Optical phase extractions based on reassigned continuous wavelet transform with application to simultaneous...

Area of Science:

• Optical Metrology
• Signal Processing
• Wavelet Analysis

Background:

• Continuous wavelet transform (CWT) with Morlet wavelet struggles with instantaneous frequency extraction in nonstationary optical interferometric fringe signals, especially near null phase gradients.
• Existing methods like phase stepping can introduce nonlinear errors and are less accurate for certain fringe signals.

Purpose of the Study:

• To develop an improved algorithm for accurate instantaneous frequency extraction of highly nonstationary optical interferometric fringe signals.
• To enhance the precision and reliability of fringe signal analysis in optical interferometry.

Main Methods:

• Optimal selection of the central frequency and time variance of the Morlet wavelet to minimize wavelet energy spread.
• Application of the reassignment technique to sharpen wavelet energy density and improve frequency resolution.
• Validation using sinusoidal frequency-modulated fringe signals and Michelson interferometer fringe signals.

Main Results:

• The developed algorithm achieved a mean square error of 0.0032 Hz for instantaneous frequency, significantly lower than the 0.0507 Hz from conventional CWT.
• The technique demonstrated higher accuracy and freedom from nonlinear errors compared to the phase stepping technique for sinusoidal fringe signals.
• Generated displacement profiles from Michelson interferometer data showed superior results compared to the phase stepping technique.

Conclusions:

• Optimal Morlet wavelet parameter selection and reassignment technique significantly enhance instantaneous frequency extraction accuracy for nonstationary optical fringe signals.
• The proposed method offers a more accurate and robust alternative to conventional CWT and phase stepping techniques for interferometric measurements.
• The technique is applicable to a broader range of signals, including arbitrary phase signals.