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Motion artifacts in optical coherence tomography with frequency-domain ranging

S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma

Open Access Open Access

Abstract

We describe results of theoretical and experimental investigations of artifacts that can arise in spectral-domain optical coherence tomography (SD-OCT) and optical frequency domain imaging (OFDI) as a result of sample or probe beam motion. While SD-OCT and OFDI are based on similar spectral interferometric principles, the specifics of motion effects are quite different because of distinct signal acquisition methods. These results provide an understanding of motion artifacts such as signal fading, spatial distortion and blurring, and emphasize the need for fast image acquisition in biomedical applications.

©2004 Optical Society of America

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Figures (18)
Fig. 1.
Fig. 1. Basic configuration of single-mode-fiber-based SD-OCT.

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Fig. 2.
Fig. 2. Illustrations of (a) axial and (b) transverse motion of a sample (scatter layer) and probe beam.

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Fig. 3.
Fig. 3. (a) Effective intensity profiles of the probe beam at four different normalized displacements. (b) Mean SNR drop for a random scattering scample as a function of the normalized transverse displacement.

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Fig. 4.
Fig. 4. Schematic of the experimental SD-OCT system. ASE; amplified spontaneous emission, G: galvanometer, LSC; line scan camera, DAQ; data acquisition board.

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Fig. 5.
Fig. 5. (a) An SD-OCT image (500 A-lines) of a mirror vibrating at a peak-to-peak amplitude of 1.76 mm and frequency of 40 Hz. (b) Maximum signal power measured (solid line, black) and calculated theoretically (dashed line, brown). (c) An image of a mirror moving at an amplitude 0.22 mm and frequency of 80 Hz. (d) Signal power measured (solid line, black) and calculated theoretically (dashed line, brown).

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Fig. 6.
Fig. 6. SD-OCT images of a 90-degree prism at various amplitudes of the galvanometer scan voltage. With increasing amplitude, the scan velocity is increased and therefore the image contains fewer A-lines. The scale bars represent 1.0 mm.

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Fig. 7.
Fig. 7. (a) Signal peak power (open circles, black) measured from the average of 10 A-line profiles for each normalized displacement. Red line: theorical fit curve for speckle-averaged signal power. (b) Minimum FWHM of the image (open circles, black) obtained from 10 A-line amplitude profiles. Blue line: theoretical curve for axial resolution expected from a mirror sample.

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Fig. 8.
Fig. 8. SD-OCT image of a human finger (256 axial×500 transverse pixels, 2.08 mm×5 mm) obtained at an A-line rate of 19 kHz. The arrow indicates a skin fold region.

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Fig. 9.
Fig. 9. Schematic of single-mode-fiber-based OFDI.

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Fig. 10.
Fig. 10. (a) The magnitude of broadening in axial and transverse resolution and (b) SNR decrease arising from transverse motion as a function of normalized displacement Δx/w for σ2=0.5.

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Fig. 11.
Fig. 11. Experimental setup of the OFDI system.

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Fig. 12.
Fig. 12. OFDI images of a moving mirror (amplitude: 0.78 mm, frequency: 30 Hz) acquired at A-line rates of 16, 8, 4, 2, and 1 kHz, respectively. The vertical axis represents the depth over 3.8 mm. The horizontal axis represents the time over 520 A-line acquisition periods. The vibration amplitude in the images is artifactually increased with increasing amount as the A-line acquisition rate decreases by Doppler shift

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Fig. 13.
Fig. 13. Normalized amplitude of mirror motion measured from the images of Fig. 12 (circles) and predicted theoretically (line).

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Fig. 14.
Fig. 14. (a) Measured A-line profiles (curves 1 to 16, black) obtained at an A-line rate of 2 kHz during a single cycle of sample mirror oscillation. The A-line profile obtained with a stationary mirror at its neutral position is also shown as a reference (curve 0, blue). (b) Simulation results. Curve labeled 17 (green) depicts the trace of actual mirror motion used in the simulation.

