Diffraction Limit Research Articles

Intensity-Product-Based Optical Sensing to Beat the Diffraction Limit in an Interferometer.

The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.

A design of compact plasmonic lens consisting of high index dielectric gratings and metal nano-film

In this paper, a hybrid ultra-thin planar subwavelength focusing structure consisting of a high refractive index dielectric grating and a nano metal film was designed. The thickness of this structure is only 200 nm. Surface plasmon polaritons (SPPs) were excited from the nano metal film, propagated along the metal-air interface, and were then converted into a radiation field by the dielectric grating, forming a focused spot in free space. By adjusting the grating position and width parameters, the shape of the focused optical field could be controlled. The simulation results showed that, under 532 nm light irradiation, the lens could produce a 270 nm (full width at half-maximum, FWHM) spot size at a focal length of 2.46λ. Moreover, under the illumination of 633 nm and 780 nm light, the designed lenses were found to produce focal spot sizes of 304 nm (0.48λ) and 364 nm (0.47λ), respectively, which were smaller than the diffraction limit. The simplicity of this plasmonic lens design, coupled with its reduced thickness and minimal absorption loss, offered significant advantages in terms of cost-effectiveness and ease of fabrication.

Designing an imaging spectrometer with high resolution using manufacturable gradient-index (MGRIN) lenses with a linear distribution of refractive index.

In this work, an imaging spectrometer with a diffraction-limited resolution of 0.043nm is designed by using two manufacturable gradient-index (MGRIN) lenses with a linear refractive index distribution to suppress the aberrations. The MGRIN lenses are made from a combination of two separate base materials that their refractive indices are determined by the fractional composition of each base material at any point. The volume fraction of each base material in both lenses changes linearly from the front edge to the rear vertex of the lens. The input light to the spectrometer originates from a single-mode fiber with a core diameter of 9μm and a numerical aperture of 0.1. The parallel rays after passing through the collimator are diffracted by a diffraction grating with a number of grooves of 1200 g/mm. The criteria determining the quality of the image show that the aberrations of the image have been optimally controlled. Comparing the results of this design with some similar studies done by other researchers shows that the root-mean-square radius of the spot diagram and Airy disk radius are significantly smaller than those designs. In addition, the modulation transfer function diagram has a better fit with the diffraction limit curve. These results make our proposed spectrometer have a stronger resolution than those in previous studies.

Tuning the excitation laser power in a stochastic optical reconstruction microscope for Alexa Fluor 647 dye in Vectashield mounting media.

Super-resolution imaging techniques have fundamentally changed our understanding of cellular architecture and dynamics by surpassing the diffraction limit and enabling the visualization of subcellular details. The popular super-resolution method known as stochastic optical reconstruction microscopy (STORM) relies on the exact localization of single fluorescent molecules. The significance of employing Vectashield as a mounting medium for the super-resolution imaging scheme called direct STORM has recently been explored. Alexa Fluor 647 (AF647), one of the most popular dyes, shows significant blinking in Vectashield. However, to observe prominent blinking of the fluorophore for the reconstruction of super-resolved images, the power of the excitation laser needs to be tuned. This work demonstrates the tuning of excitation power density in the sample plane for superior imaging performance using AF647 in Vectashield. Samples comprising MDA-MB-231 breast cancer cell line are used for the experiments. The actin filaments of the cell are stained with phalloidin-conjugated AF647 dye. For the experiment, we employ a low-cost openFrame-based STORM system equipped with a programmable Arduino-regulated laser source emitting at 638nm. An excitation power density of 0.60 kW/cm2 at 638nm in the sample plane is observed to maximize the signal-to-noise ratio, the number of switching events, and the number of photons detected per event during image acquisition, thereby leading to the best imaging performance in terms of resolution. The outcome of this work will promote further STORM-based super-resolved imaging applications in cell biology using Alexa Fluor 647 in Vectashield.

Numerical Derivation of Dual Vortex Beam Generation using Polarization‐Sensitive Dielectric Metasurfaces

AbstractMetasurfaces, composed of arranged nanoscale particles, manipulate electromagnetic waves for tailored physical properties. Recently vortex beams, carrying orbital angular momentum, have been generated through metasurfaces to realize diverse applications. Here, the study introduces a metasurface capable of generating dual‐mode vortex beams, which combines the functionalities of chiral metalenses and vortex beam generation. These dual‐mode vortex beams exhibit varying characteristics depending on the polarization state of the incident light, offering improved control over orbital angular momentum. This advancement holds promise for enhancing applications such as optical communication, optical tweezers, and imaging for overcoming diffraction limit. By employing titanium dioxide (TiO2) for its efficiency, the design concept is validated through simulations and discuss considerations for fabrication. The proposed approach paves the way for compact optical systems with heightened adaptability.

