Optical Metrology Research Articles (Page 1)

Abstract The continued narrowing of transistor pitch in semiconductor chips has boosted the demand for deep-ultraviolet (DUV, λ < 280 nm)-based high-resolution optical inspection and metrology. However, the lack of a beam control device for DUV wavelength due to the significant UV absorption in most optical materials has hindered the handy implementation of conventional high-resolution metrology techniques such as structured illumination microscopy (SIM) to the DUV regime. Here, we present a programmable DUV structured illumination for nanometer-resolution pitch and displacement inspection of periodic samples enabled by nonlinear third-harmonic generation. By manipulating a spatial phase of the near-infrared (NIR, λ = 800 nm) driving beam that is incident on crystalline solids, the emitted third harmonic beam at DUV (λ = 266 nm) can be spatially controlled so as to form a high-visibility sinusoidal distribution with a real-time adjustable pitch and orientation angle. The angle-tunable DUV structured beam allows observation of low-visibility periodic sample information in high-visibility frequency-down-converted Moiré patterns, with a magnification factor of up to 70 times. By analyzing the Moiré pattern pitch and orientation angle, the sample periods of 277.8 nm and 416.7 nm were reconstructed with an error of 1.9% (5.4 nm) and 0.5% (2.1 nm), respectively. Furthermore, a 20.0 nm lateral shift of the periodic sample – below Abbe’s diffraction limit – was measured with a repeatability of 5.3 nm via monitoring of the magnified Moiré pattern. Our DUV structured illumination will enable high-resolution monitoring of semiconductor processes such as transistor pitch variation and mask alignment.

Abstract We present a theoretical study demonstrating that the photonic spin Hall effect (PSHE) can be both actively tuned and greatly amplified by exploiting the nonlocal, nonlinear optical response of a strongly interacting Rydberg gas operating under electromagnetically induced transparency (EIT). Rather than relying on fixed phase metasurfaces or conventional Kerr materials, long range interactions between Rydberg atoms create a spatially extended, intensity dependent refractive index profile that enables dynamic spin resolved beam deflection. In a glass–Rydberg–glass trilayer model, we show that the PSHE displacement can be varied smoothly in magnitude and even reversed in sign by adjusting atomic density, probe intensity, laser detunings, and interaction strength. This nonlocal nonlinearity transforms the typically weak PSHE into a macroscopically observable and dynamically controllable effect. Our results establish a versatile platform for reconfigurable spin-dependent photonic control, with potential applications in high-sensitivity optical metrology, spin-based beam steering, and tunable quantum-optical information processing.

Advanced manufacturing places stringent demands on measurement technologies, requiring ultra-high precision, non-contact operation, high throughput, and real-time adaptability. Optical metrology, with its distinct advantages, has become a key enabler in this context. This paper reviews optical metrology techniques from the perspective of precision manufacturing applications, emphasizing precision positioning and surface topography measurement while noting the limitations of traditional contact-based methods. For positioning, interferometers, optical encoders, and time-of-flight methods enable accurate linear and angular measurements. For surface characterization, techniques such as interferometry, structured light profilometry, and confocal microscopy provide reliable evaluation across scales, from large structures to micro- and nano-scale features. By integrating these approaches, optical metrology is shown to play a central role in bridging macroscopic and nano-scale characterization, supporting both structural assessment and process optimization. This review highlights its essential contribution to advanced manufacturing, and offers a concise reference for future progress in high-precision and intelligent production.

Fourier ptychographic microscopy (FPM) is a pivotal computational imaging technique that achieves phase and amplitude reconstruction with high resolution and a wide field of view, using low numerical aperture objectives and LED array illumination. Despite its unique strengths, FPM remains fundamentally limited in retrieving low spatial frequency phase information due to the absence of phase encoding in all on-axis and slightly off-axis (bright-field) illumination angles. To overcome this, we present a hybrid approach that combines FPM with the transport of intensity equation (TIE), enabling robust phase retrieval across a wide spatial frequency range without compromising system simplicity. Our method extends standard FPM acquisitions with a single additional on-axis defocused image, from which low-frequency phase components are reconstructed via the TIE method, employing large defocus distance to suppress low-frequency artifacts and enhance robustness to intensity noise. High-frequency phase details are recovered through FPM processing. To additionally compensate for defocus-induced magnification variations caused by spherical wavefront illumination, we employ an affine transform-based correction scheme upon image registration. Notably, by restoring the missing low-frequency content, our hybrid method allows for more reliable quantitative phase recovery than standard FPM. We validated our method using a quantitative phase test target for benchmarking accuracy and biological cheek cells, mouse neurons, and mouse brain tissue slice samples to demonstrate applicability for in vitro bioimaging. Experimental results confirm substantial improvements in phase reconstruction fidelity across spatial frequencies, establishing this hybrid FPM + TIE framework as a practical and high-performance solution for quantitative phase imaging in biomedical and optical metrology applications.

