1. Introduction

Optical coherence reflectometry and tomography techniques based on various implementation schemes have been enthusiastically studied for fiber-optic measurements and bio-medical applications. In particular, optical coherence tomography (OCT), which is a 2-D or 3-D scanning version of coherence reflectometry, has attracted much attention after it was introduced in the 1990s [1]. This technique enables us to obtain rich information of objects with a micron-scale resolution in a non-invasive manner. Typical OCT systems exhibit ~10 µm axial resolution and ~1 kHz axial-line (A-line) scan rate with a sensitivity of better than - 100 dB. For better diagnostic ability required in many applications, OCT systems with better resolutions and higher acquisition speeds are still desired, and hence, have been widely investigated so far. Supercontinuum sources with wider spectral bandwidths have been used to demonstrate OCT systems with improved axial resolutions better than 1 or 2 µm [2]. And the acquisition speed can be improved to more than 10 kHz for A-line scan rate by adopting Fourier-domain OCT (FD-OCT) techniques. To capture fast dynamics or 3-D information in real time, higher A-line scan speeds are still required with an improved spatial resolution [4].

The FD-OCT technique measures axial back-reflection signals in the frequency domain, or equivalently the wave-number domain, in contrast to the conventional time-domain OCT (TD-OCT) technique, which measures an interferometric signal in the time domain, or equivalently in the delay length domain. In the FD-OCT systems, the obtained raw data are converted into the length domain using discrete Fourier transformations (DFT) with digital signal processors. There are two types of FD-OCT implementation methods. In the first type, a spectrometer is used for signal acquisition. This is also known as spectral-domain OCT (SD-OCT). The spectral response of the OCT interferometer is measured by a multi-channel photodetector array so that the signals are captured in a parallel manner [5]. In the second method, a frequency-swept light source is used instead [3, 4, 6–10]. This technique is also known as optical frequency-domain imaging (OFDI) or swept-source OCT (SS-OCT), to distinguish it from the SD-OCT. With a priori information about the source’s output wavelength as a function of time, the spectral response can also be measured by a single high-speed photodetector in the time domain. The principles and performance characteristics of these two approaches are similar to each other [11, 12, 18]. In the long-wavelength IR region around 1,300 nm, where high-speed array photodetectors are relatively less available, FD-OCT based on a frequency-swept source may be preferred. In this scheme, the A-line scan rate is not limited by the low read-out speed of a typical array detector and can be increased to >100 kHz. In addition, it can take an advantage of dual balancing detection to minimize the effect of the intrinsic relative intensity noise of a light source [6, 7]. In the frequency-swept source, the fundamental limitation of the sweep speed caused by the finite laser build-up time has been alleviated by using the Fourier-domain mode locking (FDML) technique introduced by Huber et al. [7]. They have recently demonstrated a 370-kHz A-line scan rate using a buffered FDML ring laser. However, the technical sweep rate limit of an optical band-pass filter used in this approach becomes an obstacle to obtain a higher sweeping speed that may be required in some applications. Because the filters usually rely on internal mechanical motion, reliability issues may also occur. Moreover, the maximum wavelength sweeping range of a frequency-swept laser is limited by the bandwidth of a gain medium, and is normally narrower than 100 nm. Thus, the typical axial resolution of an SS-OCT obtained with this source is >10 µm and has limited the diagnostic ability of this technique so far.

