All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis

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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 11, NO. 4, JULY/AUGUST 2005 799 All-Fiber Common-Path Optical Coherence Tomography: Sensitivity Optimization and System Analysis Utkarsh Sharma, Student Member, IEEE, Nathaniel M. Fried, and Jin U. Kang Abstract—A fully integrated all-fiber implementation of common-path interferometer-based optical coherence tomography (OCT) has been successfully demonstrated. Unlike conventional Michelson-based OCT systems, there is no separate reference arm as the reference signal is derived from the probe-end back reflec- tion. This leads to “downlead insensitivity,” which makes the device more compatible with existing endoscopic medical instruments. We also theoretically analyze the optimization of system sensitivity in balanced and unbalanced detection. We have conducted experi- ments to confirm some of our signal-to-noise ratio (SNR) analysis, which are in excellent agreement with the theory. Interestingly, our analysis predicts existence of much higher beat noise in common- path OCT as compared with the conventional OCT. We predict a maximum upper limit of only 6-dB improvement in the SNR when the balanced detection is used, as compared with the unbalanced detection. Index Terms—Medical and biological imaging, medical optics instrumentation, noise in imaging systems, optical coherence to- mography (OCT). I. INTRODUCTION O PTICAL coherence tomography (OCT) is an emerging noninvasive optical imaging technique that can be used to perform high-resolution cross-sectional in vivo and in situ imaging of microstructure in transparent and nontransparent biological tissues [1]–[4]. Resolutions as high as 1 to 5 µm have been achieved using conventional bulk optic bench-top sys- tems in tandem with broadband light sources [5], [6]. Contrast- enhancing functional extensions such as polarization-sensitive, Doppler, and spectroscopic OCT have also been more recently introduced [7]–[10]. However, despite the unparalleled resolu- tion that OCT offers, and the numerous breakthroughs made in the research frontier since the mid-1990s, several technical problems need to be overcome before OCT can be accepted among the established diagnostic imaging modalities. Although clinical applications of OCT have been success- fully demonstrated in various medical fields, the ability to use the same technology for commercial and widespread clinical applications is limited because of the prohibitive cost, cum- Manuscript received December 16, 2004 and December 17, 2004; revised April 25, 2005 and July 16, 2005. The work of U. Sharma and J. U. Kang was supported by NASA under Grant NNG04GE39G. The work of N. Fried was supported by a faculty start-up grant awarded by the Johns Hopkins University School of Medicine. U. Sharma and J. U. Kang are with the Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD 21218 USA (e-mail: [email protected]; [email protected]). N. M. Fried is with the Department of Urology, Johns Hopkins School of Medicine, Baltimore, MD 21224 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/JSTQE.2005.857380 bersome instrumentation, and technical issues that need to be overcome to make it compatible with existing medical instru- ments. One of the most important technical issues is the design of a robust and low-cost interferometric scanning system with scanning speeds capable of real-time imaging. In this study, we show some preliminary results of a novel, low-maintenance, low-cost, lightweight, and compact OCT system using an all single-mode fiber (SMF) common-path interferometer-based scanning system (Optiphase, Van Nuys, CA). The all SMF- based interferometer can provide a resolution comparable to bulk optics systems [11], and it could serve as a new technology to realize low-cost and reproducible OCT instrumentation for commercial applications [12]. Although OCT systems based on all-fiber interferometer us- ing piezoelectric fiber stretchers have been demonstrated and incorporated in endoscopic OCT (EOCT) devices, there are sev- eral technical issues that limit their application [13]. Expensive polarization-maintaining fibers (PMFs) with precisely matched lengths have to be used in the extended flexible sample arm to avoid “downlead sensitivity” (polarization fadings caused by polarization distortions due to bending of the endoscope arm). Also, the birefringence modulation caused by the modulation process broadens the coherence response and affects system sen- sitivity unless an all-PMF assembly is used. In a conventional OCT setup, it is also important to compensate for dispersion and polarization mismatch between the reference and the sam- ple arms that are not due to the sample [14]. However, in our all SMF common-path interferometer-based design, we circum- vent these problems because sample and reference arms share the same common path. There is no separate arm for reference signal because the reference is derived from the partial back re- flection at the end surface of the probe arm. Hence, the freedom to use any arbitrary length of the probe arm can provide more flexibility in making OCT technology compatible with existing medical instrumentation (e.g., for use in endoscopic OCT). A common-path interferometer has been previously demon- strated for frequency-domain OCT; however, compared with time-domain OCT, it is more sensitive to vibrations, and there is considerable technical effort needed to achieve high reso- lution [15]. The common-path interferometer-based approach for time-domain OCT has also been demonstrated with limited success using a free-space interferometer [16], [17]. However, free-space scanning mirror interferometers face shortcomings such as relatively slower scanning speeds, alignment issues, and vulnerability to environmental vibrations. Hence, we propose and demonstrate an all-fiber Autocorrelator-based design for 1077-260X/$20.00 © 2005 IEEE