Abstract We demonstrate a label-free, far-field super-resolution imaging approach based on photonic nanojets generated by tapered dielectric fibers. By systematically analyzing the dependence of nanojet confinement and focal distance on cylinder diameter (8–16 μm), we establish a geometric design framework for tunable light localization below the diffraction limit. Using this insight, we fabricate a 12-μm waist-tapered optical fiber that produces a laterally extended nanojet for non-contact imaging. This configuration resolves grating lines with 92 nm width and spacing – dimensions beyond the classical resolution limit. Ray tracing simulations confirm the experimental magnification trend and show that fiber tilt enables tunable control over magnification and field of view. Our fiber platform provides scalable alignment, mechanical tunability, and extended working distances. These findings establish tapered fibers as compact and flexible photonic elements for delivering sub-wavelength light confinement, with applications in optical metrology, field enhancement, and scanning nanophotonic systems.

Aspera is a NASA’s Astrophysics Pioneers mission, led by the University of Arizona (UofA), designed to study the presence of hot gases (T=10 5 −10 6 K) in the circumgalactic medium (CGM) and how the flow of these gases affects galactic formation. One key enabling technology in the Aspera optical system is the use of more efficient UV-reflective optical coatings, particularly at around 103.2–103.8 nm, where the O VI emission doublet is located. To meet radiometric effective area requirements, an improved version of the Al+LiF optical coating used in FUSE [ Proc. SPIE 11819 , 1181903 ( 2021 ) PSISDG 0277-786X 10.1117/12.2593001 , Proc. SPIE 13093 , 1309302 ( 2024 ) PSISDG 0277-786X 10.1117/12.3017274 ] has been applied to the flight optics and gratings. This version is based on Al (aluminum) + eLiF (enhanced lithium fluoride), where Al+LiF is annealed at an elevated temperature (∼250 ∘ C) after deposition, thus providing enhanced optical performance at 103 nm when compared to standard Al+LiF. Furthermore, these optics are encapsulated with a thin film of atomic layer-deposited MgF 2 at the Jet Propulsion Laboratory for enhanced durability [ Proc. SPIE 11819 , 1181903 ( 2021 ) PSISDG 0277-786X 10.1117/12.2593001 , Proc. SPIE 9144 , 91444G ( 2014 ) PSISDG 0277-786X 10.1117/12.2057438 ]. The efficiency and durability of these UV-sensitive coatings depend on the quality of the optical surface in terms of surface roughness and cleanliness. Roughness increases the scatter of the coating and reduces the specular reflectance. Surface contaminants can accommodate moisture and other contaminants, increase scattering, and create weak points in the coating that may affect adhesion and, subsequently, the longevity of these coatings. Extensive optical metrology is necessary to quantify the impact of surface roughness and contaminants on optical surfaces. This paper provides information on the behavior of mirror substrates and FUV coatings throughout the full inspection and coating process implemented for Aspera’s optics at Goddard Space Flight Center, from the initial receipt of the optics through post-coating. Inspection and metrology techniques include atomic force microscopy (AFM), coherence scanning interferometry (CSI), dark field microscopy (DFM), and vacuum ultraviolet (VUV) spectroscopy. Combinations of these techniques are used to inspect flight optics at each of the following steps: (i) as-received, pre-cleaning inspection, (ii) pre-coating, post-cleaning inspection, and (iii) post-coating inspection. The evolution of roughness and other surface defects is compared between each step to quantify the effect each step has on the flight optics. The final far-ultraviolet (FUV) spectral performance of witness samples coated with the flight optics is also presented, with most witnesses showing unprecedented reflectance values of ≈0.83−0.84 at a 103 nm wavelength.

