Abstract

The sensitivity and dynamic range of optical coherence tomography (OCT) are calculated for instruments utilizing two common interferometer configurations and detection schemes. Previous researchers recognized that the performance of dual-balanced OCT instruments is severely limited by beat noise, which is generated by incoherent light backscattered from the sample. However, beat noise has been ignored in previous calculations of Michelson OCT performance. Our measurements of instrument noise confirm the presence of beat noise even in a simple Michelson interferometer configuration with a single photodetector. Including this noise, we calculate the dynamic range as a function of OCT light source power, and find that instruments employing balanced interferometers and balanced detectors can achieve a sensitivity up to six times greater than those based on a simple Michelson interferometer, thereby boosting image acquisition speed by the same factor for equal image quality. However, this advantage of balanced systems is degraded for source powers greater than a few milliwatts. We trace the concept of beat noise back to an earlier paper [J. Opt. Soc. Am. 52, 1335 (1962) ].

© 2006 Optical Society of America

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References

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    [CrossRef]
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2005

H. D. Ford, R. Beddows, P. Casaubieilh, and R. P. Tatum, "Comparative signal-to-noise analysis of fibre-optic based optical coherence tomography systems," J. Mod. Opt. 52, 1965-1979 (2005).
[CrossRef]

U. Sharma, N. M. Fried, and J. U. Kang, "All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis," IEEE J. Sel. Top. Quantum Electron. 11, 799-805 (2005).
[CrossRef]

T. Yoshino, M. R. Ali, and B. C. Sarker, "Performance analysis of low-coherence interferometry, taking into consideration optical beat noise," J. Opt. Soc. Am. B 22, 328-335 (2005).
[CrossRef]

2004

C. C. Rosa and A. Gh. Podoleanu, "Limitation of the achievable signal-to-noise ratio in optical coherence tomography due to mismatch of the balanced receiver," Appl. Opt. 43, 4802-4815 (2004).
[CrossRef] [PubMed]

B. M. Hoeling, M. E. Peter, D. C. Petersen, and R. C. Haskell, "Improved phase modulation for an en-face scanning 3D optical coherence microscope," Rev. Sci. Instrum. 75, 3348-3350 (2004).
[CrossRef]

2003

2001

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, and D. C. Petersen, "Phase modulation at 125 kHz in a Michelson interferometer using an inexpensive piezoelectric stack driven at resonance," Rev. Sci. Instrum. 72, 1630-1633 (2001).
[CrossRef]

2000

1999

1998

K. Takada, "Noise in optical low-coherence reflectometry," IEEE J. Quantum Electron. 34, 1098-1108 (1998).
[CrossRef]

1995

1992

W. V. Sorin and D. M. Baney, "A simple intensity noise reduction technique for optical low-coherence reflectometry," IEEE Photon. Technol. Lett. 4, 1404-1406 (1992).
[CrossRef]

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, "High-speed optical coherence domain reflectometry," Opt. Lett. 17, 151-153 (1992).
[CrossRef] [PubMed]

1990

P. R. Morkel, R. I. Laming, and D. N. Payne, "Noise characteristics of high-power doped-fibre superluminescent sources," Electron. Lett. 26, 96-98 (1990).
[CrossRef]

1965

H. Hodara, "Statistics of thermal and laser radiation," Proc. IEEE 53, 696-704 (1965).
[CrossRef]

1962

Ali, M. R.

Baney, D. M.

W. V. Sorin and D. M. Baney, "A simple intensity noise reduction technique for optical low-coherence reflectometry," IEEE Photon. Technol. Lett. 4, 1404-1406 (1992).
[CrossRef]

Beddows, R.

H. D. Ford, R. Beddows, P. Casaubieilh, and R. P. Tatum, "Comparative signal-to-noise analysis of fibre-optic based optical coherence tomography systems," J. Mod. Opt. 52, 1965-1979 (2005).
[CrossRef]

Boppart, S. A.

Bouma, B.

Bouma, B. E.

Brezinski, M. E.

Casaubieilh, P.

H. D. Ford, R. Beddows, P. Casaubieilh, and R. P. Tatum, "Comparative signal-to-noise analysis of fibre-optic based optical coherence tomography systems," J. Mod. Opt. 52, 1965-1979 (2005).
[CrossRef]

Cense, B.

Chak, A.

Choma, M. A.

de Boer, J. F.

Fercher, A. F.

Fernandez, A. D.

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, and D. C. Petersen, "Phase modulation at 125 kHz in a Michelson interferometer using an inexpensive piezoelectric stack driven at resonance," Rev. Sci. Instrum. 72, 1630-1633 (2001).
[CrossRef]

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, E. Huang, W. R. Myers, D. C. Petersen, S. E. Ungersma, R. Wang, M. E. Williams, and S. E. Fraser, "An optical coherence microscope for 3-dimensional imaging in developmental biology," Opt. Express 6, 136-146 (2000).
[CrossRef] [PubMed]

Ford, H. D.

