Abstract

The dispersion mismatch between sample and reference arm in frequency-domain optical coherence tomography (OCT) can be used to iteratively suppress complex conjugate artifacts and thereby increase the imaging range. In this paper, we propose a fast dispersion encoded full range (DEFR) algorithm that detects multiple signal components per iteration. The influence of different dispersion levels on the reconstruction quality is analyzed experimentally using a multilayered scattering phantom and in vivo retinal tomograms at 800 nm. Best results have been achieved with 30 mm SF11, with neglectable resolution decrease due to finite resolution of the spectrometer. Our fast DEFR algorithm achieves an average suppression ratio of 55 dB and typically converges within 5 to 10 iterations. The processing time on non-dedicated hardware was 5 to 10 seconds for tomograms with 512 depth scans and 4096 sampling points per depth scan. Application of DEFR to the more challenging 1060 nm wavelength region is also demonstrated by introducing an additional optical fibre in the sample arm.

© 2010 Optical Society of America

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2009

2008

2007

2006

2005

2004

2003

2002

Aoki, G.

Applegate, B. E.

Bachmann, A. H.

Bajraszewski, T.

Bird, A. C.

Boppart, S. A.

Bouma, B.

Bouma, B. E.

Bridgford, T.

B. Považay, B. Hermann, B. Hofer, V. Kajic, E. Simpson, T. Bridgford, and W. Drexler, "Wide field optical coherence tomography of the choroid in vivo," Invest. Ophthalmol. Vis. Sci. 50, 1856-1863 (2009). http://www.iovs.org/cgi/content/abstract/50/4/1856
[CrossRef]

Cense, B.

Chen, T. C.

Chen, Z. P.

Choma, M. A.

Davis, A. M.

A. M. Davis, M. A. Choma, and J. A. Izatt, "Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal," J. Biomed. Opt. 10, 064005 (2005). http://link.aip.org/link/?JBO/10/064005/1
[CrossRef]

de Boer, J.

de Boer, J. F.

Drexler, W.

Duker, J. S.

Egan, C. A.

Endo, T.

Esmaeelpour, M.

Fabritius, T.

Fercher, A. F.

Fujimoto, J. G.

Gorczynska, W.

P. Targowski, W. Gorczynska, M. Szkulmowski, M. Wojtkowski, and A. Kowalczyk, "Improved complex spectral domain OCT for in vivo eye imaging," Opt. Commun. 249, 357-362 (2005). http://dx.doi.org/doi:10.1016/j.optcom.2005.01.016
[CrossRef]

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and W. Gorczynska, "Complex spectral OCT in human eye imaging in vivo," Opt. Commun. 229, 79-84 (2004). http://dx.doi.org/doi:10.1016/j.optcom.2003.10.041
[CrossRef]

Götzinger, E.

Hermann, B.

Hitzenberger, C. K.

Hofer, B.

Itoh, M.

Izatt, J. A.

Kajic, V.

B. Považay, B. Hermann, B. Hofer, V. Kajic, E. Simpson, T. Bridgford, and W. Drexler, "Wide field optical coherence tomography of the choroid in vivo," Invest. Ophthalmol. Vis. Sci. 50, 1856-1863 (2009). http://www.iovs.org/cgi/content/abstract/50/4/1856
[CrossRef]

Ko, T. H.

Kowalczyk, A.

Lasser, T.

Leitgeb, R.

Leitgeb, R. A.

Makita, S.

Marks, D. L.

Matz, G.

Michaely, R.

Nassif, N. A.

Nelson, J. S.

Oldenburg, A. L.

Park, B. H.

Pierce, M. C.

Pircher, M.

Považay, B.

Reynolds, J. J.

Sarunic, M. V.

Sekhar, S. C.

Simpson, E.

B. Považay, B. Hermann, B. Hofer, V. Kajic, E. Simpson, T. Bridgford, and W. Drexler, "Wide field optical coherence tomography of the choroid in vivo," Invest. Ophthalmol. Vis. Sci. 50, 1856-1863 (2009). http://www.iovs.org/cgi/content/abstract/50/4/1856
[CrossRef]

Srinivasan, V. J.

Szkulmowski, M.

P. Targowski, W. Gorczynska, M. Szkulmowski, M. Wojtkowski, and A. Kowalczyk, "Improved complex spectral domain OCT for in vivo eye imaging," Opt. Commun. 249, 357-362 (2005). http://dx.doi.org/doi:10.1016/j.optcom.2005.01.016
[CrossRef]

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and W. Gorczynska, "Complex spectral OCT in human eye imaging in vivo," Opt. Commun. 229, 79-84 (2004). http://dx.doi.org/doi:10.1016/j.optcom.2003.10.041
[CrossRef]

Tao, Y. K.

