Two-beam Interference Fringes Research Articles

A novel algorithm based on sub-fringe integration method for direct two-dimensional unwrapping phase reconstruction from the intensity of one-shot two-beam interference fringes

Phase reconstruction is extremely important in optical interferometry, where the quantitative and qualitative information is encoded in the form of two-dimensional interference interferograms. Most often, a majority of phase calculation methods return results of the wrapped phase limited in the range (? ?, ?) due to the fundamental properties of the mathematical arctangent function. It would be helpful if we could avoid the unwrapping phase step and calculate the phase directly. In this paper, we present an algorithm of phase reconstruction based on the sub-fringe integration method to avoid the ambiguities due to the properties of the arctangent function. The theoretical considerations of the proposed algorithm were presented. Also, the main steps required to implement the algorithm, in addition to providing the flowchart outlined for those steps, were presented. The algorithm is suitable to analyze the two-beam interference fringe. The proposed algorithm adds a power element to the sub-fringe method, which does not need the unwrapping process. Besides, it needs neither hardware to introduce phase shift, nor more than one interferogram. Both simulation and experimental results demonstrate the usefulness of the proposed algorithm to extract the phase from the two-beam interference interferogram, even if the fringe shifts are variable along the fiber and with the irregularity of the fiber radius across the interferogram. Appropriate and adequate interferograms were presented to clarify the basic idea of the article.

Phase Analysis Method of Interferometric Pattern Generated for Optical Axis Direction Using Three Laser Beam Interferometry

In this paper, the authors propose a phase analysis method of an interferometric pattern generated for the optical axis direction using three-beam interferometry. Authors perform shape measurement using the proposed method. In three-beam interferometry, the fringe pattern along the optical axis direction appears by superimposing each two-beam interference fringe. Therefore, the power distribution of the fringe pattern appears along the optical axis direction. This method enables us to directly obtain shape and displacement using the interferometric pattern. Our method intended for wide application with 3D shape measurements and out-of-plane displacement measurements for the inspection and maintenance of large constructions. As the first step of developing a device for 3D shape and displacement measurement, in this paper, simulation and an experiment were used to confirm that interferometric pattern for optical axis directional appeared. Further, slope of object was measured from the phase shift of optical axis directional pattern.

Peculiarities of section topograms for the multiple diffraction of X rays

The distortion of interference fringes on the section topograms of single crystal due to the multiple diffraction of X rays has been investigated. The cases of the 220 and 400 reflections in a silicon crystal in the form of a plate with a surface oriented normally to the [001] direction are considered both theoretically and experimentally. The same section topogram exhibits five cases of multiple diffraction at small azimuthal angles for the 400 reflection and MoK α radiation, while the topogram for the 220 reflection demonstrates two cases of multiple diffraction. All these cases correspond to different combinations of reciprocal lattice vectors. Exact theoretical calculations of section topograms for the aforementioned cases of multiple diffraction have been performed for the first time. The section topograms exhibit two different distortion regions. The distortions in the central region of the structure are fairly complex and depend strongly on the azimuthal angle. In the tails of the multiple diffraction region, there is a shift of two-beam interference fringes, which can be observed even with a laboratory X-ray source.

Coherent two-beam interference fringe projection for highspeed three-dimensional shape measurements

Two-beam interference is a fundamental and well-understood approach to create Fizeau's interference fringes. With a Mach-Zehnder interferometer, we utilize these two-beam interference Fizeau fringes for three-dimensional (3D) shape measurements. By introducing an acousto-optical deflector the phase of the interference fringes can be shifted with a rate of up to 200,000 Hz. When used in conjunction with highspeed cameras, this stereo-photogrammetric approach performs well for highspeed applications in comparison with the commonly used digital light processing projectors for stripe projection. Maximum speed and the achievable accuracy are discussed. Experiments and media substantiate the suitability, accuracy, and speed of this technique for very fast 3D shape measurements.

Brewster fringes from a single plate

An autocollimation system with an illuminated circular entrance aperture located in the front focal plane of a lens L is considered. In the middle between S0′ and L, a transparent plate a few millimeters thick is placed at an angle of i0 = 45° to the axis of the system, and, near the rear focal plane of the lens L, a plane reflecting mirror is placed. The plate divides the primary beam into parts during its propagation both forward and backward (after the reflection from the mirror). This ensures the formation of derivative beams that propagate toward an ocular and that are overlapped in the region of spatially separated images S0, S1, and S2. The possibility of formation of a high-contrast system of first-order two-beam interference fringes in the region of S2 is discussed. Conditions for achieving this result are also discussed.

