Multiple-beam Interference Fringes Research Articles

Effect of glow discharge plasma on step index polymer optical fiber parameters

DC glow discharge plasma of power 40 W was applied to step index polymer optical fibers for different exposure times. Nitrogen, oxygen, and hydrogen gases were used to obtain the glow discharge. The fiber core material was poly methyl methacrylate and the cladding was fluorinated polymer. The effect of plasma on the optical parameters, such as core index profile, cladding index, and the numerical aperture, was studied by multiple beam interference fringes and Fourier transformation of infrared spectroscopy spectra. It was found that the plasma treatment affected the optical parameters of both the cladding and the core regions of optical fibers. The optical parameters also changed with the treatment time. The hydrogen plasma had effects greater than those of nitrogen and oxygen plasma. These observed results can be explained by the effect of the electric field during plasma treatment. The studied optical fibers after plasma treatment can be used as inverted-graded index with its important applications.

The influence of mechanical cold drawing and drawing velocity on the molecular structure of isotactic polypropylene fiber

AbstractThe main goal of this work study is to study the influence of mechanical cold drawing and drawing velocity on the molecular orientation and physical structure parameters of isotactic polypropylene, iPP, fibers. A Video Opto‐ Mechanical device (VOM) attached with automatic multiple‐beam interferometric technique was used to cold draw iPP fibers at different draw ratio and drawing velocity. The molecular structure of iPP fiber was characterized by measuring the refractive indices, birefringence, optical orientation function, orientation angle, the percentage of the volume fraction of amorphous and crystalline regions, density and the mean square density fluctuation. The obtained microinterferograms of multiple beam interference fringes were enhanced and the noises were removed by using Fourier transform method. The obtained contour lines were analyzed via a software program for fiber refractive index determination. The results show that the drawing velocity has a less effect than the draw ratio on the molecular structure of iPP fiber. The contour lines of microinterferograms are given for illustration. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

Reconstruction of refractive indices distribution in 3D using a single pattern of multiple-beam interference fringes for online investigation of necking phenomenon

A proposed model for reconstructing the refractive indices distribution in three dimensions is introduced. The reconstruction process requires a single multiple-beam interference pattern which facilitates online investigation of structural changes. In order to increase the accuracy of the measured refractive indices, fringe analysis was applied on the basis of the inverse interferogram principle proposed in this article. Verification of the modified technique was made using reconstructed noise-free interference patterns. The modified technique is helpful in studying the necking phenomenon observed during creep extension of polypropylene fibres. Refractive index distribution in 3D across the fibre was determined and the birefringence profile was calculated. Microinterferograms are given for illustration.

Radius of curvature measurement of spherical smooth surfaces by multiple-beam interferometry in reflection

In this paper a method is presented to accurately measure the radius of curvature of different types of curved surfaces of different radii of curvatures of 38 000,18 000 and 8000 mm using multiple-beam interference fringes in reflection. The images captured by the digital detector were corrected by flat fielding method. The corrected images were analyzed and the form of the surfaces was obtained. A 3D profile for the three types of surfaces was obtained using Zernike polynomial fitting. Some sources of uncertainty in measurement were calculated by means of ray tracing simulations and the uncertainty budget was estimated within λ/40.

Surface microtopography measurement of a standard flat surface by multiple-beam interference fringes at reflection

This paper describes a multiple-beam interferometry technique at reflection for measuring the microtopography of an optical flat nominally of λ/20. The measured value is the result of a piezoelectric phase shifting that made it possible to cover the area between the orders. The exposure area of the tested optical flat covered by the collimated laser beam is about 2 cm. The images captured by the digital detector were corrected using dark/flat field method. The uncertainty in the measurement due to incomplete parallelism of the incident beam and the inhomogeneity of the reflecting layers were calculated from the departure of the fringe position produced with a written ray tracing program. The uncertainty budget was estimated to be of the order of λ/40.

