We demonstrate dispersion matching of sample and reference arms in an optical frequency domain reflectometry-optical coherence tomography (OFDR-OCT) system with a discretely swept light source centered at 1550 nm, using a dispersion-shifted fiber (DSF) in the reference arm. By adjusting the optical length of the DSF so that it is equal to that of the free space in the sample arm, we achieve a high resolution of 27.2 μm (in air), which is very close to the theoretically expected value of 26.8 μm when we measure the reflective mirror. This improves the degraded resolution (36.1 μm) in a system using a conventional single-mode fiber when the free-space length in the sample arm was 909 mm. We also demonstrate a clear interface between air and the enamel layer of an extracted human tooth with the discretely swept (DS) OFDR-OCT imaging due to the improved resolution provided by this technique. In addition, we confirmed the enhanced sharpness of the cellular structure in a dispersion matched OCT image of an onion sample. These results show the potential of our DS-OFDR-OCT system for a compact low-cost apparatus with a high axial resolution.
© 2007 Optical Society of America
Optical coherence tomography (OCT) is a promising imaging technology that enables non-invasive, noncontact cross-sectional observation of biological tissues with high-resolution operation, and commercially available diagnostic instruments have been released for ophthalmology imaging and other purposes. In clinical applications, OCT apparatuses for diagnosis should be small, because they have to share cramped hospital space with other diagnostic tools.
In OCT systems, a free-space segment for guiding probe light into a sample is inevitable [1, 2, 3, 4, 5]. To balance the optical lengths of the sample and reference arms, a free-space segment in the reference arm, which has the same optical length as that of the sample arm, has been commonly employed so far. This segment of the reference arm makes it impossible to build a compact and cost-effective OCT systems, because it consists of a few-hundreds-millimeter-long free space, lenses, and a reflective mirror. To achieve a compact OCT system at a low cost, we have developed an optical frequency domain reflectometry-optical coherence tomography (OFDR-OCT) system using a 1550-nm-range swept light source and a fiber-based Mach-Zehnder interferometer (MZI), in which the reference arm is composed of only low-cost single-mode fibers (SMFs) and SMF-based optical components [6, 7, 8]. However, the axial resolution of this system was distinctly degraded from the expected value because of a dispersion mismatch between sample and reference arms. This mismatch was caused by replacing the free-space (zero dispersion) segment in the reference arm with an SMF with the equivalent optical length, which has a certain dispersion σ = 17 ps/nm/km at the wavelength λ = 1550 nm. To resolve this problem, numerical dispersion compensation techniques are attractive, and they have been commonly used in OCT systems [9, 10]. We have also reported a numerical compensation technique, with which we achieved a compact and cost-effective OFDR-OCT system with a high resolution of 27 μm in air , which is very close to the theoretically expected value. On the other hand, the use of hardware techniques (optical components) in the OCT interferometer is also attractive for achieving dispersion matching. For example, introducing bulk compensation materials or an acousto-optical modulator with the free-space segment in the reference arm has been demonstrated a good dispersion matching [12, 13, 14]. However, for the reasons mentioned above, these systems do not offer a cost-effective solution.
To achieve real-time OCT imaging with high resolution with a compact low-cost system, we propose a dispersion matching technique by using dispersion managed fibers (DMFs) in the SMF-based reference arm. This enables us to obtain an all-fiber-based reference arm with balancing both optical lengths and dispersions of the two interferometer arms. The various types of DMFs available such as dispersion-compensation fibers (DCFs) , dispersion-shifted fibers (DSFs) , and photonic-crystal fibers (PCFs), or holey fibers (HFs) , have different characteristics and were developed to enhance a transmission length in optical fiber telecommunications systems. Among the DMFs, we chose DSFs, which have zero dispersion (σ = 0 ps/nm/km) at the wavelength λ of 1550 nm, for our OFDR-OCT system because the core diameter and index profile of DSFs are comparatively similar to those of SMFs . This leads to a good fiber splicing of SMFs with DSFs with negligibly low splicing loss and reflection at the interface.
In this paper, we describe a compact cost-effective high-resolution OFDR-OCT system comprising a 1550 nm-range discretely swept light source, a fiber-based MZI, and a DSF in the reference arm. Our techniques for dispersion matching of the two interferometer arms are described theoretically and experimentally. Using our system, we have acquired OCT images of a extracted human tooth with a sharpened interface between air and the enamel layer. Also, we show an enhanced sharpness of the cellular structure in a dispersion matched OCT image of an onion sample.
