3D surface profilometry based on 2D S-Transform method with optimized window

S-Transform method can be regarded as an extension to the ideas of the Windowed Fourier Transform (WFT) method and the Wavelet Transform (WT) method, which gives consideration to both local frequency concept of WFT and the multi-resolution strategy of WT. It has been introduced in optical 3D shape measurement recently. However, the S-Transform method suffers from poor energy concentration when some kind of signal is treated with. In order to enhance energy concentration to provide more accurate estimation of the instantaneous frequency, a modification to the existing 2D S-Transform is proposed in this paper. Two additional parameters are introduced to respectively optimize the window width in x and y direction. The paper gives the expression of 2D S-Transform with optimized window and its performance in 3D surface reconstruction. The application of proposed method is demonstrated on both simulation and experiment by comparing with traditional 2D S-Transform method. The improved performance of optimized 2D S-Transform for 3D surface shape measurement shows its feasibility and veracity.