Abstract

This paper discusses a dispersion effect in a grating-based time-domain delay line that is different from the second- or higher-order dispersion in a grating-based Fourier-domain delay line. When the lateral broadening of the beam profile after grating dispersion exceeds the collection aperture of the reference fiber, the peripheral spectrum is decoupled by the fiber. The loss of reference spectral bandwidth by this geometric-beam broadening thus degrades the axial resolution. The polarizing-beam reflector used in the Fourier-domain delay line for suppression of lateral beam walk-off is implemented in this grating-based time-domain delay line to minimize geometric-beam broadening. Theoretical analysis and experiments are given to validate the axial resolution improvement after geometric-beam broadening is minimized. In vitro and in vivo imaging results are presented to demonstrate the improvement. It is also shown that geometric-beam broadening may exist in other optical coherence tomography reference arm configurations.

© 2007 Optical Society of America

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2007 (1)

2006 (5)

2005 (2)

2004 (4)

2003 (5)

2002 (4)

2000 (1)

1999 (1)

K. K. M. B. D. Silva, A. V. Zvyagin, and D. D. Sampson, "Extended range, rapid scanning optical delay line for biomedical interferometric imaging," Electron. Lett. 35, 1404-1405 (1999).
[CrossRef]

1998 (2)

1997 (2)

1996 (1)

1991 (1)

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," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Appl. Opt. (5)

Electron. Lett. (2)

K. K. M. B. D. Silva, A. V. Zvyagin, and D. D. Sampson, "Extended range, rapid scanning optical delay line for biomedical interferometric imaging," Electron. Lett. 35, 1404-1405 (1999).
[CrossRef]

D. Piao and Q. Zhu, "Power-efficient grating-based scanning optical delay line: time-domain configuration," Electron. Lett. 40, 97-98 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

Y. Watanabe, K. Yamada, and M. Sato, "In vivo nonmechanical scanning grating-generated optical coherence tomography using an InGaAs digital camera," Opt. Commun. 261, 376-380 (2006).
[CrossRef]

Opt. Express (7)

Opt. Lett. (12)

D. Piao, L. L. Otis, and Q. Zhu, "Doppler angle and flow velocity mapping by combined Doppler shift and Doppler bandwidth measurements in optical Doppler tomography," Opt. Lett. 28, 1120-1122 (2003).
[CrossRef] [PubMed]

C. C. Rosa, J. Rogers, and A. G. Podoleanu, "Fast scanning transmissive delay line for optical coherence tomography," Opt. Lett. 30, 3263-3265 (2005).
[CrossRef]

J. Wu, M. Conry, C. Gu, F. Wang, Z. Yaqoob, and C. Yang, "Paired-angle-rotation scanning optical coherence tomography forward-imaging probe," Opt. Lett. 31, 1265-1267 (2006).
[CrossRef] [PubMed]

M. Pircher, B. Baumann, E. Götzinger, and C. K. Hitzenberger, "Retinal cone mosaic imaged with transverse scanning optical coherence tomography," Opt. Lett. 31, 1821-1823 (2006).
[CrossRef] [PubMed]

N. G. Chen and Q. Zhu, "Rotary mirror array for high-speed optical coherence tomography," Opt. Lett. 27, 607-609 (2002).
[CrossRef]

E. D. J. Smith, A. V. Zvyagin, and D. D. Sampson, "Real-time dispersion compensation in scanning interferometry," Opt. Lett. 27, 1998-2000 (2002).
[CrossRef]

X. Liu, M. J. Cobb, Y. Chen, M. B. Kimmey, and X. Li, "Rapid-scanning forward-imaging miniature endoscope for real-time optical coherence tomography," Opt. Lett. 29, 1763-1765 (2004).
[CrossRef] [PubMed]

R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher, "Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography," Opt. Lett. 25, 820-822 (2000).
[CrossRef]

S. A. Boppart, B. E. Bouma, C. Pitris, G. J. Tearney, J. G. Fujimoto, and M. E. Brezinski, "Forward-imaging instruments for optical coherence tomography," Opt. Lett. 22, 1618-1620 (1997).
[CrossRef]

G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, "High-speed phase- and group-delay scanning with a grating-based phase controldelay line," Opt. Lett. 22, 1811-1813 (1997).
[CrossRef]

I. Zeylikovich, A. Gilerson, and R. R. Alfano, "Nonmechanical grating-generated scanning coherence microscopy," Opt. Lett. 23, 1797-1799 (1998).
[CrossRef]

G. J. Tearney, S. A. Boppart, B. E. Bouma, M. E. Brezinski, N. J. Weissman, J. F. Southern, and J. G. Fujimoto, "Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography," Opt. Lett. 21, 543-545 (1996).
[CrossRef] [PubMed]

Science (1)

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," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

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Figures (12)

Fig. 1
Fig. 1

Schematics of grating-based time-domain delay line and GBB effect. The inset shows the source spectrum when there is and is not decoupling of peripheral spectral profile.

