Pattern Interferometer Research Articles

Depth range extended digital holography for precise 3D profile imaging via dual frequency interval sweeping

A 3D profile imaging method is proposed by using digital holography swept at dual frequency intervals. The dual frequency interval sweeping is achieved by altering the frequency of the tunable laser with two selected frequency intervals. An infrared camera was used to capture the interferometric patterns during two sweeping periods, and depth profile was reconstructed from multiple digital holograms. Phase image across the target region is extracted at each frequency and the phase at each pixel is varied as the frequencies are swept at a prefixed interval in each period. From measured phases, the congruence equations are constructed to achieve the 3D profile of the target object. The proposed sweeping method extends the measurement range by about ten times compared to the classical single frequency interval sweeping method, with a high depth accuracy of within 20 μm over a range of 4 cm. The proposed method is verified by both numerical simulation and experiment. Automatic extraction of reconstructed distances is achieved to facilitate automated 3D profile imaging.

Wafer Edge Metrology and Inspection Technique Using Curved-Edge Diffractive Fringe Pattern Analysis

Abstract This paper introduces a novel wafer-edge quality inspection method based on analysis of curved-edge diffractive fringe patterns, which occur when light is incident and diffracts around the wafer edge. The proposed method aims to identify various defect modes at the wafer edges, including particles, chipping, scratches, thin-film deposition, and hybrid defect cases. The diffraction patterns formed behind the wafer edge are influenced by various factors, including the edge geometry, topography, and the presence of defects. In this study, edge diffractive fringe patterns were obtained from two approaches: (1) a single photodiode collected curved-edge interferometric fringe patterns by scanning the wafer edge and (2) an imaging device coupled with an objective lens captured the fringe image. The first approach allowed the wafer apex characterization, while the second approach enabled simultaneous localization and characterization of wafer quality along two bevels and apex directions. The collected fringe patterns were analyzed by both statistical feature extraction and wavelet transform; corresponding features were also evaluated through logarithm approximation. In sum, both proposed wafer-edge inspection methods can effectively characterize various wafer-edge defect modes. Their potential lies in their applicability to online wafer metrology and inspection applications, thereby contributing to the advancement of wafer manufacturing processes.

Compact Single-Shot Dual-Wavelength Interferometry for Large Object Measurement with Rough Surfaces

Single-shot dual-wavelength interferometry offers a promising avenue for surface profile measurement of dynamic objects. However, current techniques employing pixel multiplexing or color cameras encounter challenges such as complex optical alignment, limited measurement range, and difficulty in measuring rough surfaces. To address these issues, this study presents a novel approach to single-shot dual-wavelength interferometry. By utilizing separated polarization illumination and detection, along with a monochromatic polarization camera and two slightly different wavelengths, this method enables the simultaneous recording of two frames of separated interferometric patterns. This approach facilitates straightforward optical alignment, expands measurement ranges, accelerates data acquisition, and simplifies data processing for dual-wavelength interferometry. Consequently, it enables online shape measurement of large dynamic samples with rough surfaces.

Opto-mechatronic dynamic characteristics in iron oxide-based nanofluid using spatial and frequency domain analysis

Iron oxide nanoparticles (IONPs) exhibit low toxicity and high chemical stability, attractive for developing of nanofluids (NFs) for advanced medical applications. This research focuses on the study of the optical, mechanical, and electrical dynamics of iron oxide–ethanol NFs. A novel sensitive methodology for analyzing the influence of nanoparticles (NPs) over the optical and electrical processes exhibited by IONFs is reported. The IONPs were synthesized by a microemulsion route and were characterized by transmission electron microscopy, scanning electron microscopy, and X-ray diffraction. The NPs exhibit a mean diameter of 30 nm and they were identified as Fe2O3. UV–Vis spectroscopy allows us determining the volume fraction of the fluid as a function of time. The assistance of a Michelson interferometer integrated with an image processing methodology was employed to explore the dynamics of the nanostructures. The percentage of NPs involved in linear and nonlinear dynamic fluid processes was estimated by taking a double-stage (spatial and frequency domains) Fast Fourier Transform in the interferometric pattern. A DC voltage source was used to study the electrical conductivity of the NF as it was being sedimented. The opto-mechatronic parameters were correlated, considering the volume fraction as the main variable to determine the optical and electrical characteristics. For the Fe2O3 NF, it is identified that the linear effects of sedimentation present a stronger impact on the optical properties, while the nonlinear interactions have more influence on the electrical conductivity. The main findings of this research have potential applications in rheological instrumentation to analyze complex effects using transient opto-mechatronic components.

