Smooth Lens Research Articles

Focus-switchable piezoelectric actuator: A bionic thin-plate design inspired by conch structure

Traditional camera zoom mechanisms, relying on stepper motors and intricate transmission components, suffer from bulky designs that restrict their applicability in compact systems. This study presents a novel piezoelectric focus-switchable mechanism (PFSM) directly driven by a biomimetic radial-mode piezoelectric actuator (RMPA) with inclined driving structure mimicking the conch shell. The PFSM utilizes rotational motion for optical zoom, providing a more compact and efficient alternative to conventional linear motion-based systems. By utilizing finite element method (FEM) optimization, we developed a compact prototype (34 × 34 × 3 mm³, 14.83 g) and experimentally verified its performance, achieving a peak rotational speed of 1573.14 RPM, torque output of 3.6 mN·m, and step displacement resolution of 45.8 μrad. These attributes enable smooth lens module switching for optical zoom, thus demonstrating the mechanism’s feasibility. Importantly, the PFSM offers precise positioning without relying on additional transmission parts and features a self-locking capability when de-energized, rendering it an ideal choice for camera zoom applications. In summary, this study underscores the PFSM’s potential as a compact, lightweight, and efficient camera zoom mechanism, contributing meaningfully to the field of imaging technology and optical systems.

Measuring the substructure mass power spectrum of 23 SLACS strong galaxy–galaxy lenses with convolutional neural networks

ABSTRACT Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy–galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian random field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favouring a high frequency power spectrum across our lens population.

A controllable interface design and manufacturing strategy for embossed glass hierarchical nano-lens

Constructing nanostructured surfaces on the macro/micro-scale optical lens is of great importance in the improvement of light transmittance, reflection, and surface functionality of optical devices. In this paper, a flexible and novel material interface design and manufacturing method for hierarchical macro/nano optical glass lenses is proposed. To verify the feasibility of the presented manufacturing strategy, the deformation history and flow driving mechanism of multiscale structured surfaces during second hot embossing were studied by simulations and experiments. The results showed that solid-like glass preform exhibits a higher nanoscale deformation resistance and elastic recovery, which can reduce the distortion levels of the nanostructured surface. At small scales, molecular confinement greatly reduces the tectonic deformation of nanostructured surface at relatively low applied heat and pressure. However, beyond a specific thermal energy threshold, nanostructured convex surfaces are easily compressed into a smooth flattened surface. By collaborative control of embossing conditions, the nano-surface integrity of multiscale structured surface can be ensured during second hot embossing. Compared to the smooth macroscale optical lens, the hierarchical macro/nano glass lens exhibited better optical transmittance and antireflection properties. The proposed design and manufacturing strategy provides a facile and flexible solution for building the hierarchical macro/micro/nanostructure functional optics.

A lensed radio jet at milli-arcsecond resolution – II. Constraints on fuzzy dark matter from an extended gravitational arc

ABSTRACT Using a single gravitational lens system observed at ≲ 5 mas resolution with very long baseline interferometry, we place a lower bound on the mass of the fuzzy dark matter (FDM) particle, ruling out mχ ≤ 4.4 × 10−21 eV with a 20:1 posterior odds ratio relative to a smooth lens model. We generalize our result to non-scalar and multiple-field models, such as vector FDM, with mχ,vec > 1.4 × 10−21 eV. Due to the extended source structure and high angular resolution of the observation, our analysis is directly sensitive to the presence of granule structures in the main dark matter halo of the lens, which is the most generic prediction of FDM theories. A model based on well-understood physics of ultra-light dark matter fields in a gravitational potential well makes our result robust to a wide range of assumed dark matter fractions and velocity dispersions in the lens galaxy. Our result is competitive with other lower bounds on mχ from past analyses, which rely on intermediate modelling of structure formation and/or baryonic effects. Higher resolution observations taken at 10–100 GHz could improve our constraints by up to two orders of magnitude in the future.

