Precise and fast spatial-frequency analysis using the iterative local Fourier transform

Area of Science:

• Signal Processing
• Computational Physics
• Optical Metrology

Background:

• The fast Fourier transform (fFT) is a widely used, efficient algorithm for discrete Fourier transforms.
• Limitations in frequency resolution of the fFT can hinder detailed analysis of complex signals.
• Advanced Fourier transform techniques are sought for improved resolution and computational performance.

Purpose of the Study:

• To introduce the iterative local Fourier transform (ilFT), a novel set of processing algorithms.
• To evaluate the performance of ilFT in terms of frequency resolution and computational efficiency.
• To compare ilFT with existing high-resolution Fourier transform methods.

Main Methods:

• Development of iterative algorithms applying the discrete Fourier transform in local frequency domains.
• Evaluation of ilFT's computing efficiency, resolution, and spectrum zoom-in capability.
• Comparative analysis against fFT combined with various fitting methods.

Main Results:

• The ilFT achieves 2^10 times higher frequency resolution compared to the fFT.
• The technique maintains comparable computation time to the fFT.
• Demonstrated effectiveness in analyzing Talbot self-images from an experimental setup.

Conclusions:

• The ilFT presents a significant advancement in Fourier transform techniques.
• Its high resolution and efficiency make it suitable for advanced signal processing and metrology.
• The method shows promise for analyzing complex optical phenomena like Talbot self-images.