Abstract

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

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2006

Z. Yaqoob, J. Fingler, X. Heng, and C. Yang, "Homodyne en face optical coherence tomography," Opt. Lett. 31,1815-1817 (2006).
[CrossRef] [PubMed]

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]

2005

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]

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]

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]

2003

2002

Z. Siwy and A. Fulinski, "Origin of 1/f(alpha) noise in membrane channel currents," Phys. Rev. Lett. 89, (2002).
[CrossRef] [PubMed]

2001

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]

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]

2000

1999

1996

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]

1994

V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).

1991

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]

D. L. Mazzoni and C. C. Davis, "Trace detection of hydrazines by optical homodyne interferometry," Appl. Opt. 30,756-764 (1991).
[CrossRef] [PubMed]

1990

J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
[CrossRef]

1988

M. B. Weissman, "1/f noise and other slow, nonexponential kinetics in condensed matter," Rev. Mod. Phys. 60, 537-571 (1988).
[CrossRef]

1985

L. G. Kazovsky, "Optical heterodyning versus optical homodyning: A comparison," J. Opt. Commun. 6, 18-24 (1985).

1983

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]

1982

M. S. Keshner, "1/f noise," Proc. IEEE 70,212-218 (1982).
[CrossRef]

1981

P. Dutta and P. M. Horn, "Low-frequency fluctuations in solids - 1/f noise," Rev. Mod. Phys. 53, 497-516 (1981).
[CrossRef]

1978

W. H. Press, "Flicker noises in astronomy and elsewhere," Comments Astrophys. 7, 103-119 (1978).

R. F. Voss, "Linearity of 1/f noise mechanisms," Phys. Rev. Lett. 40, 913-916 (1978).
[CrossRef]

1976

T. Musha and H. Higuchi, "1/f fluctuation of a traffic current on an expressway," Jpn. J. Appl. Phys. 15, 1271-1275 (1976).
[CrossRef]

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]

1974

M. A. Caloyannides, "Microcycle spectral estimates of 1/f noise in semiconductors," J. Appl. Phys. 45,307-316 (1974).
[CrossRef]

1972

1971

S. D. Personic, "Image band interpretation of optical heterodyne noise," AT&T Tech. J. 50, 213 (1971).

1969

B. B. Mandelbrot and J. R. Wallis, "Some long-run properties of geophysical records," Water Resources Research 5,321 (1969).
[CrossRef]

1926

W. Schottky, "Small-shot effect and flicker effect," Phys. Rev. 28, 74-103 (1926).
[CrossRef]

1925

J. B. Johnson, "The schottky effect in low frequency circuits," Phys. Rev. 26, 71-85 (1925).
[CrossRef]

Alaburda, M.

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]

Amaral, L. A. N.

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]

Amblard, F.

Barry, J. R.

J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
[CrossRef]

Beaurepaire, E.

Caloyannides, M. A.

M. A. Caloyannides, "Microcycle spectral estimates of 1/f noise in semiconductors," J. Appl. Phys. 45,307-316 (1974).
[CrossRef]

Chang, W.

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]

Chao, C.

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]

Chen, F. Y.

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]

Choma, M. A.

Choudhury, N.

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]

Clarke, J.

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]

Clegg, W.

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]

Dandliker, R.

Davis, C. C.

de Boer, J. F.

Dutta, P.

P. Dutta and P. M. Horn, "Low-frequency fluctuations in solids - 1/f noise," Rev. Mod. Phys. 53, 497-516 (1981).
[CrossRef]

Fercher, A. F.

Fingler, J.

Flotte, T.

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]

Fujimoto, J. G.

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]

Fulinski, A.

Z. Siwy and A. Fulinski, "Origin of 1/f(alpha) noise in membrane channel currents," Phys. Rev. Lett. 89, (2002).
[CrossRef] [PubMed]

Goldberger, A. L.

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]

Gontis, V.

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]

Greco, V.

V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).

Gregory, K.

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]

Hamstra, R. H.

Havlin, S.

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]

Hee, M. R.

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]

Heng, X.

Higuchi, H.

T. Musha and H. Higuchi, "1/f fluctuation of a traffic current on an expressway," Jpn. J. Appl. Phys. 15, 1271-1275 (1976).
[CrossRef]

Hitzenberger, C. K.

Holste, D.

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]

Horn, P. M.