Transcript of All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis

Page 1: All-fiber common-path optical coherence tomography: sensitivity optimization and system analysis

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 11, NO. 4, JULY/AUGUST 2005 799

All-Fiber Common-Path Optical CoherenceTomography: Sensitivity Optimization

and System AnalysisUtkarsh Sharma, Student Member, IEEE, Nathaniel M. Fried, and Jin U. Kang

Abstract—A fully integrated all-fiber implementation ofcommon-path interferometer-based optical coherence tomography(OCT) has been successfully demonstrated. Unlike conventionalMichelson-based OCT systems, there is no separate reference armas the reference signal is derived from the probe-end back reflec-tion. This leads to “downlead insensitivity,” which makes the devicemore compatible with existing endoscopic medical instruments. Wealso theoretically analyze the optimization of system sensitivity inbalanced and unbalanced detection. We have conducted experi-ments to confirm some of our signal-to-noise ratio (SNR) analysis,which are in excellent agreement with the theory. Interestingly, ouranalysis predicts existence of much higher beat noise in common-path OCT as compared with the conventional OCT. We predict amaximum upper limit of only 6-dB improvement in the SNR whenthe balanced detection is used, as compared with the unbalanceddetection.

Index Terms—Medical and biological imaging, medical opticsinstrumentation, noise in imaging systems, optical coherence to-mography (OCT).

I. INTRODUCTION

O PTICAL coherence tomography (OCT) is an emergingnoninvasive optical imaging technique that can be used

to perform high-resolution cross-sectional in vivo and in situimaging of microstructure in transparent and nontransparentbiological tissues [1]–[4]. Resolutions as high as 1 to 5 µmhave been achieved using conventional bulk optic bench-top sys-tems in tandem with broadband light sources [5], [6]. Contrast-enhancing functional extensions such as polarization-sensitive,Doppler, and spectroscopic OCT have also been more recentlyintroduced [7]–[10]. However, despite the unparalleled resolu-tion that OCT offers, and the numerous breakthroughs madein the research frontier since the mid-1990s, several technicalproblems need to be overcome before OCT can be acceptedamong the established diagnostic imaging modalities.

Although clinical applications of OCT have been success-fully demonstrated in various medical fields, the ability to usethe same technology for commercial and widespread clinicalapplications is limited because of the prohibitive cost, cum-

Manuscript received December 16, 2004 and December 17, 2004; revisedApril 25, 2005 and July 16, 2005. The work of U. Sharma and J. U. Kang wassupported by NASA under Grant NNG04GE39G. The work of N. Fried wassupported by a faculty start-up grant awarded by the Johns Hopkins UniversitySchool of Medicine.

U. Sharma and J. U. Kang are with the Department of Electrical and ComputerEngineering, Johns Hopkins University, Baltimore, MD 21218 USA (e-mail:[email protected]; [email protected]).

N. M. Fried is with the Department of Urology, Johns Hopkins School ofMedicine, Baltimore, MD 21224 USA (e-mail: [email protected]).

Digital Object Identifier 10.1109/JSTQE.2005.857380

bersome instrumentation, and technical issues that need to beovercome to make it compatible with existing medical instru-ments. One of the most important technical issues is the designof a robust and low-cost interferometric scanning system withscanning speeds capable of real-time imaging. In this study, weshow some preliminary results of a novel, low-maintenance,low-cost, lightweight, and compact OCT system using an allsingle-mode fiber (SMF) common-path interferometer-basedscanning system (Optiphase, Van Nuys, CA). The all SMF-based interferometer can provide a resolution comparable tobulk optics systems [11], and it could serve as a new technologyto realize low-cost and reproducible OCT instrumentation forcommercial applications [12].

Although OCT systems based on all-fiber interferometer us-ing piezoelectric fiber stretchers have been demonstrated andincorporated in endoscopic OCT (EOCT) devices, there are sev-eral technical issues that limit their application [13]. Expensivepolarization-maintaining fibers (PMFs) with precisely matchedlengths have to be used in the extended flexible sample armto avoid “downlead sensitivity” (polarization fadings caused bypolarization distortions due to bending of the endoscope arm).Also, the birefringence modulation caused by the modulationprocess broadens the coherence response and affects system sen-sitivity unless an all-PMF assembly is used. In a conventionalOCT setup, it is also important to compensate for dispersionand polarization mismatch between the reference and the sam-ple arms that are not due to the sample [14]. However, in ourall SMF common-path interferometer-based design, we circum-vent these problems because sample and reference arms sharethe same common path. There is no separate arm for referencesignal because the reference is derived from the partial back re-flection at the end surface of the probe arm. Hence, the freedomto use any arbitrary length of the probe arm can provide moreflexibility in making OCT technology compatible with existingmedical instrumentation (e.g., for use in endoscopic OCT).