Targowski, P.

P. Targowski, W. Gorczynska, M. Szkulmowski, M. Wojtkowski, and A. Kowalczyk, "Improved complex spectral domain OCT for in vivo eye imaging," Opt. Commun. 249, 357-362 (2005). http://dx.doi.org/doi:10.1016/j.optcom.2005.01.016
[CrossRef]

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and W. Gorczynska, "Complex spectral OCT in human eye imaging in vivo," Opt. Commun. 229, 79-84 (2004). http://dx.doi.org/doi:10.1016/j.optcom.2003.10.041
[CrossRef]

Tearney, G.

Tearney, G. J.

Torti, C.

Tumlinson, A. R.

Unterhuber, A.

Vakoc, B. J.

Wojtkowski, M.

Yang, C.

Yang, C. H.

Yasuno, Y.

Yatagai, T.

Yun, S.

Yun, S. H.

Zhang, J.

Zhao, M.

Appl. Opt.

Invest. Ophthalmol. Vis. Sci.

B. Považay, B. Hermann, B. Hofer, V. Kajic, E. Simpson, T. Bridgford, and W. Drexler, "Wide field optical coherence tomography of the choroid in vivo," Invest. Ophthalmol. Vis. Sci. 50, 1856-1863 (2009). http://www.iovs.org/cgi/content/abstract/50/4/1856
[CrossRef]

J. Biomed. Opt.

A. M. Davis, M. A. Choma, and J. A. Izatt, "Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal," J. Biomed. Opt. 10, 064005 (2005). http://link.aip.org/link/?JBO/10/064005/1
[CrossRef]

Opt. Commun.

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and W. Gorczynska, "Complex spectral OCT in human eye imaging in vivo," Opt. Commun. 229, 79-84 (2004). http://dx.doi.org/doi:10.1016/j.optcom.2003.10.041
[CrossRef]

P. Targowski, W. Gorczynska, M. Szkulmowski, M. Wojtkowski, and A. Kowalczyk, "Improved complex spectral domain OCT for in vivo eye imaging," Opt. Commun. 249, 357-362 (2005). http://dx.doi.org/doi:10.1016/j.optcom.2005.01.016
[CrossRef]

Opt. Express

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Opt. Express 12, 2404-2422 (2004). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-11-2404
[CrossRef] [PubMed]

B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S. H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, "Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography," Opt. Express 12, 2435-2447 (2004). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-11-2435
[CrossRef] [PubMed]

S. Yun, G. Tearney, J. de Boer, and B. Bouma, "Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting," Opt. Express 12, 4822-4828 (2004). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-20-4822
[CrossRef] [PubMed]

A. H. Bachmann, R. A. Leitgeb, and T. Lasser, "Heterodyne Fourier domain optical coherence tomography for full range probing with high axial resolution," Opt. Express 14, 1487-1496 (2006). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1487
[CrossRef] [PubMed]

E. Götzinger, M. Pircher, R. A. Leitgeb, and C. K. Hitzenberger, "High speed full range complex spectral domain optical coherence tomography," Opt. Express 13, 583-594 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-2-583
[CrossRef] [PubMed]

M. V. Sarunic, M. A. Choma, C. H. Yang, and J. A. Izatt, "Instantaneous complex conjugate resolved spectral domain and swept-source OCT using 3x3 fiber couplers," Opt. Express 13, 957-967 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-957
[CrossRef] [PubMed]

A. H. Bachmann, R. Michaely, T. Lasser, and R. A. Leitgeb, "Dual beam heterodyne Fourier domain optical coherence tomography," Opt. Express 15, 9254-9266 (2007). http://www.opticsexpress.org/abstract.cfm?URI=oe-15-15-9254
[CrossRef] [PubMed]

S. Makita, T. Fabritius, and Y. Yasuno, "Full-range, high-speed, high-resolution 1-μm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye," Opt. Express 16, 8406-8420 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-12-8406
[CrossRef] [PubMed]

B. Hofer, B. Považay, B. Hermann, A. Unterhuber, G. Matz, and W. Drexler, "Dispersion encoded full range frequency domain optical coherence tomography," Opt. Express 17, 7-24 (2009). http://www.opticsexpress.org/abstract.cfm?URI=oe-17-1-7
[CrossRef] [PubMed]

B. Považay, B. Hofer, C. Torti, B. Hermann, A. R. Tumlinson, M. Esmaeelpour, C. A. Egan, A. C. Bird, and W. Drexler, "Impact of enhanced resolution, speed and penetration on three-dimensional retinal optical coherence tomography," Opt. Express 17, 4134-4150 (2009). http://www.opticsexpress.org/abstract.cfm?URI=oe-17-5-4134
[CrossRef] [PubMed]

Opt. Lett.

