Xu, J; Wei, X; Yu, L; Zhang, C; Xu, J; Wong, KKY; Tsia, KKM. Citation Optics Express, 2014, v. 22 n. 19, p

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1 Title Performance of megahertz amlified otical time-tretch otical coherence tomograhy (AOT-OCT) Author() Xu, J; Wei, X; Yu, L; Zhang, C; Xu, J; Wong, KKY; Tia, KKM Citation Otic Exre, 014, v. n. 19, Iued Date 014 URL htt://hdl.handle.net/107/097 Right Otic Exre. Coyright Otical Society of America.

2 Performance of megahertz amlified otical time-tretch otical coherence tomograhy (AOT-OCT) Jingjiang Xu, Xiaoming Wei, Luoqin Yu, Chi Zhang, Jianbing Xu, K. K. Y. Wong, and Kevin K. Tia * Deartment of Electrical and Electronic Engineering, The Univerity of Hong Kong, Pokfulam Road, Hong Kong, China * tia@hku.hk Abtract: Enabled by the ultrahigh-eed all-otical wavelength-wet mechanim and broadband otical amlification, amlified otical timetretch otical coherence tomograhy (AOT-OCT) ha recently been demontrated a a ractical alternative to achieve ultrafat A-can rate of multi-mhz in OCT. With the aim of identifying the otimal cenario for MHz oeration in AOT-OCT, we here reent a theoretical framework to evaluate it erformance metric. In articular, the analyi dicue the unique feature of AOT-OCT, uch a it uerior coherence length, and the relationhi between the otical gain and the A-can rate. More imortantly, we evaluate the enitivity of AOT-OCT in the MHz regime under the influence of the amlifier noie. Notably, the model how that AOT-OCT i articularly romiing when oerated at the A-can rate well beyond multi-mhz not trivially achievable by any exiting wet-ource OCT latform. A enitivity beyond 90 db, cloe to the hot-noie limit, can be maintained in the range of 10 MHz with an otical net gain of ~10dB. Exerimental meaurement alo how excellent agreement with the theoretical rediction. While ditributed fiber Raman amlification i mainly conidered in thi aer, the theoretical model i generally alicable to any tye of amlification cheme. A a reult, our analyi erve a a ueful tool for further otimization of AOT-OCT ytem a a ractical alternative to enable MHz OCT oeration. 014 Otical Society of America OCIS code: ( ) Otical coherence tomograhy; ( ) Noie in imaging ytem; ( ) Interferometry. Reference and link 1. D. Huang, E. A. Swanon, C. P. Lin, J. S. Schuman, W. G. Stinon, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Otical Coherence Tomograhy, Science 54(5035), (1991).. H. C. Lee, J. J. Liu, Y. Sheikine, A. D. Aguirre, J. L. Connolly, and J. G. Fujimoto, Ultrahigh eed ectraldomain otical coherence microcoy, Biomed. Ot. Exre 4(8), (013). 3. L. An, P. Li, G. P. Lan, D. Malchow, and R. K. K. Wang, High-reolution 1050 nm ectral domain retinal otical coherence tomograhy at 10 khz A-can rate with 6.1 mm imaging deth, Biomed. Ot. Exre 4(), (013). 4. B. Potaid, I. Gorczynka, V. J. Srinivaan, Y. L. Chen, J. Jiang, A. Cable, and J. G. Fujimoto, Ultrahigh eed Sectral / Fourier domain OCT ohthalmic imaging at 70,000 to 31,500 axial can er econd, Ot. Exre 16(19), (008). 5. R. Wang, J. X. Yun, X. C. Yuan, R. Goodwin, R. R. Markwald, and B. Z. Gao, Megahertz treak-mode Fourier domain otical coherence tomograhy, J. Biomed. Ot. 16(6), (011). 6. D. Choi, H. Hiro-Oka, H. Furukawa, R. Yohimura, M. Nakanihi, K. Shimizu, and K. Ohbayahi, Fourier domain otical coherence tomograhy uing otical demultilexer imaging at 60,000,000 line/, Ot. Lett. 33(1), (008). 7. D. H. Choi, H. Hiro-Oka, K. Shimizu, and K. Ohbayahi, Sectral domain otical coherence tomograhy of multi-mhz A-can rate at 1310 nm range and real-time 4D-dilay u to 41 volume/econd, Biomed. Ot. Exre 3(1), (01). (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 498

