Abstract

An inertial-free, ultrafast frequency comb source based on two chirped optical frequency combs (OFCs) is proposed and experimentally demonstrated. The high linearity frequency sweeping is realized by the Vernier effect between the two OFCs rather than any mechanical motion component, so that good stability and reliability are ensured and no recalibration or resampling process is required. Swept rate up to 1 MHz is realized while keeping a narrow instantaneous linewidth of 0.03 nm, thanks to the extra-cavity frequency sweeping method. The wavelength step is proportional to the swept rate (3.8 pm at 10 kHz), and can be tuned by changing the repetition rate difference between the two OFCs. This swept source is applied for high-speed wavelength encoded imaging and achieves 4.4-μm spatial resolution at a 329-kHz frame rate. Compared with the traditional time-stretch microscopy, the signal acquisition bandwidth decreased from 3.8 GHz to below 90 MHz to achieve the same spatial resolution. Furthermore, the exposure time for a specific wavelength is much longer due to the discrete sweeping feature, which is a benefit for higher sensitivity. This discrete swept source provided a promising low-cost option for high-speed biomedical imaging systems and high-accuracy spectroscopy.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

2017 (5)

2016 (2)

2015 (2)

2014 (5)

2013 (5)

2012 (2)

2011 (4)

2010 (4)

2009 (5)

2008 (2)

2007 (3)

2006 (3)

2005 (5)

2004 (1)

S. H. Yun, C. Boudoux, M. C. Pierce, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Technol. Lett. 16(1), 293–295 (2004).
[Crossref] [PubMed]

2003 (1)

1998 (1)

1997 (2)

Adler, D. C.

T.-H. Tsai, C. Zhou, D. C. Adler, and J. G. Fujimoto, “Frequency comb swept lasers,” Opt. Express 17(23), 21257–21270 (2009).
[Crossref] [PubMed]

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(1), 709–716 (2007).
[Crossref]

Ahr, F.

An, X.

Asano, M.

Barry, S.

Baumann, B.

Biedermann, B.

Biedermann, B. R.

Blatter, C.

M. Siddiqui, A. S. Nam, S. Tozburun, N. Lippok, C. Blatter, and B. J. Vakoc, “High-speed optical coherence tomography by circular interferometric ranging,” Nat. Photonics 12(2), 111–116 (2018).
[Crossref] [PubMed]

Boudoux, C.

Bouma, B.

Bouma, B. E.

C. Jun, M. Villiger, W.-Y. Oh, and B. E. Bouma, “All-fiber wavelength swept ring laser based on Fabry-Perot filter for optical frequency domain imaging,” Opt. Express 22(21), 25805–25814 (2014).
[Crossref] [PubMed]

S. C. Schlachter, D. Kang, M. J. Gora, P. Vacas-Jacques, T. Wu, R. W. Carruth, E. J. Wilsterman, B. E. Bouma, K. Woods, and G. J. Tearney, “Spectrally encoded confocal microscopy of esophageal tissues at 100 kHz line rate,” Biomed. Opt. Express 4(9), 1636–1645 (2013).
[Crossref] [PubMed]

W.-Y. Oh, B. J. Vakoc, M. Shishkov, G. J. Tearney, and B. E. Bouma, “>400 kHz repetition rate wavelength-swept laser and application to high-speed optical frequency domain imaging,” Opt. Lett. 35(17), 2919–2921 (2010).
[Crossref] [PubMed]

W. Y. Oh, S. H. Yun, G. J. Tearney, and B. E. Bouma, “115 kHz tuning repetition rate ultrahigh-speed wavelength-swept semiconductor laser,” Opt. Lett. 30(23), 3159–3161 (2005).
[Crossref] [PubMed]

W. Y. Oh, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Wide tuning range wavelength-swept laser with two semiconductor optical amplifiers,” IEEE Photonics Technol. Lett. 17(3), 678–680 (2005).
[Crossref] [PubMed]

S. H. Yun, C. Boudoux, M. C. Pierce, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Technol. Lett. 16(1), 293–295 (2004).
[Crossref] [PubMed]

S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. 28(20), 1981–1983 (2003).
[Crossref] [PubMed]

B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+:forsterite laser,” Opt. Lett. 22(22), 1704–1706 (1997).
[Crossref] [PubMed]

Bozic, I.