In this letter, we report on a stretched-pulse OCT (SP-OCT) scheme as an alternative ultra-high-speed OCT technique that is based on using a stretched pulse supercontinuum source. Instead of using a broadband CW light source or a frequency-swept laser source, we have utilized a wide-band supercontinuum pulse source of which output pulse is stretched in the time domain by a long dispersive single-mode fiber. With the pre-calibrated time-wavelength relationship of the generated stretched pulse, we can measure the spectral interferogram in the time domain with a high-speed photodetection system. The light source does not contain any moving part inside, and consequently, it is able to exhibit a very high effective frequency-sweeping rate. Since the sweeping mechanism is truly passive, the frequency-time relationship is substantially stable, and does not require any re-calibration process. Using a filtered supercontinuum that spanned a wavelength range from 1,200 to 1,550 nm, a frequency sweep rate of 5 MHz was achieved in our experiments. The effective sweep rate was more than 10 MHz, considering that the blank interval between the successive stretched pulses was >100 ns. Ultra-high-speed reflectometry and tomography with a 5-MHz axial-line rate were demonstrated with this SP-OCT scheme. It took only 60 ns to acquire the data of an A-line in the experiment. According to the best of our knowledge, this speed is over ten times higher than the previous maximum record. The measured axial resolution was 8 µm in air. Using a supercontinuum source of wider output bandwidth would further enhance the resolution with ease in this scheme. The sensitivity of the system was measured to be approximately -40 dB. The poor sensitivity originated from the significant intensity noise of the supercontinuum used in our experiments. The scheme of Fourier-domain reflectometry and OCT that is proposed in this report can be used in applications where higher speeds and better resolution are needed.

2. Principle

The key characteristic of an FD-OCT system is determined by the scheme that is used in measuring the interferometric spectrum. The A-line data of FD-OCT is basically a spectral interferogram of a Michelson interferometer, and the axial reflectance profile of a sample is obtained by doing inverse Fourier transformation of the interferogram. In an SD-OCT system, it is obtained in the spectral domain with a spectrometer. On the other hand, the interferometric information is obtained in OFDI with a priori knowledge of the source’s sweeping characteristic. Tong et al. have introduced an interesting spectrum measurement technique that measures the spectral response in the time domain using a stretched wide-band pulsed source [13]. This spectrum measurement technique known as time-wavelength spectroscopy has been applied in fiber dispersion measurements, gas sensing and microwave photonic signal processing [13, 14]. Figure 1 is a schematic diagram that shows the basic principle of the time-wavelength-domain spectrum measurement technique. An ultra-wideband short pulse from a supercontinuum (SC) source is stretched to a long pulse with a dispersive fiber in the time domain. As the pulse propagates through the dispersive fiber, the spectral information in the wavelength domain is conveyed to the amplitude in the time domain with help of the group-velocity dispersion. The spectral information can be acquired by a photodetector (PD) in the time domain using the pre-calibrated relationship of the wavelength-to-time conversion that is produced by the dispersive fiber. Therefore, the spectral measurement is done in the time-wavelength domain. The spectral response of an optical system can be measured by placing this unknown system before the PD with ease. Because the time-wavelength-domain spectrum measurement scheme does not rely on any moving parts or a multi-channel detector, the measurement speed is limited only by the photodetection system and can be very high.

 

Fig. 1. Basic principle of the time-wavelength-domain spectrum measurement technique: The amplitude of a wide-band pulse is acquired in the time domain after being stretched by a dispersive fiber with the pre-calibrated data of the time-to-wavelength conversion.

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When a wide-band short pulse is transmitted through a dispersive fiber, each wavelength component experiences a characteristic group delay that is dependent on its wavelength. The group delay, τ(λ), as a function of wavelength can be expressed as

where L and D(λ) are the fiber length and the dispersion coefficient of the dispersive fiber, respectively, and τ₀ is a group delay for a reference wavelength, λ₀. This relation between τ and λ can be obtained experimentally by time-of-flight measurements using a monochromator. After being stretched, a wavelength component of the pulse at λ with an infinitesimal bandwidth of Δλ occupies a characteristic time slot of width Δτ with temporal delay τ in the time domain as

holds. This stretched optical pulse is converted to a current pulse by a photodetector according to the opto-electronic conversion rate of ε=hν·Q/ηq, where ε is the optical energy, h is Planck’s constant, ν is the optical frequency, Q is the generated photo-charge, η is the quantum efficiency and q is the electron charge. Therefore, the energy spectral density, s(λ) for the optical pulse can be converted into photo-current, i(τ)≡Q(τ)/Δτ as

Neglecting the slowly varying contribution of hνLD/ηq, the spectral fringe in the wavelength domain is converted directly to the fringed photo-current in the temporal delay domain.

