Numerical Investigation on High-Performance Cu-Based Surface Plasmon Resonance Sensor for Biosensing Application

This numerical research presents a simple hybrid structure comprised of TiO2-Cu-BaTiO3 for a modified Kretschmann configuration that exhibits high sensitivity and high resolution for biosensing applications through an angular interrogation method. Recently, copper (Cu) emerged as an exceptional choice as a plasmonic metal for developing surface plasmon sensors (SPR) with high resolution as it yields finer, thinner SPR curves than Ag and Au. As copper is prone to oxidation, especially in ambient conditions, the proposed structure involves the utilization of barium titanate (BaTiO3) film as a protection layer that not only preserves Cu film from oxidizing but enhances the performance of the sensor to a great extent. Numerical results also show that the utilization of a thin adhesive layer of titanium dioxide (TiO2) between the prism base and Cu film not only induces strong interaction between them but also enhances the performance of the sensor. Such a configuration, upon suitable optimization of the thickness of each layer, is found to enhance sensitivity as high as 552°/RIU with a figure of merit (FOM) of 136.97 RIU-1. This suggested biosensor design with enhanced sensitivity is expected to enable long-term detection with greater accuracy and sensitivity even when using Cu as a plasmonic metal.

Model of the light sword intraocular lens: in-vitro comparative studies

This work presents the first models of light sword intraocular lenses (LS IOLs) with angularly modulated optical power. We performed an experimental, comparative study with multifocal and extended depth of focus intraocular lenses, which are available on the market. The measurements conducted in an original optical bench were utilised for an analysis of point spread functions, elongated foci, modulation transfer functions and the areas defined by them. The LS IOL models perform homogeneous imaging in the whole range of designed defocus. The proposed concept of extended depth of focus seems to be promising for the development of presbyopia-correcting intraocular lenses capable of regaining fully functional vision.

The Light Sword Lens - A novel method of presbyopia compensation: Pilot clinical study

Purpose

Clinical assessment of a new optical element for presbyopia correction–the Light Sword Lens.

Methods

Healthy dominant eyes of 34 presbyopes were examined for visual performance in 3 trials: reference (with lens for distance correction); stenopeic (distance correction with a pinhole ϕ = 1.25 mm) and Light Sword Lens (distance correction with a Light Sword Lens). In each trial, visual acuity was assessed in 7 tasks for defocus from 0.2D to 3.0D while contrast sensitivity in 2 tasks for defocus 0.3D and 2.5D. The Early Treatment Diabetic Retinopathy Study protocol and Pelli-Robson method were applied. Within visual acuity and contrast sensitivity results degree of homogeneity through defocus was determined. Reference and stenopeic trials were compared to Light Sword Lens results. Friedman analysis of variance, Nemenyi post-hoc, Wilcoxon tests were used, p-value < 0.05 was considered significant.

Results

In Light Sword Lens trial visual acuity was stable in tested defocus range [20/25–20/32], Stenopeic trial exhibited a limited range of degradation [20/25–20/40]. Light Sword Lens and reference trials contrast sensitivity was high [1.9–2.0 logCS] for both defocus cases, but low in stenopeic condition [1.5–1.7 logCS]. Between-trials comparisons of visual acuity results showed significant differences only for Light Sword Lens versus reference trials and in contrast sensitivity only for Light Sword Lens versus stenopeic trials.

Conclusions

Visual acuity achieved with Light Sword Lens correction in presbyopic eye is comparable to stenopeic but exhibits none significant loss in contrast sensitivity. Such correction method seems to be very promising for novel contact lenses and intraocular lenses design.

Assessment of imaging with extended depth-of-field by means of the light sword lens in terms of visual acuity scale

We present outcomes of an imaging experiment using the refractive light sword lens (LSL) as a contact lens in an optical system that serves as a simplified model of the presbyopic eye. The results show that the LSL produces significant improvements in visual acuity of the simplified presbyopic eye model over a wide range of defocus. Therefore, this element can be an interesting alternative for the multifocal contact and intraocular lenses currently used in ophthalmology. The second part of the article discusses possible modifications of the LSL profile in order to render it more suitable for fabrication and ophthalmological applications.

