skip to main content


Title: Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review

In fringe projection pro lometry (FPP), temporal phase unwrapping is an essential procedure to recover an unambiguous absolute phase even in the presence of large discontinuities or spatially isolated surfaces. So far, there are typically three groups of temporal phase unwrapping algorithms proposed in the literature: multi-frequency (hierarchical) approach, multi-wavelength (heterodyne) approach, and number-theoretical approach. In this paper, the three methods are investigated and compared in details by analytical, numerical, and experimental means. The basic principles and recent developments of the three kind of algorithms are firstly reviewed. Then, the reliability of different phase unwrapping algorithms is compared based on a rigorous stochastic noise model. Moreover, this noise model is used to predict the optimum fringe period for each unwrapping approach, which is a key factor governing the phase measurement accuracy in FPP. Simulations and experimental results verified the correctness and validity of the proposed noise model as well as the prediction scheme. The results show that the multi-frequency temporal phase unwrapping provides the best unwrapping reliability, while the multi-wavelength approach is the most susceptible to noise-induced unwrapping errors.
 [1] ;  [2] ;  [1] ;  [3] ;  [4]
  1. Nanjing Univ. of Science and Technology, Nanjing (China). Smart Computational Imaging Lab. (SCILab); Nanjing Univ. of Science and Technology, Nanjing (China). Jiangsu Key Lab. of Spectral Imaging & Intelligent Sense
  2. Brookhaven National Lab. (BNL), Upton, NY (United States)
  3. Nanjing Univ. of Science and Technology, Nanjing (China). Jiangsu Key Lab. of Spectral Imaging & Intelligent Sense
  4. Nanyang Technological Univ., Singapore (Singapore). Centre for Optical and Laser Engineering (COLE), School of Mechanical and Aerospace Engineering
Publication Date:
Report Number(s):
Journal ID: ISSN 0143-8166
Grant/Contract Number:
SC0012704; 11574152; 61505081
Accepted Manuscript
Journal Name:
Optics and Lasers in Engineering
Additional Journal Information:
Journal Volume: 85; Journal Issue: C; Journal ID: ISSN 0143-8166
Research Org:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Natural Science Fund of China
Country of Publication:
United States
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Phase measurement; Fringe projection profilometry; Temporal phase unwrapping
OSTI Identifier: