Formation Of Interference Fringes Research Articles

Transmission interference fringe (TIF) technique for the dynamic visualization of evaporating droplet

The transmission interference fringe (TIF) technique was developed to visualize the dynamics of evaporating droplets based on the Reflection Interference Fringe (RIF) technique for micro-sized droplets. The geometric formulation was conducted to determine the contact angle (CA) and height of macro-sized droplets without the need for the prism used in RIF. The TIF characteristics were analyzed through experiments and simulations to demonstrate a wider range of contact angles from 0 to 90°, in contrast to RIF's limited range of 0–30°. TIF was utilized to visualize the dynamic evaporation of droplets in the constant contact radius (CCR) mode, observing the droplet profile change from convex-only to convex-concave at the end of dry-out from the interference fringe formation. The TIF also observed the contact angle increase from the fringe radius increase. This observation is uniquely reported as the interference fringe (IF) technique can detect the formation of interference fringe between the reflection from the center convex profile and the reflection from the edge concave profile on the far-field screen. Unlike general microscopy techniques, TIF can detect far-field interference fringes as it focuses beyond the droplet-substrate interface. The formation of the convex-concave profile during CCR evaporation is believed to be influenced by the non-uniform evaporative flux along the droplet surface.

Measurements of the geometrical characteristics and refractive index of specimens made with X-ray interferometers

The theoretical background to the formation of interference fringes in a triple Laue X-ray interferometer by a specimen having plano-concave form is presented. The interference fringes in the general case have an elliptical form. The relation between the radius of the specimen, the refractive index and the radii of the interference fringes is established. For two epoxy lenses having different radii, the interference fringes are registered. The refractive index and the radii are determined by measuring the radii of the obtained interference fringes.

Optical interference fringes in CsPbBr3 perovskite microplate

While high-reflectivity end faces have been used as resonant cavities to achieve low-threshold lasing in various micro-nano structures of all-inorganic perovskites, the specific influence of the natural surface cavity of a sample on its optical properties has rarely been reported. Herein, we systematically investigate the effect of interference effect induced by the surface cavity of wedge-shaped microplates on their optical properties. The competition between interference and re-absorption effects causes oscillation shifts in the fluorescence spectrum and the formation of interference fringes. Variations in the microplate’s thickness have a considerable impact on the interference effect, modifying the sample’s optical properties.

Dual-core optical fiber tweezers based on all-dielectric metasurface

A transverse multi-position optical fiber tweezer is designed and studied by integrating an all-dielectric metasurface on the end of the dual-core optical fiber. The emitted beams from two cores of the fiber deflect towards two opposite directions with the same deflection angle and converge to form interference fringes in the far field. The dependences of optical force characteristics on light deflection angle, size and refractive index of the nanoparticle are discussed. The calculated results show that the proposed fiber device can achieve multi-position optical trapping of nanoscale nanoparticles in far field. Compared with the metal-based metasurface, dielectric metasurface-based fiber tweezer has higher efficiency and stronger capturing force. Our research expands applications of all-dielectric metasurface to optical tweezers and provides new ideas on the emerging platform of fiber-based metasurface.

Asymmetric structure optical fiber humidity sensor assisted by the virtual Vernier effect.

In this paper, an asymmetric structure optical fiber sensor is proposed to measure relative humidity (RH). The sensing structure is composed of splicing dispersion compensation fiber (DCF) and coreless fiber (NCF), and two sections of single-mode fiber (SMF) at both ends. Peanut shaped structure is used as a beam splitter at the input side, and the NCF is used as a beam combiner at the output side to form interference fringes. The partial cladding of DCF was etched, and polyvinyl alcohol (PVA) was coated on the etched area to form a hygroscopic film. When the ambient humidity changes, the refractive index and thickness of the hygroscopic film will change, which will lead to the wavelength shift of the resonant dip. The experimental results show that the sensitivity of the sensor is 0.1304 nm/RH% and 0.4452 nm/RH% in the RH range of 55%-75% and 75%-95%, respectively. In order to improve the sensitivity further, the original spectrum data is filtered by fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT), and the high-frequency interference components of high-order mode (LP09) and fundamental mode are obtained, which is superimposed with a simulated signal to form Vernier effect. With the method of virtual Vernier effect, the sensitivity in the RH range of 55%-75% is improved to 2.869 nm/RH%, which is 22 times larger than the original sensitivity, and the sensitivity in the RH range of 75%-95% is improved to 2.64 nm/RH%, which is 6 times larger than the original sensitivity.

