**3. Results**

Firstly, a frequency characterisation of the interferogram with a single interferometer configuration was performed, for the case where the DVV correction is applied versus the case where the DVV correction is not applied, for two OPD values (2.55 mm and 17.55 mm), as shown in Figure 4. When the DVV correction is not applied, the invalid signal regions present within the interferometric signal introduce additional frequencies; therefore the red traces in both plots display multiple peaks. These additional frequencies, when not eliminated, degrade the A-scan and also axially move the main A-scan peak from its "true" location.

For the first part of the study, described in Section 3.1, the single interferometer configuration (Figure 2a) with a single reflector in the object arm was used, thus generating a single modulation frequency in the interferogram. In the second part of the study (Section 3.2), the dual interferometer configuration of Figure 2b was used, with single reflectors employed as samples in the object arms of either interferometer.

**Figure 4.** Comparison of A-scans obtained for two separate OPD values by Fourier-transforming the interferogram ((**a**) −2.55 mm; (**b**) −17.55 mm), with (black trace) and without (red trace) DVV correction. Data normalized to the maximum value in each data set, and the logarithmic dB scale on all A-scan profiles was computed with 10 × log10*<sup>A</sup>*˜ , where *A*˜ is the normalized A-scan profile.

#### *3.1. Complex Master–Slave/Hybrid Master–Slave Operation with Pre-Stored Masks*

As mentioned in Section 2.1, any attempts to use the CMS–OCT method described in [10] on any non-DVV-corrected data have proven unsuccessful. The method did work on DVV-corrected interferograms, and the full width at half-maximum (FWHM) for the A-scan peaks was approximately 11.7 μm. The transform-limited peak width was also measured as 11.6 μm, following the procedure described in Appendix C of Reference [10]. This procedure removes all non-linearities present in the phase, preserving only the spectral shape of the signal; therefore, it yields the minimum width attainable by the system for the tuning range specified.

To study the suitability of the MS–OCT method in non-DVV-corrected cases, complexvalued Master masks were generated using the HyMS–OCT method described in Section 2.1,and compared against a single Slave signal. Similar OPD values to those in Figure 4, of 2.55 mm and 17.55 mm, were used here, representing a "short" and "large" OPD depth range, respectively. This HyMS–OCT method was evaluated for three sampling/processing protocols as follows:


For these three sampling/processing protocols, A-scans were obtained by comparing the Slave signal corresponding to a reflector placed in the middle of the depth range intervals under study (corresponding to a "short" 2.55 mm and "large" 17.55 mm OPD range, both spanning 1 mm) against a pre-recorded, complex-valued set of Master signals recorded over the same depth range interval, using a matrix multiplication, as described in Bradu et al. [19]. The result of these comparisons is plotted against the TS position, thus generating A-scan profiles as depicted in Figure 5a,b alongside those obtained by Fourier transforming the DVV-corrected interferograms.

As Figure 5a,b show, the A-scan profiles obtained with the HyMS–OCT method on all sampling/processing protocols are very similar, both in terms of peak width and S/N ratio. In other words, the HyMS–OCT method works equally well with DVV-corrected and DVV-uncorrected data.

The location of the A-scan peaks obtained with the FT processing differs slightly from those obtained with the HyMS–OCT due to the different manner the OPD coordinate is determined: in the FT processing, the full A-scan profile needs to be mapped to the distance coordinate by taking several position measurements and interpolating the distance between them, which introduced some imprecision. In the HyMS–OCT processing, each Master signal is directly mapped to a single position of the TS, effectively providing an absolute calibration of each depth point.

**Figure 5.** A-scans for three sampling cases as detailed in the insets taken at small ( ≈2–3 mm) (**a**) and large ( ≈17–18 mm) (**b**) OPD values with the HyMS–OCT method for the different sampling cases considered. The conventional procedure, the Fourier transform of the DVV-corrected interferogram, is plotted in black in both graphs.

The FWHM of all peaks plotted in Figure 5 are listed in Tables 1 and 2, and their corresponding signal-to-noise ratio values in Table 3 and in the second column of Table 2. These contain the FHWM peak values from the DVV-corrected interferograms and from the non-DVV corrected ones, respectively.