Interferometric characterization of high-frequency piezoelectric effects in hydroxyapatite thin films

Hydroxyapatite (HAp) qualities such as biocompatibility and piezoelectricity make it an excellent material for biomedical applications. Here, HAp thin film samples were fabricated onto silica substrates to study their piezoelectric behavior with optical interference. Thin solid films were deposited using previously synthesized HAp powder, sol-gel, and spin-coating techniques. The samples were characterized by scanning electron microscopy, energy dispersive X-ray, Raman, and UV-Vis spectroscopies. The statical piezoelectric effect of the samples was studied by using a finite element method and computational software. Additionally, an experimental Bode analysis allows computing the internal electrical components of the films using high-frequency AC voltage. The electrical behavior is related to the equivalent circuit of a piezoelectric crystal, which indicates the range of frequencies where the electromechanical effect is maximum. A Sagnac interferometer was used to characterize the strain in the HAp as a function of the electrical input frequency. The displacement of the interferometric fringe pattern allows us to estimate the change in the thickness of the sample and compute the piezoelectric constant. The synthesis of HAp thin films with piezoelectric properties provides an effective way to produce sensors and actuators for technological applications.

Line-edge-roughness characterization of photomask patterns and lithography-printed patterns

This paper presents the line-edge-roughness (LER) characterization of the photomask patterns and the lithography-printed patterns by enhanced knife edge interferometry (EKEI) that measures the interferometric fringe patterns occurring when the light is incident on the patterned edge. The LER is defined as a geometric deviation of a feature edge from an ideal sharp edge. The Fresnel number-based computational model was developed to simulate the fringe patterns according to the LER conditions. Based on the computational model, the photomask patterns containing LER features were designed and fabricated. Also, the patterns were printed on the glass wafer by photolithography. The interferometric fringe patterns of those two groups of patterns were measured and compared with the simulation results. By using the cross-correlation method, the LER effects on the fringe patterns were characterized. The simulation and experimental results showed good agreement. It showed that the amplitude of the fringe pattern decreases as the LER increases in both cases: photomask patterns and printed wafer patterns. As a result, the EKEI and its analysis methods showed the potential to be used in photomask design and pattern metrology, and inspection for advancing semiconductor manufacturing processes.

The influence of the tear film on the intraocular pressure and the corneal biomechanical properties analyzed with the Ocular Response Analyzer

PurposeAs ocular dryness and glaucoma are more prevalent with increasing age, understanding how the tear film affects tonometry is important. The present study aims to understand the impact that changes in the tear film have on intraocular pressure (IOP), corneal hysteresis, and corneal resistance factor measurements. MethodsCross-sectional research was conducted and 37 patients were assessed. The tear film lipid layer and the non-invasive break-up time (NIBUT) were evaluated using the Tearscope Plus (Keeler, Windsor, UK). Dry eye symptoms were evaluated using the Ocular Surface Disease Index (OSDI) questionnaire. IOP was measured using rebound tonometry and the Ocular Response Analyzer (ORA, Reichert). Corneal biomechanical properties were measured using ORA. ResultsIt was found that an increase in the IOP measured with the iCare was directly correlated with the subclass that evaluated symptomatology associated with environmental factors (r = 0.414, p<0.05, Spearman). Goldmann-correlated IOP (IOPg) and Corneal-compensated IOP (IOPcc) values were statistically significantly different between the various interferometric patterns (p<0.05). It was also found that an increase in the corneal biomechanical properties measured with ORA was directly correlated with the overall scores obtained when using the OSDI and some of its subclasses. ConclusionsTear film interferometric patterns were shown to have some impact on the IOP measured using ORA. The IOP measured with iCare seems to be related to the symptomatology obtained from OSDI. Corneal biomechanical properties were related to the OSDI total score and some of its subclasses. An increase in symptomatology was associated with an increase in the measured biomechanical properties of the cornea.