Figure 1(a) shows the basic configuration of the discretely swept (DS) -OFDR-OCT system (System 1) we developed. The system, which is described in the next section in detail, is mainly composed of a super-structured-gratings distributed Bragg reflector-laser diode (SSG-DBR-LD) source , a fiber-based MZI with a free-space segment in the reference arm, a balanced receiver, and a computer. As the SSG-DBR-LD is discretely swept with an equal interval δk from the initial wavenumber k 0, the wavenumber of the i-th output light from the laser is expressed as ki = k 0 + iδk (i = 0,1,…,Ns - 1), where Ns is the total number of wavenumber channels (sampling). The output from the laser is divided by a coupler into the sample and reference arms. The interference signal between the reflected lights from the sample and reference mirror in each arm is detected with a photodetector. The detector current Id,i for the i-th sampling is given by
where η is the detector sensitivity, q is the quantum electric charge, hv is the single-photon energy, Pr is the optical power reflected from the reference arm at the detector, and Po is the optical power illuminating the sample [5, 6]. The first two terms in parentheses refer to noninterference background currents and the third term denotes the interference signal. The z is the axial coordinate, where z = 0 corresponds to zero optical path-length difference between the two interferometer arms. The r(z) and ϕi,(z) are the amplitude and phase of the reflectance profile of the sample, respectively. The Γ(z) is the coherence function of the instantaneous laser output.
We consider interference signal current Is,i of a single reflector with reflectivity r 2 located at z = z 0, and the reflectivity profile is given by delta function r(z) = rδ(z -z 0). Since the laser has a long coherence length due to the narrow instantaneous linewidth (~ 10 MHz) of the single-mode emission spectrum , we set Γ(z) = 1 within a certain depth range. As the noninterference background currents are subtracted by the balanced detector, Is,i can be expressed as
where Ps(= r 2 Po) is the optical power reflected from the sample at the detector. For the discretely sampled interference currents Is,i in Eq. (2), the position of the reflector z 0 can be determined as a point-spread function (A-line signal) by the discrete Fourier transform (DFT) of Is,i, and then doublet peaks are observed periodically at z = ±z 0 + mπ/δk, where m is an integer . This leads to a depth range given by
The axial resolution δz in the DS-OFDR-OCT system defined as a full width at half maximum (FWHM) of the peak of the A-line signal is expressed as 
where ∆k = Nsδk is the wavenumber range of the laser output. In this system, we set the optical lengths of the two interferometer arms equal (L A-B-C-D-C-E-F = L A-G-H-F) and constant, where LA-B-C-D-C-E-F and LA-G-H-F are the optical lengths of the sample arm (optical path A-B-C-D-C-E-F) and the reference arm (optical path A-G-H-F), respectively.
Figure 1(b) shows a schematic diagram of a compact low-cost DS-OFDR-OCT system (System 2) without a free-space segment in the reference arm. To reduce both the size of the system and number of optical components, we replace the optical path G-I-H [Fig. 1(a)] comprising a circulator, a free-space segment, and lenses with an SMF with optical path G-H. That is, LB-C-D-C-E = LG-H, where LB-C-D-C-E and LG-H are the optical lengths of the optical path B-C-D-C-E and G-H (SMF), respectively. As the effective index derived from materials and the index profile of the fiber depends on a wavenumber, the SMF widely used in telecommunications systems has a dispersion characteristics (σ = 17 ps/nm/km at λ = 1550 nm). This results in a dispersion mismatch between the two arms in System 2, because the optical path C-D-C in the sample arm has zero dispersion (except few-millimeter-long lenses). In this case, interference signal current Is,i given by Eq. (2) is rewritten as
where δzi denotes the phase difference due to the dispersion mismatch . Since this mismatch is caused by the SMF, we can write
where ℓG-H is a physical length of the SMF, and nSMF,i is the effective index of the SMF at ki. The propagation constant βi of the SMF, which is the product of nSMF,i and ki, is approximated by the Taylor series around the center angular frequency ω 0 as 
where βc = β(ω0), and ∆ωi is the angular frequency difference from ω0. That is, ∆ωi = ωi - ω0. The first term of Eq. (7) is the constant offset, and the second term relates to multi-mode dispersion. Although the the latter leads to a significant signal distortion in multi-mode fibers, it can be treated as a constant delay for the SMF. The chirping of the interference signal in the system shown in Fig. 1(b) is caused by the third term in Eq. (7), which is called a chromatic dispersion term coming from material and waveguide dispersion of the SMF. The magnitude σ of chromatic dispersion is given by 
3. Experimental setup
Figure 1(c) shows a schematic diagram of the newly developed DS-OFDR-OCT system (System 3). To achieve a high axial resolution, the system incorporates a DSF (ITU-T G. 653 compliant) in the reference arm. The 1550 nm-ranged SSG-DBR-LD (prototype of NTT Photonics laboratories) can discretely sweep 400 channels (Ns = 400) of a single-mode light from k 0 = 3.99363 × 104 cm-1 to k 399 = 4.09737 × 104 cm-1 with the equal interval of δk = 2.6 cm-1 . Thus, the laser can offer a very long depth range of 6.0 mm (in air) as calculated from Eq. (3). The average optical output power of the light source is 3.0 mW. The scan speed of 10 μs/channel leads to an A-line rate of 250 Hz, and the OCT image (B-scan) rate for 500 A-line signals is 0.5 frame/s.
