system.

Parallel fractional correlation: an optical implementation

An optical setup to obtain all the fractional correlations of a one-dimensional input in a single display is implemented. The system works as a multichannel parallel correlator for a continuous set of fractional orders and presents a variable shift variance. Some experimental results together with computer simulations are performed to illustrate the performance of our proposal.

All-diffractive achromatic Fourier-transform setup

An achromatic Fourier transformation under broadband converging spherical-wave illumination is optically achieved by use of only two on-axis blazed zone plates. The novel optical configuration provides the achromatic Fraunhofer diffraction pattern of an arbitrary input signal with adjustable magnification. Further analysis of the system permits us to obtain a simple analytical expression to evaluate both the longitudinal and the transversal residual chromatic aberration, resulting in a compact achromatic Fourier transformer with low chromatic errors, even for a wide spectral content of the point source.

Radon–Wigner display: a compact optical implementation with a single varifocal lens

A new optical implementation of the Radon‐Wigner display for one-dimensional objects is presented, making use of the fractional Fourier transform approach. The proposed setup makes use of only two conventional refractive elements: a cylindrical lens and a varifocal lens. Although the exact magnifications cannot be achieved simultaneously for all the fractional transforms, an optimum design can be obtained through balancing the conflicting magnification requirements. Experimental results are obtained with a commercially available progressive addition lens. For comparison, computer simulations are also provided. © 1997 Optical Society of America

Optical propagation of fractal fields. Experimental analysis in a single display

An experimental device to show in a single display all the diffraction patterns generated by a 1D fractal structure is proposed. It is found that in addition to being the optimum display to see the evolution of the diffracted field through free space, some interesting features, such as continuous evaluation of self-similarity from the object to the far field, can be obtained experimentally.

Wavefront sensing using a graphical user interface

Contract grant sponsor: Ministerio de Economia y Competividad; Contract grant number: FIS2011-23175; Contract grant sponsor: Generalitat Valenciana; Contract grant number: PROMETEOII/2014/072; Contract grant sponsor: Universitat de Valencia; Contract grant number: UV-SFPIE_DINV14-222801

Design, characterization and visual performance of a new multizone contact lens

Objectives: To analyze the whole process involved in the production of a new bifocal Multizone Contact Lens (MCL) for presbyopia. Methods: The optical quality of a new MCL was evaluated by ray tracing software in a model eye with pupil different diameters with the lens centered and decentered. A stock of low addition (+1.5 D) MCL for presbyopia was ordered for manufacturing. Power profiles were measured with a contact lens power mapper, processed with a custom software and compared with the theoretical design. Nine lenses from the stock were fitted to presbyopic subjects and the visual performance was evaluated with new APPs for iPad Retina. Results: Numerical simulations showed that the tr…

Bifractal focusing and imaging properties of Thue-Morse Zone Plates.

We present a new family of Zone Plates (ZPs) designed using the Thue-Morse sequence. The focusing and imaging properties of these aperiodic diffractive lenses coined Thue-Morse Zone Plates (TMZPs) are examined. It is demonstrated that TMZPs produce a pair of self-similar and equally intense foci along the optical axis. As a consequence of this property, under broadband illumination, a TMZP produces two foci with an extended depth of focus and a strong reduction of the chromatic aberration compared with conventional periodic ZPs. This distinctive optical characteristic is experimentally confirmed.

Statistical analysis when dealing with astigmatism: assessment of different spherocylindrical notations.

Ophthalmic epidemiological studies frequently deal with ocular refractive errors, which are commonly expressed in the form sphere/cylinder x axis. However, this representation has been shown not to be the most suitable one for performing statistical analysis. Although alternative analytical and graphic methods to represent this kind of data have been developed, these formalisms have often gone unnoticed by researchers, despite their usefulness and versatility. Besides, there has been no discussion of how each of them fits in with a particular type of study. In this paper, several mathematical representations of dioptric power are revisited in a comprehensive way. The aim is to encourage res…

Multiple-plane image formation by Walsh zone plates.

[EN] A radial Walsh filter is a phase binary diffractive optical element characterized by a set of concentric rings that take the phase values 0 or ¿, corresponding to the values + 1 or ¿1 of a given radial Walsh function. Therefore, a Walsh filter can be re-interpreted as an aperiodic multifocal zone plate, capable to produce images of multiple planes simultaneously in a single output plane of an image forming system. In this paper, we experimentally demonstrate for the first time the focusing capabilities of these structures. Additionally, we report the first achievement of images of multiple-plane objects in a single image plane with these aperiodic diffractive lenses.

Fractal zone plates for wideband imaging with low chromatic aberration and extended depth of field

Fresnel zone plates are diffractive elements that are essential to form images in many scientific and technological areas, especially where refractive optics is not available. One of the main shortcomings of Fresnel zone plates, which limit their utility with broadband sources, is their high chromatic aberration. Recently presented, Fractal Zone Plates (FZPs) are diffractive lenses characterized by an extended focal depth with a fractal structure. This behaviour predicts an improved performance of FZPs as image forming devices with an extended depth of field and a reduced chromatic aberration. Here we report the achievement of the first polychromatic images obtained with a FZP that confirm …

