Microlens Research Articles

The Search for Exoplanets: Methods and History

The discovery of exoplanets, planets beyond the solar system, has raised key questions about extraterrestrial life and the technology needed to find it. While considerable progress in exoplanet detection has been achieved over the past three decades, the methods currently in use still face notable limitations. Indeed, the detection of exoplanets has come a long way since its first confirmation in 1992. At first, these celestial objects were considered as figment of movies and science fiction, but it is credible today that Radial Velocity, Transit, Gravitational Microlensing, Direct Imaging, and Astrometry approaches have found these planetary bodies. While each of the methods works well, all techniques possess specific systematic errors depending on orbital radius, planetary size, and so on. For the past few decades, missions like Hubble, Spitzer as well as Kepler have delivered the fundamental catalogs and enormously improved the knowledge in the field of exoplanets. Recent developments, specifically with the JWST, have provided new ideas with indications of biosignatures on planet exoplanet K2-18b. The future prospects for exoplanet discovery also look good, for example, with the help of the machine learning for analysis and planned instruments like Nancy Grace Roman Space Telescope and the concept of Habitable Worlds Observatory. These observatories are oriented towards the search of potentially habitable exoplanets and for exploration of other universal enigmatic processes. In this paper, the advancement of technique in identifying exoplanets is outlined with specific focus on significant accomplishments, trends, technologies, and future outlook, which shows a fairly promising field that holds great potential for finding more habitable planets.

Transport-of-intensity phase imaging using commercially available confocal microscope.

Confocal microscopy is an indispensable tool for biologists to observe samples and is useful for fluorescence imaging of living cells with high spatial resolution. Recently, phase information induced by the sample has been attracting attention because of its applicability such as the measurability of physical parameters and wavefront compensation. However, commercially available confocal microscopy has no phase imaging function. We reborn an off-the-shelf confocal microscope as a phase measurement microscope. This is a milestone in changing the perspective of researchers in this field. We would meet the demand of biologists if only they had measured the phase with their handheld microscopes. We proposed phase imaging based on the transport of intensity equation (TIE) in commercially available confocal microscopy. The proposed method requires no modification using a bright field imaging module of a commercially available confocal microscope. The feasibility of the proposed method is confirmed by evaluating the phase difference of a microlens array and living cells of the moss Physcomitrium patens and living mammalian cultured cells. In addition, multi-modal imaging of fluorescence and phase information is demonstrated. TIE-based quantitative phase imaging (QPI) using commercially available confocal microscopy is proposed. We evaluated the feasibility of the proposed method by measuring the microlens array, plant, and mammalian cultured cells. The experimental result indicates that QPI can be realized in commercially available confocal microscopy using the TIE technique. This method will be useful for measuring dry mass, viscosity, and temperature of cells and for correcting phase fluctuation to cancel aberration and scattering caused by an object in the future.

Transport-of-intensity differential phase contrast imaging: defying weak object approximation and matched-illumination condition

Quantitative phase imaging (QPI) has emerged as a promising label-free imaging technique with growing importance in biomedical research, optical metrology, materials science, and other fields. Partially coherent illumination provides resolution twice that of the coherent diffraction limit, along with improved robustness and signal-to-noise ratio, making it an increasingly significant area of study in QPI. Partially coherent QPI, represented by differential phase contrast (DPC), linearizes the phase-to-intensity transfer process under the weak object approximation (WOA). However, the nonlinear errors caused by WOA in DPC can lead to phase underestimation. Additionally, DPC requires strict matching of the illumination numerical aperture (NA) to ensure the complete transmission of low-frequency information. This necessitates precise alignment of the optical system and limits the flexible use of objective and illumination. In this study, the applicability of the WOA under different coherence parameters is explored, and a method to defy WOA by reducing the illumination NA is proposed. The proposed method uses the transport-of-intensity equation through an additional defocused intensity image to recover the lost low-frequency information due to illumination mismatch, without requiring any iterative procedure. This method overcomes the limitations of DPC being unable to recover large phase objects and does not require the strict illumination matching conditions. The accurate quantitative morphological characterization of customized artifact and microlens arrays that do not satisfy WOA under non-matched-illumination conditions demonstrated the precise quantitative capability of the proposed method and its excellent performance in the field of measurement. Meanwhile, the phase retrieval of tongue slices and oral epithelial cells demonstrated its application potential in the biomedical field. The ability to accurately recover phase under a concise and implementable optical setup makes it a promising solution for widespread application in various label-free imaging domains.