A common-path interferometer has been previously demon-strated for frequency-domain OCT; however, compared withtime-domain OCT, it is more sensitive to vibrations, and thereis considerable technical effort needed to achieve high reso-lution [15]. The common-path interferometer-based approachfor time-domain OCT has also been demonstrated with limitedsuccess using a free-space interferometer [16], [17]. However,free-space scanning mirror interferometers face shortcomingssuch as relatively slower scanning speeds, alignment issues, andvulnerability to environmental vibrations. Hence, we proposeand demonstrate an all-fiber Autocorrelator-based design for

1077-260X/$20.00 © 2005 IEEE

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OCT, offering a simple, compact, and low-cost approachwithout any significant compromises on performance.

Common-path-based OCT systems can have suboptimal sen-sitivity due to the fixed reference reflectivity; hence, it is not pos-sible to tune the reference power to optimize sensitivity. How-ever, the probe end (or fiber tip) can be appropriately coated withspecified reflectivity coating to optimize sensitivity. Referencereflectivity, a thorough signal-to-noise ratio (SNR) analysis as afunction of parameters like source power, is of primary impor-tance for sensitivity optimization in unbalanced and balanceddetection operations in common-path OCT. Previous SNR anal-ysis by Tatam et al. failed to identify the existence of unusuallyhigh beat noise in common-path OCT (as compared with con-ventional OCT) [16]. Hence, the SNR boost provided by thebalanced detection in common-path OCT would be rather lim-ited according to our analysis.

II. THEORY: INTERFEROMETER DESIGN

The design of the common-path interferometer-based OCTsystem is shown in Fig. 1. As can be seen from the design,no separate arm for reference is required in the common-path-based OCT system, and this unique configuration provides theadvantage of using any arbitrary length of detachable probe arm.The option to have detachable low-cost probes could simplifythe instrumentation of EOCT and could also be very useful incases where probes might need to be disposable to meet healthsafety standards.

In our proposed common-path interferometer-based approach(Fig. 1), the light from the broadband source enters the circulatorat port 1, exits at port 2 to the sample arm, and is delivered tothe sample through a suitably designed probe (e.g., a GRINlens probe described later in the paper). A small fraction ofthe light is reflected back from the end surface of the probe(Fresnel reflection due to the glass-air interface) and acts as areference signal. The remaining light is focused on the sample,and backscattered light from the sample is then collected viathe same probe. The combined optical signal (consisting ofreference and sample signal) returns via the sample arm, backto port 2 of the circulator, and can be written as

ETot(t) = Er (t) + Es(t + τs) (1)

where τs is the time delay between probe end and the samplesurface, Er is the reference electric field signal, and Es is theelectric field signal returning from the sample.

The input optical signal at port 2 of the circulator exits atport 3 and is routed to a self-contained, path-balanced scanning

Fig. 1. Common-path interferometer-based OCT system with the aboveconfiguration was used in tandem with a translational stage to obtain two-dimensional cross-sectional OCT images. SLD is the broadband light source,C1 is the circulator, D1 is the detector, and L1 and L2 are the path lengths ofthe two arms of the scanning interferometer.

Michelson interferometer. The sweeping interferometer acts toautocorrelate the combined optical signal (henceforth, we referto this sweeping interferometer as an autocorrelator). The time-averaged photocurrent measured at the detector is proportionalto the autocorrelation function of the combined optical signal(1) and is given by (2) (shown at the bottom of the page),where T is the integration time of the detector, η is the detectorquantum efficiency, e is the electronic charge, hυ is photonenergy, η0 is the intrinsic impedance of free space, and τ isthe delay caused by the sweeping action of piezoelectric fiberstretchers in the interferometer. Based on the assumption that|Er | |Es | (due to extremely low levels of backscattered lightin tissue as compared with the level of the reference signal), theac component of the current will be proportional to

〈Iac(τ)〉 ∝ Re 〈Er1(t)E∗r2(t + τ)〉

2

+Re 〈Er2(t)E∗

s1(t + τ + τs)〉2

+Re 〈Es2(t + τs)E∗

r1(t + τ)〉2

. (3)

The first term on the right side in (3) corresponds to the cen-tral autocorrelation peak [peak 2 in Fig. 2(a)]. The second andthird terms in (3) give identical measurements of the samplesignal on either side of the central autocorrelation peak [peaks

〈I(τ)〉 =1T

∫ T

0

ηe

2hυ

1η0

[(ETot(t) + ETot(t + τ)

2

]

·[(E∗

Tot(t) + E∗Tot(t + τ)

2

]dt

∝⟨∣∣∣∣Er1(t) + Es1(t + τs) + Er2(t + τ) + Es2(t + τ + τs)

2

∣∣∣∣2⟩

. (2)

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SHARMA et al.: ALL-FIBER COMMON-PATH OPTICAL COHERENCE TOMOGRAPHY: SENSITIVITY OPTIMIZATION AND SYSTEM ANALYSIS 801

Fig. 2. Measurement of signal in an Autocorrelator-based interferometer. (a)Double-sided measurement in a path-balanced autocorrelator. (b) Single-sidedmeasurement and increase in scan region by introducing an optimum offset.