High Resolution Nanostructuring of Perovskites With Tunable Morphologies by Ultrafast Laser Direct Writing

AbstractMetal halide perovskites (MHPs) have attracted increasing attention in various optoelectronic devices due to their exceptional optical and electrical properties. The high precision patterning of MHPs is crucial adjective for device fabrication, while it is severely hindered by the active and sensitive chemistry of MHPs. In this work, high resolution and tunable nanostructuring of 2D MHP films are achieved by ultrafast laser direct writing (ULDW). The feature size of the created structure is down to 47 nm (λ/21), which is far beyond the diffraction limit of the optical system. The study proves the critical influence of the thermodynamic properties of materials on structure morphologies and establish a new mechanism of molten phase self‐evolution (MPSE) for the formation of super‐solution convex structures, which provides a new understanding for ultrafast laser‐matter interaction and high‐resolution patterning with ULDW. Different structure morphologies bring tunable optical properties. The applications are demonstrated in multimode information storage and encryption. The findings open new approaches to achieve hyperfine multi‐morphological structures on MHPs, which can boost many MHPs integration applications in nanophotonics, on‐chip electronics, and information encryption.

Bessel-Beam Single-Photon High-Resolution Imaging in Time and Space

Synchronous laser beam scanning is a common technique used in single-photon imaging where the spatial resolution is primarily determined by the beam divergence angle. In this context, Bessel beams have been investigated as they can overcome the diffraction limit associated with traditional Gaussian beams. Notably, the central spot of a Bessel beam retains its size almost unchanged within a non-diffractive distance. However, the presence of sidelobes in the Bessel beam can negatively impact spatial resolution. To address this challenge, we have developed a single-photon imaging system with high-depth resolution, which allows for the suppression of echo photons from the sidelobe light in the depth image, particularly when their flight time differs from that of the central spot. In our LiDAR setup, we successfully achieved high-resolution scanning imaging with a spatial resolution of approximately 0.5 mm while also demonstrating a high-depth resolution of 12 mm.

Raman spectroscopy capabilities for advanced semiconductor technology devices

In semiconductor processing and metrology, Raman spectroscopy is a valuable characterization tool because of its nondestructive nature, high throughput, and versatility in terms of parameter sensitivity. However, with the miniaturization of semiconductor devices, the inherent diffraction limit of the optical technique becomes a roadblock. In order to re-enable the strengths of Raman spectroscopy at the nanometer scale, we exploit polarization-induced enhancement effects that focus the excitation light into the region of interest, without the need for external probes or particles. This allows the detection of structures with dimensions far smaller than the excitation wavelength, unlocking the strengths of Raman spectroscopy at the nanoscale for, e.g., stress and composition measurements. Moreover, under these conditions the experiment probes the totality of the materials stack and we show how this transforms the technique into a volumetric and geometric measurement. The result is a completely new application domain for Raman spectroscopy as a critical dimensional metrology toolkit for a wide variety of semiconducting and metallic materials.

Design of a catadioptric mid-wave infrared telecentric microscope with high numerical aperture and long working distance

Infrared microscopy is widely used in the field of thermal analysis. This paper proposes a design method for a catadioptric mid-wave infrared telecentric microscope system that solves the problem of traditional microscopy systems being unable to simultaneously meet high numerical aperture, long working distance and large magnification requirements. The system is composed of a microscope objective and a tubelens. The objective uses an improved Schwarzschild structure and is connected to the tubelens through an externally located pupil. The system works in the wavelength range of 3.7 μm–4.8 μm, achieves a 0.82 numerical aperture, a 15.5 mm working distance, an 8× magnification and a 2.75 μm object-side resolution. The image size of the detector is 17um, and the MTF of the microscope system at the detector cutoff frequency is greater than 0.2, which is close to the diffraction limit. Finally, tolerance analysis and athermal analysis are conducted on the system, and the results indicate that the system possesses good manufacturability and thermal stability.