Comparison of two different devices to assess intraocular lenses

[EN] In this paper, we have compared the performance of two commercial systems, Kaleo-I and IOLA Plus, in the characterization of monofocal intraocular lenses (IOLs) according to the International Standard requirements (ISO 11979-2). The dioptric power (DP) and the Modulation Transfer Function (MTF) at 100.1p/mm and 3.0 mm aperture have been measured with both instruments in twenty commercial monofocal HEMA IOLs and their agreement was assessed by Bland Altman analysis. Compared with the designed power, IOLA Plus gave lower values in 85% of measures: Kaleo I errors are dependent on the power of the lens: measurements were higher than the designed power in the low-medium power range and lowe…

Variable fractional Fourier processor: a simple implementation: erratum

Multiplexing THz Vortex Beams With a Single Diffractive 3-D Printed Lens

[EN] We present a novel method for experimentally generating multiplexed THz vortex beams by using a single three-dimensional printed element that combines a set of radially distributed spiral phase plates, and a binary focusing Fresnel lens. With this element, we have experimentally demonstrated that THz multiplexing can be tailored to fit within a small space on an optical bench. Results are presented beside numerical simulations, demonstrating the robust nature of the experimental method.

Detection of wave aberrations in the human eye using a retinoscopy-like technique

The influence of optical aberrations on the retinoscopic reflex is theoretically analyzed from a geometrical point of view. The relationship between the wave aberrations to the ray aberrations is applied to explain the appearance of the retinoscopic patterns for different types of ocular aberrations. Several schematic models of the human eye are tested numerically, showing that a careful retinoscopic examination can detect the usual eye aberrations.

Perfiles de potencia de las lentes de contacto medidas con NIMO TR1504

This study was supported by the Ministerio de Economía y Competitividad and FEDER (Grant DPI2015-71256-R) and by the Generalitat Valenciana (Grant PROMETEOII-2014-072), Spain.

Through-focus response of multifocal intraocular lenses evaluated with a spatial light modulator

A new testing technique based on the use of a liquid crystal spatial light modulator (SLM) is proposed to analyze the optical quality of multifocal intraocular lenses (MIOLs). Different vergences and decentrations of the incident beam can be programmed onto the SLM in order to record the point spread function (PSF) for different object positions. From these axial PSFs, the through-focus modulation transfer function is computed. Because there are no moving parts in the experimental setup, this method is fast and versatile to assess MIOLs. Experimental results confirm the potential of the proposed method.

Ophthalmic: Laboratorio virtual para el diseño de nuevas lentes oftálmicas

This work presents a new virtual laboratory, OPHTALMIC, developed with MATLAB GUI for using in Optics and Optometry courses as a computer tool for studying the focusing properties of multifocal diffractive both on unconventional structures both periodic and aperiodic. This virtual laboratory enables students to quickly and easily analyze the influence of the different parameters of construction and find the best solution for a user.

The stenopaeic slit: an analytical expression to quantify its optical effects in front of an astigmatic eye.

The stenopaeic slit is a trial case accessory used in subjective refraction, especially when high astigmatism is present. In spite of its simplicity, the effect of the slit when it is not oriented along one of the principal meridians of the examined eye is difficult to predict, even in terms of classical geometrical optics. In this paper, the optical principles of the slit are considered with full details in the theoretical framework of the dioptric power space. An analytical expression to obtain the residual refractive error when a stenopaeic slit is placed in front of an astigmatic eye at any orientation is deduced. In the light of these results, some aspects of the clinical procedure are…

Fractal-structured multifocal intraocular lens

[EN] In this work, we present a new concept of IOL design inspired by the demonstrated properties of reduced chromatic aberration and extended depth of focus of Fractal zone plates. A detailed description of a proof of concept IOL is provided. The result was numerically characterized, and fabricated by lathe turning. The prototype was tested in vitro using dedicated optical system and software. The theoretical Point Spread Function along the optical axis, computed for several wavelengths, showed that for each wavelength, the IOL produces two main foci surrounded by numerous secondary foci that partially overlap each other for different wavelengths. The result is that both, the near focus an…

White-light imaging with fractal zone plates

We report the achievement of the first images to our knowledge obtained with a fractal zone plates (FraZPs). FraZPs are diffractive lenses characterized by the fractal structure of their foci. This property predicts an improved performance of FraZPs as image forming devices with an extended depth of field and predicts a reduced chromatic aberration under white-light illumination. These theoretical predictions are confirmed experimentally in this work. We show that the polychromatic modulation transfer function of a FraZP affected by defocus is about two times better than one corresponding to a Fresnel zone plate.

Visual acuity and contrast sensitivity screening with a new iPad application

We present a new iPad application (app) for a fast assessment of Visual Acuity (VA) and Contrast Sensitivity (CS) whose reliability and agreement was evaluated versus a commercial screening device (Optec 6500). The measurement of VA was programmed in the app in accordance with the Amblyopia Treatment Study protocol. The CS was measured with sinusoidal gratings of four different spatial frequencies: 3, 6, 12 and 18 cpd at the same contrast values of the Functional Acuity Contrast Test (FACT) included in the Optec 6500. Forty-five healthy subjects with monocular corrected visual acuities better than 0.2 logMAR participated in the agreement study. Bland-Altman analyses were performed to assess…

Multiplexed vortex beam-based optical tweezers

The design and implementation of a multiplexed spiral phase mask in an experimental optical tweezer setup are presented. This diffractive optical element allows the generation of multiple concentric vortex beams with independent topological charges. The generalization of the phase mask for multiple concentric vortices is also shown. The design for a phase mask of two multiplexed vortices with different topological charges is developed. We experimentally show the transfer of angular momentum to the optically trapped microparticles by enabling orbiting dynamics around the optical axis independently within each vortex. The angular velocity of the confined particles versus the optical power in …