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Abstract
Linear-wavenumber swept-source optical coherence tomography (SS-OCT) enables real-time, high-quality OCT imaging by eliminating the need for data resampling, as required in conventional SS-OCT. In this study, we introduced a high-performance linear-wavenumber swept source (k-SS) with a broad scanning range and high output power. The linear k-SS is an acousto-optic-modulator-based external-cavity laser diode analogous to the Littrow configuration. The k-SS exhibits strong linearity in the 1.3 µm region, justified by a high goodness of fit R2 value of 0.9998. Additionally, its scanning range, output power, and linewidth are 120 nm, more than 43 mW, and approximately 1.6 nm, respectively. The sweep rate is 280 Hz after the linear k compensation of the experimental equipment. We demonstrated the effectiveness of the linear k-SS by applying it to measure a sample distribution without k-domain resampling before the Fourier transform. This successful implementation indicates that the linear k-SS has practical potential for application in SS-OCT systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical coherence tomography (OCT) is an optical imaging modality that enables noncontact, high-resolution, and noninvasive optical imaging in the medical [1–4], biological [5–7], industrial [8–10], and archeological fields [11]. OCT provides information on the internal microstructure by analyzing the time delay or phase difference in an interference signal, which is caused by the constructive interference between the signal from an object under investigation and a local reference signal. Recently, swept source (SS) OCT has emerged as the preferred method for real-time and three-dimensional OCT imaging. This method employs high wavelength scanning, making it possible to realize high-speed data acquisition. Therefore, the measurement time in SS-OCT is much faster than that in time-domain OCT, which necessitates mechanical movements. Furthermore, SS-OCT provides a longer imaging depth range and better detection sensitivity compared with spectral-domain OCT. Therefore, in SS-OCT systems, an advanced SS must operate in a broad wavelength scanning range and with a narrow linewidth and high sweep speed.
Numerous types of SSs have been reported, and their development has been strongly linked to the performance of SS-OCT systems. Most SSs consist of a broadband gain medium and wavelength filter in a laser cavity. External-cavity laser diodes (ECLDs) are primarily used as SSs because they have a simple configuration, broad scanning range, and allow continuous wavelength scanning. ECLDs operate using either the Littrow or Littman configurations, and their specifications are strongly affected by the external cavity. In the Littman configuration, an ECLD requires a grating and an additional mechanically controlled mirror [12,13]. In contrast, in the Littrow configuration, an ECLD includes only a grating within a cavity, and the first-order diffracted light from the grating is coupled back to the resonant cavity [14]. This configuration experiences only one diffraction at a grating, resulting in minimal losses and enhancing the efficiency of optical feedback. Therefore, the Littrow configuration is used to achieve an overall high output efficiency. Importantly, the Littrow configuration allows the light beam travels back along the same path, contributing to the stability of the optical cavity of the laser. Wavelength scanning is performed by simultaneously rotating and translating an external grating [14–17]. Thus, it is challenging for conventional bulky equipment to achieve high sweep rates and increased reliability, such as rotating wedge prisms [18], polygon mirrors [19], and microelectromechanical system scanner mirrors [20]. Thus, these technologies exploit complex mechanical scanning methods that degrades the overall stability and reduces the sweeping speed of ECLDs, whether in the Littman or Littrow configuration. Conversely, ECLDs do not use mechanical motion have been proposed: a Littman configuration that uses a potassium tantalite niobate (KTN) single crystal [21], an acousto-optic (AO) device [22,23], and a liquid crystal pixel mirror (LCPM) [24]. And Littrow-type ECLDs consisting of a electro-optical (EO) prism [25], electro-optical crystal [26,27], and AO filter [28–30] are proposed. EO and AO techniques rely on the changes of the refractive index of the material caused by electro-magnetic and acousto-optic effects, respectively. These non-mechanical scanning methods are free of drawbacks associated with mechanical devices, such as mechanical noise and vibration, wear and tear.