The information of the reflection points in the proposed SP-OCT can be acquired by this time-wavelength spectroscopy technique with a Michelson interferometer. The reflection profile is obtained by doing inverse Fourier transformation of the acquired spectral interferogram. The principle of data processing in the SP-OCT system is almost same as OFDI systems that use frequency-swept lasers [3, 4, 6–10]. Let us suppose that there is a single reflection point of complex reflectance r·exp(jφ) at a point of the sample arm of an OCT interferometer where the optical path difference is 2·z with respect to the mirror of the reference arm. Since the path difference between the reference arm and the sample arm of the interferometer is usually smaller than 5 mm in OCT, the relative temporal delay between the pulses transmitted through the two arms is less than 20 ps, even smaller than the response time of the photodetector used in the signal acquisition. Thus, we can use a single time coordinate, t=τ+τ_mi to express the total field at the output port of the Michelson interferometer, where τ_mi is the additional temporal delay that the Michelson interferometer makes. When $E_{\mathit{input}}=\sqrt{P\left(\tau \right)}·\exp \left(j\left(kz\prime -\omega \tau \right)\right)$ is inputted to the interferometer, the output field can be expressed as

where T_r and T_s are the absolute value of the optical power transfer characteristics from the input to the output port of the interferometer via the reference arm and the sample arm, respectively, and k(t) is the wave number which is varied in time monotonically according to the group delay characteristic of the dispersive fiber. For a small path difference, the frequency-dependent spectral interferogram generates sinusoidally modulated photo-current, i(t) in the temporal delay domain as

The optical transfer functions; T_r and T_s as well as η and ν are originally functions of wavelength but can be translated to those of time delay, t by Eq. (1). The third term in Eq. (5) contains the information of the reflection point and makes the desired interferometric fringe. Because k(t) is a nonlinear function of t, the sinusoidal photo-current interferogram must be chirped nonlinearly. So, the obtained data should be converted to the wave-number domain using the pre-calibrated time-wavelength conversion of Eq. (1) and should be re-sampled with equally spaced wave numbers before doing discrete Fourier transformation.

The depth range of the SP-OCT system is determined by the finite response time of the photodetector as well as the instantaneous line-width of the source. The resolution bandwidth in the viewpoint of spectrum measurement is closely related to the depth range. The spectral resolution is defined as the minimum resolvable wavelength spacing of two clearly distinct spectral components in the time-wavelength spectrum measurement scheme. The limiting factor for resolving these components comes from the initial pulse-width of the supercontinuum pulse and the finite response time of the photodetection system. Thus, even by neglecting the internal dispersion of the two componential pulses by minimizing the bandwidths of the components, the photodetection system will receive two electric pulses with a finite pulse-width of

where δτ_sc is the initial pulse-width of the supercontinuum pulse, and δτ_pd is the impulseresponse pulse-width of the photodetection system. The two pulses can be resolvable only if the temporal spacing between them is larger than δτ. From Eq. (2), the resolution bandwidth, δλ of the time-wavelength spectroscopy system can be written as

Note that the resolution bandwidth is a function of group-velocity dispersion that depends on the wavelength in this equation. The resolution of the time-wavelength-domain spectrum measurement corresponds to the instantaneous line-width of a frequency-swept source in OFDI. The instantaneous line-width of the stretched supercontinuum pulse is equal to the resolution bandwidth if the bandwidth of the photodetection system is even wider than the modulation bandwidth of the initial supercontinuum pulse so that δτ_pd≪δτ_sc. Because the sweep rate is too high in our SP-OFDI system, we can not neglect the finiteness of the photodetector bandwidth. Based on the convention of the maximum depth range of OFDI [3], the effective axial range Δz_eff can be defined as

where λ_c is the center wavelength of the source. Approximately, the effective axial range, Δz_eff corresponds to the path difference or axial depth where the reflection response decreases to the half, comparing to the zero-path-difference region.