H. D. Ford, R. Beddows, P. Casaubieilh, and R. P. Tatum, "Comparative signal-to-noise analysis of fibre-optic based optical coherence tomography systems," J. Mod. Opt. 52, 1965-1979 (2005).
[CrossRef]

Fraser, S. E.

Fried, N. M.

U. Sharma, N. M. Fried, and J. U. Kang, "All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis," IEEE J. Sel. Top. Quantum Electron. 11, 799-805 (2005).
[CrossRef]

Fujimoto, J. G.

Haskell, R. C.

B. M. Hoeling, M. E. Peter, D. C. Petersen, and R. C. Haskell, "Improved phase modulation for an en-face scanning 3D optical coherence microscope," Rev. Sci. Instrum. 75, 3348-3350 (2004).
[CrossRef]

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, and D. C. Petersen, "Phase modulation at 125 kHz in a Michelson interferometer using an inexpensive piezoelectric stack driven at resonance," Rev. Sci. Instrum. 72, 1630-1633 (2001).
[CrossRef]

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, E. Huang, W. R. Myers, D. C. Petersen, S. E. Ungersma, R. Wang, M. E. Williams, and S. E. Fraser, "An optical coherence microscope for 3-dimensional imaging in developmental biology," Opt. Express 6, 136-146 (2000).
[CrossRef] [PubMed]

Hee, M. R.

Hitzenberger, C. K.

Hodara, H.

H. Hodara, "Statistics of thermal and laser radiation," Proc. IEEE 53, 696-704 (1965).
[CrossRef]

Hoeling, B. M.

B. M. Hoeling, M. E. Peter, D. C. Petersen, and R. C. Haskell, "Improved phase modulation for an en-face scanning 3D optical coherence microscope," Rev. Sci. Instrum. 75, 3348-3350 (2004).
[CrossRef]

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, and D. C. Petersen, "Phase modulation at 125 kHz in a Michelson interferometer using an inexpensive piezoelectric stack driven at resonance," Rev. Sci. Instrum. 72, 1630-1633 (2001).
[CrossRef]

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, E. Huang, W. R. Myers, D. C. Petersen, S. E. Ungersma, R. Wang, M. E. Williams, and S. E. Fraser, "An optical coherence microscope for 3-dimensional imaging in developmental biology," Opt. Express 6, 136-146 (2000).
[CrossRef] [PubMed]

Huang, D.

Huang, E.

Izatt, J.

Izatt, J. A.

Kang, J. U.

U. Sharma, N. M. Fried, and J. U. Kang, "All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis," IEEE J. Sel. Top. Quantum Electron. 11, 799-805 (2005).
[CrossRef]

Kobayashi, K.

Laming, R. I.

P. R. Morkel, R. I. Laming, and D. N. Payne, "Noise characteristics of high-power doped-fibre superluminescent sources," Electron. Lett. 26, 96-98 (1990).
[CrossRef]

Leitgeb, R.

Lin, C. P.

Mandel, L.

L. Mandel, "Interference and the Alford and Gold effect," J. Opt. Soc. Am. 52, 1335-1340 (1962).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 9.

Morkel, P. R.

P. R. Morkel, R. I. Laming, and D. N. Payne, "Noise characteristics of high-power doped-fibre superluminescent sources," Electron. Lett. 26, 96-98 (1990).
[CrossRef]

Myers, W. R.

Park, B. H.

Payne, D. N.

P. R. Morkel, R. I. Laming, and D. N. Payne, "Noise characteristics of high-power doped-fibre superluminescent sources," Electron. Lett. 26, 96-98 (1990).
[CrossRef]

Peter, M. E.

B. M. Hoeling, M. E. Peter, D. C. Petersen, and R. C. Haskell, "Improved phase modulation for an en-face scanning 3D optical coherence microscope," Rev. Sci. Instrum. 75, 3348-3350 (2004).
[CrossRef]

Petersen, D. C.

B. M. Hoeling, M. E. Peter, D. C. Petersen, and R. C. Haskell, "Improved phase modulation for an en-face scanning 3D optical coherence microscope," Rev. Sci. Instrum. 75, 3348-3350 (2004).
[CrossRef]

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, and D. C. Petersen, "Phase modulation at 125 kHz in a Michelson interferometer using an inexpensive piezoelectric stack driven at resonance," Rev. Sci. Instrum. 72, 1630-1633 (2001).
[CrossRef]

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, E. Huang, W. R. Myers, D. C. Petersen, S. E. Ungersma, R. Wang, M. E. Williams, and S. E. Fraser, "An optical coherence microscope for 3-dimensional imaging in developmental biology," Opt. Express 6, 136-146 (2000).
[CrossRef] [PubMed]

Pierce, M. C.