P. Dutta and P. M. Horn, "Low-frequency fluctuations in solids - 1/f noise," Rev. Mod. Phys. 53, 497-516 (1981).
[CrossRef]

Hsiang, T. Y.

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]

Huang, D.

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]

Huang, Y. J.

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]

Iemmi, C.

V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).

Ivanov, P. C.

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]

Izatt, J. A.

Jacques, S. L.

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]

Jenkins, D. F. L.

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]

Johnson, J. B.

J. B. Johnson, "The schottky effect in low frequency circuits," Phys. Rev. 26, 71-85 (1925).
[CrossRef]

Kaulakys, B.

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]

Kazovsky, L. G.

L. G. Kazovsky, "Optical heterodyning versus optical homodyning: A comparison," J. Opt. Commun. 6, 18-24 (1985).

Keshner, M. S.

M. S. Keshner, "1/f noise," Proc. IEEE 70,212-218 (1982).
[CrossRef]

Ledesma, S.

V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).

Lee, E. A.

J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
[CrossRef]

Leitgeb, R.

Li, W. T.

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]

Lin, C. P.

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]

Liu, B.

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]

Liu, X. Q.

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]

Mandelbrot, B. B.

B. B. Mandelbrot and J. R. Wallis, "Some long-run properties of geophysical records," Water Resources Research 5,321 (1969).
[CrossRef]

Mannoni, A.

V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).

Matthews, S.

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]

Mazzoni, D. L.

Mertz, J.

Molesini, G.

V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).

Moreaux, L.

Musha, T.

T. Musha and H. Higuchi, "1/f fluctuation of a traffic current on an expressway," Jpn. J. Appl. Phys. 15, 1271-1275 (1976).
[CrossRef]

Nuttall, A. L.

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]

Pellegrini, B.

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]

Peng, G. S.

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]

Personic, S. D.

S. D. Personic, "Image band interpretation of optical heterodyne noise," AT&T Tech. J. 50, 213 (1971).

Press, W. H.

W. H. Press, "Flicker noises in astronomy and elsewhere," Comments Astrophys. 7, 103-119 (1978).

Prudenziati, M.

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]

Puliafito, C. A.

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]

Quercioli, F.

V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).

Rollins, A. M.

Rosenblum, M. G.

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]

Saletti, R.

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]

Salvade, Y.

Sarunic, M.

Schottky, W.

W. Schottky, "Small-shot effect and flicker effect," Phys. Rev. 28, 74-103 (1926).
[CrossRef]

Schuman, J. S.

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]

Siwy, Z.

Z. Siwy and A. Fulinski, "Origin of 1/f(alpha) noise in membrane channel currents," Phys. Rev. Lett. 89, (2002).
[CrossRef] [PubMed]

Song, G. J.

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]

Stanley, H. E.

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]

Stinson, W. G.

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]

Struzik, Z. R.

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]

Su, C. S.

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]

Swanson, E. A.

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]

Tan, O. K.

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]

Terreni, P.

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]

Tschinkel, T.

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]

Voss, R. F.

R. F. Voss, "Linearity of 1/f noise mechanisms," Phys. Rev. Lett. 40, 913-916 (1978).
[CrossRef]

Wallis, J. R.

B. B. Mandelbrot and J. R. Wallis, "Some long-run properties of geophysical records," Water Resources Research 5,321 (1969).
[CrossRef]

Wang, Z. H.

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]

Weissman, M. B.

M. B. Weissman, "1/f noise and other slow, nonexponential kinetics in condensed matter," Rev. Mod. Phys. 60, 537-571 (1988).
[CrossRef]

Wendland, P.

Wu, C. M.

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]

Yang, C.

Yang, C. H.

Yaqoob, Z.

Zheng, J. F.

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]

Zhu, W. G.

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]

Appl. Opt.

AT&T Tech. J.

S. D. Personic, "Image band interpretation of optical heterodyne noise," AT&T Tech. J. 50, 213 (1971).

Chaos

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]

Comments Astrophys.

W. H. Press, "Flicker noises in astronomy and elsewhere," Comments Astrophys. 7, 103-119 (1978).

Hearing Res.

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]

IEEE Trans. Instrum. Meas.

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]

J. Appl. Phys.

M. A. Caloyannides, "Microcycle spectral estimates of 1/f noise in semiconductors," J. Appl. Phys. 45,307-316 (1974).
[CrossRef]

J. Opt. Commun.

L. G. Kazovsky, "Optical heterodyning versus optical homodyning: A comparison," J. Opt. Commun. 6, 18-24 (1985).

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

T. Musha and H. Higuchi, "1/f fluctuation of a traffic current on an expressway," Jpn. J. Appl. Phys. 15, 1271-1275 (1976).
[CrossRef]

Metrologia

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]

Opt. Express

Opt. Lett.

