In fringe projection profilometry, applying pre-distortion to fringe patterns reduces the errors caused by projector lens distortion. However, it is important to note that discontinuous fringe patterns, such as binary fringe patterns, introduce additional errors when using pre-distortion methods. While post-undistortion methods are applicable for discontinuous fringe patterns, the computation is typically time-consuming. We propose a linear-grid model for correcting lens distortion. First, we select multiple equidistant points within the grid to calculate the linear parameters and store them as look-up tables (LUTs). Second, by rounding down the captured distorted point to the nearest integer point, we obtain the index value for LUTs. Finally, we achieve real-time compensation for distortion error through linear expressions. The experimental results show that the proposed effectively mitigates the distortion by a factor of 6 × in terms of root mean squared error. Additionally, it exhibits a computational speed of 409.50 fps, which is an improvement compared to the traditional iterative model at 39.48 fps and the scale-offset model at 264.48 fps.
A sample-titling strategy is proposed for the correction of the relative slope of microstructures and the scanning stylus during the surface profile measurement of microstructures with steep slopes. The correct surface profile of a measurement sample was reconstructed by data fusion of the probe trace, rotation angles of a sample and the motion of the scanner. Slope prediction and scanner control methods were also proposed to determine the rotation angle of a sample. Simulation was performed using a stylus with a tip of 2 μm and included angle of 90 degrees, and a trapezoid microstructure with a slope of 60 degrees to verify the feasibility of the proposed method. The measurement error of the proposed method is 0.31 μm while that of an existing scanning method is 4.50 μm in the simulation. Simulation results indicated that the proposed method could be used to increase the maximum detectable slope of a stylus profiling system and to reduce slope measurement errors as well.
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