Donghak Choi

Numerical Compensation of Dispersion Mismatch in Discretely Swept Optical-Frequency-Domain-Reflectometry Optical Coherence Tomography

We propose a numerical method to compensate dispersion mismatch in optical coherence tomography (OCT) based on optical-frequency-domain reflectyometry (OFDR). Dispersion mismatch causes phase distortion in interferograms depending on wavelength and results in a loss of resolution. We introduce a method to perform the numerical compensation directly to experimental interferograms in real space. Experimental tests are performed for the case of the Mach–Zehnder type OFDR-OCT using a super-structured-grating distributed-Bragg-reflector (SSG-DBR) laser, in which the wavenumber of the optical source is swept discretely by equal interval. It is shown that the method is effective to improve images for layered transparency sheets. We also apply the method to OFDR-OCT imaging of a human nail.

Amplitude truncation of Gaussian 1/fα noises

Abstract An interesting experimental fact concerning Gaussian 1/ f noise was reported a few years ago: when the noise amplitude is truncated at two levels under rather general conditions, the power spectral density remains the same. In this Letter, we present a theoretical derivation of this invariant property of 1/ f noise, together with a generalization for Gaussian 1/ f α noises with 0 α α ≤1, a transformation of keeping only the sign of 1/ f α noise, i.e. y ( t )=sgn[ x ( t )], leads to the same 1/ f α spectrum. When 1 α f ( α +1)/2 noise. Our theoretical results are confirmed by numerical simulations.

Improved sensitivity of optical frequency domain reflectometry-optical coherence tomography using a semiconductor optical amplifier

We demonstrate an approach to enhance the optical frequency domain reflectometry (OFDR)-optical coherence tomography (OCT) sensitivity using a semiconductor optical amplifier (SOA) and a superstructure grating-distributed Bragg reflector (SSG-DBR) laser. We find that the sensitivity of the OCT images of an extracted canine tooth increases as a function of SOA injection current due to amplification through stimulated emission. At the injection current of 150 mA, the sensitivity of the OCT image is increased to a factor of 22.8 dB when compared to the unamplified OCT. Furthermore, an 18 µm axial resolution of the OCT in dental tissue is achieved using the discrete wavelength-swept SSG-DBR laser with an axial scan rate of 0.25 kHz. The observed results suggest that the optical amplification by SOA can significantly enhance the sensitivity of the OFDR-OCT system with a high-resolution.

Amplitude truncation of Gaussian 1/fα noises: Results and problems

An interesting property of Gaussian 1/f noise was found experimentally a few years ago: The amplitude truncation does not change the power spectral density of the noise under rather general conditions. Here we present a brief theoretical derivation of this invariant property of band-limited Gaussian 1/f noise and include 1/fα noises also with 0⩽α<2. It is shown that when α⩽1, a transformation of keeping only the sign of the zero-mean 1/fα noise does not alter the shape of the spectral density. The theoretical results are extended to truncation levels differing significantly from the mean value. Numerical simulation results are also presented to draw attention to unsolved problems of amplitude truncation using asymmetric levels.

Phonon Number Fluctuations in One-Dimensional Fermi-Pasta-Ulam Lattices

We study the long-term behavior of one-dimensional Fermi-Pasta-Ulam lattices by varying the system size and the degree of nonlinearity. The power spectral density of the lowest mode energy obeys the power law P(f)∝1/fα over a wide range of frequencies: f S\lesssimf\lesssimf1, where f1 is the lowest mode frequency. In the low frequency region f\lesssimf S, white spectra are observed. The shoulder frequency f S first increases and then decreases as the system size increases, which can be qualitatively explained in terms of two competing factors. If the system is not very small, the spectrum is Lorentzian at low frequencies, i.e., the spectral exponent α is closer to 2 than 1.

Generalized Amplitude Truncation of Gaussian 1/fα Noise

We study a kind of filtering, an amplitude truncation with upper and lower truncation levels x_max and x_min. This is a generalization of the simple transformation y(t)=sgn[x(t)], for which a rigorous result was obtained recently. So far numerical experiments have shown that a power law spectrum 1/f^alpha seems to be transformed again into a power law spectrum 1/f^beta under rather general condition for the truncation levels. We examine the above numerical results analytically. When 1<alpha<2 and x_max = -x_min = a, the transformed spectrum is shown to be characterized by a certain corner frequency f_c which divides the spectrum into two parts with different exponents. We derive f_c depending on a as f_c sim a^(-2/(alpha-1)). It turns out that the output signal should deviate from the power law spectrum when the truncation is asymmetrical. We present a numerical example such that 1/f^2 noise converges to 1/f noise by applying the transformation y(t)=sgn[x(t)] repeatedly.We study a kind of filtering, an amplitude truncation with upper and lower truncation levels x max and x min . This is a generalization of the simple transformation y ( t )= sgn[ x ( t )], for which a rigorous result was obtained recently. So far numerical experiments have shown that a power law spectrum 1/ f α appears to be transformed again into a power law spectrum 1/ f β under rather general condition for the truncation levels. We examine the above numerical results analytically. When 1<α<2 and x max =- x min = a , the transformed spectrum is shown to be characterized by a certain corner frequency f c which divides the spectrum into two parts with different exponents. We derive f c depending on a as f c ∼ a -2/(α-1) . It turns out that the output signal should deviate from the power law spectrum when the truncation is asymmetric. We present a numerical example such that 1/ f 2 noise converges to 1/ f noise by applying the transformation y ( t )= sgn[ x ( t )] repeatedly.

Theoretical and experimental results concerning the amplitude truncation of Gaussian 1/fα noises

An interesting property of Gaussian 1/f noise was found a few years ago: amplitude truncation does not change the power spectral density of the noise under rather general conditions. Here we present a brief theoretical derivation of this invariant property of Gaussian 1/f noise and include 1/fα noises also with 0⩽α⩽2. The theoretical results are also extended to levels differing significantly from the mean value. We also present numerical simulation results. Which draw attention to unsolved problems of amplitude truncation using asymmetric levels.