Determination of surface inclination angles of thin plates by holographic moiré method

Abstract

This work shows that if, when recording holograms, the recording medium is located at a considerable distance from the surface of the working raster, then the recorded optical information is largely determined by the angles of inclination of the surface being studied. When deriving the resolving equation, the normal component of the displacement vector was expanded into a Taylor series in the vicinity of a point on the surface under study, forming a reference beam. Only the linear term of the series was retained in the equation. It is also taken into account that for plates of medium thickness, the displacements tangent to the plate are proportional to the angle of inclination. The article describes the technique of applying a working raster to the surface under study using a replica raster. The results of a study of the bending of a thin, round, rigidly clamped plate are presented. Hard pinching was modeled by a sharp change in the thickness of the plate. The plate was made on a lathe. The average cylindrical stiffness was determined experimentally, based on the maximum deflection of the plate determined using holographic interferometry. During the tests, a spirit-exposure hologram was recorded in colliding beams at different levels of hydrostatic pressure on the plate. The patterns of interference fringes observed in light passing through the hologram in +1 and –1 diffraction orders were recorded. The coordinates of the center of the interference fringes in the paintings were determined manually. Information obtained in the +1 and –1 orders was approximated by power polynomials using the Excel spreadsheet program. The half-difference of these polynomials was taken as the equation for the inclination angles of the midline of the plate. A good agreement between the experimental data processed using new resolving equations and the theoretical solution was obtained.