**1. Introduction**

Optical Coherence Tomography (OCT) is an established, non-invasive imaging modality, which uses low-coherence interferometry to obtain three-dimensional representations of translucent media. Having made its debut in ophthalmology, OCT is now widely used across many different medical imaging fields as well as for non-destructive testing [1]. OCT imaging can be achieved with both time- and frequency-domain detection, with the latter presenting significant improvements in imaging speed and noise performance over the former [2]. Frequency-domain detection in OCT can be implemented by either (a) sampling the output optical spectrum of the OCT interferometer driven by a broadband source using a spectrometer (spectral-domain OCT) or (b) sweeping a narrow frequency emission tuned within a wide spectral band and measuring the signal with a point photo-detector (swept source OCT).

One of the main strengths of swept-source OCT is the larger axial imaging range than can be found in spectral-domain OCT systems, enabled by the long instantaneous coherence length of the swept source. Recently reported swept-source implementations [3,4] demonstrated coherence lengths on the order of meters. However, swept-source OCT still lags behind spectral-domain OCT with respect to phase stability. Electrically tunable, all-semiconductor optical sources, such as the monolithic cavity one developed by Insight (Lafayette, CO, USA) employed in this work, are akinetic by nature, making them less prone to phase instabilities [5], while achieving long instantaneous coherence lengths (over 200 mm). Moreover, their tuning rate and tuning range can easily be reconfigured by

**Citation:** Marques, M.J.; Cernat, R.;Ensher, J.; Bradu, A.; Podoleanu, A.Akinetic Swept-Source Master-Slave-Enhanced Optical Coherence Tomography. *Photonics* **2021**, *8*, 141. https://doi.org/ 10.3390/photonics8050141

Received: 26 March 2021 Accepted: 21 April 2021 Published: 24 April 2021

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electronically changing the driving signal, allowing extra flexibility and high sweeping rates (over 600 kHz), meaning that the source has been successfully used in a number of previous studies [5–8].

The electrical tuning procedure employed by the swept source employed in this study is based on Vernier tuning of multiple sections within an all-semiconductor laser structure. Using this tuning mechanism, the laser may be swept over a wide wavelength range in a single longitudinal laser mode, with a linear sweep of optical frequency versus time within valid regions of the sweep. Although this procedure has its benefits, there are short (<10 ns), sporadic periods during the sweep where the optical frequency is not swept linearly as shown in Figure 1, corresponding to invalid data regions. These time periods repeat deterministically and therefore can be identified during the calibration routine prepared for each source and subsequentially eliminated. The laser generates a data-valid vector (DVV), which specifies the samples of the time-record that are valid, while the invalid data (which may account for 25% of the total samples in a 100 kHz spectral sweep) are removed from the output interferogram prior to the depth profile (A-scan) generation. An advantage of the akinetic source is that the valid data are already *k*-space linearised, meaning that once the invalid data are removed, no further k-space resampling or optical *k*-clock is needed prior to data processing. However, the removal procedure requires (i) a strict synchronous clock (provided by the control electronics in the optical source) and (ii) robust communication between the source and the digitising hardware to transfer the DVV after each source self-calibration.

**Figure 1.** (**a**) Channelled spectrum as acquired from the photo-detector in the OCT system with the optical source used in this study. (**b**) Zoomed version of (**a**), with the shaded regions denoting the portions of time when the optical frequency is not swept linearly, which are invalid and therefore removed based on the information carried by the data valid vector. (**c**) Phase of the interferogram (trimmed to one cycle) represented in (**a**), showing discontinuities (red arrows) pertaining to the portions of time when the optical frequency is not swept linearly.

Master–Slave OCT [9] (MS–OCT) processes the raw OCT data differently. Instead of employing a Fast-Fourier Transform (FFT), MS–OCT performs a comparison of the raw OCT data against either: (i) pre-recorded (or pre-generated) spectra for all axial positions considered [10] or (ii) against "live" spectra provided in real-time by a several optical interferometers using the down-conversion Master–Slave procedure [11] detailed below. Effectively, MS–OCT implements a "calibration" of the system that makes the whole operation tolerant to both the non-linear sweeping [9] as well as to the dispersion left uncompensated in the interferometer [12], enabling swept-source operation without a *k*-clock [13]. The Vernier tuning enables linear frequency sweeping in time; however, within the sweep there are short, deterministically located regions where the tuning is not linear with the optical frequency. This represents a different set of challenges from those tackled by the MS-based methods in the literature, hence the subject of this paper.