Frequency-multiplexed aberration measurement for confocal microscopy.

In single-photon confocal fluorescence microscopy, optical aberration affects both excitation and detection light paths, thus can severely degrade image quality. We incorporated an adaptive optics (AO) module into a confocal microscope and used a frequency-multiplexed aberration measurement method to measure and correct sample-induced aberration. We demonstrated that this method can measure aberration using signals from features of different sizes and recover diffraction-limited imaging performance. Applying our AO confocal microscope to imaging through and within living zebrafish larvae, as well as in the mouse brain in vivo, we showed that aberration correction can substantially improve confocal image brightness, resolution, and contrast.

Broadband super-resolution wavelength-controlled zoom metalens

A design method is proposed for a broadband super-resolution wavelength-controlled zoom metalens with simultaneous modulation of phase, dispersion, and amplitude, and on the basis of enhancing the axial zoom capability of the metalens, the point spread function of the metalens is continuously compressed using the hierarchical direct binary search algorithm, so that the full width at half maximum of the metalens is continuously close to or even less than the diffraction limit of 0.5λ/NA (NA is the numerical aperture). As a theoretical verification, a super-resolution wavelength-controlled zoom metalens was designed operating in the wavelength range of 68–80 μm. The simulation results show that its axial zoom capability is about 1.65 times that of the conventional diffractive metalens, and the lateral resolution in the wavelength range of 68–80 μm is less than the diffraction limit.

Image metric-based multi-observation single-step deep deterministic policy gradient for sensorless adaptive optics.

Sensorless adaptive optics (SAO) has been widely used across diverse fields such as astronomy, microscopy, and ophthalmology. Recent advances have proved the feasibility of using the deep deterministic policy gradient (DDPG) for image metric-based SAO, achieving fast correction speeds compared to the coordinate search Zernike mode hill climbing (ZMHC) method. In this work, we present a multi-observation single-step DDPG (MOSS-DDPG) optimization framework for SAO on a confocal scanning laser ophthalmoscope (SLO) system with particular consideration for applications in preclinical retinal imaging. MOSS-DDPG optimizes N target Zernike coefficients in a single-step manner based on 2N + 1 observations of the image sharpness metric values. Through in silico simulations, MOSS-DDPG has demonstrated the capability to quickly achieve diffraction-limited resolution performance with long short-term memory (LSTM) network implementation. In situ tests suggest that knowledge learned through simulation adapts swiftly to imperfections in the real system by transfer learning, exhibiting comparable in situ performance to the ZMHC method with a greater than tenfold reduction in the required number of iterations.

Multiplexed spatial transcriptomics methods and the application of expansion microscopy.

While spatial transcriptomics has undeniably revolutionized our ability to study cellular organization, it has driven the development of a great number of innovative transcriptomics methods, which can be classified into in situ sequencing (ISS) methods, in situ hybridization (ISH) techniques, and next-generation sequencing (NGS)-based sequencing with region capture. These technologies not only refine our understanding of cellular processes, but also open up new possibilities for breakthroughs in various research domains. One challenge of spatial transcriptomics experiments is the limitation of RNA detection due to optical crowding of RNA in the cells. Expansion microscopy (ExM), characterized by the controlled enlargement of biological specimens, offers a means to achieve super-resolution imaging, overcoming the diffraction limit inherent in conventional microscopy and enabling precise visualization of RNA in spatial transcriptomics methods. In this review, we elaborate on ISS, ISH and NGS-based spatial transcriptomic protocols and on how performance of these techniques can be extended by the combination of these protocols with ExM. Moving beyond the techniques and procedures, we highlight the broader implications of transcriptomics in biology and medicine. These include valuable insight into the spatial organization of gene expression in cells within tissues, aid in the identification and the distinction of cell types and subpopulations and understanding of molecular mechanisms and intercellular changes driving disease development.

Expansion-assisted selective plane illumination microscopy for nanoscale imaging of centimeter-scale tissues.