Podoleanu, A. Gh.

Puliafito, C. A.

Rollins, A.

Rollins, A. M.

Rosa, C. C.

Sarker, B. C.

Sarunic, M. V.

Sharma, U.

U. Sharma, N. M. Fried, and J. U. Kang, "All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis," IEEE J. Sel. Top. Quantum Electron. 11, 799-805 (2005).
[CrossRef]

Sivak, M. V.

Sorin, W. V.

W. V. Sorin and D. M. Baney, "A simple intensity noise reduction technique for optical low-coherence reflectometry," IEEE Photon. Technol. Lett. 4, 1404-1406 (1992).
[CrossRef]

Swanson, E. A.

Takada, K.

K. Takada, "Noise in optical low-coherence reflectometry," IEEE J. Quantum Electron. 34, 1098-1108 (1998).
[CrossRef]

Tatum, R. P.

H. D. Ford, R. Beddows, P. Casaubieilh, and R. P. Tatum, "Comparative signal-to-noise analysis of fibre-optic based optical coherence tomography systems," J. Mod. Opt. 52, 1965-1979 (2005).
[CrossRef]

Tearney, G. J.

Ung-arunyawee, R.

Ungersma, S. E.

Wang, R.

Williams, M. E.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 9.

Wong, R. C. K.

Yang, C.

Yoshino, T.

Appl. Opt.

Electron. Lett.

P. R. Morkel, R. I. Laming, and D. N. Payne, "Noise characteristics of high-power doped-fibre superluminescent sources," Electron. Lett. 26, 96-98 (1990).
[CrossRef]

IEEE J. Quantum Electron.

K. Takada, "Noise in optical low-coherence reflectometry," IEEE J. Quantum Electron. 34, 1098-1108 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

U. Sharma, N. M. Fried, and J. U. Kang, "All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis," IEEE J. Sel. Top. Quantum Electron. 11, 799-805 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

W. V. Sorin and D. M. Baney, "A simple intensity noise reduction technique for optical low-coherence reflectometry," IEEE Photon. Technol. Lett. 4, 1404-1406 (1992).
[CrossRef]

J. Mod. Opt.

H. D. Ford, R. Beddows, P. Casaubieilh, and R. P. Tatum, "Comparative signal-to-noise analysis of fibre-optic based optical coherence tomography systems," J. Mod. Opt. 52, 1965-1979 (2005).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Proc. IEEE

H. Hodara, "Statistics of thermal and laser radiation," Proc. IEEE 53, 696-704 (1965).
[CrossRef]

Rev. Sci. Instrum.

B. M. Hoeling, A. D. Fernandez, R. C. Haskell, and D. C. Petersen, "Phase modulation at 125 kHz in a Michelson interferometer using an inexpensive piezoelectric stack driven at resonance," Rev. Sci. Instrum. 72, 1630-1633 (2001).
[CrossRef]

B. M. Hoeling, M. E. Peter, D. C. Petersen, and R. C. Haskell, "Improved phase modulation for an en-face scanning 3D optical coherence microscope," Rev. Sci. Instrum. 75, 3348-3350 (2004).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 9.

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Figures (6)

Fig. 1
Fig. 1

Schematic of an unbalanced Michelson interferometer configuration. A single 2 × 2 fiber coupler is used with a splitting ratio of γ M (chosen equal to 1 2 for optimized performance). A single photodetector samples the interference fringes.

Fig. 2
Fig. 2

Schematic of a dual-balanced OCT configuration. Two 2 × 2 fiber couplers are used; the primary coupler has a splitting ratio of γ bal while the second coupler sends 50% to each detector. Two optical circulators (OC) are employed, one in the sample arm and one in the reference arm. Typically light is coupled from port 1 to port 2 or from port 2 to port 3 with 85 % efficiency. The outputs of two balanced detectors are subtracted to reject common-mode intensity noise.

Fig. 3
Fig. 3

Measured noise variance at the output of an OCM as a function of P ref and P incoh . The OCM instrument is based on a simple Michelson interferometer design, as illustrated in Fig. 1. The 12 data points (black squares, with error bars approximately the size of the squares) are fitted to the form of expression (7): A + B ( P ref + P incoh ) + C ( P ref + P incoh ) 2 + CD P ref P incoh . The solid curves are the fitted curves yielding a reduced chi square of 0.60 (77% chance of exceeding). The fitted value of D = 2.04 ± 0.10 is consistent with the integer 2 in the last term of Eq. (3). The dashed curves are the best fit to the form of expression (7) without the beat noise term (the last term) and yield a reduced chi square of 113. The beat noise term is clearly needed to describe the data adequately.

