Two-beam Interferogram Research Articles

Fractographic characterization of isotactic polypropylene fibers.

In this article we present an opto-thermo-mechanical characterization of isotactic polypropylene monofilament during failure by fracture. The digital photoelasticity, the two-beam Pluta polarising interference microscope and the computed tomography are used to provide quantitative data and visual models of the fracture regions of isotactic polypropylene fibers suffering failure by fracture at different thermal and mechanical conditions. Birefringence values and the intrinsic stress-anisotropy are measured at the fracture surface. 3D models of the fracture regions are reconstructed. Photoelastic patterns and two-beam interferograms are included for illustration.

Interference Method for Estimating the Coordinates of a Moving Noise Source in Shallow Water Using High-Frequency Signals

The article presents the results of a high-frequency experiment to localize a moving noise source using a cylindrical small-sized vector–scalar array. Time–frequency processing was used, matched to the interference pattern formed by the source. The time dependences of the bearing, velocity, distance, and depth of the source are reconstructed. The experimental data are qualitatively and quantitative explained using a model two-beam interferogram formed by a direct beam and a beam reflected from the free surface.

Disintegration of multiple-beam Fizeau fringes in transmission using FFT analysis

An investigation of fast Fourier transformation (FFT) spectrum appears from multiple-beam Fizeau fringes is presented. It is proven theoretically and demonstrated experimentally that the number of the appeared peaks is related to the interfered rays’ number. In addition, a detailed interpretation of (FFT) yields from multiple-beam Fizeau fringes analyses is illustrated. This interpretation proved that every peak of the FFT spectrum represents a set of two-beam interference. Therefore, the higher order FFT peaks are not an error. It is found that the frequencies of the appeared peaks are separated by a constant increment. Therefore, when we apply the inverse fast Fourier transformation (IFFT) on a selected peak we can get a two-beam intensity distribution image with a fringe frequency depending on the peak order number. This study removes confusion and answers some important questions concerning the multiple-beam interference. The presented analysis leads to disintegrate multiple-beam interferogram to its components of two-beam interferograms. This could facilitate recovering the phase map and provides more information from one multiple-beam interferogram.

Single-shot 3 × 3 beam grating interferometry for self-imaging free extended range wave front sensing.

Crossed grating 3×3 beam lateral shear interferometry for extended range wave front sensing is presented. A Fresnel diffraction pattern of two multiplicatively superimposed linear diffraction gratings each generating three diffraction orders is recorded. A simple solution employs a common crossed binary amplitude Ronchi grating with spatial filtering. Digital processing of a single-shot pattern includes separating multidirectional pairs of orthogonal lateral shear interferograms, retrieving second harmonics of their intensity distribution, and calculating shearing phases. Single-frame automatic fringe pattern processing based on the Hilbert-Huang transform is used for this purpose. Using second harmonics extends the aberration measurement range since they encode self-imaging free two-beam interferograms without contrast modulations. Experimental works corroborate the principle and capabilities of the proposed approach.

Diffraction grating three-beam interferometry without self-imaging regime contrast modulations.

Achromatic grating shearing interferometry method for wave front sensing is developed. Two Fresnel diffraction patterns formed by grating three lowest diffraction orders are recorded. The beam-splitter grating is displaced laterally by half its period between exposures. Calculating the sum of two patterns results in a two-beam interferogram free of inherent light propagation direction and observation plane contrast modulations imposed by the self-imaging phenomenon (Talbot effect). Single-frame automatic fringe pattern processing provides the interferogram phase distribution. The technique enables continuous shear variations suitable for dynamic range sensing. Experimental works corroborate enhanced capabilities of the proposed approach.