In SS-OCT systems, sample depth information is derived from the detected interference signals using the Fourier transform. Maintaining uniformity in the wavenumber and imaging depth during the Fourier transform [31] requires the resampling of interference signals to ensure uniform sampling in the wavenumber-domain. Hence, a linear-wavenumber SS with no wavenumber-domain resampling can feasibly realize real-time OCT imaging.
Several studies have been performed to achieve linear-wavenumber sweep in different types of SSs, including those on the Fourier domain mode-locked laser (FDML) [32], microelectromechanical-systems-based vertical-cavity surface-emitting lasers (MEMS-VCSELs) [33,34], Vernier-tuned distributed Bragg reflector (VT-DBR) laser [35], and active mode locking fiber laser [36] for OCT systems. In FDML and MEMS-VCSEL lasers, the optimum driven waveforms applied to the mechanically tuned filters are complex, and the additional nonlinear response of the filters during high-speed sweeping should be considered. In the absence of mechanical motion, VT-DBR in [35] used a spectral calibrated current drive waveform to achieve linear wavenumber sweep (using an optical spectrum analyzer). Moreover, in [36], the linear-wavenumber sweep also required an optimal driving waveform obtained using an algorithm. Although an ECLD using an AO deflector (AOD) has been demonstrated to achieve a linear-wavenumber sweep in [37], and its wavelength scanning range is limited by the fixed grating, as discussed in Section 2.
A simple SS design with the AO is employed for achieving a broad wavelength scanning range. Yumoto [38] and Lyakh [39,40] presented a tunable laser for potential applications in spectroscopy, infrared standoff detection, and combustion/explosion diagnostics. However, the wavenumber linearity characteristics of all these acousto-optic-based swept sources have not been sufficiently discussed in relation to SS-OCT imaging. In addition, we have recently demonstrated an SS design that uses an AOD as a tunable grating [41], wherein the theoretical wavelength scanning is exclusively dependent on the acoustic frequency. In this study, we focused on the wavelength tunability of this tunable grating type SS that uses an AO modulator (AOM) instead of an AOD and reported a linear-wavenumber SS (k-SS, $k = \frac{1}{\lambda }$) in the 1.3 µm region. A linear-wavenumber SS is simply realized by linearly varying the driving frequency of the AOM utilized in the system. The sweeping behavior is determined by using a fully electrical signal without a mechanical mechanism. Consequently, we can easily control the wavenumber (e.g., linear-wavenumber sweeps for OCT imaging). We used the proposed k-SS to measure a sample distribution without k-domain resampling before the Fourier transform.
2. ECLD principle and simulations
Figure 1 shows the evolution of the SS in the Littrow configuration using a laser diode (LD) as the gain medium. The principles that govern wavelength scanning in the typical ECLD configurations are described below.
Fig. 1. Evolution of the ECLD in the Littrow configuration. (a) Classical mechanical tuning system. (b) Conventional acousto-optic tuning system. (c) Proposed ECLD analogous to the Litrrow type. LD, laser diode; G, grating; PZT, piezoelectric transducer; AOD, acousto-optic deflector; AOM, acousto-optic modulator; M, mirror.
A classical Littrow ECLD configuration consists of a movable grating that revolves around a fulcrum using a pair of PZTs, as shown in Fig. 1(a). In this configuration, the incident angle is equivalent to the diffraction angle. Therefore, the equation for the diffraction grating is expressed as
where λ is the wavelength, d is the groove pitch, and θi is the incident angle. If light is incident on the grating at an angle that varies as a function of Δθi, the resonant wavelength in the external cavity changes according to when the grating revolves by Δθi. By subtracting Eq. (1) from Eq. (2), we observe a wavelength shift caused by the rotation of the grating, which is given byThe wavelength is varied by controlling the incident angle using the revolving grating.
