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

Extended-depth-of-focus wavefront design from pseudo-umbilical space curves

Designing extended-depth-of-focus wavefronts is required in multiple optical applications. Caustic location and structure analysis offer a powerful tool for designing such wavefronts. An intrinsic limitation of designing extended-depth-of-focus wavefronts is that any smooth surface, with a non-constant mean curvature, unavoidably introduces a separation between caustic sheets, which is proportional to the ratio of change of the mean curvature along a curve embedded in the wavefront. We present a method to obtain extended-depth-of-focus wavefronts where the mean curvature variation ratio is reduced thanks to using a long circle-involute space curve effectively filling the wavefront surface. Additionally, we present a variant of the method in which the wavefront is modified within a small tubular neighborhood of the circle involute in order to partially meet the umbilical condition along that tubular region. Finally, we provide some numerical results showing the potential of our method in an application example.

Objective method for visual performance prediction

We propose, implement, and validate a new objective method for predicting the trends of visual acuity through-focus curves provided by specific optical elements. The proposed method utilized imaging of sinusoidal gratings provided by the optical elements and the definition of acuity. A custom-made monocular visual simulator equipped with active optics was used to implement the objective method and to validate it via subjective measurements. Visual acuity measurements were obtained monocularly from a set of six subjects with paralyzed accommodation for a naked eye and then that eye compensated by four multifocal optical elements. The objective methodology successfully predicts the trends of the visual acuity through-focus curve for all considered cases. The Pearson correlation coefficient was 0.878 for all tested optical elements, which agrees with results obtained by similar works. The proposed method constitutes an easy and direct alternative technique for the objective testing of optical elements for ophthalmic and optometric applications, which can be implemented before invasive, demanding, or costly procedures on real subjects.

Inverse design of a near-infrared metalens with an extended depth of focus based on double-process genetic algorithm optimization

Metalens with extended depth of focus (EDOF) can extend the mapping area of the image, which leads to novel applications in imaging and microscopy. Since there are still some disadvantages for existing EDOF metalenses based on forward design, such as asymmetric point spread function (PSF) and non-uniformly distributed focal spot, which impair the quality of images, we propose a double-process genetic algorithm (DPGA) optimization to inversely design the EDOF metalens for addressing these drawbacks. By separately adopting different mutation operators in successive two genetic algorithm (GA) processes, DPGA exhibits significant advantages in searching for the ideal solution in the whole parameter space. Here, the 1D and 2D EDOF metalenses operating at 980 nm are separately designed via this method, and both of them exhibit significant depth of focus (DOF) improvement to that of conventional focusing. Furthermore, a uniformly distributed focal spot can be maintained well, which can guarantee stable imaging quality along the longitudinal direction. The proposed EDOF metalenses have considerable potential applications in biological microscopy and imaging, and the scheme of DPGA can be promoted to the inverse design of other nanophotonics devices.

Smooth multifocal wavefronts with a prescribed mean curvature for visual optics applications

Multifocal lenses comprising progressive power surfaces are commonly used in contact and intraocular lens designs. Given a visual performance metric, a wavefront engineering approach to design such lenses is based on searching for the optimal wavefront at the exit pupil of the eye. Multifocal wavefronts distribute the energy along the different foci thanks to having a varying mean curvature. Therefore, a fundamental step in the wavefront engineering approach is to generate the wavefront from a prescribed mean curvature function. Conventionally, such a thing is done by superimposing spherical wavefront patches and maybe adding a certain component of spherical aberration to each spherical patch in order to increase the depth-of-field associated with each focus. However, such a procedure does not lead to smooth wavefront solutions and also restricts the type of available multifocal wavefronts. We derive a new, to the best of our knowledge, mathematical method to uniquely construct multifocal wavefronts from mean curvature functions (depending on radial and angular coordinates) under certain numerically justified approximations and restrictions. Additionally, our procedure leads to a particular family of wavefronts (line-umbilical multifocal wavefronts) described by 2 conditions: (1) to be smooth multiplicative separable functions in the radial and angular coordinates; (2) to be umbilical along a specific segment connecting the circle center with its edge. We provide several examples of multifocal wavefronts belonging to this family, including a smooth variant of the so-called light sword element.