Accurate segmentation of interferogram is critical for optical measurements and metrology. Deep learning methods for interferogram segmentation represent a developing trend but face significant challenges due to the scarcity of annotated real interferograms. Although simulation techniques can provide alternative training data, substantial domain gaps between synthetic and real interferograms severely degrade neural network performance in practical scenarios. To bridge this gap, we proposed a fringe property-guided deep learning method that incorporates fringe property to guide what and how neural networks learn. The method contains a dual-level domain adaptation framework that synergistically integrates pixel-level and feature-level domain adaptation through joint optimization. Pixel-level domain adaptation enhances visual realism of simulated interferograms. Our feature-level domain adaptation method that leverages fringe semantics depends mainly on spatial structures. It guides the feature processing module to focus on structural patterns while de-emphasizing domain-sensitive distractors. Therefore, the neural network trained with this method will achieve enhanced cross-domain robustness. We also proposed a fringe-context-aware loss function that embeds the fringe continuity property to enhance neural network performance. This integrated approach achieves state-of-the-art segmentation using only 60 unlabeled real interferograms and 30 background images. Our method delivers an annotation-efficient solution for interferogram segmentation, offering actionable insights for deep learning optical image processing under domain shifts and label scarcity.

A new Optics Metrology Laboratory for assembling and characterizing beamline x-ray optical systems has been built. This replaces the old laboratory, which was demolished to make space for construction of a new flagship beamline for the forthcoming Diamond-II facility upgrade. The new cleanroom laboratory is located between several beamlines and laboratories, which intermittently generate significantly higher levels of acoustic noise and floor vibrations. A threefold design strategy was employed to create an ultra-stable environment for the sensitive, optical metrology instruments. First, the walls, ceiling and doors of the laboratory were constructed to attenuate acoustic noise. Second, the air handling systems were designed to minimize self-production of noise and vibrations. Finally, engineering solutions were developed to further isolate the metrology instruments from environmental fluctuations. Overall, despite higher levels of external disturbances, this strategy enables nano-metrology to be successfully conducted in the new laboratory. The shielded environment around each instrument achieves noise rating NR30, which is 5-25 dB quieter than the old laboratory. Over 60-h, the temperature inside the Diamond-NOM's enclosure varied by only 0.004 °C rms, and humidity changed by <1% RH. All optical metrology instruments are now performing better than in the old laboratory: the slope error repeatability of Diamond-NOM is improved from 15 to 9 nrad rms; the GTX micro-interferometer has measured super-polished substrates with micro-roughness <40pm rms; the new gantry for Speckle Angular Measurement is commissioned; and the HDX Fizeau interferometer has measured mirrors with slope errors <50 nrad.

Abstract Phase unwrapping is a fundamental procedure in optical metrology and image processing. The least-squares (LS) method has been widely adopted in phase unwrapping (PU) tasks due to its computational efficiency and mathematical elegance.Since PU-LS issues can be formulated as a two-dimensional integration, modal wavefront (MW) integration techniques have been extensively employed for the numerical solution. Although regional wavefront (RW) integration methods preserve the independence of measurement points through a distinctive geometric structure and offer improved robustness in the presence of incomplete data, they have not yet been applied to PU-LS issues. Therefore, this study introduces a Southwell RW integration approach based on Hermite interpolation and applies it to the PU-LS framework.Compared with existing MW and discrete cosine transform (DCT) methods, the proposed RW approach achieves a reduction of approximately 50% in peak-to-valley (PV) error. It exhibits superior robustness to phase occlusion. Experimental results validate the practical feasibility and effectiveness of the RW-based strategy for PU-LS applications.