1 and 3 in Fig. 2(a)]. The sample information is derived fromthe cross-correlation of the reference signal in one arm and thesample signal in the other arm of the scanning interferome-ter. Thus, a path-balanced autocorrelator will give a symmetricdouble-sided measurement [Fig. 2(a)]. However, the offset (dif-ference between the path lengths of two arms in the scanninginterferometer; see Fig. 1) can be changed to get the desiredlongitudinal scan region [Fig. 2(b)]. Hence, an autocorrelatorwith the correct offset in optical path lengths can mimic a typicalMichelson interferometer for all practical purposes in OCT [11].

Assuming the 3-dB coupler splits the light equally into thetwo arms of the autocorrelator, the fields and optical power inthe two arms can be related by

〈|Er1|2〉 = 〈|Er2|2〉 = Pr1 =Pr

2; 〈|Es1|2〉

= 〈|Es2|2〉 = Ps1 =Ps

2(4)

where Pr is the reference power, and Ps is the optical power re-turning from the sample. The sample power (Ps) is related to theoptical power incident on the sample (Pout) by the expressionPs = Rs · Pout, where Rs is defined as the sample reflectivity.

The dc component of the current is given by

Idc = ρ(Pr + Ps)/2 (5)

where ρ is the detector responsivity. The ac component of thephotocurrent (3) can be simplified and rewritten in terms ofoptical power and normalized temporal coherence function as

〈Iac(τ)〉 = |G(τ)|ρ√

Pr1Pr2 Cos[2πυ0τ ]

+ |G(τ + τs)|ρ√

Pr2Ps1 Cos[2πυ0(τ + τs)]

+ |G(τ − τs)|ρ√

Pr1Ps2 Cos[2πυ0(τ − τs)] (6)

where υ0 is the central frequency of the broadband source, andG(τ)is the normalized complex coherence function related tothe power spectral density of the source by Weiner–Khinchintheorem [4].

III. EXPERIMENTAL OCT SETUP

In our experimental setup, the probe is mounted on a high-speed translational stage (850G-HS, Newport, Irvine, CA), in-

Fig. 3. Schematic diagram of the concentric GRIN lens probe. Dotted linesdenote the partially backreflected light due to Fresnel reflection at the glass-airinterface.

terfaced with a motor controller (ESP 300, Newport, lrvine,CA) with the sample scanned in the transverse plane. The re-flection from the air-glass interface provides the reference signaland the piezoelectric fiber stretchers implement the longitudi-nal scanning function. The scan range of the system is 7 mm(in air) at a scanning frequency of 30 Hz. The Doppler fre-quency of the interferometer is approximately 695 kHz. Fara-day mirrors are used instead of simple reflectors in the scan-ning interferometer to ensure high interferometric visibility, aswell as to reverse the effects of polarization or birefringencemodulation caused by sweeping the fiber stretchers [18]. Thisallows the entire design to be comprised of low-cost single-mode fiber. A superluminescent light-emitting diode (SLED1018, Covega Corp., Jessup, MD) with a center wavelength of1320 nm and a 50-nm, 3-dB optical bandwidth was used asthe light source. Our optical receiver (LDPF0065, Tyco ElecPINFET., with 80 kV/W sensitivity, 80 kΩ transimpedanceat 1300 nm) has a saturation limit of approximately 25 uWand a responsivity of approximately 0.8 A/W. OCT imag-ing was done at an average output power of approximately5 mW. The average SNR of our system is measured to bearound 35 dB when an onion sample is illuminated by 5-mWincident power.

The most critical technical issue of a common-pathinterferometer-based OCT system is the design of a suitableimaging probe. Because the signal is reconstructed from theautocorrelation of the combined reference and sample signal, avery clean reference signal is required to avoid multiple refer-ence reflections resulting in superposition of replicated imagesat different longitudinal offsets. For our probe, we implementeda concentric fiber GRIN lens (1.8 mm diameter, 0.29 pitch, New-port) assembly enclosed in a glass tubing. A glass ferrule wasused in the lens assembly to center the optical fiber tip with theGRIN lens (Fig. 3). Index matching gel was used to eliminatemultiple back reflections.

