Two-dimensional Interferograms Research Articles

Extreme shearing interferometry: Theoretical limits with practical consequences

In this work we analyze the frequency response, the spatial distribution and continuity of the recovered phase in Lateral Shearing Interferometry (LSI). This frequency content and topology of the recovered phase is analyzed for the forward LSI operator as well as its inverse LSI operator using one, two, or n two-dimensional sheared interferograms. The spatial frequency response of the shearing interferometer is well known and for the reader's convenience, it is briefly revisited in a new perspective. It is however less well-known and more interesting to analyze the spatial distribution of the sheared data as well as the spatial topology of the recovered phase produced by some inverse LSI operators. Also we define a useful space of functions S with the property that any sheared data available, along any direction, may be used to recovered a smooth continuous phase with the bonus property of fully covering the pupil of the wavefront being tested. These combined aspects allow us to find the best possible wave-front reconstruction from the available sheared data using one, two or n sheared interferograms.

Three-Dimensional Measurements of Nanometer-Thick Lubricant Films Using Low-Coherence Phase-Shifting Interferometry

We have developed a method utilizing low-coherence phase-shifting interferometry (LCPSI) to directly visualize molecularly thin lubricant films coated on diamond-like carbon (DLC) surfaces. In contrast to conventional point-by-point scanning methods, this method straightforwardly measures lubricant distributions in three dimensions using phase-shifted two-dimensional interferograms which are generated by a Michelson interferometer and a robust feedback controlled phase-shifting system. To effectively suppress the image noise caused by unwanted interference, we employed a low-coherence light source rather than a laser. Moreover, an image subtraction method, in which the pseudo lubricant thickness attributed to surface roughness and system noise is first measured on a non-lubricated disk and is then subtracted from the result obtained on the lubricated disk, was introduced to eliminate the influence of surface roughness and system noise. By measuring nanometer-thick perfluoropolyether films coated on DLC surfaces, we demonstrated that the LCPSI is capable of providing real-time three-dimensional measurements with a thickness resolution of sub-nanometer and a spatial resolution of several micrometers.

Nonlinear Wave-Packet Interferometry and Molecular State Reconstruction in a Vibrating and Rotating Diatomic Molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.

Joint spectrum of photon pairs measured by coincidence Fourier spectroscopy

We propose and demonstrate a method for measuring the joint spectrum of photon pairs via Fourier spectroscopy. The biphoton spectral intensity is computed from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I downconversion source using a pair of common-path Mach-Zehnder interferometers based on Soleil compensators. The experimental results agree well with calculated frequency correlations that take into account the effects of coupling into single-mode fibers. The Fourier method is advantageous over scanning spectrometry when detectors exhibit high dark count rates leading to dominant additive noise.

Depth-resolved whole-field displacement measurement using wavelength scanning interferometry

We describe a technique for measuring depth-resolved displacement fields within a three-dimensional (3D) scattering medium based on wavelength scanning interferometry. Sequences of two-dimensional interferograms are recorded whilst the wavelength of the laser is tuned at a constant rate. Fourier transformation of the resulting 3D intensity distribution along the time axis reconstructs the scattering potential within the medium, and changes in the 3D phase distribution measured between two separate scans provide one component of the 3D displacement field. The technique is illustrated with a proof-of-principle experiment involving two independently controlled reflecting surfaces. Advantages over the corresponding method based on low-coherence interferometry include a depth range unlimited by mechanical scanning devices, and immunity from fringe contrast reduction when imaging through dispersive media.

Formation and analysis of the interference field of a bifocal lens when a laser beam is transmitted off-axis

This paper proposes a device that operates on the basis of a polarization interferometer and makes it possible to use laser radiation to form two-dimensional interferograms and interference signals that satisfy the quadratic frequency modulation (QFM) law. QFM signals with smoothly varying informational parameters are investigated, and it is shown that they can be used to monitor small linear and angular displacements. © 2004 Optical Society of America

Discrete phase reconstruction technique for two-dimensional interferograms

A discrete technique for the reconstruction of the phase of a carrier frequency interferogram is presented. In this technique the interferogram is used to generate two functions that are utilised to form partial differential equations. Interpolating polynomials of degree N are used to approximate the unknowns in these equations using Legendre–Gauss–Lobatto collocation points and sets of algebraic equations are developed. These algebraic equations are solved and the phase of the interferogram is reconstructed. An example is included to demonstrate the validity and applicability of the technique where a comparison is made with exact results.