Recent advances in tissue processing, labeling, and fluorescence microscopy are providing unprecedented views of the structure of cells and tissues at sub-diffraction resolutions and near single molecule sensitivity, driving discoveries in diverse fields of biology, including neuroscience. Biological tissue is organized over scales of nanometers to centimeters. Harnessing molecular imaging across intact, three-dimensional samples on this scale requires new types of microscopes with larger fields of view and working distance, as well as higher throughput. We present a new expansion-assisted selective plane illumination microscope (ExA-SPIM) with aberration-free 1×1×3 μm optical resolution over a large field of view (10.6×8.0 mm 2 ) and working distance (35 mm) at speeds up to 946 megavoxels/sec. Combined with new tissue clearing and expansion methods, the microscope allows imaging centimeter-scale samples with 250×250×750 nm optical resolution (4× expansion), including entire mouse brains, with high contrast and without sectioning. We illustrate ExA-SPIM by reconstructing individual neurons across the mouse brain, imaging cortico-spinal neurons in the macaque motor cortex, and visualizing axons in human white matter.

ISCAT microscopy and particle tracking with tailored spatial coherence

Interferometric scattering (iSCAT) microscopy has demonstrated unparalleled performance among label-free optical methods for detecting and imaging isolated nanoparticles and molecules. However, when imaging complex structures such as biological cells, the superposition of the scattering fields from different locations of the sample leads to a speckle-like background, posing a significant challenge in deciphering fine features. Here, we show that by controlling the spatial coherence of the illumination, one can eliminate the spurious speckle without sacrificing sensitivity. We demonstrate this approach by positioning a rotating diffuser coupled with an adjustable lens and an iris in the illumination path. We report on imaging at a high frame rate of 25 kHz and across a large field of view of 100µm×100µm, while maintaining diffraction-limited resolution. We showcase the advantages of these features by three-dimensional (3D) tracking over 1000 vesicles in a single COS-7 cell and by imaging the dynamics of the endoplasmic reticulum (ER) network. Our approach opens the door to the combination of label-free imaging, sensitive detection, and 3D high-speed tracking using wide-field iSCAT microscopy.

Bayesian multi-exposure image fusion for robust high dynamic range ptychography.

The limited dynamic range of the detector can impede coherent diffractive imaging (CDI) schemes from achieving diffraction-limited resolution. To overcome this limitation, a straightforward approach is to utilize high dynamic range (HDR) imaging through multi-exposure image fusion (MEF). This method involves capturing measurements at different exposure times, spanning from under to overexposure and fusing them into a single HDR image. The conventional MEF technique in ptychography typically involves subtracting the background noise, ignoring the saturated pixels and then merging the acquisitions. However, this approach is inadequate under conditions of low signal-to-noise ratio (SNR). Additionally, variations in illumination intensity significantly affect the phase retrieval process. To address these issues, we propose a Bayesian MEF modeling approach based on a modified Poisson distribution that takes the background and saturation into account. The expectation-maximization (EM) algorithm is employed to infer the model parameters. As demonstrated with synthetic and experimental data, our approach outperforms the conventional MEF method, offering superior phase retrieval under challenging experimental conditions. This work underscores the significance of robust multi-exposure image fusion for ptychography, particularly in imaging shot-noise-dominated weakly scattering specimens or in cases where access to HDR detectors with high SNR is limited. Furthermore, the applicability of the Bayesian MEF approach extends beyond CDI to any imaging scheme that requires HDR treatment. Given this versatility, we provide the implementation of our algorithm as a Python package.

Automatic dendritic spine segmentation in widefield fluorescence images reveal synaptic nanostructures distribution with super-resolution imaging.

Dendritic spines are the main sites for synaptic communication in neurons, and alterations in their density, size, and shapes occur in many brain disorders. Current spine segmentation methods perform poorly in conditions with low signal-to-noise and resolution, particularly in the widefield images of thick (10 μm) brain slices. Here, we combined two open-source machine-learning models to achieve automatic 3D spine segmentation in widefield diffraction-limited fluorescence images of neurons in thick brain slices. We validated the performance by comparison with manually segmented super-resolution images of spines reconstructed from direct stochastic optical reconstruction microscopy (dSTORM). Lastly, we show an application of our approach by combining spine segmentation from diffraction-limited images with dSTORM of synaptic protein PSD-95 in the same field-of-view. This allowed us to automatically analyze and quantify the nanoscale distribution of PSD-95 inside the spine. Importantly, we found the numbers, but not the average sizes, of synaptic nanomodules and nanodomains increase with spine size.