Generation of a strong uniform transversely polarized nondiffracting beam using a high-numerical-aperture lens axicon with a binary phase mask

We present a theoretical approach to generate a nondiffracting beam with extended depth of focus (DOF) and a smaller focal spot along the optical axis, by tight focusing of an azimuthally polarized beam with a circular symmetrical binary phase mask and an interference effect over a high-numerical-aperture (NA) lens axicon system. We find a general azimuthal diffraction integral for the circularly symmetric binary phase mask and examine it in two special cases: a high-NA lens and a high-NA lens axicon. The azimuthally polarized beam remains well behaved in both cases. We verify that the longitudinal component generated by azimuthally polarized illumination produces the narrowest spot size for a wide range of geometries. Finally, we discuss the effects of tight focusing on a dielectric interface and provide some ideas for circumventing the effects of the binary phase mask interface and even utilize them for spot size reduction.

Diffuserless holographic projection working on twin spatial light modulators

An improved efficient projection of holographic images is presented. It uses two phase spatial light modulators (SLMs) with two iteratively optimized Fresnel holograms displayed simultaneously--each for one modulator. The phase distribution on the second modulator is taking into account the light distribution coming from the first one. A pixelated structure of the modulator and fluctuations of liquid-crystal molecules cause a zero-order peak that was separated in experiment. Use of two SLMs gives clear and containing almost no speckles images. Thanks to the compensation of phase distribution from the first modulator, we can abandon diffusers in the iterative process and that is why we can control both amplitude and phase distribution in the image plane independently.

Double peacock eye optical element for extended focal depth imaging with ophthalmic applications

The aged human eye is commonly affected by presbyopia, and therefore, it gradually loses its capability to form images of objects placed at different distances. Extended depth of focus (EDOF) imaging elements can overcome this inability, despite the introduction of a certain amount of aberration. This paper evaluates the EDOF imaging performance of the so-called peacock eye phase diffractive element, which focuses an incident plane wave into a segment of the optical axis and explores the element's potential use for ophthalmic presbyopia compensation optics. Two designs of the element are analyzed: the single peacock eye, which produces one focal segment along the axis, and the double peacock eye, which is a spatially multiplexed element that produces two focal segments with partial overlapping along the axis. The performances of the peacock eye elements are compared with those of multifocal lenses through numerical simulations as well as optical experiments in the image space. The results demonstrate that the peacock eye elements form sharper images along the focal segment than the multifocal lenses and, therefore, are more suitable for presbyopia compensation. The extreme points of the depth of field in the object space, which represent the remote and the near object points, have been experimentally obtained for both the single and the double peacock eye optical elements. The double peacock eye element has better imaging quality for relatively short and intermediate distances than the single peacock eye, whereas the latter seems better for far distance vision.

Generation of sub wavelength super-long dark channel using high NA lens axicon

We investigate the focusing properties of a double-ring-shaped azimuthally polarized beam by a high numerical aperture (NA) lens axicon based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal hole of 0.5λ having large uniform focal depth of 48λ without any annular aperture. We also observed that the distribution of the total intensity near the focus has little variation with the degree of truncation β of the incident beam by the pupil. The authors expect such a super-long dark channel may find applications in optical, biological, and atmospheric sciences.

Imaging properties of the light sword optical element used as a contact lens in a presbyopic eye model

The paper analyzes the imaging properties of the light sword optical element (LSOE) applied as a contact lens to the presbyopic human eye. We performed our studies with a human eye model based on the Gullstrand parameterization. In order to quantify the discussion concerning imaging with extended depth of focus, we introduced quantitative parameters characterizing output images of optotypes obtained in numerical simulations. The quality of the images formed by the LSOE were compared with those created by a presbyopic human eye, reading glasses and a quartic inverse axicon. Then we complemented the numerical results by an experiment where a 3D scene was imaged by means of the refractive LSOE correcting an artificial eye based on the Gullstrand model. According to performed simulations and experiments the LSOE exhibits abilities for presbyopia correction in a wide range of functional vision distances.

