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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 7 — Apr. 2, 2007
  • pp: 3833–3848

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

Emily J. McDowell, Xiquan Cui, Zahid Yaqoob, and Changhuei Yang  »View Author Affiliations

Optics Express, Vol. 15, Issue 7, pp. 3833-3848 (2007)

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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/fα distribution. The noise model reveals that, for α > 1, 1/fα noise significantly impacts the 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 and find 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, α, as well as the characteristic integration time, are system and photodetector dependent.

© 2007 Optical Society of America

OCIS Codes
(110.4280) Imaging systems : Noise in imaging systems
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.4500) Medical optics and biotechnology : Optical coherence tomography

ToC Category:
Imaging Systems

Original Manuscript: December 18, 2006
Revised Manuscript: March 13, 2007
Manuscript Accepted: March 13, 2007
Published: April 2, 2007

Virtual Issues
Vol. 2, Iss. 5 Virtual Journal for Biomedical Optics

Emily J. McDowell, Xiquan Cui, Zahid Yaqoob, and Changhuei Yang, "A generalized noise variance analysis model and its application to the characterization of 1/f noise," Opt. Express 15, 3833-3848 (2007)

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  1. P. Dutta and P. M. Horn, "Low-frequency fluctuations in solids - 1/f noise," Rev. Mod. Phys. 53, 497-516 (1981). [CrossRef]
  2. W. H. Press, "Flicker noises in astronomy and elsewhere," Comments Astrophys. 7, 103-119 (1978).
  3. M. B. Weissman, "1/f noise and other slow, nonexponential kinetics in condensed matter," Rev. Mod. Phys. 60, 537-571 (1988). [CrossRef]
  4. W. T. Li and D. Holste, "Universal 1/f noise, crossovers of scaling exponents, and chromosome-specific patterns of guanine-cytosine content in DNA sequences of the human genome," Phys. Rev. E 71, 041910 (2005). [CrossRef]
  5. R. F. Voss, "Linearity of 1/f noise mechanisms," Phys. Rev. Lett. 40, 913-916 (1978). [CrossRef]
  6. P. C. Ivanov, L. A. N. Amaral, A. L. Goldberger, S. Havlin, M. G. Rosenblum, H. E. Stanley, and Z. R. Struzik, "From 1/f noise to multifractal cascades in heartbeat dynamics," Chaos 11, 641-652 (2001). [CrossRef]
  7. T. Musha and H. Higuchi, "1/f fluctuation of a traffic current on an expressway," Jpn. J. Appl. Phys. 15, 1271-1275 (1976). [CrossRef]
  8. E. Milotti, "1/f noise: A pedagogical review," invited talk to E-GLEA-2 (2001).
  9. B. Kaulakys, V. Gontis, and M. Alaburda, "Point process model of 1/f noise vs a sum of lorentzians," Phys. Rev. E 71, 051105 (2005). [CrossRef]
  10. J. B. Johnson, "The schottky effect in low frequency circuits," Phys. Rev. 26, 71-85 (1925). [CrossRef]
  11. W. Schottky, "Small-shot effect and flicker effect," Phys. Rev. 28, 74-103 (1926). [CrossRef]
  12. Z. Siwy and A. Fulinski, "Origin of 1/f(alpha) noise in membrane channel currents," Phys. Rev. Lett. 89, (2002). [CrossRef] [PubMed]
  13. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991). [CrossRef] [PubMed]
  14. A. M. Rollins and J. A. Izatt, "Optimal interferometer designs for optical coherence tomography," Opt. Lett. 24, 1484-1486 (1999). [CrossRef]
  15. J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990). [CrossRef]
  16. S. D. Personic, "Image band interpretation of optical heterodyne noise," AT&T Tech. J. 50, 213 (1971).
  17. L. G. Kazovsky, "Optical heterodyning versus optical homodyning: A comparison," J. Opt. Commun. 6, 18-24 (1985).
  18. V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).
  19. X. Q. Liu, W. Clegg, D. F. L. Jenkins, and B. Liu, "Polarization interferometer for measuring small displacement," IEEE Trans. Instrum. Meas. 50, 868-871 (2001). [CrossRef]
  20. C. M. Wu, C. S. Su, G. S. Peng, and Y. J. Huang, "Polarimetric, nonlinearity-free, homodyne interferometer for vibration measurement," Metrologia 33,533-537 (1996). [CrossRef]
  21. C. Chao, Z. H. Wang, W. G. Zhu, and O. K. Tan, "Scanning homodyne interferometer for characterization of piezoelectric films and microelectromechanical systems devices," Rev. Sci. Instrum. 76,063906 (2005). [CrossRef]
  22. D. L. Mazzoni and C. C. Davis, "Trace detection of hydrazines by optical homodyne interferometry," Appl. Opt. 30,756-764 (1991). [CrossRef] [PubMed]
  23. E. Beaurepaire, L. Moreaux, F. Amblard, and J. Mertz, "Combined scanning optical coherence and two-photon-excited fluorescence microscopy," Opt. Lett. 24,969-971 (1999). [CrossRef]
  24. M. A. Choma, C. H. Yang, and J. A. Izatt, "Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers," Opt. Lett. 28,2162-2164 (2003). [CrossRef] [PubMed]
  25. Z. Yaqoob, J. Fingler, X. Heng, and C. Yang, "Homodyne en face optical coherence tomography," Opt. Lett. 31,1815-1817 (2006). [CrossRef] [PubMed]
  26. N. Choudhury, G. J. Song, F. Y. Chen, S. Matthews, T. Tschinkel, J. F. Zheng, S. L. Jacques, and A. L. Nuttall, "Low coherence interferometry of the cochlear partition," Hearing Res. 220,1-9 (2006). [CrossRef]
  27. R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, "Performance of Fourier domain vs. time domain optical coherence tomography," Opt. Express 11,889-894 (2003). [CrossRef] [PubMed]
  28. M. A. Choma, M. Sarunic, C. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11,2183 - 2189 (2003). [CrossRef] [PubMed]
  29. J. F. de Boer, C. B., B. Park, M. Pierce, G. Tearney, and B. Bouma, "Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography," Opt. Lett. 28,2067 -2069 (2003). [CrossRef] [PubMed]
  30. Y. Salvade and R. Dandliker, "Limitations of interferometry due to the flicker noise of laser diodes," J. Opt. Soc. Am. A 17,927-932 (2000). [CrossRef]
  31. R. H. Hamstra and P. Wendland, "Noise and frequency-response of silicon photodiode operational amplifier combination," Appl. Opt. 11,1539 (1972). [CrossRef] [PubMed]
  32. J. Clarke and T. Y. Hsiang, "Low-frequency noise in tin and lead films at superconducting transition," Phys. Rev. B 13,4790-4800 (1976). [CrossRef]
  33. M. S. Keshner, "1/f noise," Proc. IEEE 70,212-218 (1982). [CrossRef]
  34. B. Pellegrini, R. Saletti, P. Terreni, and M. Prudenziati, "1/f-gamma noise in thick-film resistors as an effect of tunnel and thermally activated emissions, from measures versus frequency and temperature," Phys. Rev. B 27,1233-1243 (1983). [CrossRef]
  35. M. A. Caloyannides, "Microcycle spectral estimates of 1/f noise in semiconductors," J. Appl. Phys. 45,307-316 (1974). [CrossRef]
  36. B. B. Mandelbrot and J. R. Wallis, "Some long-run properties of geophysical records," Water Resources Research 5,321 (1969). [CrossRef]
  37. A. Yariv and P. Yeh, Photonics: Optical electronics in modern communications (Oxford University Press, New York, 2007).

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