1. Introduction

Optical coherence tomography (OCT) has been broadly and successfully adopted as an influential high resolution, high-speed 3D imaging technique in research and industry, filling in a significant resolution gap between ultrasound and confocal microscopy. Its micron-scale resolution and precise depth ranging make it well-suited for non-destructive materials inspection and non-invasive biomedical imaging [1]. However, expansion of applications and ease of translation call for continued advances and improvement in imaging speed, imaging range, and field-of-view. For example, clinical environments present a need for imaging devices that can adjust the imaging range to account for variation in patient anatomy, surgical operations and irregular sample topography. While OCT technology has adjusted to suit the operating room and clinic by adopting new form factors [2], sub-optimal workflow integration, such as the repeated, manual adjustment of working distance, increases imaging time while compromising image quality. Applications such as surgical guidance and endoscopy frequently require an adjustable, multi-centimeter imaging range. To better address these challenges, new strategies are needed.

One emerging application field for OCT is in the ear, nose and throat (ENT) clinic. While OCT is routinely used in ophthalmology, a key difference between ophthalmic and ENT surgical microscopes is the fixed working distance of ophthalmic surgical microscopes. This configuration is well-suited for OCT integration in applications where the sample can be located at a specific depth range, as this limits the signal bandwidth and, thus, data acquisition and management requirements. On the other hand, ENT surgical microscopes employ an electronically-adjustable working distance range of up to 42.5 cm (e.g., ZEISS TIVATO 700) to account for a wide variation in procedural operations and anatomical distances. To integrate OCT in ENT microscopes, an OCT system with a similarly long, electronically-controlled working distance is needed to allow dual-modality, real-time imaging.

Increased depth range is of growing interest in many applications of OCT to reduce constraints on sample size, topology, and location. Typical OCT implementations have a limited ranging depth, constrained by the selection of imaging speed, spectral sampling, and acquisition bandwidth. Recent work has aimed to address extension of imaging range by several strategies including optical aliasing [3–5], constant frequency working distance variation [6,7], and high frequency acquisition [8,9]. Optical aliasing and high frequency acquisition methods aim to capture a multi-centimeter range simultaneously, utilizing data compression strategies. On the other hand, constant frequency working distance variation captures the original acquisition rate-limited imaging range. This strategy maintains the optical pathlength difference while varying the working distance to place the sample within the acquisition bandwidth. Optical aliasing methods, such as circular ranging [3], take advantage of custom comb lasers to achieve a multi-centimeter imaging range; however, this method suffers from aliasing artifacts during reconstruction of depth profiles in post-processing and requires complex detection. The optical Vernier effect has been increasingly combined with optical aliasing to resolve absolute depth [10–13]. Variations in temporal or optical frequency step of specialized sources (e.g., dual comb spectroscopy using time-stretched comb sources) allow recovery of extended depth profiles [14,15]. While these methods have achieved extended range, avoid moving parts and reduce acquisition bandwidth requirements, further development of these techniques is needed to enable widespread implementation. The use of specialized equipment such as custom comb lasers and arbitrary waveform generators and electro-optic modulators hinders immediate adoption of these methods by other application-oriented groups for long-distance ranging. Other tradeoffs of this strategy include significant post-processing to reconstruct the extended depth and extract the relevant signal and, in some implementations, reduced imaging rate for otherwise MHz-rate time-stretch sources. Alternatively, down-conversion has been achieved using translation stages and multiple interferometers [16,17]. Translation stages have been used by our group and others to achieve a variable working distance range of several centimeters through maintenance of the optical pathlength difference [6,7]. However, these designs increase the weight and footprint of the OCT system, while achieving limited improvement in the working distance range (∼5 cm). Finally, high frequency hardware has been used to record increasingly high frequency fringes corresponding to samples at large optical pathlength differences, up to 1.5 m [8,9]. However, the requirement of large bandwidth electronics for acquisition and post-processing implies increased acquisition and processing time and system cost, which is not easily compatible with routine, in vivo or clinical imaging. Thus, despite the availability of long coherence length swept lasers, a long-range variable working distance OCT system that is convenient for translation has not been demonstrated.

In this work, a new strategy for increased OCT depth range is demonstrated to facilitate a variable working distance of tens of centimeters and approach the requirements of the ENT clinic. The proposed OCT system aims to avoid the use of bulky hardware by allowing a large optical path length difference and utilizing electronic down-conversion to mitigate the need for high frequency digitization. We demonstrate that a conventional swept-source OCT system with a tunable lens can be combined with electronic frequency shifting to achieve an akinetic, electronically-controlled working distance with a working distance range of 10s of centimeters. System characterization and the utility of the approach for morphological and functional imaging are presented. The use of commercially available components shows proof-of-concept for commercial translation of the system architecture and convenient adoption of the method.