Analysis of the Full Spitzer Microlensing Sample. I. Dark Remnant Candidates and Gaia Predictions

In the pursuit of understanding the population of stellar remnants within the Milky Way, we analyze the sample of ∼950 microlensing events observed by the Spitzer Space Telescope between 2014 and 2019. In this study we focus on a subsample of nine microlensing events, selected based on their long timescales, small microlensing parallaxes, and joint observations by the Gaia mission, to increase the probability that the chosen lenses are massive and the mass is measurable. Among the selected events we identify lensing black holes and neutron star candidates, with potential confirmation through forthcoming release of the Gaia time-series astrometry in 2026. Utilizing Bayesian analysis and Galactic models, along with the Gaia Data Release 3 proper-motion data, four good candidates for dark remnants were identified: OGLE-2016-BLG-0293, OGLE-2018-BLG-0483, OGLE-2018-BLG-0662, and OGLE-2015-BLG-0149, with lens masses of 3.0−1.3+1.8M⊙ , 4.7−2.1+3.2M⊙ , 3.15−0.64+0.66M⊙ and 1.40−0.55+0.75M⊙ , respectively. Notably, the first two candidates are expected to exhibit astrometric microlensing signals detectable by Gaia, offering the prospect of validating the lens masses. The methodologies developed in this work will be applied to the full Spitzer microlensing sample, populating and analyzing the timescale (t E) versus parallax (π E) diagram to derive constraints on the population of lenses in general and massive remnants in particular.

An integrated hot embossing and thermal reflow method for precision manufacture of plano-convex glass microlens arrays

An integrated hot embossing and thermal reflow method for precision manufacture of plano-convex glass microlens arrays

Electromagnetic signatures of black hole clusters in the center of super-Eddington galaxies

Supermassive black holes (SMBHs) at the centers of active galaxies are fed by accretion disks that radiate from the infrared or optical to the X-ray bands. Several types of objects can orbit SMBHs, including massive stars, neutron stars, clouds from the broad- and narrow-line regions, and X-ray binaries. Isolated black holes with a stellar origin (BHs of ∼10 M⊙) should also be present in large numbers within the central parsec of the galaxies. These BHs are expected to form a cluster around the SMBH as a result of the enhanced star formation rate in the inner galactic region and the BH migration caused by gravitational dynamical friction. However, except for occasional microlensing effects on background stars or gravitational waves from binary BH mergers, the presence of a BH population is hard to verify. In this paper, we explore the possibility of detecting electromagnetic signatures of a central cluster of BHs when the accretion rate onto the central SMBH is greater than the Eddington rate. In these supercritical systems, the accretion disk launches powerful winds that interact with the objects orbiting the SMBH. Isolated BHs can capture matter from this dense wind, leading to the formation of small accretion disks around them. If jets are produced in these single microquasars, they could be sites of particle acceleration to relativistic energies. These particles in turn are expected to cool by various radiative processes. Therefore, the wind of the SMBH might illuminate the BHs through the production of both thermal and nonthermal radiation.

Low-cost, high-volume, manufacturable 0.88 NA multi-wavelength diffractive lens array for optical document security

We design, manufacture, and characterize a high-numerical-aperture (NA=0.88, f/0.27), multi-wavelength (480 nm, 550 nm, and 650 nm) multilevel diffractive microlens array (MLA). This MLA achieves multi-wavelength focusing with a depth of focus (DoF) twice the diffraction-limited value. Each microlens in the array is closely packed with a diameter of 70 µm and a focal length of 19 µm in air. The MLA is patterned on one surface of a polymer film via UV casting, positioning the focal plane at the distal end of the polymer film. Each microlens focuses light at three design wavelengths into a focal spot with an estimated FWHM of ∼310nm. By placing this MLA directly on a standard high-resolution banknote print (minimum feature width of 10–15 µm), we demonstrate color-integral imaging for anti-counterfeiting. In contrast, refractive MLAs cannot achieve high-NA, multi-wavelength focusing or extended DoF. The extended DoF of our MLA ensures reliable performance despite variations in the polymer film’s thickness. Our MLA, produced via UV casting, enables extremely low-cost, high-volume production, making it ideal for flat optics in banknotes and document security.