Direct visualization of Young’s boundary diffraction wave

Experimental investigations on Young’s boundary diffraction wave are presented where a wavefront division interferometric scheme is used on diffracted wavefront to generate two-beam interference fringes in the geometrically shadow region. These fringes have good visibility and are observable in the whole space, strongly advocating the physical existence of Young’s boundary diffraction wave as a separate entity. Analysis of these fringes may provide vital information about the structure and nature of boundary diffraction wave e.g. existence in whole space, dependence of amplitude on obliquity factor etc.

Measurement of residual wedge angle with a reversal shear interferometer

A technique for determination of residual wedge angle of high optical quality transparent parallel plate using a reversal shear interferometer-based optical system has been discussed. In this technique the parallel plate to be tested is used to introduce angular tilt in the preset two-beam interference fringes of a reversal shear interferometer. The parallelism is calculated from the angular tilt of the fringes. The technique is more sensitive compared to techniques using Fizeau interferometer and is most suitable for highly parallel transparent plate with very low residual wedge angle.

Fabrication of Two-Dimensional Gratings Using Photosensitive Gel Films and Their Characterization

Two-dimensional (2D) surface-relief gratings have been fabricated by the two-beam interference method on photosensitive gel films, which are derived from chemically modified metal-alkoxides, and characterized with respect to surface morphology and antireflection effect. Photosensitive ZrO2 gel film was deposited on a silica glass substrate using the sol that was prepared from Zr-tetrabutoxide chemically modified with benzoylacetone. The gel film was exposed to two-beam interference fringe (1.0 μm period) of He-Cd laser and then rotated by 90° in its own plane, followed by an additional exposure. Leaching of the gel film with ethanol gave lattice or island types of 2D-gratings depending on the dose of laser irradiation. The morphology of the gratings changed with irradiation time of laser, leaching conditions and so on. The formation of 2D-grating of island type on a silica glass substrate substantially reduced the reflection at its surface in a wavelength range of 1.3 to 2.6 μm.

Fringes of equal tangential inclination by curvature-induced birefringence

A new kind of interference fringes, fringes of equal tangential inclination by curvature-induced birefringence, is presented. These are two-beam interference fringes produced by bending a thin sheet of birefringent material into a part of an exact cylinder such that the curvature is constant. Due to this curvature there is a uniform birefringence being induced. The change in birefringence induced by applying different radii of curvatures to a Fortepan sheet is measured. The stored (fixed) or natural birefringence of this sheet is deduced.

Single femtosecond pulse holography using polymethyl methacrylate

Holographic gratings have been written on the surface and inside transparent polymethyl methacrylate (PMMA) with individual 130 fs laser pulses at 800 nm. A surface-relief grating is fabricated by ablation and the diffraction efficiency is measured to be about 20%. A volume grating inside PMMA is formed by the change in the refractive index induced by the two-beam interference fringes. Holographic data storage on the surface is realized when one beam carries information. The stored information can be nondestructively reconstructed when the fluence of the read beam is reduced below the threshold.

Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays

We report single-layer holographic polymer-dispersed liquid-crystal materials with multiple reflection and/or diffraction gratings. Three switchable gratings are observed in a single film formed in a three-beam interference pattern. Two reflection gratings and one transmission grating are formed, corresponding to each of the three possible two-beam interference fringes. We present scanning electron microscopy and electro-optic results which are in good agreement with our model based on matrix methods and coupled-wave theory.

Opto-mechanical properties of fibres. Part 3. Structural characterization of uniaxial orientation in drawn poly(ethylene terephthalate) by means of optical parameters

Changes in the structure of polyethyleneterephthalate (PET) (Egyptian woollen type) fibres, with strain produced by different stresses, are evaluated from optical and density measurements. Calculation of the optical parameters is carried out using two-beam interference fringes, and the density data are obtained from the resultant optical data. The results are utilized for calculating the virtual refractive index, the harmonic mean polarizability of the dielectric, the harmonic mean specific refractivity, the form birefringence and the number of monomeric units per unit volume. Relations between the structural parameters with different strains are given for these PET fibres. Calculations are also carried out to evaluate some other parameters and constants. A comparison between Hermans' optical orientation function formula and the corrected formula by de Vries is given. Microinterferograms and curves are given for illustration.