Silica-on-silicon waveguides are widely used in various fields of optics, including optical fiber communications and optical metrology, because they have low-loss characteristics, mechanical and thermal stability, and mass producibility. To enable more sophisticated optical signal processing on silica-on-silicon platforms, the polarization of light must be controlled. A waveplate is a key functionality for polarization management. In this study, we demonstrated a waveplate integrated in a waveguide on a silica-on-silicon platform by managing the internal stress of the waveguide. Generally, silica-on-silicon waveguides have strong internal stress arising from their fabrication procedure, resulting in birefringence whose optic axis is aligned to the coordinates of the wafer substrate. We devised a waveplate function by forming a stress-relieving groove on one side of the waveguide. Because the internal stress is localized at the corners of the groove, oblique stress is induced in the waveguide, making the optic axis of the birefringence rotate. We analyzed the behavior of the internal stress by using a multi-physics finite element method and confirmed that the groove is effective in applying oblique stress to the waveguide. We also experimentally demonstrated that, by changing the distance from the waveguide core to the groove and the groove length, arbitrary retardation along an arbitrary optic axis can be achieved. As an example, the waveplate length required to achieve polarization conversion between orthogonal transverse electric (TE) and transverse magnetic (TM) modes at a wavelength of 1550 nm was experimentally confirmed to be approximately 3700 µm. This length is practical for typical silica-on-silicon waveguides, which generally allow bending radii of a few millimeters. The proposed structure does not simply rotate the polarization, but also controls the phase difference between polarizations, making it possible to generate arbitrary polarization states. Our method is versatile and can be applied to a variety of optical devices that require manipulation of polarizations.

Abstract Point‐of‐care diagnostics, in situ monitoring during nanomanufacturing, and in‐line metrology are stimulating demands for portable, ultracompact, and robust optical imaging and metrology systems. In this paper, an on‐chip computational wavefront sensor (OCWS) is proposed and demonstrated by fusing photonic integrated circuits and single‐layer metasurfaces. By simultaneously measuring the optical intensities coupled into the metagratings, OCWS enables the single‐shot acquisition of two orthogonal phase gradient images, from which the wavefront can be computationally reconstructed. Moreover, phase imaging of vortex beams and Gaussian phases is experimentally performed using the OCWS system. This miniaturized system may catalyze diverse applications such as point‐of‐care diagnostics, endoscopy, in situ QPI, and in‐line surface profile measurement.

MXenes have attracted significant attention in recent years due to their remarkable properties for electrochemical and optoelectronic applications. While the physical properties of MXene thin films, consisting of stacked delaminated flakes, have been extensively studied, the intrinsic MXene properties can only be derived from individual flakes. Indeed, flake interconnectivity, intercalated species, and film morphology introduce extrinsic factors that affect charge transport and optical properties. In this work, we quantitatively characterize the intrinsic optical, structural, and transport properties of micrometer-sized Ti3C2Tx MXene flakes by employing our non-invasive, advanced spectroscopic micro-ellipsometry (SME) technique in the visible-near-infrared spectral range. SME exploits back-focal-plane imaging in a reflection microscopy geometry to simultaneously capture the spectral and incidence-angle-dependent optical response of individual flakes with up to diffraction-limited lateral resolution. Through a comprehensive multi-flake analysis, encompassing flakes from mono- to 32 layers, we reveal thickness-dependent variations in the complex refractive index and charge transport properties of ultrathin flakes, where resistivity increases as the number of Ti3C2Tx layers (NoLs) decreases. Flake thicknesses, non-uniformities, and NoLs, determined via SME with sub-nm precision, closely match nanoscale observations from atomic force microscopy (AFM) and scanning transmission electron microscopy (STEM). Additionally, charge transport properties derived from SME agree with four-probe measurements performed on single-flake devices. Unveiling the intrinsic optical, structural, and charge transport properties of Ti3C2Tx MXene single flakes, this study establishes SME as a robust platform for quantitative MXene analyses, enabling precise optical metrology of MXene-based optoelectronic and electrochemical devices.

Abstract Residual stresses are one of the main challenges in metal additive manufacturing, particularly in direct metal laser sintering (DMLS). These stresses often lead to deformation once parts are removed from the build plate. In this study, we investigated the causal relationship between internal stresses and deformation behavior using a specially designed twin-cantilever geometry. This setup allowed parallel evaluation of different stress-relief treatments on a single component while minimizing cross-effects. High-precision optical 3D scanning was used to measure full-surface deformations before and after support removal and stress-relief heat treatment. The 1.2709 maraging steel (X3NiCoMoTi18-9-5) specimens were produced using a DMLS process with standard parameters, and stress-relief annealing was performed at 600 °C for 24 h. Results show that the heat treatment significantly reduced distortion on the supported side of the parts, with changes under 5%, while unsupported regions showed increased deformation, exceeding 60% in some cases. This indicates that internal stresses remain largely intact during heating and can further distort softened material if not mechanically constrained. The study confirms the critical role of constraint during heat treatment and demonstrates that optical metrology offers a reliable method to evaluate deformation trends. The results provide important insights into stress management strategies for DMLS parts and highlight the limitations of thermal relief in unconstrained geometries.