Fabrication of phase masks with variable diffraction efficiency using HEBS glass technology

A new fabrication method of apodized diffractive optical elements is proposed. It relies on using high energy beam sensitive glass as a halftone mask for variable diffraction efficiency phase masks generation in a resist layer. The presented technology is especially effective in mass production. Although fabrication of an amplitude mask is required, it is then repeatedly used in a single shot projection photolithography, which is much simpler and less laborious than the direct variable-dose pattern writing. Three prototypes of apodized phase masks were manufactured and characterized. The main advantages as well as limitations of the proposed technology are discussed.

Closed-loop adaptive optics with a single element for wavefront sensing and correction

We propose a closed-loop adaptive optical arrangement based on a single spatial light modulator that simultaneously works as a correction unit and as the key element of a wavefront sensor. This is possible by using a liquid crystal on silicon display whose active area is divided into two halves that are respectively programmed for sensing and correction. We analyze the performance of this architecture to implement an adaptive optical system. Results showing a closed-loop operation are reported, as well as a proof of concept for dealing with aberrations comparable to those typically found in human eyes.

Strehl ratios characterizing optical elements designed for presbyopia compensation

We present results of numerical analysis of the Strehl ratio characteristics for the light sword optical element (LSOE). For comparison there were analyzed other optical imaging elements proposed for compensation of presbyopia such as the bifocal lens, the trifocal lens, the stenopeic contact lens, and elements with extended depth of focus (EDOF), such as the logarithmic and quartic axicons. The simulations were based on a human eye's model being a simplified version of the Gullstrand model. The results obtained allow to state that the LSOE exhibits much more uniform characteristics of the Strehl ratio comparing with other known hitherto elements and therefore it could be a promising aid to compensate for the insufficient accommodation range of the human eye.

Improvement of lens axicon's performance for longitudinally polarized beam generation by adding a dedicated phase transmittance

The focal field of high NA lens axicon with a binary-phase optical component is calculated by using vector diffraction theory. Numerical results show that for a radially polarized Bessel Gaussian input field, the proposed system generates a subwavelength (0.395λ) longitudinally polarized beam with large uniform depth of focus (approximately 6 λ).

Modeling of amplification and light generation in one-dimensional photonic crystal using a multiwavelength transfer matrix approach

We present an analysis of amplification and lasing in one-dimensional isotropic nonlinear photonic crystal (1D PC), which is based on a generalized (multiwavelength) transfer matrix method. This approach was used for modeling a Raman signal amplification in 1D PC and in an homogenous structure, showing advantages of a stratified medium. Moreover, the threshold operation of a 1D PC Raman laser is studied, assuming both strong as well as depleted pump. The normalized threshold gain characteristics for various end reflections and photonic crystal laser length were calculated.

Imaging with extended focal depth by means of the refractive light sword optical element

The paper presents first experiments with a refractive light sword optical element (LSOE). A refractive version of the LSOE was prepared in photoresist by gray scale photolithography. Then we examined chromatic aberrations of the produced element and compared them with those corresponding to two different lenses. For this purpose we performed two experiments, the first one where white light illumination was used and the latter one by the help of monochromatic illumination with three different wavelengths. The obtained results lead to the conclusion that the refractive LSOE does not exhibit significant chromatic aberrations and can be successfully used for imaging with extended depth of focus in polychromatic illumination.

Measurement and compensation of optical aberrations using a single spatial light modulator

We describe a compact adaptive optical system using a spatial light modulator (SLM) as a single element to both measure and compensate optical aberrations. We used a low-cost, off-the-shelf twisted nematic liquid-crystal display (TNLCD) optimally configured to achieve maximum phase modulation with near constant transmittance. The TNLCD acts both as the microlens array of a Hartmann-Shack wavefront sensor and as the aberration compensation element. This adaptive setup is easy to implement and offers great versatility.

Imaging with extended focal depth by means of lenses with radial and angular modulation

The paper presents imaging properties of modified lenses with the radial and the angular modulation. We analyze three following optical elements with moderate numerical apertures: the forward logarithmic axicon and the axilens representing the radial modulation as well as the light sword optical element being a counterpart of the axilens with the angular modulation. The abilities of the elements for imaging with extended depth of focus are discussed in detail with the help of structures of output images and modulation transfer functions corresponding to them. According to the obtained results only the angular modulation of the lens makes possible to maintain the acceptable resolution, contrast and brightness of the output images for a wide range of defocusing. Therefore optical elements with angular modulations and moderate numerical apertures seem to be especially suitable for imaging with extended focal depth.