3. Stretched supercontinuum pulse source

We had previously reported a pulsed supercontinuum source based on an amplified diode-laser pulse (ADP) source and a dispersion-shifted fiber (DSF) [15]. The pulse source was originally generated by gain-switching a laser diode operating at 1,550-nm wavelength, and was amplified by triply concatenated erbium-doped fiber amplifiers (EDFAs) to obtain a high peak power. All the parts inside the source are widely available fiber-optic components so that the system is cost-effective and exhibits good reliability. Moreover, the ADP source has an advantage in producing pulses with an arbitrary repetition rate. The same type of supercontinuum source based on ADP pumping was used in our experiments of this report. The configuration of the source is identical to that used in our previous research described in Ref. 15 except that the DSF was replaced by a 20-m highly-nonlinear dispersion-shifted fiber (HN-DSF) to obtain a higher supercontinuum output power. The repetition rate of pulse generation was set to 5 MHz and the pulse period was 200 ns. Since the full width of the stretched pulse was less than 70 ns, and the blank interval between the successive stretched pulses is >100 ns, the effective frequency sweep rate was more than 10 MHz. We have observed that the output spectrum covered a wide wavelength range from 1,200 nm to 1,770 nm that is the maximum measurable wavelength of our optical spectrum analyzer.

 

Fig. 2. (a). Spectrum of the filtered supercontinuum after passing through the 20-km DSF and (b) the measured relative time delays according to the wavelengths.

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A 20-km DSF (Sumitomo) that complies ITU-T G.653 standard for fiber-optic communications was used to stretch the supercontinuum pulse. The zero-dispersion wavelength (ZDW) of the DSF was 1,547 nm and the dispersion slope at the ZDW is 0.066 ps/nm².km. The propagation speed of an optical spectral component at the ZDW is the highest in the fiber. Therefore, there is two-fold ambiguity between wavelength components below and above the ZDW in mapping temporal delay onto wavelength for the stretched supercontinuum pulse made with the DSF. There is always another wavelength above the ZDW that exhibits a time delay identical to that of a given wavelength below the ZDW. A short-wavelength-pass filter (SWPF) utilizing bending loss of a single mode fiber was employed to avoid this problem by eliminating the long-wavelength spectral part beyond the ZDW. The rejection of the filter was measured to be more than 50 dB at wavelengths beyond 1,600 nm. Figure 2(a) shows the spectrum of the filtered supercontinuum measured with an optical spectrum analyzer (OSA). The filtered output still spanned a wide wavelength range from 1,200 to 1,550 nm with a 200-nm FWHM spectral bandwidth. The time-to-wavelength conversion relation was measured and calibrated as shown in Fig. 2(b). The blue solid line shown in Fig. 2(b) represents the 4th-order polynomial fitting curve of the measured data that are denoted by the black rectangular points. The data were measured using a monochromator with a 10-nm resolution bandwidth and an oscilloscope with 4-GHz bandwidth in addition to a 10-GHz bandwidth photodetector. The reference time, or ‘0 ns’ on the Y-axis of Fig. 2(b), is the arrival time of the 1,550-nm component i.e. the residual pump pulse. As can be seen in Fig. 2(a), there was a small distinct peak at 1,550 nm in the spectrum due to the residual pump that would also appear as a small peak in the time domain, right after the leading edge of the stretched pulse, because the time delay is nearly minimal at this wavelength. This leading pulse was used as a time-alignment flag in our experiments. This method reduces timing errors that are possibly caused by temperature-induced delay variations of the dispersive fiber.