Regarding the peak width values obtained with the FFT method, it is clear that for the two OPD values considered, larger widths than the expected transform-limited value are obtained. For the larger OPD value ( ≈17.5 mm), the peak width is significantly larger, and a depth-dependent widening is observed. Since the interferometer used in this study was not fully compensated for material dispersion between its two arms, this result is to be expected. This depth-dependent widening is not observed in the results obtained with either CMS– OCT or HyMS–OCT since the MS–OCT method automatically compensates [12] for any material dispersion imbalance in the system.

**Table 1.** Full-width at half-maximum values of the A-scan peaks (in μm) for the methods evaluated for a short (2.55 mm) and a large (17.55 mm) OPD value, employing DVV-corrected data. No spectral windowing was employed in any of interferograms used to obtain these A-scan peaks.


**Table 2.** Full-width at half-maximum values of the A-scan peaks (in μm) and their respective signal-to-noise ratio (SNR) values (in dB) for the HyMS–OCT method, employing data sampled without DVV correction. No spectral windowing was employed in any of the interferograms used to obtain these A-scan peaks.


**Table 3.** Signal-to-noise ratios (SNR) of the A-scan peaks (in dB) for the methods evaluated for a short (2.55 mm) and a large (17.55 mm) OPD value, employing DVV-corrected data. No spectral windowing was employed in any of interferograms used to obtain these A-scan peaks.


The CMS method employing synthesised complex-valued masks provides the closest peak width value to the transform-limited width (the ground truth), differing by less than 100 nm in the short OPD case.

The last column of Table 1 and the middle column of Table 2 relate to peak width values obtained using the HyMS–OCT method employing pre-recorded Master masks, as described in Section 2.1. In this case, the peak width was estimated from a shorter run of the TS (500 points over a travel range of ≈300 μm, centred at the relevant OPD where the Slave signal was acquired). The larger values (when compared with those obtained for the CMS–OCT method employing synthesised complex-valued masks) may be due to the precision limitations of the mechanical translation stage encoder, and the settling time allowed for each individual position recording of the channelled spectra. Still, it is clear that no depth-dependent peak widening is observed when using the HyMS–OCT method, as shown in Tables 1 and 2. For most cases, the peak widths are smaller than those obtained with the FFT method.

In Table 2, the peak widths for the HyMS–OCT under asynchronous clock operation between source and digitizer are only slightly larger (by ≈2 μm) than the other two cases obtained with the same processing method; this is due to the fact that the digitiser used has fixed, pre-set clock settings that do not match the clock signal frequency used in the other two cases (400 MHz). In this particular case, the maximum clock frequency allowed by the digitiser card, 500 MHz, was used, but the number of sampled points was kept constant. This has an impact in terms of the sampled region of the spectrum, with the digitised spectral range not fully covering the sweep range of the source, which was expected to negatively impact the axial resolution measured.

We present the signal-to-noise ratio (SNR) values for the A-scan peaks in Figure 5a,b in Tables 2 and 3. These SNR values should be interpreted with some reservation, as they represent single run events and no average or detailed noise analysis was performed. Data employed in the SNR calculations were collected in separate events. This may explain some variations in the values presented. To avoid signal saturation, a different attenuation of the reference power was applied when switching from one regime to another, which was maintained consistently for measurements on each regime for different OPD values, for instance, but not when switching between regimes.

In both Tables 2 and 3, the larger the OPD value for both CMS–OCT and HyMS– OCT methods, the larger the SNR, despite the system sensitivity decreasing with OPD, showing that noise decreases at a higher rate than the sensitivity when moving to larger RF frequency values. There might be other noise components with larger strength at smaller RF frequency values (shallow OPD values) that may explain this. As far as the FFT case, the noise floor lies more than 5 dB below the noise floor of the other three traces at short OPD values. The trend of S/N noise with OPD cannot be commented on for the FFT data as no dispersion compensation was applied.