We optimized the SNR of our system by varying the spacebetween the fiber tip and the GRIN lens, which in turn af-fected the power levels of reference signal. Although this de-sign limits the option of performing a lateral scan by laterallymoving the fiber tip with respect to the lens, external scanningmechanisms can be employed to overcome this limitation. Forexample, circumferential (lateral) scanning in endoscopic OCT

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Fig. 4. Envelope-detected signal from the interferogram to demonstrate thick-ness measurement of stacked cover glasses. The thickness of each cover glassis about 1 mm (±0.02 mm), and the refractive index is 1.52 at 1.3 µm.

systems might be performed by using a 45 prism mountedon a miniaturized microelectromechanical systems rotatingmotor [19].

IV. RESULTS

During preliminary studies, stacked glass microscope slidesand onion samples were used. Because information about thethickness and structure of these samples is already known [20],they can be used to check the imaging performance of our sys-tem. Stacked glass slides were used with paper sheets as spacers.The thickness of each glass slide is about 1 mm (±0.02 mm),and the refractive index is 1.52 at 1.3 µm. Fig. 4 shows theenvelope signal clearly distinguishing each glass slide and theair gap between them. The thickness measurements of glassslides (optical path = 1.52 mm in air) and paper sheet spacers(170 µm) with Vernier calipers are in good agreement with theexperimentally measured envelope-detected signal.

To demonstrate imaging of a nontransparent sample, we per-formed two-dimensional cross-sectional OCT imaging of anonion sample [Fig. 5(a)]. The resolution of our OCT system is20 µm (lateral) ×16 µm (longitudinal). Although the resolutionis moderate due to the limited bandwidth of the SLED sourceand the focusing limitations of GRIN lenses, the boundaries ofthe onion cellular structure can still be identified. The image sizeis 400× 180 pixels, covering an area of 1.5× 1.8 mm. Fig. 5 (b)shows the OCT image of the thin layer structure of the trans-parent peel of an onion sample. It also shows a clearly distin-guishable cross-sectional image of the stomata cell wall (striatedfibrous structure) in the onion sample [Fig. 5(b) and (c)].

Although we successfully demonstrate preliminary OCTimaging based on this novel interferometer design, there is fur-ther need for improving the dynamic range of the system.

Utilization of broader bandwidth sources will improve thelongitudinal resolution. Single or a pair of achromatic doubletlenses can be used instead of GRIN lenses to obtain tighter fo-cusing, superior off-axis performance, and enhanced efficiencyin the collection of backscattered light, thereby increasing the

Fig. 5. Acquired OCT images of onion samples. Resolution of the OCT im-ages is 20 µm (lateral) × 16 µ m (longitudinal). (a) Boundaries of the cellularstructure in the onion sample can be seen in top two layers. (b) Air gap andthe structure of the thin layer of transparent peel on the onion sample can beobserved (A). (b) OCT image of the stomata cell wall structure in onion (B) and(c) corresponding magnified photograph of the same sample.

SNR. Furthermore, SNR performance of the system can alsobe improved by an optimized reference reflection level. This isdiscussed in detail in the next section.

V. NOISE ANALYSIS AND SYSTEM OPTIMIZATION

A. Balanced and Unbalanced Operation

Noise analysis and its dependence on parameters such as ref-erence reflectivity and source power are of primary importancein OCT [21], [22]. A theoretical study by Podoleanu comparesbalanced and unbalanced detection operation in conventional

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Fig. 6. Schematic design for balanced detection operation in improvedcommon-path OCT.

OCT systems [23]. However, the results of the previous SNRanalysis cannot simply be extended to the case of common-pathOCT because of its unique common-path interferometer design.In our analysis, we calculated SNR in balanced and unbalanceddetection schemes in common-path OCT. Balanced detectioncan be easily incorporated into common-path OCT by integra-tion of an additional circulator (Fig. 6).

Like Rollins and Izatt [21], we define the SNR of an interfer-ometer as the ratio of the mean square signal photocurrent 〈I2

ac〉and the total photocurrent variance (σ2

i ):

SNR =

⟨I2ac

⟩σ2

i

. (7)

In the case of our common-path OCT configuration (Fig. 1), thesignal can be derived from the ac component of the current givenby (6). The third term in the right side of (6) is of interest, andthe first two terms can be neglected because their correspond-ing normalized temporal coherence functions tend to zero dueto low coherence (at τ = τs). Hence, the mean square signalphotocurrent is given by [from (4) and (6)]⟨

I2ac(τ)

⟩= (ρ2Pr1Ps2/2) = (ρ2PrPs/8). (8)

The total photocurrent variance is given by the sum of the John-son noise (σ2

th), the shot noise (σ2sh), and the excess photon

noise (σ2ex), respectively:

σ2i = σ2

th + σ2sh + σ2

ex

= (4kB TB/RL ) + 2eIdcB + ((1 + V 2)I2dcB/∆υ) (9)

where kB is the Boltzman’s constant, T is the temperature, RL

is the equivalent noise resistance, B is the detection electricalbandwidth, V is the degree of polarization of the source, and∆υ is the effective line width of the source. Hence, in the caseof unbalanced detection operation, SNR is given by

SNR =(ρ2PrPs/8)

(4kB TB/RL ) + 2eIdcB + ((1 + V 2)I2dcB/∆υ)

.