Cable, A. E.

Cao, Y.

Capewell, D.

Carbajo, S.

Carruth, R. W.

Caswell, A. W.

Chen, H.

Chen, L.

Chen, M.

Chen, N.

Chen, Y.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(1), 709–716 (2007).
[Crossref]

Cheung, K. K. Y.

Chinn, S. R.

Chui, P. C.

Connolly, J.

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(1), 709–716 (2007).
[Crossref]

Dagel, D.

de Boer, J. F.

S. H. Yun, C. Boudoux, M. C. Pierce, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Technol. Lett. 16(1), 293–295 (2004).
[Crossref] [PubMed]

Don Lee, H.

Dong, X.

Duker, J. S.

Eibl, M.

Eigenwillig, C. M.

El-Haddad, M. T.

Feng, P.

Feng, X.

Fujimoto, J.

Fujimoto, J. G.

I. Grulkowski, J. J. Liu, B. Potsaid, V. Jayaraman, J. Jiang, J. G. Fujimoto, and A. E. Cable, “High-precision, high-accuracy ultralong-range swept-source optical coherence tomography using vertical cavity surface emitting laser light source,” Opt. Lett. 38(5), 673–675 (2013).
[Crossref] [PubMed]

I. Grulkowski, J. J. Liu, B. Potsaid, V. Jayaraman, C. D. Lu, J. Jiang, A. E. Cable, J. S. Duker, and J. G. Fujimoto, “Retinal, anterior segment and full eye imaging using ultrahigh speed swept source OCT with vertical-cavity surface emitting lasers,” Biomed. Opt. Express 3(11), 2733–2751 (2012).
[Crossref] [PubMed]

B. Potsaid, B. Baumann, D. Huang, S. Barry, A. E. Cable, J. S. Schuman, J. S. Duker, and J. G. Fujimoto, “Ultrahigh speed 1050nm swept source/Fourier domain OCT retinal and anterior segment imaging at 100,000 to 400,000 axial scans per second,” Opt. Express 18(19), 20029–20048 (2010).
[Crossref] [PubMed]

T.-H. Tsai, C. Zhou, D. C. Adler, and J. G. Fujimoto, “Frequency comb swept lasers,” Opt. Express 17(23), 21257–21270 (2009).
[Crossref] [PubMed]

L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, “High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy,” Opt. Express 15(23), 15115–15128 (2007).
[Crossref] [PubMed]

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(1), 709–716 (2007).
[Crossref]

R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14(8), 3225–3237 (2006).
[Crossref] [PubMed]

R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, and A. E. Cable, “Three-dimensional and C-mode OCT imaging with a compact, frequency swept laser source at 1300 nm,” Opt. Express 13(26), 10523–10538 (2005).
[Crossref] [PubMed]

B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+:forsterite laser,” Opt. Lett. 22(22), 1704–1706 (1997).
[Crossref] [PubMed]

S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. 22(5), 340–342 (1997).
[Crossref] [PubMed]

Goda, K.

Godbout, N.

Golubovic, B.

Gora, M.

Gora, M. J.

Grulkowski, I.

Guan, B. O.

Guo, Q.

Hakert, H.

Herold, R. E.

Hsu, K.

Huang, D.

Huang, S.-W.

B. Li, S.-W. Huang, Y. Li, C. W. Wong, and K. K. Y. Wong, “Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics,” Nat. Commun. 8(1), 61 (2017).
[Crossref] [PubMed]

Huber, R.

J. P. Kolb, T. Pfeiffer, M. Eibl, H. Hakert, and R. Huber, “High-resolution retinal swept source optical coherence tomography with an ultra-wideband Fourier-domain mode-locked laser at MHz A-scan rates,” Biomed. Opt. Express 9(1), 120–130 (2017).
[Crossref] [PubMed]

T. Klein, W. Wieser, L. Reznicek, A. Neubauer, A. Kampik, and R. Huber, “Multi-MHz retinal OCT,” Biomed. Opt. Express 4(10), 1890–1908 (2013).
[Crossref] [PubMed]