Fig. 4
Fig. 4

Dynamic range (DR) plotted as a function of source power: The upper curves are values calculated for the balanced Ai configuration, and the lower curves are values for the unbalanced Michelson configuration. The solid curves are values calculated assuming no incoherent light backscattered from the sample path ( R incoh = 0 ) , while the dashed curves are for R incoh = 3.5 × 10 4 , a typical value for tissue. The dashed–dotted curves are calculated assuming R incoh = 3.5 × 10 4 , but with the beat noise terms omitted from Eqs. (3, 5). (The Ai dashed–dotted and solid curves are superposed and are barely distinguishable.) Note that the beat noise term accounts for essentially all of the reduction in the DR of the Ai system as R incoh changes from 0 to 3.5 × 10 4 , while approximately one third of the reduction in the Michelson is due to beat noise. Typical values for source powers range from 1 to 20 mW .

Fig. 5
Fig. 5

Values for the optimal reference reflectivity in Michelson configurations and values for the optimal fiber–splitter ratio in balanced Ai configurations, plotted as a function of source power. With higher source powers in Michelson systems, lower reference reflectivities are used to reduce Bose–Einstein photon bunching and optimize the DR. With higher source powers in balanced Ai configurations, more power is diverted from the reference arm (lower γ bal ) to the sample arm to optimize the DR. Note that for very low source powers, the Michelson DR is maximized with the maximum reference reflectivity ( R ref = 1 ) .

Fig. 6
Fig. 6

Improvement in the DR of the balanced Ai design over that of the Michelson configuration is plotted as a function of source power. The solid curve is calculated neglecting the incoherent light backscattered from the sample ( R incoh = 0 ) , while the dashed curve assumes R incoh = 3.5 × 10 4 , a typical value for tissue. The dashed curve peaks at a value of 2.5 for approximately 3 mW of source power. The dashed–dotted curve is calculated with R incoh = 3.5 × 10 4 but without the beat noise term in Eq. (3). The dashed curve (with beat noise in the Michelson) falls above the dashed–dotted curve (no beat noise in the Michelson) because beat noise degrades the performance of the Michelson configuration.

Tables (2)

Tables Icon

Table 1 Results of Fitting the Data in Fig. 3 to the Functional Form of Expression (7)

Tables Icon

Table 2 Values for Parameters Used to Calculate the Data for Figs. 4, 5, 6

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

SNR = mean - square fringe amplitude from a mirror variance of photon and detector noise ,
DR = SNR = rms fringe amplitude from a mirror rms detector and photon noise = F η h P ref P coh rms noise .
P ref = P s γ M ( 1 γ M ) R ref , P coh = P s γ M ( 1 γ M ) R coh ,
P incoh = P s γ M ( 1 γ M ) R incoh ,
P ref = P s γ bal T circ 2 R ref , P coh = P s ( 1 γ bal ) T circ 2 R coh ,
P incoh = P s ( 1 γ bal ) T circ 2 R incoh .
A + B ( P ref + P incoh ) + C ( P ref + P incoh ) 2 + CD P ref P incoh .
P coh P 0 exp ( μ attn z ) μ back l coh exp ( μ attn z ) ,
P incoh 0 P 0 exp ( 2 μ attn z ) μ back d z = P 0 μ back l attn 2 .
P incoh P coh l attn 2 l coh exp ( 2 μ attn z ) .
P incoh P coh 200 μ m 20 μ m exp ( 4 ) = 546 .
S 2 2 ¯ = α ¯ ( I ¯ 1 + I ¯ 2 ) B ( ν ) 2 d ν { 1 + α ¯ ( I ¯ 1 + I ¯ 2 ) Ψ 44 I ( ν 1 ) [ 1 + 2 I ¯ 1 I ¯ 2 ( I ¯ 1 + I ¯ 2 ) 2 γ 12 2 ( 0 ) cos ( 2 π ν 1 T ) ] } .
Var ( S 2 ) = 2 BW ( α ¯ I ¯ 1 + α ¯ I ¯ 2 ) + 2 BW τ coh ( α ¯ I ¯ 1 + α ¯ I ¯ 2 ) 2 + 2 BW τ coh 2 α ¯ I ¯ 1 α ¯ I ¯ 2 .
( Δ P Michelson ) 2 = 2 BW ( e R ) ( P ref + P incoh ) + 2 BW τ coh ( P ref + P incoh ) 2 + 2 BW τ coh 2 P ref P incoh .
( Δ P Michelson ) 2 = ( NEP ) 2 ( BW ) + 2 BW ( e R ) ( P ref + P incoh ) + BW τ coh ( 1 + Pol 2 ) ( P ref + P incoh ) 2 + BW τ coh ( 1 + Pol 2 ) 2 P ref P incoh ,
σ SE - SE 2 [ 3 + sinc 2 ( π B 0 τ ) + 4 sinc ( π B 0 τ ) cos ( ω 0 τ ) ] .

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