Dynamic imaging of interfacial electrochemistry on single Ag nanowires by azimuth-modulated plasmonic scattering interferometry

Direct visualization of surface chemical dynamics in solution is essential for understanding the mechanisms involved in nanocatalysis and electrochemistry; however, it is challenging to achieve high spatial and temporal resolution. Here, we present an azimuth-modulated plasmonic imaging technique capable of imaging dynamic interfacial changes. The method avoids strong interference from reflected light and consequently eliminates the parabolic-like interferometric patterns in the images, allowing for a 67-fold increase in the spatial resolution of plasmonic imaging. We demonstrate that this optical imaging approach enables comprehensive analyses of surface chemical dynamics and identification of previously unknown surface reaction heterogeneity by investigating electrochemical redox reactions over single silver nanowires as an example. This work provides a general strategy for high-resolution plasmonic imaging of surface electrochemical dynamics and other interfacial chemical reactions, complementing existing surface characterization methods.

Modelling, experimental validation and analysis of a multiple stage PC-PMF Sagnac loop interferometer with spectral shape versatility using an optimized fitting algorithm

Here we experimentally demonstrate a multi-stage Sagnac loop with high spectral shape versatility by employing a serial sequence of different polarization controllers (PC) and Polarization-Maintaining Fibres (PMF), and we develop a general mathematical model to simulate it for N PMF stages inside of its loop using the Jones formalism. Our model is then validated for the cases of 2 and, for the first time, 3 stages by comparing the numerical simulation results with the experimental data, achieving a very small Root Mean Squared Error (RMSE) of around 10−4. Additionally, we propose a heuristic optimization capable of retrieving physical information from the measured spectra about the polarization states inside the loop, opening up the possibility of the use of such modelling as an interrogation tool for sensing applications. Finally, we perform a brief analysis of the interferometric pattern curves obtained in order to further understand its versatility. This spectral flexibility makes such interferometers interesting candidates for use as tunable optical filters and quasi-distributed sensors.

Speckle-noise filtering based on non-local mean sparse principal component analysis method

Speckle-noise filtering is an extensive and key process in coherent interferometric techniques to obtain important and accurate information from the recorded interferogram or fringe pattern. The speckle-noise inherent to these interferograms, recorded by digital image sensors in these optical techniques, is eliminated by an appropriate image processing method. Since the beginning and further development of these techniques, a wide variety of speckle noise filtering methods and techniques have been proposed. The present research work aims to exploit the performance of the non-local sparse principal component analysis (NLS-PCA) method for speckle noise reduction as applied to the interferometric fringe patterns obtained from digital holographic and digital speckle pattern interferometric techniques. The performance of the NLS-PCA is evaluated on numerical simulations using different types of speckle fringe patterns resulting in the method being highly effective in filtering the speckle noise and providing superior results evaluated in terms of peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), Edge preservation Index (EPI), and Equivalent Number of look (ENL), in comparison to widely known methods such as windowed Fourier transform method, Lee filter, Weiner filter. Furthermore, the proposed method maintains the finer details and preserves the fringe edges effectively. The performance of the NLS-PCA method is also demonstrated on experimental speckle fringe patterns and digital holograms.

