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

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2 Scopus citations

Abstract

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 x 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Original languageEnglish (US)
Pages (from-to)22110-22120
Number of pages11
JournalOptics Express
Volume24
Issue number19
DOIs
StatePublished - Sep 19 2016

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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