Abstract

Past studies of the effects of bit depth on OCT magnitude data concluded that 8 bits of digitizer resolution provided nearly the same image quality as a 14-bit digitizer. However, such studies did not assess the effects of bit depth on the accuracy of phase data. In this work, we show that the effects of bit depth on phase data and magnitude data can differ significantly. This finding has an important impact on the design of phase-resolved OCT systems, such as those measuring motion and the birefringence of samples, particularly as one begins to consider the tradeoff between bit depth and digitizer speed.

© 2012 OSA

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References

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  1. V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
    [CrossRef] [PubMed]
  2. W. Wieser, B. Biedermann, T. Klein, C. Eigenwillig, and R. Huber, “Multi-megahertz OCT: high quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express18(14), 14685–14704 (2010).
    [CrossRef] [PubMed]
  3. D. C. Adler, R. Huber, and J. G. Fujimoto, “Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers,” Opt. Lett.32(6), 626–628 (2007).
    [CrossRef] [PubMed]
  4. C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett.30(16), 2131–2133 (2005).
    [CrossRef] [PubMed]
  5. G. Liu, M. Rubinstein, A. Saidi, W. Qi, A. Foulad, B. Wong, and Z. Chen, “Imaging vibrating vocal folds with a high speed 1050 nm swept source OCT and ODT,” Opt. Express19(12), 11880–11889 (2011).
    [CrossRef] [PubMed]
  6. J. Zhang, W. Jung, J. S. Nelson, and Z. Chen, “Full range polarization-sensitive Fourier domain optical coherence tomography,” Opt. Express12(24), 6033–6039 (2004).
    [CrossRef] [PubMed]
  7. E. Gotzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express13(25), 10217–10229 (2005).
    [CrossRef] [PubMed]
  8. B. D. Goldberg, B. J. Vakoc, W-Y Oh, M. J. Suter, S. Waxman, M. I. Freilich, B. E. Bouma, and G. J. Tearney, “Performance of reduced bit-depth acquisition for optical frequency domain imaging,” Opt. Express17(19), 16957–16968 (2009).
    [CrossRef] [PubMed]
  9. Z. Lu, D. K. Kasaragod, and S. J. Matcher, “Performance comparison between 8- and 14-bit- depth imaging in polarization-sensitive swept-source optical coherence tomography,” Biomed. Opt. Express4(2), 794–804 (2011).
    [CrossRef]
  10. R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett.31(20), 2975–2977 (2006).
    [CrossRef] [PubMed]
  11. A. B. Vakhtin, D. J. Kane, W. R. Wood, and K. A. Peterson, “Common-path interferometer for frequency-domain optical coherence tomography,” App. Opt.42(34), 6953–6958 (2003).
    [CrossRef]
  12. M. A. Choma, A. K. Ellerbee, C. Yang, T. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett.30(10), 1162–1164 (2005).
    [CrossRef] [PubMed]
  13. M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett.31(10), 1462–1464 (2006).
    [CrossRef] [PubMed]
  14. A. K. Ellerbee, T. L. Creazzo, and J. A. Izatt, “Investigating nanoscale cellular dynamics with cross-sectional spectral domain phase microscopy,” Opt. Express15(13), 8115–8124 (2007).
    [CrossRef] [PubMed]
  15. A. K. Ellerbee and J. A. Izatt, “Phase retrieval in low-coherence interferometric microscopy,” Opt. Lett.32(4), 388–390 (2007).
    [CrossRef] [PubMed]
  16. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express11(22), 2953–2963 (2003).
    [CrossRef] [PubMed]
  17. R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express11(8), 889–894 (2003).
    [CrossRef] [PubMed]
  18. A. Oppenheim and R. Schafer, Discrete-time Signal Processing, 3rd ed. (Prentice Hall, 2009).
  19. W. Kester, The Data Conversion Handbook (Elsevier, 2005).
  20. D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE7372. 73720R (2009).
    [CrossRef]
  21. S. Vergnole, D. Lvesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express18(10), 10446–10461 (2010).
    [CrossRef] [PubMed]
  22. C. Copeland and A. K. Ellerbee, “The effects of different gold standards on the assessment of the accuracy of different resampling techniques for optical coherence tomography,” Proc. SPIE. 8225–8237 (2012).
  23. 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,” Science254(5035), 1178–1181 (1991).
    [CrossRef] [PubMed]

2012

C. Copeland and A. K. Ellerbee, “The effects of different gold standards on the assessment of the accuracy of different resampling techniques for optical coherence tomography,” Proc. SPIE. 8225–8237 (2012).