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T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
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X. Wei, J. Xu, Y. Xu, L. Yu, J. Xu, B. Li, A. K. S. Lau, X. Wang, C. Zhang, K. K. Tsia, and K. K. Y. Wong, “Breathing laser as an inertia-free swept source for high-quality ultrafast optical bioimaging,” Opt. Lett. 39(23), 6593–6596 (2014).
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B. Li, S.-W. Huang, Y. Li, C. W. Wong, and K. K. Y. Wong, “Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics,” Nat. Commun. 8(1), 61 (2017).
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S. Tan, L. Yang, X. Wei, C. Li, N. Chen, K. K. Tsia, and K. K. Y. Wong, “High-speed wavelength-swept source at 2.0 μm and its application in imaging through a scattering medium,” Opt. Lett. 42(8), 1540–1543 (2017).
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T. Yang, X. Wei, C. Kong, S. Tan, K. K. Tsia, and K. K. Y. Wong, “An Ultrafast Wideband Discretely Swept Fiber Laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 8800105 (2017).

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W. Y. Oh, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Wide tuning range wavelength-swept laser with two semiconductor optical amplifiers,” IEEE Photonics Technol. Lett. 17(3), 678–680 (2005).
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S. H. Yun, C. Boudoux, M. C. Pierce, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Technol. Lett. 16(1), 293–295 (2004).
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S. Tan, L. Yang, X. Wei, C. Li, N. Chen, K. K. Tsia, and K. K. Y. Wong, “High-speed wavelength-swept source at 2.0 μm and its application in imaging through a scattering medium,” Opt. Lett. 42(8), 1540–1543 (2017).
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J. Xu, X. Wei, L. Yu, C. Zhang, J. Xu, K. K. Y. Wong, and K. K. Tsia, “High-performance multi-megahertz optical coherence tomography based on amplified optical time-stretch,” Biomed. Opt. Express 6(4), 1340–1350 (2015).
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Ueno, M.

M. Ueno, Y. Okabe, S. Toyoda, T. Sakamoto, Y. Sasaki, J. Kobayashi, K. Naganuma, and S. Yagi, “Improvement of coherence length in a 200 kHz swept light source with a KTa1-xNbxO3 deflector using an etalon,” Appl. Phys. Express 6(12), 122501 (2013).
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B. Li, S.-W. Huang, Y. Li, C. W. Wong, and K. K. Y. Wong, “Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics,” Nat. Commun. 8(1), 61 (2017).
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J. Kang, P. Feng, X. Wei, E. Y. Lam, K. K. Tsia, and K. K. Y. Wong, “102-nm, 44.5-MHz inertial-free swept source by mode-locked fiber laser and time stretch technique for optical coherence tomography,” Opt. Express 26(4), 4370–4381 (2018).
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B. Li, S.-W. Huang, Y. Li, C. W. Wong, and K. K. Y. Wong, “Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics,” Nat. Commun. 8(1), 61 (2017).
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T. Yang, X. Wei, C. Kong, S. Tan, K. K. Tsia, and K. K. Y. Wong, “An Ultrafast Wideband Discretely Swept Fiber Laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 8800105 (2017).

S. Tan, L. Yang, X. Wei, C. Li, N. Chen, K. K. Tsia, and K. K. Y. Wong, “High-speed wavelength-swept source at 2.0 μm and its application in imaging through a scattering medium,” Opt. Lett. 42(8), 1540–1543 (2017).
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J. Xu, X. Wei, L. Yu, C. Zhang, J. Xu, K. K. Y. Wong, and K. K. Tsia, “High-performance multi-megahertz optical coherence tomography based on amplified optical time-stretch,” Biomed. Opt. Express 6(4), 1340–1350 (2015).
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X. Wei, A. K. Lau, Y. Xu, C. Zhang, A. Mussot, A. Kudlinski, K. K. Tsia, and K. K. Y. Wong, “Broadband fiber-optical parametric amplification for ultrafast time-stretch imaging at 1.0 μm,” Opt. Lett. 39(20), 5989–5992 (2014).
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C. Zhang, Y. Qiu, R. Zhu, K. K. Y. Wong, and K. K. Tsia, “Serial time-encoded amplified microscopy (STEAM) based on a stabilized picosecond supercontinuum source,” Opt. Express 19(17), 15810–15816 (2011).
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T. Yang, X. Wei, C. Kong, S. Tan, K. K. Tsia, and K. K. Y. Wong, “An Ultrafast Wideband Discretely Swept Fiber Laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 8800105 (2017).