To study the applicability of the HyMS–OCT method to large axial range measurements, an A-scan was produced over the full range of OPD values allowed by the sampling clock from the digitiser card for the locations where the two Slave signals were previously recorded. This behaviour was tested for the case with asynchronous clock operation between source and digitiser (operating at 500 MHz, which translates into ≈21 mm of depth range, with 18 mm of it represented in the plot). The resulting A-scans were compared against those obtained from FFT processing of the interferogram, with and without DVV correction. These results are shown in Figure 6.

As expected, if the non-DVV-corrected interferogram is processed using the FFT method, not only is there a rise in the noise floor level, but also the appearance of satellite peaks, whose heights are comparable to those of the main interferometric peak, as has already been shown in Figure 4. The trace corresponding to the non-DVV corrected, HyMS–OCT-processed interferogram also presents some residual satellite peaks, although these are significantly reduced when compared to those present in the non-DVV-corrected, FFT-processed trace, being attenuated by more than 10 dB.

The noise floor behaviour mimics what was presented before: the DVV-corrected interferogram, when processed using the FFT method, possesses a lower noise floor (by about 5 dB) when compared to the same data processed using the HyMS–OCT method (without DVV correction, and without using the clock signal from the source). However at a larger OPD value, closer to the sampling limit of the digitiser, the difference between the noise floor of the DVV-corrected, FFT-processed interferogram and that processed using the HyMS–OCT method is not significant, possibly due to the fact that no dispersion compensation was applied on the FFT-processed data, as mentioned earlier.

No S/N ratio value is presented for the coherence limited peak in Table 3, as this is obtained from the envelope of the spectrum, that is similar to that obtained from the reference or sample wave only. In other words, we cannot associate a separate signal or noise measurement to this procedure (signal in OCT is measured with both waves on and noise with the sample wave obstructed).

Since the primary concern with this study was to assess any peak width degradation when using any of the methods evaluated, no spectral windowing was applied to any of the interferograms processed, which may explain the existence of side-lobes in some of the A-scans presented in Figures 4–6.

**Figure 6.** A-scan comparison between the FT method (on both DVV and non-DVV corrected interferograms) and the HyMS–OCT method (asynchronous clock case, no DVV correction), for a total OPD value scan range of 18 mm. Arrows depict the corresponding OPD at which the Slave signal was acquired for the two sub-figures ((**a**) −2.55 mm; (**b**) −17.55 mm), and also the OPD values of the interferograms subject to FT processing.

#### *3.2. Down-Conversion (DC) OCT Implementation with Two Physical Interferometers*

To evaluate the axial resolution with the DC-OCT method, the OPD in one of the two interferometers is scanned mechanically using the TS in Interferometer A, as presented in Section 2. This leads to the graph in Figure 7. This is not, however, the way the DC-OCT method is normally used, where no mechanical depth scanning is applied; as demonstrated by Podoleanu et al. [11], DC-OCT allows the production of constant depth images of the object under study (*en-face* images) by setting both interferometers to the same optical path difference and comparing the channelled spectra of similar modulation.

The second interrogating interferometer performs real-time generation of the mask, therefore operating as an Optical Master. In contrast, in all previous MS papers, masks were generated electrically and/or numerically by Electronic Masters, and then stored in the PC memory.

A down-conversion factor *N* can be calculated as the ratio between the frequency of the photo-detected signal for the maximum OPD recoverable and the frequency of the processor performing the down-conversion (composed of the mixer and the low-pass filter). Considering the Nyquist limit, this should be at least twice the sweep frequency value, therefore giving a value of *N* = 600 MHz 200 kHz = 3000. This means that by using DC-OCT, the bandwidth of photo-detected signal was reduced by a factor of 3000. The A-scan peak obtained using the down-conversion method exhibits a width of ≈14 μm, slightly larger than the expected 11.6 μm.

**Figure 7.** A-scan obtained with the down-conversion procedure, with the Master interferometer having an OPD value of ∼80 mm, and the reference arm of the Slave interferometer being mechanically scanned over a range of 200 μm at ∼80 mm OPD. The main peak has a FWHM of ∼28 μm, which corresponds to an axial resolution of ∼14 μm due to the double-pass interferometer configuration.