3 8. W. Y. Oh, B. J. Vakoc, M. Shihkov, G. J. Tearney, and B. E. Bouma, > 400 khz reetition rate wavelengthwet laer and alication to high-eed otical frequency domain imaging, Ot. Lett. 35(17), (010). 9. R. Huber, M. Wojtkowki, and J. G. Fujimoto, Fourier Domain Mode Locking (FDML): A new laer oerating regime and alication for otical coherence tomograhy, Ot. Exre 14(8), (006). 10. B. Potaid, B. Baumann, D. Huang, S. Barry, A. E. Cable, J. S. Schuman, J. S. Duker, and J. G. Fujimoto, Ultrahigh eed 1050nm wet ource / Fourier domain OCT retinal and anterior egment imaging at 100,000 to 400,000 axial can er econd, Ot. Exre 18(19), (010). 11. T. H. Tai, B. Potaid, Y. K. Tao, V. Jayaraman, J. Jiang, P. J. S. Heim, M. F. Krau, C. Zhou, J. Hornegger, H. Mahimo, A. E. Cable, and J. G. Fujimoto, Ultrahigh eed endocoic otical coherence tomograhy uing micromotor imaging catheter and VCSEL technology, Biomed. Ot. Exre 4(7), (013). 1. I. Grulkowki, J. J. Liu, B. Potaid, V. Jayaraman, C. D. Lu, J. Jiang, A. E. Cable, J. S. Duker, and J. G. Fujimoto, Retinal, anterior egment and full eye imaging uing ultrahigh eed wet ource OCT with verticalcavity urface emitting laer, Biomed. Ot. Exre 3(11), (01). 13. W. Wieer, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, Multi-Megahertz OCT: High quality 3D imaging at 0 million A-can and 4.5 GVoxel er econd, Ot. Exre 18(14), (010). 14. T. Klein, W. Wieer, L. Reznicek, A. Neubauer, A. Kamik, and R. Huber, Multi-MHz retinal OCT, Biomed. Ot. Exre 4(10), (013). 15. S. Moon and D. Y. Kim, Ultra-high-eed otical coherence tomograhy with a tretched ule uercontinuum ource, Ot. Exre 14(4), (006). 16. K. Goda, D. R. Solli, and B. Jalali, Real-time otical reflectometry enabled by amlified dierive Fourier tranformation, Al. Phy. Lett. 93(3), (008). 17. K. Goda, A. Fard, O. Malik, G. Fu, A. Quach, and B. Jalali, High-throughut otical coherence tomograhy at 800 nm, Ot. Exre 0(18), (01). 18. T. J. Ahn, Y. Park, and J. Azana, Ultraraid Otical Frequency-Domain Reflectometry Baed Uon Dierion- Induced Time Stretching: Princile and Alication, IEEE J. Sel. To. Quantum Electron. 18(1), (01). 19. K. Goda, K. K. Tia, and B. Jalali, Serial time-encoded amlified imaging for real-time obervation of fat dynamic henomena, Nature 458(74), (009). 0. T. T. W. Wong, A. K. S. Lau, K. K. Y. Ho, M. Y. H. Tang, J. D. F. Roble, X. M. Wei, A. C. S. Chan, A. H. L. Tang, E. Y. Lam, K. K. Y. Wong, G. C. F. Chan, H. C. Shum, and K. K. Tia, Aymmetric-detection timetretch otical microcoy (ATOM) for ultrafat high-contrat cellular imaging in flow, Sci. Re. 4, 3656 (014). 1. H. W. Chen, C. Lei, F. J. Xing, Z. L. Weng, M. H. Chen, S. G. Yang, and S. Z. Xie, Multiwavelength timetretch imaging ytem, Ot. Lett. 39(7), 0 05 (014).. J. J. Xu, C. Zhang, J. B. Xu, K. K. Y. Wong, and K. K. Tia, Megahertz all-otical wet-ource otical coherence tomograhy baed on broadband amlified otical time-tretch, Ot. Lett. 39(3), 6 65 (014). 3. Y. Park, T. J. Ahn, J. C. Kieffer, and J. Azaña, Otical frequency domain reflectometry baed on real-time Fourier tranformation, Ot. Exre 15(8), (007). 4. S. Tozburun, M. Siddiqui, and B. J. Vakoc, A raid, dierion-baed wavelength-teed and wavelengthwet laer for otical coherence tomograhy, Ot. Exre (3), (014). 5. X. M. Wei, A. K. S. Lau, T. T. W. Wong, C. Zhang, K. K. M. Tia, and K. K. Y. Wong, Coherent Laer Source for High Frame-Rate Otical Time-Stretch Microcoy at 1.0 mu m, IEEE J. Sel. To. Quantum Electron. 0, 5 (014). 6. M. E. Marhic, Fiber Otical Parametric Amlifier, Ocillator and Related Device (Cambridge Univerity, 007). 7. G. P. Agrawal, Fiber-Otic Communication Sytem, 3rd ed. (Wiley, 00). 8. K. Goda, D. R. Solli, K. K. Tia, and B. Jalali, Theory of amlified dierive Fourier tranformation, Phy. Rev. A 80(4), (009). 9. K. K. Tia, K. Goda, D. Caewell, and B. Jalali, Performance of erial time-encoded amlified microcoe, Ot. Exre 18(10), (010). 30. B. R. Biedermann, W. Wieer, C. M. Eigenwillig, T. Klein, and R. Huber, Dierion, coherence and noie of Fourier domain mode locked laer, Ot. Exre 17(1), (009). 31. Z. L. Hu, Y. S. Pan, and A. M. Rollin, Analytical model of ectrometer-baed two-beam ectral interferometry, Al. Ot. 46(35), (007). 3. M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, Senitivity advantage of wet ource and Fourier domain otical coherence tomograhy, Ot. Exre 11(18), (003). 33. D. R. Solli, J. Chou, and B. Jalali, Amlified wavelength-time tranformation for real-time ectrocoy, Nat. Photonic (1), (008). 34. M. N. Ilam, Raman amlifier for telecommunication, IEEE J. Sel. To. Quantum Electron. 8(3), (00). 35. K. Goda, A. Mahjoubfar, and B. Jalali, Demontration of Raman gain at 800 nm in ingle-mode fiber and it otential alication to biological ening and imaging, Al. Phy. Lett. 95(5), (009). 36. A. Mahjoubfar, K. Goda, G. Bett, and B. Jalali, Otically amlified detection for biomedical ening and imaging, J. Ot. Soc. Am. A 30(10), (013). 37. C. Headley and G. Agrawal, Raman Amlification in Fiber Otical Communication Sytem (Academic Pre, 005). (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 499