(10)

In the case of balanced detection operation, the excess pho-ton noise can be replaced by the beat noise arising due to the

out-of-phase components of the photocurrents in the two pho-todetectors [24]. If we denote I+ as the photocurrent at thephotodetector D1, and I− as the photocurrent at the photode-tector D2, then the dc components of the photocurrents can begiven by

I±dc = ρ(Pr1 + Ps1 + Pr2 + Ps2)2

= I ′dc + I ′′dc =ρ(Pr + Ps)

2(11)

where

I ′dc =ρ(Pr1 + Ps1)

2) =

Idc

2and

I ′′dc =ρ(Pr2 + Ps2)

2=

Idc

2are the mutually incoherent dc components of the photocurrentcorresponding to the optical signal in the two arms of the auto-correlator. If we assume Pr Ps , then the overall beat noiseterm (σ2

be) in the balanced detection can be given by [23], [24]

σ2be = 2((1 + V 2)I ′dcI

′′dcB/∆υ)

=

((1 + V 2)I2

dcB/∆υ)

2. (12)

The Johnson noise (σ2th) and the shot noise (σ2

sh) at the twophotodetectors is independent and will add up incoherently. Thetotal photocurrent variance is hence given by

σ2i = 2σ2

th + 2σ2sh + σ2

be

= (8kB TB/RL ) + 4eIdcB +((1 + V 2)I2

dcB/2∆υ).

(13)

For a balanced receiver, the total signal photocurrent is the sumof the mean square photocurrents in individual detectors and isgiven by ⟨

I2ac(τ)

⟩= 2(ρ2PrPs/8). (14)

Hence, in the case of balanced detection operation, SNR is givenby

SNR =(ρ2PrPs/8)

(4kB TB/RL ) + 2eIdcB + ((1 + V 2)I2dcB/4∆υ)

.

(15)

When comparing (10) and (15), it is interesting to note that ex-cess photon noise is reduced by only a factor of four in balancedoperation in the autocorrelator-based scanning of the signal.Beat noise arises due to the beating of various Fourier com-ponents within the broad band spectra of two incoherent lightsignals. The additional time delay caused by the autocorrela-tor results in one half of the dc component (I ′dc) becoming outof phase with respect to the other half (I ′′dc) (at τ = τs). Thisresults in the existence of a large amount of beat noise that isalmost of the same order of excess photon noise. This does notoccur in cross-correlator-based configurations used in conven-tional OCT systems. Equation (15) puts a theoretical limit onSNR improvement by a maximum of 6 dB (due to decrease in

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Fig. 7. Calculated SNR for unbalanced, balanced, and ideal shot noise lim-ited operations as a function of reference reflectivity in common-path OCT.Equations (10) and (11) are used to plot the SNR for unbalanced and bal-anced detection operations. The shot noise limited detection curve is plot-ted by neglecting the contribution due to excess photon noise in (10). Thefollowing values were used for calculation: Source power = 5 mW, Sam-ple reflectivity = 10−7, ρ = 0.8 A/W, Johnson noise = 0.1pA2/Hz, B = 0.7MHz.

excess photon noise by a factor of 4), even at higher sourcepowers in balanced detection operations in common-path OCT.Hence, our analysis predicts that higher reference power can bedetrimental for the system sensitivity even in the balanced de-tection operation. In fact, the marginal improvement in the SNRdue to balanced detection might easily be outweighed whenwe take into account the losses due to additional circulator andoffset caused by imperfect matching of the balanced receivers.Our analysis also predicts that the best SNR can be obtainedby reducing the reference reflectivity to approximately 0.2% to0.4% (sample reflectivity ∼10−7) for operation near the shotnoise limited regime (Fig. 7).

B. Experimental Results

SNR experiments were conducted to verify our theoreticalanalysis by measuring SNR as a function of the ratio of thesample and the reference powers [Fig. 8(a)], and SNR as afunction of the source output power [Fig. 8(b)], for unbalanceddetection operations.

The experiment was conducted using a right-angle-cleavedbare fiber probe (reference reflectivity = 4%) and a glass slide(sample reflectivity = 4%) as a sample. The ratio of the sampleto the reference power was changed by varying the distance be-tween the fiber tip and the sample. The diverging beam comingout of the fiber tip would result in increased losses in the col-lected sample power as the distance between the fiber tip andthe sample is increased. Standard Gaussian beam approxima-tion analysis was used to find out the change in the ratio of thesample to the reference power as a function of distance betweenthe distal end of the fiber and the sample. This was also verifiedby measuring the coupled signal power. As expected, the SNRincreases with increasing the signal power as shown in Fig. 8(a).The theorectical curve is obtained by numerically solving (10)

Fig. 8. Comparison of experimental and theoretically predicted SNR data (a).SNR as a function of the ratio of sample to reference power. The power incidenton the sample is around 3.1 mW. (b) SNR as a function of power incident on thesample. The ratio of sample to reference power is approximately 2.2 × 10−4.

and using the experimental parameters given previously and isin good agreement with the experimental data.