Optik

V. Greco, C. Iemmi, S. Ledesma, A. Mannoni, G. Molesini, and F. Quercioli, "Multiphase homodyne displacement sensor," Optik 97, 15-18 (1994).

Phys. Rev.

J. B. Johnson, "The schottky effect in low frequency circuits," Phys. Rev. 26, 71-85 (1925).
[CrossRef]

W. Schottky, "Small-shot effect and flicker effect," Phys. Rev. 28, 74-103 (1926).
[CrossRef]

Phys. Rev. B

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]

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]

Phys. Rev. E

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]

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]

Phys. Rev. Lett.

R. F. Voss, "Linearity of 1/f noise mechanisms," Phys. Rev. Lett. 40, 913-916 (1978).
[CrossRef]

Z. Siwy and A. Fulinski, "Origin of 1/f(alpha) noise in membrane channel currents," Phys. Rev. Lett. 89, (2002).
[CrossRef] [PubMed]

Proc. IEEE

J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
[CrossRef]

M. S. Keshner, "1/f noise," Proc. IEEE 70,212-218 (1982).
[CrossRef]

Rev. Mod. Phys.

M. B. Weissman, "1/f noise and other slow, nonexponential kinetics in condensed matter," Rev. Mod. Phys. 60, 537-571 (1988).
[CrossRef]

P. Dutta and P. M. Horn, "Low-frequency fluctuations in solids - 1/f noise," Rev. Mod. Phys. 53, 497-516 (1981).
[CrossRef]

Rev. Sci. Instrum.

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]

Science

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]

Water Resources Research

B. B. Mandelbrot and J. R. Wallis, "Some long-run properties of geophysical records," Water Resources Research 5,321 (1969).
[CrossRef]

Other

A. Yariv and P. Yeh, Photonics: Optical electronics in modern communications (Oxford University Press, New York, 2007).

E. Milotti, "1/f noise: A pedagogical review," invited talk to E-GLEA-2 (2001).

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Figures (10)

Fig. 1.
Fig. 1.

The total time frame of an experiment, T, determines the lowest frequency noise components that are incorporated into a measured signal. The upper panel depicts the raw signal, or amplitude modulated ‘message’ that is encoded on a 1/f noise dominated light source (see Section 2.1). If the message is band limited such that it does not contain frequency components beyond fsignal , the message can be optimally collected by integrating the collected signal in times steps of τ=2/fsignal . In the left panel, low frequency noise (f > fmin ) in the light source causes a net DC shift in the acquired signal. As T is increased (right panel) the same low frequency noise dramatically impacts the measured noise variance between subsequent time steps (τ), which can lead to a degradation in the SNR of the collected message.

Fig. 2.
Fig. 2.

Theoretical results for noise standard deviation versus integration time, square root of Eq. (9) and Eq. (10) for white noise and 1/f noise, respectively. The 1/f noise transitions from the square-root dependence of white noise (α=0) to a linear dependence as α increases from 0 to 1, and maintains a linear dependence on integration time for α>1.

Fig. 3.
Fig. 3.

Theoretical results for SNR versus integration time. As expected, the white noise limited SNR increases linearly with integration time. In the case of dominant 1/f noise, the SNR increases with decreasing slope for 0<α<1, and tapers to a constant value for α>1.

Fig. 4.
Fig. 4.

The dependence of the 1/f noise variance is dependent on integration time varies with the 1/f exponent, α. For α>2, this dependence is given by τ2. Open circles represent a values that cannot be simply approximated by Eq. (11).

Fig. 5.
Fig. 5.

(a). Schematic of 3x3 homodyne OCT system employed in this study. (b) Diagram of the vector relationship between the signals detected at ports 1–3. SLD: Superluminescent diode; Di: ith detector; M: Mirror; X–Y: X–Y Scanner; OBJ: Microscope objective.

Fig. 6.
Fig. 6.

Power spectral density of the interferometric noise, measured with the sample arm blocked. The data were averaged over 85 data sets, and sampled at 30 kHz. The initial portion of the curve was fit, and an exponent of α=1.39 was determined. The 1/f to white noise corner can be seen at approximately 70 Hz.

Fig. 7.
Fig. 7.