4 38. H. Mauda, S. Kawai, and K. I. Suzuki, Otical SNR enhanced amlification in long-ditance recirculating-loo WDM tranmiion exeriment uing 1580 nm band hybrid amlifier, Electron. Lett. 35(5), (1999). 39. H. Mauda and S. Kawai, Wide-band and gain-flattened hybrid fiber amlifier coniting of an EDFA and a multiwavelength umed Raman amlifier, IEEE Photon. Technol. Lett. 11(6), (1999). 40. S. A. E. Lewi, S. V. Chernikov, and J. R. Taylor, Characterization of double Rayleigh catter noie in Raman amlifier, IEEE Photon. Technol. Lett. 1(5), (000). 41. American National Standard Intitute, American national tandard for afe ue of laer, ANSI Z (ANSI, 000). 1. Introduction Otical coherence tomograhy (OCT) ha roven to be a owerful noninvaive otical bioimaging modality becaue of it ability to offer label-free tiue tomograhic and functional aement in three-dimenional (3D) without relying on exciional bioy and hitoathology. It i found ueful in clinical alication including ohthalmology, dermatology and gatroenterology to name a few [1]. Thee alication, in articular for thoe involving image-guided bioy or urgery, very often demand for real-time 3D imaging, referably at the video rate. To enable a comlete volumetric OCT at uch imaging eed, it i a mandate to realize an A-can rate well beyond MHz an unreachable eed regime with the current commercial-grade OCT ytem, which tyically run at ~1 10 khz. An aorted of technological advancement have been demontrated for caling the A- can rate of OCT cloe to or even exceeding MHz. For intance, ectral domain OCT (SD- OCT) can now achieve the A-can rate u to 100 khz, beyond which i challenging becaue of the fundamental eed limitation of the line can camera (CCD or CMOS camera) [ 4]. It wa reorted that an effective A-can rate of MHz can be realized by caturing the SD- OCT ignal in a treak mode by a high-eed -dimenional CMOS camera and a ynchronized treak reonant-canning mirror [5]. It however require relatively high illumination ower and involve comlicated canning mirror ynchronization to enable the treak mode. SD-OCT uing an arrayed waveguide grating-tye otical demultilexer together with a hotodiode array (with hundred of ingle hotodiode) ha alo been demontrated to achieve more than 10 MHz A-can rate at the cot of coniderably comlex ytem configuration [6, 7]. On the other hand, wet-ource OCT (SS-OCT) ha been another attractive and ractical OCT modality enabling fat A-can rate. Over the at decade, the fundamental wet rate, i.e. A-can rate, ha to ignificantly boot to hundred of kilohertz by the ue of fat-rotating olygon canning filter [8] or Fourier-domain mode locked (FDML) laer [9, 10]. SS-OCT baed on vertical cavity urface emitting laer (VCSEL) [11, 1], or time-interleave of FDML ule together with multi-ot illumination [13, 14] can further uh the A-can rate u to the MHz regime. Neverthele, the high-eed wavelength-wet oeration in thee SS-OCT modalitie all rely on mechanical moving art (iezoelectric-driven Fabry-Pérot cavity, rotating-mirror, or microelectromechanical ytem (MEMS)). The erformance i thu inevitably ubject to long-term mechanical tability. An all-otical wet ource baed on otical time-tretch i a otential alternative a a robut inertia-free wavelength-wet mechanim enabling ultrahigh eed and long term SS- OCT oeration [15 18]. In otical time-tretch (alo known a dierive Fourier tranform) [19 ], a broadband ule i otically wavelength-wet (or time-tretched) by grou velocity dierion (GVD) in a dierive fiber (e.g. dierion comenated fiber (DCF), or chired fiber Bragg grating), with no mechanical wavelength-wet mechanim. The A-can rate i thu governed by the reetition rate of the laer ule train, which i tyically 10 MHz for mot of the broadband ule laer. However, otical time-tretch had not been widely acceted a an effective aroach for SS-OCT until now. It i rimarily becaue that reviou work on time-tretch-baed OCT had inufficient bandwidth (~10 nm) to rovide ractical axial reolution of OCT [16, 17, 3], and oor enitivity (< 40 db) [15]. Recently, we have demontrated a ractical time-tretch OCT modality, called amlified otical timetretch OCT (AOT-OCT) which achieve tiue bioimaging with a record high enitivity above 80 db at an A-can rate a high a 7.14 MHz []. The key attribute enabling uch (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 500

5 erformance i the imlementation of broadband otical amlification in-line with the timetretch roce. It comenate the intrinic otical lo, and even rovide net otical gain, in the dierive fiber and thu coniderably enhance the enitivity of OCT. We alo note that a recent work demontrated the otential of a high-eed wavelength-teed laer for MHz AOT [4]. It howed that uch novel laer deign baed on intracavity ule tretching and comreion uing ecialty GVD engineering can achieve a wet rate of 9 MHz. Further imrovement of the AOT-OCT erformance require in-deth undertanding of the role of key determining arameter in the ytem. The effect of the otical amlification and the aociated noie are in articular critically governing the enitivity of AOT-OCT. Yet, they have not been invetigated in detailed in the rior work. Therefore, in thi aer, we reent a general theoretical framework evaluating the erformance of AOT-OCT, with an aim of identifying the otimal cenario for MHz oeration in AOT-OCT. Secifically, we will dicu the unique feature of AOT-OCT, uch a it uerior coherence length, and the relationhi between the otical gain and the A-can rate. More imortantly, we will evaluate the enitivity of AOT-OCT in the MHz regime under the influence of the otical amlification noie. While the theoretical model reented in thi aer can be generically alicable to any tye of otical amlifier, we will articularly conider the ue of ditributed fiber Raman amlification (FRA) becaue of it unique advantage over other amlification cheme for otical time-tretch oeration. Our model reveal that the amlifier noie critically affect the enitivity of the AOT-OCT and ha to be carefully controlled in order to otimize the imaging quality. The exerimental meaurement how excellent agreement with the theoretical rediction. The model alo how that AOT-OCT i uniquely favorable for multi-mhz oeration in term of attaining ractical OCT enitivity for bioimaging alication (> 90dB). We anticiate that the reent tudy could rovide a comrehenive inight for deigning a robut AOT-OCT ytem a a ractical SS-OCT alternative running in the MHz regime.. Theoretical model of AOT-OCT Figure 1 how the general chematic of an AOT-OCT ytem baed on a Mach-Zehnder interferometer (MZI) with two couler, a circulator and a fiber delay line. The all-otical wet-ource emloyed in thi ytem i derived from a broadband uled laer which can be generated either by uercontinuum generation in a highly-nonlinear fiber [] or by the dierion-managed fiber mode-locking [5]. The broadband ectrum of the ule (with a bandwidth of few ten to hundred of nanometer) i then maed into the wavelength-wet temoral waveform in a dierive fiber via GVD. Thi i the roce called otical timetretch. To counteract the dierive lo in the fiber, the wavelength-wet waveform i otically amlified in order to enhance the OCT enitivity. In it generic form, the otical amlification cheme could be imlemented before, during and/or after the time-tretch roce. There i no trict requirement on the tye of amlifier adoted in the ytem. It include rare-earth-doed fiber amlifier (e.g. erbium-doed fiber amlifier (EDFA) for 1.5 μm oeration, or ytterbium-doed fiber amlifier (YDFA) for 1 μm oeration), emiconductor otical amlifier (SOA), fiber Raman amlifier (FRA), or fiber otical arametric amlifier (FOPA) [6]. It can alo be a multi-tage amlifier ytem baed on either the ame amlifier tye or the hybrid amlifier tye. It i known in the realm of telecommunication that the deign criteria of the amlification cheme in uch wet-ource cloely relate to it overall noie erformance [7] which ultimately influence the OCT enitivity (a dicued in the later ection). A a conequence of the AOT, a raidly wavelength-wet waveform with a reetition rate well above the megahertz regime (governed by the tyical uled laer ource) i generated a the light ource for AOT-OCT. In the AOT-OCT ytem, we utilize a fiber-baed MZI which conit of a fiber couler litting the wet-ource light into the reference arm and amle arm. The AOT-OCT interferogram are acquired by recombining the reference and amle arm ignal by another couler, and are then catured by a hotodetector. While balanced detection could further be (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 501

