Abstract
Abstract. Measuring specular surfaces can be realized by means of deflectometric measurement systems with at least two reference planes as proposed proposed by Petz and Tutsch (2004). The results are the point coordinates and the normal direction of each valid measurement point. The typical evaluation strategy for continuous surfaces involves an integration or regularization of the measured normals. This method yields smooth results of the surface with deviations in the nanometer range but it is sensitive to systematic deviations. The measured point coordinates are robust against systematic deviations but the noise level is in the order of micrometers. As an alternative evaluation strategy a data-fusion process that combines both the normal direction and the point coordinates has been developed. A linear fitting technique is proposed to increase the accuracy of the point coordinate measurements by forming an objective functional as the mean squared misfit of the gradients with respect to the point coordinates on the one hand and to the normals on the other hand. Moreover, a constraint on the maximal change of the coordinate measurements is added to the optimization problem. To minimize to objective under the constraint a projected gradient method is used. The results show that the proposed method is able to adjust the point coordinate measurement to the measured normals and hence decrease the spatial noise level by more than an order of magnitude.
Highlights
Introduction and measurement principleThe combination of close range photogrammetry and structured illumination is well established in the field of threedimensional measurements of diffusely reflecting surfaces
We deduce that the expected value of this sum is equal to N σ 2. We use this value as tolerance δ = N σ 2 and define the set in which the point coordinates are allowed to be shifted as B = { problem becomes minPz F (Pz) − Pz 2 ≤ δ}, the sphere with radius δ around the measured z coordinate Pz
Due to the local and absolute measurement, the point coordinates are very robust against systematic deviations but with stochastic deviations in the order of 10 μm
Summary
The combination of close range photogrammetry and structured illumination is well established in the field of threedimensional measurements of diffusely reflecting surfaces. By means of structured illumination, which especially involves phase shifting techniques, the surface under test is optically coded Based on this spatial coding, the camera images can be evaluated in a way that delivers a three-dimensional object point for each image pixel. This fringe projection technique depends on the optical imaging of the surface under test onto the image sensor of the camera. The enhanced approach uses at least two different positions of the reference pattern, which can be realized by moving the reference structure with a linear stage With this approach the camera defines a unique ray for each image point, and the information from the spatially coded reference patterns delivers an unambiguous ray.
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