A generalized noise variance analysis model and its application to the characterization of 1/f noise.

We present a novel generalized model for the analysis of noise with a known spectral density. This model is particularly appropriate for the analysis of noise with a 1/f(a) distribution in a homodyne interferometer. The noise model reveals that, for alpha>1, 1/f(a) noise significantly impacts the homodyne signal-to-noise ratio (SNR) for integration times that near a characteristic time, beyond which the SNR will no longer significantly improve with increasing integration time. We experimentally verify our theoretical findings with a set of experiments employing a quadrature homodyne optical coherence tomography (OCT) system, finding good agreement. The characteristic integration time is measured to be approximately 2 ms for our system. Additionally, we find that the 1/f noise characteristics, including the exponent, alpha, as well as the characteristic integration time, are system and photodetector dependent.

[1]  Leonid G. Kazovsky,et al.  Optical Heterodyning Versus Optical Homodyning: A Comparison , 1985 .

[2]  C. Davis,et al.  Trace detection of hydrazines by optical homodyne interferometry. , 1991, Applied optics.

[3]  M. Weissman.  1/f noise and other slow, nonexponential kinetics in condensed matter. , 1988 .

[4]  Steven L. Jacques,et al.  Low coherence interferometry of the cochlear partition , 2006, Hearing Research.

[5]  B Kaulakys,et al.  Point process model of 1/f noise versus a sum of Lorentzians , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Zhihong Wang,et al.  Scanning homodyne interferometer for characterization of piezoelectric films and microelectromechanical systems devices , 2005 .

[7]  B. Bouma,et al.  Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography. , 2003, Optics letters.

[8]  Jeff Fingler,et al.  Homodyne en face optical coherence tomography. , 2006, Optics letters.

[9]  Salvade,et al.  Limitations of interferometry due to the flicker noise of laser diodes , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  Edoardo Milotti,et al.  1/f noise: a pedagogical review , 2002, physics/0204033.

[11]  G. Ripandelli,et al.  Optical coherence tomography. , 1998, Seminars in ophthalmology.

[12]  Changhuei Yang,et al.  Instantaneous quadrature low coherence interferometry with 3 x 3 fiber optic couplers , 2003, Conference on Lasers and Electro-Optics, 2003. CLEO '03..

[13]  Edward A. Lee,et al.  Performance of coherent optical receivers , 1990, Proc. IEEE.

[14]  Wentian Li,et al.  Universal 1/f noise, crossovers of scaling exponents, and chromosome-specific patterns of guanine-cytosine content in DNA sequences of the human genome. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  S. Ledesma,et al.  Multiphase homodyne displacement sensor , 1994 .

[16]  M. A. Caloyannides,et al.  Microcycle spectral estimates of 1/f noise in semiconductors , 1974 .

[17]  J. Izatt,et al.  Optimal interferometer designs for optical coherence tomography. , 1999, Optics letters.

[18]  W. Press.  Flicker noises in astronomy and elsewhere. , 1978 .

[19]  Roberto Saletti,et al.  1 f γ noise in thick-film resistors as an effect of tunnel and thermally activated emissions, from measures versus frequency and temperature , 1983 .

[20]  J. Johnson,et al.  The Schottky Effect in Low Frequency Circuits , 1925 .

[21]  C. Su,et al.  Polarimetric, nonlinearity-free, homodyne interferometer for vibration measurement , 1996 .

[22]  R. H. Hamstra,et al.  Noise and frequency response of silicon photodiode operational amplifier combination. , 1972, Applied optics.

[23]  Walter Schottky,et al.  Small-Shot Effect and Flicker Effect , 1926 .

[24]  T. Musha,et al.  The 1/f Fluctuation of a Traffic Current on an Expressway , 1976 .

[25]  J Mertz,et al.  Combined scanning optical coherence and two-photon-excited fluorescence microscopy. , 1999, Optics letters.

[26]  Changhuei Yang,et al.  Sensitivity advantage of swept source and Fourier domain optical coherence tomography. , 2003, Optics express.

[27]  J. R. Wallis,et al.  Some long‐run properties of geophysical records , 1969 .

[28]  P. Yeh,et al.  Photonics : optical electronics in modern communications , 2006 .

[29]  A. Fercher,et al.  Performance of fourier domain vs. time domain optical coherence tomography. , 2003, Optics express.

[30]  Bo Liu,et al.  Polarization interferometer for measuring small displacement , 2001, IEEE Trans. Instrum. Meas..

[31]  Z. Siwy,et al.  Origin of 1/f(alpha) noise in membrane channel currents. , 2002, Physical review letters.

[32]  M. S. Keshner.  1/f noise , 1982, Proceedings of the IEEE.

[33]  Luís A. Nunes Amaral,et al.  From 1/f noise to multifractal cascades in heartbeat dynamics. , 2001, Chaos.

[34]  John Clarke,et al.  LOW FREQUENCY NOISE IN TIN and LEAD FILMS AT THE SUPERCONDUCTING TRANSITION , 1976 .

[35]  P. M. Horn,et al.  Low-frequency fluctuations in solids: 1/f noise , 1981 .

[36]  S. Personick,et al.  An Image Band Interpretation of Optical Heterodyne Noise , 1971 .