To optically capture the topography of a hot measurement object with high precision, the light deflection by the inhomogeneous refractive index field-induced by the heat transfer from the measurement object to the ambient medium-has to be considered. We used the 2D background oriented schlieren method with illuminated wavelet background, an optical flow algorithm, and Ciddor's equation to quantify the refractive index field located directly above a red-glowing, hot measurement object. A heat transfer simulation has been implemented to verify the magnitude and the shape of the measured refractive index field. Provided that no forced external flow is disturbing the shape of the convective flow originating from the hot object, a laminar flow can be observed directly above the object, resulting in a sharply bounded, inhomogeneous refractive index field.

Optical three-dimensional (3-D) geometry measurements are state of the art when it comes to contactless quality control and maintenance of the shape of technical components that exclude tactile measurements due to filigree or internal structures. Optical inspection methods are also characterized by a fast and high-resolution 3-D inspection of complex geometries. And due to their noncontact principle, they can carry out measurements in places that would otherwise not be accessible due to harsh environmental conditions or specimens such as hot forged parts. However, there are currently no methods to estimate the reconstruction quality for the optical 3-D geometry measurements of hot objects. The mainly used geometric measurement standards cannot be used for the characterization of hot measurements since the calibrated geometrical values are not transferable to high temperatures. For the development of such a metric, we present the fundamentals of the concepts and algorithms for an estimation of the reconstruction quality are presented and evaluated using a two-dimensional simulation model. The generated findings were applied to the 3-D geometry measurement of a hot object in a laboratory environment. The results are compared with general state-of-the-art reconstruction quality metrics. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

In this paper, we present a system to compensate for the light deflection effect during the optical geometry measurement of a wrought-hot object. The acquired 3D data can be used to analyze the formed geometry of a component directly after a hot forging process without waiting for the needed cooling time to room temperature. This may be used to parameterize the process and to detect defect components early in the production process, among others. The light deflection as the deviation from the linear path of the light is caused by an inhomogeneous refractive index field surrounding the hot object. We present the design and setup for a nozzle-based forced air flow actuator, which suppresses the light deflection effect. The design process includes a simulation of the developing field, as well as of the interaction of the field with an external forced air flow. The cooling effect of the air flow is evaluated, and conclusions are drawn from the conflicting interests of good measurement conditions against the forced cooling of the hot object. The findings are then implemented in the physical setup of the suppression system. The system is evaluated using a previously established method based on optical triangulation and fringe projection. Other occurring effects and their influence on the evaluation are considered and discussed.

The optical inspection of wrought hot workpieces between subsequent forming steps of a multistage process chain can yield diverse advantages. Deficient components can be detected in an early forming stage. Moreover, the eliminated cooling economizes heating energy. The present workpiece temperature can be exploited in the following chain steps. Challenges arise due to the heat input into the air surrounding the workpiece, as triangulation techniques rely on homogeneous optical conditions. The effect of an inhomogeneous refractive index field (RIF) in air on a 3-D geometry measurement by optical triangulation is modeled exemplary by a virtual measurement of a hot cylinder. To our knowledge, this is the first simulation approach that fully considers both light deflection from the illumination unit to object and from object to camera. Simulated measurement results in a homogeneous and an inhomogeneous RIF are compared. The presented approach predicts measurement deviations in inhomogeneous optical media and can help to design actuated or computer-assisted compensation routines in order to reduce deflection effects when measuring hot objects.

A robust calibration approach for a telecentric stereo camera system for threedimensional (3-D) surface measurements is presented, considering the effect of affine mirror ambiguity. By optimizing the parameters of a rigid body transformation between two marker planes and transforming the two-dimensional (2-D) data into one coordinate frame, a 3-D calibration object is obtained, avoiding high manufacturing costs. Based on the recent contributions in the literature, the calibration routine consists of an initial parameter estimation by affine reconstruction to provide good start values for a subsequent nonlinear stereo refinement based on a Levenberg-Marquardt optimization. To this end, the coordinates of the calibration target are reconstructed in 3-D using the Tomasi-Kanade factorization algorithm for affine cameras with Euclidean upgrade. The reconstructed result is not properly scaled and not unique due to affine ambiguity. In order to correct the erroneous scaling, the similarity transformation between one of the 2-D calibration plane points and the corresponding 3-D points is estimated. The resulting scaling factor is used to rescale the 3-D point data, which then allows in combination with the 2-D calibration plane data for a determination of the start values for the subsequent nonlinear stereo refinement. As the rigid body transformation between the 2-D calibration planes is also obtained, a possible affine mirror ambiguity in the affine reconstruction result can be robustly corrected. The calibration routine is validated by an experimental calibration and various plausibility tests. Due to the usage of a calibration object with metric information, the determined camera projection matrices allow for a triangulation of correctly scaled metric 3-D points without the need for an individual camera magnification determination.