Analysis the State-of-art Exoplanets Exploring Schemes: Radial Velocity, Transit and Gravitational Microlensing

Since the first planet beyond the solar system managed to be examined in 1995, the concept of “exoplanet” has been created. The exoplanet, officially defined as extrasolar planets circling other stars that are not part of the solar system, quickly arose an influential curiosity, as scientists began to consider how many stars and planets truly exist in the periphery of the solar system and what the properties of these objects have. In the following years, a series of detection schemes appeared and applied to this theme. This study has listed five of them that are utilized most in current decades, providing a specific view of the Radial velocity method, Transit method, and Gravitational microlensing method. Each of these three explores exoplanets depends on different theories, like Doppler shifts of the RV method, the light variations of the transit method caused by the shadow of planets, and the subtle peaks of luminance of the microlensing method. By outlining the information of several instruments, the goal is to obtain a comprehensive understanding and concise synopsis of the methods employed in the exoplanetary area, which may provide with fresh inspiration to create more sophisticated appliances by understanding the underlying principles of the ones that already exist.

Full-angle light out-coupling enhancement of quantum dot light-emitting diodes by Mie-scattering micro-lens arrays

High efficiency, high brightness, and long-life quantum dot light-emitting diodes (QLEDs) are crucial for realizing integrated display and lighting applications. However, about 80% of the light is confined inside the device with substrate mode, waveguide mode, and plasma mode, which greatly weakens the brightness, efficiency and lifetime of the device. Here, a quasi-periodic concave template with large area was fabricated through the spontaneous condensation of droplets on the substrate surface. Based on the quasi-periodic template, SiO2 micro-lens arrays (SiO2-MLAs) Mie scattering composite structure was fabricated by imprinting on a SiO2-nanosphere thin film, which significantly improved light out-coupling at full angles with optimized quasi-Lambertian luminescence characteristics. In comparison to the planar QLED with state-of-the-art, the external quantum efficiency (EQE) demonstrated a qualitative improvement (>20%). Accordingly, the EQE, luminance (L), T50 lifetime (reduce to half brightness) of the green QLEDs with SiO2-MLAs structure have been optimized by 22%, 28%, 31%, and up to 24.21%, 381962.6 cd/m2, 111335 h, respectively. This strategy provides valuable insights into mass-producing and utilizing SiO2-MLA Mie scattering composite structures to boost QLED performance in high-efficiency display and lighting applications.

Scalable fabrication approach and fill factor optimization for single pixel microlens arrays

Microlenses are a suitable approach to improve the performance of optical systems. An important optical efficiency determining parameter is the fill factor, which describes the relation of the lens area to the total optical active area. In this work, an optimization of the fill factor by optimizing the fabrication process steps is presented. The approach here is the use of i-line waferstepper lithography in combination with thermal reflow of photoresist and subsequent 1:1 pattern transfer in the lens material by reactive ion etching. For this method, the fill factor is determined by the minimum lens gap and, thus, the optical efficiency is strongly limited by the resolution limit of the i-line waferstepper lithography (350 nm). The goal of this investigation is to achieve the lowest possible lens gap even below the stepper-based resolution limit by optimizing each single process step without developing a new approach. The final result of the optimization was a fill factor improvement of 15%.

Fabrication of Microstructured Hydrogels via Dehydration for On-Demand Applications.

