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Three-dimensional (3D) shape measurement for specular surfaces is becoming increasingly important in various applications. A novel orthogonal dual-frequency fringe is proposed in the specular surface shape measurement to overcome the phase jumping and discontinuities in spatial phase unwrapping. The fringe recalibrated high-accuracy phase information from its high-frequency fringe component with low-ambiguity phase information from its low-frequency fringe component. An improved Fourier transform deflectometry method based on the orthogonal dual-frequency fringe is proposed to measure 3D specular surface shapes. Simulation results showed that the orthogonal dual-frequency Fourier transform deflectometry (ODD) method could precisely reconstruct flat surfaces with an error of 2.16 nm rms, and concave surfaces with an error of 1.86 μ m rms. Experimental results showed that the reconstructed shapes of both the flat mirror and the concave mirror measured by the ODD measurement system were highly comparable to those obtained by the phase-measuring deflectometry (PMD) method. This new fringe provides a distinctive approach to structured pattern construction and reduces the phase unwrapping ambiguities in specular surface shape measurement. The ODD method can achieve accurate 3D shape measurement for specular surfaces by sampling only one fringe, providing a possible basis for future real-time measurement of specular surfaces. [ABSTRACT FROM AUTHOR]

The three-dimensional (3D) shape of specular surfaces is important in aerospace, precision instrumentation, and automotive manufacturing. The phase measuring deflectometry (PMD) method is an efficient and highly accurate technique to measure specular surfaces. A novel simulation model with simulated fringe patterns for monoscopic PMD is developed in this study. Based on the pre-calibration and the ray-tracing model of the monoscopic PMD system, a comprehensive model from deformed pattern generation to shape reconstruction was constructed. Experimental results showed that this model achieved high levels of measuring accuracy in both planar and concave surfaces measurement. In planar surface measurement, the peak to valley (PV) value and root mean square (RMS) value of the reconstructed shape can reach 26.93 nm and 10.32 nm, respectively. In addition, the accuracy of the reconstructed concave surface can reach a micrometre scale. This work potentially fills critical gaps in monoscopic PMD simulation and provides a cost-effective method of PMD study. [ABSTRACT FROM AUTHOR]