Two-step phase-shifting algorithms with background removal and no background removal

• Ten two-step phase-shifting algorithms are compared. • Euclidean matrix norm of sum and difference map and fast least-squares algorithm provides the best overall performance. • Background removal method should be improved for two-step phase-shifting algorithms with background removal. • Iterative time, iterative accuracy and valid phase shift range should be improved for two-step phase-shifting algorithms with no background removal. To balance the accuracy and speed of phase reconstruction, two-step phase-shifting algorithms (TS-PSAs) have been developed. TS-PSAs can be divided into two types, one is TS-PSAs with background removal (TS-PSAs-BR), and the other is TS-PSAs with no background removal (TS-PSAs-NBR). We select 6 well-reputed TS-PSAs-BR and 4 TS-PSAs-NBR proposed by the authors of this paper for performance comparison. In order to remove the background, the Hilbert-Huang Transform (HHT) and mean intensity subtraction are used respectively. We compare 10 TS-PSAs with different fringe types, different levels of noise, different phase shifts, different fringe numbers and computational time in the simulations, and the experiments are also performed to compare them. Finally, we rank TS-PSAs according to their comparative results, and Euclidean matrix norm of sum and difference map and fast least-squares algorithm (EMNSD&FLSA) provides the best overall performance, it can achieve high accuracy and high efficiency.