A method for phase retrieval from dense phase fringe in phase-shifting electronic speckle pattern interferometry (ESPI)
using fast windowed Fourier filtering (FWFF) method is presented. Phase-shifting method is an accurate method in ESPI
for phase retrieval. However, the wrapped phase map is corrupted by the speckle noise which will significantly affect the
phase unwrapping technique to acquire the accurately unwrapped phase map. For relatively large deformation
measurement, the wrapped phase map becomes dense and hence becomes difficult to be demodulated properly.
Conventional sine-cosine average filtering technique is difficult to reduce the noise in such case. FWFF algorithm is
useful for noise reduction of wrapped phase maps. In this paper we propose to measure relatively large deformation by
reducing noise using FWFF. Both the simulation and experimental results are presented to show that the proposed
method can efficiently reduce the noise of the dense wrapped phase map and the deformation can be obtained using
phase unwrapping technique. Further, the effect of speckle size on the results is also discussed.
Time-frequency analysis is widely applied to the optical measurement for phase retrieval from fringe patterns.
Windowed Fourier transform (WFT) is one of the time-frequency analysis methods and has recently received extensive
study on phase retrieval from fringe patterns generated by the optical interferometry or structured light illumination.
WFT has been applied for shape and deformation measurement in dynamic nondestructive testing. However, the
computation time of WFT is longer than that of conventional Fourier transform method for fringe demodulation. This
has restricted the WFT in the application for dynamic measurement. Therefore, a modified WFT is introduced to reduce
the computation time. In this approach, the fast Fourier transform is implemented in the WFT algorithm to improve the
computational efficiency and border effect of the proposed method for fringe analysis is discussed. The phase retrieval of
the proposed method is simulated and the simulation results are compared with conventional Fourier transform method
and convolution method of WFT in terms of noise reduction. The experimental work on shape and deformation
measurement is conducted to verify the effectiveness and validity of the proposed method.
Temporal Paul wavelet analysis for instantaneous phase extraction using shadow moire technique is proposed. Unlike the
Morlet wavelet, the Paul wavelet has less restriction on the adjustment of wavelet parameters and can provide an optimal
time and frequency resolution for a particular application by selecting the proper parameters. The Paul wavelet is a
complex wavelet and is suitable for processing the temporal intensity data obtained from the shadow moire technique for
the phase retrieval. The proposed method can extract the phase information related to the state of the dynamic object at
every instant in temporal domain. The phase information is associated to the displacement, three-dimensional (3D)
surface-profile and the instantaneous state of the dynamic object. In addition, the instantaneous frequency of vibrating
object can be obtained using the scale of the wavelet ridge by direct integration without temporal and spatial phase
unwrapping. Thus the phase unwrapping error can be avoided. An experiment is conducted on the central loaded beam to
demonstrate the validity of the proposed technique.