Thickness and refractive index measurements using multiple beam interference fringes (FECO)

We report on the use of optical interferometry employing fringes of equal chromatic order (FECO) in a surface force apparatus (SFA) to determine film thicknesses and refractive indices of confined media for a wide range of separations. In particular, we show how to calculate the surface separation (film thickness) based on two fringes whose contact position was not measured. We discuss the measurement accuracy, and though the theoretical accuracy is 1 Å for all separations, we show that in practice, for large separations, it is very hard to get to this accuracy.

Phase-shifting Fizeau interference microscope with a wavelength-shifted laser diode

A phase-measuring Fizeau interference microscopy with a laser diode (LD) source is studied that is based on a phase-shifting method using wavelengths varied stepwise by changing the current in the LD. The effect of the multiple-beam interference fringes on three kinds of phase-extraction algorithms is theoretically and numerically investigated. The phase error due to multiple reflections has a periodicity to one-fourth of the fringe spacing and a four-stepping method has the smallest error among interesting algorithms. The measurement error with a four-stepping method can be minimized by averaging two sets of measurements with an initial phase difference of π/4. This eases the adjustment of an initial phase by a tunable LD. A phase error caused by the power change in the LD is eliminated by normalizing the captured interferograms. Experimental results are presented with a Fizeau interferometer to show the usefulness of such procedures.

Interferometric determination of refraction and dispersion of human blood-serum, saliva, sweat and urine

Multiple-beam interference fringes of equal chromatic order are produced in air and liquid sample interferometric gaps. The two gaps are of the same thickness and simultaneously enclosed in a wedge interferometer. A single shot interferogram containing fringes in the two gaps is sufficient to deduce the needed experimental data. Locations of the fringe maxima, in the two gaps, are introduced in a non-numerical procedure for determining the gap thickness and the liquid-phase refractive indices across the visible spectrum. The method has been used for measuring the phase refractive indices of human blood-serum, saliva, sweat, urine and water liquids. A third-order polynomial dispersion relation is applied for fitting the measured phase indices. Group refractive indices have been derived and fitted to the same dispersion formula.

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.

On the determination of the refractive index of a fibre. II. Graded index fibre

Two- and multiple-beam interference fringes are used to measure the refractive index of graded index fibres. A general expression considering the refraction of the beam by the graded index fibre has been derived, from which expressions for homogeneous and skin-core fibres can be obtained. Comparison between the results with the method used when neglecting refraction is dealt with using Philips, LDF (TM) optical fibres and drawn polypropylene. Considering the derived expressions in the refractive index determination gives a correction even when a matching liquid is used, this suggests that the refraction method should be used especially for graded index fibre.

A Novel Shearing Interferometer with Direct Display of Lens Lateral Aberrations

We describe a new shearing interferometer for lens testing which has high precision and direct display of lens aberrations. Shear is obtained by reflecting a wavefront collimated by the lens under test from the front and rear surfaces of a wedged glass plate. The surfaces of the plate are coated to increase their reflection coefficient and give sharp multiple beam interference fringes which are easy to measure and interpret. We show mathematically that the interference fringes map out the lateral aberration curve of the lens under test directly, and present experimental results which display the advantages of this system over conventional two-beam shearing interferometers.

Interference profiles with multiple spherical waves: general case

Characteristics of multiple-beam interference fringes, as in a Fabry–Perot interferometer with monochromatic light, are analyzed. The optical path and the optical-path difference between interfering beams are calculated for the most general case. Different refractive indices in the inner and outer media, and arbitrary locations of the light source and the point of observation, are taken into account. An expression for the impulse response of the system is given. The results obtained from experimental tests confirm the theoretical predictions.

Diffusion of Ag through Se and its effect on interferometric thickness measurement

The effect of diffusion of silver through Se thin films, on the visibility of two and multiple beam interference fringes has been studied. For thickness measurements, Al has been found to be a suitable overcoating metallic layer as it does not diffuse through Se. The thickness was measured by multiple beam fringes at reflection.

