Plane Of Lens Research Articles

Outcomes of Zero Power Intraocular Lenses: Insights into the Keratometric Index and Axial Length.

We analyzed intraocular lens (IOL) power calculation in a series of patients with a zero diopter power implant. The idea was to bypass the Estimated Lens Plane (ELP), an important variable in normal IOL calculation. Large multi-center group practice. Retrospective, observational study. A consecutive series of patients undergoing cataract surgery after optical biometry and implantation of a zero (0.0 D) power IOL were studied. Complete biometry was performed with an optical low coherence optical biometer. The predicted refraction was calculated with and without recalibrating the axial length (AL) using a Sum-Of-Segments (SOS) approach with the Hoffer Q, Holladay 1, SRK/T, Haigis, Barrett Universal II, and Olsen formulas. A ray tracing model to back-calculate the corneal power from the observed postoperative refraction and AL was also included. In 52 eyes of 52 patients, mean prediction errors for the Hoffer Q, Holladay 1, SRK/T, Haigis, Barrett Universal II, and the Olsen formulas were +1.48, +1.15, +0.91, +0.65, +0.15 and +0.11 D respectively using standard AL and after SOS correction of the AL the mean errors changed to +1.08, +0.75, +0.52, +0.26, -0.25, and -0.27 D respectively. The mean back-calculated corneal power was 1.25 D lower than the mean keratometer reading using the standard keratometric index of 1.3375 and corresponded to an effective index of 1.328. The hyperopic error commonly seen in highly myopic eyes with classical thin-lens formulas is only partly corrected by SOS recalibration of the AL. We suggest the source of the residual error is an incorrect keratometric index.

Two-photon nanolithography of sub-micrometer thickness microlenses designed by NPCC assisted Rayleigh Sommerfeld diffraction integral

Recent development of artificial neural networks (ANNs) and inverse design methods have demonstrated their prospective significance for planar diffractive lens design, with a plethora of optical lenses designed for wavelengths ranging from visible to Thz wavelengths. However, previous research to design planner diffractive lenses only considers the maximum intensity in the focus area or its derivatives as the optimization function, leaving the intensity outside the focus area unconsidered. We proposed and investigated a two-dimensional (2D) physics-driven ANN method assisted by the negative Pearson correlation coefficient (NPCC) to design microlenses with varied focusing distances, which takes the entire 2D intensity distribution at the focus plane as an optimization function. Taking advantage of 3D two-photon nanolithographic technology, sub-micrometer thickness microlenses with varied focusing lengths are designed and fabricated, achieving an average focusing efficiency of around 35%, and an average focusing spot size of about 1 µm. Furthermore, a microlens array (19 by 19 microlenses with a total size of 4 mm2) with a curved focusing plane was fabricated and integrated into a CMOS sensor, achieving direct object imaging under incoherent white light illumination. Our results demonstrate that the NPCC is a very useful optimization function for designing planar diffractive lenses, and the use of NPCC in ANNs is of great potential for the future design of functional diffractive optical elements in optics and nanophotonics.

A stability inequality for planar lens partition

Abstract Recently it has been shown that the unique local perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens, hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem.

Optical Fresnel zone plate flat lenses made entirely of colored photoresist through an i-line stepper

Light manipulation and control are essential in various contemporary technologies, and as these technologies evolve, the demand for miniaturized optical components increases. Planar-lens technologies, such as metasurfaces and diffractive optical elements, have gained attention in recent years for their potential to dramatically reduce the thickness of traditional refractive optical systems. However, their fabrication, particularly for visible wavelengths, involves complex and costly processes, such as high-resolution lithography and dry-etching, which has limited their availability. In this study, we present a simplified method for fabricating visible Fresnel zone plate (FZP) planar lenses, a type of diffractive optical element, using an i-line stepper and a special photoresist (color resist) that only necessitates coating, exposure, and development, eliminating the need for etching or other post-processing steps. We fabricated visible FZP lens patterns using conventional photolithography equipment on 8-inch silica glass wafers, and demonstrated focusing of 550 nm light to a diameter of 1.1 μm with a focusing efficiency of 7.2%. Numerical simulations showed excellent agreement with experimental results, confirming the high precision and designability of our method. Our lenses were also able to image objects with features down to 1.1 μm, showcasing their potential for practical applications in imaging. Our method is a cost-effective, simple, and scalable solution for mass production of planar lenses and other optical components operating in the visible region. It enables the development of advanced, miniaturized optical systems to meet modern technology demand, making it a valuable contribution to optical component manufacturing.