With the wavenumber range ∆k = 1037.4 cm-1 (corresponding spectral bandwidth in wavelength ∆λ ≃ 40 nm), the axial resolution δz is calculated to be 26.8 μm (in air) from Eq. (4). Since the laser has a narrow linewidth ∆f (≤ 10 MHz) as mentioned before, the coherence length lc ∼ (2ln2/π)(c/∆f) is longer than 10 m, assuming a Gaussian spectral profile, where c is the velocity of light in vacuum.
The output light from an SSG-DBR laser is launched into both the reference and sample arms via a 9:1-coupler (90% of the light into the sample arm). The light launched into the sample arm reaches a circulator via an attenuator (ATT 1). Then, the light illuminates the sample (Po = 2.2 mW) via a galvanometer mirror, and the light backscattered from the sample is fed back into the circulator along the same optical path. The reflected light reaches the 5:5-coupler via a polarization controller (PC 1). So, the optical path length of the sample arm (optical path A-B-C-D-C-E-F) is denoted as LA-B-C-D-C-E-F . On the other hand, the light input into the reference arm passes through another attenuator (ATT 2), then reaches the SMF (ITU-T G. 652. D compliant) and DSF. Finally, the light is fed into a 5:5-coupler via another polarization controller (PC 2). We also denote the optical length of the reference arm (optical path A-G-J-H-F) as LA-G-J-H-F. In this system, we set the optical lengths of the two interferometer arms equal (LA-B-C-D-C-E-F = LA-G-J-H-F) and constant. Also, we set the optical lengths of paths A-B and A-G and paths E-F and H-F equal, that is LA-B = LA-G and LE-F = LH-F. In this system, Pr = 0.152 mW (-8.2 dBm), which is almost the same as Pr in System 2, 0.174 mW (-7.6 dBm), because the insertion loss of the DSFs is comparable to that of SMFs. So, the excess loss of incorporating the DSF in OCT systems is estimated to be as small as 0.6 dB. Pr in System 1, however, decreased to 0.103 mW (-9.9 dBm) due to the optical coupling loss of 2.3 dB in the free-space segment of the reference arm.
The reference and sample lights interfere in the 5:5-copuler, and the interference signals are detected by a balanced receiver. The detected interference signals are acquired and digitized with a 16-bit analog-to-digital (A/D) converter board installed in the computer. To obtain an axial reflectivity profile (A-line signal), the DFT is carried out to each interferogram data sampled at an equal wavenumber interval.
To reduce both the cost and size of the system while maintaining a high resolution, we replaced the segment comprising a circulator, free-space, and lenses with an SMF and DSF with the optical length equivalent to that of the segment. Thus, we have L B-C-D-C-E = LG-J+LJ-H, where LB-C-D-C-E, LG-J and LJ-H are the optical lengths of the segment (B-C-D-C-E), the SMF (G-J), and DSF (J-H), respectively. Here, we adjust LJ-H to LC-D-C using a fusion splicing machine, where LC-D-C is the optical length of the free-space segment (C-D-C) in the sample arm. For example, we set the physical length of the DSF ℓDSF = 345 mm, when LC-D-C = 500 mm, assuming the effective index of the DSF nDSF = 1.45 at λ = 1550 nm. We can therefore balance both the dispersion and optical length between the free-space segment in the sample arm and the DSF in the other arm, because the DSF has zero dispersion at λ = 1550 nm as mentioned before. We also set LG-J = LB-C+LC-E,where LG-J,LB-C and LC-E are the optical lengths of the SMF (G-J) and of optical paths B-C and C-E, respectively. Although the lenses in the free-space segment and optical components inside the circulator also have dispersive characteristics, we did not take the dispersion into account in these adjustments because the lengths of these components are very short compared with those of the rest of the optical paths. In the above way, we succeeded in balancing both the dispersion and optical lengths between the two interferometer arms. We would also realize this balancing by using an all-DSF-based MZI, but it must not be practical due to the much higher cost of DSF-based optical components than that of the SMF-based ones.