An improved ECLD-based AOD is shown in Fig. 1(b). The AOD is driven by acoustic waves induced by an externally applied radio frequency (RF) signal. In addition, it is characterized by the Bragg angle, which is strongly exaggerated for visual clarity and is expressed as
where fa and va are the frequency and velocity of the acoustic wave traveling through the AOD, respectively. The variation in the incident angle of the grating caused by the first-order deflected beam of the AOD is referred to as the deflection angle due to the deviation in the applied frequency (Δf) from the Bragg condition. We can represent this variation asThen, the resonant wavelength in this configuration is expressed as
The grating acts as a wavelength-selective device, as shown in Figs. 1(a) and 1(b). In these configurations, the wavelength-scanning process involves a complicated relationship between the wavelength and modulation parameters, as expressed by Eqs. (3) and (6). However, it is achieving linear wavenumber sweeping for an SS is challenging. We addressed this by introducing a simpler configuration, as shown in Fig. 1(c). The key device in this configuration is an AOM, which acts as a transparent grating. The AOM adjusts its grating constant using an external control signal. We used an inexpensive AOM over an AOD because the output beam from the AOM is not deflected in space, allowing for the use of a fixed cavity. First, the light emitted from the LD (antireflection LD) is incident on the AOM at angle θB. Subsequently, the 1st diffraction beam of the AOM is deflected by 2θB and is perpendicularly incident on the mirror. Finally, the beam reflected from the mirror retraces its path and returns to the LD. This process completes the optical resonator, leading to the amplification of the light beam. In principle, the wavelength can be tuned based on the transmission-type Littman system because the terminal reflector is a mirror. However, the configuration is analogous to the Littrow system because the optical path maintained. Since the Bragg conditions are maintained in the AOM, Eq. (4) shows that λ and fa are concurrent variables in the cavity. If we set an initial pair of variables (λ0 and f0) that satisfy the Bragg condition and substitute the Bragg angle in Eq. (4), we can derive the following simple relationship:
Consequently, the wavenumber is directly proportional to the frequency of the acoustic wave, which can be expressed as
Equation (8) indicates that we can linearly sweep k by linearly varying the frequency (fa) applied to the AOM. Generally, the AOM driver has a hardware limit for linearly increasing the frequency; therefore, we must compensate for the nonlinear process. This is discussed in Section 3.2.
Figure 2(a) shows the calculated wavelength scanning ranges of the conventional and proposed ECLDs. We used a grating groove pitch of d = 1/600 mm, θi = 22.02°, λ = 1308 nm, fa = 76 MHz, and va = 667 m/s in Eq. (6) to calculate the wavelength scanning range of the conventional ECLD. Equation (7) is used to calculate the scanning range of the proposed ECLD, where λ0 = 1308 nm and f0 = 76 MHz. Thus, the Bragg angle is 4.3°. The wavelength scanning range of the proposed system is approximately three times that of the conventional system. This is because the magnitude of the wavelength scanning range is determined by the frequency of the acoustic wave applied to the AO device. In the conventional system, the frequency of acoustic wave is confined within the phase component of the sinusoidal function [Eq. (6)], leading to a limited and narrow wavelength scanning range. In contrast, in the proposed system, the frequency is inversely proportional to the wavelength [Eq. (7)], allowing for a broader wavelength scanning range.
Fig. 2. Theoretically calculated wavelength and wavenumber versus the frequency of the acoustic wave applied to the AO device. (a) Wavelength range of conventional and proposed ECLDs and (b) wavenumber distribution.
Figure 2(b) shows the calculated wavenumber sweeps of the conventional and proposed ECLDs. The simulation results prove that the wavenumber linearly varies with the frequency for the proposed ECLD, as predicted by Eq. (8).
As analyzed above, the proposed ECLD configuration in the evolutionary stage (Fig. 1), provides numerous advantages over its predecessors. For instance, (1) it provides a reliable and high-speed k-linear sweep, (2) the optical cavity is fixed because the Bragg condition is consistently maintained in the AOM across various wavelengths, and (3) the optical feedback in the cavity is stable and better than that of the conventional ECLD, as shown in Fig. 1(b). This is because the reflectivity of the mirror is almost constant for different wavelengths and considerably larger than that of the grating.