General n-dimensional quadrature transform and its application to interferogram demodulation.

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.

Wave packet interferometry for short-time electronic energy transfer: Multidimensional optical spectroscopy in the time domain

We develop a wave packet interferometry description of multidimensional ultrafast electronic spectroscopy for energy-transfer systems. After deriving a general perturbation-theory-based expression for the interference signal quadrilinear in the electric field amplitude of four phase-locked pulses, we analyze its form in terms of the underlying energy-transfer wave packet dynamics in a simplified oriented model complex. We show that a combination of optical-phase cycling and polarization techniques will enable the experimental isolation of complex-valued overlaps between a “target” vibrational wave packet of first order in the energy-transfer coupling J, characterizing the one-pass probability amplitude for electronic energy transfer, and a collection of variable “reference” wave packets prepared independently of the energy-transfer process. With the help of quasiclassical phase-space arguments and analytic expressions for local signal variations, the location and form of peaks in the two-dimensional interferogram are interpreted in terms of the wave packet surface-crossing dynamics accompanying and giving rise to electronic energy transfer.

Interferometric diagnostics of ablation craters formed by femtosecond laser pulses

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text A. S. Zakharov, M. V. Volkov, I. P. Gurov, V. V. Temnov, K. Sokolovski-Tinten, and D. von der Linde, "Interferometric diagnostics of ablation craters formed by femtosecond laser pulses," J. Opt. Technol. 69, 478- (2002) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Two-axis bend measurement using multicore optical fibre

We describe the first use of a four-core optical fibre to measure bending about two orthogonal axes simultaneously. Individual cores in the fibre act as independent strain gauges where local curvature determines the difference in strain between cores. The multicore sensing element, interrogated in reflection, generates a two-dimensional far-field interferogram. The component of fibre curvature in the plane of the two cores shifts the corresponding fringes in the interferogram. Bend angle is then calculated using phase values derived from Fourier analysis of the far-field interferogram. This technique achieved a bend angle resolution better than 120 μrad.

Measurement of Three-Dimensional Density and Velocity Distributions Using HPIV. Evaluation of Simultaneous Recording and Filtering Extraction.

A technique for simultaneous measurement of three-dimensional density and velocity distributions was evaluated. Holographic particle image velocimetry (HPIV) was used to reconstruct three-dimensional velocity distributions from three-dimensional particle images recorded on a hologram. Optical tomography (OT) was used to reconstruct three-dimensional density distributions from multidirectional two-dimensional interferogram images. When a flow field with density variation was illuminated by coherent plane waves, spherical waves were scattered by the particles (particle images), and the illuminating beam was modulated by the density variation (interferogram images). Using a reference beam, both particle and interferogram images could be recorded on a single hologram. Using the spatial filtering extraction (FX) technique, information on both images could be extracted separately from the hologram. In the experiment, a jet of helium gas introduced into air containing small particles was measured. Both particle position and fringe shift caused by the density variation could be observed, demonstrating the effectiveness of the proposed technique

Computer-aided interferometer for testing microdisplacement of piezoelectric ceramics

This paper proposes a kind of computer-aided contact-type interferometer for testing the microdisplacement of piezoelectric ceramics (PZT). Its accuracy is better than 0.01 μm. A data acquisition system, including a CCD, grabber, etc., has been used to detect and digitize interferograms. This system analyzes a two-dimensional interferogram automatically and quickly, while both calibrate with monochromatic fringes and test with achromatic fringes. Software has been used to analyze the two-dimensional interferogram and to test the nonlinearity and hysteresis of PZT. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 72–74, 1999.

Two-dimensional interferogram of an exploding selenium foil using a soft X-ray laser interferometer

We have developed a soft X-ray interferometer capable of probing large high-density plasmas with micron spatial resolutions. A neon-like yttrium X-ray laser operating at 155 /spl Aring/ was combined with the Mach-Zehnder interferometer to obtain electron density profiles of a laser-produced exploding selenium foil plasma. The plasma was produced with one Nova laser beam using a 120-/spl mu/m line focus, the same conditions used to create a selenium X-ray laser. The interferogram of the selenium plasma was obtained from an end-on perspective.

Flux measurements on ferromagnetic microprobes by electron holography.

