Impact of background and modulation on parameter estimation using fractional Fourier transform and its solutions

Area of Science:

• Optical Interferometry
• Signal Processing

Background:

• Closed-fringe patterns with quadratic phase are crucial in optical interferometry.
• Fractional Fourier Transform (FRFT) is effective for analyzing these patterns due to spectral separation in the fractional domain, unlike the Fourier domain.
• Existing FRFT-based parameter estimation is sensitive to non-uniform illumination causing varying backgrounds and modulations, lacking theoretical justification.

Purpose of the Study:

• To theoretically analyze the impact of varying background and modulation on FRFT-based parameter estimation in optical interferometry.
• To introduce and evaluate fringe normalization techniques to mitigate these impacts.
• To improve the accuracy of parameter estimation for closed-fringe patterns.

Main Methods:

• Theoretical analysis of the effects of varying background and modulation on FRFT.
• Application of three fringe normalization techniques to preprocess fringe patterns.
• Parameter estimation using the FRFT-based method on the normalized cosine-only term of the fringe pattern.

Main Results:

• Identified key factors for optimal results when using normalization methods.
• Demonstrated that the proposed normalization approach significantly improves parameter estimation accuracy compared to previous FRFT-based methods.
• Validated the feasibility and applicability of the enhanced approach through simulations and experimental results.

Conclusions:

• The developed fringe normalization technique effectively eliminates the detrimental impact of varying backgrounds and modulations on FRFT-based parameter estimation.
• The enhanced FRFT method provides more accurate physical quantity retrieval in optical interferometry.
• The study offers a robust and applicable solution for analyzing challenging fringe patterns.