6 imroved the OCT enitivity, we here emloy a ingle hotodetector for the ake of imlicity in our AOT-OCT theoretical model. Fig. 1. Schematic of a generic AOT-OCT ytem..1 Intantaneou linewidth of AOT-OCT Similar to all the SS-OCT modalitie, the intantaneou linewidth of the AOT wet-ource determine the intrinic roll-off erformance of AOT-OCT. Given that the GVD i large enough (i.e. in the far-field regime of otical time-tretch [8]), uch intantaneou linewidth or equivalently the ectral reolution originate from the ambiguity in the wavelength-totime maing roce. It mean that not only one wavelength contribute to the temoral waveform at any one time oint. Such ectral reolution can be etimated by tationary hae aroximation (SPA) which i defined a [9]: δλspa = λ, (1) D c where λ i the center wavelength of the light ource, D = DcL i the total dierion of the dierive fiber (tyically in n/nm) with a length of L (in km) and a GVD coefficient of D c (in /km-nm), c i the eed of light in vacuum. Note that Eq. (1) doe not take into account the higher-order GVD coefficient which are eential for recalibrating the nonlinear wavelength-to-time maing. Neverthele, Eq. (1) rovide ufficiently good aroximation to etimate the achievable ectral reolution and thu the roll-off erformance. In AOT-OCT, the A-can rate i eentially equivalent to the reetition rate of the laer. It imoe the uer bound of the required total dierion D max, beyond which the conecutive wavelength-wet (time-tretched) waveform overla each other. Here we define D max when the 3 db bandwidth of the time-tretched waveform occuie 80% of the interval of the adjacent waveform. It mean that D max ha an invere relationhi with the A-can rate, 0.8 which i exreed a. Dmax = f AΔ λ, where f A i the A-can rate, Δ λ i the bandwidth of the light ource. Thu, the coherence length l c of AOT-OCT, which i another arameter quantifying the roll-off erformance, i given by (auming a Gauian ectral hae): ln l = λ c. π δλ () SPA Figure how the general trend of the ectral reolution and coherence length for different A-can rate, articularly in the megahertz regime. From Eq. (1)-(), it i clear that there i a trade-off between the A-can rate and the ectral reolution. It mean that caling the A-can rate comromie the coherence length in AOT-OCT. Neverthele, a coherence length a long a centimeter can be achieved at an A-can rate cloe to 10MHz. Such coherence length i ignificantly longer than that achieved in tyical SS-OCT which deend on the ectral reolution of the tunable filter [13, 30]; and SD-OCT which deend on the (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 50

7 ixel reolution of the image enor [31]. Therefore, the long coherence length achieved in AOT-OCT make it attractive for long deth-range imaging in the megahertz regime. In general, aart from the wavelength-to-time maing ambiguity (characterized by SPA-limited reolution, i.e. Eq. (1)), the ectral reolution of the AOT-OCT can alo be governed by another limiting factor, which i the temoral reolution (or equivalently the electrical bandwidth) of the hotodetector [8, 9]. In thi limiting regime, the ectral reolution i given by δλ det = 0.35 ( Dmax Be ). Conider the megahertz A-can rate (from 1 10 MHz), the required detection bandwidth Be hould be beyond 1 GHz (auming there are 000 amle oint), according to Nyquit amling criterion. The correonding ectral reolution imoed by the detection bandwidth i well below 40 m and i maller than the SPA-limited reolution for the A-can rate exceeding 1MHz. Therefore, the actual ectral reolution of a multi-mhz AOT-OCT ytem hould be rimarily governed by the SPAlimited reolution a long a the detection bandwidth i ufficiently wide (>1GHz). Fig.. Coherence length and ectral reolution a a function of A-can rate in AOT-OCT. The center wavelength i 160 nm and the otical bandwidth i 80 nm. The D max i determined by 0.8 / ( f Δ λ) in the unit of n/nm. A. Signal-to-noie (SNR) and enitivity of AOT-OCT The key feature of AOT-OCT i the ue of broadband otical amlification to overcome the otical lo in the dierive fiber and thu to enhance the enitivity in the ytem. Auming that the AOT roce can rovide a net otical ower gain of G to the inut ignal which ha the average ower of P in, the total ower inut to the OCT ytem i thu GP in. Uing a couler and a circulator to guide the light into the amle arm, the ower incident on the amle i CTGP 1 c in, where C1 i the ower couling ratio to the amle arm and Tc i the oneway tranmiion through circulator to the amle. Conider a mirror with a reflectivity of R i laced in the amle arm and the tranmiion of fiber delay line in reference arm i T d, the otical ower catured at the hotodetector from the reference arm and the amle arm are Pr = (1 C1)(1 C) TdGPin = TGP r in and P = CC 1 Tc RGP in = TGP in, reectively, where Tr = (1 C1)(1 C) Td and T = CC 1 Tc R are the ower tranmiion in the reference arm and the amle arm. C i the ower couling ratio of the couler before the hotodetector. A a reult, we can write the hotocurrent detected in the AOT-OCT ytem a: i = ρ[ TGP + TGP + GP TT co( kδ z)], (3) d r in in in r where ρ i the detector reonivity (in A/W), k i the otical wavenumber which will be maed into time-ace via GVD, thu ha a relationhi of k = k π( t t ) Dλ by (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 503