2011

Z. Lu, D. K. Kasaragod, and S. J. Matcher, “Performance comparison between 8- and 14-bit- depth imaging in polarization-sensitive swept-source optical coherence tomography,” Biomed. Opt. Express4(2), 794–804 (2011).
[CrossRef]

G. Liu, M. Rubinstein, A. Saidi, W. Qi, A. Foulad, B. Wong, and Z. Chen, “Imaging vibrating vocal folds with a high speed 1050 nm swept source OCT and ODT,” Opt. Express19(12), 11880–11889 (2011).
[CrossRef] [PubMed]

2010

2009

2008

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

2007

2006

2005

2004

2003

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Adler, D. C.

Akkin, T.

Biedermann, B.

Bouma, B. E.

Cense, B.

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, Y. L.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Chen, Z.

Choma, M. A.

Copeland, C.

C. Copeland and A. K. Ellerbee, “The effects of different gold standards on the assessment of the accuracy of different resampling techniques for optical coherence tomography,” Proc. SPIE. 8225–8237 (2012).

Creazzo, T.

Creazzo, T. L.

de Boer, J. F.

Duker, J. S.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Eigenwillig, C.

Ellerbee, A. K.

Fercher, A. F.

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Foulad, A.

Freilich, M. I.

Fujimoto, J. G.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

D. C. Adler, R. Huber, and J. G. Fujimoto, “Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers,” Opt. Lett.32(6), 626–628 (2007).
[CrossRef] [PubMed]

R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett.31(20), 2975–2977 (2006).
[CrossRef] [PubMed]

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Goldberg, B. D.

Gorczynska, I.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Gotzinger, E.

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hillmann, D.

D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE7372. 73720R (2009).
[CrossRef]

Hitzenberger, C. K.

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Huber, R.

Huttmann, G.

D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE7372. 73720R (2009).
[CrossRef]

Iftimia, N.

Izatt, J. A.

Joo, C.

Jung, W.

Kane, D. J.

A. B. Vakhtin, D. J. Kane, W. R. Wood, and K. A. Peterson, “Common-path interferometer for frequency-domain optical coherence tomography,” App. Opt.42(34), 6953–6958 (2003).
[CrossRef]

Kasaragod, D. K.

Z. Lu, D. K. Kasaragod, and S. J. Matcher, “Performance comparison between 8- and 14-bit- depth imaging in polarization-sensitive swept-source optical coherence tomography,” Biomed. Opt. Express4(2), 794–804 (2011).
[CrossRef]

Kester, W.

W. Kester, The Data Conversion Handbook (Elsevier, 2005).

Klein, T.

Koch, P.

D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE7372. 73720R (2009).
[CrossRef]

Lamouche, G.

Leitgeb, R.

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Liu, G.

Lu, Z.

Z. Lu, D. K. Kasaragod, and S. J. Matcher, “Performance comparison between 8- and 14-bit- depth imaging in polarization-sensitive swept-source optical coherence tomography,” Biomed. Opt. Express4(2), 794–804 (2011).
[CrossRef]

Lvesque, D.

Matcher, S. J.

Z. Lu, D. K. Kasaragod, and S. J. Matcher, “Performance comparison between 8- and 14-bit- depth imaging in polarization-sensitive swept-source optical coherence tomography,” Biomed. Opt. Express4(2), 794–804 (2011).
[CrossRef]

Nelson, J. S.

Oh, W-Y

Oppenheim, A.

A. Oppenheim and R. Schafer, Discrete-time Signal Processing, 3rd ed. (Prentice Hall, 2009).

Park, B. H.

Peterson, K. A.

A. B. Vakhtin, D. J. Kane, W. R. Wood, and K. A. Peterson, “Common-path interferometer for frequency-domain optical coherence tomography,” App. Opt.42(34), 6953–6958 (2003).
[CrossRef]

Pircher, M.

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Qi, W.

Rubinstein, M.

Saidi, A.

Sarunic, M. V.

Schafer, R.

A. Oppenheim and R. Schafer, Discrete-time Signal Processing, 3rd ed. (Prentice Hall, 2009).

Schuman, J. S.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Srinivasan, V. J.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Suter, M. J.

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

Vakhtin, A. B.

A. B. Vakhtin, D. J. Kane, W. R. Wood, and K. A. Peterson, “Common-path interferometer for frequency-domain optical coherence tomography,” App. Opt.42(34), 6953–6958 (2003).
[CrossRef]

Vakoc, B. J.

Vergnole, S.

Waxman, S.

Weinberg, S.

Wieser, W.

Wong, B.

Wood, W. R.

