A Gaussian process and image registration based stitching method for high dynamic range measurement of precision surfaces

Optical instruments are widely used for precision surface measurement. However, the dynamic range of optical instruments, in terms of measurement area and resolution, is limited by the characteristics of the imaging and the detection systems. If a large area with a high resolution is required, multiple measurements need to be conducted and the resulting datasets needs to be stitched together. Traditional stitching methods use six degrees of freedom for the registration of the overlapped regions, which can result in high computational complexity. Moreover, measurement error increases with increasing measurement data. In this paper, a stitching method, based on a Gaussian process, image registration and edge intensity data fusion, is presented. Firstly, the stitched datasets are modelled by using a Gaussian process so as to determine the mean of each stitched tile. Secondly, the datasets are projected to a base plane. In this way, the three-dimensional datasets are transformed to two-dimensional (2D) images. The images are registered by using an (x, y) translation to simplify the complexity. By using a high precision linear stage that is integral to the measurement instrument, the rotational error becomes insignificant and the cumulative rotational error can be eliminated. The translational error can be compensated by the image registration process. The z direction registration is performed by a least-squares error algorithm and the (x, y, z) translational information is determined. Finally, the overlapped regions of the measurement datasets are fused together by the edge intensity data fusion method. As a result, a large measurement area with a high resolution is obtained. A simulated and an actual measurement with a coherence scanning interferometer have been conducted to verify the proposed method. The stitching result shows that the proposed method is technically feasible for large area surface measurement.