Roughness Measurements with Polychromatic Speckles on Tilted Surfaces

Surface light scattering enables contactless and fast measurements of surface roughness.A surface inclination alters the direction of the scattering beam and thus the measured surface roughness is calculated from the detected intensity distribution.Hence,an accurate sensor-surface alignment is necessary.In order to achieve tilt-independent roughness measurements,a model-based evaluation approach for polychromatic speckle patterns is presented.By evaluating the shape of the superposed speckles,which occur for polychromatic illumination,with regard to the distance to the scattering centre,surfaces with an Sa roughness value in the range of 0.8-3.2μm are measurable.Experimental investigations demonstrate that the influence of a surface tilt up to±1.25°on the roughness measurement is reduced by 90%.As a result,the robustness of the polychromatic speckle roughness measurement is improved,which allows to speed up the adjustment of the measurement system or the surface sample,respectively.

Discussion on the Complete-Form Vorticity Equation and Slantwise Vorticity Development

The complete form of the vertical vorticity tendency equation （the complete-form vorticity equation） is derived from the Ertel potential vorticity equation to contain thermodynamic factors. In this study, a new complete-form vorticity equation, which has the same form as the original complete-form vorticity equation, is deduced from the absolute vorticity vector equation combined with the continuity equation and the expression of three-dimensional （3D） entropy gradient. By comparing the complete-form vorticity equation with the classical vertical vorticity equation, it is found that regardless of whether or not the isentropic surface is tilting, the two vorticity equations are in essence the same. The ＂baroclinic term＂ of the complete-form vorticity equation is exactly equal to the solenoidal term of the classical one, and there is a significant amount of cancellation between the two baroclinic items （the ＂slantwise term＂ and the horizontal vorticity change term） in the complete-form vorticity equation. In operational weather analysis, the tilt of the isentropic surface can be diagnosed according to the density of the isotherm on the upper-level isobaric map. For synoptic-scale motion, the vertical vorticity produced by the tilt of the isentropic surface is due to the contribution of atmospheric baroclinicity, which is measured by the solenoid. The 3D solenoid is parallel to the isentropic surface, so the more tilted the isentropic surface, the bigger the projection of the 3D solenoid in the vertical direction. The baroclinic contribution can be interpreted based on the PV thinking theory, but the relationship between the vorticity field and the potential vorticity field is not immediate.