Lower-frequency characteristics of the terahertz regime confer advantageous low photon energy for biochemical sensing while imposing inherent sensitivity constraints. Here, we demonstrate a terahertz asynchronous twin-comb sensor and an extra-spectrum sensing mechanism through cascading microchannel architecture within a metallic waveguide. The extra-spectrum sensing prefigures an enhanced sensitivity of 4 orders of magnitude compared to existing terahertz biosensing and surpasses its counterpart in the optical band. Hypersensitivities of 0.398 GHz mm2 pg−1 in trace detection manifest through the located characteristic resonance frequency beyond the spectrum domain. Additionally, we observed the photoisomerization of azo dye in the terahertz band with a photoresponse sensitivity of 0.91 GHz cm2 mW−1, opening possibilities for photoactive material-assisted terahertz sensors. In summary, we instantiate an asynchronous twin-comb sensing beyond the spectrum domain, offering a perspective for ultrasensitive sensing, and promising applications in optical frequency comb precision metrology, artificial intelligence photonics, and integrated sensing and communications.

Accurate determination of molecular transition intensities is vital to quantum chemistry and metrology, yet even simple diatomic molecules have historically been limited to 0.1% accuracy. Here, we show that frequency-domain measurements of relative intensity ratios outperform absolute methods, achieving 0.003% accuracy using dual-wavelength cavity mode dispersion spectroscopy. Enabled by high-precision frequency metrology, this approach reveals systematic discrepancies with state-of-the-art ab initio calculations, exposing subtle electron correlation effects in the dipole moment curve. Applied to line-intensity ratio thermometry (LRT), our technique determines gas temperatures with 0.5 millikelvin statistical uncertainty, exceeding previous LRT precision by two orders of magnitude. These results redefine the limits of optical gas metrology and enable International System of Units–traceable measurements for applications from combustion diagnostics to isotopic analysis. Discrepancies of up to 0.02% in transition probability ratios challenge theorists to refine models, establishing intensity ratios as a paradigm in precision molecular physics.

The creation and manipulation of photonic skyrmions provide a novel degree of freedom for light-matter interactions, optical communication and nanometrology. Since the localized vortex within skyrmions arises from the twist and curl of the phase structure, the orbital angular momentum of light is essential for their construction. While numerous skyrmionic textures have been proposed, they are formed within the spatial domain and induced by the longitudinal orbital angular momentum. Here we theoretically propose and experimentally observe spatiotemporal skyrmions within a picosecond pulse wavepacket, generated through vectorial sculpturing of spatiotemporal wavepackets. The skyrmionic textures emerge within the spatiotemporal distribution of a vector field encompass all possible polarization states. Constructed upon the transverse orbital angular momentum, spatiotemporal skyrmions, in contrast to spatial skyrmions, exhibit no helical twisting perpendicular to the skyrmion plane, demonstrating potential stability against deformations or perturbations. These results expand the skyrmion family and offer new insights into optical quasiparticles, potentially leading to advanced applications in optical metrology, sensing, and data storage.

Conventional f-theta(f-θ) lens systems often rely on cascading multiple lenses or adopting complex surface profiles to achieve high-precision scanning and laser processing over a large field of view (FOV), leading to significant increases in system volume and manufacturing complexity. This study presents an ultra-thin f-θ lens for a 10.6µm laser processing system, realizing high-performance scanning through a collaborative optimization method of cascaded metasurfaces. Simulation results based on dual-layer cascaded metasurfaces show that within the ±32° light deflection range, the spot diameter remains below 20µm, the maximum f-θ distortion is controlled at 0.19%, and the Strehl ratio (SR) across the entire FOV exceeds 0.99, verifying the system's imaging performance approaching the diffraction limit. Phase sampling analysis of the cascaded metalenses indicates that when the sampling step varies within 3-9µm, there is no significant difference in spot performance, which greatly reduces the fabrication difficulty and cost. Further research demonstrates that when the phase mutation rate is controlled within 8%, the system maintains stable scanning characteristics, while exceeding 9% leads to severe wavefront distortion and drastic deterioration of optical performance, providing a quantitative basis for processing error control. The wavelength analysis of the designed f-θ lens reveals that it maintains good performance within an 80 nm bandwidth. This study provides an integrated solution for compact laser processing systems, and its technical achievements can promote the large-scale application of metasurface optical elements in optical imaging, optical metrology, and laser processing.