2. Methods

2.1 System concept

A novel strategy for a variable working distance OCT system is proposed by allowing the sample arm pathlength to vary through the refocusing of a tunable lens, while the reference arm is fixed. The optical pathlength difference ($\Delta z$) varies proportionally leading to a proportional change in the interferometric fringe frequency (f_OCT). For example, a swept laser with sweep rate of 200 kHz and spectral bandwidth of ∼60,000 m^-1 (∼100 nm centered at 1.3 µm) has a fringe frequency of 5.4 GHz at $\Delta z$=22.5 cm and 10.8 GHz when $\Delta z$=45 cm (see Supplemental document for details of calculation). In order to avoid the use of high frequency data acquisition systems, we can implement electronic mixing to down-convert the signal to a more manageable frequency. In the system design herein, high frequency fringes were measured on a high frequency balanced photodetector. A commercial radiofrequency (RF) synthesizer and mixer were then used to shift the high-frequency fringes into the bandwidth of our digitizer (200 MHz) by electronic mixing of the interferogram with center frequency, f_OCT, with a local oscillator (LO) with frequency, f_LO. We refer to this strategy as electronic frequency shifting OCT (EFS-OCT).

We considered using a typical swept laser that sweeps nonlinearly in wavenumber, k, because it would make the approach more broadly applicable. However, the nonlinearity leads to broader temporal bandwidth compared with a linearized (or linear in k) laser sweep. Since k appears in the argument of the cosine in the interference equation as a product with Δz, as the Δz gets larger, the bandwidth of the interferometric signal grows much faster with a nonlinear sweep compared to a linear sweep. We tested this using a nonlinear-in-k, swept laser (Thorlabs MEMS-VCSEL, SL1310V1-20024). In varying the $\Delta z$, the temporal bandwidth of the interferogram was observed to grow significantly, exceeding the Nyquist frequency (200 MHz) of our digitization rate, over a relatively small f_OCT range. This is consistent with the scaling of the interferometric bandwidth with the spectral sampling interval, dk (which is non-constant for a nonlinear swept laser), and $\Delta z$. Simulation of the source A-line confirmed this effect, with a 3.6X increased signal bandwidth between f_OCT of 100 and 500 MHz measured at -10 dB (see Supplemental document). Although the spectral bandwidth remains unaltered through electronic mixing, increasingly large digitization rates would be required to acquire these increasing temporal frequency bandwidths when using a nonlinear-in-k laser. This also presents challenges in maintaining linear performance through electronic frequency shifting. Based on this observation, we concluded that we would need to use a linear-in-k swept laser to efficiently apply electronic down-conversion.

As the degree of sweep linearity is increased, the bandwidth of the OCT signal is reduced for increasing Δz and a larger depth range can be achieved with EFS-OCT. To achieve the significant depth range required by our application (on the order of tens of centimeters), we selected a quasi-linear-in-k, swept laser (Insight, Inc.) with a sweep frequency of 100 kHz and centered at 1.3 µm. The all-semiconductor laser cavity is programmatically tuned to produce linear-in-k sweeps during known intervals on a 400 MHz clock [18]. Each sweep in k is calibrated and consists of tens of transition periods to complete the total sweep bandwidth. During these transition periods the laser wavenumber is updated for the next wavenumber interval and is not well controlled. Hence, the samples acquired during the transition are called “invalid points” and discarded in post-processing. Although the analog laser sweep is nonlinear-in-k due to the non-constant sweep profile, once the invalid points are removed in post-processing, dk is constant. In the analog domain, the laser sweep is highly repeatable and results in interferograms with a non-constant, but narrow temporal bandwidth. This laser then provides the generally limited interferometric bandwidth required by EFS-OCT.

Two Insight lasers with different specifications were used to assess the performance of EFS-OCT. Due to differences in semiconductor chip properties and design spectral bandwidth, each Insight laser can achieve a different dk, and, thus, a different $\Delta z$-to-fringe frequency relationship. To measure over the largest working distance enabled by the system design, an Insight laser with a small dk (Laser 1: ${\lambda _0}$ = 1287.435 nm, axial resolution in air = 29.2 µm, dk = 9.79 m^-1) was employed for assessing performance over $\Delta z$. For imaging, an Insight laser with a larger bandwidth (Laser 2: ${\lambda _0}$=1305.41 nm, axial resolution in air = 19 µm, dk = 16.96 m^-1) was used to achieve higher axial resolution.