8 neglecting higher-order GVD coefficient ( k0, λ 0, t0 are the center wavenumber, center wavelength and the correonding time oition of the tretched ule), Δ z i the otical ath length difference between the two arm. The exreion of the AOT-OCT ignal i given by the interference term, i.e. the third term of Eq. (3): i = ρgpin TT r co( kδ z). (4) Following the conventional definition, the SNR of AOT-OCT i obtained by conidering the Fourier tranform of the interference ignal term and the noie variance. In thi way, the mean-quare eak ignal at the oition of Δ z after the Fourier tranform can be written a [3]: i ρ TT r GPin M = ( ), (5) where M i the number of amle oint auming higher-order dierion i negligible, i.e. the wavelength-wet waveform i evenly tretched. To evaluate the Fourier tranform of the noie variance, we aume that all noie ource have a white noie characteritic. The uncorrelated noie variance are added incoherently in the dicrete Fourier tranform ummation, giving rie σnoie = Mσnoie, where σ noie i given by σ = σ + σ + σ (6) noie Tt am h re, where Tt = Tr + T i the total tranmiion in the interferometer. The total noie variance include: (1) Shot noie σ h = eidcbewhich follow the Poion roce. Idc = ρ( Tr + T ) GPin i the mean hotodetector hotocurrent. e i elementary electric charge. B e i the electrical detection bandwidth; () Receiver noie σ = NEP B, where the NEP i noie-equivalent re ower (NEP) (in A / Hz ); (3) Amlifier noie σ am i evaluated deending uon different tye of amlification mechanim, which will be further dicued in the next ection. A a reult, the ignal-to-noie ratio (SNR) of an AOT-OCT ytem can be generically given by: ρ TT r ( GPin) M SNRAOTOCT = i / σ noie =. (7) Tt σ am + eρtgp t inbe + σ re The enitivity of AOT-OCT i defined a recirocal of the minimal amle reflectivity R,min, at which the SNR equal one, i.e. SAOTOCT = 1/ R,min. Similar to mot of the OCT ytem, it i tyical for R 1 that we can neglect the reflected ower from the amle arm for enitivity etimation. Thu, the total tranmiion can be imly exreed a Tt = Tr + T Tr. Baed on thi aroximation, the enitivity of AOT-OCT ytem can be exreed a: e S AOTOCT = T ρ TT ( GP ) M r,0 in rσ am + eρtgp r inbe + σ re, (8) where T = CC T i the tranmiion of amle arm with a amle reflection of R = 1.,0 1 c Note that the detection bandwidth B e hould be bounded by the Nyquit Shannon amling criterion, i.e. B = f. Here, f i the data amling rate which can be related to the A-can rate f A by f = MfA. e (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 504

9 .3 Noie analyi of AOT-OCT baed on fiber Raman amlification Otical amlification lay a deciive role in an AOT-OCT ytem articularly in term of enhancing it enitivity in the megahertz A-can regime. A it i mentioned earlier that a number of fiber amlification cheme can generally be adoted in AOT-OCT, e.g. EDFA, YDFA, SOA, FOPA and FRA. Among them, FRA, articularly ditributed FRA, oee everal key advantage over other amlification cheme for otical time-tretch oeration. They include: (i) the widely tunable Raman gain ectrum deending uon the available um wavelength; (ii) it naturally broadband gain ectrum allowed by the amorhou nature in otical gla fiber; (iii) the gain bandwidth can be further broadened by uing multiwavelength um laer. Note alo that broadband gain ectra can be realized uing incoherent um ource [33]; (iv) the noie figure of FRA i uerior to rare-earth doed fiber amlifier and SOA [34 36]. By chooing the roer um ource and dierive fiber, all thee FRA feature are favorable for high-quality AOT-OCT in a wide wavelength range, anning from 1μm to 1.5μm the common window of OCT-baed bioimaging alication. In thi ection, we will further invetigate how the noie in FRA influence the SNR and thu the enitivity erformance of AOT-OCT, baed on Eq. (8). To evaluate the enitivity of AOT-OCT baed on FRA, it i neceary to model the Raman gain and the relevant noie ource in FRA. Similar analyi for biomedical ening and imaging baed on FRA ha been dicued in [36]. For the ake of comletene, we here lay down the key conideration for AOT-OCT. Auming no um deletion and the ignalinduced cro-hae modulation (XPM), the Raman gain (otical intenity gain) along the dierive fiber i given by [37]: z Gz ( ) = ex gr I( zdz ) αz, (9) 0 where g R i the Raman gain coefficient in the dierive fiber, I ( z ) i the um intenity at the oition z in the dierive fiber. α i the linear roagation lo of the fiber (in km 1 ). Conider a dierive fiber with a length of L and the cae of bidirectional uming, we can obatin I ( z) = I f(0)ex( αz) + Ib(L)ex[ α( L z)], where I f (0) and Ib(L) are the inut um intenitie of the forward and backward um at the two fiber end, i.e. at z = 0 and z = L. Thee two inut intenitie can be exreed a: Pf (0) Pb ( L) I (0) = f, I ( ), b L π( d / ) = π( d / ) (10) where P f (0) and Pb ( L ) are the inut um ower in the forward and backward direction, reectively, and d i the mode field diameter of the um in the dierive fiber. There are everal factor that may influence the noie erformance for FRA. We will decribe all the noie ource in term of variance of hotocurrent generated by detector. The main noie ource (noie variance) of a ditributed FRA include [37]: (a) The variance of double Rayleigh backcattering (DRB) noie. Thi noie arie from a time-delayed crotalk with the amlified ignal light which i cattered backward and then forward in the fiber. Thi DRB noie can be exreed a: L L σ DRB DRB in = f [ ρg( L) P ], (11) where fdrb = r G ( z) G ( z')dz'dz 0 i the faction of the crotalk-to-ignal by DRB in z the fiber. r i the Rayleigh backcattering coefficient. (b) The variance of um-to-stoke relative intenity noie (RIN) tranfer which can be etimated a: (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 505