One aspect that is common to all SS-OCT implementations is that the resulting interferometric signal needs to be digitised in order to be processed and the resulting OCT volume rendered. In SS-OCT, the desire or need to image at greater depths demands a larger coherence length for the swept source. The larger the axial range, the higher the sampling rates of the data acquisition system, which drives up costs and electrical power consumption. Furthermore, if the frequency exceeds several GHz, the dynamic range suffers as the available digitizer bit depths for higher sampling rates are 8–10 bit only.

Beyond employing high-speed digitizer cards, other approaches have been reported, such as circular ranging by Siddiqui et al. [14] (the same method improved by Lippok and Vakoc in 2020 [15]) and Chun et al. [16]. This method takes advantage of the aliasing intervals to "unfold" the imaging domain whilst maintaining a lower sampling rate. While this method is advantageous in terms of obtaining a single-shot depth profile, it relies on having single surfaces with no multiple interfaces across the entire "unfolded" imaging range.

Recently, Podoleanu et al. [11] have reported a novel variant of MS–OCT processing, where unlike in the previous MS–OCT paper, the Master and Slave interferometers are two separate physical entities. The comparison operation between the signals returned by them is carried out by using an analogue broadband mixer, prior to digitisation, to mix the signals. The resulting signal is effectively down-converted to frequencies within the order of magnitude of the sweep frequency, enabling the use of lower-speed digitiser cards to acquire the signal and carry out the remainder of operations (signal conditioning and image rendering) digitally.

In this communication, the suitability of MS–OCT is investigated for processing the signal delivered by an OCT interferometer when driven by an electrically tunable, akinetic swept source presenting non-linearities throughout the sweep. In a short preliminary study [17], a demonstration was performed of two of the possibilities of using the MS methods. Here, we expand to more modalities, as presented, and document details of procedures, calibrations, and results, compared with conventional modalities in terms of axial resolution and axial range.

If MS–OCT is proven suitable as a processing method, then a Vernier tuning principle could be used in a simpler manner: there would be no need for a DVV-based correction and, ultimately, no need for an external clock (synchronous with the optical source), thus somewhat simplifying the overall system. Unlike earlier studies with the MS–OCT method, here we compare against a "Master" mask that contains a few non-linearly tuned intervals in the spectrum, which are otherwise eliminated by the DVV calibration. When using the MS–OCT procedure, the entire photo-detected signal is compared against itself; i.e., the signal contains the intervals otherwise eliminated by the DVV correction. We also evaluate the use of the down-conversion OCT method [11], which would bypass the need for both DVV correction (including the synchronous clock) and a high-speed digitiser card to cope with the large frequency of the photo-detected signal. Due to the comparison of spectra that is fundamental to MS–OCT, some tolerance to distorted spectral behaviour should also be expected.

#### **2. Materials and Methods**

Throughout this study, an optical source from Insight (model SLE-101) [18], with a sweep rate of 100 kHz and the maximum tuning range setting (roughly 90 nm), centred at *λ*0 = 1.31 μm, is employed.

At the sample clock frequency setting used (400 MHz), a maximum of 4000 sampling points are enabled at a source sweep duty cycle of 100%. Due to the presence of the invalid regions in the tuned spectrum, the DVV returns useful data within a duty cycle of 70% only. During this study, two separate interferometric setups were employed, which are schematically represented in Figure 2a,b.

**Figure 2.** Schematic diagrams of the two interferometric configurations used with the electrically tunable akinetic optical source throughout this study. (**a**) Single interferometer configuration, illuminated by the Insight akinetic source SLE-101, driving a balanced photo-detector BPD. (**b**) Dual interferometer configuration to implement the down-conversion MS–OCT method.

In the first case, as shown in Figure 2a, MS–OCT processing is explored in a single interferometer configuration with a recirculating reference path, following the procedures described by Rivet et al. [10]. Bus (i) carries the DVV produced during the source's self-calibration, and bus (ii) synchronises the acquisition clock from the digitiser board (ATS9350) with that of the optical source. As shown by the large green arrow in Figure 2a, Master–Slave (MS) or FFT processing can be implemented on the PC. An electronically adjustable translation stage TS (Newport M-VP-25XA) is used to vary the optical path difference (OPD) in the reference arm. The resulting interferometric signal is detected by a balanced photo-detector unit (Insight BPD-1, cut-off frequency 400 MHz) and digitised using an AlazarTech ATS9350 board (12-bit digitisation bit depth, maximum sampling rate 500 MS/s). For the digitisation procedure, it is possible to use the clock signal provided by the optical source (represented as bus (ii) in Figure 2a), or the built-in hardware clock from the AlazarTech digitiser card (asynchronous clock operation). The DVV correction (bus (i)) is only possible with synchronous clock operation.

