Windowed Fourier transform profilometry based on improved S-transform

Area of Science:

• Optics and Photonics
• Signal Processing
• Metrology

Background:

• Windowed Fourier Transform (WFT) profilometry is a key technique for surface measurement.
• Existing WFT methods can be limited by phase deviations affecting accuracy.
• The S-transform offers time-frequency analysis but requires refinement for precise phase retrieval.

Purpose of the Study:

• To develop a novel WFT profilometry method based on an improved S-transform.
• To derive and address the impact of the second-order phase derivative on the S-transform ridge.
• To achieve more accurate instantaneous frequency estimation and phase map generation.

Main Methods:

• Development of an improved S-transform incorporating phase deviation analysis.
• Derivation of the second-order phase derivative's impact (φ''(b)) on the S-transform.
• Estimation and removal of phase deviation for accurate instantaneous frequency calculation.
• Application of WFT using a window size map derived from instantaneous frequency.

Main Results:

• The improved S-transform effectively estimates and corrects for phase deviations.
• Accurate instantaneous frequency is obtained after deviation removal.
• A precise phase map of fringe patterns is generated using the WFT with the derived window size map.
• The novel method demonstrates superior performance compared to WFT based on wavelet transform.

Conclusions:

• The proposed WFT profilometry method based on improved S-transform provides highly accurate phase maps.
• The technique effectively addresses limitations of previous WFT approaches.
• Numerical simulations and experimental results validate the method's practical applicability in metrology and surface analysis.