Optical metrology techniques such as fringe projection technology and phase-measuring deflectometry, which use cameras as image sensors for 3D coordinate measurement and inspection, are becoming increasingly demanding. The necessary precise and at the same time robust calibration of image sensors of these systems is offered by so called vision ray calibration. This generic approach is a model-free description of a vision ray and are determined for each imaging sensor pixel. Numerous images of the sinusoidal fringe images displayed on the active calibration target (LCD) are captured in different poses. This generates a large amount of data and consequently leads to time-consuming evaluation for the camera calibration. In this paper, we propose a new optimization method that uses “vision threads" instead of vision rays to enhance the computation efficiency associated with conventional vision ray calibration. We present MATLAB simulation results in to validate our novel approach.
KEYWORDS: Calibration, Cameras, Stereoscopic cameras, LCDs, Imaging systems, Visual process modeling, 3D metrology, Refraction, Ray tracing, Projection systems
Vision Ray Calibration provides a description of imaging properties of cameras by identification of an independent vision ray for each sensor pixel. Due to this approach, no model parameters of any cameras are determined in the non-linear optimization procedure of the calibration. Therefore, a setup of multiple cameras can be considered as one imaging system. This enables simultaneous and holistic calibration of an arbitrary number of cameras. Vision Ray Calibration utilizes Liquid Crystal Displays as calibration targets since these can provide the required continuous spatial coding of their surfaces by means of Phase Shifting Technique. However, displays employed as calibration targets exhibit some unfavorable properties such as flatness deviations of the surface. It is known that extending the Vision Ray Calibration by a polynomial parameterization of the display surface increases the calibration accuracy. This work investigates the influence of the order of polynomial terms employed for display surface parameterization. The stereoscopic Fringe Projection enables the evaluation of the calibration accuracy since Vision Ray Calibration of a stereo camera setup provides full system calibration for this technique. Our results confirm the significant improvement of calibration accuracy due to parameterization of flatness deviations of the display. Best calibration results were obtained by limiting the maximum order of polynomial terms to three. Our results indicate that terms of higher orders do not contribute true surface shape features.
Phase Measuring Deflectometry (PMD) is a non-coherent full-field measurement technique based on geometrical optics, usually employed for specular surfaces. The measured phase in PMD corresponds to the position on the display recorded by the camera pixels. Concerning the measurement uncertainty in PMD systems, the camera can be regarded as the best described and most thoroughly modelled part, followed by the display with its nonlinearity or flatness deviation of the monitor surface shape. However, the effect of the properties of technical surfaces on the measurement deviation still lacks detailed investigation. As the errors in phase measurement will introduce subsequent errors into the slope and shape measurement, it is important to study these error sources. This paper investigates the effects of the properties of technical surfaces on phase measurements in a PMD system. We demonstrate the dependence of the deviations of phase measurements on surface roughness using well-defined samples manufactured by high precision diamond turning.
Camera calibration is fundamental for camera based measurement processes. While photogrammetric calibration models are widely established, the more sophisticated approach, describing an independent ray for every pixel, still requires thorough investigation to achieve its full potential. Such a Generic-Camera-Calibration or so called Vision-Ray-Calibration (VRC) compensates the effects of lens distortions more precisely than other techniques and can calibrate various lenses. Our current efforts are to improve calibration algorithms for VRC and find geometrically optimal calibration procedures. As a step towards this goal we present a metric to compare calibration results and therefore the necessary procedure to ensure that the coordinate systems of the calibrations are similar. With this new metric it is easier to investigate VRC procedures.
Phase Measuring Deflectometry is a highly precise and full-field measurement technique suitable for specular surfaces. Typically, computer displays are used to provide reference patterns whose distortions, when observed as reflections at the surface under test, provide the information to determine its shape. During the evaluation, an ideal display is usually assumed, ignoring properties like shape deviation with respect to a plane. Such deviations, however, limit the accuracy of this technique. To provide a starting point for the development of a more sophisticated evaluation technique, this paper presents our models and results for the simulation of non-ideal display properties in deflectometry. Our simulations contain the geometrical calibration of components of our setup as well as the shape measurement. Evaluations are based on global deviations of the measured surface. The display properties under consideration are investigated individually as well as in combination. As a result of our model-based investigation, we find that shape deviations of the display are the most dominant influence when measuring the global shape of the surface under test while the influence of angle-dependent emission characteristics of the display is neglectable.
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