A look-up table (LUT) method for solving the problem of phase unwrapping is presented. Considering the effect of noise on the unwrapping process, a concept called “tolerance” is advanced, and an associated algorithm called the “equipartition of tolerance” algorithm is proposed. The proposed algorithm eliminates the need for a high signal-to-noise ratio while retaining the LUT method’s advantages of extended measurement range and high precision. Further, it improves the tolerance of the LUT method and enables reconstruction of discontinuous objects. In simulations and experiments conducted, the proposed algorithm successfully unwrapped the absolute phase of a slope model and a three-step model. The proposed algorithm is significantly more accurate and has better stability and sensitivity than the heterodyne algorithm.
A method of phase retrieval based on windowed Fourier transform has been proved to be one of the most effective
algorithms for carrier fringe patterns. The calculation speed of windowed Fourier transform ridge (WFTR) is time
consuming. The accuracy and calculation speed of phase retrieval using WFTR depend on the scanning frequency
interval, but how to determine a proper frequency interval is still a problem. In this paper we see WFTR as a response of
a linear time-invariant system. Then we calculate the system response function by means of numerical analysis, finding
that there is always an area of zero phase response near the local frequency and its width nearly equals to the width of the
main lobe of the amplitude response function. This means a system response function with bigger main lob width and
fast decay rate allows a bigger frequency interval and less calculation times. These operations only increase a little error
at the edge of the fringe pattern, but give a fast calculation speed. Finally we compare the carried fringe pattern phase
with a standard phase extracted by the four-step phase-shifting algorithm.
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