Fig. 2
Fig. 2

(a) GBB effect for negative ranging when the grating center is at focus. The coupling to the fiber facet in (a) is equivalent to that in (b) where the beam is on-axis but the grating center has negative offset from the focal point of the lens.

Fig. 3
Fig. 3

Unfolded view of Fig. 2b. The inset details the beam profile at the fiber facet.

Fig. 4
Fig. 4

(a) Truncated spectrum of a Gaussian source may be approximated by a “slimmer” Gaussian spectrum that has the same center spectral density and the same overall spectral power as the truncated one. (b) Axial resolution degradation at different extents of spectrum truncation. The dotted line represents the optimal resolution.

Fig. 5
Fig. 5

Complete GBB compensation by PBR for on-axis and at-focus beam. The incident beam is linearly polarized by a polarizing beam splitter and becomes circularly polarized after the quarter wavelet. The first diffraction from the grating is converted to linear polarization orthogonal to the incoming one after the quarter-wave plate; therefore it is directed to the mirror of the PBR. The double-pass reflection from the mirror directs the light backward precisely to the incoming path. Since the dispersed beam is collimated in parallel to the optical axis, the broadened beam is reflected along the incident optical path for complete coupling to the fiber.

Fig. 6
Fig. 6

Incomplete GBB compensation for on-axis and off-focus scanning. (b) Unfolded view of (a) from the first diffraction to the PBR mirror. (c) Unfolded view of (a) from the second diffraction to the fiber. (d) The virtual imaging point used in ray tracing.

Fig. 7
Fig. 7

Axial image resolution measurement. Interference signals at target separation of 50 μ m are overlapped to calibrate the pixel size, which in turn is used to calculate FWHM of the intensity envelope profile.

Fig. 8
Fig. 8

Calculated and measured axial resolution at single pass. The dashed line indicates the optimum resolution obtained when the grating center is off the focal point of the achromatic lens.

Fig. 9
Fig. 9

Axial resolution improvement after GBB minimization: (a) resolution for the on-axis beam in comparison with the single-pass beam; (b) signal-intensity for the on-axis beam; (c) resolution within a 2.5 mm depth ranging for scanning of at-focus grating.

Fig. 10
Fig. 10

In vivo imaging of a human nail. The upper row was taken at single pass and the bottom row was taken at double pass. The nail anatomy is adapted from www.footdoc.ca.

Fig. 11
Fig. 11

In vitro imaging of a porcine coronary artery at different axial resolution settings. Histology reference is given at lower right.

Fig. 12
Fig. 12

GBB effects in other OCT configurations. (a) A transmissive Fourier-domain delay line [26, 27]; (b) a Littrow-mounted grating for nonscanning or full-field OCT [12, 28, 29].

Equations (44)