Lens axicons in oblique illumination

Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line. In the design of most lens axicons, only on-axis properties have been considered. We present the design of a lens axicon with improved off-axis characteristics. It is constructed from a singlet lens but with a double-pass feature that allows for a line of uniform width and a stop positioned to minimize aberrations. We perform off-axis analysis and experiments for this system and for another lens axicon, one designed for its on-axis characteristics. We conclude that the off-axis performance of the double-pass axicon is better than both that of an ordinary cone axicon and that of the other lens axicon.

Efficient compensation of Zernike modes and eye aberration patterns using low-cost spatial light modulators

Off-the-shelf spatial light modulators (SLMs) like those commonly included in video projection devices have been seldom used for the compensation of eye aberrations, mainly due to the relatively low dynamic range of the phase retardation that can be introduced at each pixel. They present, however, some interesting features, such as high spatial resolution, easy handling, wide availability, and low cost. We describe an efficient four-level phase encoding scheme that allows us to use conventional SLMs for compensating optical aberrations as those typically found in human eyes. Experimental results are obtained with artificial eyes aberrated by refractive phase plates introducing either single Zernike terms or complex eye aberration patterns. This proof-of-concept is a step toward the use of low-cost, general purpose SLMs for the compensation of eye aberrations.

Presbyopia Compensation with a Quartic Axicon

PURPOSE

The purpose of this study was to evaluate the performance of quartic axicons for presbyopia compensation. The working principle relies on profiting the high depth of focus of the axicons to supplement the reduced accommodation amplitude of presbyopes.

METHODS

We present the design equations of a particular kind of axicon to compensate a general presbyopia condition using simultaneous vision. A rotationally symmetric polynomial of fourth-order, corresponding to the well-known Seidel spherical aberration term, was chosen as its refractive profile. To validate its performance, we computed the retinal images with Stiles-Crawford apodization for a presbyopic eye compensated with this quartic axicon and compared them with those obtained without compensation or with other available solutions based on the simultaneous vision principle.

RESULTS

The quartic axicon provides an important improvement of the image quality for intermediate distance vision in comparison with conventional bifocal and trifocal solutions. The image quality, however, is still not optimum for all distances.

CONCLUSIONS

The results show the usefulness of the proposed approach and point out the need for developing further adapted optimizations.

Chromatic compensation in the near-field region: shape and size tunability

We report a diffractive-lens triplet with which to achieve wavelength compensation in the near field diffracted by any aperture. On the one hand, the all-diffractive triplet allows us to tune, in a sequential way, the Fresnel-irradiance shape to be achromatized by changing the focal length of one diffractive lens. On the other hand, we can adjust the scale of the chromatically compensated Fresnel diffraction field by shifting the aperture along the optical axis. Within this framework, we present an extremely flexible white-light Fresnel-plane array illuminator based on the kinoform sampling filter. A variable compression ratio and continuous selection of the output pitch are the most appealing features of this novel application.

Equilateral hyperbolic moiré zone plates with variable focus obtained by rotations

We present equilateral hyperbolic zone plates with variable focal length, which are formed as moiré patterns by a mutual rotation of two identical basic grids. Among others, all principal zone plates, except of the spherical one, can be used as these basic transmittances. Three most important advantages of the proposed moiré zone plates are: a constant aperture of the created element during the mutual movement of basic grids, lack of aberrations due to their undesired mutual lateral displacements and high diffraction efficiency of the binary phase version. To obtain clearer moiré fringe pattern, a radial carrier frequency can be added additionally to the transmittances of basic grids. The destructive interference between both arms of the focal cross of the equilateral hyperbolic moiré zone plate can be obtained by a constant phase shift introduced in the transmittances of the basic grids. Potential applications of discussed elements are indicated, including the most promising one in the three-point alignment technique.

