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High speed full range complex spectral domain optical coherence tomography

Erich Götzinger, Michael Pircher, Rainer A. Leitgeb, and Christoph K. Hitzenberger

Open Access Open Access

Abstract

We present a high speed full range spectral domain optical coherence tomography system. By inserting a phase modulator into the reference arm and recording of every other spectrum with a 90° phase shift (introduced by the phase modulator) we are able to distinguish between negative and positive optical path differences with respect to the reference mirror. A modified two-frame algorithm eliminates the problem of suppressing symmetric structure terms in the final image. To demonstrate the performance of our method we present images of the anterior chamber of the human eye in vivo recorded with an A-scan rate of 10000 depth profiles per second.

©2005 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. High speed complex spectral domain optical coherence tomography system. SLD, superluminescent diode; FC, fiber coupler; Pol, polarizer; NPBS, nonpolarizing beamsplitter; VDF, variable density filter; PM, electro optic phase modulator; M, mirror; DC, dispersion compensation; SC, galvo scanner; L, lens; S, sample; HWP, half wave plate; PMF, polarization maintaining fiber; DG, diffraction grating; LSC, linescan camera.

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Fig. 2.
Fig. 2. A-lines obtained from single reflecting surface (mirror attenuated by neutral density filter). Abscissa: distance (mm), ordinate: signal amplitude (linear scale, arbitrary units, normalized to amplitude of structure peak of signal S1 in (b)). (a) Inverse Fourier transform of real-valued spectrum I(ν); (b) signals S 1 (black) obtained from complex spectrum and S 2 (red) obtained from complex conjugate spectrum (enlarged central section of depth profile); (c) difference signal ΔS=S 1-S 2; (d) final signal ΔS + (corresponds to final result of original two-frame algorithm).

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Fig. 3.
Fig. 3. Images of anterior chamber of human eye in vivo. Size of imaged area: 5.9 mm (horizontal, optical distance)×8 mm (vertical); each image consists of 800 A-lines. Logarithmic intensity scale. (a) Image obtained from inverse Fourier transform of real-valued spectrum I(ν), mirror terms corrupt the image. (b) Image corresponding to signal ΔS + (original two frame algorithm); mirror terms are removed, shadow like artifacts remain. (c) Symmetric structure terms recovered by new algorithm. (d) Final image (gated sum of (b) and (c)) obtained by enhanced two-frame algorithm.

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Fig. 4.
Fig. 4. Effect of phase error. A-lines obtained from single reflecting surface (cf. fig. 2). Abscissa: distance (mm), ordinate: signal amplitude (linear scale, arbitrary units, normalized to amplitude of structure peak of signal S1 in (a)). (a) Signals S1 (black) obtained from complex spectrum and S2 (red) obtained from complex conjugate spectrum; (b) difference signal ΔS=S 1-S 2; (c) final signal ΔS + (corresponds to final result of original two-frame algorithm).

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Fig. 5.
Fig. 5. Image of human anterior chamber showing motion artifacts. Size of imaged area: 5.9 mm (horizontal, optical distance)×8 mm (vertical); each image consists of 800 A-lines. Logarithmic intensity scale. (a) Image obtained from inverse Fourier transform of real-valued spectrum I(ν). (b) Image after applying two-frame algorithm.

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Equations (15)

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FT − 1 { I ( ν ) } = Γ rr ( τ ) + ∑ n Γ nn ( τ ) + ∑ n ≠ m { Γ [ τ + ( τ m − τ n ) ] + Γ [ τ − ( τ m − τ n ) ] }
∑ n { Γ [ τ + ( τ r − τ n ) ] + Γ [ τ − ( τ r − τ n ) ] } ,
I ˜ ( ν ) = I ( ν ) + iI ( ν , Δ ϕ = 90 ° ) ,
S ˜ 1 ( τ ) = FT − 1 { I ˜ ( ν ) } = DC + iDC + AC + iAC + 2 ∑ n Γ [ τ + ( τ r − τ n ) ] ,
S ˜ 2 ( τ ) = FT − 1 { I ˜ * ( ν ) } = DC − iDC + AC − iAC + 2 ∑ n Γ [ τ − ( τ r − τ n ) ] ,
S 1 ( τ ) = ∣ S ˜ 1 ( τ ) ∣ = 2 DC + 2 AC + 2 ∑ n Γ [ τ + ( τ r − τ n ) ] ,
S 2 ( τ ) = ∣ S ˜ 2 ( τ ) ∣ = 2 DC + 2 AC + 2 ∑ n Γ [ τ − ( τ r − τ n ) ] .
Δ S ( τ ) = S 1 ( τ ) − S 2 ( τ ) = 2 ∑ n Γ [ τ + ( τ r − τ n ) ] − 2 ∑ n Γ [ τ − ( τ r − τ n ) ] ,
Δ S + ( τ ) = Φ [ Δ S ( τ ) ] Δ S ( τ ) .
∣ FT − 1 { I ( ν ) } ∣ → M 1 ( τ ) = ∣ ∑ n Γ [ τ + ( τ r − τ n ) ] + ∑ n Γ [ τ − ( τ r − τ n ) ] ∣ ,
∣ FT − 1 { I * ( ν , Δ ϕ = 90 ° ) } ∣ → M 2 ( τ ) = ∣ ∑ n Γ [ τ + ( τ r − τ n ) ] − ∑ n Γ [ τ − ( τ r − τ n ) ] ∣ ,
Δ M ( τ ) = ∣ M 1 ( τ ) − M 2 ( τ ) ∣
M 1 , sym ( τ ) = 2 ∣ Γ [ τ + ( τ r − τ 1 ) ] + Γ [ τ − ( τ r − τ 1 ) ] ∣ ,
M 2 , sym ( τ ) = 0 ,
F ( τ ) = Φ [ − Δ M ( τ ) ] Δ S + ( τ ) + Φ [ Δ M ( τ ) ] S 1 ( τ ) ,
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