Complete numerical description of the laser-induced thermal profile in a liquid, to explain complex self-induced diffraction patterns

In the past, laser propagation in a fluid with heat transfer has been modeled using simplistic conduction and convection conditions yielding inaccurate predictions. Here we present a detailed numerical study describing the thermal profile of the fluid and its interaction with the laser. Furthermore, we evaluate the diffraction field in the far field produced by a pump beam impinging in the fluid and the interferometric pattern obtained normal to the propagation direction to test our model. Direct comparison between experimental results and numerical simulation allows for a complete understanding of the energy transfer from the laser to the liquid and the subsequent effect on the laser propagation. Spatial self-phase modulation and propagation control from small-phase diffraction to aberration-controlled diffraction and up to diffraction oscillation are observed and explained with our modeling.

Conjugate complex function coupling strategy of interferometric field: Synthetic-wavelength interferometric fringe extraction in simultaneous dual-wavelength interferometry

Simultaneous dual-wavelength interferometry (SDWI) supplies a better solution to extend the measurement range of traditional single-wavelength interferometry with higher efficiency. To decompose the needed longer beat-frequency synthetic-wavelength (λS) information from the generated moiré fringe pattern in SDWI, a conjugate complex function coupling strategy (CCFC) of interferometric field is proposed in this study. By the Fourier transform and the half-band filter in one side of the spectrum, the positive half spectrum is obtained. The inverse Fourier transform and conjugate operation are performed on the half spectrums to obtain the two conjugate complex functions of the interferometric field. Coupled by the multiplication for the conjugate complex functions, the lower beat-frequency synthetic-wavelength interferometric fringe pattern is derived directly. And if the SDWI is implemented with the π/2 phase shift at λS, the obtained phase-shift interferogram for λS could be demodulated by the conventional phase-shift algorithm. Compared with other spatial-domain Fourier transform demodulation theory, the half-band filter used in CCFC method is appropriate for the different spectral width and carrier spatial frequency. The necessary introduced linear carrier is merely about 0.0947 times of the carrier in the former numerically. And it is only used to pursue the separation between the ±1 order phase lobes instead of the separation between the different wavelength phase lobes. The feasibility and applicability of the CCFC method are verified using simulation and experimental results.

Measurement of the fractional topological charge of an optical vortex beam through interference fringe dislocation.

An optical vortex beam carrying fractional topological charge (TC) has become an immerging field of interest due to its unique intensity distribution and fractional phase front in a transverse plane. Potential applications include micro-particle manipulation, optical communication, quantum information processing, optical encryption, and optical imaging. In these applications, it is necessary to know the correct information of the orbital angular momentum, which is related to the fractional TC of the beam. Therefore, the accurate measurement of fractional TC is an important issue. In this study, we demonstrate a simple technique to measure the fractional TC of an optical vortex with a resolution of 0.05 using a spiral interferometer and fork-shaped interference patterns. We further show that the proposed technique provides satisfactory results in cases of low to moderate atmospheric turbulences, which has relevance in free-space optical communications.

Microstructured molecular BIO-gratings by means of UV induced denaturation - INVITED

Rapid, reliable and low cost techniques to fabricate biosensors is a hot topic nowadays. Here, we present a BIO-grating fabricated by means of local, selective denaturing of molecules using UV radiation. A phase-mask is used to generate an interferometric pattern of 1420 nm pitch that, when illuminating a biolayer of BSA molecules lead to its periodic deactivation. After the biorecognition of the specific antibody, aBSA, a BIO-grating is generated due to the height difference between the protein, and the complex protein + antibody. We present the optimization of the fabrication of the BIO-gratings and their AFM characterization. Also, the biosensor performance in terms of limit of detection and limit of quantification will be presented.