Simple lens axicon

We present the design of a cemented doublet-lens axicon made from spherical surfaces only. Compared with diffractive axicons, refractive cone axicons, and earlier lens axicons with aspheric surfaces, this element is inexpensive and easy to manufacture even with large apertures. The lens axicon is based on the deliberate use of the spherical aberration of the surfaces. The design principles of the element and its characterization, numerically and experimentally, are presented in detail. Although performance was traded for simplicity and robustness, the results show that the lens axicon has the main axicon properties: a narrow, extended line focus of relatively constant width.

High-contrast white-light Lau fringes

We present a new optical assembly with which to achieve Lau fringes with totally incoherent illumination. Gratinglike codification of the spatially incoherent source combined with an achromatic Fresnel diffraction setup allows us to achieve Lau fringe-pattern visibility of almost 100% with broadband light. The white-light character to our proposed setup is in stark contrast to previous monochromatic implementations. Potential implications of this fact are identified.

Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons

Axicons in oblique illumination produce broadened focal lines, a problem, e.g., in scanning applications. A compact mathematical description of the focal segment is presented, for the first time, to our knowledge, and the results are compared with elliptical axicons in normal illumination. In both cases, analytical expressions in the form of asteroid curves are obtained from asymptotic wave theory and caustic surfaces. The results are confirmed by direct diffraction simulations and by experiments. In addition we show that at a fixed angle an elliptical axicon can be used to compensate for the adverse effects of oblique illumination.

Design of diffractive axicons producing uniform line images in Gaussian Schell-model illumination

We present a design method for diffractive axicons in spatially partially coherent Gaussian Schell-model illumination. The method of stationary phase applied to the Fresnel diffraction integral for on-axis intensity leads, on requiring a uniform axial image profile, to a second-order differential equation for the optimal axicon phase function. The first integral can be formally performed, and the phase function is subsequently obtained numerically. The correctness of the synthesized phase profiles is confirmed by numerical simulations using partially coherent Fresnel diffraction theory. The effects of input-beam spot size and coherence width are assessed, and influences of different forms of apodization, including asymmetric functions for narrow incident beams, in annular-aperture diffractive axicons are examined.

Synthesis of diffractive axicons for partially coherent light based on asymptotic wave theory

A general, noniterative method for designing diffractive axicons is derived. This new technique clarifies the earlier phenomenological design principle that was used for coherent light and extends it to the domain of partial coherence. The approach is based on the method of stationary phase in fluctuating diffracted wave fields, and it applies to arbitrary axially symmetric radiation of the Schell-model type. It is shown that the general design equation can be solved numerically, in a straightforward way, for any reasonable illumination and image specifications.

Lens-based theory of the Lau effect

A new theoretical model of the Lau effect is presented. The transmittance of a diffraction grating can be expressed in an equivalent form as the sum of transmittances of thin cylindrical lenses. Therefore it is possible to explain the Lau effect on the basis of the well-known imaging properties of lenses. According to the given approach, the Lau fringes are created by overlapped images of the first grating that are formed by a set of lenses corresponding to the second grating in the setup. The theory leads to an exhaustive description of the Lau-effect parameters. In particular, one can indicate the shape of the Lau fringes and localize planes of the fringes dependent on the axial distance between gratings and their periods.

Directional narrowing of the diffractive pattern through a combination of spherical and spiral optical elements within a single aperture

The intensity pattern produced by the zero-order Bessel beam can be squeezed along certain directions if it interferes with the Bessel beam of a higher order. The concept of directional narrowing can be extended onto the zone plates by the division of the aperture into a set of concentric annuli; within some of the apertures the phase function of the spherical optical element is substituted or supplemented by the spiral optical element. The proposed approach is verified by the numerical simulation of the interference of Bessel beams, linear axicons, and spherical zone plates of zero order and second order.

Diffractive patterns of small cores generated by interference of Bessel beams

The characteristic dimensions of Bessel beams are fully determined by the corresponding Bessel functions. We consider a way of obtaining a narrower diameter of the central core of a diffractive pattern generated by the Bessel beams. The method relies on superposition of two or more Bessel beams with appropriately chosen amplitudes and widths. The disturbing influence of the aperture's edges can be eliminated by addition of the proper amplitude filter.