2.2 Electronic frequency-shifting OCT design

The optical system consisted of a Mach Zehnder interferometer with an electronically tunable lens (Optotune, EL-16-40-TC-NIR-5D-C) in the sample arm (Fig. 1(a)) to enable dynamic refocusing and adjustment of the working distance. The sample arm optics were modeled in Zemax and optimized to have a 14.5 cm working distance range within the typical tunable lens diopter range, lateral resolution of 40.3 µm and a field-of-view of 7.5 mm.

 

Fig. 1. a) Experimental OCT sample arm with tunable lens: COL, optical collimator; RL, relay lens; OBJ, objective. b) Analog signal processing: f_IF, intermediate frequency; LPF, low pass filter; f_c, cutoff frequency; DAQ, data acquisition system. Components added in EFS-OCT experiments are indicated by a dashed red box. c) Simulated interferogram for a single reflector before mixing (i), after mixing and lowpass filtering (ii), and after digitization and invalid point removal (iii), corresponding to positions (i)-(iii) in (b).

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Photodetection and radiofrequency mixing electronic components were chosen to enable down-conversion of signals up to several gigahertz. The analog signal processing is shown in Fig. 1(b). High frequency fringes, created by refocusing of the tunable lens, were recorded by a high frequency balanced photodetector (Thorlabs, PDB-480C-AC, 1.6 GHz bandwidth). Before digitization, the analog interferogram, with center frequency, f_OCT, was mixed with a local oscillator (LO) to down-convert the signal to the baseband of a digitizer with a sampling rate of 400 MS/s. A radiofrequency mixer evaluation board (Analog Devices Inc., ADL5801) was used to achieve down-conversion, in combination with a programmable RF synthesizer evaluation board (Texas Instruments, LMX2592). The mixer and synthesizer were selected to have operation bandwidths and high linearity over the expected f_OCT range (up to ∼5 GHz for a 40 cm $\Delta z$ range). To accommodate restraints on the RF input power level of the mixer, a variable attenuator (Mini-Circuits, ZX73-2500-S+) adjusted the analog signal envelope peak-to-peak voltage, output by the photodetector. The output frequency and power level of the RF synthesizer were set programmatically via a USB-based interface adapter and software development kit (USB2ANY, Texas Instruments) and custom Python code. LO frequency (f_LO) was chosen to give a product frequency of 100 MHz. At short $\Delta z$, LO was altered from this regime to avoid product overlap with upconverted DC and low frequency signals.

The frequency mixing process generates a sum and difference product signal at center frequencies (f_OCT ± f_LO). As only the difference product is desired, the mixed signal was low-pass filtered (Mini-Circuits, SLP-200+, f_c= 190 MHz) and digitized (AlazarTech, ATS9373). All OCT data was recorded using custom software written in Python, C++, and Cuda C. During EFS-OCT experiments, LO drive level was set to 0 dBm and the analog interferogram was attenuated to -10 dBm. Separation in power levels between LO and RF signals was maintained, as possible, to ensure optimal mixing specifications (e.g. conversion loss, gain, intermodulation distortion, isolation and dynamic range) and, thus, linearity across the frequency bandwidth.