Microstructured hydrogels show promising applications in various engineering fields from micromolds to anisotropic wetting surfaces and microfluidics. Although methods like molding by, e.g., casting as well as 3D printing are developed to fabricate microstructured hydrogels, developing fabrication methods with high controllability and low-cost is an on-going challenge. Here, a method is presented for creating microstructures through the dehydration of double network hydrogels. This method utilizes common acrylate monomers and a mask-assisted photopolymerization process, requiring no complex equipment or laborious chemical synthesis process. The shape and profile of microstructures can be easily controlled by varying the exposure time and the mask used during photopolymerization. By altering the monomer and the mask used for fabricating the second network hydrogel, both convex and concave microstructures can be produced. To showcase the utility of this method, the patterned hydrogel is utilized as a mold to fabricate a polydimethylsiloxane microlens array via soft lithography for imaging application. In addition, a patterned hydrogel surface exhibiting obvious anisotropic wetting properties and open microfluidic devices which can achieve fast directional superspreading within milliseconds are also fabricated to demonstrate the versatility of the method for different engineering fields.

Size and kinematics of the low-ionization broad emission line region from microlensing-induced line profile distortions in gravitationally lensed quasars

Microlensing-induced distortions of broad emission line profiles observed in the spectra of gravitationally lensed quasars can be used to probe the size, geometry, and kinematics of the broad-line region (BLR). To this end, single-epoch Mg ii or Halpha line profile distortions observed in five gravitationally lensed quasars, J1131-1231, J1226-0006, J1355-2257, J1339+1310, and HE0435-1223, have been compared with simulated ones. The simulations are based on three BLR models, a Keplerian disk (KD), an equatorial wind (EW), and a polar wind (PW), with different sizes, inclinations, and emissivities. The models that best reproduce the observed line profile distortions were identified using a Bayesian probabilistic approach. We find that the wide variety of observed line profile distortions can be reproduced with microlensing-induced distortions of line profiles generated by our BLR models. For J1131, J1226, and HE0435, the most likely model for the Mg ii and Halpha BLRs is either KD or EW, depending on the orientation of the magnification map with respect to the BLR axis. This shows that the line profile distortions depend on the position and orientation of the isovelocity parts of the BLR with respect to the caustic network, and not only on their different effective sizes. For the Mg ii BLRs in J1355 and J1339, the EW model is preferred. For all objects, the PW model has a lower probability. As for the high-ionization C iv BLR, we conclude that disk geometries with kinematics dominated by either Keplerian rotation or equatorial outflow best reproduce the microlensing effects on the low-ionization Mg ii and Halpha emission line profiles. The half-light radii of the Mg ii and Halpha BLRs are measured in the range of 3 to 25 light-days. We also confirm that the size of the region emitting the low-ionization lines is larger than the region emitting the high-ionization lines, with a factor of four measured between the sizes of the Mg ii and C iv emitting regions in J1339. Unexpectedly, the microlensing BLR radii of the Mg ii and Halpha BLRs are found to be systematically below the radius-luminosity ($R -L$) relations derived from reverberation mapping, confirming that the intrinsic dispersion of the BLR radii with respect to the $R-L$ relations is large, but also revealing a selection bias that affects microlensing-based BLR size measurements. This bias arises from the fact that, if microlensing-induced line profile distortions are observed in a lensed quasar, the BLR radius should be comparable to the microlensing Einstein radius, which varies only weakly with typical lens and source redshifts.

Comparative analysis of microlens array formation in fused silica glass by laser: Femtosecond versus picosecond pulses

The growing demand for flexible, high-quality fabrication of free-form micro-optics drives the development of laser-based fabrication techniques for both the shape formation and surface polishing of optical elements. In this paper, we performed a thorough and systematic study on fused silica glass ablation using 10 ps and 320 fs duration pulses. Ablation processes for both pulse durations were optimized based on the measurements of the removed material layer thickness and surface roughness, and by analyzing the topographies of ablated cavities to remove material layers as thin as possible with minimum surface damage. Our findings demonstrate higher process resolution and surface quality for femtosecond pulses. Ablation of pre-roughened glass reduced the minimal removable glass layer thickness well below the 1 μm mark for both pulse durations, improving the process resolution. The minimal removable glass layer thickness was 14 times smaller for the femtosecond pulses, with up to 4.5 times lower surface roughness compared to samples processed with picosecond pulses. On the other hand, results revealed faster glass removal rates with picosecond pulses. In the end, arrays of microlenses were fabricated with both pulse durations and subsequently polished with a CO2 laser. Results revealed higher performance of microlenses fabricated with femtosecond pulses, providing better focusing capabilities and lesser beam scattering. Finally, this study demonstrated the successful fabrication of free-form optical elements with femtosecond and picosecond pulses, demonstrating the versatility and the potential of laser-based techniques.