Evaluation of optical parameters of quasi-parallel plates with single-frame interferogram analysis methods

The surface flatness of transparent plates is frequently tested in Fizeau and Twyman-Green interferometers. In case of quasi-parallel plates, however, a common problem is the additional reflection from the plate rear surface and three-beam interference is encountered. Our new method of deriving shape and optical thickness variations of the plate requires recording two interferograms: a two-beam interferogram without a reference beam and the three-beam interference one. The images are processed using single-frame techniques only. The proposed method does not require modification of a sample or sophisticated equipment and complicated data analysis. Full Text: PDF

Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination

Two-beam interferogram intensity modulation decoding using spatial carrier phase shifting interferometry is discussed. Single frame recording, simplicity of experimental equipment, and uncomplicated data processing are the main advantages of the method. A comprehensive analysis of the influence of systematic errors (spatial carrier miscalibration, nonuniform average intensity profile, and nonlinear recording) on the modulation distribution determination using automatic fringe pattern analysis techniques is presented. The results of searching for the optimum calculation algorithm are described. Extensive numerical simulations are compared with laboratory findings obtained when testing vibrating silicon microelements under various experimental conditions.

Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer

The application of the optical vortex interferometer (OVI) to small-angle rotation measurements is presented. The OVI is based on a regular lattice of optical vortices. In our experimental setup a regular lattice of optical vortices is produced by the interference of three plane waves. The vortex points are stable, pointlike structures within the interference field. Distortion of one, two, or three of the interference waves results in a characteristic vortex lattice deformation. This deformation can be measured and related to the physical quantities being investigated. We show the ability of the OVI to measure the deflection angle and the orientation of the wave vector in a single measurement. Two different methods that allow comparing the geometry of the vortex lattice are used to analyze the results of the experiment. They are compared with the method based on standard two-beam interferograms. The results show that the OVI system can be successfully used to measure the deflection and orientation of the wave vector. The vortex methodology is more accurate than classical two-beam interferometry for rotation angles in the range of a few arcseconds.

Interferogram intensity modulation calculations using temporal phase shifting: error analysis

The phase shifting method is an effective tool to determine the intensity modulation distribution of a two-beam interferogram. We present numerical studies of the influence of two experimental errors on the results obtained using temporal phase stepping, i.e., the phase step miscalibration and average intensity changes between the component interferograms. Experimental studies of vibration mode patterns by time-average interferometry provide excellent verification of numerical findings. Comparative analysis of interferogram contrast and intensity modulation determination is included.

Identification of nonlinear recording error in phase shifting interferometry

The phase shifting method for quantitative fringe pattern analysis provides high accuracy if stringent requirements on the component interferogram recording are met. In the paper the issue of detection and identification of error sources in the two-beam interferogram phase shifting experiment is discussed. The phase shift angle histogram and lattice-site representation are applied for that purpose. Special attention is paid to possible nonlinear recording of component interferograms in the presence of linear and nonlinear phase step errors. Four and five step phase shifting algorithms are considered. The superiority of the lattice-site representation is shown. In the case of phase steps equal to π/2, however, the lattice-site representation of shift angles for five frame algorithm does not allow to detect recording nonlinearity. The four frame counterpart shows to be very helpful in this respect. Its properties related to the fringe pattern profile under study, including a defocused Ronchi grating, are discussed.

Simulation of dispersive Fourier interferograms of gases in the visible wave number range

Dispersive two-beam Fourier interferograms of N2-gas in the visible wave number range are calculated numerically for nonabsorbing as well as absorbing gas and compared with experiment. Some problems of inverse Fourier transformation of dispersive interferograms are also discussed.

Determination of In-Plane Strain Using a Holographic Modulated Diffraction Grating

A method for obtaining a highly-sensitive in-plane strain contour as a two-beam interferogram is devised. Using an optical setup in which an object is illuminated from two directions, deformation of the object is recorded in a form of a holographic modulated diffraction grating (MDG) modulated by the in-plane (x) and out-of-plane (z) components of displacement. Two identical MDGs are introduced into a system which connects two coherent double diffraction systems in series. Two spatial filtering processes are incorporated so that the z-component of displacement is cancelled and the difference between the two x-components inherent in the two MDGs, slightly shifted, forms an interferogram. Then the derivative of the in-plane displacement, i.e. the strain, is contoured in the image plane. In a simple experiment with a bent rectangular beam, the resultant interference pattern agreed well with the theoretical pattern and the amount of strain per fringe space was 3.6×10-5.