Clumpiness of lens galaxies as a window on dark matter

AbstractWhile the direct detection of the dark-matter particle remains very challenging, the physical properties of dark matter could potentially be constrained indirectly – by comparing the population characteristics of substructures in real galaxies with predictions from the phenomenological dark-matter models, such as cold, warm or self-interacting dark matter. Whereas these models are practically indistinguishable with respect to the expected abundance and statistical properties of massive galactic substructures, the critical difference lies in the low-mass regime ≲ 108M⊙. Galaxy-galaxy strong gravitational lensing provides a unique opportunity to search for gravitational signatures of such low-mass substructures in galaxies acting as a strong gravitational lens on a more distant background galaxy, serendipitously located along the same line of sight. In [Bayer et∼al.(2023)Bayer, Chatterjee, Koopmans, Vegetti, McKean, Treu, Fassnacht, and Glazebrook, Bayer et∼al.(2023)Bayer, Koopmans, McKean, Vegetti, Treu, Fassnacht, and Glazebrook, Bayer et∼al.(2023)Bayer, Vernardos, and Koopmans], we have recently introduced a novel approach to investigate the collective perturbative effect of low-mass substructures in the inner regions of massive elliptical lens galaxies and observationally constrain their power spectrum (on 1-10 kpc scales) based on the Fourier analysis of the associated surface-brightness anomalies in the lensed images (i.e., Einstein rings and gravitational arcs) observed with the Hubble Space Telescope. Here, we present a concise summary of the methodology, the encountered modelling challenges and the inferred observational constraints on the sub-galactic matter power spectrum. The future comparison of these results with predictions from hydrodynamical simulations might either verify the cold-dark-matter paradigm or require its substantial revision. Moreover, we demonstrate that the grid-based smooth lens modelling might model away surface-brightness anomalies caused by the presence of substructures in the lens galaxy and incorrectly interpret them as surface-brightness structure in the lensed background galaxy itself. If not properly understood and accounted for, such signal suppression might lead to severely biased constraints on the properties of substructures in galactic haloes.

The very knotty lenser: Exploring the role of regularization in source and potential reconstructions using Gaussian process regression

ABSTRACTReconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are included. Regularization has traditionally been used to constrain the solutions where the data failed to do so, e.g. in unlensed parts of the source. In this exploratory work, we go beyond the usual choices of regularization and adopt observationally motivated priors for the source brightness. We also perform a similar comparison when reconstructing lens potential perturbations, which are assumed to be stationary, i.e. permeate the entire field of view. We find that physically motivated priors lead to lower residuals, avoid overfitting, and are decisively preferred within a Bayesian quantitative framework in all the examples considered. For the perturbations, choosing the wrong regularization can have a detrimental effect that even high-quality data cannot correct for, while using a purely smooth lens model can absorb them to a very high degree and lead to biased solutions. Finally, our new implementation of the semi-linear inversion technique provides the first quantitative framework for measuring degeneracies between the source and the potential perturbations.

Comprehensive design method of a soft multifocal contact lens with NURBS.

This study presents a comprehensive method for designing a multifocal contact lens (MCL) with Snell's law and non-uniform rational B-spline (NURBS) curves. Instead of using thin lens approximation, general mathematical formulas have been developed to achieve the accurate coordinates of points on the anterior lens surface profile of the MCL to meet various given optical power distributions. Then the NURBS curve is adjusted to fit these data points to obtain the smooth front lens surface profile. This method not only improves the accuracy of the optical power profiles of MCLs but also reduces the spherical aberration in near/distance optical zones. The experimental results show that the power profiles of soft MCLs agree with those of the simulation results and original design requirements. The proposed method has been proven for the MCL design, and it can be feasibly applied in complex optical lens designs.

Christiansen filters realized with cylindrical lenses of even symmetry

A type of Christiansen filter that takes the form of a smooth cylindrical lens of even symmetry is proposed. By varying the shape of the lens, the filter can be made to realize many common filtering responses, including the polynomial function response, the Gaussian function response, and the sinc function response. A systematic design technique based on inverse scattering is established, and a desired, prescribed response can be tailored by properly shaping the lens of the filter. Three prototypical Christiansen filters, namely, a second-order all-real-roots filter, a second-order sinc filter, and a Gaussian filter, are synthesized using the proposed method. A prescribed response at 545 nm with a FWHM of 2 nm is achieved systematically by all of the three Christiansen filters.

