Journal of Optics

, Volume 47, Issue 4, pp 534–541 | Cite as

A novel phase retrieval method in fringe projection based on phase-shifting algorithm

  • Naosheng QiaoEmail author
  • Chenggen Quan
Research Article


In order to reduce nonlinear phase error in fringe projection based on phase-shifting algorithm, a novel phase retrieval method is proposed. Firstly, on the basis of expression for wrapped phase and corresponding phase in N-step phase-shifting algorithm, the nonlinear phase error and its simple expression is deduced. Secondly, based on the four-step phase-shifting algorithm, the wrapped phase expression of actual measured object is obtained. The corresponding nonlinear phase error is derived in a simple form, and then the new phase error value is obtained by offsetting π/4 from the nonlinear phase value. The mean of the new and original phase error values yields the final phase error; hence, the nonlinear phase errors are significantly reduced. Finally, the results of numerical simulations and experiments show that the proposed method is effective to reduce the nonlinear phase error due to system gamma nonlinearity in phase-shifting algorithm.


Phase retrieval Phase error System gamma nonlinearity Phase-shifting algorithm Fringe projection 



We are grateful for the support from the National Natural Science Foundation of China (61475045) and the State Scholarship Fund of China Scholarship Council (201508430221).


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Copyright information

© The Optical Society of India 2018

Authors and Affiliations

  1. 1.School of Physics and Electronic, Hunan Province Cooperative Innovation Center for the Construction & Development of Dongting Lake Ecological Economic Zone, Hunan Province Key Laboratory of Photoelectric Information Integration and Optical Manufacturing TechnologyHunan University of Arts and ScienceChangdeChina
  2. 2.Department of Mechanical EngineeringNational University of SingaporeSingaporeSingapore

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