A. B. Vakhtin, D. J. Kane, W. R. Wood, and K. A. Peterson, “Common-path interferometer for frequency-domain optical coherence tomography,” App. Opt.42(34), 6953–6958 (2003).
[CrossRef]

Yang, C.

Yun, S. H.

Zhang, J.

App. Opt.

A. B. Vakhtin, D. J. Kane, W. R. Wood, and K. A. Peterson, “Common-path interferometer for frequency-domain optical coherence tomography,” App. Opt.42(34), 6953–6958 (2003).
[CrossRef]

Biomed. Opt. Express

Z. Lu, D. K. Kasaragod, and S. J. Matcher, “Performance comparison between 8- and 14-bit- depth imaging in polarization-sensitive swept-source optical coherence tomography,” Biomed. Opt. Express4(2), 794–804 (2011).
[CrossRef]

Invest. Ophthalmol. Vis. Sci.

V. J. Srinivasan, D. C. Adler, Y. L. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci.49(11), 5103–5110 (2008).
[CrossRef] [PubMed]

Opt. Express

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express11(8), 889–894 (2003).
[CrossRef] [PubMed]

S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express11(22), 2953–2963 (2003).
[CrossRef] [PubMed]

J. Zhang, W. Jung, J. S. Nelson, and Z. Chen, “Full range polarization-sensitive Fourier domain optical coherence tomography,” Opt. Express12(24), 6033–6039 (2004).
[CrossRef] [PubMed]

E. Gotzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express13(25), 10217–10229 (2005).
[CrossRef] [PubMed]

A. K. Ellerbee, T. L. Creazzo, and J. A. Izatt, “Investigating nanoscale cellular dynamics with cross-sectional spectral domain phase microscopy,” Opt. Express15(13), 8115–8124 (2007).
[CrossRef] [PubMed]

B. D. Goldberg, B. J. Vakoc, W-Y Oh, M. J. Suter, S. Waxman, M. I. Freilich, B. E. Bouma, and G. J. Tearney, “Performance of reduced bit-depth acquisition for optical frequency domain imaging,” Opt. Express17(19), 16957–16968 (2009).
[CrossRef] [PubMed]

S. Vergnole, D. Lvesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express18(10), 10446–10461 (2010).
[CrossRef] [PubMed]

W. Wieser, B. Biedermann, T. Klein, C. Eigenwillig, and R. Huber, “Multi-megahertz OCT: high quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express18(14), 14685–14704 (2010).
[CrossRef] [PubMed]

G. Liu, M. Rubinstein, A. Saidi, W. Qi, A. Foulad, B. Wong, and Z. Chen, “Imaging vibrating vocal folds with a high speed 1050 nm swept source OCT and ODT,” Opt. Express19(12), 11880–11889 (2011).
[CrossRef] [PubMed]

Opt. Lett.

Proc. SPIE

D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE7372. 73720R (2009).
[CrossRef]

C. Copeland and A. K. Ellerbee, “The effects of different gold standards on the assessment of the accuracy of different resampling techniques for optical coherence tomography,” Proc. SPIE. 8225–8237 (2012).

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,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Other

A. Oppenheim and R. Schafer, Discrete-time Signal Processing, 3rd ed. (Prentice Hall, 2009).

W. Kester, The Data Conversion Handbook (Elsevier, 2005).

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Figures (8)

Fig. 1
Fig. 1

Vector plot of the measured OCT data (z-domain). I = signal vector, N = noise vector, and Y = the resultant. Components of the noise vector in quadrature with the signal vector lead to error δθ in the measured phase compared to the actual phase θ.

Fig. 2
Fig. 2

Method to simulate reduced ADC resolution, including fractional bits. An unresampled interferogram iraw(k) is captured with a 12-bit ADC and modified in post-processing to produce an N + F-bit output, where 0 < F < 1. The NDFT (non-uniform DFT) combines resampling and Fourier transformation into a single operation.

Fig. 3
Fig. 3

Behavior of a non-ideal (N + 1)-bit ADC. ne accounts for internal noise and thresholding errors of the ADC. Left: ideal (N + 1)-bit quantizer (i.e., a perfect rounding operation); the resulting ADC output has a resolution < N + 1 due to ADC imperfections described by ne. Right: the ideal quantizer can be replaced with an equivalent white-noise model in which QN is an uncorrelated additive noise.