Determination of in-plane and Out-of-plane Components of Deformation of an Object from One Double-exposure Hologram

The deformation of an object illuminated from two directions is recorded once on a hologram as a series of two-dimensional, grating-like interference fringes. The transparency on which the reconstructed interferogram is recorded acts as a modulated diffraction grating (MDG). When the MDG is illuminated by two plane waves and two suitably selected components of its Fourier spectrum are superposed and spatially filtered, two-beam interferograms which represent in-plane and out-of-plane components of deformation are obtained separately. Fringe multiplication was also possible. The interferogram of in-plane deformation corresponding to a spacing of 0·224 μm per fringe was obtained experimentally.

Changes in orientation of etch pits produced on the cubic faces of diamond

Abstract Cube faces of synthetic and natural diamonds have been etched in KNO3 in the temperature range 500° to 800°C Some of the square pits change orientation at 600°c, their sides lying along <100> instead of <110>. The re-orientation is inhibited by agitation of the crystals during etching. Two-beam interferograms show that only the deeper, larger pits undergo such re-orientation. It is conjectured that this occurs at sites of rapid local etching, and is associated with accumulation of reaction by-products.

A Modified Measuring Projector for the Evaluation of Interferograms

The projector is designed to present a photoelectric scan of an interference fringe pattern together with a fiducial pulse as cathode-ray oscilloscope traces. Using alignment of the two traces as a setting criterion the position of fringes within an interferogram may be evaluated to better than 1/50 of the fringe period. The projector is able to make measurements from two-beam interferograms of low contrast and varying periodicity.

The determination of refractive index spectra by fourier spectrometry

If a dispersive medium is introduced into one arm of a Michelson interferometer irradiated by a wide band of radiation, the two-beam interferogram contains detailed information about the variation of the complex refractive index of the medium with wave-number. Recent experimental work in the infra-red spectral region has shown that this information may be recovered to give the complex refraction spectrum of the material. Details of the mathematical theory and the necessary observations and computations are given, and illustrated by the results of recent investigations of the refraction spectra of specimens in each of the three material phases.

Dispersion Measurements on Polytetrafluorethylene in the Far Infrared

The reflection spectrum of polytetrafluorethylene has been determined in the far infrared over the range 22-143 micro by a Fourier method using observations made on a dispersive two-beam interferogram. The utility of the method, particularly when applied to the anomalous dispersion associated with a resonance absorption, is demonstrated, and values of the real and imaginary parts of the complex refractive index are determined. The relation between these parts of the index for the resonance at 202 cm(-1) (49.5 micro) agrees with the classical expectation of a circular plot in the complex plane.

Refractometry in the Far Infra-red using a Two-beam Interferometer

A MICHELSON two-beam interferometer can be used for refractive-index determination by measuring the shift of the achromatic fringe when a specimen of known thickness is placed in one arm of the interferometer. Such a measurement using a broad spectrum and ‘white-light’ fringes gives only a single index value and that cannot be related to a definite wave-length. Monochromatic radiation cannot be used because of the impossibility of identifying a given fringe after displacement. It appeared plausible, however, that a spectrum of refractive index could be obtained by making observations of intensity over a range of path-difference and taking the Fourier transform of the two-beam interferogram, the method being an extension of that used for obtaining infra-red power-spectra1. This has been realized in the far infra-red region, where the method has been used to determine the refractive-index spectrum of crystalline quartz over the wave-length range 500–180µ (20–56 cm−1). No values have been previously reported over much of this range.

The evaluation of interferograms by displacement and stereoscopic methods

A method of obtaining pairs of interferograms is described which makes possible the accurate and rapid evaluation of the optical path variations in the system tested. Such a pair of two-beam interferograms may be measured by displacement methods to an accuracy of about 0.002 wavelength if the path variations are small, or the pair may be viewed stereoscopically to give an impression of the path variation from point to point over the whole area.