3985Utilizing EllipticalRingIMI-Plasmonic Waveguides, Nanomaterials in Nanophotonic Structure for All-Optical 2 × 1 Demultiplexer

In many industries, particularly electronics, photonic devices are indispensable. However, the diffraction limit and miniaturization are the two problems that have hampered the development of photonics devices. These problems are resolved by plasmonic devices, which enable nanophononics and nanodevices. One of the primary all-optical demultiplexer components utilized in an all-optical Athematic Logic Unit (ALU), which is regarded as the basic building block for all-optical computers, is a plasmonic demultiplexerThis paper provides a new design for an elliptical ring insulator-metal-insulator (IMI) plasmonic waveguide-based all-optical demultiplexer (Demux). The suggested device has a small footprint (300 nm × 250 nm) and works at a 1550 nm wavelength. Demux has a 0.5 transmission threshold between logic zero and logic one states. Transmission (T), extinction ratio (contrast ratio (CR)), modulation depth (MD), and insertion loss (IL) are the four metrics that best explain the performance of the plasmonic Demux. The suggested structural dimensions are outstanding and optimal based on the values of MD for Demux which is (95.87%). The device's maximum transmission efficiency is 56.84%. The suggested plasmonic Demux structure makes a substantial contribution to all-optical signal processing Nano-circuits and nano-photonics integrated circuits. Using COMSOL Multiphysics, wesimulate the proposed plasmonic Demux using the Finite Element Method (FEM).

Singular dielectricnanolaser with atomic-scale field localization.

Compressing the optical field to the atomic scale opens up possibilities for directly observing individual molecules, offering innovative imaging and research tools for both physical and life sciences. However, the diffraction limit imposes a fundamental constraint on how much the optical field can be compressed, based on the achievable photon momentum1,2. In contrast to dielectric structures, plasmonics offer superior field confinement by coupling the light field with the oscillations of free electrons in metals3-6. Nevertheless, plasmonics suffer from inherent ohmic loss, leading to heat generation, increased power consumption and limitations on the coherence time of plasmonic devices7,8. Here we propose and demonstrate singular dielectric nanolasers showing a mode volume that breaks the optical diffraction limit. Derived from Maxwell's equations, we discover that the electric-field singularity sustained in a dielectric bowtie nanoantenna originates from divergence of momentum. The singular dielectric nanolaser is constructed by integrating a dielectric bowtie nanoantenna into the centre of a twisted lattice nanocavity. The synergistic integration surpasses the diffraction limit, enabling the singular dielectricnanolaser to achieve an ultrasmall mode volume of about 0.0005 λ3 (λ, free-space wavelength), along with an exceptionally small feature size at the 1-nanometre scale. To fabricate the required dielectric bowtie nanoantenna with a single-nanometre gap, we develop a two-step process involving etching and atomic deposition. Our research showcases the ability to achieve atomic-scale field localization in laser devices, paving the way for ultra-precise measurements, super-resolution imaging, ultra-efficient computing and communication, and the exploration of light-matter interactions within the realm of extreme optical field localization.

Ptycho-endoscopy on a lensless ultrathin fiber bundle tip

Synthetic aperture radar (SAR) utilizes an aircraft-carried antenna to emit electromagnetic pulses and detect the returning echoes. As the aircraft travels across a designated area, it synthesizes a large virtual aperture to improve image resolution. Inspired by SAR, we introduce synthetic aperture ptycho-endoscopy (SAPE) for micro-endoscopic imaging beyond the diffraction limit. SAPE operates by hand-holding a lensless fiber bundle tip to record coherent diffraction patterns from specimens. The fiber cores at the distal tip modulate the diffracted wavefield within a confined area, emulating the role of the ‘airborne antenna’ in SAR. The handheld operation introduces positional shifts to the tip, analogous to the aircraft’s movement. These shifts facilitate the acquisition of a ptychogram and synthesize a large virtual aperture extending beyond the bundle’s physical limit. We mitigate the influences of hand motion and fiber bending through a low-rank spatiotemporal decomposition of the bundle’s modulation profile. Our tests demonstrate the ability to resolve a 548-nm linewidth on a resolution target. The achieved space-bandwidth product is ~1.1 million effective pixels, representing a 36-fold increase compared to that of the original fiber bundle. Furthermore, SAPE’s refocusing capability enables imaging over an extended depth of field exceeding 2 cm. The aperture synthesizing process in SAPE surpasses the diffraction limit set by the probe’s maximum collection angle, opening new opportunities for both fiber-based and distal-chip endoscopy in applications such as medical diagnostics and industrial inspection.