Demystifying speckle field interference microscopy

Dynamic speckle illumination (DSI) has recently attracted strong attention in the field of biomedical imaging as it pushes the limits of interference microscopy (IM) in terms of phase sensitivity, and spatial and temporal resolution compared to conventional light source illumination. To date, despite conspicuous advantages, it has not been extensively implemented in the field of phase imaging due to inadequate understanding of interference fringe formation, which is challenging to obtain in dynamic speckle illumination interference microscopy (DSI-IM). The present article provides the basic understanding of DSI through both simulation and experiments that is essential to build interference microscopy systems such as quantitative phase microscopy, digital holographic microscopy and optical coherence tomography. Using the developed understanding of DSI, we demonstrated its capabilities which enables the use of non-identical objective lenses in both arms of the interferometer and opens the flexibility to use user-defined microscope objective lens for scalable field of view and resolution phase imaging. It is contrary to the present understanding which forces us to use identical objective lenses in conventional IM system and limits the applicability of the system for fixed objective lens. In addition, it is also demonstrated that the interference fringes are not washed out over a large range of optical path difference (OPD) between the object and the reference arm providing competitive edge over low temporal coherence light source based IM system. The theory and explanation developed here would enable wider penetration of DSI-IM for applications in biology and material sciences.

Novel Approach to Improve the Optical Performance by Machining Process Without Surface Finishing

With the increase in dimensions of optical elements in addition to ever rising demand for aspherical optics, the millimeter-scale periodic waviness that is naturally produced by machining (such as diamond turning) process in precision optical engineering has been one of the most crucial issues in the development of high surface quality optical elements. Even an extremely small waviness can affect the laser beam profile significantly through interference caused by Bragg scattering. This paper presents a novel method for improving a laser beam profile by utilizing the characteristics of Bragg scattering without requiring established final surface finishing processes such as optical polishing. By engraving an artificial periodic structure with a period of a few hundred microns, the Bragg scattering angle that influences the formation of interference fringes in the laser beam profile was drastically enlarged. Consequently, the quality of the beam profile was improved at a propagation distance where the 0th and 1st (− 1st) order beam modes are spatially separated, only by diamond turning machining without the surface finishing process. In addition, this approach represents an important contribution to green technology, which seeks energy saving and waste reduction in the optical surface manufacturing process.

Nonlinear Rosen-Zener-Stückelberg interferometry of a Bose-Einstein condensate

We adopt a nonlinear two-mode model to investigate the Rosen-Zener-St\uckelberg (RZS) interferometry of an interacting Bose-Einstein condensate trapped in double-well potential with a periodically modulating barrier. For symmetric potential, we analyze the properties of interference patterns and derive the interference conditions. For asymmetric potential, we explore the resonance structures caused by destructive interference at the weakly coupling limit and obtain the resonance conditions. In particular, we find that the chaotic motions in the asymmetric case with low-frequency modulation, can destroy the formation of interference fringes. In the symmetric case with high-frequency modulation, we see Fano-line-like resonance structures and find that the reso- nance positions exactly correspond to the boundary of macroscopic quantum self-trapping. We show that the nonlinearity can significantly alter both the shape and position of interference fringes and resonance structures. We discuss the experimental feasibility by comparing the solution of the Gross-Pitaevskii equation with both the solution of the two-mode model and the truncated Wigner simulation as well. The results suggest important applications of nonlinear RZS interferometry both in precisely controlling the dynamics and in accurately measuring the parameters of interacting many-body systems.

A novel manifestation at optical leaky waveguide modes for sensing applications

We report a very simple biosensor based on the direct observation of leaky waveguide (LW) modes as exponentially decaying interference fringes in the reflectivity curve. This phenomenon was only observed when the refractive index contrast between the waveguide and sample was low (0.002–0.005) and the LW was illuminated with a range of angles of incidence simultaneously. The LW acts as a phase object in angle space, resulting in Fresnel diffraction and formation of interference fringes for each waveguide mode. We present theory, a qualitative explanation and a mathematical model governing the formation of these fringes. The binding of an analyte to recognition elements immobilised in the LW changes its refractive index and thus the angular position of the fringes, which provides the biosensing mechanism. The reported LWs comprised a film of polyacrylamide and copolymers on glass slides, and provided high sensitivity, mass manufacturability and simple instrumentation.

Electro-Optical Imaging Technology Based on Microlens Array and Fiber Interferometer

To reduce the volume and weight of traditional optical telescopes effectively, this article proposes an electro-optical imaging technology based on a microlens array and fiber interferometer. Pairs of microlenses in the microlens array collect light and couple it into a fiber interferometer to form interference fringes. Then the amplitude and phase of a large number of interferometer baselines are analyzed to generate images. In this work, the principle of electro-optical imaging technology has been analyzed according to the partially coherent light theory. The microlens-array arrangement method and baseline pairing method have been optimized for arbitrary targets. From the simulation results, it was found that the imaging resolution depends on the maximum baseline length, and the imaging quality could be effectively improved by adjusting the Nyquist sampling density and baseline pairing method. This technology can provide an important reference for the miniaturization and complanation of imaging systems.