The influence of anterior chamber depth on the calculation of piggyback intraocular lenses.

Demonstrate the variability of the spherical and toric ratios between the refraction at the intraocular lens (IOL) plane and the refraction at the spectacle plane when the sphere and the cylinder power of toric piggyback IOLs are calculated. Also, a comparison of the results of piggyback power calculation with variable ratios, to the power calculation performed by a major manufacturer online calculator using a fixed ratio. Experimental study with theoretical eye models. Private practice, Buenos Aires Argentina. Schematic eyes with different values of pseudophakic anterior chamber depth (ACD), refractive cylinder and sphere were used to calculate the exact toric and spherical power of the IOL needed to achieve emmetropia. The toric ratio could range between 0.88 and 1.6, while the spherical ratio between 1.01 and 1.61. Therefore, using fixed ratios can lead to errors in IOL power calculation up to 1 diopter. The most likely errors are undercorrection in eyes with deep ACD and low amounts of sphere and astigmatism and overcorrections in eyes with shallow ACD and high preoperative sphere and/or cylinder. Manufacturers that calculate the power of piggyback IOLs with a fixed ratio of toricity and sphere should develop calculators that change this ratio according to the preoperatively measured variables. An excel file with the calculator used is provided.

Measuring line-of-sight distances to haloes with astrometric lensing B-mode

Relative astrometric shifts between multiply lensed images provide a valuable tool to investigate haloes in the intergalactic space. In strong lens systems in which a single lens plays the primary role in producing multiple images, the gravitational force exerted by line-of-sight (LOS) haloes can slightly change the relative positions of multiply lensed images produced by the dominant lens. In such cases, a LOS halo positioned sufficiently far from the dominant lens along the LOS can create a pattern in the scaled deflection angle that corresponds to the B-mode (magnetic or divergence-free mode). By measuring both the B-mode and E-mode (electric or rotation-free mode), we can determine the LOS distance ratios, as well as the `bare' convergence and shear perturbations in the absence of the dominant lens. However, scale variations in the distance ratio lead to mass-sheet transformations in the background lens plane, introducing some uncertainty in the distance ratio estimation. This uncertainty can be significantly reduced by measuring the time delays between the lensed images. Additionally, if we obtain the redshift values of both the dominant and perturbing haloes, along with the time delays between the multiply lensed images that are affected by the haloes, the B-mode can break the degeneracy related to mass-sheet transformations in both the foreground and background lens planes. Therefore, measuring the astrometric lensing B-mode has the potential to substantially decrease the uncertainty in determining the Hubble constant.

Clinical Classification and Management Outcomes of Anterior Segment Dominated Persistent Fetal Vasculature: the CCPMOH report.