Research on the NI-MLA Method for Enhancing the Spot Position Detection Accuracy of Quadrant Detectors Under Atmospheric Turbulence

The distorted spots induced by atmospheric turbulence significantly degrade the spot position detection accuracy of the quadrant detector (QD). In this paper, we utilize angular measurement and homogenization characteristics of non-imaging microlens array (NI-MLA) systems, effectively reducing the distortion degree of the spots received on the QD target surface, thereby significantly enhancing the spot detection accuracy of the QD. First, based on the principles of geometric optics and Fourier optics, it is proved that the NI-MLA system possesses the angular measurement characteristic (AMC) within the paraxial region while deriving and verifying the focal length of the system. Then, the QD computation curve characteristics of the system under non-turbulence are explored. This study further elucidates the mathematical principle of the NI-MLA system for mitigating the spot position detection random error of QD (SPDRE-QD) and discusses in depth the relationship between the NI-MLA system’s capability to mitigate the SPDRE-QD and the system’s parameters under various turbulence intensities. Finally, it is experimentally verified that the root-mean-square error (RMSE) of the QD computation values using the NI-MLA system are reduced by a significant improvement of at least 2.44 times and up to 17.36 times compared with that of the conventional optical system of QD (COS-QD) under turbulence conditions ranging from weak to strong.

A Review: Laser Interference Lithography for Diffraction Gratings and Their Applications in Encoders and Spectrometers

The unique diffractive properties of gratings have made them essential in a wide range of applications, including spectral analysis, precision measurement, optical data storage, laser technology, and biomedical imaging. With advancements in micro- and nanotechnologies, the demand for more precise and efficient grating fabrication has increased. This review discusses the latest advancements in grating manufacturing techniques, particularly highlighting laser interference lithography, which excels in sub-beam generation through wavefront and amplitude division. Techniques such as Lloyd’s mirror configurations produce stable interference fringe fields for grating patterning in a single exposure. Orthogonal and non-orthogonal, two-axis Lloyd’s mirror interferometers have advanced the fabrication of two-dimensional gratings and large-area gratings, respectively, while laser interference combined with concave lenses enables the creation of concave gratings. Grating interferometry, utilizing optical interference principles, allows for highly precise measurements of minute displacements at the nanometer to sub-nanometer scale. This review also examines the application of grating interferometry in high-precision, absolute, and multi-degree-of-freedom measurement systems. Progress in grating fabrication has significantly advanced spectrometer technology, with integrated structures such as concave gratings, Fresnel gratings, and grating–microlens arrays driving the miniaturization of spectrometers and expanding their use in compact analytical instruments.

Fabrication of high-quality microlens arrays on fused silica based on combined rapid evaporative ablation and precision melting polishing of CO2 lasers

Microlens arrays (MLAs) made from fused silica possess broad applications in wavefront sensing, optical focusing, beam shaping, etc. However, it is challenging to fabricate the hard-brittle silica MLAs with high accuracy and low cost by conventional manufacturing techniques efficiently. In this work, a novel two-step method, which consists of rapid evaporative ablation and precision melting polishing by CO2 lasers, is proposed to fabricate high-quality MLAs. The first step is to rapidly ablate and engrave micro-pillar arrays (MPAs) with flat groove bottom by high-energy density CO2 lasers. The second step is to precisely polish and shape the flat-topped MPAs into the dome-topped MLAs with good surface roughness (Sa) by low-energy density CO2 lasers. The whole preparation process could be achieved through a set of machining system. Firstly, the geometric dimension (period, p and height, h) of the microlens is determined by the Monte Carlo ray tracing method. Secondly, to diminish the groove depth inconsistency caused by heat accumulation, the multiple ablation compensation strategy is developed. The MPAs (p = 200–400 μm), of which maximum height error is 7.1%, are prepared in 1 s by the proposed compensation strategy. Then, the MPAs are smoothed into the MLAs by low-energy density CO2 lasers, and the average Sa is improved from 960 nm to 32.56 nm. Finally, the optical performances of the MLAs are verified from the effectiveness of imaging, focusing and homogenization. The proposed two-step processing method paves a new way to fabricate high-performance MLAs on hard-brittle fused silica with low cost and high efficiency.

