Development of a multi-view fringe projection system for coordinate metrology

The aim of the thesis is the development of a novel methodology for the characterisation of a multi-view fringe projection system, comparing the developed methodology with the conventional approach, and performing the verification tests on the multi-view fringe projection system. In general, commercially available single-view fringe projection systems struggle to acquire the full form/shape in one acquisition due to multiple occlusions, complex freeform geometries, limited field of view and the line of sight issues. Multi-view fringe projection systems are considered an effective solution to overcome the limitations of existing single-view optical systems. However, characterisation of a multi-view system is challenging due to the complexity involved, the need for defining a global coordinate system for multiple cameras and projectors and the fusion of the data from multiple perspectives. In order to identify the constraints of the single-view systems, a fringe projection system with a single camera and projector, similar to available commercial systems, has been designed. The system is tested by measuring the three-dimensional shape of different complex additive manufactured artefacts. Additionally, to investigate the error originating from gamma non-linearity, limited depth of field and the environmental noise, commercially available low-cost pico digital light processing and laser projectors are compared for use in fringe projection applications. The outcome reveals that the eye-safe laser projector outperforms the pico digital light processing projector providing a higher quality of sinusoidal fringe patterns, has a much longer depth-of-focus ($ \times 10$ that of the pico digital light processing projector) and suitable for measuring large objects. Another case study is performed on the uncertainty evaluation of the form measurement of an industrial test case using contact and non-contact methods. Multi-view fringe projection systems are considered an active research area. In such systems, characterisation has a decisive influence on the system performance and accurate three-dimensional surface reconstruction. The characterisation of a multi-view fringe projection system relies on finding the intrinsic and extrinsic parameters of the cameras and projectors and bringing them into the global frame of reference. A generic approach is the extension of the methods for characterising the single camera-projector systems, where each camera is characterised with an accurately manufactured target whilst the projector is modelled as an inverse of the camera and needs additional information to develop a one-to-one correspondence between the camera and projector intensity pixels, which is provided in terms of absolute phase map. The relationship between different views is obtained by global optimisation of the extrinsic parameters of all the multiple perspectives. Two approaches for characterising the multi-view fringe projection system are demonstrated, a conventional one and a novel approach based on stereo rectification of phase maps. In the conventional approach, an automated characterisation method is used, which utilises a checkerboard to characterise the system and determine the intrinsic and extrinsic parameters of all the cameras and projectors. The phase information from the phase-stepped fringes is used to establish the global reference frame by automated image processing and parameter optimisation. The three-dimensional surface reconstructions have been shown to overcome the limitations of the single-view system, mainly associated with occlusions, shading and high slope angles. In the conventional approach, the transformation from the camera image pixels to the projector image pixels is carried out by a phase-stepped fringe projection technique. However, mapping error induces if the camera pixels are not aligned with the projector pixels, which affects the performance and accuracy of the fringe projection system. To address this issue, a novel method to characterise a multi-view fringe projection system is introduced, which is independent of projector characterisation and alleviates the influence of mapping error. The proposed method depends on the stereo matching between rectified unwrapped stereo phase maps based on the epipolar constraint, and the matched phase points in the stereo phase maps are triangulated for three-dimensional reconstructions. Furthermore, the developed methodology is used to perform the verification tests on the multi-view fringe projection system