Y. K. Tao, M. Zhao, and J. A. Izatt, "High-speed complex conjugate resolved retinal spectral domain optical coherence tomography using sinusoidal phase modulation," Opt. Lett. 32, 2918-2920 (2007). http://ol.osa.org/abstract.cfm?URI=ol-32-20-2918
[CrossRef] [PubMed]

R. A. Leitgeb, R. Michaely, T. Lasser, and S. C. Sekhar, "Complex ambiguity-free Fourier domain optical coherence tomography through transverse scanning," Opt. Lett. 32, 3453-3455 (2007). http://ol.osa.org/abstract.cfm?URI=ol-32-23-3453
[CrossRef] [PubMed]

B. J. Vakoc, S. H. Yun, G. J. Tearney, and B. E. Bouma, "Elimination of depth degeneracy in optical frequency domain imaging through polarization-based optical demodulation," Opt. Lett. 31, 362-364 (2006). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-3-362
[CrossRef] [PubMed]

M. A. Choma, C. Yang, and J. A. Izatt, "Instantaneous quadrature low-coherence interferometry with 3×3 fiber-optic couplers," Opt. Lett. 28, 2162-2164 (2003). http://ol.osa.org/abstract.cfm?URI=ol-28-22-2162
[CrossRef] [PubMed]

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). http://ol.osa.org/abstract.cfm?URI=ol-28-22-2201
[CrossRef] [PubMed]

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). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-16-1415
[CrossRef]

M. V. Sarunic, B. E. Applegate, and J. A. Izatt, "Real-time quadrature projection complex conjugate resolved Fourier domain optical coherence tomography," Opt. Lett. 31, 2426-2428 (2006). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-16-2426
[CrossRef] [PubMed]

J. Zhang, J. S. Nelson, and Z. P. Chen, "Removal of a mirror image and enhancement of the signal-to-noise ratio in Fourier-domain optical coherence tomography using an electro-optic phase modulator," Opt. Lett. 30, 147-149 (2005). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-2-147
[CrossRef] [PubMed]

Other

B. Hofer, B. Považay, B. Hermann, A. Unterhuber, G. Matz, F. Hlawatsch, and W. Drexler, "Signal post processing in frequency domain OCT and OCM using a filter bank approach," 6443, 64 430O (2007). http://link.aip.org/link/?PSI/6443/64430O/1

R. K. Wang, "In vivo full range complex Fourier domain optical coherence tomography," Appl. Phys. Lett. 90, 054103 (2007). http://link.aip.org/link/?APL/90/054103/1
[CrossRef]

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Supplementary Material (1)

» Media 1: AVI (875 KB)     

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Figures (12)

Fig. 1.
Fig. 1.

Block diagram of the fast dispersion encoded full range (DEFR) algorithm. The iterative procedure is indicated by iteration index i. The multi peak detector is denoted as MPD; further notations: measured interference signal f, dispersive phase term ϕ , fast Fourier transform (FFT), inverse FFT (IFFT), residual signal r, intermediate spatial signal c; and finally the complex full range tomogram line t̂ ∈ ℂ N .

Fig. 2.
Fig. 2.

Simulation of 2 reflective sites positioned at n 1 = 512 and n 2 = 1536. (a) Solid green line: initial residual r 0 = f after dispersion compensation and IFFT; dashed magenta line: threshold level of multi peak detector for first iteration, δ = 0.75; solid black line: residual after 12 iterations. (b) Solid red line: original signal t̃ without dispersion and complex detection; solid blue line: DEFR reconstruction of complex full range signal t̂ (Media 1).

Fig. 3.
Fig. 3.

Signal of single reflection after dispersion compensation for various levels of dispersion. The signal peak is located at -100 μm and the overlapping broad arc corresponds to the double dispersed conjugate mirror artifact. Inset: Dispersion diversity obtained with different amounts of SF11 [cf. Eq. (12)].

Fig. 4.
Fig. 4.

Depth dependency of spectral envelope for various levels of dispersion and different mirror positions. (a) No dispersion mismatch; (b) SF11 5 mm; (c) SF11 40 mm; (d) SF11 150 mm. Dotted line: mirror at -600 μm; solid line: mirror at 200 μm; dashed line: mirror at 1000 μm.

Fig. 5.
Fig. 5.

(a) Signal loss, (b) artifact suppression ratio of DEFR algorithm, (c) resolution with different amounts of SF11 and data from a plane mirror. Parameters for DEFR: δ = 0.5, I = 10, final residual added.

