Generalized method for the computational phase correction of arbitrary dual comb signals.

Area of Science:

• Spectroscopy
• Optical Engineering
• Signal Processing

Background:

• Dual comb spectroscopy (DCS) offers high-resolution spectral analysis.
• Phase and timing fluctuations in DCS limit accuracy.
• Existing correction methods can be complex or system-specific.

Purpose of the Study:

• To develop a versatile computational algorithm for correcting phase and timing fluctuations in arbitrary dual comb spectra.
• To establish theoretical limits for self-correction accuracy in DCS.
• To provide a robust and hands-off method for improving DCS signal quality.

Main Methods:

• Augmenting a Kalman filter with a global search.
• Decoupling interferogram estimation.
• Deriving an upper bound for self-correction accuracy.
• Utilizing expectation maximization for parameter learning.

Main Results:

• The algorithm successfully corrects phase and timing fluctuations in diverse dual comb signals.
• The augmented Kalman filter achieves the derived theoretical accuracy bound for bandlimited noise.
• Expectation maximization enables parameter learning without free parameters, enhancing robustness.
• Demonstration code is provided for practical application.

Conclusions:

• The developed computational phase correction algorithm is effective for arbitrary dual comb systems.
• The method is robust, accurate, and approaches theoretical limits for phase correction.
• This approach simplifies and enhances the reliability of dual comb spectroscopy analysis.