#### **4. Discussion and Conclusions**

This study has evaluated the suitability of three versions of the MS–OCT method to decode interferograms, delivered by an interferometer driven by an electrically tunable (Vernier tuning) swept source that presents invalid regions throughout its tuning. The three MS–OCT versions are as follows: (i) using pre-synthesised, complex-valued masks (CMS– OCT); (ii) a hybrid (HyMS–OCT) modality, where multiple Master masks are generated by multiple stepped OPD changes and compared against a complex-valued Slave signal; and (iii) a DC-OCT version. As demonstrated, both (ii) and (iii) methods can be used with some success, even when interferograms are not corrected by the manufacturer's DVV. The CMS–OCT method with pre-synthesised masks can only work with DVV-corrected spectra. Therefore, the MS–OCT methods present a suitable alternative for the signal processing of OCT systems driven by swept sources employing a similar tuning modality as that of the Insight source used in this study. If the use of a DVV correction can be eliminated, as allowed by both (ii) and (iii) methods, signal processing is simplified with an overall cost advantage for the whole OCT system. A summary of the advantages (and disadvantages) of the approaches presented in this study is shown in Table 4.

One of the advantages of the electrically tunable source used in this study is its long axial range, which can be on the order of tens of centimetres or more; in order to digitise such interferograms, ultra-fast digitiser cards with multi-GHz sampling clocks are needed. However, if the DC procedure presented in this study (and detailed by Podoleanu et al. [11]) is used, one can do without the digitiser card altogether. In effect, this has also been demonstrated in this study, where an A-scan taken at an OPD value of 80 mm is obtained, which would have otherwise been impossible to obtain with the ATS-9350 digitiser card, as the 80 mm OPD corresponds to a dominant channelled spectrum frequency of more than 200 MHz over the digitiser's aliasing limit. This conclusion can be scaled to larger frequency sweeping rates, exceeding tens of MHz, where the DC procedure would allow processing of tens of GHz-frequency signals using digitisers with sampling rates in the range of the sweeping rate.

**Table 4.** Summary of positive and negative aspects of using the MS–OCT method with the akinetic, electrically tunable swept source employed in this study.


As demonstrated, the method described by Rivet et al. [10] to pre-synthesise the Master signals for the CMS–OCT procedure is only applicable to the case where the DVV correction is applied. However, the DVV correction and external clock sampling only address one of the issues encountered with SS-OCT, that of securing linear sweeping. The other issue is the dispersion in the interferometer. The MS calibration addresses both nonlinear sweeping and dispersion. Therefore, when compared with the conventional usage case of these optical sources (DVV correction followed by FT), the MS procedure presented here offers some benefit, in the sense that it is tolerant to dispersion in the system [12]. This is demonstrated in Table 1 by the improvement in the peak width brought by the CMS–OCT with synthesised masks when compared against that obtained by simple FFT.

The HyMS–OCT procedure with non-DVV-corrected interferograms was made working with pre-recorded spectra. A similar approach was used in the earlier MS–OCT implementations [9,12], and while it worked well enough for the demonstrations, it has a negative impact on the flexibility and usability of the system, as a large number of masks need to be collected. The procedure for synthesising the masks from a small sub-set of channelled spectra, however, can potentially be upgraded to something more tolerant of the extra frequency terms (e.g., by suppressing the satellite terms during capture using band-pass filtering). More research will need to be carried out with regards to this aspect.

Running the HyMS–OCT procedure on non-DVV-corrected data appears to raise the noise floor, especially when imaging at lower OPD values; moreover, some satellite terms, similar to those observed when Fourier-transforming a non-DVV-corrected interferogram, also appear in the A-scan, albeit significantly attenuated. This could pose a problem, especially if low-bit-depth digitiser cards are used, as they will present lower dynamic range in the digitisation. Still, bypassing the requirement for DVV correction means that the need for synchronous sampling operation between source and digitiser is eliminated, with potential cost savings and additional flexibility. For example, with a sufficiently large sampling rate digitiser, OPD values beyond the limit introduced by the source clock can be accessed, as has already been demonstrated in Marques et al. [13].

