Fringes Of Equal Inclination Research Articles

Interference fringes of equal inclination at large angles of incidence

Interference in thin films, including the formation of fringes of equal inclination, is usually considered for small angles of incidence of light. However, it is necessary in a number of cases to use large angles of incidence of the rays, when it is illicit to replace the sine of an angle by its argument. This paper presents an exact calculation of the parameters of an interference pattern formed at large angles. A nonmonotonic dependence of the distance between the interference fringes on the angle of incidence is detected in this case. Moreover, an expression that connects the distance between the fringes with the angle of incidence, the wavelength of the light source being used, and the thickness of the sample is obtained in this paper that is not limited by the traditional approximation and more accurately describes the fringes of equal inclination. An experimental verification confirms the results.

Optimal geometry for Sagnac and Michelson interferometers used as spectral imagers

High-etendue Fourier transform imaging spectrometers can be useful tools for acquiring airborne hyperspectral images, since they do not need moving parts and, as Fourier transform spectrometers, they benefit from the Felgett advantage. The Sagnac interferometer and the Michelson interferometer with dihedrons can be used in such an instrument. These two interferometers act very similarly on the entering beam, and in particular they both work with fringes of equal inclination. This property enables them to benefit from the Jacquinot advantage, too. Nevertheless, to fully benefit from this advantage, it is necessary to maximize the geometrical etendue accepted by the interferometer. From this point of view, the Michelson interferometer with dihedrons appears to be much more interesting than the Sagnac interferometer. Indeed, calculation shows that, in the optimal symmetric configuration, and for the same beamsplitter diameter, the etendue accepted without vignetting by the Michelson interferometer is more than five times greater than the etendue accepted by the Sagnac interferometer. Even if, in a real instrument, the optical scheme cannot be exactly this optimal configuration, this result is a strong argument in support of the Michelson interfero-meter with dihedrons

Application of a liquid crystal spatial light modulator on optical roughness measurements by a speckle correlation method using two refractive indices

A system of roughness measurements using a CCD camera and a liquid crystal spatial light modulator (LCSLM) has been developed. The scattered light patterns from the surface, which is covered by liquids with several different refractive indices, are acquired by the CCD camera and stored in a frame grabber in a computer. The superposition of two arbitrary patterns is calculated by the computer and displayed on the LCSLM. It is then illuminated by coherent light to produce interference fringes of equal inclination at infinity. The surface roughness can be determined through the relationship between the fringe visibility and the difference of refractive indices. The performance of this system is estimated by experiments.

Influence of distortions on the determination of liquid crystal parameters by the attenuated total reflection technique

Theoretical considerations and measurements on a thin plane-parallel plate show that the fringes of equal inclination and the shift of the whole interference pattern, induced by an external magnetic field, must be used for a correct determination of optical and anchoring properties of liquid crystals.

Interferences with a Plane Parallel Plate Near the Critical Angle of Total Reflection

The fringes of equal inclination with a plane parallel plate surrounded by an optically denser medium start at an angle of incidence less than the critical angle of total reflection. Despite its practical importance this effect was disregarded in optics up to now.

Fringe Loci and Visibility in Holographic Interferometry with Diffuse Objects

Fringe formation in double-exposure holographic interferometry applied to diffuse objects has been investigated. For fringes observed in the region conjugate to the source of object illumination (fringes of equal inclination), relations giving the three-dimensional distributions of the fringe loci and visibility have been derived in the case of an arbitrary combination of object translation, rotation and strain as well as optical set-up. The role of speckle in the fringe formation is explained. Results of computer calculation for several examples are shown graphically.

Influence of Interference Fringes of Equal Inclination on the Reflection of Laser Beams from Plane Parallel Plates

The coefficient of reflection of plane parallel plate beam splitters is very often taken as twice that of a single surface reflection. It is shown that this introduces appreciable errors in the majority of cases, because of the interference fringes of equal inclination. Formulas are derived for the angular dependence of the coefficient of reflection as well as for its average value. The angular distance between adjacent fringes has been evaluated and represented graphically. It is finally demonstrated that the influence of incomplete interference due to the lateral displacement of the reflected beam can be neglected if the beam splitter is followed by an integrating sphere or a similar element.