Dark lens candidates from Gaia Data Release 3

Gravitational microlensing is a phenomenon that allows us to observe the dark remnants of stellar evolution, even if these bodies are no longer emitting electromagnetic radiation. In particular, it can be useful to observe solitary neutron stars or stellar-mass black holes, providing a unique window through which to understand stellar evolution. Obtaining direct mass measurements with this technique requires precise observations of both the change in brightness and the position of the microlensed star. The European Space Agency's satellite can provide both. Using publicly available data from different surveys, we analysed events published in the Data Release 3 ( ) microlensing catalogue. Here, we describe our selection of candidate dark lenses, where we suspect the lens is a white dwarf (WD), a neutron star (NS), a black hole (BH), or a mass-gap object, with a mass in the range between the heaviest NS and the least massive BH. We estimated the mass of the lenses using information obtained from the best-fitting microlensing models, source star, Galactic model, and the expected parameter distributions. We found eleven candidates for dark remnants: one WDs, three NSs, three mass-gap objects, and four BHs.

Through the looking glass into the dark dimension: Searching for bulk black hole dark matter with microlensing of [formula omitted]-ray pulsars

Primordial black holes (PBHs) hidden in the incredible bulk of the dark dimension could escape constraints from non-observation of their Hawking radiation. Since these five-dimensional (5D) PBHs are bigger, colder, and longer-lived than usual 4D PBHs of the same mass M, they could make all cosmological dark matter if 1011≲M/g≲1021, i.e., extending the 4D allowed region far down the asteroid-mass window. We show that these evasive PBHs could be search for by measuring their X-ray microlensing events from faraway pulsars. We also show that future X-ray microlensing experiments will be able to probe the interesting range (1016.5≲M/g≲1017.5g) where an all dark matter interpretation in terms of 4D Schwarzschild PBHs is excluded by the non-observation of their Hawking radiation.

Learned liquid crystal microlens array for joint optimized deep optical architecture in identifying metameric materials.

Multispectral imaging holds great promise for the detection of metameric materials. However, traditional multispectral imaging systems are characterized by their large volume, complex structure, and high computational requirements, limiting their practical application. We propose a jointly optimized deep optical architecture that combines the liquid crystal (LC) microlens array (MLA) characteristics and a multi-level perceptual spectral reconstruction network (MLP-SRN). The core of the architecture is to integrate the physical properties of the LC-MLA into the MLP-SRN using point spread function (PSF) optical convolution kernels, decoupling the light-field characteristic information collected by the LC-MLA at different voltages. Experimental results demonstrate that the incorporation of the physical properties of the LC-MLA not only reduces the system size and computational complexity but demonstrates excellent performance in identifying a metameric material.

Exploiting incoherent synthetic apertures in integral imaging for optical super-resolution.

Integral imaging (InIm) working with a pixelated device (e.g., a display panel) and a microlens array (MLA) suffers from low spatial resolution because of a significant trade-off between the spatial and angular resolution. The system bandwidth is presumed to be limited by the Nyquist frequency set by the pixel pitch. This study demonstrates that InIm intrinsically works in an incoherent synthetic aperture (ISA) manner with unexploited resolution capabilities. The sampling shifts between lenslets can be controlled and utilized to construct "computational galvos" to introduce varying aliasing; as a result, the Nyquist frequency is broken for optical super-resolution (SR). In particular, an InIm system can be configured for an N-fold oversampling rate with N lenslets. Furthermore, in an InIm display, the fill factor of a pixel's emitting area is always lower than 100%, so the bandwidth limit set by the pixel shape, i.e., two times the Nyquist frequency, is loosened. An InIm display prototype was built with an oversampling rate of four and a pixel fill factor of 75%. In the experiment, the proposed SR method achieved a 2.12 times resolution without dynamic devices or time-multiplexing.