Non-uniform non-harmonic analysis method development and verification of applicability to swept source optical coherence tomography

Abstract

Abstract:We generally analyze data measured at equal time intervals using fast Fourier transforms (FFTs). However, when for some reason we can only obtain unequally spaced measurement points, then the data become non-uniform and cannot be analyzed directly using FFTs. In this paper, the non-uniform trapezoidal integral discrete Fourier transform (TIN-UDFT) is proposed to replace the FFT, and is implemented in non-harmonic analysis (NHA) to develop non-uniform NHA (NUNHA) for non-uniform data. NUNHA improved the SNR by over 70 dB compared with the simple non-uniform sinusoidal signal frequency. NUNHA's effectiveness for swept source optical coherence tomography (SS-OCT) is shown by simulation.

Numerical simulation validation of nonuniform, nonharmonic analysis of spectral-domain optical coherence tomography

“…In Figs. [14][15][16] In the conventional methods, distortion caused by interpolation occurs in addition to the effect of nonequivalence. In Fig.…”

“…16 The accuracy of NUNHA for SS-OCT interference signal analysis has been verified and it achieved a signal-to-noise enhancement of 70 dB during analysis of a nonuniform sinusoidal signal. 16 The accuracy of NUNHA for SS-OCT interference signal analysis has been verified and it achieved a signal-to-noise enhancement of 70 dB during analysis of a nonuniform sinusoidal signal.…”

“…14,16 In NHA, the cost function evaluates the difference between the analyzed object signal and the parameters deduced from the sinusoidal model. 14,16 In NHA, the cost function evaluates the difference between the analyzed object signal and the parameters deduced from the sinusoidal model.…”

“…8 Moreover, the sensitivity fall-off for SS-OCT is very small relative to SD-OCT and is thus superior in terms of its axial resolution for the deep imaging range. [14][15][16] Initially, we demonstrated by means of numerical simulation that NHA achieves an improvement in the resolution of eight digits or more in an ideal environment. 8 Zurauskas et al demonstrated an imaging depth of 17 mm.…”

Visualizing the Periods of Stock Prices Using Non-Harmonic Analysis of the NASDAQ Composite Index Since 1985

“…Under NHA, the analysis precision does not decrease, because it can deal with an element with high resolving power in a period, even if it is analyzed in a short window length. For more details about NHA further, please refer to the following paper (Yoshizawa, Hirobayashi and Misawa, 2011;Ichinose, 2012;Xu Cao, et al, 2012;Uchida, et al, 2013).…”