Dynamic phase measurement based on spatial carrier-frequency phase-shifting method

Abstract

Combining spatial carrier-frequency phase-shifting (SCPS) technique and Fourier transform method, from one-frame spatial carrier-frequency interferogram (SCFI), a novel phase retrieval method is proposed and applied to dynamic phase measurement. First, using the SCPS technique, four-frame phase-shifting sub-interferograms can be constructed from one-frame SCFI. Second, using Fourier transform method, the accurate phase-shifts of four sub-interferograms can be extracted rapidly, so there is no requirement of calibration for the carrier-frequency in advance compared to most existing SCPS methods. Third, the wrapped phase can be retrieved with the least-squares algorithm through using the above phase-shifts. Finally, the phase variations of a water droplet evaporation and a Jurkat cell apoptosis induced by a drug are presented with the proposed method. Both the simulation and experimental results demonstrate that in addition to maintaining high accuracy of the SCPS method, the proposed method reveals more rapid processing speed of phase retrieval, and this will greatly facilitate its application in dynamic phase measurement.

Precise phase demodulation of single carrier-frequency interferogram by pixel-level Lissajous figure and ellipse fitting

“…ILSM 19 can effectively compensate variations of background and modulation as well as the local phase shift error. It is, therefore always regarded as a reference when comparing the performance of SCPS methods 20 , 22 . In this simulation, most parameters in Xu’s simulation 19 are purposely inherent to facilitate a straightforward comparison, thereby avoiding the personal ILSM error.…”

“…Although the correctness of the mathematical model and the high accuracy of the proposed PLEF method were demonstrated in the previous simulation, theoretical errors remain. As previously outlined 20 , 22 , 23 , the background, modulation, encoded phase, phase carrier, fringe tilt angle and additive noise can all affect the accuracy of SCPS algorithms. Yet the proposed method performs well.…”

“…Hereafter, the classic SCPS demodulates the phase using conventional PSAs with the predetermined carrier frequency of π /2 rad/pixel 17 . With the development of generalized PSA in temporal PSI, especially the advanced iterative algorithm (AIA) 7 and the principle component analysis method (PCA) 18 , the CFI can now be demodulated without pre-calibrating the carrier frequency 19 – 22 . However, variations in background/modulation and local phase shift over adjacent pixels are still the main error sources leading to distinct detuning errors in all modified algorithms, except for the iterative least squares method (ILSM) proposed by Xu et al .…”

“…Using these parameters, the final encoded phase can be reconstructed in many different ways, e.g. it can be integrated with local phase shift (without phase unwrapping process) 21 , demodulated directly from two sinusoidal expressions 27 and the least squares fitting method can also be applied 21 , 22 . Detailed characteristics and the capability of the method proposed in this paper will be discussed and corroborated in the following sections.…”

Phase Extraction Algorithm Based on the Spatial Carrier-Frequency Phase-Shifting Gradient

“…The SCFPS algorithm without above problems is first proposed in [9] by introducing onedimensional spatial carrier-frequency, then the phase extraction can be implemented by the threestep phase-shifting algorithm, but the accuracy of phase extraction is not high. Subsequently, by introducing the two-dimensional spatial carrier-frequency, the phase extraction is achieved by the least squares iteration (SCFPS-LSI) [10], the least squares iteration and the Fourier transform (SCFPS-FTLS) [11], the principal component analysis (SCFPS-PCA) [12], the diamond diagonal vectors (SCFPS-DDV) [16] and other algorithms. However, above these SCFPS algorithms need construct four-frame sub-interferograms, so the data redundancy and calculation time will be increased.…”