10 B e σ = [ ρglp ( ) ] RIN( f) df, (1) RIN in 0 where the comlete tranfer function of the um RIN to the Stoke RIN ( f ) can be found in [36]. (c) The variance of amlified ontaneou emiion (ASE) noie. The ectral denity of L the ASE in Raman amlifier i defined by SASE = nhυ grg( L) I( z) G( z) dz, where the inverion arameter n = { 1 ex h( υ υ )/( k T ) } 1 B f [37]. Here k B i the Boltzmann contant, h i Planck contant, T f i the temerature in the fiber. υ and υ are the otical frequencie of the ignal (Stoke) and um, reectively. There are two different beating noie ource related to ASE: One i the beating noie of ignal with ASE: The other one i the beating noie of ASE with itelf: σ σ ASE = 4 ρ GLPS ( ) in ASEBe. (13) Be = 4 ρ S B ( B ), (14) ASE ASE ASE e o where B o i the otical bandwidth of the hotodetector. The total noie of FRA i the ummation of the aforementioned noie ource: σ = σ + σ + σ + σ (15). am DRB RIN ASE ASE ASE Subtituting Eq. (15) into Eq. (7) or (8), we can evaluate the SNR or enitivity of AOT- OCT baed on FRA. Again, the amlifier noie term in Eq. (7) and (8) i a generic term decribing the noie mechanim of any tye or form of otical amlification cheme, including the hybrid configuration (i.e. a multitage amlification combining different tye of otical amlifier [, 38, 39]). Hence, by identifying the relevant noie ource of the emloyed otical amlification cheme, one can evaluate the correonding SNR and enitivity of the AOT-OCT baed on Eq. (7) and (8). 3. Reult and dicuion 3.1 The effect of couling ratio on the enitivity of AOT-OCT It i evident that the term T r and T,0 in Eq. (8) deend on couling ratio of the couler in the MZI. To exemlify the influence of the couling ratio on the AOT-OCT enitivity and SNR, we here aume that the two couler have the ame couling ratio, i.e. C 1 = C and evaluate the enitivity uch AOT-OCT ytem running at an A-can rate of 5 MHz baed on Eq. (8). Other ractical value of the arameter adoted in thi analyi are detailed in the cation of Fig. 3, which how the enitivity a a function of the couling ratio. We mainly invetigate three main amlification condition: (i) Net gain of G = 10 db without amlifier noie (i.e. σ am = 0 for an ideal amlifier); (ii) Net gain of G = 10 db with the amlifier noie from 30dB to 0dB of the inut ower (e.g. for 30dB amlifier noie, it mean 3 σam = (10 ρgpin ) ); (iii) No amlification, i.e. net gain G i relaced by dierive lo of 10 db in the fiber. In general, adjuting the couling ratio between 0 and 1 reult in order-of-magnitude variation in enitivity. In articular, a maximum enitivity a high a ~90dB can be achieved when the couling ration i ~0.9 in both cae (i) and (ii). More imortantly, the eential role of amlification i clearly illutrated in Fig. 3. Emloying amlification in AOT-OCT can eaily imrove the AOT-OCT enitivity by at leat 0 db. It i rimarily 0 (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 506

11 becaue of that otical amlification overcome the inherent dierive lo during the otical time-tretch roce within the long dierive fiber. 3. The effect of the FRA erformance on the enitivity of AOT-OCT In thi ection, we will invetigate how the noie erformance of FRA affect the enitivity and thu the SNR of the AOT-OCT, articularly in the ultrafat A-can regime, i.e. the A- can rate beyond MHz. The arameter value adoted in the analyi are lited in Table 1. In articular, we choe the couling ratio C 1 = C = 0.9 a they give high enitivity baed on the analyi decribed in Section 3.1. Fig. 3. AOT-OCT Senitivity (A-can rate of 5MHz) a a function of the MZI couling ratio. The inut ower i 0.5mW. The electrical bandwidth of the detector i 5 GHz with a reonivity of ρ = 1 A / W and a noie-equivalent ower of NEP = A / Hz. The delay line tranmiion T = 0.8, the circulator tranmiion T = 0.85,and the number of amling d c oint M = 000. Table 1. Parameter Value for Senitivity Evaluation of AOT-OCT Baed on FRA Parameter Value Parameter Value Detector reonivity ρ = 1 A / W Grou velocity at 8 v = m/ Stoke wavelength Elementary charge 19 e = C Grou velocity at 8 v = m / um wavelength Noie-equivalent GVD ower NEP = A / Hz D = 100( / nm) / km c Delay line T = 0.8 Mode field d = 6.01μm d tranmiion diameter at Stoke wavelength Circulator T = 0.85 Mode field d = 5.84μm c tranmiion diameter at um wavelength Number of M = 000 Forward um f 13 1 RIN = 10 Hz amling oint RIN Planck contant 34 h = J Backward um b 13 1 RIN = 10 Hz RIN Boltzmann contant 3 Temerature of k = J / K T B f Raman gain = 93K medium (fiber) Fiber attenuation at 4 1 Rayleigh α um wavelength = m r = km backcattering coefficient Fiber attenuation at 4 1 Otical bandwidth α Stoke wavelength = m B = 9.145THz o Stoke wavelength λ = 160nm Couling ratio C1 = C = 0.9 Pum wavelength λ = 150nm 5 1 (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 507