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Fig. 15.
Fig. 15. (a) Normalized axial resolution obtained at an A-line rate of 2 kHz, normalized to the unperturbed resolution obtained with a stationary mirror. (b) Normalized axial resolution obtained at an A-line rate of 16 kHz. Black circles: measured values. Red line: simulation.

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Fig. 16.
Fig. 16. OFDI images of a prism at various amplitudes of the galvanometer scan voltage. With increasing amplitude, the scan velocity is increased and therefore the image contains a fewer number of A-line. The

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Fig. 17.
Fig. 17. (a) Signal peak power (squares, black) measured from the average of 10 A-line profiles for each normalized displacement. Red line: theorical curve for speckle-averaged signal power with α=0.4 in Eq. (26). (b) Normalized minimum FWHM of the image (circles, black) obtained from 10 A-line profiles. Theorical curve of axial resolution assuming a single scatter sample (line, blue).

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Fig. 18.
Fig. 18. OFDI image of a human finger near skin fold (300 axial×300 transverse pixels, 3.8 mm×5.8 mm) acquired with the OFDI system at an A-line rate of 15.7 kHz.

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Equations (30)

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i ( k ) = γ S r ( k ) S s ( k ) Re { ∭ dxdydz r ( x , y , z ) g ( x − x b , y − y b , z − z b ) exp [ − i 2 k ( z − z b ) ] } .
g ( x , y , z ) ≈ 4 ln 2 π w 0 2 exp [ − 4 ln 2 ( x 2 + y 2 ) ⁄ w 0 2 ] ,
N ( k ) = γ S r ( k ) S s ( k ) ∫ − T . 2 T ⁄ 2 dt ∭ dxdydz r ( x , y , z ) g ( x − x b , y − y b ) exp [ − i 2 k ( z − z b ) ]
F ( Z ) ≈ ∫ − ∞ ∞ N ( k ) e i 2 k Z d ( 2 k ) ,
F ( Z ) ∝ γ P 0 T w 0 2 δ z 0 ∭ dxdydz r ( x , y , z ) e i 2 k 0 ( Z − z + z b ) e − 4 ln 2 ( x − x b ) 2 w 0 2 e − 4 ln 2 ( y − y b ) 2 w 0 2 e − 4 ln 2 ( Z − z + z b ) 2 δ z 0 2 ,
N ( k ) = γ S r ( k ) S s ( k ) ∫ − T / 2 T ⁄ 2 dt ∭ dxdy r ( x , y ) g ( x − x b , y − y b ) exp [ − i 2 k { z ( x , y ) − z b + v z t } ] .
N ( k ) = γ T S r ( k ) S s ( k ) ∬ dxdy r ( x , y ) g ( x − x b , y − y b ) exp [ − i 2 k ( z − z b ) ] sin ( k Δ z ) k Δ z
= N 0 ( k , Δ z = 0 ) sin ( k Δ z ) k Δ z ,