Experimental and theoretical investigations of an X-ray LLL interferometer with a wedge-shaped mirror plate.

An X-ray LLL interferometer with a wedge-shaped mirror plate is experimentally and theoretically investigated. Experimentally obtained interference patterns show that the Moiré fringes are superposed on Pendellösung fringes and the period of the Pendellösung fringes is not changed after passing the analyzer plate. An eikonal theory of interference-fringe formation in an LLL interferometer with a wedge-shaped mirror plate is developed, and provides predictions that coincide with experimentally obtained results.

Coherent states for ladder operators of general order related to exceptional orthogonal polynomials

We construct the coherent states of general order, m, for the ladder operators and , which act on rational deformations of the harmonic oscillator. The position wavefunctions of the eigenvectors involve type III Hermite exceptional orthogonal polynomials. We plot energy expectations, time-dependent position probability densities for the coherent states and for the even and odd cat states, Wigner functions, and Heisenberg uncertainty relations. We find generally non-classical behaviour, with one exception: there is a regime of large magnitude of the coherent state parameter, z, where the otherwise indistinct position probability density separates into m + 1 distinct wavepackets oscillating and colliding in the potential, forming interference fringes when they collide. The Mandel Q parameter is calculated to find sub-Poissonian statistics, another indicator of non-classical behaviour. We plot the position standard deviation and find squeezing in many of the cases. We calculate the two ‘photon’ number probability density for the output state when the m = 4, coherent states (where μ labels the lowest weight in the superposition) are placed on one arm of a beamsplitter. We find that it does not factorize, again indicating non-classical behaviour. Calculation of the linear entropy for this beamsplitter output state shows significant entanglement, another non-classical feature. We also construct linearized versions, , of the annihilation operators and their coherent states and calculate the same properties that we investigate for the coherent states. For these we find similar behaviour to the coherent states, at much smaller magnitudes of z, but comparable average energies.

Investigation on the impact of irregular fringe patterns of a single-fiber Mach-Zehnder interferometer on its sensing capabilities

Abstract A novel single-mode single-fiber (SMSF) MZI formed by cascading of two non-adiabatic fiber tapers, with stable and repeatable spectrum, has been found to be useful in sensing applications in recent times. A multimode interference based novel simulation approach is proposed to predict the sensing characteristics of SMSF-MZI and is validated with experimental observation. The proposed method includes solving of simultaneous non-homogenous equations for determining the amplitudes of the interfering modes excited in the tapered section of the interferometer. The simulated fringe pattern and the experimental spectral response converge to some important comprehension reported for the first time. A linear shift in output spectral response, of SMSF-MZI, due to change in optical path length induced by temperature/strain etc., is likely to be characterized by three modes interference occurring in the interference region of the interferometer. Whereas if the spectral shift starts saturating at moderately higher temperature/strain, then the formation of interference fringes are possibly governed by two modes interference. Further, it was also explained that a SMSF-MZI with variable fringe widths in its spectral pattern exhibits higher sensitivity than that of the SMSF-MZI having wavelength spectrum with uniform free spectral range. These findings are useful in selecting and predicting the sensitivity of a given SMSF-MZI, based on its spectrum, for sensing applications.

Neotectonic interpretations and PS-InSAR monitoring of crustal deformations in the Fujian area of China

AbstractA neotectonic structural interpretation was conducted in the Fujian Province, west of the Taiwan Strait, by using computer image processing and 3D visualizations to enhance linear structural traces. The major faults in this area can be grouped into two conjugate shear fracture zones, with one trending to the northeast and the other trending to the northwest. PS-InSAR technology uses stable permanent target scatterer points to determine deformation rates and can effectively reduce the influence of spatiotemporal decorrelations and atmospheric anomalies that affect conventional D-InSAR techniques and prevent the formation of interference fringes. This study focuses on the fault zones located in the Quanzhou area of Fujian Province, where the 1604 M7.5–8.0 historic earthquake occurred. In total, 22 scenes of ERS SAR data from 1996 to 1999 were processed using PS-InSAR methods. The results show that the line of sight direction displacement rate of the main fault in the study area is 3–5 mm/yr, which indicates that the faults in this area are still active and subject to earthquake risk.

Measurements of interfacial dynamics of gas–liquid displacement in a capillary

Measurement of liquid film thickness in gas–liquid plug/slug flows is a challenging task. A novel laser interference method for measuring the interfacial film thickness of gas–liquid displacement in a plug flow has been developed. This novel technique utilizes light scattering from different liquid/gas interfaces in forming interference fringes. The interference fringes are used for calculating the film thickness. A set of simultaneous equations is derived based on geometrical optics. The experiment set up is not complex and is easy to install. The fringes are recorded by a charge-coupled device high speed camera and the image data are calculated using fast Fourier transform (FFT) and a non-linear least squares Levenberg–Marquardt algorithm. The uncertainty of this measurement technique is quite small (0.3 μm) and the entire film thickness profile can be measured at the same time.