The resolution bandwidth of the time-wavelength-domain spectrum measurement was calculated by using the data of Fig. 2(b) from Eq. (6) and Eq. (7). We had δτ_sc≅200 ps for the initial supercontinuum pulse-width and δτ_pd=110 ps for the photodetection system. From Eq. (4), the time-domain resolution was calculated to be δτ=228 ps. Based on the slope of Fig. 2(b), the dispersion is estimated to be LD(λ)=0.376 ns/nm for λ=1,250 nm and 0.107 ns/nm for λ=1,450 nm. We have obtained δλ=0.61 nm at λ=1,250 nm and δλ=2.1 nm for λ=1,450 nm. The effective axial range was calculated by using Eq. (8) and also varied with wavelength. It was calculated to be 0.8 mm at 1,250 nm, and 0.2 mm at 1,450 nm when λ_c=1,350 nm. Thus, as the axial depth, z increased, the reflection response must have decreased smoothly to z=0.8 mm and thereafter decreased more rapidly beyond this depth. This means that the axial resolution must have worsened for deeper points as available effective optical bandwidth collapsed. Because of this complex nature caused by the non-uniform resolution bandwidth properties of the spectrum measurement scheme, the performance could differ by the observation depth. A depth range from 0.3 to 0.6 mm was used in the experiments. So, the axial resolution and sensitivity must have been degraded slightly with respect to the potential values of the 0-to-0.3-mm depth range.

4. Experimental setup and results

A fiber-optic Michelson interferometer was constructed to test the feasibility and the performance of the SP-OCT. Figure 3(a) shows a schematic diagram of the experimental setup, and Fig. 3(b) shows an example of time-domain interferogram captured by an oscilloscope when there is a single reflection point at the sample arm of the interferometer. A 3-dB fused-fiber coupler split the stretched supercontinuum pulse into the reference and sample arms of the interferometer. In the sample arm, the objective lens focused the beam onto the sample with a focusing NA, ~0.15. A polarization controller (PC) was put on the sample arm just before the objective lens to adjust the state of polarization. With the adjustable free-space optical delay in the reference arm, the path length difference was also adjusted so that the reference arm was slightly shorter than the sample arm. The length difference was analyzed to be ~0.2 mm. A 4-GHz-bandwidth real-time oscilloscope (TDS7404, Tektronics) in combination with a 10-GHz-bandwidth InGaAs photoreceiver (DSC-R402-PIN, Discovery Semiconductors) that equips an internal electric amplifier with a 500-V/A transimpedance was used to detect interferometric spectral information in the time domain. The sampling rate was 20 giga-samples per second (GS/s) and the acquisition resolution was 8-bit (256-level) for the oscilloscope. The average power of light source was 7.2 mW before the DSF, 1.5 mW after the DSF and ~0.4 mW at the sample. As shown in Fig. 3(b), the reflected light from a single reflection point generated a sinusoidal fringe with a nonlinear chirp as predicted in Eq. (5). A small peak highlighted by an arrow at 0 ns in Fig. 3(b) corresponding to the residual 1,550-nm pump pulse was used as the time-alignment flag. A computer received raw time-domain data from the oscilloscope and carried out the post-processing of discrete Fourier transformations (DFT) with a Hanning window to retrieve the length-domain reflection response. The 4th-order polynomial fitted curve of the time delay up to 60 ns in Fig. 2(b) was used to convert the time-domain data into the wavelength-domain ones. The oscilloscope could record up to 200,000 data points at 20-GS/s sampling rate, which correspond to 50 axial lines for the 5-MHz sweep rate of the source.

 

Fig. 3. (a). Schematic diagram of the experimental setup and (b) an example of the oscilloscope trace captured with a single reflection point at the sample position.

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Fig. 4. Measured reflection profile of a ~20-µm thick transparent plastic film placed on a thick glass plate.

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In order to evaluate the basic performance of our SP-OCT system, we have tested an object with a simple one-dimensional structure: 20-µm thick transparent plastic film placed on a thick glass plate. Figure 4 shows the measured reflection profile for this sample. The reflection points at 380 and 410 µm correspond to the upper and lower faces of the film, respectively. The reflection point at 450 µm corresponds to the upper surface of the glass plate. The raw data were acquired within an interval of 60 ns and were composed of ~1,200 data points. As seen in Fig. 4, the resolution was estimated to be 8 µm in air while the theoretical resolution limit is slightly less than 4 µm for our supercontinuum source. The chromatic dispersion imbalance between the arms, applying Hanning window for DFT and the limited available effective bandwidth for the ~400-µm-deep regions that was mentioned in the previous section, are responsible for the degradation in axial resolution.