Metasurface lens with angular modulation for extended depth of focus imaging

The depth of focus (DOF) indicates the tolerance of the imaging displacement. The axial long-focal-depth is significant in practical applications, including optical imaging and communication. The importance of extending the DOF is rapidly growing with the advance of metasurface lenses. Angular modulation, as a promising way to extend the DOF, offers an additional degree of freedom to improve the imaging quality. Here we theoretically and experimentally demonstrate an angular modulated metasurface lens for extended DOF imaging by means of applying the geometrical phase. Unlike previous studies of the geometrical phase, which is sensitive to the polarity of circular polarization incidence, the polarity of circular polarization independence and broadband characteristic of angular modulation yield the potential of robust and efficient extension of the DOF imaging, thus providing novel opportunities for highly integrated optical circuits.

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.

Dependence of depth of focus on spherical aberration of optical systems

This paper presents a theoretical analysis and computation of aberration coefficients of the third and fifth order of transverse spherical aberration of an optical system, which generates a ray bundle with a diameter of a geometric-optical circle of confusion smaller than a predetermined limit value. Equations were derived for the calculation of aberration coefficients of an optical system, which satisfy given conditions, and for the determination of the maximum possible depth of focus for given conditions.

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.

Imaging properties of three refractive axicons

The imaging properties of three types of refractive axicons are examined by using them in an imaging system. A linear axicon, a logarithmic axicon, and a Fresnel axicon are characterized by determining their point spread functions (PSFs) experimentally and by numerical simulation. The PSFs, which vary along the depth of field for the cases considered in the present investigation, are used in digital filters to denoise the images. A comparison of the imaging performance of these three optical elements is presented.

Logarithmic axicon characterized by scanning optical probe system

A scanning optical probe system is proposed to measure a logarithmic axicon (LA) with subwavelength resolution. Multiple plane intensity profiles measured by a fiber probe are interpreted by solving an optimization problem to get the phase retardation function (PRF) of the LA. Experimental results show that this approach can accurately obtain the PRF with which the optical path difference of the generated quasi-nondiffracting beam in the propagation is calculated.

Multiple-frame photography for extended depth of field

For extending the depth of field, we analyze the result of superimposing several snapshots, which are taken while changing the amount of focus error, at full pupil aperture. We unveil the use of a varifocal lens for controlling the amount of focus error, without modifying either the lateral magnification or light throughput. After recording a set of snapshots, we use suitable acquisition factors for shaping an optical transfer function, which has reduced sensitivity to focus errors.

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.

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).

Intrastriatal botulinum toxin abolishes pathologic rotational behaviour and induces axonal varicosities in the 6-OHDA rat model of Parkinson's disease

Central pathophysiological pathways of basal ganglia dysfunction imply a disturbed interaction of dopaminergic and cholinergic circuits. In Parkinson's disease (PD) imbalanced cholinergic hyperactivity prevails in the striatum. Interruption of acetylcholine (ACh) release in the striatum by locally injected botulinum neurotoxin A (BoNT-A) has been studied in the rat 6-hydroxydopamine (6-OHDA) model of PD (hemi-PD). The hemi-PD was induced by injection of 6-OHDA into the right medial forebrain bundle. Motor dysfunction provoked by apomorphine-induced contralateral rotation was completely reversed for more than 3 months by ipsilateral intrastriatal application of 1-2 ng BoNT-A. Interestingly, BoNT-A injected alone into the right striatum of naïve rats caused a slight transient ipsilateral apomorphine-induced rotation, which lasted only for about one month. Immunohistochemically, large axonal swellings appeared within the striatum injected with BoNT-A, which we tentatively named BoNT-A-induced varicosities. They contained either choline acetyltransferase or tyrosine hydroxylase. These findings suggest a selective inhibition of evoked release of ACh by locally applied BoNT-A. Intrastriatal application of BoNT-A may antagonize localized relative functional disinhibited hypercholinergic activity in neurodegenerative diseases such as PD avoiding side effects of systemic anti-cholinergic treatment.

