Single Interferogram Research Articles

Application of multiple-beam white-light fringes for measuring the refraction and dispersion of mica

Multiple-beam white-light interference fringes are applied to measure the two refractive indices of a mica sample and their dispersion across the visible spectrum. In addition, the mica birefringence and its dispersion are measured. A mica sample of dimensions 2 x 5 mm 2 and an immersion liquid of nearly the same refractive index are used. Only a single shot interferogram is needed to measure all the aforementioned parameters. Cauchy's and a modified single-term Sellmeier dispersion formula are used for fitting the experimental data and extracting the parameters required.

Interferograms obtained with a X-ray laser by means of a wavefront division interferometer

A wavefront division interferometer has been used for the first time with a soft X-ray laser (λ = 21.2 nm). The experiment aims to demonstrate X-ray laser interferometry in this configuration and to investigate the phase shifting measurement accuracy as well. The X-ray laser is generated in a neon-like zinc plasma in which it makes two passes thanks to a multilayer mirror half-cavity. The X-ray pulse duration is ≈50 ps. The beam has a very high brightness (≈4 × 10 15 W cm −2 sr −1 in 0.01% bandwidth) which allows us to place the interferometer far from the source (2.8 m) and thus to benefit by a large transverse coherence width. The interferometer consists of a Fresnel bi-mirror which adds coherently one part of the X-ray laser beam section to the other one. Single laser-shot interferograms of a reflecting sample provided with a λ 2 dephasing step (51.7 nm height) have then been successfully recorded. The phase shifting accuracy resulting from the smallest observable fringe change is about λ 20 .

Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique

We present a two-dimensional regularized phase-tracking technique that is capable of demodulating a single fringe pattern with either open or closed fringes. The proposed regularized phase-tracking system gives the detected phase continuously so that no further unwrapping is needed over the detected phase.

Simultaneous measurement of three orthogonal components of displacement by electronic speckle-pattern interferometry and the Fourier transform method

The measurement of three-dimensional displacement by electronic speckle-pattern interferometry with three object beams and one reference beam is presented. Multiple interference fringes corresponding to different sensitivity vectors are recorded in a single interferogram and separated by means of the Fourier transform method to give three components of displacement. The relationship between the ratio of the speckle size to the pixel size of a TV camera and the measurement error is investigated experimentally and compared with the research of others. The optimum condition leading to a minimum measurement error occurs when the speckle size is approximately equal to the pixel size. With this condition satisfied, the measurement error varies from 1.5% to 6.0%.

Determination of the optical properties of a monomode optical fibre by fringes of equal chromatic order

Multiple beam fringes of equal chromatic order are used to study the optical properties of a monomode optical fibre. The material dispersion of the core and that of the cladding of the fibre are measured. A modified single term Sellmeier dispersion formula is adopted and fitted to the experimental data. A new simple scheme of calculation is applied to reduce the interferogram. A single interferogram is sufficient to give the whole dispersion information needed across the visible spectrum.

Interferometric determination of the dispersion and atomic parameters of some eye vitreous substitute solutions

Multiple-beam fringes of equal chromatic orders are applied to obtain the dispersion and atomic parameters of silicon oil and salt solution as eye vitreous substitute solutions. The corresponding parameters for distilled water and eye tears are studied for comparison. A single interferogram for each sample is sufficient to deduce the whole set of parameters needed. A modified single-term Sellmeier dispersion formula has been used for fitting the experimental data and deducing the atomic parameters.

Improved interferometer for measuring unsteady film thickness

An interferometer previously developed for measuring instantaneous film thickness of the order of 10 μm–1 mm [T. Ohyama, K. Endoh, A. Mikami, and Y. H. Mori, Rev. Sci. Instrum. 59, 2018 (1988)] has been improved with respect to both facility of handling and accuracy of thickness determination. The improved version of the interferometer uses an expanded laser beam focused aslant on the subject film. The rays reflected from the front and rear surfaces of the film form interference fringes on a screen, which are then recorded in the form of a single snapshot interferogram or as a set of serial interferograms to be geometrically analyzed. Experiments with thin glass plates as sample films verified the expected advantages of the new version over the original one. The improved version of the interferometer was also tested on a liquid film asymptotically thinning as it drained down a vertical plate. The test indicated that the accuracy and precision of the new improved version far exceed those of other transient film-thickness measuring techniques.

Simple holographic interferometric method of investigating the Poisson coefficient and elasticity moduli

A simple method to determine the moduli of elasticity <i>E</i> and <i>G</i> and the Poisson coefficient <i>v</i> of a linear elastic isotropic structural material on the basis of a cylindrical beam, from a single double-exposure holographic interferogram, is described. The method is applicable to different types of materials. The measurement of a steel beam is presented as an example.