Interferometric determination of the birefringence dispersion of anisotropic materials

A channelled spectrum resulting from two-beam interference fringes is formed by illuminating an anisotropic material, placed between two crossed polarizers in front of a spectrograph, with a parallel beam of white light. The resulting interferogram is analyzed by a simple approach to deduce the birefringence and its dispersion across the visible spectrum. A Cauchy and a fourth-order polynomiaI dispersion formula are used to fit the experimental data for a mica sheet and a transparency film. The method is simple, direct and accurate for deducing the birefringence of anisotropic materials and its dispersion.

Interferometric Optical Tweezers

Summary form only given. Optical trapping of micron-size dielectric microspheres using a single beam gradient force was first demonstrated by Ashkin in 1986. Since then, extensive research and development of this technique have turned it into a practical device (known as optical tweezers), which has been used in a wide variety of biological and biomedical applications. In this paper, we report the first experimental observation, we believe, of trapping and manipulation of dielectric particles by a set of two-beam interference fringes.

Optical differentiation of displacement patterns using moire interferometry

New methods of optical differentiation of fringe patterns obtained by the moire interferometry method are presented. They provide spatial derivatives of in-plane and out-of-plane displacements of the specimen under load in the form of moire or two-beam interference fringes. Either the uniform or finite fringe detection mode can be used. Simulation experiments using specially prepared transmission-type gratings are given to verify the principles.

Optical Differentiation of Displacement Patterns Obtained by Double-exposure Moiré-holographic Method

Double diffraction and spatial filtering is used for coherent processing of two identical copies of the doubly exposed image of the grating photorecorded on a transparent model. Proper orientation of the copies in space yields high-contrast two-beam shearing interference fringes after single-order spatial filtering. The fringes correspond to partial derivatives of in-plane displacement components.

Méthode de traitement des interférogrammes à deux ondes pour accroître leur sensibilité

Two-beam interference fringes are not always able to give sufficient information to determine the topography of very weakly deformed wave surfaces. The process described allows us to intercalate several intermediate levels, which vary linearly in terms of the phase, between the brightness extrema of a fringe. The interference pattern is submitted to an optoelectronics treatment where the photoelectric signal is compared with an adjustable electric reference signal.

Measurement and calculation of phase and visibility of two-beam fringes in a cube-corner interferometer as a function of the state of polarization of the incoming beam

First measurements of visibility and phase of two-beam interference fringes are presented for a large number of different states of polarization of light entering an interferometer. The measurements were made with a cube-corner interferometer. Results confirm the theory of complex visibility. It is demonstrated, that exact computer calculations are possible and informative. A comparison of observed and calculated values is represented in the s-diagram and some important relations and conclusions are discussed.

Moiré Fringe Multiplication with a Nonsymmetrical Doubly Blazed Reference Grating

A fine reference grating and coarse specimen grating in series are illuminated so that two dominant diffraction sequences take symmetrical paths in the intergrating space. In this optimum configuration, observation is on or near the axis of symmetry. Moiré sensitivity is that of the reference grating and independent of the specimen grating. The contour map described by moiré fringes depicts in-plane displacements uniquely, being insensitive to thickness and taper of gap between gratings. Moiré fringes are nearly perfect two-beam interference fringes of superb contrast. Existing gratings blazed for single-order dominance can be used under conditions that produce the required double-order dominance. In experimental evaluations, coarse gratings of 200 rulings/cm were mated with various reference gratings up to 12,000 rulings/cm for fringe multiplications by factors up to 60.

Are Biprism Experiments Possible and Significant for Protons and Others?(Proposal of a New Application of Mass Spectroscopy) I.

Electron biprism technique, if extended to any charged particles, will make comparison possible among two-beam interference fringes of electrons and other particles under the same(including wave length)geometrical condition. Combination of the technique with sharply focusing mass spectroscopy will realize such experiments. Due to the tradition since Young-Fresnel, it is believed that two-beam visibilities of particles of various masses under the same geometrical setup are constant and independent of each total sum of macroscopically separated path-lengths, which is not to be confused with ordinary path-difference.(See Fig. 2.)But the assumption of such constant visibility has never been verified experimentally and seems to become gradually unnatural as the masses increase. Experimental reexamination of the assumption is proposed with method of observing an expected mass effect on interdependence between visibility and pathlengths. The smaller visibilities are expected for the heavier masses and the longer path-lengths, contrary to conventional constant visibility; e.g., ≅0.4 for protons of wave length 0.02A and beam width0.2μ in a realizable experimental setup. Technical problems for the experiment and effects to the observation theory are discussed.