In the second part of the experiment, we measured the SNRby varying the source power but keeping the ratio of sampleto reference power constant [Fig. 8(b)]. The distance betweenthe fiber tip and the sample surface was maintained constantat 2 mm during the experiment. As expected, the SNR initiallyincreases with the increase in source power but then saturatesat around ∼30 dB at higher powers due to excess photon noise.This is close to the theoretical limit of 30 dB based on theparameter values and components used in the experiment. Thetheoretical analysis results were obtained by using the samestandard Gaussian beam analysis to determine the sample powerand by solving for the SNR using (10). Unbalanced detectionwas used to measure the SNR in both parts of the experiment.The error in measurement of the SNR was on the order of 1 dB.The experimental results were in very good agreement with thetheoretical analysis.

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SHARMA et al.: ALL-FIBER COMMON-PATH OPTICAL COHERENCE TOMOGRAPHY: SENSITIVITY OPTIMIZATION AND SYSTEM ANALYSIS 805

VI. CONCLUSION AND FUTURE SCOPE

In summary, we demonstrate a novel, fully integrated all-fiber common-path-based OCT system and present a thoroughanalysis of the system sensitivity optimization. We conductedsystematic SNR measurement experiments that were in verygood agreement with our analysis. Our analysis predicts thattuning of reference reflectivity is the key parameter in sensi-tivity optimization, especially because the unusually high beatnoise limits the increase in SNR in balanced detection opera-tions. We are currently developing lens probes with optimumreference reflection (based on our optimization analysis) to op-timize the sensitivity and resolution of the system. We also planto demonstrate a balanced detection version of our common-path OCT system and experimentally verify the SNR predictedin this paper. Overall, this technology is promising because itmay significantly reduce the cost of commercial EOCT systemsdue to its simple and robust all-fiber design.

ACKNOWLEDGMENT

The authors would like to thank J. Bush for his invaluablefeedback and fruitful discussions.

REFERENCES

[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, vol. 254, pp. 1178–1181, 1991.

[2] J. A. Izatt, M. R. Hee, E. A. Swanson, C. P. Lin, D. Huang, J. S. Schuman,C. A. Puliafito, and J. G. Fujimoto, “Micrometer-scale resolution imagingof the anterior eye in vivo with optical coherence tomography,” Arch.Opthalmol., vol. 112, no. 12, pp. 1584–1589, 1994.

[3] G. J. Tearny, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J.F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy withoptical coherence tomography,” Science, vol. 276, pp. 2037–2039, 1997.

[4] J. M. Schmitt, “Optical coherence tomography (OCT): A review,” IEEEJ. Sel. Top. Quantum Electron., vol. 5, pp. 1205–1215, Jul./Aug. 1999.

[5] B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A.F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight,P. St. J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axialresolution optical coherence tomography,” Opt. Lett., vol. 27, pp. 1800–1802, 2002.

[6] K. Bizheva, B. Povazay, B. Hermann, H. Sattmann, W. Drexler, M. Mei,R. Holzwarth, T. Hoelzenbein, V. Wacheck, and H. Pehamberger, “Com-pact, broad-bandwidth fiber laser for sub-2-µm axial resolution opticalcoherence tomography in the 1300-nm wavelength region,” Opt. Lett.,vol. 28, pp. 707–709, 2003.

[7] J. F. de Boer, T. E. Milner, M. J. C. Van Gambert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett., vol. 22, pp. 934–936,1997.

[8] J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, J. K. Barton, and A. J. Welch, “Invivo color Doppler flow imaging of picoliter blood volumes using opticalcoherence tomography,” Opt. Lett., vol. 22, pp. 1439–1441, 1997.

[9] Z. Chen, T. E. Milner, D. Dave, and J. S. Nelson, “Optical Doppler tomo-graphic imaging of fluid flow velocity in highly scattering media,” Opt.Lett., vol. 22, pp. 64–66, 1997.

[10] U. Morgner, W. Drexler, F. X. Kartner, X. D. Li, C. Pitris, E. P. Ippen,and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt.Lett., vol. 25, pp. 111–113, 2000.

[11] J. Bush, P. Davis, and M. A. Marcus, “All-fiber optic coherence domaininterferometric techniques,” in Proc. SPIE 4204A-08, 2000.

[12] U. Sharma, N. M. Fried, J. U. Kang, and J. Bush, “Optical coherencetomography based on an all-fiber autocorrelator using probe-end reflectionas reference,” presented at the CLEO/IQEC 2004, CWJ3, San Francisco,CA, May 2004.