Fourier-transform spectrophotometer for time-resolved emission measurements using a 100-point transient digitizer

An infrared time-resolved Fourier-transform emission spectrophotometer has been constructed and its use has been demonstrated. The instrument is based on a commercial interferometer combined with a CAMAC-based data acquisition system. The use of a transient digitizer permits acquisition of a single interferogram point at 100 time intervals following a single photoexcitation. The instrument operates in the ‘‘smooth scan’’ mode. The combination of this mode of operation with the use of a transient digitizer provides great time efficiency for data acquisition because there is no mirror settling time at each optical retardation. Complete interferograms free from the artifacts associated with assembly of interferograms arising from multiple scans are available after each mirror scan. The maximum resolution of the present instrument is 0.1 cm−1, limited only by data storage considerations; the maximum resolution of the commercial interferometer is 0.02 cm−1 (with apodization) and could be utilized with long scans. The shortest time that can be resolved by the instrument, currently ∼1–2 μs, is limited only by the infrared detector/preamplifier combination. The longest time interval which is permitted between successive photochemical or photophysical events (nominally 3.16 ms) is limited by the slowest scan velocity of the moving mirror, (0.01 cm/s). Usable data can be acquired from 10 to 50 mirror scans, where acquisition, storage, and coaddition of a single 1 cm−1 resolution scan takes ∼5 min.

Use of step-scan FT-IR to obtain the photoacoustic/photothermal response phase

This paper describes the extraction of photoacoustic (PA)/photothermal (PT) or other experimental response phase from data measured by step-scan FT-IR. The signal processing used with step-scan FT-IR is discussed and contrasted to the signal processing used to extract the experimental phase from data acquired by conventional continuous-scan FT-IR methods. Step-scan operation decouples the FT-IR spectral multiplexing from time, simplifying a variety of time-dependent spectroscopic measurements both conceptually and practically. A consequence of the decoupling is the separation of the temporal phase from the FT-IR instrument (beamsplitter) phase. Data are presented which show clearly that the temporal phase is completely separated from the FT-IR phase by step-scan. This is in contrast to the case of continuous-scan FT-IR, in which the phases are added together. In continuous-scan operation, a single interferogram, which is the average of a number of scans, is recorded. Typically, in step-scan operation, two interferograms, the in-phase and quadrature responses, are recorded simultaneously point-by-point. The beam splitter phase is the same for both of the step-scan interferograms, while the temporal response (sample) phase appears as their relative intensities, specifically, the arctangent of their ratio. Photoacoustic and photothermal beam deflection data are presented here as illustrations of the points discussed.

Whole-field measurement of gas density from two simultaneously recorded interferograms

The visualization technique presented herein is based on white light differential interferometry using large Wollaston biprisms. The particularity of our set-up is that it yields two instantaneous interferograms, taken at precisely the same time, on which the interference fringes are differently oriented. Thus, the instantaneous fields of two different partial derivatives of density are simultaneously recorded and it is possible, through the use of both interferograms, to obtain the value of the density in domains where this cannot be done using a single interferogram. This method has been successfully tested in the two-dimensional unsteady flow past a cylinder.

Radius of curvature measurement by Twyman- Green's interferometer

The radius of curvature of a spherical surface has been measured by a non-contact interferometric method using Twyman-Green's interferometer. This interferometer has been used without adding the traditional moving focusing lens in one of its arms. Similar to Newton's rings method, a single interferogram gives the radius of curvature of the spherical surface. Six spherical mirrors, both convex and concave, with radii ranging from 959 mm to 2221 mm have been measured. The results of the measurements have been compared with those obtained by Newton's rings method.

Three ways to implement interfacial techniques: application to measurements of chromatic dispersion, birefringence, and nonlinear susceptibilities

Depending on the spectal width of the source illuminating an interferometer, measurement procedures can utilize either the whole interferogram, or only the fringe envelope, or only the fringe quick oscillations. With an ultraband spectrum source, a simplified adaptation of the methods of Fourier transform spectroscopy yields the variations of the test-fiber propagation constant over the whole wavelength-interval of the source. Chromatic dispersion can then be computed from a single interferogram. With narrower spectrum sources, only the fringe envelopes are utilized and yield measurements of mode delay, with application to chromatic and polarization mode dispersion. In this case, however, interferograms at several wavelengths are necessary. With even narrower spectrum sources, the fringe quick oscillations provide measurements of phase shifts, related to changes in the mode propagation constant, when outside perturbations are applied to the test fiber. A direct method for measuring the third-order nonlinear susceptibilities is discussed. In this case the outside perturbation is an intense pump laser field.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Phase-amplitude imaging: The fully automated analysis of megagauss magnetic field measurements in laser-produced plasmas