Ultra-low noise lasers are essential tools in various applications, including data communication, light detection and ranging (LiDAR), quantum computing and sensing, and optical metrology. Recent advances in integrated photonics, specifically the development of the ultra-low loss silicon nitride ($Si3N4$) platform, have allowed attaining performance that exceeds conventional legacy laser systems, including the phase noise of fiber lasers. This platform can be combined with the monolithic integration of piezoelectric materials, enabling frequency-agile low-noise lasers. However, this approach has not yet surpassed the trade-off between ultra-low frequency noise and frequency agility. Here, we overcome this challenge and demonstrate a fully integrated laser based on the $Si3N4$ platform with frequency noise lower than that of a fiber laser while maintaining the capability for high-speed modulation of the laser frequency. The laser achieves an output power of 30 mW with an integrated linewidth of 4.3 kHz and an intrinsic linewidth of 3 Hz, demonstrating phase noise performance that is on par with or lower than commercial fiber lasers. Frequency agility is accomplished via a monolithically integrated piezoelectric aluminum nitride micro-electro-mechanical system (MEMS) actuator, which enables a flat frequency actuation bandwidth extending up to 400 kHz. Such a MEMS device is one of the largest fabricated structures, featuring MHz-level bandwidth, which is significantly higher than the typical kHz-level bandwidth of similarly sized mm-scale MEMS devices. The chirp nonlinearity of the frequency-modulated output reaches 0.08% without any linearization or pre-distortion, making it compliant with the requirement for long-range FMCW LiDAR. This ultra-low noise and frequency-agility combination is a useful feature enabling tight laser locking for frequency metrology, fiber sensing, and coherent sensing applications. Our results demonstrate the ability of “next generation” integrated photonic circuits (beyond silicon) to exceed the performance of legacy laser systems in terms of coherence and frequency actuation.

In this work, we developed a vacuum-compatible long trace profiler (LTP) for in situ metrology of ultra-precise x-ray optics within synchrotron vacuum chambers. Although traditional LTPs operate ex situ under atmospheric pressure, earlier optical setups-such as that by Qian et al.-performed in situ distortion measurements by directing laser beams through vacuum viewports. While these configurations enabled in situ monitoring of mirror deformation, their accuracy was constrained by optical distortions from vacuum windows and by beam deviations caused by air turbulence. To overcome these limitations, we developed a fully in-vacuum LTP system installed directly inside the vacuum chamber, fully compatible with ultrahigh vacuum (UHV) conditions (<1 × 10-8 Torr). Based on the original Takacs LTP design, the system incorporates a vacuum-compatible CMOS sensor, an external laser to reduce heat and weight, and a motorized four-axis alignment stage. This system is designed to measure low-spatial-frequency slope error, which is critical for evaluating optical figure quality. Performance was validated under identical atmospheric conditions using a conventional LTP for comparison. Under identical conditions, the in-vacuum LTP measured slope errors of 100 nrad RMS (flat) and 200 nrad RMS (curved). However, measurable deviations in curvature radius and coma coefficient were observed, attributed to stage wobble and lens aberrations. These findings confirm baseline performance and demonstrate the system's feasibility for UHV-compatible slope metrology. The in-vacuum LTP is intended to support real-time slope monitoring and feedback correction of active optical components during operation at synchrotron beamlines.

Abstract The concept of the three-dimensional optical transfer function (3D-TF) has become an increasingly important tool in understanding and modeling the measurement behavior of modern optical surface metrology systems, particularly in the context of coherence scanning interferometry (CSI). The 3D-TF enables a comprehensive description of how spatial frequency components, both lateral and axial, of electromagnetic fields are transmitted through the optical system. This opens up a wide range of applications: from fast simulation of the measurement processes to enhanced signal analysis and surface reconstruction techniques, and to the full characterization and calibration of measurement systems. In this paper we describe our attempts to determine the 3D-TF, which was already calculated analytically, also in practice.