On the Triangle Path Interferometer

An explicit formula giving the optical path difference of the triangle path interferometer is obtained by applying the same principle as used in the operator formulation in optical instrument design. The result shows that the interferometer gives fringes of equal inclination in usual cases and hence extended light source can be utilized so that greater luminosity is available than in the case of fringes of equal thickness. Several properties of this interferometer are also discussed.

Messungen zur Röntgenstrahl-Optik des Idealkristalls. II. Diffraction Pattern mit `Pendellösung' gleicher Neigung

A double diffractometric verification of diffraction patterns of thin perfect crystals has been tried. In this case the diffraction patterns should be accompanied by `Pendellösung' fringes of equal inclination. This aim could not be reached directly on account of the difficulty of preparing crystal sheets of the necessary extremely small thickness without lattice bending. But photographically the expected fringes appeared as fringes of `equal orientation' on double diffractometric topographs of silicon sheets between 5 and 2μ in thickness, not only in the Laue case but also in the Bragg case. This is the first observation of Pendellösung in the Bragg case.

Theory of the Fabry-Perot interferometer with nonparallel reflectors

Taking into account the wave structure of the light beam, determined by diffraction theory, we consider the harmful effect of the inclination of the mirrors of a Fabry-Perot interferometer when fringes of equal inclination are being observed. It is found that the contrast and resolution of the fringes of equal inclination are reduced as the angle of the wedge so formed is increased, and the interferometer (resonator) completely loses its high-resolution capability (Q-factor) when the mirrors deviate from parallelism by an angle equal to half the diffraction angle at its aperture. The advantages of stopping down both the incoming and outgoing beams in improving the contrast and increasing the resolution of the fringes of equal inclination are pointed out.

Coherence of Light Filtered by Fabry-Perot Etalons

The spatial and temporal coherence of the light filtered by Fabry-Perot etalons was experimentally investigated. Fringes of equal inclination are photographically shown as they are closely related to spatial coherence. The visibility of fringes of equal thickness was measured for the several combinations of etalons and light sources, the radiations was measured from low and high pressure mercury lamps at 0.5461 µ. Peaks were found spaced at every 20 mm and 2.3 mm in visibility when the etalons of the same spacings were used. Non-linear variation in the phase angle of fringes associated with the peaks was examined in comparison with that of fringes formed with the 0.5461 µ line of Hg 198.

Multiple-beam ‘Transmission-like’ Fizeau Fringes in the Reflexion Interference System

MULTIPLE reflexions between close, nearly parallel surfaces of high reflectivity give rise to the well-known sharpened Fizeau fringes of equal thickness1. For two surfaces of equal reflectivity R and equal transmittivity T, neglecting absorption, the successive interfering beams in the transmitted system have intensities T2, R2T2, R4T2. … = T2 (1, R2, R4, …). For the reflected system the intensities are R, RT2, R2T2. . . = R, RT2(1, R2, R4, …). As shown by Tolansky, the Airy summation of the corresponding amplitudes is valid for non-parallel plates provided certain conditions are met, and we thus obtain the intensity distribution of the transmitted and reflected fringe systems. It is found that, except for the term R (and neglecting the factor R, close to unity for high-reflectivities), the reflected series is identical to the transmitted series. The term R represents the beams directly reflected from the upper surface. If these beams can be eliminated from the reflected system we are left with exactly the transmitted fringe system (reduced slightly in intensity by the factor R). That the usual reflexion fringes (minima on a light field) then become ‘transmission-like’ (maxima on a dark field) was shown by Lummer2 for fringes of equal inclination at infinity. Tolansky3 refers to the effect as “a property that can be exploited in special cases”.

Fringes of Equal Inclination in the Double-Passed Michelson Interferometer

The formation of fringes of equal inclination in the double-passed Michelson interferometer is discussed and a theoretical expression is obtained for the intensity distribution in the interference pattern. It is shown that the intensity distribution in these fringes undergoes a periodic modulation as the path difference in the interferometer is varied. Accurate measurements are possible with these fringes using a photometric setting criterion.

269. Fringes of equal inclination in the double-passed Michelson interferometer: P. Hariharan and D. Sen, J. Opt. Soc. Amer., 51, No. 6, June 1961

269. Fringes of equal inclination in the double-passed Michelson interferometer: P. Hariharan and D. Sen, J. Opt. Soc. Amer., 51, No. 6, June 1961