12 Figure 4 how how the AOT-OCT enitivity generally cale with the inut ignal ower. In the FPA cheme, we incororate both the forward and backward um with the equal ower ( P f (0) = Pb ( L ) = 40 mw) uch that the net otical gain of G = 10 db i achieved in a 0-km long dierive fiber (with D c = 100 /nm/km, ee Table 1). For mall inut ignal (below 0 dbm), FRA can rovide the enitivity enhancement a high a ~45 db, comared to the time-tretch oeration without FRA clearly demontrating the ivotal role of otical amlification in AOT-OCT. The enitivity of AOT-OCT i however aturated (at ~95 db) at high inut ower. It i mainly becaue that the otical gain i counteracted by the rogreively tronger DRB and RIN in FRA when the inut ignal ower i high [36]. Note that at the inut ower of ~0 dbm, the ytem aroache to hot-noie limited oeration with a enitivity a high a ~95dB. Here the hot-noie limited oeration (i.e. the red curve in Fig. 4) i defined a SAOTOCT, hot = ρt,0gpin efa. Fig. 4. AOT-OCT enitivity a a function of inut ignal ower. We conider the AOT-OCT ytem oerating at 5 MHz A-can rate uing a hotodetector with a bandwidth of 5 GHz. In thi otical amlification cheme baed on FRA, we incororate both the forward and backward um with the equal ower of 40 mw uch that the net otical gain of G = 10 db i achieved in a 0-km long dierive fiber (with D c = 100 /nm/km, ee Table 1). We next invetigate how the enitivity i affected by FRA gain a well a the A-can rate. It i now traightforward to exect, on one hand, higher otical gain lead to imroved enitivity. On the other hand, fater A-can rate generally cale down the enitivity becaue of lo of collected light ignal in a horter A-can time window. Notwithtanding thee two general trend, there i ubtle relationhi between the required A-can rate and the given FRA gain in AOT-OCT a unique feature abent in all other tyical wet-ource OCT modalitie and could influence the enitivity erformance, which i hown in Fig. 5. In the earlier ection, we define the duty cycle of the wet-ource to be 80% (with a timetretch bandwidth of 80 nm) for ractical AOT-OCT oeration regardle the A-can rate. It imlie that for a given GVD of the dierive fiber, the fiber length ha to be adjuted to enure the 80% duty-cycle of the time-tretched ule (or wavelength-wet waveform) at a certain A-can rate. Varying the fiber length however alo require the change in FRA um ower if the net gain i meant to be fixed acro different A-can rate. The contour lot in Fig. 5(a) how the required total FRA um ower a a function of the net FRA gain a well a the A-can rate in the MHz regime. A exected, generally le um ower i required for the horter fiber length, and thu higher A-can rate for a given net gain. A decribed in Section.3, variation in um ower of FRA directly tranlate to that in the amlifier noie (ee Eq. (11)-(14)), and thu the overall enitivity of AOT-OCT. Baed on the enitivity analyi decribed in Section (i.e. Eq. (8)), a contour lot of AOT-OCT enitivity a a function of net gain and A-can rate can be obtained (Fig. 5(b)), imilar to Fig. (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 508

13 5(a). From the lot, a enitivity of more than 90 db with the net gain of 10 15dB can be achieved at the A-can rate of -10 MHz. Notably, it i referable and ractical to oerate AOT-OCT beyond MHz a it require le um ower (le than 30 dbm total um ower) to achieve the ame 10 15dB gain (ee Fig. 5(a)). It make AOT-OCT uniquely uitable for ractical MHz OCT not trivially achievable by any exiting SS-OCT latform. Fig. 5. (a) Required total um ower for FRA and (b) the correonding AOT-OCT enitivity a a function of net otical gain and the A-can rate. The inut ignal ower i P in = 0.5 mw. Other key arameter adoted in thi analyi are ecified in Table 1. In (b), the horizontal dahed line indicate the AOT-OCT enitivity a a function of A-can rate at a fixed net (FRA) gain of 10 db (further elaborated in Fig. 6). On the other hand, the vertical dahed line indicate the AOT-OCT enitivity a a function of net (FRA) gain at a fixed A- can rate of 5 MHz (further elaborated in Fig. 7). The advantage of oerating AOT-OCT well above the MHz regime can be further areciated in Fig. 6 which how the cae of contant net gain of 10 db (i.e. the horizontal dahed line indicated in Fig. 5(b)). For the A-can rate of le than 1 MHz, the required dierive fiber length for the AOT roce ha to be hundred of kilometer, which demand for very high um ower >> 30 dbm, and thu introduce ignificant amlifier noie (articularly due to DRB noie [37]). Hence, the enitivity dro ignificantly below 1 MHz. Oerating at 10 MHz, AOT-OCT can achieve cloe-to-hot-noie-limited regime and maintain the enitivity a high a > 90 db ractical for mot clinical and reearch-grade in vivo imaging [14]. Without the FRA imlementation (green curve in Fig. 6), the ower of outut light i too weak becaue of the dierive fiber lo. It thu reult in a oor enitivity, more than 30 db wore than AOT-OCT. We note that the AOT-OCT enitivity can be further imroved and aroach cloer to the hot-noie limit by contructing iolated multitage FRA to ure the DRB [40]. Such multitage and multile-um (more than ) FRA configuration i not aumed in our model for imlicity. (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 509

14 Fig. 6. AOT-OCT enitivity (blue) a a function the A-can rate at a fixed net (FRA) gain of 10 db. It i alo comared to the cae of hot-noie limited AOT-OCT oeration (red) a well a the cae of AOT-OCT without otical amlification (green). Other key arameter adoted in thi analyi are ecified in Table 1. Fig. 7. (a) Senitivity and (b) the correonding noie comonent at the hotodetector a a function the net FRA gain at a fixed A-can rate of 5 MHz. Other key arameter adoted in thi analyi are ecified in Table 1. To tudy the enitivity deendence on the net FRA gain, we focu on the cae of 5 MHz A-can rate a hown in Fig. 7 (i.e. the vertical dahed line in Fig. 5(b)). In the range of mall FRA gain, the receiver noie i the dominant factor (ee Fig. 7(b)) determining the enitivity of AOT-OCT which i coniderably below the hot-noie limited enitivity. A the FRA gain increae, the enitivity i enhanced and aroache to the hot-noie limit (red curve in Fig. 7(a)). Once again, imlementation of amlification in AOT-OCT i crucial a it enhance the ignal level and thu the enitivity. However, the DRB noie take over to be the limiting factor of the enitivity a the FRA gain continue to increae beyond 10 db (ee Fig. 7(b)). Other factor uch a gain aturation and um deletion will alo become non-negligible in the high FRA gain regime. Thee effect exlain why the enitivity dro when the FRA cale beyond db (ee the blue curve in Fig. 7(a)). Neverthele, the critical role of amlification in AOT-OCT i well exemlified in Fig. 7(a) that the enitivity can only be < 60 db without the ue of FRA. Thi clearly exlain why the rior work on time-tretch-baed OCT without amlification cheme wa unable to erform in vivo biological imaging (e.g [15].). We alo note that the illumination ower on the amle hould be limited within the afety tandard, uch a ANSI [41]. Auming continuou illumination, the incident ower (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 510

