Abstract

We provide a framework for compensating errors within passive optical quadrature demodulation circuits used in swept-source optical coherence tomography (OCT). Quadrature demodulation allows for detection of both the real and imaginary components of an interference fringe, and this information separates signals from positive and negative depth spaces. To achieve a high extinction (∼60 dB) between these positive and negative signals, the demodulation error must be less than 0.1% in amplitude and phase. It is difficult to construct a system that achieves this low error across the wide spectral and RF bandwidths of high-speed swept-source systems. In a prior work, post-processing methods for removing residual spectral errors were described. Here, we identify the importance of a second class of errors originating in the RF domain, and present a comprehensive framework for compensating both spectral and RF errors. Using this framework, extinctions >60 dB are demonstrated. A stability analysis shows that calibration parameters associated with RF errors are accurate for many days, while those associated with spectral errors must be updated prior to each imaging session. Empirical procedures to derive both RF and spectral calibration parameters simultaneously and to update spectral calibration parameters are presented. These algorithms provide the basis for using passive optical quadrature demodulation circuits with high speed and wide-bandwidth swept-source OCT systems.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2014 (1)

2012 (1)

2006 (1)

2005 (3)

2004 (2)

S.H. Yun, G.J. Tearner, J.F. de Boer, and B.E Bouma, “Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting,” Opt. Express 12, 4822–4828 (2004).
[Crossref] [PubMed]

P. Targowski, M. Wojkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczyska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun. 229, 79–84 (2004).
[Crossref]

2003 (2)

2002 (2)

Bajraszewski, T.

P. Targowski, M. Wojkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczyska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun. 229, 79–84 (2004).
[Crossref]

R.A. Leitgeb, C.K. Hitzenberger, A.F. Fercher, and T. Bajraszewski, “Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography,” Opt. Lett. 28, 2201–2203 (2003).
[Crossref] [PubMed]

Banholsbeeck, F.

Bouma, B.E

Bouma, B.E.

Chen, Z.

Choma, M.A.

Coen, S.

de Boer, J.F.

Ding, Z.

Fercher, A.F.

Gorczyska, I.

P. Targowski, M. Wojkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczyska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun. 229, 79–84 (2004).
[Crossref]

Gotzinger, E.

Hitzenberger, C.K.

Iftimia, N

Izatt, J.A.

Kowalczyk, A.

P. Targowski, M. Wojkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczyska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun. 229, 79–84 (2004).
[Crossref]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A.F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
[Crossref]

Leitgeb, R.

Leitgeb, R.A.

Leonhardt, R.

Lippok, N.

Nelson, J.S.

Nielsen, P.

Pircher, M.

Ren, H.

Sarunic, M.

Siddiqui, M.

Szkulmowski, M.

P. Targowski, M. Wojkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczyska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun. 229, 79–84 (2004).
[Crossref]

Targowski, P.

P. Targowski, M. Wojkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczyska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun. 229, 79–84 (2004).
[Crossref]

Tearner, G.J.

Tearney, G.J.

Tozburun, S.

Vakoc, B.J.

Wojkowski, M.

P. Targowski, M. Wojkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczyska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun. 229, 79–84 (2004).
[Crossref]

Wojtkowski, M.

Yang, C.

Yun, S.H.

Zhao, Y.

Opt. Commun. (1)

P. Targowski, M. Wojkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczyska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun. 229, 79–84 (2004).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

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Figures (9)

Fig. 1
Fig. 1

Schematic of a polarization-based quadrature demodulation circuit with polarization diversity and balanced detection. Components contained within the blue dotted box are part of the optical demodulation circuit. PCI = in-phase polarization controller, PCQ = quadrature polarization controller, MI = measured in-phase signal, MQ = measured quadrature signal, PBS/PBC = polarization beam splitter/combiner.

Fig. 2
Fig. 2

Calibration algorithm flowchart outlining the steps in computing spectral (α(k) and β (k)) and RF (H(Δ)) errors from an input of measured MI and MQ. A MATLAB minimization function is used to update coefficients A – T based on minimizing the residual error. If parameters M through T from H(Δ) are known, α(k) and β(k) can be easily updated with inputs from a single depth.

Fig. 3
Fig. 3

(A) Incoherent averaging of 600 A-lines. (B) Coherent averaging of the same A-lines. A 28 dB improvement in SNR was achieved. The signal SNR in (B) was 75 dB, sufficient to optimize parameters to extinctions of 60-65 dB.

Fig. 4
Fig. 4

Quadrature signals at two depths (−1 mm and −2.5 mm) after coherent averaging. Black = prior to spectral error calibration. Red = after spectral error calibration. (A) −1 mm PSF self-calibrated. (B) −1 mm PSF corrected with −2.5 mm error calibration. (C) −2.5 mm PSF corrected with −1 mm error calibration. (D) −2.5 mm PSF self-calibrated.

Fig. 5
Fig. 5

PSFs without (black) and with (red) quadrature correction. Multiple depths are concatenated on the same plot for convenience, although the PSFs were recorded separately. Dechirping and dispersion correction was applied to limit PSF overlap and improve clarity. (A) Only spectral error, α(k), β(k), correction. (B) Only RF error, H(Δ), correction. (C) Both spectral and RF error correction.

Fig. 6
Fig. 6

The algorithm successfully removes residual errors at various depths at 18 MHz Aline rates. Black = prior to spectral error calibration. Red = after spectral error calibration. (A) +40μm (B) +80μm (C) +120μm (D) +240μm

Fig. 7
Fig. 7

Plot of the extinction for seven depths ranging from 1 mm to 2.5 mm over a period of 13 days. The depths from Time 0 mins were used to compute α(k), β(k), and H(Δ) and these were used to calibrate all subsequent timepoints.

Fig. 8
Fig. 8

Plot of the extinction for seven depths ranging from 1 mm to 2.5 mm over a period of 13 days. The depths from Time 0 mins were used to initially compute α(k), β(k), and H(Δ) and α(k), β(k) was renewed with depth 1.75 mm from each timepoint.

Fig. 9
Fig. 9

Image of an IR card on a tilt so that it spans both positive and negative depth spaces; the vertical axis is depth. (A) No optical demodulation used. (B) Optical demodulation with a polarization-demodulation circuit alone. (C) Optical demodulation with a polarizationdemodulation circuit and our error removal algorithm.

Equations (8)

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S I ( k ) = M I ( k )
S Q ( k ) = Re [ α ( k ) M I ( k ) + β ( k ) M Q ( k ) ]
S Q ( t ) = δ ( τ - T ) [ M Q ( t - τ ) ] d τ
S Q ( t ) = h ( τ ) [ M Q ( t - τ ) ] d τ
S Q ( k ) = 1 β ( k ) FT - 1 [ FT { M Q ( t ) } H Δ ] - α ( k ) β ( k ) M I ( k )
α ( k ) = Ak 2 + Bk + C + i [ Dk 2 + Ek + F ]
β ( k ) = Gk 2 + Hk + I + i [ Jk 2 + Kk + L ]
H ( Δ ) = M Δ 3 + N Δ 2 + O Δ + P + i [ Q Δ 3 + R Δ 2 + S Δ + T ]

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