Fig. 4
Fig. 4

Demonstration of the two-step fractional requantizer from Fig. 2 to generate ENOBs of 3.2 (a and b) and 1.5 (c and d) bits from a 4-bit sinusoidal input sampled 32 times per period (gray). Simulated ADC signals appear in red. Step i (a and c): apply a pseudorandom noise sequence (blue) of the appropriate variance to the input to account for ADC non-idealities. Step ii (b and d): Quantize the resulting noisy sequence (red) to yield an output with the appropriate ENOB.

Fig. 5
Fig. 5

Common-path OCT system used in this work. The sample comprised either a coverslip or a piezo-mounted mirror imaged from behind the coverslip. The reflectivity of the coverslip was changed by adding liquid droplets of varying refractive index.

Fig. 6
Fig. 6

Displacement sensitivity vs ENOB for (a) glass-air, (b) glass-water, and (c) glass-gel interfaces. Error bars indicate one standard deviation of variation between trials. Theoretical curves are based on Eq. (7) and Eq. (9); the latter is clearly a better fit to the data. Experimental data and theoretical predictions converge with decreasing sample reflectivity or ENOB, as predicted. The arrows in (a)–(c) indicate the point at which the experimental sensitivity worsened by 3 dB. Note that plot axes differ to improve visibility of the data. The dotted black lines in (d) indicate the point at which SNR dropped by 1 dB relative to the SNR at 12 bits.

Fig. 7
Fig. 7

1mm x 1mm views of the topography of a coverslip (CS) and neutral density filter (NDF) generated from phase using 12-bit, 8-bit, and 5-bit data. Due to the high reflectivity of the coverslip surface, quantization-induced phase noise is small, allowing accurate phase extraction even at very low bit-depths. Phase noise increases more rapidly with reduced ENOB when the reflectivity is lower, as for the NDF (the box shows an area of strong degradation with the arrow pointing to a ring that disappears in the 5-bit image). Note that scales are different in the top and bottom images.

Fig. 8
Fig. 8

Displacement of a PZT driven at 100 Hz sinusoidal drive as calculated from 12-bit data. Fig. (b) shows the error in the displacement that would result if the waveform were instead generated using lower ENOBs (the waveform from 12-bit data is considered error-free and the waveforms from lower ENOBs are subtracted); the dashed horizontal lines show the RMS vibration noise (0.5 nm corresponds to 8% of the dynamic range). Except at very low bit depths, quantization noise is insignificant compared to vibration noise, since the sample reflectivity is large.

Tables (1)

Tables Icon

Table 1 Accuracy of the fractional requantizer in generating desired ENOBs for unquantized (Case 1) and quantized (Case 2) sinusoidal inputs.

Equations (15)

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

i ( k , t ) = A ( k ) R R R S cos ( 2 k n ( Δ z + δ z ( t ) ) ) ,
I ( 2 n Δ z , t 2 ) I ( 2 n Δ z , t 1 ) = 2 k 0 n ( δ z ( t 2 ) δ z ( t 1 ) ) = 4 π n ( δ z ( t 2 ) δ z ( t 1 ) ) λ 0 ,
σ n 2 = σ shot 2 + σ RIN 2 + σ dark 2 + σ amp 2 + σ DAQ 2 = σ det 2 + σ D A Q 2 .
σ q n 2 = Δ 2 12 = V F S 2 12 ( 2 2 B )
σ eff 2 = σ q n 2 + σ e 2 .
V F S 2 12 ( 2 2 E N O B ) = σ eff 2
σ D A Q 2 = σ eff 2
σ δ θ = 1 SNR ,
δ θ tan ( δ θ ) = N Q | I + N I | N Q | I |
σ δ θ = σ N 2 | I |
σ N + F 2 = V F S 2 12 ( 2 2 ( N + F ) ) , σ N + 1 2 = V F S 2 12 ( 2 2 ( N + 1 ) ) , σ e 2 = σ N + F 2 σ N + 1 2 = V F S 2 12 ( 2 2 ( N + F ) ) V F S 2 12 ( 2 2 ( N + 1 ) ) .
σ e , 12 2 = [ V F S 2 12 ( 2 2 ( N + F ) ) V F S 2 12 ( 2 2 ( N + 1 ) ) ] V F S 2 12 ( 2 2 ( 12 ) ) .
σ δ θ = P ( V F S 2 12 ( 2 2 E N O B ) + K 1 ( R S + R R ) + K 2 ( R S + R R ) 2 + σ dark 2 + σ amp 2 ) K 3 2 R S
σ p n 2 = σ a 2 + P σ q 2 2 | I | 2 + σ v 2 . σ q 2 = 2 | I | 2 ( σ p n 2 σ v 2 ) σ a 2 P .
ENOB = log ( V F S 2 12 σ q 2 ) / log ( 4 ) .

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