To describe clinical features, management, and outcomes of anterior segment dominated persistent fetal vasculature (aPFV) . A secondary analysis of aPFV data from a longitudinal cohort study. The age and gender of each participant upon initial presentation, along with biological parameters, best-corrected visual acuity (BCVA), and biomicroscopic assessments were collected. The aPFV eyes were categorized into 3 groups (type I:pupillary-iris-anterior lens plane, type II:retrolental-anterior hyaloid membrane plane and type III:combined) according to the location of the vascular abnormalities and further classified into mild (a) and severe (b) according to the degree of severity. The surgical techniques used in this investigation were reported. Visual outcomes, ocular hypertension, postoperative adverse events, and additional surgical interventions were recorded at each follow-up visit. A total of 470 individuals (619 eyes) were enrolled (ages 36.7±45.4 months, range 1 to 394 months), divided into 129 eyes (20.8%) Type 1, 420 eyes (67.9%) Type 2, and 70 eyes (11.3%) Type 3. Cataracts were identified in 505 eyes (81.6 %): for type I, the common forms were nuclear and membranous opacity (both 12/50 eyes, 24%); type II: subcapsular opacity (214/399 eyes, 53.6%) and type III: complete cortex (17/56 eyes, 30.4%). Posterior capsular tear was mostly present in type II a. Type III had the shallowest anterior chamber depth and the largest corneal astigmatism. Six hundred patients (96.7%) had surgery. After surgery, 119 eyes experienced adverse events: intravitreal hemorrhages occurred in 0.2% of eyes, visual axis obscuration occurred in 9.4% of eyes, and ocular hypertension which required eye drop medication occurred in 19.2% of eyes. In 47 patients (7.6%), a second surgery procedure was done. In 456 eyes (73.7%), visual acuity had improved at the last follow-up. The worst BCVA was associated with types IIb and IIIb. The magnitude of aPFV can be usefully characterized by a classification protocol focusing on the location and disease severity. Here, we propose a surgical and medical management algorithm for aPFV to achieve favorable outcomes with limited intraoperative and postoperative complications.

Design and demonstration of DEA-based tunable planar liquid crystal Alvarez lenses

Design and demonstration of DEA-based tunable planar liquid crystal Alvarez lenses

Relationship Between Aberration Coefficients of an Optical Device and Its Focusing Property

The best focus point of a focused Gaussian beam subject to a phase aberration is generally shifted with respect to the focal plane of the focusing lens. This focus shift is attributed to a lensing effect that belongs to the phase aberration, which mean focal length can be determined from the aberration coefficients determined in the framework of a Zernike polynomial decomposition. In this paper, we have checked the validity of this procedure, already available in literature, applied to three aberration types: a pure primary spherical aberration, the Kerr effect induced by a Gaussian beam, and an axicon illuminated by a Gaussian beam. Note that usually, the mean focal length of an aberrated lens is based on the relation between the effective radius of curvature of the wavefront before and after the lens. However, in this paper, the focal length associated with the phase aberration under study is defined from the point of the best focus, where the diffracted intensity on the axis is the maximum.

Strong-lensing and kinematic analysis of CASSOWARY 31: Can strong lensing constrain the masses of multi-plane lenses?

We present a mass measurement for the secondary lens along the line of sight (LoS) from the multi-plane strong lens modeling of the group-scale lens CASSOWARY 31 (CSWA 31). The secondary lens at redshift z = 1.49 is a spiral galaxy well aligned along the LoS with the main lens at z = 0.683. Using the MUSE integral-field spectroscopy of this spiral galaxy, we measured its rotation velocities and determined the mass from the gas kinematics. We compared the mass estimation of the secondary lens from the lensing models to the mass measurement from kinematics, finding that the predictions from strong lensing tend to be higher. By introducing an additional lens plane at z = 1.36 for an overdensity known to be present, we find a mass of ≃1010 M⊙ enclosed within 3.3 kpc of the centroid of the spiral galaxy, which approaches the estimate from kinematics. This shows that secondary-lens mass measurements from multiple-plane modeling are affected by systematic uncertainties from the degeneracies between lens planes and the complex LoS structure. Conducting a detailed analysis of the LoS structures is therefore essential to improve the mass measurement of the secondary lens.