SNR of the homodyne interferometric signal plotted versus integration time. The initial portion of the curve displays a linear trend, indicative of dominant white noise processes. The final portion of the curve is constant with increasing integration time, in agreement with the theorectical 1/f noise variance derived above.

Fig. 8.
Fig. 8.

A comparison of homodyne (blue) and heterodyne (red) SNR versus integration time. The black curve represents the upper limit on SNR for shot noise limited signals. A line drawn through the initial portion of the homodyne curve intersects the heterodyne data (dashed line). This implies that the homodyne data is white noise limited for short integration times, after which 1/f noise becomes dominant.

Fig. 9.
Fig. 9.

The form of the 1/f noise amplitude [Apink in Eq. (10)] is unknown, although we might expect it to depend on the reference arm power in some fashion. The blue dots represent experimental measurements and the black line is a linear fit to the data. The amplitude was found to follow a linear trend versus reference arm power, similarly to the shot noise amplitude.

Fig. 10.
Fig. 10.

Power spectra of initial detectors (a), and replacement detectors (b), showing a notable increase in the 1/f noise exponent, α. c) SNR versus integration time for both sets of detectors. The larger 1/f exponent of the Thorlabs detectors (TL #DET10C) caused 1/f noise to become a dominant process for shorter integration times than was seen in the New Focus detectors (NF #2011).

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

x ( t ) = x 0 + Δ x ( t )
= x 0 + i = 1 2 S ( f i ) Δ f cos ( 2 π f i t + δ i )
Δ X ( τ ) = 0 τ Δ x ( t ) dt
E ( Δ X ( τ ) ) = 0
σ X 2 ( τ ) = E ( Δ X ( τ ) 2 ) = E ( [ 0 τ ( i = 1 2 S ( f i ) Δ f cos ( 2 π f i t + δ i ) ) d t ] 2 )
σ X 2 ( τ ) = E ( [ 0 τ i = 1 2 S ( f i ) Δ f cos ( 2 π f i t + δ i ) d t ] [ 0 τ j = 1 2 S ( f j ) Δ f cos ( 2 π f i t + δ j ) d t ] )
σ X 2 ( τ ) = E ( i = 1 [ 0 τ 2 S ( f i ) Δ f cos ( 2 π f i t + δ i ) d t ] 2 )
= E ( i = 1 [ 2 S ( f i ) Δ f 2 π f i ( sin ( 2 π f i τ + δ i ) sin ( δ i ) ) ] 2 )
= E ( i = 1 2 S ( f i ) Δ f ( 2 π f i ) 2 [ sin 2 ( 2 π f i τ + δ i ) 2 sin ( 2 π f i τ + δ i ) sin ( δ i ) + sin 2 ( δ i ) ] )
σ X 2 = 1 2 π o 2 π ( i = 1 S ( f i ) Δ f 2 ( π f i ) 2 [ sin 2 ( 2 π f i τ + δ i ) 2 sin ( 2 π f i τ + δ i ) sin ( δ i ) + sin 2 ( δ i ) ] ) d δ i
σ X 2 ( τ ) = 0 S ( f ) 2 ( π f ) 2 [ 1 cos ( 2 π f τ ) ] d f
σ X,white 2 ( τ ) = 0 A white 2( π f ) 2 [ 1 cos ( 2 π f τ ) ] d f
σ X,white 2 ( τ ) = 0 A white τ 2
σ X,pink 2 ( τ , f min ) = f min A pink 2 π 2 f α + 2 [ 1 cos ( 2 π f τ ) ] d f
σ X,pink 2 ( τ , f min ) A pink 2 [ ( 2 π ) α τ α + 1 ( α + 1 ) α Γ ( α ) cos ( α π 2 ) ] 0 < α < 1
A pink [ τ 2 ( α 1 ) f min α 1 ] α > 1
except when α∈ Z +
SNR ( τ ) O ( τ 1 α ) 0 < α < 1
O ( τ 0 ) α > 1
except when α Z +
P j ( z ) = P r , j + P s , j + 2 ( 1 s j ) α 4,1 α 4 , j α 5 , 1 α 5 , j P r ( P s ( z ) γ ( z ) cos ( θ ( z ) + ϕ j ) )
SNR = x 0 2 τ 2 σ X,pink 2 + σ X,white 2
A white τ 2 = ω min A pink 2 π 2 f α + 2 [ 1 cos ( 2 π f τ ) ] d ω

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