Magnetooptic Beam Shifter and Polarization Converter Using Wedge Etalons

We present a magnetooptic beam shifter (beam scanner) and polarization converter using multiple beam interference fringes from wedge etalons with high finesse. A theoretical expression for the fringe shift and for the polarization conversion is derived. Experiments were made with an etalon of refractive index 1.69, Verdet constant -0.24 mim/cm·Oe, thickness 2 mm, surface reflectivity 95%, and wedge angle 1.2 sec, using an He–Ne 633 nm laser light. The fringe shift obtained is 0.24 mm/k Oe. The degree of polarization conversion obtained for small magnetic fields (H\\lesssim1 k Oe) is 12%/(k Oe)2, which is 7.6×102 times as large as the single-pass Faraday rotation. Very good agreement is obtained between the experimental and theoretical results.

Optical anisotropy in cotton

The successful observation of multiple-beam interference fringes in cotton is reported, and the method of measuring the optical anisotropy (birefringence) is explained.

Interferometer for Determining Autocollimator Errors

A simple interferometer comprised of two glass plates and a frame for changing the angle between the plates is described for the determination of the measurement errors of an autocollimator. The interferometer is useful in that it generates angles which are measured with an autocollimator and allows the values of these angles to be determined by counting the passage of multiple beam interference fringes. The instrument is easy to use and is very insensitive to both thermal gradients and vibration. The sensitivity of the interferometer depends upon the wave-length and the distance from the wedge apex to the point at which the fringes are observed and, for this instrument, can be varied from about 1 to 3″/fringe. For the particular location at which the fringes were observed in this experiment, the sensitivity of the interferometer is 1.429±0.004″/fringe. Typical percentage errors obtained in measurements of three autocollimators varied from 0.2 to 1.0% over a range of 285.8″.

Precise Measurement of Planeness

Interference methods are reviewed-particularly those developed at the German Academy of Sciences in Berlin-with which the deviations of an optically flat surface from the ideal plane can be measured with a high degree of exactness. One aid to achieve this is the relative methods which measure the differences in planeness between two surfaces. These are then used in the absolute methods which determine the absolute planeness of a surface. This absolute determination can be effected in connection with a liquid surface, or (as done by the authors) only by suitable evaluation of relative measurements between unknown plates in various positional combinations. Experimentally, one uses two- or multiple-beam interference fringes of equal thickness(1) or of equal inclination. The fringes are observed visually, scanned, or photographed, and in part several wavelengths or curves of equal density (Aquidensiten) are employed. The survey also brings the following new methods: a relative method, where, with the aid of fringes of superposition, the fringe separation is subdivided equidistantly thus achieving an increase of measuring precision, and an absolute method which determines the deviations of a surface from ideal planeness along arbitrary central sections, without a liquid surface, from four relative interference photographs.

Long-Path Multiple-Wavelength Multiple-Beam Interference Fringes*

Multiple-beam interference fringes between two closely spaced highly reflecting surfaces have long been used for sensitive examination of surface contours. The spacing between the two surfaces has been limited to a few millimeters at most to minimize the walk-off effect of the beam between the two slightly angled surfaces and to obtain fringes having a narrow width compared to their spacing, usually referred to as a high finesse.A system consisting of two spherical surfaces with a lens between them gives sharp multiple-beam fringes at a spacing of 50 cm. Fringes with a contour interval of λ/6 result from the use of the separate wavelengths of a helium–neon laser as a source.This long-path system can be used to examine the index homogeneity in a sizeable thickness of transparent solids, plasmas, or gases. The system should be useful for examining thermal, pressure, or composition gradients in wind tunnels, shock tubes, or plasma studies with about ten times normal sensitivity.

Phase Modulation of the First Beam in Reflected Multiple Beam Interference Fringes

A new method is given for evaluating the intensity in the multiple beam interference pattern in reflection based on considering the interfering beams as two vectors only and summing them diagrammatically. The method is applied to calculate the effect on the intensity distribution of modulating the phase of the first beam. The phase modulation is achieved by introducing a thin silver film of predetermined phase shift in transmission.

Multiple-Beam Interferometry Applied to Oscillating Systems

By illustrations, it is shown that correctly formed multiple-beam interference fringes have a high information content. The application of multiple-beam fringes to the study of oscillating crystals is described. In particular, it is shown that the fringe character is such as to permit much overlap of order without destroying fringe visibility.