Showing papers on "Moiré pattern published in 1968"

Radial gratings as moiré gauges

Abstract: A theory on the formation of moire patterns by mutually interfering radial gratings is developed. It is shown that the moire fringes formed inside the circle, which has as diameter the centre-to-centre distance of the gratings, belong to the additive moire type and they represent families of confocal equilateral hyperbolae. Outside this circle the subtractive moire pattern is valid, which consists of circles of different radii whose centres lie on the perpendicular bisector of the centre-to-centre distance. For the radial grating moire gauge the additive moire pattern is of importance since two sectors of radial gratings are used with a large centre-to-centre distance. The radial gauge is convenient for determining the normal components of strains. The advantage of this type of gauge over the line grating gauge is that the radial grating corresponds to an infinite number of line gratings of progressively varying pitch. This allows a correct evaluation of displacement and strain at a suitably selected gauge length.

Moire gauging systems

Abstract: A moire gauging system for measuring deviations of complex surfaces of a master compared to a replica thereof or of a master compared to a deformed or vibrating master. To this end, optical fringes are generated interferometrically to project substantially plane sheets of light parallel to each other onto the object to be measured. These fringes on the master can be recorded photographically or by creating a hologram, for example, and compared to the replica, or deformed master or the like which is also illuminated with the same fringe pattern. Distinctions between the two objects to be compared can be detected and measured by the resulting moire pattern.

Theory of Spatial Moiré Fringes

Abstract: The obstruction theory and analytical geometry were used to determine the equations of the rays emerging from a pair of gratings separated by an air gap, and a theory of the formation and location of spatial moire fringes was developed. Fringes resulting from plane gratings lie in planes; the location and inclination of these moire planes depend upon the magnitude and sign of the following parameters: (i) the linear disparity, (ii) the air gap, and (iii) the relative grating inclination.The appearance of spatial moire fringes from any point of view and the resulting interfringe spacing on a camera image plane were investigated. In particular, the appearance of the spatial moire fringes, which have been utilized in strain analysis, was investigated. Experimental evidence satisfactorily supported the theoretical findings.

Optical Wave-Front Mapping by Dual Interferometry*

Abstract: Some advanced methods of wave-front mapping by coupling of two interferometers are described. Moire-like superposition of interferograms eliminates certain inherent interferometer errors. Moire interferometry indicates the direction of the order of interference.The same instrument in different alignment enhances the sharpness of reflection multiple-beam fringes or reverses their contrast for a transmissionlike appearance.

Measurement of interference fringe separation by a moiré technique

Abstract: The superposition of a parallel grating on a divergent grating will generate hyperbolic moir? fringes. Within this pattern of hyperbolic fringes one fringe, the limiting hyperbola, will be a straight line, and the position of this line can very effectively measure the separation of the parallel grating once the divergent grating has been calibrated. This method is used for measuring the spacing of Fizeau fringes.

Surface topography by multisource moiré patterns: Moiré patterns of multisource type yield surface topography

Abstract: Moire patterns produced by interference of a series of periodically arranged linear light sources with a line-specimen grating of similar pitch are located at a plane parallel to the sources and the specimen grating and at some distance away from these planes. A transparent or reflecting specimen located at a distance from the specimen grating distorts the image of the multisource projected on the specimen grating due to its surface irregularities and forms a moire pattern. This pattern yields the partial-slope contours of the topography of the specimen along a direction normal to the lines of the grating. Two such contour patterns taken at mutually perpendicular directions are sufficient to yield the complete topographic picture of the surface.

General interpretation of moiré patterns in strain analysis

Abstract: A simple theoretical treatment of moire patterns is given with the use of relations between diagonal systems that have the physical meaning of contour lines of the functions in question. The general approach and knowledge of diagonal-system properties can simplify various problems of strain measurement by the moire method, and this is demonstrated by the compensation of a moire pattern and by the method of two-dimensional strain measurement.

Magnified interferometric measurements of small displacements

Abstract: A simple optical system is described which permits a doubling of the fringe movement in the application of a Fizeau interferometer to measure small displacements. The amplitude of the light emerging from the interferometer is divided, one of the beams is inverted by means of a Dove prism, and the two images of the Fizeau fringes are superposed to form moire fringes in the same focal plane as the Fizeau fringes.

Anti-parallax device for observation of moiré fringes

Abstract: A parallax corrected grating system, consisting of two coarse plane gratings close together, enables relative displacements of 0?0005 in to be observed visually by use of the moir? effect, in ambient light conditions.