Spoke wheel filtering strategy for on-axis flattop shaping

Spoke wheel filtering strategy is developed using the proposed spoke wheel filter (SWF) and solving the nonlinear optimization model established by introducing a super-Gaussian function. Theoretical calculations through simulated annealing algorithm indicate that high focal depth is obtained by increasing the number of curved sectors composing SWF, while the peak-valley intensity oscillation is reduced by bending them appropriately and slightly changing their amplitude transmittances. The transverse in-focus spot compresses when the center-shaded circle of SWF enlarging. Comparison shows that SWF outperforms radial-symmetric pupil filters in its largely reduced intensity oscillation and very flexible design of focal depth extension.

Diffractionless beam in free space with adiabatic changing refractive index in a single mode tapered slab waveguide

We propose a novel design to produce a free space diffractionless beam by adiabatically reducing the difference of the refractive index between the core and the cladding regions of a single mode tapered slab waveguide. To ensure only one propagating eigenmode in the adiabatic transition, the correlation of the waveguide core width and the refractive index is investigated. Under the adiabatic condition, we demonstrate that our waveguide can emit a diffractionless beam in free space up to 500 micrometers maintaining 72% of its original peak intensity. The proposed waveguide could find excellent applications for imaging purposes where an extended depth of field is required.

Creating an extended focus image of a tilted object in Fourier digital holography

We present a new method to numerically reconstruct images on a tilted plane by digital holography in Fourier configuration. The proposed technique is based on a quadratic deformation of spatial coordinates of the digital hologram. By this approach we demonstrate that it is possible to recover the extended focus image (EFI) of a tilted object in a single reconstruction step from the deformed hologram.

Binary sub-wavelength diffractive lenses with long focal depth and high transverse resolution

This study explores two-dimensional binary sub-wavelength diffractive lenses (BSDLs) for implementing long focal depth and high transverse resolution based on the rigorous electromagnetic theory and the finite-difference time-domain method. Focusing performances, such as the actual focal depth, the ratio between the focal depth of the designed BSDL and the focal depth of the conventional sub-wavelength lens and the spot size of the central lobe at the actual focal plane, for different f-numbers, have been studied in the case of TE incidence polarization wave. The rigorous numerical results indicate that the designed BSDLs indeed have long focal depth and high transverse resolution by modulating the binary sub-wavelength characteristic sizes. Because BSDLs have the ability for monolithic integration and can require only single step fabrication, the investigations may provide useful information for BSDLs' application in micro-optical systems.

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.

Depth of field extension with spherical optics

The introduction of spherical aberration in a lens design can be used to extend the depth of field while preserving resolution up to half the maximum diffraction-limited spatial frequency. Two low-power microscope objectives are shown that achieve an extension of +/- 0.88 lambda in terms of wavefront error, which is shown to be comparable to alternative techniques but without the use of special phase elements. The lens performance is azimuth-independent and achromatic over the visible range.

Optimized free-form phase mask for extension of depth of field in wavefront-coded imaging

To achieve a further extension of the depth of field in wavefront-coded imaging by reducing the impact of focus error in the optical transfer function, we propose the use of a free-form phase mask (FPM) instead of a conventional cubic phase mask (CPM). We optimized the shape of the FPM using the simulated annealing algorithm and confirmed that the optimized FPM provides a much larger focal tolerance and better final images than the CPM in the noise-free case.

Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus

The paper presents the polychromatic analysis of two diffractive optical elements with extended depth of focus: the linear axicon and the light sword optical element. Chromatic aberration produces axial displacement of the focal segment line. Thus, we explore the possibility of extending the focal depth of these elements to permit superposition of the chromatic foci. In the case of an axicon, we achieve an achromatic zone where focusing is produced. In the case of the light sword element, we show that the focusing segment is out of axis. Therefore a superposition of colors is produced, but not on axis overlapping. Instead, three colored and separated foci are simultaneously obtained in a single plane. Three dimensional structures of the propagated beams are analyzed in order to provide better understanding of the properties and applications of such elements.