3. Experimental methods and results
3.1 Experimental setup
Figure 3 illustrates the configuration of the OCT system with the ECLD as the SS. The ECLD consists of a single-angled facet gain chip (Thorlabs, SAF1174S) whose tuning range is 130 nm at a center wavelength of 1310 nm, an external cavity formed by a molded aspherical lens (Edmund, 83607), AOM (ISOMET, OAM1060-T80L-3), and mirror.
Fig. 3. (a) Experimental setup. (b) Extraction of the interference signal from a sequence of images. LD, laser diode; AOM, acousto-optic modulator; M, mirror; SMF, single-mode fiber; MO, micro-objective; BS, beam splitter; RM, reference mirror; S, sample; T, transparent tape; G, cover glass.
The light emitted by the LD (antireflection LD) is collimated by the lens before entering the AOM. The AOM diffracts a first-order beam, which is perpendicularly incident on a mirror. The beam reflected by the mirror passes through the AOM, and a new first-order diffraction beam from the AOM is fed to the LD. Then, the optical resonator is completed, and the light beam is amplified. Finally, the amplified light is coupled to a single-mode optical fiber as the SS. The LD is driven with a constant current of 400 mA and maintained at 24 ± 0.1°C.
A Michelson interferometer is used to examine the performance of the proposed SS. It consists of a beam splitter, reference mirror, and homemade sample. This sample consists of a single layer of transparent tape that adheres to a piece of cover glass. A charge-coupled device camera is used to capture fringes.
3.2 Performance of the SS system
We examined the performance of the SS, including the wavelength scanning capability, linewidth, output power, and k-linearity.
The wavelength was examined using an optical spectrum analyzer with a wavelength resolution of 0.005 nm. Figure 4(a) shows that the sweep range is 1240.9–1361.5 nm. The wavelength scanning range is 120 nm without mode hopping. A single spectrum is observed at a center wavelength of 1331.4 nm, and the peak power is 42.9 mW, as shown in Fig. 4(b). The linewidth of the spectrum is 1.6 nm at the full width at half maximum.
Fig. 4. Normalized spectra observed during wavelength scanning. (a) Scan data for the entire wavelength range. (b) Single power spectrum at the center wavelength of 1331.4 nm.
The wavenumber sweep of the proposed ECLD is entirely governed by the AOM driven exclusively by electrical signals. Thus, it demonstrates real-time k-linearity when the AOM varies linearly. Nevertheless, in a practical experiment, we observed a quadratic relationship between the AOM frequency and linearly varying applied voltage, as shown in Fig. 5(a). This relationship is caused by the nonlinearity of a varicap diode used in the AOM driver. To compensate for this nonlinearity, a digital look-up table installed on a microcomputer can be used. Consequently, a linear distribution of the AOM frequency is obtained, as shown in Fig. 5(b). The maximum scanning rate is confirmed to be equal to 280 Hz under the compensation condition.
Figure 6 shows the measured results of the wavelength scanning and k-linearity distribution for the proposed ECLD system. The measured results of wavelength scanning are in good agreement with the theoretical calculation results. Figure 6(b) shows the results of the k sweep based on the proposed ECLD, and the goodness of fit (R2) is 0.9998. The residual values for each measured wavenumber of the frequency of radio frequency varies between 0.0008 µm-1 and -0.0004 µm-1, as shown in Fig. 6 (c). When the SS has a high wavenumber linearity, it enables real-time imaging without an additional process for the k-linear resampling of the interferometric signal to ensure high-quality OCT imaging.
Fig. 6. Experimental measurement results of wavelength and k versus frequency of the acoustic wave applied to the AOM. (a) Wavelength of the proposed ECLD based on the theoretical calculation shown in Fig. 2(a). (b) k distribution, and (c) residual values.
3.3 Performance evaluation of the OCT using the proposed SS
We applied the ECLD to set up an SS-OCT system to verify its performance as an SS. Figure 3 presents the details of the SS-OCT system. The thickness of the sample is 0.198 mm (tape: 0.050 mm, glass: 0.148 mm), as obtained using a mechanical micrometer with a resolution of 10 µm. The refractive indices of the tape and glass are 1.50 (n1) and 1.51 (n2), respectively. Figure 7 shows the detailed structure of the sample. Light is incident on the sample on three different surfaces, and the beams reflected from these surfaces interfere with the light from the reference arm, resulting in interference signals (L1, L2, and L3) that contain optical path difference (OPD) information. These reflected beams also interfere with each other, causing self-interference signals whose OPDs are denoted by differences [L31 (L3-L1) and L23 (L3-L2)].