[13] A. M. Sergeev, V. M. Gelikonov, G. V. Gelikonov, F. I. Feldchtein,R. V. Kuranov, N. D. Gladkova, N. M. Shakhova, L. B. Snopova, A.V. Shakhov, I. A. Kuznetzova, A. N. Denisenko, V. V. Pochinko, Yu.P. Chumakov, and O. S. Streltzova, “In vivo endoscopic OCT imagingof precancer and cancer states of human mucosa,” Opt. Express, vol. 1,pp. 432–440, 1997.

[14] Y. Chen, X. Li, M. Cobb, X. Liu, and R. Thariani, “Full dispersioncompensation in real-time optical coherence tomography involving aphase/frequency modulator,” presented at the CLEO/IQEC 2004, CThT76,San Francisco, CA, May 2004.

[15] A. B. Vakhtin, D. J. Kane, W. R. Wood, and K. A. Peterson, “Common-path interferometer for frequency-domain optical coherence tomography,”Appl. Opt., vol. 42, pp. 6953–6958, 2003.

[16] R. Beddows, S. W. James, and R. P. Tatam, “Improved performance in-terferometer designs for optical coherence tomography,” presented at the15th Int. Conf. Optical Fibre Sensors (OFS-15), Portland, OR, May 2002,pp. 527–530.

[17] P. Casaubieilh, H. D. Ford, and R. P. Tatam, “Optical fibre Fizeau-basedOCT,” presented at the 2nd European Workshop on Optical Fibre Sensors,Proc. SPIE 5502, Santander, Spain, Jun. 2004, pp. 338–341.

[18] A. D. Kersey, M. J. Marrone, and M. A. Davis, “Polarization insensi-tive fiber optic Michelson interferometer,” Electron. Lett., vol. 27, no. 6,pp. 518–519, Mar. 1991.

[19] P. H. Tran, D. S. Mukai, M. Brenner, and Z. Chen, “In vivo endoscopic op-tical coherence tomography by use of a rotational microelectromechanicalsystem probe,” Opt. Lett., vol. 29, pp. 1236–1238, 2004.

[20] B. E. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, andJ. G. Fujimoto, “High-resolution optical coherence tomographic imagingusing a mode-locked Ti:Al2O3 laser source,” Opt. Lett., vol. 20, pp. 1486–1488, 1995.

[21] A. M. Rollins and J. A. Izatt, “Optimal interferometer designs for opticalcoherence tomography,” Opt. Lett., vol. 24, pp. 1484–1486, 1999.

[22] A. G. Podoleanu and D. A. Jackson, “Noise analysis of a combined opticalcoherence tomography and confocal scanning ophthalmoscope,” Appl.Opt., vol. 38, pp. 2116–2127, 1999.

[23] A. G. Podoleanu, “Unbalanced versus balanced operation in an opticalcoherence tomography system,” Appl. Opt., vol. 39, pp. 173–182, 1999.

[24] K. Takada, “Noise in optical low-coherence reflectometry,” IEEE J. Quan-tum Electron., vol. 34, pp. 1098–1108, Jul. 1998.

Utkarsh Sharma (S’05) received the B.Tech. degree in engineering physicsfrom the Indian Institute of Technology, Bombay, India, in 2001, and the M.S.degree in electrical and computer engineering from the Johns Hopkins Univer-sity, Baltimore, MD, in 2003. He is currently pursuing the Ph.D. degree at theJohns Hopkins University.

His research interests include optical coherence tomography, fiber lasers, andoptical fiber-based devices.

Nathaniel M. Fried received the B.A. and M.S. degrees in physics fromSwarthmore College, Swarthmore, PA, in 1992, and Rensselaer Polytech-nic Institute, Troy, NY, in 1994, respectively. He received the Ph.D. de-gree in biomedical engineering from Northwestern University, Evanston,IL, in 1998.

He completed a postdoctoral fellowship with the Applied Physics Labora-tory and the Biomedical Engineering Department at Johns Hopkins University,Baltimore, MD, in 2000. He is currently an Assistant Professor of Urology atJohns Hopkins Medical School and Director of the Biophotonics Laboratoryat Johns Hopkins Bayview Medical Center, Baltimore. His research interestsinclude therapeutic and diagnostic applications of lasers in urology.

Jin U. Kang received the Ph.D. degree in electrical engineering and opticalsciences from the University of Central Florida, Orlando, in 1996.

After completing the Ph.D. degree, he was a Research Engineer with the U.S.Naval Research Laboratory, Washington, DC, until 1998. He is currently anAssociate Professor in the Department of Electrical and Computer Engineeringat Johns Hopkins University, Baltimore, MD. His research interests includenonlinear fiber optics, novel fiber laser systems, and ultrafast optoelectronicdevices.