Speckle interferometry in polar and cylindrical coordinates: Configurations and engineering applications

Most configurations used in speckle interferometry are naturally configured in Cartesian coordinates, allowing the measurement of the Cartesian components of displacements and deformations. However, some engineering measurement problems are best solved in polar or cylindrical coordinates. Although it is usually possible to analytically convert Cartesian coordinates into another coordinate system, measurements become simpler, faster and measurement uncertainties potentially smaller, if the optical system measures directly in polar or cylindrical coordinates. This paper presents a few speckle interferometer configurations able of measuring in polar or cylindrical coordinates. They use conical mirrors or axicon diffractive optical elements in the optical setup. In addition to the particular configurations, this paper presents practical engineering applications involving radial deformations measurement of internal and external cylindrical surfaces, residual stresses measurement and a shearography non-destructive testing application.