Uniformization of the axial intensity of diffraction axicons by polychromatic illumination

The axial intensity of axicons illuminated by a coherent wave usually exhibits rapid oscillations from diffraction on the sharp edges of the aperture of the element. These oscillations can be suppressed when the diffractive version of the axicon is illuminated from a polychromatic source. This possibility is examined based on the example of the annular-aperture logarithmic axicon. The estimate for the wavelength interval of the illuminating source required for uniformization is obtained with the help of the stationary-phase method. Furthermore the shape of the radial intensity distribution can be maintained almost unchanged. These findings are confirmed by numerical evaluation of the Fresnel diffraction integral.

Refractive-index profiling of planar gradient-index waveguides by phase-measuring microinterferometry

A novel measurement technique based on phase-stepping microinterferometry is proposed for the refractive-index profiling of planar waveguides fabricated by ion exchange in glass. The sample preparation simplicity and easy instrumental implementation, together with high accuracy and improved resolution, are argued.

Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions

We show that the apodized annular-aperture logarithmic axicon preserves excellent uniformity of the on-axis intensity, energy flow, and lateral resolution. Numerical evaluation of the Fresnel diffraction integral leads to results very close to geometrical-optics predictions. Once again the geometrical law of energy conservation turns out to be a useful tool in designing axicons.

Diffractive elements of variable optical power and high diffraction efficiency

The generation of diffractive elements of variable optical parameters and high diffraction efficiency is presented. It can be realized by a superposition of two conjugate kinoforms. In particular, the method gives rise to zone plates of variable focusing power as well as to circular and linear gratings of variable deflection angles. The theoretical description is illustrated by an experimental example of the blazed grating with a changeable period; some possible applications are mentioned.

Nonparaxial design of generalized axicons

The geometric law of energy conservation is utilized in evaluating the phase transmittance function for axicons with arbitrary distribution of the on-axis intensity. Several simple analytical solutions are presented, and a computer-generated holographic version of the uniform-intensity axicon is examined.

Zone plates with black focal spots

Computer-designed linear and circular zone plates are considered that utilize a pi ;-phase jump in order to create destructive interference in the focus. Intensity distributions in the focal plane as well as along the optical axis are calculated for a few examples. A significant decrease of the black spot diameter in comparison with the dimensions of the ordinary focal spot is obtained. Further reduction is achieved when the central region of the zone plate is obstructed. Some applications to alignment and the schlieren technique are suggested. Experimental results that confirm the calculated distributions are presented.

Phase retardation of the uniform-intensity axilens

A method for determining the phase-retardation function of the uniform-intensity axilens is discussed and compared with that of an earlier publication [Opt. Lett. 16, 523 (1991)]. Within the presented formulation good agreement is achieved between the geometrical-optics prediction and the numerically evaluated diffraction integral.

Determination of basic grids for subtractive moire patterns

The simple formula derived in the paper establishes a direct relationship between moire beat patterns and basic grids for minute displacements. The possibilities of finding a basic grid for a desired moire pattern are pointed out. The analysis is illustrated by several examples of Fresnel moire zone plate patterns and concentric equidistant circular moire patterns obtained by changes of scale and rotation. Possible advantages of the practical use of this element are outlined.

Interferometric alignment using parabolic and off-axis conical zone plates

The use of zone plates in optical alignment and displacement measurement is discussed. A simple theory of positioning using two coherent wavefronts is proposed. A few examples, already described in the literature as well as new ones, are presented as an illustration of the theory. The application of the specific case of the offaxis cylindrical zone plate (so-called parabolic zone plate) and off-axis conical zone plate for sensing the motion along a straight line parallel and inclined to the hologram plane is established. There are also adduced results of simple experiments supporting the analysis.

Aberrationless phase difference amplification in holographic interferometry

Two improved techniques of aberrationless phase difference amplification are presented. Both make use of double-exposure holographic interferometry. In contrast to the ordinary technique, not only the state of the tested object is changed between exposures but also the direction of the hologram fringes. This approach allows one to separate desired higher diffraction orders of the double-exposed hologram, to eliminate setup aberrations, and, consequently, to achieve an amplification of the phase difference given by the tested object alone.