Yu, L.

Yun, S.

Yun, S. H.

Zhang, C.

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Appl. Phys. Express (1)

M. Ueno, Y. Okabe, S. Toyoda, T. Sakamoto, Y. Sasaki, J. Kobayashi, K. Naganuma, and S. Yagi, “Improvement of coherence length in a 200 kHz swept light source with a KTa1-xNbxO3 deflector using an etalon,” Appl. Phys. Express 6(12), 122501 (2013).
[Crossref]

Biomed. Opt. Express (6)

J. Xu, X. Wei, L. Yu, C. Zhang, J. Xu, K. K. Y. Wong, and K. K. Tsia, “High-performance multi-megahertz optical coherence tomography based on amplified optical time-stretch,” Biomed. Opt. Express 6(4), 1340–1350 (2015).
[Crossref] [PubMed]

J. D. Malone, M. T. El-Haddad, I. Bozic, L. A. Tye, L. Majeau, N. Godbout, A. M. Rollins, C. Boudoux, K. M. Joos, S. N. Patel, and Y. K. Tao, “Simultaneous multimodal ophthalmic imaging using swept-source spectrally encoded scanning laser ophthalmoscopy and optical coherence tomography,” Biomed. Opt. Express 8(1), 193–206 (2016).
[Crossref] [PubMed]

S. C. Schlachter, D. Kang, M. J. Gora, P. Vacas-Jacques, T. Wu, R. W. Carruth, E. J. Wilsterman, B. E. Bouma, K. Woods, and G. J. Tearney, “Spectrally encoded confocal microscopy of esophageal tissues at 100 kHz line rate,” Biomed. Opt. Express 4(9), 1636–1645 (2013).
[Crossref] [PubMed]

T. Klein, W. Wieser, L. Reznicek, A. Neubauer, A. Kampik, and R. Huber, “Multi-MHz retinal OCT,” Biomed. Opt. Express 4(10), 1890–1908 (2013).
[Crossref] [PubMed]

J. P. Kolb, T. Pfeiffer, M. Eibl, H. Hakert, and R. Huber, “High-resolution retinal swept source optical coherence tomography with an ultra-wideband Fourier-domain mode-locked laser at MHz A-scan rates,” Biomed. Opt. Express 9(1), 120–130 (2017).
[Crossref] [PubMed]

I. Grulkowski, J. J. Liu, B. Potsaid, V. Jayaraman, C. D. Lu, J. Jiang, A. E. Cable, J. S. Duker, and J. G. Fujimoto, “Retinal, anterior segment and full eye imaging using ultrahigh speed swept source OCT with vertical-cavity surface emitting lasers,” Biomed. Opt. Express 3(11), 2733–2751 (2012).
[Crossref] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Yang, X. Wei, C. Kong, S. Tan, K. K. Tsia, and K. K. Y. Wong, “An Ultrafast Wideband Discretely Swept Fiber Laser,” IEEE J. Sel. Top. Quantum Electron. 24(3), 8800105 (2017).

IEEE Photonics Technol. Lett. (2)

S. H. Yun, C. Boudoux, M. C. Pierce, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Technol. Lett. 16(1), 293–295 (2004).
[Crossref] [PubMed]

W. Y. Oh, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Wide tuning range wavelength-swept laser with two semiconductor optical amplifiers,” IEEE Photonics Technol. Lett. 17(3), 678–680 (2005).
[Crossref] [PubMed]

Nat. Commun. (1)

B. Li, S.-W. Huang, Y. Li, C. W. Wong, and K. K. Y. Wong, “Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics,” Nat. Commun. 8(1), 61 (2017).
[Crossref] [PubMed]

Nat. Photonics (2)

M. Siddiqui, A. S. Nam, S. Tozburun, N. Lippok, C. Blatter, and B. J. Vakoc, “High-speed optical coherence tomography by circular interferometric ranging,” Nat. Photonics 12(2), 111–116 (2018).
[Crossref] [PubMed]

D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(1), 709–716 (2007).
[Crossref]

Nature (1)

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
[Crossref] [PubMed]

Opt. Express (25)