Fig. 7. Detailed structure of the sample. T, transparent tape; G, cover glass; ni = 1,2 and ti = 1,2 represent the refractive indices and thicknesses of the tape and cover glass, respectively; Li = 1,2,3, indicate interference signals containing optical path difference information from different surfaces; L23 and L31 are self-interference signals containing optical path differences between surfaces 2&3 and surfaces 3&1, respectively.
To detect a clear fringe, the wavelength tuning range is restricted to 1262.4–1358.4 nm, and the AOM is driven by a compensated RF signal with a frequency in the range of 73.07–78.89 MHz, as shown in Fig. 5(b). A k-linear sweep is realized using the compensated RF signal, and 256 interferograms are captured using a camera (ARTCAM-991SWIR-TRG) with a resolution of 65 × 75 pixels. The pixel size is 5 × 5 µm. The SS scanning speed is restricted by the frame rate (60 ms) of the camera in this experiment. The one-dimensional (1D) interference signal is generated by tracing the intensity at the same coordinates across all the 256 interferograms (orange dots), as shown in Fig. 3(b).
Figure 8(a) shows an example of a 1D uniformly spaced interference signal with the linear k-SS. The Fourier transform (Fig. 8(b)) without the resampling of the interference signal shows three peaks that correspond to the OPDs in the interference between reflections from different internal surfaces and the reference arm (i.e., the peaks of L1, L2, and L3 at 0.1367, 0.2735, and 0.7152 mm, respectively). In addition, the peaks of L23 and L31 at 0.4417 and 0.5785 mm, respectively, represent self-interference within samples (L3-L2 and L3-L1). These five peaks are listed in Table 1. Since the value of L12 (L31-L23) is similar to that of L1, the peak of L12 appears to be superimposed on that of L1. The positions of the L12, L23, and L31 peaks agree with the differences between L2-L1, L3-L2, and L3-L1, respectively. These self-interference results are used to validate the experimental results.
Fig. 8. One-dimensional sample information of interference signal and imaging depth data. Examples of (a) interference signal and (b) its Fourier transform.
Table 1. Summarized measurement data along the optical path difference axisa
The thicknesses of the tape and glass in the sample are calculated as t1 = 0.0456 and t2 = 0.1463 mm, respectively, using the equations listed in Fig. 8(b). These results agree well with those obtained using the mechanical micrometer.
The 2D cross-sectional images of the samples are shown in Fig. 9. The OPDs are converted to the imaging depths using the refractive index of each sample. We can clearly distinguish the tomographic structure of the sample based on its detailed internal structural information shown in Fig. 7. These results demonstrate that the proposed SS is stable and applicable to OCT systems.
4. Conclusion
We developed a new design for an analogous to Littrow-type ECLD with the optimum SS features. Wavelength scanning and k-linear sweep were theoretically examined, and the ECLD was constructed to perform experiments. The scanning range was confirmed to be 120 nm at a center wavelength of 1310 nm. The linear k-SS with a high goodness of fit (R2= 0.9998) enabled OCT imaging without the k-domain resampling process before the application of the Fourier transform. The details of the tomographic structural information of the sample were distinguished from the sectional profile of a sample. With the resampling process being eliminated, a lower storage for large comprehensive data sets becomes feasible, and the imaging speed increases, paving the way for ultrafast real-time OCT systems. The scanning rate of the proposed SS is limited by the software that implements a digital look-up table. Future work will focus on optimizing the laser cavity design to further reduce the spectral linewidth. The scanning rate will be much improved by replacing the software with a hardware circuit or feedback control in the compensation path of the AOM driver.
Funding
Japan Society for the Promotion of Science (JP21K04922).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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