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Three-dimensional (3D) shape measurement methods based on fringe analysis could achieve high resolution and high accuracy. Fourier transform profilometry (FTP) uses a single fringe pattern is sufficient to recover the carrier phase for 3D shape measurement. Basically, FTP method applies Fourier transform to a fringe image and extracts the desired phase by applying a band-pass filter to obtain the desired carrier phase. Though successful, the single-pattern FTP method has the following major limitations: 1) it is sensitive to noise; 2) it is difficult to accurately measure an object surface with strong texture variations; and 3) it is difficult to measure detailed complex surface structures. To alleviate the influence of averaged background (i.e., DC) signal, the modified FTP method was proposed by taking another fringe pattern to remove DC from the fringe pattern. Even more robust, the modified FTP method still cannot achieve high accuracy for complex surface geometry or objects with strong texture. This is because to properly recover the carrier phase, FTP requires a properly designed filter to recover the carrier phase that might be polluted by surface texture or geometry. Hilbert transform, in contrast, is based on one inherent property of Hilbert transform: it shifts the phase of a sine function by $\pi/2$. For a fringe pattern without DC component, the phase can be directly retrieved using Hilbert transform without filtering. This paper examines differences between these two methods and presents both simulation and experimental comparing results.
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