Fringe Position Research Articles

Automated optical field mapping using a single-mode fiber interferometer

Spatial distribution of optical phase and amplitude can be measured by using a single-mode optical-fiber interferometric system. Following the first proposal of the measuring principle by the present authors in 1978, a further development of the measuring system is now reported. The major achievement is the use of a novel spatial filter and a set of photodetectors by which the interference fringe position is located. Combining them with analog signal-processing circuitry and with a mechanical feedback system, fully automated recording of the optical phase and amplitude distribution is successfully achieved. The method is used to measure phase-front distribution near a Gaussian beam waist.

Optical Ramsey fringes: Effect of velocity averaging on fringe shape and position

A theoretical analysis of Ramsey fringes produced by the interaction of a molecular beam and a three-zones electromagnetic resonator is reported. After averaging over the longitudinal velocity distribution of the particles, the relation between the fringe envelope width and the velocity distribution width is discussed. If the second-order Doppler shift is introduced, the fringe envelope displacement is found to be of the same amount expected for the second-order Doppler effect, but in the opposite direction. This analysis can be of some interest for the discussion of the performance of beam frequency standards in the near optical region.

Three-beam effects inPendellösungfringes

The perturbations of standard two-beam Pendellösung fringes due to simultaneous excitation of an additional Bragg beam have been studied. For a qualitative understanding of the observed local changes in both fringe position and intensity, a plane-wave description has proved to be sufficient. Through three-beam calculations of Bloch-wave excitation coefficients it is found that the main intensity terms may be ascribed to the same four dispersion surface branches which are excited also in the corresponding two-beam case. The continuous variation observed in the fringe period and position is explained from the variation in the width of the dispersion surface gap. This gap varies with the sign and size of the deviation parameter of the simultaneously excited beam. For a given deviation parameter the gap width also depends on the sign of the product between the three structure factors involved. The resulting dependence of the fringe displacement on this sign may be utilized to determine the three-phase structure invariant experimentally.

Theoretical considerations of extra equal-thickness fringes around a dislocation outcrop observed with an X-ray plane wave

An analytical interpretation is presented of extra half-line equal-thickness fringes observed at a dislocation outcrop in X-ray and electron micrographs of wedge-shaped crystals taken at off-Bragg conditions. Extra fringes arc well explained as the interference of two wavefields deduced from Takagi's equations for dynamical diffraction in distorted crystals. Theoretical discussions given in the present paper confirm the experimentally obtained rule of Δn = h. b (h is the diffracting vector and b the Burgers vector of a dislocation), which determines the extra number of fringes, Δn, at the dislocation outcrop. When h. b ≠ integer, it is predicted that a discontinuous shift will occur in the position of equal-thickness fringes along the topographic image of a dislocation.

Computer-aided fringe-pattern analyzer—A case of photoelastic fringe

A real-time “Computer-Aided FRinge-pattern AN-alyzer” (CAFRAN) system for the analysis of photoelastic fringe is developed. The pattern-analyzing process which utilizes image analysis or pattern-recognition technique and discretized-computation process in terms of finite-element method play an important role in this system. The former makes it possible to readout the fringe position and the fringe order of both isochromatic and isoclinic informations, and the latter analyzes the sum of the principal stresses which constitutes the Laplace field. Both results are combined to give the distributions of stress components over the domain under consideration.

High resolution lattice images of aluminum-copper alloy containing Guinier-Preston zones

Imaging of atomic structure of sinple crystals such as A1 and Au by the conventional high resolution electron microscope operated at 100 kV is still not very easy, because the lattice spacing of the crystals are smaller than about 2. 3 A, which equivalent to the resolving power of the microscopes. However, if the crystal lattice image is taken at the “Aberration Free Focus” condition(l), the fine structure of the crystal lattice can be photographed. Using this technique, atomic structure arround G.P. zone is studied in the present paper. Since local orientation in the specimen film disturbes the Bragg condition, we did not succeed to observe the atomic structure but could see the lattice fringes, which are formed by the systematic reflection from the crystal position. The fringe position obtained such condition corresponds to the position of atomic rows.Disc specimens were spark-cut from the sheet of an Al-3.97%Cu alloy.

Beugungstheoretische Behandlung eines Differentialinterferometers für ausgedehnte Phasenobjekte

The diffraction theory of image construction has been used, in the case of a differential interferometer employing a Wollaston prism, to derive the position of the interference fringes in dependence upon the phase object and the prism position. This procedure is not only more correct, but proves also to be simpler than the corresponding geometric-optical treatment. An example is presented in which the fringe shift resulting from a symmetrical gas flow has been used to evaluate the gradient of the optical path perpendicular to the rotational axis of symmetry.