Chromatic focus variation microscopy for surface metrology

Optical metrology plays a vital role in a wide range of research and inspection areas in the industry. At present, the market offers a variety of optical metrology instruments, among which the focus variation microscope stands out for its capability of measuring steep surfaces with high slopes. The traditional focus variation (FV) instrument mechanically scans the surface by sweeping the focal plane of the objective lens using linear motion stages and simultaneously capturing images at different scanning positions, forming a stack of images. The mechanical motion stages require regular maintenance and calibration to ensure accuracy over time. Another issue associated with the mechanical scanning methods is their physical size, which creates a limiting factor to compactness for in-situ measurement applications. This work proposes a chromatic focus variation (CFV) method that replaces mechanical scanning with a wavelength scanning mechanism to overcome the above limitations. Unlike traditional focus variation, the CFV system employs a dispersive objective lens (i.e. chromatically aberrated objective lens) to axially shift the focus along the optical axis to provide vertical/depth scanning. This approach brings significant enhancements in measurement speed and reduces the instrument size for on-machine metrology tasks. In this paper, a detailed analysis of the optical performance of the dispersive objective lens is conducted, and then the measurement performance of the proposed CFV system is validated using samples including a step height of 30 µm and a sine wave shape with a peak-to-valley amplitude of 19 µm. The experiment results were compared to those from the state-of-the-art commercial instrument (Alicona G5), which showed a good agreement between the two. Furthermore, a detailed analysis and discussions are provided to investigate the measurement’s accuracy.

Imaging dark matter at the smallest scales with z ≈ 1 lensed stars

Recent observations of caustic-crossing galaxies at redshift 0.7 ≲ z ≲ 1 show a wealth of transient events. Most of them are believed to be microlensing events of highly magnified stars. Earlier work predicts such events should be common near the critical curves (CCs) of galaxy clusters (“near region”), but some are found relatively far away from these CCs (“far region”). We consider the possibility that substructure on milliarcsecond scales (few parsecs in the lens plane) is boosting the microlensing signal in the far region. We study the combined magnification from the macrolens, millilenses, and microlenses (“3M lensing”), when the macromodel magnification is relatively low (common in the far region). After considering realistic populations of millilenses and microlenses, we conclude that the enhanced microlensing rate around millilenses is not sufficient to explain the high fraction of observed events in the far region. Instead, we find that the shape of the luminosity function (LF) of the lensed stars combined with the amount of substructure in the lens plane determines the number of microlensing events found near and far from the CC. By measuring β (the exponent of the adopted power law LF, dN/dL = ϕ(L)∝(1/L)β), and the number density of microlensing events at each location, one can create a pseudoimage of the underlying distribution of mass on small scales. We identify two regimes: (i) positive-imaging regime where β > 2 and the number density of events is greater around substructures, and (ii) negative-imaging regime where β < 2 and the number density of microlensing events is reduced around substructures. This technique opens a new window to map the distribution of dark-matter substructure down to ∼103 M⊙. We study the particular case of seven microlensing events found in the Flashlights program in the Dragon arc (z = 0.725). A population of supergiant stars having a steep LF with β = 2.55−0.56+0.72 fits the distribution of these events in the far and near regions. We also find that the new microlensing events from JWST observations in this arc imply a surface mass density substructure of Σ∗ = 54 M⊙ pc−2, consistent with the expected population of stars from the intracluster medium. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of ∼1.3 × 108 M⊙ (within its Einstein radius) in the galaxy cluster.

Gain enhancement of mm-wave antenna using graded index lens integrated frequency selective surface for 5G NR FR2 applications

In this study, the gain of a printed antenna is boosted for utilization in 5G systems by employing a phase-oriented graded index-type lens system. In the prescribed design, various metamaterial unit cells are arranged as arrays with radial phases for the graded meta lens to optimize transmission characteristics. The suggested arrangement creates a meta lens with spatially varying surface impedance and locally varying refractive index, allowing the conversion of spherical wavefronts into planar wavefronts for beam collimation in the 5G band. The focal length-to-diameter ratio (f/d) is fixed at 0.38 in this prescribed design. The integration of the FSS structure with the patch antenna enhances the efficiency above 98% and increases gain by 2.635dBi owing to the focusing effect of the properly placed lens. The prescribed planar lens is easy to realize during manufacturing compared to 3D lenses. The meta lens integrated patch yields a gain of around 8.936dBi at 29 GHz. The performance of the lens antenna is evaluated through simulation studies and then validation of results is performed with experimental arrangement to ensure accuracy and reliability of the suggested methodology for gain enhancement of the functioning antenna at FR2 5G spectrum.