Image segmentation for analyzing galaxy-galaxy strong lensing systems

Aims. The goal of this Letter is to develop a machine learning model to analyze the main gravitational lens and detect dark substructure (subhalos) within simulated images of strongly lensed galaxies. Methods. Using the technique of image segmentation, we turn the task of identifying subhalos into a classification problem, where we label each pixel in an image as coming from the main lens, a subhalo within a binned mass range, or neither. Our network is only trained on images with a single smooth lens and either zero or one subhalo near the Einstein ring. Results. On an independent test set with lenses with large ellipticities, quadrupole and octopole moments, and for source apparent magnitudes between 17−25, the area of the main lens is recovered accurately. On average, only 1.3% of the true area is missed and 1.2% of the true area is added to another part of the lens. In addition, subhalos as light as 108.5 M⊙ can be detected if they lie in bright pixels along the Einstein ring. Furthermore, the model is able to generalize to new contexts it has not been trained on, such as locating multiple subhalos with varying masses or more than one large smooth lens.

Imagist Poetry and Clinical Medicine: Arts of Observation, Precision, and Expression.

Microcosm Ajay Soni, MD A sympathetic drop in the tiny deep dark pool: the passage widens . . . A soft incandescent glow illuminates the bowl. The calculated curve of a smooth glass lens condenses reflected rays. A floating real image in glistening clarity: the web of blood and neurons onto which all the world projects. Vision Gurwant Kaur, MD Amber urine spin, don’t splash drop on glass. Focus. Here it comes: crystals and casts. Screening Sanam Razeghi, MD It comes into view the monster within this tunnel. Ominous tentacles of tissue climbing these walls while she sleeps. Time stutters. The clock spins faster. Life sputters on. Epinephrine Ann Ouyang, MD Pulsing plume on a gelatinous lake washed with cool water repools, flooding the plain carrying life away. The needle plunges a frost blanches the surface: crimson column wavering, collapsing. Water clears the murky lake restores the landscape. Heart Failure José Stoute, MD A horse gallops water settles and bubbles; the ground swells. Wisdom of Fingers George Simms, MD, PhD Light touch, soft belly; warm sun on the skin. Deep touch, firm mass; clouds move across a darkening sky. Progress Karuna Spiegelman, MD Bloody beefy breasts dripping crimson red, stench of rotting flesh as the tumor spreads. Tactile Navigation Shane Kinard, MD Glacially gliding, sinews submitting, a pop? Crystal elixir! Solitary Kathleen Julian, MD A dark building, lone doctor’s office light still on. Beacon bright. Burning…

Quantifying the structure of strong gravitational lens potentials with uncertainty-aware deep neural networks

ABSTRACTGravitational lensing is a powerful tool for constraining substructure in the mass distribution of galaxies, be it from the presence of dark matter sub-haloes or due to physical mechanisms affecting the baryons throughout galaxy evolution. Such substructure is hard to model and is either ignored by traditional, smooth modelling, approaches, or treated as well-localized massive perturbers. In this work, we propose a deep learning approach to quantify the statistical properties of such perturbations directly from images, where only the extended lensed source features within a mask are considered, without the need of any lens modelling. Our training data consist of mock lensed images assuming perturbing Gaussian Random Fields permeating the smooth overall lens potential, and, for the first time, using images of real galaxies as the lensed source. We employ a novel deep neural network that can handle arbitrary uncertainty intervals associated with the training data set labels as input, provides probability distributions as output, and adopts a composite loss function. The method succeeds not only in accurately estimating the actual parameter values, but also reduces the predicted confidence intervals by 10 per cent in an unsupervised manner, i.e. without having access to the actual ground truth values. Our results are invariant to the inherent degeneracy between mass perturbations in the lens and complex brightness profiles for the source. Hence, we can quantitatively and robustly quantify the smoothness of the mass density of thousands of lenses, including confidence intervals, and provide a consistent ranking for follow-up science.

Lens modelling of the strongly lensed Type Ia supernova iPTF16geu

ABSTRACT In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Σ ∝ r1 − η, and to constrain the universal expansion rate H0. Imaging with Hubble Space Telescope provides an upper limit on the slope η, in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller η implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for η ∼ 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, $H_0 \gtrsim 40\, {\rm km \ s^{-1} Mpc^{-1}}$, at 68.3 per cent confidence level.