N s ( k ) = γ S r ( k ) S s ( k ) ∫ − T / 2 T ⁄ 2 dt ∬ dxdy r ( x , y ) g ( x − x b + v x t , y − y b ) exp [ − i 2 k ( z − z b ) ] ,
N s ( k ) = γ T S r ( k ) S s ( k ) ∬ dxdy r ( x , y ) G ( x − x b , y − y b ) exp [ − i 2 k ( z − z b ) ] ,
G ( x , y ) = 1 T ∫ − T ⁄ 2 T ⁄ 2 g ( x + v x t , y ) dt .
P out ( t ) = P 0 exp [ − 4 ln 2 t 2 / ( σ T ) 2 ] ,
i ( t ) = γ P r ( t ) P s ( t ) Re { ∭ dxdydz r ( x , y , z ) g ( x − x b , y − y b ) e − i 2 k ( t ) ( z − z b ) } .
F ( Z ) = ∫ − k 1 T k 1 T i ( κ ) e i κ Z d κ .
F ( Z ) = γ P 0 ∭ dxdydz r ( x , y , z ) g ( x − x b , y − y b ) e − i 2 k 0 ( z − z b ) ∫ − ∞ ∞ e − 4 ln 2 κ 2 ( 2 k 1 T σ ) 2 e i κ ( Z + z b − z ) d κ .
F ( Z ) ∝ γ P 0 w 0 2 δ z 0 ∭ dxdydz r ( x , y , z ) e − i 2 k 0 ( Z − z b ) e − 4 ln 2 ( x − x b ) 2 w 0 2 e − 4 ln 2 ( y − y b ) 2 w 0 2 e − 4 ln 2 { Z + z b − z ( x , y ) } 2 δ z 0 2 ,
F ( Z ) = γ P 0 ∭ dxdydz r ( x , y , z ) g ( x − x b , y − y b ) e − i 2 k 0 Z ∫ − ∞ ∞ e − 4 ln 2 κ 2 ( 2 k 1 T σ ) 2 e i ( 2 k 0 + κ ) ( Z − z 0 − v z 2 k 1 κ ) d κ
∝ γ P 0 w 0 2 δ z ∭ dxdydz r ( x , y , z ) e − i 2 k 0 z 0 e − 4 ln 2 ( x − x b ) 2 w 0 2 e − 4 ln 2 ( y − y b ) 2 w 0 2 e − 4 ln 2 { Z − [ z 0 + ( k 0 ⁄ k 1 T ) Δ z ] } 2 δ z 0 2 ( 1 + 4 σ 2 Δ z 2 ⁄ δ z 0 2 )
Z = z 0 + z D ,
z D ≡ k 0 k 1 T Δ z = π σ 2 ln 2 δ z 0 λ Δ z .
δ z δ z 0 = 1 + 4 σ 2 Δ z 2 δ z 0 2 .
i ( t ) = γ P r ( t ) P s ( t ) ∭ dxdydz r ( x , y , z ) g ( x − x b + Δ x T t , y − y b ) e − i 2 k 0 z 0 e − i 2 k 1 t z 0 ,
F ( Z ) = γ P 0 w 0 2 ∭ dxdydz r ( x , y , z ) e − i 2 k 0 z 0 e − 4 ln 2 ( y − y b ) 2 w 0 2 ∫ − k 1 T k 1 T e − 4 ln 2 κ 2 ( 2 k 1 T σ ) 2 e − 4 ln 2 ( x − x b + Δ x 2 k 1 T κ ) 2 w 0 2 e i κ ( Z − z 0 ) d κ ,
F ( Z ) ∝ γ P 0 w 0 w x δ z 0 ∭ dxdydz r ( x , y , z ) e − i 2 k 0 z 0 e − 4 ln 2 ( y − y b ) 2 w 0 2 e − 4 ln 2 ( x − x b ) 2 w x 2 e − 4 ln 2 ( Z − z 0 ) 2 δ z 2 ,
w x w 0 = δ z δ z 0 = 1 + σ 2 Δ x 2 w 0 2 .
SNR decrease ≈ ( 1 + σ 2 Δ x 2 w 0 2 ) − α ,
t = T τ − ( k 2 ⁄ k 1 ) T 2 τ 2 + [ 2 ( k 2 ⁄ k 1 ) 2 − ( k 3 ⁄ k 1 ) ] T 3 τ 3 + ⋯ ,
i ( ξ ) = γ P r ( τ ) P s ( τ ) ∭ dxdydz r ( x , y , z ) g ( x − x b , y − y b ) exp [ − i Σ ω m τ m ] ,
ω 0 = 2 k 0 z 0 , ω 1 = 2 ( k 1 z 0 + k 0 z 1 ) T , ω 2 = 2 { k 1 z 1 − ( k 0 k 2 ⁄ k 1 ) z 1 + k 0 z 2 } T 2 .
δ z δ z 0 = 1 + σ 4 ω 2 2 ( 4 ln 2 ) 2 .
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