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A fast Gabor wavelet transform for high-precision phase retrieval in spectral interferometry.

J Bethge, C Grebing, G Steinmeyer

|June 25, 2009

Summary

A new Gabor wavelet transform offers faster phase retrieval for spectral interferometry. This method improves accuracy by reducing noise and artifacts compared to traditional Fourier filtering, enabling real-time applications.

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Area of Science:

Optical Physics
Signal Processing

Background:

Spectral interferometry is crucial for characterizing ultrashort laser pulses.
Accurate phase retrieval is essential for electric-field reconstruction.
Traditional Fourier filtering methods can be susceptible to noise and artifacts.

Purpose of the Study:

To develop and evaluate a fast Gabor wavelet transform for phase retrieval in spectral interferometry.
To compare the performance of wavelet-based ridge tracking with Fourier filtering techniques.
To demonstrate the algorithm's application in characterizing supercontinuum pulses using SPIDER.

Main Methods:

Implementation of a fast Gabor wavelet transform algorithm.
Experimental demonstration using spectral phase interferometry for direct electric-field reconstruction (SPIDER).
Evaluation of wavelet-based ridge tracking for frequency demodulation.

Main Results:

The wavelet-based strategy shows significantly reduced susceptibility to experimental noise and avoids cycle slip artifacts.
Optimum performance of the Gabor transform is achieved with a unity aspect ratio Heisenberg box.
Phase jitter is reduced by a factor of 2, and the detection window increases by 20% compared to Fourier filtering.

Conclusions:

The fast Gabor wavelet transform provides a superior alternative to Fourier filtering for phase retrieval in spectral interferometry.
The optimized implementation achieves retrieval rates of several 10Hz, suitable for real-time applications like SPIDER.
This method enhances accuracy and robustness in electric-field reconstruction.