Direct detection of dark matter substructure in strong lens images with convolutional neural networks

Strong gravitational lensing is a promising way of uncovering the nature of dark matter, by finding perturbations to images that cannot be accounted for well by modeling the lens galaxy without additional structure, be it subhalos (smaller halos within the smooth lens) or line-of-sight (LOS) halos. We present results attempting to infer the presence of substructure from images without requiring an intermediate step in which a smooth model has to be subtracted, using a simple convolutional neural network (CNN). We find that the network is only able to infer the presence of subhalos with greater than 75% accuracy when they have masses of greater than or equal to $5\ifmmode\times\else\texttimes\fi{}{10}^{9}{M}_{\ensuremath{\bigodot}}$ if they lie within the main lens galaxy. Since less massive foreground LOS halos can have the same effect as higher-mass subhalos, the CNN can probe lower masses in the halo mass function. The accuracy does not improve significantly if we add a population of less massive subhalos. With the expectation of experiments such as Hubble Space Telescope and Euclid yielding thousands of high-quality strong lensing images in the next years, having a way of analyzing images quickly to identify candidates that merit further analysis to determine individual subhalo properties while preventing extensive resources being used for images that would yield null detections could be very useful. By understanding the sensitivity as a function of substructure mass, nondetections could be combined with the information from images with substructure to constrain the cold dark matter scenario, in particular if the sensitivity can be pushed to lower masses.

Dual-surface lens with ring-shaped structures for optical tuning of GaN ultraviolet photodetectors at low temperature

This study aims to enhance the optical sensitivity of gallium nitride ultraviolet (UV) photodetectors at low temperatures using a multifunctional microlens with ring-shaped structures. This dual-surface lens with ring-shaped structures (i.e., DSLR), a unique microlens, was fabricated by employing a curable polymer and three-dimensional printed mold, and it has two primary regions: An upper and a lower region. The upper region of the DSLR serves as a smooth lens surface to focus the incident UV rays by delaying frost formation at low temperatures. The lower region captures condensed water droplets, thus allowing for only local frost formation. When compared to a photodetector without the DSLR, the photodetector covered by the DSLR generated a higher photocurrent at low temperatures (corresponding to a ∼13.85% increase in generated photocurrent in the temperature range of −20 °C to −1.2 °C). Thus, the findings of this study support the use of a facile, cost-effective, and multifunctional dual-surface polymer lens for higher-sensitivity UV detection in various low-temperature environments, such as the Arctic, outer space, and the environment within cryostats.

Dispensing Technology of 3D Printing Optical Lens with Its Applications

Current 3D printed lens technology faces reduced efficiency due to stepped and stacked lens surfaces. This research employs a faster jet dispensing method which reduces these issues. It uses UV-curable material and merges droplets before they are cured to obtain very smooth lens surfaces without any post-processing and without manufacturing a mold for lens structures. This technology can be applied to lens manufacturing in a variety of products, especially in the form of arrays, saving development time and reducing cost. Two experiments of LED (Light-emitting diode) lens and solar cell lens array mask implementations are presented to demonstrate the power of the method. Furthermore, this study analyzes the effect of different contact angles created by jet dispensing technology, including a detailed exploration of fluid viscosity and tooling heating parameters. Our results show that the LED lens can be manufactured to increase the luminous flux of large angles. Furthermore, the lens array mask for solar cells can be manufactured to reduce sunlight reflection and increase secondary refraction, which enables solar cells to achieve higher photoelectric conversion efficiency and to increase their power generation up to 4.82%.