Über den Einfluß der Beugung auf die interferentielle Längenmessung

In interferometry ideal plane or spherical waves are supposed to propagate between the reflecting surfaces. Diffraction effects however, due to the finite diameter of the beams, cause distortions of the wavefronts, changing fringe position and contrast of the interference pattern. Corrections for length measurements with a two beam interferometer have been calculated. If for example the wavelength of a He-Ne-laser, stabilized by saturated absorption of methane at 3.39 μm, is determined by a precision length measurement in a Michelson interferometer with a beam diameter of 25 mm and a path difference of 400 mm a correction of Δλ/λ = 5.10-9 was found.

Contribution à l'étude de la diffraction de Bragg par les empilements épitaxiques de couches minces réalisés sur substrat amorphe

Often a strong texture is found when metal thin films are evaporated in vacuum on amorphous substrates: the hkl dense planes have an average orientation parallel to the substrate. Then, in the hkl X-ray diffraction pattern, secondary fringes are observed on both sides of the Bragg central peak, although they do not appear on other Bragg lines. It is shown that such properties are consistent with lattice distortions and deformations peculiar to each crystal. When the sample consists of an epitaxic 'sandwich' stacking (i.e. two thin films with the same material and the same thickness separated by one or several foreign atomic layers) contrast and angular positions of the secondary fringes are modified. The geometrical interpretation suggested here explains the change in the diffraction pattern shape, and its evolution when foreign atoms are diffusing into the neighbouring films.

Growth of Guinier-Preston zones and the θ″-phase in Al-4%Cu alloys

The structures of Guinier-Preston, G.P., zones and the θ‘-phase are studied by means of high resolution electron microscopy including the lattice image technique. G.P. zones can be observed mainly as black lines in the bright field, but sometimes white lines, depending on the diffraction condition. the θ’-phase appears as black lines aligned in parallel with about 8 Å separation, but a different separation can also be recognized. In lattice images, the relative positions of lattice fringes around precipitates which are observed as white lines are measured. The result shows an existence of an asymmetric strain field around the G.P. zones.

Simplified interpretation of interference fringes obtained by time-average holography

A method of evaluating time-average holograms which gives the vibration amplitudes of an object is described. The method is based on the holodiagram, from which a value of sensitivity ( k value) is obtained. For sinusoidal vibrations of an object, a k values are calculated from the roots of the zero order Bessel function; these give the values of the vibration amplitude at the dark interface fringes directly by multiplication with the wave-lenght of the laser light and appropriate k value. a k values are tabulated for the first twenty fringes. a He values which incorporate the wavelenght of the commonly used He-Ne laser are also tabulated. The evaluation of a hologram of a metal sheet is described. Finally the difference between the position of fringes obtained from objects with sinusoidal and square-wave amplitudes of vibration is shown.

Automatic measurement of intereference photographs from the ultracentrifuge

With a computer-linked densitometer and an algorithm built around the Fourier transform, it is possible to automate the reading of Rayleigh interference patterns such as those obtained from an analytical ultracentrifuge. Measurements of fringe position are at least as precise as data collected manually.

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.

透過型顕微干渉法による微小球面の形状測定

An application of transmitted-type microinterferometry on the form measurement of small spherical parts is investigated.Replicas of the spherical parts to be measured, made of methyl-and ethyl-metaacrylate on a plane mirror, are immersed in oil and observed on an interference microscope with a low magnification. By using proper oil, Newton's rings can be observed over required area on the spherical part irrespective of surface finish.By measuring the radii of curvature of five steel balls and their repricas with microscopic collimation method (Guild's mirror method), it is confirmed that the replicas have satisfactory reproducibility and stability.The equation of a sphere representing the form of each specimen is derived by measuring the positions of interference fringes and by applying Deming's method of least squares and mean radius of curvature and form errors are evaluated.As an example of practical application, the tip forms of the standard hammers for Shore hardness test are measured by this method. The result is compared with the measurement by microscopic collimation and it is revealed that the radius of about 1 mm can be measured with the precision of about 3 μm in standard deviation if the specimen has a good sphericity.

An Interference Method for Determining the Degree of Parallelism of (Laser) Surfaces

A method for measuring the angle between two nearly parallel surfaces is presented. Convenient to use, the method has ample brightness and sensitivity for use in aligning the various surfaces often found in laser cavities. A cw laser is focused to provide a point source of light which illuminates the two surfaces in question. The reflected light beams form an interference pattern from which the angle between the surfaces can be easily measured. A simple equation is given relating the fringe position to angular separation.