Lens height paraments comparison according to ciliary sulcus width (CSW): a pilot study of the predictive role of CLR and STSL for vault after ICL implantation

BackgroundTo assess the relationship between postoperative implantable collamer lens (ICL) vault and lens height obtained from two different measurements.MethodsA retrospective case series study enrolled eyes with horizontally implanted ICL. Crystal lens rise (CLR) and the distance between STS plane and anterior crystalline lens surface (STSL) were measured in the horizontal and vertical directions using ultrasound biomicroscopy (UBM). We compared the differences in the parameters measured in both horizontal and vertical directions. The participants were categorized into three groups according to ciliary sulcus width (CSW) which is defined as the distance between the posterior angle of the iris and the anterior angle of the ciliary process: narrow CSW group (NSG); medium CSW group (MSG); and wide CSW group (WSG). The correlations between CLR/STSL and vault were examined in each of the three groups. Biased correlation analysis was used further to contrast the correlation between CLR/STSL and vault.ResultsThis retrospective study included 223 myopic eyes. Vertical STSL (VSTSL) and vertical CLR (VCLR) exhibited significantly greater values compared to their horizontal counterparts (both P < 0.05). None of the indicators were statistically different between the three groups. In both NSG and MSG, STSL/CLR correlated with vault, while in WSG, only STSL correlated with vault (r=-0.316, P = 0.013). In contrast to HCLR, the correlation between HSTSL and vault remained after controlling for HCLR (r=-0.162, P = 0.015).ConclusionsSTSL should deserve more attention in the preoperative evaluation of ICL compared to CLR especially when CSW is large.

Ray-transfer matrix for GRIN lenses: application to the crystalline lens.

We present a Hamiltonian optics approach to determine the paraxial propagation of rays in gradient-index (GRIN) media. A derivation of the evolution equation for the corresponding ray-transfer matrix is given. An analytical solution can be found for a certain class of GRIN media. The proposed matrix is shown to be a generalization of the well-known matrices for planar and cylindrical GRIN lenses. We provide the accuracy results when applying our analytical method to arbitrary refractive indices and verify its validity by comparing it to other matrices in the literature with satisfactory results.

Weak lensing of strong lensing: beyond the tidal regime

The analysis of strong lensing images usually involves an external convergence and shear, which are meant to model the effect of perturbations along the line of sight, on top of the main lens. Such a description of line-of-sight perturbations supposes that the corresponding gravitational fields can be treated in the tidal regime. Going one step further introduces additional effects, known as flexion, which have been hitherto neglected in strong lensing. In this work, we build a minimal model for the line-of-sight flexion, which adds four new complex parameters to the lens model. Contrary to convergence and shear, the line-of-sight flexion cannot be projected onto the main lens plane. For a ΛCDM cosmology, we predict the typical line-of-sight flexion to be on the order of 10-3 arcsec-1 on galactic scales. Neglecting its effect in lens modelling is found to bias the recovery of other parameters; in particular, the line-of-sight shear can be biased up to 2σ. Accounting for the line-of-sight flexion in our minimal framework restores accuracy, at the cost of degrading precision. With current imaging capabilities, the line-of-sight flexion is unlikely to be measurable on individual strong lensing images; it must therefore be considered a nuisance parameter rather than an observable in its own right.

Perfect space-time vortices.