Ghost reflections of Gaussian beams in anamorphic optical systems with an application to Michelson interferometer.

In this paper, a methodology is developed to model and analyze the effect of undesired (ghost) reflections of Gaussian beams that are produced by anamorphic optical systems. The superposition of these beams with the nominal beam modulates the nominal power distribution at the recording plane. This modulation may cause contrast reduction, veiling parts of the nominal image, and/or the formation of spurious interference fringes. The developed methodology is based on synthesizing the beam optical paths into nominal and ghost optical beam paths. Similar to the nominal beam, we present the concept that each ghost beam is characterized by a beam size, wavefront radius of curvature, and Gouy phase in the paraxial regime. The nominal and ghost beams are sequentially traced through the system and formulas for estimating the electric field magnitude and phase of each ghost beam at the recording plane are presented. The effective electric field is the addition of the individual nominal and ghost electric fields. Formulas for estimating Gouy phase, the shape of the interference fringes, and the central interference order are introduced. As an application, the theory of the formation of the interference fringes by Michelson interferometer is presented. This theory takes into consideration the ghost reflections that are formed by the beam splitter. To illustrate the theory and to show its wide applicability, simulation examples that include a Mangin mirror, a Michelson interferometer, and a black box optical system are provided.

Far-field interference from a sphere and its applications

A theoretical model of far-field interference from a sphere has been established, and its applications have been investigated. When two coherent parallel laser beams shine on a smooth sphere surface from opposite directions, the reflected lights form interference fringes at far field. The fringes have hyperbolic shapes and are not uniformly distributed. This paper derives a method for calculating the path-length difference between two parallel reflected lights, analyzes the interference field, and discusses reasons that cause the fringe density variations. A formula for calculating the highest orders of interference fringes is also provided. A method for using a spectrometer, CCD camera, and computer to measure the sphere diameter is demonstrated. The results agree with those from an Abbe comparator. The theory and methods are also suitable for measuring diameters of smooth cylinders.

Measurement of objects with low vibration frequencies using modified Michelsoninterferometry

A simple, low-cost, and non-contact optical method using modified Michelsoninterferometry is proposed for measuring the vibration frequencies of objects. Two beamswhich are split from a laser beam project onto two rough surfaces (compared withthe laser-beam wavelength) of a fixed reference object and a vibrating testedobject respectively, and two quasi-spherical waves scattered or diffused from thetwo rough surfaces individually are combined to form interference fringes on anobservation plane. The vibration frequencies of the tested object can be derived byanalyzing the time-dependent gray-value signal (caused by the fringe-shiftingphenomena) for a specified position on the observation plane. The signal is transformedfrom the time domain to the frequency domain to form a spectrum by first usingthe fast Fourier transformation. Then, all the spectrum values correspondingto different frequencies in the spectrum are compared with a threshold value.Finally, all frequencies in the spectrum with local peaks higher than the thresholdvalue are considered to be the vibration frequencies of the tested object. Theexperiment is a non-contact type with no lenses and is able to be conducted easily withhigh accuracy and low cost for testing objects vibrating with one, two, or threefrequencies. The results and features confirm the utility of the proposed method.

Early days of coherence theory and the first Rochester conference on coherence

The terms coherence and correlations seem to have entered the optics vocabulary about the beginning of the twentieth century, many years after Maxwell discovered that light was an electromagnetic phenomenon. Prior to that time there were only a few investigations, which have a bearing on this subject. The first one was made by a distinguished French optical scientist E. Verdet who around 1865 asked a question which is equivalent to the following: if sunlight illuminates directly two pinholes in an opaque screen, how close must the pinholes be, so that the light which emerges from them can form interference fringes on superposition? He estimated the distance to be about 1/50 millimeter. In modern language this small distance is the diameter of the area of coherence formed by sunlight on the surface of the earth.

Detection of phase singularity using a lateral shear interferometer

We demonstrate use of lateral shear interferometry for the detection of phase singularities in optical fields. Existing interferometric methods of vortex detection entail a separate reference wave front, either plane or spherical, to yield fork or spiral fringes as vortex signatures. The method of vortex detection reported here is a self-referencing technique, as the reference wave front required to form interference fringes is drawn from the test wave front itself. The technique is simple, robust and vibration insensitive. Isolated vortices as well as randomly distributed vortices in a speckle field are detected using this technique. It is shown that detection of optical vortices is possible even with an ordinary glass plate acting as the shear plate.