4. Results and discussion
Figure 2 shows interference signal intensities as a function of the channel number of the wavenumber i obtained by our OFDR-OCT systems. The black and red lines are the signals acquired with System 2 and 3, respectively, at the LC-D-C = 909 mm. In System 2, a chirped signal (i.e. a decrease of the frequency as i increases) was clearly observed due to the dispersion mismatch between the two interference arms. However, in System 3, chirping of the signal was negligibly small; that is, the frequency of the signal was almost constant thanks to the balanced dispersion of the two arms. Although the chirping characteristics are distinctly different between System 2 and 3, the amplitude of those signals are almost the same as shown in Fig. 2. This is because the optical power in the reference arm of System 2 and 3 is almost the same as mentioned in the last section.
Figure 3 shows A-line signals of the reflective mirror at the LC-D-C = 909 mm. The blue, black and red lines are the signals obtained with System 1, 2, and 3, respectively. In Fig. 3, a clear broadening of the signal peak, which comes from the chirped interference signal shown in Fig. 2, was observed in System 2. This leads to the degradation of the axial resolution as mentioned above. (The resolution is further discussed in the next paragraph.) The signal-to-noise ratios (SNRs) are 56, 59 and 60 dB for System 1, 2, and 3, respectively. The improved SNR in System 2 and 3 was mainly attributed to the increased optical power in the reference arm, since we did not employ the free-space segment, which has an inevitable optical loss of 2.3 dB, in the arm of both systems.
Figure 4 shows A-line signals of the reflective mirror around the peak intensity at the LC-D-C = 909 mm. The signals are displayed on a linear scale for ease of comparison. The blue, black and red lines are the signals obtained with System 1, 2, and 3, respectively. The green line is the signal of System 2 obtained when we used our numerical dispersion compensation technique . In System 1, the axial resolution dz defined as the FWHM of the A-line signal peak was 26.8 μm , which is same as the expected value mentioned in the last section. This comes from the well-balanced dispersion of the two interference arms due to their identical configuration as shown in Fig. 1(a). We, however, acquired a noticeably broadened peak (black line) and deteriorated dz of 36.1 μm, which are attributed to the unbalanced dispersion of the two arms. By incorporating the DSF in the reference arm, System 3 exhibited a high resolution of 27.2 μm which is very close to the expected value (low increase rate of 1.9%). These results show that our dispersion matching technique provides a compact cost-effective OFDR-OCT system with high resolution. Moreover, since the δz obtained with System 3 was the same as that obtained with System 2 with numerical compensation, using the DSF for dispersion matching can be compared to numerical compensation in terms of the improvement of the resolution.
The peak intensity of System 2 was lower than that of System 3. This comes from the dispersion broadening effect in System 2, not from the reference optical power difference, because the power of both systems is almost identical. The decreased intensity of System 1, however, is caused by the lower reference optical power compared with System 2 and 3 as mentioned in the last section. The highest peak intensity was obtained in System 2 with numerical compensation. This is because the acquired A-line signal was transformed from the pure sinusoidal interference signal via DFT thanks to the numerical compensation technique.
As a loss of δz depends on LC-D-C when dispersion mismatch exists in the MZI, we measureddz of the A-line signal of the reflective mirror as a function of LC-D-C, as shown in Fig. 5. The blue triangle, black circle, and red rectangular depict δz of System 1, 2 and 3, respectively. In System 1, δz was constant and the expected value of 26.8 μm at any LC-D-C because of the well-balanced dispersion of the two arms. On the other hand, in System 2, δz distinctly degraded as LC-D-C increased due to the dispersion broadening. For example, we obtained δz = 28.6 μm (+7.1%) at LC-D-C = 297 mm, but 36.1 μm (+35.2%) at LC-D-C = 909 mm.
In System 3, we achieved a good δz of less than 27.2 μm (+1.9%) at any LC-D-C. This is because of using the DSF with LJ-H, which is equivalent to LC-D-C (free-space segment) in the reference arm. This result means that the system we developed enables us to achieve dispersion matching independently of the length of the free-space segment in the sample arm by adjusting the length of the DSF in the other arm. Residual dispersion mismatch would lead to little degradation of δz in System 3, because the DSF has small dispersion (∣σ∣ < 3 ps/nm/km) in the wavelength range (1530 ≤ λ ≤ 1570 nm) of the laser, except at λ = 1550 nm .