We introduce the concept of perfect space-time vortices (PSTVs) that can exist in media with anomalous dispersion. If the topological charge of a PSTV is not too large, the spatiotemporal intensity distribution of the vortex field does not depend on the magnitude of the topological charge. We show theoretically how a PSTV can be realized in the optical context through spatiotemporal focusing of a Bessel-Gaussian space-time optical vortex source that is placed in the focal plane of a space-time lens composed of an ordinary lens and a time lens with matched spatial and temporal focal lengths.

Statistics of magnification for extremely lensed high redshift stars

Microlensing of stars in strongly lensed galaxies can lead to temporary extreme magnification factors (μ&gt; 1000), enabling their detection at high redshifts. Following the discovery of Icarus, several stars at cosmological distances (z &gt; 1) have been observed using the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST). This emerging field of gravitational lensing holds promise to study individual high redshift stars. It also offers the opportunity to study the substructure in the lens plane with implications for dark matter models, as more lensed stars are detected and analysed statistically. Due to the computational demands of simulating microlensing at large magnification factors, it is important to develop fast and accurate analytical approximations for the probability of magnification in such extreme scenarios. In this study, we consider different macro-model magnification and microlensing surface mass density scenarios and study how the probability of extreme magnification factors depends on these factors. To achieve this, we created state-of-the-art large simulations of the microlensing effect in these scenarios. Through the analysis of these simulations, we derived analytical scaling relationships that can bypass the need for expensive numerical simulations. Our results are useful to interpret current observations of stars at cosmic distances which are extremely magnified and under the influence of microlenses.

Patterned microsphere-lens projection lithography using an electrohydrodynamic-jet-printing-assisted assembly

Microlens arrays have been widely used in the fields of micro-optics and micro- and nanofabrication. Traditional preparation methods utilize commercial photoresists and thermosetting materials, thereby restricting the optical properties of microlenses. In recent years, significant advancements have been achieved in near-field super-resolution imaging by utilizing microspheres and forming arrays of microsphere lenses via self-assembly. However, self-assembly approaches lack flexibility in terms of pattern selection. This study proposes a method that utilizes electrohydrodynamic jet (E-jet) printing to code ultraviolet (UV)-curable adhesives and assist in the assembly of patterned microsphere-lens arrays. Simulation results demonstrate that the UV-curable adhesive has little impact on the optical properties of the microsphere lens. Moreover, the microsphere lens exhibits a superior imaging resolution compared with traditional microlenses. A projection-lithography system is developed to achieve an accurate alignment between the focal plane of the microsphere lenses and the plane of the photoresist, facilitating the fabrication of patterned nanostructures. The lithographic nanostructures have a minimum feature size of 850 nm. This method enables the fabrication of arrays of microsphere lenses with arbitrary patterns and presents an inexpensive and simple strategy for fabricating micro- and nanostructure arrays with submicrometer features.

Monolithically Structured van der Waals Materials for Volume-Polariton Refraction and Focusing.

Polaritons, hybrid light and matter waves, offer a platform for subwavelength on-chip light manipulation. Recent works on planar refraction and focusing of polaritons all rely on heterogeneous components with different refractive indices. A fundamental question, thus, arises whether it is possible to configure two-dimensional monolithic polariton lenses based on a single medium. Here, we design and fabricate a type of monolithic polariton lens by directly sculpting an individual hyperbolic van der Waals crystal. The in-plane polariton focusing through sculptured step-terraces is triggered by geometry-induced symmetry breaking of momentum matching in polariton refractions. We show that the monolithic polariton lenses can be robustly tuned by the rise of van der Waals terraces and their curvatures, achieving a subwavelength focusing resolution down to 10% of the free-space light wavelength. Fusing with transformation optics, monolithic polariton lenses with gradient effective refractive indices, such as Luneburg lenses and Maxwell's fisheye lenses, are expected by sculpting polaritonic structures with gradually varied depths. Our results bear potential in planar subwavelength lenses, integrated optical circuits, and photonic chips.