C. Zhang, Y. Qiu, R. Zhu, K. K. Y. Wong, and K. K. Tsia, “Serial time-encoded amplified microscopy (STEAM) based on a stabilized picosecond supercontinuum source,” Opt. Express 19(17), 15810–15816 (2011).
[Crossref] [PubMed]

J. Kang, P. Feng, X. Wei, E. Y. Lam, K. K. Tsia, and K. K. Y. Wong, “102-nm, 44.5-MHz inertial-free swept source by mode-locked fiber laser and time stretch technique for optical coherence tomography,” Opt. Express 26(4), 4370–4381 (2018).
[Crossref] [PubMed]

K. K. Tsia, K. Goda, D. Capewell, and B. Jalali, “Performance of serial time-encoded amplified microscope,” Opt. Express 18(10), 10016–10028 (2010).
[Crossref] [PubMed]

T.-H. Tsai, C. Zhou, D. C. Adler, and J. G. Fujimoto, “Frequency comb swept lasers,” Opt. Express 17(23), 21257–21270 (2009).
[Crossref] [PubMed]

M. Siddiqui and B. J. Vakoc, “Optical-domain subsampling for data efficient depth ranging in Fourier-domain optical coherence tomography,” Opt. Express 20(16), 17938–17951 (2012).
[Crossref] [PubMed]

S. Tozburun, M. Siddiqui, and B. J. Vakoc, “A rapid, dispersion-based wavelength-stepped and wavelength-swept laser for optical coherence tomography,” Opt. Express 22(3), 3414–3424 (2014).
[Crossref] [PubMed]

M. Wan, L. Wang, F. Li, Y. Cao, X. Wang, X. Feng, B. O. Guan, and P. K. A. Wai, “Rapid, k-space linear wavelength scanning laser source based on recirculating frequency shifter,” Opt. Express 24(24), 27614–27621 (2016).
[Crossref] [PubMed]

Q. Guo, H. Chen, Z. Weng, M. Chen, S. Yang, and S. Xie, “Compressive sensing based high-speed time-stretch optical microscopy for two-dimensional image acquisition,” Opt. Express 23(23), 29639–29646 (2015).
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Photon. Res. (1)

Other (1)

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Application, 2nd ed. (Springer, 2008).

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Figures (7)

Fig. 1
Fig. 1 (a) The principle of the proposed ultrafast swept source. (b) The frequency-to-time mapping relation of the FWM process. (c) Frequency versus time of the output swept source.
Fig. 2
Fig. 2 (a) Detailed experimental setup to demonstrate the proposed swept source. EDF: Erbium doped fiber, PC: polarization controller, PZT: piezoelectric ceramic transducer; PID: proportional-integral-differential controller; SG: signal generator. (b) Optical spectrum of the FWM process. (c) Optical spectrum of the swept source.
Fig. 3
Fig. 3 (a) Temporal waveform of the swept source at 10 kHz and (b) its zoom-in observations. (c-f) Temporal waveforms of the swept source at different swept rates.
Fig. 4
Fig. 4 (a) Static linewidth at different wavelength measured by OSA. (b) The PSFs measured by an interferometer.
Fig. 5
Fig. 5 (a) Interference signal (blue line) and its unwrapped phase (red line) at 12- mm OPLD. (b) Fringes at different child windows and (c) their normalized spectra.
Fig. 6
Fig. 6 The schematic diagram of the microscopy system utilizing the proposed swept source. A personal computer (PC) is used to implement low-pass filtering in the post-processing and reconstruct the image.
Fig. 7
Fig. 7 (a) Reference image captured by OSA. (b-f) Images created by the proposed swept source at different swept rates, with PSNR to evaluate the image quality. (g-h) The line scans of the element 6 in group 7.

Equations (4)

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E i E s ( t ) E p 2 ( t ) = a s ( t ) a p 2 ( t+Δt )exp( j2 ω p Δt )exp( j Δ t 2 Φ p )exp[ j( 1 Φ p 1 2 Φ s ) t 2 ]exp[ j( ω i + 2Δt Φ p )t ] = a i ( t )exp[ j( 1 Φ p 1 2 Φ s ) t 2 ]exp[ j( ω i + 2Δt Φ p )t ]
E i a i ( t )exp[ j( ω i + Δt Φ 0 )t ]
Δω= Δf Φ 0 f 2
δλ= 0.35 D f det

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