This paper describes the application of phase-amplitude imaging to the measurement of self-generated magnetic fields in laser-produced plasmas. The magnitude of the magnetic field is determined by polarimetry and the plasma density profile by interferometry. Both pieces of information are recorded on a single interferogram in a form that can be analyzed automatically using computer-based image processing. We describe a method for successfully determining the magnetic field profile in plasmas generated by 70-ps Nd laser pulses at high intensity on planar targets when plasma motion or turbulence introduces an additional difficulty by reducing the visibility of the fringes.

Chromatic dispersion measurement from Fourier transform of white-light interference patterns

Single-mode fibres were inserted in one arm of a classical Mach-Zehnder interferometer, illuminated with a light source having a broad spectral width. A simple numerical Fourier transform method, applied to a single interferogram, leads to the variations in neff(λ) over a broad λ-range. The chromatic dispersion is then derived via numerical differentiation.

Digital and optical moiré detection of flaws applied to holographic nondestructive testing

Superposition of two double-exposure holographic interferograms creates moiré patterns that can be used to detect flaws. Relative magnification can be used to correct for imprecise replication of loading when the second interferogram is formed; it also can be used to detect flaws when only a single interferogram is used if the basic deformation field is radially symmetric. Digital image processing is a rapid and versatile technique for forming such moiré patterns.

A simple laser interferometer for wind tunnel flow visualisation

A simple interferometer design based on a conventional wind tunnel schlieren system is described. This new interferometer arrangement employs a laser light source, a lens which splits off the reference beam after test beam expansion and a lens and Lloyd mirror to recombine the two beams. The reference beam passes through the test section but is contracted to a narrow waist and displaced well away from the model location. The design combines a number of characteristics which render it particularly useful for wind tunnel tests. These characteristics include: simplicity, optical robustness, low vibration sensitivity, modest coherence requirements and ease of interferogram analysis. The main disadvantage is that only half the total field of view can be recorded on a single interferogram. Test results, confirming the above advantages, are presented from an interferometer based on the 406 mm aperture schlieren system fitted to the Aeronautical Research Laboratories transonic wind tunnel.

Determination of the dihedral angle errors of a corner cube from its Twyman-Green interferogram

A technique is devised for calculating the magnitudes of the dihedral angle errors of a corner cube from a single Twyman-Green interferogram. Experimental examples are given in which the dihedral angles of two corner cubes are determined to within 2 arc sec by this procedure. These values are also shown to be in good agreement with independent goniometer measurements.

Interferometric Spectropolarimetry: Alternate Experimental Methods

Three alternate methods of obtaining spectra of the intensity and state of polarization of light are proposed. The methods make use of a two-beam amplitude division interferometer using the technique of Fourier spectroscopy. They can be applied to either emerging beam, source beam, or detector beam r to both. They do not require the presence of polarizers in the arms of the instrument. In one method (Method 2) a single analyzer is used in front of the detector with three successive orientations of its transmission axis azimuth (0 degrees , 45 degrees , 90 degrees ). In another method (Method 3) a (linear) polarizer assuming the same set of orientations is placed in the incident beam. A third method (Method 4), a hybrid of the former two methods, makes use of both a polarizer and an analyzer in the locations indicated. The latter method presents itself three alternate possibilities. Method 2 permits the determination of all four Stokes parameters of polarization, whereas Methods 3 and 4 cannot yield the ellipticity parameter. All methods require the recording of three interferograms. However, two interferograms can provide the intensity and degree of polarization in any of the methods described. The theory of our earlier method (Method 1, Fymat and Abhyankar, 1970) is also established more rigorously concerning the proposed interferometric arrangements, the applicability of the method to the source beam, and the possibility of deriving the orientation of the plane of polarization and the ellipticity from a single interferogram.

Qualitative Interferometry of Expanding Metal Vapor

The metal vapor from a wire exploded in a gas is assumed to be contained between the walls of a hollow cylinder which has boundaries that are linear functions of time. It is shown that the presence of the ambient gas can be ignored in the qualitative descriptions of the flow determined from interferograms. Studies of the single and multiple fringe interferograms expected from such a cylindrical flow are made. Graphical plotting techniques are developed to obtain these expected interferograms and supplementary mathematical relations describing the interferograms are demonstrated. Finally, comparison of interferograms obtained by these methods is made with those interferograms obtained during actual exploding wire experiments.