In the second part of this study, the operation of this optical source without the need for a high-speed digitiser was also investigated, by means of the down-conversion OCT method [11]. By using two near-identical optical interferometers and mixing their output interferograms with an analogue RF mixer, long-range operation at an OPD value of 120 mm is demonstrated. When compared with the results from the first part of our study, the axial resolution obtained was not significantly deteriorated. Indeed, it actually presented a >2 μm improvement over the width measured for DVV-corrected, FT-processed data at 17 mm.

The peak width is, however, slightly larger than all results obtained using the CMS/ HyMS–OCT procedures. This is explained by some dispersion difference between the two optical interferometers. Moreover, it was not possible to perform any spectral windowing on these time-based signals, which can also explain the presence of side-lobes in the A-scan.

The peak contrast is also significantly reduced, to less than 10 dB, compared with the ≈20 dB obtained with the CMS/HyMS–OCT procedures. The bandwidth of the Insight BPD-1 (employed in the Slave interferometer), narrower than the Thorlabs photo-detector employed in the Master interferometer, explains the lower peak contrast at large OPD values.

This is only a constructive disadvantage due to the non-availability of two 1 GHz balanced photo-detectors. Even so, DC-OCT is worth pursuing due to the lowering of the signal processing bandwidth to levels comparable to the sweeping frequency. This allows a low-cost route via low-cost digitizers, a procedure that also enables real-time delivery capability of *en-face* views, as when using ultra-high-speed digitizers, the amount of data is so high that it needs to be buffered locally before being transferred out of the digitizer for post-acquisition. The more important disadvantage of DC-OCT is the need for a second high-speed, large-bandwidth photo-detector unit.

In summary, Master–Slave OCT (both in its HyMS–OCT and DC-OCT guises) offers some simplification over the conventional DVV-based invalid region removal procedure, allowing the user to employ both the valid and invalid regions, as long as a reference interferometer (Master) signal is available (either pre-stored at a Master step or as a physical interferometer as in the down-conversion case). Another advantage of the MS approach is that it may enable better analysis of phase errors, particularly at higher imaging depths. These phase errors may occur around the invalid-to-valid transitions due to slight imperfections in the discontinuity resolution with the DVV or simply due to a change in the performance of the laser over time or ambient temperature.

**Author Contributions:** Conceptualization, A.P. and M.J.M.; methodology, A.P. and M.J.M.; software, M.J.M. and A.B.; validation, M.J.M. and R.C.; formal analysis, M.J.M.; investigation, M.J.M. and R.C.; resources, A.P. and J.E.; data curation, M.J.M.; writing—original draft preparation, M.J.M.; writing—review and editing, M.J.M., R.C., J.E., A.B., and A.P.; visualization, M.J.M.; supervision, A.P. and A.B.; project administration, A.P.; funding acquisition, A.P. and A.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** A. Podoleanu, A. Bradu, and M. J. Marques are supported by the Biotechnology and Biological Sciences Research Council (BBSRC) (*5DHiResE*, BB/S016643/1) and the Engineering and Physical Sciences Research Council (EPSRC) (*REBOT*, EP/N019229/1). M. J. Marques and A. Podoleanu acknowledge support from the Image Guided Therapy EPSRC Plus Network, EP/N027078/1. A. Podoleanu and R. Cernat acknowledge the support of National Institute for Health Research (NIHR) Biomedical Research Centre at the UCL Institute of Ophthalmology, University College London, the Moorfields Eye Hospital NHS Foundation Trust, and the NETLAS Marie-Curie ITN 860807. A. Podoleanu also acknowledges the Royal Society Wolfson research merit award.

**Acknowledgments:** The authors are grateful to Insight Corporation for the loan of the Insight SLE-101 necessary for this study. The authors also thank Sally Makin for the thorough readability review prior to submission.

**Conflicts of Interest:** A.P. and A.B. are inventors of patents: US10760893 and US9383187 in the name of the University of Kent. R.C. and M.J.M., no conflicts of interest. J.E. is the chief technological officer (CTO) and executive vice-president (EVP) of Insight Photonic Solutions, Inc. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