In the second case, schematically represented in Figure 2b, the down-conversion OCT (DC-OCT) Master–Slave method [11] was employed on a long axial range (>100 mm)- swept source-based system. To achieve this goal, an additional optical interferometer, Interferometer B (Master) was set up with the same optical path difference as Interferometer A presented above (Slave), both having 80 mm of SMF-28e fibre in their reference arms, which introduces an optical path difference of ≈120 mm; these two interferometers were both fed by the Insight source using a 60/40 fused fibre-based directional coupler DC, as depicted in Figure 2b. The outputs of each interferometer are photo-detected by balanced photo-detectors BPD1 (Insight BPD-1) and BPD2 (Thorlabs model PDB481C, AC-coupled, bandwidth 30 kHz–1 GHz). The resulting electrical signals from either photo-detector are high-pass-filtered (Thorlabs, model EF513, 6.7 MHz cutoff frequency, not shown in diagram) and directed to a RF frequency mixer, shown as a circled X in the diagram in Figure 2b (Minicircuits, model ZFM-4, operating bandwidth 5–1250 MHz). Its output is first low-pass filtered and amplified (Stanford Research low-noise pre-amplifier, model SR560) and then displayed by a digital storage oscilloscope, DSO (LeCroy model LC534A), running at a sample rate of ∼25 kS/s. To produce an A-scan in this case, the OPD of Interferometer A is varied whilst the DSO reads the filtered output of the pre-amplifier and displays it against time on its screen.

At this very large OPD of ≈120 mm, the frequency of the photo-detected signal exceeds 600 MHz. The Nyquist limit of the digitiser board used earlier in the study is 250 MHz (if working with the asynchronous clock of the digitiser board), therefore, the board is not able to sample the resulting interferogram.

#### *2.1. Channelled Spectrum Processing for MS–OCT*

To evaluate MS–OCT processing in a single interferometer configuration (Figure 2a), the procedure demonstrated in Rivet et al. [10] is employed, allowing masks to be synthesised from a small set of experimentally acquired channelled spectra. This procedure is schematically represented in Figure 3a. Briefly, during the Master step, a small number of channeled spectra are acquired for several OPD settings and used to infer a pair of system model calibration functions (*g* and *h*). These two functions can then be used to render an arbitrary number of complex-valued Master signals, which are then compared against the real-valued channeled spectra acquired during the Slave step, finally generating the full A-scan profile.

While the procedure was successfully validated when the interferograms were DVVcorrected (as one would normally use the Insight source), it failed otherwise. This is expected, due to the discontinuities in the phase of the interferogram, as evidenced by the plot in Figure 1c. Moreover, as shown later in Section 3, the frequency spectrum of the interferogram acquired with no DVV correction presents multiple peaks due to the aforementioned discontinuities; since the generation of masks requires a channeled spectrum whose variation in peak density with wavenumber is monotonic, it was not possible to infer the system model calibration functions *g* and *h*, as per Figure 3a, and ultimately the complex-valued Master signals. This is not a failure of the MS principle, but rather of the specific algorithm to synthesise masks from experimentally acquired spectra for different OPD values, which has been successfully employed so far on other commercial swept sources.

Instead, a hybrid operation mode was implemented (HyMS–OCT), comprising portions of the original MS–OCT concept [9] but employing complex-valued spectra (as explained in a subsequent paper on MS–OCT, where masks are complex-valued, for which reason such a MS–OCT version denominated CMS–OCT [10]) to enhance the tolerance to phase fluctuations [10].

The hybrid procedure is described diagrammatically in Figure 3b. To obtain an A-scan for a single reflector, the procedure is split into two stages, the Master and the respective Slave. In the Master stage, the reference arm length was varied over the depth range under study using the translation stage TS, whilst constantly retrieving the Master signals, which were then Hilbert-transformed (producing complex-valued spectra) and stored in the computer's memory. Following this, in the Slave stage, the object under test, considered here a mirror, was positioned in the middle of the depth range under study, and a single Slave signal was acquired. This signal was then compared against the set of Master signals by means of a matrix multiplication, as described in Bradu et al. [19] and the result of these comparisons plotted against the TS position, thus generating an A-scan.

**Figure 3.** (**a**) Simplified description of the Complex Master–Slave OCT procedure presented in Rivet et al. [10]; (**b**) Diagrammatic description of the hybrid HyMS–OCT method to perform MS– OCT processing of the non-DVV-corrected interferograms retrieved with the akinetic swept source system used in this study.