Interference of Gaussian and/or Airy beams in coupled PT-symmetric nonlocal system

We investigate the interference of Gaussian and/or Airy beams based on coupled parity-time (PT) symmetric nonlocal nonlinear Schrödinger (NNLS) equation, which can be decoupled into two paraxial diffraction equations through a general linear transformation under the balance among nonlocal nonlinear effects. Various superposed solutions of the coupled NNLS equation can be obtained with the help of linear transformation and the solutions of linear diffraction equation. Based on these solutions, we analytically explore the abundant interference phenomena of Gaussian beam train, two Gaussian and/or Airy beams, which can be modulated by the linear transformation, the transverse displacement and relative phase difference between adjacent beams. The results presented here may be helpful to design complex interferometric patterns that can be applied to photoetching or optical printing etc.

Highly selective, compact and efficient vertical in-coupling for interferometric optical biosensors

One of the challenges in using integrated optical biosensors is their ability to operate in environments outside laboratories. This occurs, among other reasons, because suitable source coupling components are not considered at the design stage. In this work, a highly selective, compact and efficient in-coupling method is proposed with the aim to develop a genuine Point-of-care (PoC) platform. The proposed configuration consists of a single-mode fiber core placed in parallel and centered above an inverted non-linear taper, which can also be seen as a pigtailed input stage. These components are separated by the cladding of the taper that acts as a gap. In this setup, light is coupled from the fiber to the taper, which then becomes the core of a multimode waveguide. The coupled modes depend on the position of the fiber and the geometry of the taper. For interferometric biosensors, the power distribution between the modes is very important because each one reacts differently to the sample placed on the optical transducer. Therefore, the selectivity of the coupling stage affects the interferometric pattern and, consequently, the detection process. In the model presented in this work, the input is set as the fundamental mode (LP01) of the fiber. Since it is centered, only the even modes are excited in the taper. The width of the taper varies from 2 µm to 3 µm, in order to select only high-order modes, due to their large evanescent tails lead to highly sensitive biosensors. The non-linear format optimizes the design by dividing the entire taper into a cascade of linear sections. Those in which the coupling of the desired modes occurs are prioritized by increasing their lengths, thus making the transition smoother. Instead, the other sections maintain a reduced length. To select other modes or change the power distribution between them, one may just simply change the width of the taper and the length of the prioritized sections. In this work, a fiber-to-taper configuration of 8 mm length is presented, which couples 48% and 17% of the input power to TE8 and TE10 modes, respectively.

Investigation of the Effect of Molecular Weight, Density, and Initiator Structure Size on the Repulsive Force between a PNIPAM Polymer Brush and Protein

This paper focuses on the effect of degree of polymerization (N), density ( σ ), and pattern size ( x ) on the interaction force between a periodically patterned Poly(N-isopropylacrylamide) (PNIPAM) brush and protein. The hydrophobic interaction, the Van der Waals attractive force, and the steric repulsive force were expressed in terms of N , σ , and x . The osmotic constant (k1) and the entropic constant (k2) were determined from the fit of the steric repulsive force to an experimentally obtained force distance curve. The osmotic constant was 0.105, and the entropic constant was 0.255. Using these constants, the steric repulsive force was plotted as a function of the separation distance(s) between the substrate and the protein. The forces were determined at a separation distance equal to 0.3 nm, where L0 is the equilibrium thickness of the PNIPAM brush. At this separation distance, the value of the steric repulsive force was much higher than the value of the sum of the hydrophobic interaction and the Van der Waals attractive force for large degree of polymerization ( N &gt; 100 ) and density ( σ &gt; 0.2 chains/nm2). However, the repulsive force was comparable to the sum of the hydrophobic interaction and the Van der Waals attractive force for a small degree of polymerization ( N &lt; 100 ) and density ( σ = 0.2 ). Furthermore, the steric repulsive force was plotted as a function of pattern size x . The plot indicated that the steric repulsive force becomes nearly zero for all degrees of polymerization and density when the value of the initiator structure size was less than 200 nm. In addition to the steric repulsive force, the lateral extension of the chains in the periodically patterned PNIPAM brush was calculated by scaling low and compared with the experimental data taken from previously published literatures. The polymer brush structure was modelled as if the immediate bare substrate is so wide that even a stretched polymer segment cannot reach to the next polymer brush structure. In such models, the value of the lateral extension was equal to the thickness of the homogenous brush. It was independent of the pattern size. However, when the polymer brush structure was modelled as if there is another polymer brush structure at a distance half of the size of the period, the lateral extension was found to be dependent on the size of the initiator structure size due to chain bridging. This was witnessed by the patterning of polymer brushes using the interferometric patterning of PNIPAM brushes and an atomic force microscopy imaging of the polymer brush structures both in air and in water. The polymer brush structure resolution in water was much lower than the resolution in air, which indicates the lateral extension of the polymer chains in water. For such kind of periodic polymer brush structures, the gap between them was calculated, and it was found dependent on the degree of polymerization, density, and initiator structure size.

