Reconstruction of partial envelope of interference pattern based on chirp Z-transform

Area of Science:

• Optics and Photonics
• Signal Processing
• Interferometry

Background:

• Accurate determination of interference pattern envelope peak positions is crucial in multi-pulse train interferometers.
• Traditional methods often rely on the discrete Fourier transform (DFT) for envelope estimation.
• Existing techniques may require estimating the entire interference pattern envelope, which can be computationally intensive.

Purpose of the Study:

• To present a novel algorithm for the partial reconstruction of interference pattern envelopes.
• To improve the accuracy and efficiency of determining peak positions in interference fringes.
• To introduce an alternative to DFT-based envelope estimation using the chirp Z-transform (CZT).

Main Methods:

• Developed a new algorithm based on the chirp Z-transform (CZT).
• The algorithm focuses on reconstructing only the relevant part of the interference pattern envelope around the peak.
• Applied and demonstrated the algorithm using optical fringes for the first time.

Main Results:

• The proposed algorithm successfully performs partial reconstruction of interference pattern envelopes.
• It accurately determines the peak position of the envelope without needing to reconstruct the entire pattern.
• Experimental results validate the reliability of the CZT-based approach for partial envelope determination.

Conclusions:

• The novel CZT-based algorithm offers a reliable and efficient method for partial envelope reconstruction.
• This approach simplifies the process of determining peak positions in interference fringes.
• The findings have significant implications for multi-pulse train interferometry and related optical applications.