Prof. Xian G. Kong Profile

Prof. Xian G. Kong

at Xi'an Univ of Posts & Telecoummunications

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Publications (2)

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Proceedings Article | 31 August 2021 Paper

Novel four-step phase shifting algorithm based on the products of sines and cosines

Jin Lu, Xian G. Kong, Jian Xu, Xiao G. Sun, Fu P. Wang

Proceedings Volume 11907, 119071Q (2021) https://doi.org/10.1117/12.2603038

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Wrapped phase extraction is an essential process for the retrieval of absolute phase and even the computation of object height information in fringe projection profilometry. Over the past few decades, tremendous efforts have been devoted to developing various techniques for computing wrapped phase. By comparison, four-step phase-shifting techniques play an important vehicle for obtaining the wrapped phase of 3D objects. At present, a variety of four-step phase-shifting algorithms show the comprehensive mathematical deduction and their theories are very clear. Analysis from the perspective of theoretical integrity, however, the phase-shifting techniques lack the exploration of arbitrary phase shift. In view of this, inspired by the prosthaphaeresis in trigonometric, we present a novel four-step phase-shifting algorithm. The proposed method includes 16 kinds of four-step phase-shifting fringe combination and corresponding calculation formula of wrapped phase, which are deduced with two frames fringe images of sines and two ones of cosines. Furthermore, simulations and experiments have been carried out to reveal the influence law of variable phase shift on the performance of these approaches.

Proceedings Article | 28 February 2021 Paper

Geometric analysis and new discoveries for phase-shifting algorithms based on the orthogonal resolution and resultant of forces

Jin Lu, Yuan Li, Xian G. Kong, Hui B. Sun, Xiao G. Sun

Proceedings Volume 11781, 1178105 (2021) https://doi.org/10.1117/12.2591118

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In fringe projection profilometry, the wrapped phase extraction is an essential process for absolute phase unwrapping and even the computation of object height information. Over the past few decades, tremendous efforts have been devoted to developing various techniques for computing wrapped phase. By contrast, the phase-shifting techniques process more advantages including higher accuracy, higher spatial resolution, and lower sensitivity to variations of background intensity and surface reflectivity. At present, a variety of phase-shifting algorithms show the comprehensive mathematical deduction and their theories are very clear. Analysis from the perspective of theoretical integrity, however, the phase-shifting techniques lack the exploration of geometric algebra. For that reason, inspired by the orthogonal resolution and resultant of forces in physics, we present a geometric analysis method. Furthermore, exploiting the proposed method to explore the double three-step algorithm, four-step algorithm and extended averaging technique, we obtain three new discoveries. Simulations and experiments have been carried out to verify the performance of these new discoveries. In addition, these results also reflect the necessity of the geometric analysis method for phase-shifting techniques.

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