Experimental display of generalized wave-particle duality.

The quantification of wave-particle duality (WPD) by means of measurable features associated to it, such as fringe visibility ($\mathcal {V}$) and path distinguishability ($\mathcal {D}$), led to the establishment of the constraint $\mathcal {V}^{2}+\mathcal {D}^{2} \leq \,1$. The two involved quantities refer to so-called "quantons", physical objects that are capable of generating an interferometric pattern, while being at least partially localizable. Any quanton's internal degree of freedom (DOF) can in principle be used as a path-marker. When the quanton and its internal DOF are simultaneously engaged, new constraints can be derived and experimentally tested. Generalized constraints show how $\mathcal {V}$ and $\mathcal {D}$ relate to other quantifiers and bring to light coherences that might remain otherwise hidden in both quantum and classical light. We submitted two-qubit constraints to experimental tests, using optical light beams. This shows that, despite the rather contrived nature of the constraints, linear optics setups are appropriate to test them. Our experimental results are in very good agreement with theoretical predictions related to the tested constraints. Our results also show that quantifiers such as $\mathcal {V}$ and $\mathcal {D}$ help not only to quantify, but also to generalize the concept of WPD.

1D Interferometric Rayleigh Scattering Velocimetry And Thermometry Using VIPA

One-dimensional interferometric Rayleigh scattering is applied to simultaneous measure velocity and temperature by using virtually imaged phased array. The Doppler shift of interferometric pattern was produced by flow velocity plus laser drifts. Online monitoring of the laser wavelength is achieved by adding an additional F-P etalon-based IRS system. Velocity measurements at a low flow rates show an accuracy of 10 m/s. The Rayleigh-Brillouin spectrum is function of pressure and temperature, and provides temperature diagnostics in isobaric flows. The different fringes of interferometric pattern represent different measurements in temperature fitting. This make it possible that one-time experiment but multi-times measurement. The instrument precision of temperature was 3.5% at 809K, which was contributed by the signal to noise ratio decrease at high temperature.

Real-Time Plasmonic Imaging of the Compositional Evolution of Single Nanoparticles in Electrochemical Reactions.

Real-time probing of the compositional evolution of single nanoparticles during an electrochemical reaction is crucial for understanding the structure-performance relationship and rationally designing nanomaterials for desirable applications; however, it is consistently challenging to achieve high-throughput real-time tracking. Here, we present an optical imaging method, termed plasmonic scattering interferometry microscopy (PSIM), which is capable of imaging the compositional evolution of single nanoparticles during an aqueous electrochemical reaction in real time. By quantifying the plasmonic scattering interferometric pattern of nanoparticles, we establish the relationship between the pattern and composition of single nanoparticles. Using PSIM, we have successfully probed the compositional transformation dynamics of multiple individual nanoparticles during electrochemical reactions. PSIM could be used as a universal platform for exploring the compositional evolution of nanomaterials at the single-nanoparticle level and offers great potentials for addressing the extensive fundamental questions in nanoscience and nanotechnology.