Highly Magnified Stars in Lensing Clusters: New Evidence in a Galaxy Lensed by MACS J0416.1-2403

Abstract We examine a caustic-straddling arc at z = 0.9397 in the field of the galaxy cluster MACS J0416.1-2403 (z = 0.397) using archival multiband Hubble Space Telescope images and show that its surface brightness exhibits anomalies that can be explained by a single highly magnified star undergoing microlensing. First, we show that the surface brightness pattern is not perfectly symmetric across the cluster critical curve, which is inconsistent with a locally smooth lens model; the location of the candidate star exhibits the most significant asymmetry. Second, our analysis indicates that the asymmetric feature has ∼30% higher flux in the 2012 visits compared to the Frontier Fields program visits in 2014. Moreover, the variable asymmetric feature shows an anomalous color between the F814W and F105W filters in 2014. These anomalies are naturally explained by microlensing-induced variability of a caustic-transiting blue supergiant in a star-forming region, with a mean magnification factor around μ ∼ 200. We extend this study to a statistical analysis of the whole arc image and find tentative evidence of the increased mismatch of the two images in the proximity of the critical line. Robust detection of one or multiple caustic-transiting stars in this arc will enable detailed follow-up studies that can shed light on the small-scale structure of the dark matter inside the cluster halo.

3D Printed Radar Lenses with Anti-Reflective Structures

Background: The purpose of this study was to determine if 3D printed lenses with wavelength specific anti-reflective (AR) surface structures would improve beam intensity and thus radar efficiency for a Printed Circuit Board (PCB)-based 60 GHz radar. This would have potential for improved low-cost radar lenses for the consumer product market. Methods: A hyperbolic lens was designed in 3D Computer Aided Design (CAD) software and was then modified with a wavelength specified AR structure. Electromagnetic computer simulation was performed on both the ‘smooth’ and ‘AR structure’ lenses and compared to actual 60 GHz radar measurements of 3D printed polylactic acid (PLA) lenses. Results: The simulation results showed an increase of 10% in signal intensity of the AR structure lens over the smooth lens. Actual measurement showed an 8% increase in signal of the AR structure lens over the smooth lens. Conclusions: Low cost and readily available Fused Filament Fabrication (FFF) 3D printing has been shown to be capable of printing an AR structure coated hyperbolic lens for millimeter wavelength radar applications. These 3D Printed AR structure lenses are effective in improving radar measurements over non-AR structure lenses.

Adhesive Contact of Model Randomly Rough Rubber Surfaces

We study experimentally and theoretically the equilibrium adhesive contact between a smooth glass lens and a rough rubber surface textured with spherical microasperities with controlled height and spatial distributions. Measurements of the real contact area $A$ versus load $P$ are performed under compression by imaging the light transmitted at the microcontacts. $A(P)$ is found to be non-linear and to strongly depend on the standard deviation of the asperity height distribution. Experimental results are discussed in the light of a discrete version of Fuller and Tabor's (FT) original model (\textit{Proceedings of the Royal Society A} \textbf{345} (1975) 327), which allows to take into account the elastic coupling arising from both microasperities interactions and curvature of the glass lens. Our experimental data on microcontact size distributions are well captured by our discrete extended model. We show that the elastic coupling arising from the lens curvature has a significant contribution to the $A(P)$ relationship. Our discrete model also clearly shows that the adhesion-induced effect on $A$ remains significant even for vanishingly small pull-off forces. Last, at the local asperity length scale, our measurements show that the pressure dependence of the microcontacts density can be simply described by the original FT model.

Fast design method of smooth freeform lens with an arbitrary aperture for collimated beam shaping.

A method is presented for the fast design of a smooth freeform lens to tailor a collimated light beam with an arbitrary contour. This method begins by calculating an initial surface based on a simplified ray mapping. Then the surface is fitted by a system of Zernike polynomials, whose weights are treated as the optimization variables for further optimization. In the optimization, the objective function is analytically calculated using a partial differential-equation-based approach. To validate the effectiveness of the proposed method, a freeform lens is designed for a collimated Gaussian beam with a spline contour to form a uniform illumination distribution with another spline contour, which takes only 26 s. A freeform lens is also fabricated and experimented, and its practical performance approaches the design.

Minimal smooth lenses for perfect imaging of two wavefronts.

The problem of designing a lens for perfectly imaging two incident wavefronts into two respective refracted wavefronts is considered. In particular, the problem of deriving a unique such lens of prescribed smoothness is analyzed. Building upon an idea by Benitez and Minano et al., we propose a method for constructing such twice-differentiable lenses and derive equations for computing them. The theoretical considerations are supplemented by a few examples.