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l scan = 4 f 1 β 0 tan θ L ,
2 sin θ L = λ 0 p ,
sin θ L + sin ( θ L ± θ d ) = λ 0 ± λ d p .
θ d λ d p cos θ L .
h d = f 1 θ d = f 1 λ d p cos θ L .
θ VA = arctan ( h d f 2 ) = arctan ( f 1 f 2 λ d p cos θ L ) ,
θ VA < θ NA ,
tan θ VA = f 1 2 + ( f 2 l o g ) Δ f f 1 f 2 tan θ d ,
θ d = arctan ( f 1 f 2 f 1 2 + ( f 2 l o g ) Δ f tan θ NA ) .
θ d = arctan ( f 1 f 2 f 1 2 + ( f 2 l o g ) Δ f tan θ f ) ,
tan θ f = d 2 Δ x = f 1 2 + ( f 2 l o g ) Δ f 2 f 2 2 Δ f d ,
S 0 ( λ ) = 2 ln 2 π Δ λ 0 exp [ 4 ln 2 ( λ λ 0 Δ λ 0 ) 2 ] ,
Δ λ cut = 2 p cos θ L sin θ d .
S equ ( λ ) = 2 ln 2 π Δ λ 0 exp [ 4 ln 2 ( λ λ 0 Δ λ equ ) 2 ] ,
Δ λ equ = Δ λ 0 erf ( ln 2 Δ λ cut Δ λ 0 ) ,
erf ( λ ) = 2 π 0 λ exp ( x 2 ) d x .
ρ deg = 2 ln 2 π λ 0 2 Δ λ equ = ρ opt erf ( ln 2 Δ λ cut Δ λ 0 ) ,
ρ opt = 2 ln 2 π λ 0 2 Δ λ 0 ,
θ d arctan { f 1 3 f 2 2 Δ f cos θ L ( l 2 + l 3 ) [ f 1 2 + ( l 1 + l 2 f 2 ) ( f 1 k u ) ] tan θ NA } ,
u = f 1 + Δ f 2 Δ f cos β sin θ sin ( θ L β ) cos [ θ L sgn ( Δ f ) θ ] ,
β θ L θ θ d ,
θ = arctan [ ( 1 2 l 2 + 2 l 3 f 1 2 Δ f ) tan θ d ] .
P r = λ 0 ( Δ λ cut 2 ) λ 0 + ( Δ λ cut 2 ) 2 ln 2 π Δ λ 0 exp [ 4 ln 2 ( λ λ 0 Δ λ 0 ) 2 ] d λ = erf ( ln 2 Δ λ cut Δ λ 0 ) .
θ 2 = arctan ( 2 cos 2 β tan θ d 1 + cos 4 β ( 1 cos 4 β ) Δ f 2 f 2 tan 2 θ d ) ,
h d = ( 1 + 1 cos 2 β ) Δ f cos θ g tan θ 2 = ( 1 + 1 cos 2 β ) Δ f cos θ g 2 cos 2 β tan θ d 1 + cos 4 β ( 1 cos 4 β ) Δ f 2 f 2 tan 2 θ d 2 Δ f θ d cos θ g .
h d = 2 f Δ f 2 ( f Δ f ) Δ f tan θ d Δ f tan θ d ,
h d = ( f 1 2 Δ f + l o g ) tan θ 1 = ( f 1 2 Δ f + l o g ) Δ f f 1 tan θ d ,
tan θ V A = h d Δ x + f 2 = f 1 2 + ( f 2 l o g ) Δ f f 1 f 2 tan θ d ,
h d = ( f 1 2 Δ f l g ) Δ f f 1 tan θ d ,
tan θ V A = h d f 2 Δ x = f 1 2 + ( f 2 l o g ) Δ f f 1 f 2 tan θ d .
Δ λ cut = 2 p cos θ L sin θ d .
S P cut = λ 0 ( Δ λ cut 2 ) λ 0 + ( Δ λ cut 2 ) S 0 ( λ ) d λ = λ 0 ( Δ λ cut 2 ) λ 0 + ( Δ λ cut 2 ) 2 ln 2 π Δ λ 0 exp [ 4 ln 2 ( λ λ 0 Δ λ 0 ) 2 ] d λ .
S P cut = 2 π 0 ln 2 Δ λ cut Δ λ 0 exp ( λ 2 ) d λ = erf ( ln 2 Δ λ cut Δ λ 0 ) .
S equ ( λ ) = Δ λ equ Δ λ 0 2 ln 2 π Δ λ equ exp [ 4 ln 2 ( λ λ 0 Δ λ equ ) 2 ] ,
0 S equ ( λ ) d λ = Δ λ equ Δ λ 0 = S P cut ( λ ) = erf ( ln 2 Δ λ cut Δ λ 0 ) ,
Δ λ equ Δ λ 0 erf ( ln 2 Δ λ cut Δ λ 0 ) .
tan θ = ( 1 2 l 2 + 2 l 3 f 1 2 Δ f ) tan θ d ,
α = θ L + θ = θ L + arctan [ ( 1 2 l 2 + 2 l 3 f 1 2 Δ f ) tan θ d ] .
p ( sin α + sin β ) = λ 0 + Δ λ 0 2 = p [ sin θ L + sin ( θ L + θ d ) ] ,
β = arcsin [ sin θ L + sin ( θ L + θ d ) sin ( θ L + θ ) ] θ L + θ d θ .
tan θ V A = f 1 2 + ( l 1 + l 2 f 2 ) ( f 1 u ) f 1 f 2 tan ( θ L β ) ,
u f 1 + Δ f 2 cos β sin θ sin ( θ L β ) cos ( θ L + θ ) Δ f .
tan ( θ L β ) sin ( θ L θ d ) sin ( θ L θ ) sin ( θ L + θ d ) + sin ( θ L + θ ) 2 cos θ L ( tan θ tan θ d ) .
tan θ d = f 1 3 f 2 2 Δ f cos ( θ L ) ( l 2 + l 3 ) [ f 1 2 + ( l 1 + l 2 f 2 ) ( f 1 k u ) ] tan θ NA ,

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