We propose using non-uniform FFT to minimize the degrading effect of frequency tuning nonlinearity of a tunable laser source (TLS) in an optical frequency-domain reflectometry (OFDR) system. We use an auxiliary interferometer to obtain the required instantaneous optical frequency of the TLS and successfully demonstrate 100 times enhancement in spatial resolution of OFDR with only a 20% increase in computation time. The corresponding measurement reflectivity sensitivity is better than -80 dB, sufficient to detect bending induced index changes in an optical fiber.
The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D Discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform and inverse DFT sequence can be exploited for coding. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.
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