We also confirmed the effect of the dispersion matching technique by acquiring images of an extracted human tooth with our DS-OFDR-OCT system at LC-D-C = 909 mm. Figure 6 (a) and (b) are the images of the tooth acquired with System 2 and 3, respectively. In both images, the enamel layer, dentin layer, and some cracks are observed. The interface between the enamel layers and air is blurred in Fig. 6(a) due to the degraded axial resolution caused by dispersion broadening, but it is clear in Fig. 6(b) owing to the use of the dispersion matching technique. Also, the crack at the center of both images was much more clearly observed with System 3 than with System 2 for the same reason.
Figure 7 shows A-line signals of the tooth around the peak intensity (interface between the enamel layer and air) obtained with System 2 and 3. The signals and peaks correspond to the broken lines and arrows in Fig. 6 , respectively. This graph proves that the broadened peak (black line) attributed to the dispersion mismatch caused the interface blurring in Fig. 6(a). On the other hand, dispersion matched system (red line) offered a sharpened peak, which leads to the clear interface with a high contrast in Fig. 6(b).
We acquired DS-OFDR-OCT images of the cellular structure of an onion sample with and without dispersion matching at LC-D-C = 909 mm. Figure 8 (a) and (b) are the images of the onion obtained with System 2 and 3, respectively. Although the cellular structure is observed in both images, the axial image sharpness is enhanced by a factor of more than 2 in System 3 due to the improved axial resolution afforded by the dispersion matching technique.
In the DS-OFDR-OCT system, we achieved dispersion matching between the two interferometer arms using the DSF We confirmed that this technique is very effective in preventing the loss of the resolution in the compact cost-effective OCT system with the all-fiber based reference arm. However, the 27-μm resolution of our system is relatively low compared with other systems because of the narrow bandwidth (∆λ ≃ 40 nm) of our light source (SSG-DBR-LD). Since a single SSG-DBR-LD has a spectral range of about 40 nm, we plan to expand the range of the light source to 160 nm by operating four SSG-DBR-LDs with different spectral ranges to achieve ultra-high resolution (≤ 6.5 μm in air) . To demonstrate this concept, our group recently achieved improved resolution of 15.3 μm (in air) using two SSG-DBR-LDs with expanded ∆λ of 62.8 nm . In such a system with an ultra-wide wavelength range, the dispersion matching technique will be much more effective in achieving a high axial resolution without dispersion broadening than it is in the system we report here.
Although the DSF is suitable for dispersion compensation in only 1550-nm-range OCT systems, the basic concept of this technique could be adapted to OCT systems with spectral ranges of 800, 1000, and 1300 nm using other types of DMFs. Both a zero dispersion wavelength shift to wavelengths shorter than 1300 nm and flattened dispersion characteristics (∣γ∣ < 1 ps/nm/km) in a very wide wavelength range of more than 100 nm have been demonstrated using PCFs with an optimized design by various groups [24, 25, 26]. We believe that those PCFs are promising for dispersion compensation in OCT systems with a short-wavelength and very-wide-spectral-range light source.
We demonstrated a dispersion matching technique for a fiber-based MZI in a DS-OFDR-OCT system with a 1550-nm-range discretely swept light source. The technique using the DSF in the reference arm provides a compact low-cost OCT system with a high axial resolution of ≤ 27.2 μm (in air), which is very close to the expected value, independently of the free-space length of the sample arm. Our OCT system using this technique enabled us to clearly image the interface between air and the enamel layer of an extracted human tooth and cracks. We also successfully obtained OCT images of an onion sample, showing enhanced sharpness of the cellular structure. The dispersion matching technique we developed is promising for realizing a compact low-cost OCT system with high axial resolution. The principle of this technique can be expanded to OCT systems with other spectral ranges using other types of DMFs.
The authors would like to thank Dr. T. Amano, Dr. H. Hiro-Oka, Dr. D. Choi, Dr. H. Furukawa, Dr. M. Nakanishi and Dr. K. Shimizu of Kitasato University for their support and fruitful discussion. One of the authors (K. Asaka) acknowledges Dr. T. Miyazawa, Dr. H. Ishii, Dr. K. Kato and Dr. H. Itoh of NTT Photonics Laboratories for their valuable advice and encouragement.
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