The sensitivity of our SP-OCT system was also measured using a glass surface with approximately -15-dB reflection. Figure 5 shows (a) the point spread function (PSF) of a -15-dB reflection point and (b) the system noise with no optical input in dB. The sensitivity of our SP-OCT system was about -40 dB while the noise level of our photodetection system was about -60 dB. This difference of 20 dB was thought to come from the intensity noise of the supercontinuum source. Although the multi-shot averaged spectrum measured by an OSA looked smooth and exhibited no fine structure as seen in Fig. 2(a), each single-shot spectrum was found to have randomly varying fine structures or intensity fluctuations, as Gu et al. had also found in their experiments [16]. A dual-balanced detection that is commonly used in many OCT systems may be adapted to reduce the effect of the intensity noise.

 

Fig. 5. (a). PSF of a -15-dB reflection point and (b). the system noise with no optical input in dB.

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Fig. 6. (a). Obtained tomographic image (50 A-lines) and (b) a microscope image of lint-free paper. The data of the tomogram was acquired within a period of 10 µs with an A-line scan rate of 5 MHz.

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Two-dimensional (2D) OCT imaging was demonstrated by applying a transverse movement to a sample. Because of the poor sensitivity, our system was not able to obtain an image of a biological sample with a reasonable image quality. Instead, a piece of lint-free cleaning tissue was used as a sample for its relatively strong reflection and micron-scale structure. The tissue sample was sandwiched by an ~20-µm thick transparent plastic film and a thick glass plate. Figure 6(a) shows the tomographic image composed of 50 A-lines, and Fig. 6(b) shows a wide-field microscope image of the lint-free cleaning tissue sample. The complete data for the tomogram were acquired within a period of 10 µs with an A-line scan rate of 5 MHz. To improve the image quality, five adjacent lines were averaged for each A-line. A graph shown just below the 2D image of Fig. 6(a) is the measured reflection profile of the last A-line without averaging. X-axis in Fig. 6(a) represents the depth range, which is the optical path difference. In the 2D image or in the A-line plot of Fig. 6(a), the clear lines at axial positions of 410 and 440 µm correspond to the upper and lower surfaces of the covering plastic film, respectively. Fiber fabrics of the tissue were observed in axial depth range from 450 to 500 µm. A fuzzy straight line in the 2D image at 510-µm axial position corresponds to the upper surface of the glass plate.

5. Conclusion

We have demonstrated SP-OCT, a new approach for an ultra-high-speed FD-OCT imaging methodology by using a stretched supercontinuum pulse source. An ultra-wideband pulse source based on supercontinuum generation in addition to a dispersive fiber generates stretched pulses that can be used as frequency-swept light for OCT imaging. It has been verified experimentally that extremely high speeds in A-line acquisition rate can be obtained using this kind of light source. An OCT system with 5-MHz A-line acquisition rate was demonstrated. The axial resolution and sensitivity were 8 µm and -40 dB, respectively. It is expected that the SP-OCT can achieve superb resolution with ease because it can utilize an ultra-wideband supercontinuum source. Moreover, as there is no moving part both in the source and in the interferometer system, this scheme provides a high acquisition speed and good reliability. The re-calibration of the sweep characteristics that is usually required in the other OFDI systems is not essential in our method, since the sweeping mechanism is truly passive. Because of the low sensitivity and narrow depth range, the application of this proposed SP-OCT would be limited in monitoring a fast process or an interaction that does not require a high sensitivity and long axial range. The problem of the poor SNR is expected to be solved by adopting a low-noise wide-band pulse source or an improved technique of noise cancellation in signal processing. And the axial range can be increased if more efficient stretching method is developed. This technique can be used in studying rapidly occurring phenomena that should be captured in a short time with a high resolution. And microsecond dynamics can be analyzed with the high-speed reflectometer based on this scheme.