15 level onto the kin in the multi-mhz AOT-OCT hould be ket below 10 mw [41]. Therefore, the net otical gain for an inut ower of 0.5 mw in our AOT-OCT ytem hould not exceed 14 db. Within thi afety limit, the otical gain enable the enitivity a high a 90 db enitivity at the A-can rate of 5 MHz (ee Fig. 7(a)). 3.3 Exerimental enitivity meaurement of AOT-OCT We here exerimentally meaure the enitivity of an AOT-OCT ytem to verify the reent theoretical model, a hown in Fig. 8. The light ource i a femtoecond mode-lock fiber laer centered at 1560 nm with a bandwidth of ~50 nm and a reetition rate of 11 MHz. In thi cae, we have 1.5 mw inut ignal ower for time-tretch in a DCF with the length of 10.6 km. And the Rayleigh backcattering coefficient of the DCF for the bandwidth near 1560 nm i about 10 4 km 1. We ue the 50/50 couler to lit and recombine the beam in the MZI configuration (Fig. 1). The electrical bandwidth of our hotodetector i 15 GHz with 30 A / Hz NEP. We ut a mirror in the amle arm and meaure the SNR by calculating the ratio between the eak of the oint read function (PSF) amlitude and the noie floor in db cale (i.e 0 time the logarithmic cale of thi ratio). Here, we imlement the fiber otical amlification by launching a ingle um laer for FRA into the DCF in the forward direction. A the FRA gain increae, the otical ower from the reference and amle arm for detection may exceed the uer limit of the hotodetector dynamic range. To revent ower aturation or hotodetector damage, we kee the ower reflected from the amle arm a low a 0.5 μ W by tilting the angle of the amle mirror and introduce an additional lo of 16 db in the reference arm. Excet the arameter decribed in thi ection, all other exerimental arameter can be found in the Table 1. Baed on the ingle-um configuration, the model give the very agreement with calculated enitivity baed on the exerimental meaurement a hown in Fig. 8(a). In articular, the theoretical model redict well the degradation in enitivity when the gain exceed ~16 db. It i mainly due to that the DBR noie become increaingly dominant and imair the imrovement of enitivity in the reent AOT-OCT ytem. The enitivity imrovement i alo exerimentally verified by the AOT-OCT image hown in Fig. 8(b) and 8(c) when the gain i increaed u to 15dB. However, the AOT-OCT image become noiier when the gain cale u to 19 db (Fig. 8(d)), conitent with the dro in enitivity hown in Fig. 8(a). Fig. 8. (a) Meaured and theoretical enitivity in AOT-OCT ytem baed on FRA. The olid red line i obtained by the theoretical model wherea the olid black circle are the calculated enitivity baed on exerimental meaurement in AOT-OCT ytem. The error bar rereent a tandard-deviation of the meaured enitivity in 0 reeated meaurement. (b-d) AOT-OCT cro-ectional image of kiwifruit taken with a net FRA gain of 7dB, 15dB and 19 db, reectively. (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 511

16 4. Concluding remark We have reented a theoretical model to evaluate the erformance of an AOT-OCT ytem, articularly in the multi-mhz A-can rate regime. A an all-otical SS-OCT modality, AOT- OCT can achieve a coherence length a long a ~10 mm even the A-can rate i increaed u to ~10 MHz. Uing the MZI configuration, the enitivity can be otimized by chooing the roer litting ratio of the couler. More imortantly, the enitivity i critically determined by the otical amlifier gain a well a the aociated amlifier noie ource. Clearly the theoretical model reveal the eential role of amlification for enhancing the enitivity. In addition, we have dicued a unique feature abent in all other tyical SS-OCT modalitie and could influence the enitivity erformance, i.e. the ubtle relationhi between required A-can rate and the given FRA gain in AOT-OCT. Proer FRA gain and the length of the dierive fiber ha to be carefully taken into account for enitivity otimization, a revealed in Fig. 5. Notably, the model alo how that AOT-OCT i articularly romiing when oerated at the A-can rate well beyond multi-mhz not trivially achievable by any exiting SS-OCT latform. A enitivity beyond 90 db, cloe to the hot-noie limit, can be maintained in the range of 10 MHz with an otical net gain of ~10dB. The theoretical model ha alo been validated by the exerimental meaurement, which howed excellent agreement in enitivity with the model. Although only FRA i conidered a the amlification cheme in the aer, the theoretical model can alo be alicable to any tye of otical amlifier, uch a EDFA, YDFA, SOA, FOPA. It can alo be extended to the hybrid amlifier configuration (i.e. a multitage amlification combining different tye of otical amlifier [, 38, 39]). A a reult, the analyi dicued here i exected to erve a a ueful tool for further otimization of AOT-OCT ytem a a ractical alternative to enable MHz OCT oeration. Acknowledgment Thi work wa artially uorted by grant from the Reearch Grant Council of the Hong Kong SAR, China (Project No. HKU 717/1E, E, E, 7011E) and Univerity Develoment Fund of HKU. (C) 014 OSA Setember 014 Vol., No. 19 DOI: /OE OPTICS EXPRESS 51