Fig. 6.
Fig. 6.

Evaluation of DEFR scheme with composite signal. (a) Reconstructed composite signal for 40 mm SF11 and δ = 0.5, (b) conjugate artifact suppression (CAS) for 40 mm SF11, (c) CAS after 1 iteration dependent on stability parameter δ, (d) convergence curves with δ = 0.5 for different levels of dispersion.

Fig. 7.
Fig. 7.

Demonstration of fast DEFR algorithm on data from scattering phantom. (a) Dispersion balanced; (b,c) dispersion due to 5 mm and 80 mm SF11 respectively has been numerically compensated; (d,e) DEFR reconstruction after 7 iterations with stability parameter δ=0.5 for 5 mm and 80 mm SF11 respectively; each tomogram is 2048×512 pixels corresponding to 2746 μm×445 μm in air. (f) Vertically zoomed tomogram portions for balanced dispersion, 5 mm, 40 mm, 80 mm and 150 mm SF11 respectively; zoomed region is indicated by magenta colored frame for 80 mm SF11.

Fig. 8.
Fig. 8.

Behavior of fast DEFR algorithm under various parameters for in vivo retinal imaging at 800 nm with dispersion mismatch due to 20 mm SF11. Each tomogram is 2048×512 pixels corresponding to 2746 μm×5.5 mm in air.

Fig. 9.
Fig. 9.

Behavior of fast DEFR algorithm for in vivo retinal imaging at 800 nm with dispersion mismatch due to different amounts of SF11. Each tomogram is 2048×512 pixels corresponding to 2746 μm×5.5 mm in air. (a) DEFR with 1 iteration and stability parameter δ=0.7; (b) DEFR with 5 iterations and δ=0.5.

Fig. 10.
Fig. 10.

Application of fast DEFR algorithm for wide field in vivo retinal imaging at 800 nm. Each tomogram is 2048×2048 pixels corresponding to 2746 μm×11 mm in air.

Fig. 11.
Fig. 11.

Application of fast DEFR algorithm for wide field in vivo retinal imaging at 1060 nm. (a) Dispersion due to 160 mm SF11 has been compensated numerically; (b) DEFR after 10 iterations and δ=0.5; (c) dispersion due to 2.1 m patch-cord, DEFR after 10 iterations and δ=0.5. Each tomogram is 1024×1024 pixels corresponding to 7086 μm×11 mm in air.

Fig. 12.
Fig. 12.

Comparison of fast DEFR algorithm with standard processing for retinal imaging at 1060 nm. Dispersion due to 2.1 m patch-cord; numerical dispersion compensation (upper row), DEFR with 10 iterations and δ=0.5 (lower row). Each tomogram is 1152×1024 pixels corresponding to 7972 μm×5.5 mm in air.

Tables (4)

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Table 1. Vector notation used for algorithm formulation.

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Table 2. Complex signal values and average absolute errors for simulated signals at two different positions.

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Table 3. Simulation results for different values of stability parameter.

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Table 4. Dispersion coefficients employed in the different experiments.

Equations (12)

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S ˜ ( ω ) = e ( ω ) n I n ( ω ) e τ n S ˜ d ( ω ) + e ( ω ) n I n * ( ω ) e τ n . S ˜ m ( ω )
ϕ ( ω ) = i = 2 a ˜ i ( ω ω 0 ) i .
f = s b = Φd = Φ * d * + w = 2 { ΦΨt } + w .
t ̂ = arg min t t 1 subject to 2 { Vt } = f .
n i = arg max n = 1 N c i , n , with c i , n = v n , r i 1 v n .
c ˜ i = P i c i , with P i = diag ( p i ) , p i , n = { 0 c i , n < c i , n i ( 1 δγ ) 1 c i , n c i , n i ( 1 δγ ) .
t ̂ i = t ̂ i 1 + c ˜ i ,
r i = r i 1 2 { V c ˜ i } .
t ̂ = t ̂ I ( + V H r I ) .
γ ϕ b = 1 max Ψ H diag ( b ) { Φ ψ N / 4 } max Ψ H Φ * diag ( b ) { Φ ψ N / 4 } .
f = 2 { Φ diag ( b ) ψ 3 N / 4 g 1 d 1 + Φ diag ( b ) ψ N / 4 g 2 d 2 } + w ,
DD = 20 log max diag ( u ) Ψ H Φ * diag ( b ) { Φ ψ N / 4 } max Ψ H Φ * diag ( b ) { Φ ψ N / 4 } , u N , u n = { 0 n < N / 2 1 n N / 2 ,

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