Improvement of Recorded Holographic Fringes By Feedback Control

A feedback control system has been designed to stabilize the position of interference fringes, particularly those which occur in holography. The result of closed loop operation of the system is that rather severe phase perturbations may occur in either of the beams, and yet be compensated for such that the fringes in the holographic recording medium are essentially stabilized. This paper discusses the design and analysis of an experimental model and its performance for phase perturbations due to acoustic and mechanical vibration, thermal drift, large perturbations, warm air turbulence, and small doppler shifts. The authors then speculate that more advanced designs may stabilize interference fringes even with larger phase perturbations such as large doppler shifts, optical frequency differences, motion of the scene, and holographic interferometry.

Absolute Positions of Pendellösung Fringes in X-Ray Cases

The positions of Pendellosung fringes with respect to the entrance surface were studied experimentally. In section-type experiments, the following results were obtained. (1) At the entrance surface the intensity of the wave field takes the maximum. (2) The distance between the first and second fringes is larger than the averaged one. (3) The positions of fringes in a deeper region are shifted by a quarter of the averaged fringe distance towards the entrance surface, compared with the fringe positions expected. from the conventional plane-wave theory of dynamical crystal diffraction. The traverse-type experiments were also carried out. These results are predictable by a spherical wave theory (N. Kato: Acta cryst. 14 (1961) 526, 627). The fact (3) is due to the phase jumps of the crystal waves at a kind of caustic region near the entrance surface. The phenomenon is similar to the phase anomaly near the focal point of lenses.

Pendell�sung fringes in elastically deformed silicon

The propagation of pairs of coherent X-ray wavefield beams in a crystal deformed elastically by a uniform temperature gradient, has been studied in the symmetric Laue case by observing interference between the beams when they are superimposed on the X-ray exit surface of the crystal. Information concerning the relative phases of the beams was obtained from the position of Pendellosung fringes in section patterns. The measured change of the relative phase between the two beams was in good agreement with predictions made by the theory ofPenning andPolder. Variations in the magnitude and sign of the deformation, in the X-ray wavelength and in the X-ray structure factor resulted in relative phase changes which were in agreement with the theory.

Determination of the Molecular Weight Distribution of Chondroitin Sulfate B by Sedimentation Equilibrium

Summary of molecular weight data of the solute (assumed independent molecular weight and Nominal initial concentration - I -- btor speed - __ COlUlUll height g/lv 1.2 iiz:/iiT: 1.5 - _- Molecular weight concentration), X the wave length of light used, and C the con- centration. The values for the various parameters in Equation Yii” -O I I M zo 1 are listed in “Experimental Procedure.” With these values the la w * constant, K, of the equation, with f in microns and C in g per liter, becomes eaual to 2593. 23.5 23.5 23.0 x 10-q 27.3 27.3 27.3 27.3 27.3 27.3 26.3 26.3 26.3 26.3 44 41 41 41 40 39.5 40.5 Under the conditions used by us, a fringe position correspond- ing to zero concentration cannot be established. Thus, observed values of j are only relative, containing an unknown additive constant. However, the difference between the f values at any two positions is given directly by the data, and we have therefore based all calculations on values of f - ja, where f0 is the fringe height at the upper meniscus (r = r,). Where C, is the concen- tration at that position, f - fa = K(C - Co) (2)

Test of the Effect of Edge Parameters on Small-Angle Fresnel Diffraction of Light at a Straight Edge

Precision photometric measurements of the optical Fresnel diffraction pattern produced by a straight edge were made on eight edges of various materials and with various edge cross sections to ascertain the effect of these parameters on the pattern. For unpolarized light at a wavelength of 5461 A, approximately 600 fringes were detected and measured in each pattern, and 800 fringes were detected in some of the patterns. The theoretical position of the geometric shadow (I/I0 = 0.25) is verified to an angular accuracy of 1 × 10−4 deg. The light intensity distribution was scanned at a constant speed and detected by a 1P21 photomultiplier tube cooled to dry-ice temperature. The distance between the light source and the photometer was 52 m, and the edge was placed 20 m from the source. A simple technique for automatic compensation for fluctuations of the primary light source is also described. Accuracy of approximately 0.2% in the intensity measurements and of 0.03% in fringe position far from the shadow boundary is claimed. To within the accuracy of the experiment, the intensity distribution for all eight edges agreed throughout the complete pattern, but there is a slight variation in fringe position from the simple scalar theory.