Bulk ferromagnetic microprobes, as commonly used in magnetic force microscopy, have been analyzed by electron holography. Using the double exposure technique, detailed holograms have been obtained from nickel probes. The resulting two-dimensional interferograms can be well reproduced by numerical calculations which are based on the assumption that the probes stray field is produced by a macrodipole of several micrometers in length. By treating the dipole charge as a variational free parameter to be fitted against the experimental data, it is possible to determine the stray field produced by the probes, their effective leakage flux, and the surface area of a sample which may seriously be affected by the probes stray field. The results are considered especially important for those applications of magnetic force microscopy where the sample is likely to be magnetically perturbed by the stray field which is produced by the imaging probe itself.

Two-dimensional Phase Locked Loop Demodulation of Interferograms

Abstract A new technique for continuous phase determination of an interferogram based on a digital phase locked loop is presented. The main advantage of this method, with respect to well established techniques such as Fourier or phase stepping demodulation, is that the traditional approach to phase unwrapping processes by removal of discontinuities is not required. The phase is determined continuously as the phase locked loop scans the two-dimensional interferogram. Because of the sequential nature of the algorithm proposed, this can be implemented using a special purpose video processor for phase determination at video rates. The above mentioned properties makes the presented technique a fast algorithm for phase determination of carrier frequency interferograms modulated by a two-dimensional smooth phase function.

Holographic techniques for whole-field thermal and fluid measurements

SummaryMeasurement methods using holography are non-invasive, whole-field and can be applied in real-time. They are particularly appropriate for experimental validation of current CFD (computational fluid dynamics) codes which have 3-dimensional, transient, irregular geometry capabilities.In holographic interferometry, the fringes formed by refractive index changes represent lines of constant Mach number in isentropic compressible flows and isotherms in convection. Examples are given of two-dimensional inter-ferograms in these areas, and their quantitative interpretation.Automatic fringe and data processing is a necessity, and the method is extendable to three dimensions using tomographical reconstruction. These issues are discussed, together with the general question of comparison with flow predictions.Fluid fields may also be treated on a three-dimensional time-dependent basis, using HCV (holocinematographic velocimetry), a holographic extension of PIV (particle image velocimetry). It is proposeds to run an experiment to measure both fluid and thermal fields, and surface temperatures simultaneously, using HCV or PIV, holographic interferometry and liquid crystal methods respectively.

Digital Fringe Reduction Techniques Applied To The Measurement Of Three-Dimensional Transonic Flow Fields

A system for digital inteferogram evaluation based on an image-processing system connected to a host computer has been implemented. The system supports one- and two-dimensional interferogram evaluations. Interferograms are digitized, enhanced, and segmented. The fringe coordinates are extracted, and the fringes are represented as polygon data structures. Fringe numbering and fringe interpolation modules are implemented. The system supports editing and interactive features as well as graphic visualization. An application of the system to the evaluation of double exposure interferograms from the transonic flow field around a helicopter blade and the reconstruction of the 3-D flow field are given.

Study of Exothermic Processes in Shock Ignited Gases by the use of Laser Shear Interferometry

Abstract The paper reports on the measurements of maximum exothermic power pulses attainable from a given chemical system. Experimental tests involved the use of a shock tube technique whereby the exothermic process of combustion was controlled by reflected shock, so that it occurred under virtually inviscid flow conditions, while the measurements were performed at a resolution commensurate with the actual rate of chemical reaction. Experimental observations were made by means of a novel method of laser shear interferometry—a cross-breed between holography and the conventional means for measuring refractive index fields, in that, on one hand, it was based on the exploitation of the phase coherence of the laser light beam, recording first a diffraction image of the wave fronts which, for the desired final result, had to be optically reconstructed, and, on the other, it yielded eventually either two-dimensional interferograms or schlieren photographs of the observed phenomena. Chemical systems treated in this manner comprised primarily of stoichiometric hydrogen-oxygen mixtures with 80 and 90 per cent argon, the experiments covered the full permissible range of initial thermodynamic conditions, with the scope being bounded on the lower side by the density limit resulting in illegibly small fringe shifts, and on the upper side by the onset of unstable detonation phenomena.

High Resolution Two-Dimensional Interferometry

A method for increasing the fringe shift resolution of a two-dimensional optical interferogram by more than an order of magnitude without loss of spatial resolution is described. A Fabry-Perot cavity is used as an interferometer to increase the number of passes. The sharpened fringes are multiplied in number by using a multimode laser as a light source. The fringe pattern (observed without a lens) is equivalent to that of a Mach-Zehnder interferometer except that a shift of one fringe corresponds to an optical path length difference of λ/2α (instead of λ) when the cavity lengths are in the ratio L/L0=1/α, and α is the number of excited laser modes.