3. Results

3.1 Data post-processing

Using an Insight laser, electronic frequency shifting was observed to yield large and varying fine structure in A-lines after normal OCT processing (see, for instance, Fig. 2(d)). The fine structure was presumed to be related to the presence of laser transition periods in the analog interferogram during electronic frequency shifting. The magnitude and spacing of the fine structure relative to the main lobe was found to be dependent on the f_LO. When mixing the interference signal, the removal of the invalid points, which would nominally correct phase discontinuities in the digitized interference signal, introduces additional phase discontinuities because the LO signal is continuous (Fig. 1(c)). A potential solution was to compensate analytically for the signal phase distortion by adding the correct amount of phase back into the signal in post-processing. This was tested by simulating electronic mixing as multiplication with a LO. An Insight laser interferogram for a single reflector was simulated using parameters from Laser 1. Random values were inserted between linear-in-k intervals to represent transition periods. The product interferogram was lowpass-filtered and down-sampled at 400 MS/s. Figure 2(a) and (b) show the simulated product interferogram after invalid points were removed and the A-line resulting from an FFT with a Hann window. As can be seen, phase discontinuities in the signal lead to a spectrally broad point spread function (PSF) with extensive fine structure. A phase correction vector was calculated as the phase accumulation of the f_LO over the temporal interval of the transition periods (i.e., ${\varphi _c} = 2\pi \ast \left[ {0,\; \frac{1}{{{f_{LO}}}}{N_1}dt,\; \frac{1}{{{f_{LO}}}}{N_2}dt, \ldots \; \frac{1}{{{f_{LO}}}}{N_m}dt} \right]$, where N_m is the number of invalid samples in a transition interval, dt is the temporal sampling and $\varphi$_c is the phase correction vector). This correction was applied as a complex phase, in a similar way as in numerical dispersion correction (i.e., ${s_1} = {s_0}.\ast {e^{i({{\varphi_c}} )\textrm{}}}$, where s₀ and s₁ are the interferogram after invalid point removal and after correction, respectively). The A-line following phase correction (Fig. 2(c)) shows that the distortion due to f_LO-based phase discontinuities is largely suppressed. Figure 2(d) and Fig. S1,a-c shows the result of applying this correction to a measured interferogram from a mirror with the same f_OCT and down-converted with the same f_LO. Phase correction yielded a distortion suppression of -8 dB with a PSF closely resembling the source A-line acquired without mixing. We explored the performance of the phase correction in the f_OCT range of 235-1488 MHz (Fig. S1,d-h). The results reveal that distortion suppression is reduced with increasing f_OCT. At the same time, the spectral bandwidth measured at -10 dB of the normalized A-line peak steadily increases from ∼0.28 to 5 MHz over $\Delta z$, but is still reduced by ∼50% compared to uncorrected A-lines, for which the bandwidth increases to ∼10 MHz at the largest $\Delta z$ (Fig. S2, a,b). The corrected down-converted A-lines for the lowest and highest f_OCT are shown in Fig. 2(d). Clearly, the f_LO-based phase correction is not accounting for all of the effects that lead to the degradation of the A-line.

 

Fig. 2. Simulation and experimental results of phase correction for EFS-OCT using Laser 1 specifications. Simulated product interferogram (a) and A-line (b) for a single reflector with f_OCT= 235 MHz and f_LO= 185 MHz following invalid point removal. Discontinuities dependent on the f_LO are seen to be introduced at the transition period stitching locations of the signal, resulting in additional nonlinearities relative to normal OCT. (c) Phase discontinuity-correction of the simulated A-line results in reduced fine structure and spectral bandwidth. Experimental, down-converted A-lines over the f_OCT (and $\Delta z$) range of the system, phase-corrected based on $\varphi$_c(f_LO) (d) and measured, overall phase corrections (e).

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There are a number of potential sources of noise and phase error that could be contributing to the apparent residual nonlinearities in the A-lines. The analytical phase correction did not take into account the effects of varying mixer drive level or the introduction of inherent mixer and LO noise over the frequency bandwidth. Inadequate mixer drive level (set by LO power) results in incomplete commutation of the mixer and, consequently, increased conversion loss, reduced dynamic range and increased intermodulation distortion. Sub-optimal drive level therefore leads to increased nonlinearity in performance over frequency. On the other hand, mixer and LO noise are known to increase at increased operating frequencies. Together, these effects could lead to reduced signal-to-noise ratio (SNR) and increased spectral broadening at higher f_OCT. Similarly, we could be seeing effects due to the nonlinearities in the laser sweep, as larger and smaller nonlinearities exist in transition periods and “linear regions” of the analog sweep, respectively. This would be consistent with our observation using the nonlinear-in-k laser, where we showed the signal bandwidth increase rapidly with f_OCT. Assuming transition period nonlinearities are addressed by removal of invalid points, small deviations in the linearity of the sweep are known to result in fine structure and a non-finite PSF bandwidth using the Insight laser in normal OCT [8,18]. In the end, we did not have a good way to reliably model these sources of distortion and derive an analytical solution for correcting the A-line. Instead, we chose a numerical approach that is agnostic to the source of phase error. This was done in the same way numerical dispersion correction is measured, using the interferogram from a mirror reflection to calculate the phase correction as the Hilbert phase. The Hilbert phase measured with a mirror sample should be a line; hence, the correction is simply the deviation from linearity. Practically, we subtract a best fit line from the Hilbert phase to extract the phase correction. Since the laser sweeps are not perfectly repeatable between the 400 MS/s intervals, the correction was measured 1000 times. Each correction was applied to 1000 interferograms and the average A-line was taken among them. The optimal correction was selected as the correction providing the maximum average A-line intensity. The reprocessed product PSFs are plotted in Fig. 2(e) (and Fig. S1,i-m). At low f_OCT, a distortion suppression of -30.5 dB is achieved, nearing the level of Hann window sidelobes (i.e., -31.5 dB); for increasing f_OCT, distortion suppression decreases toward -20 dB. This is attributed to changes in mixer performance which increase the presence of non-linear and noise-related fine structure and may not be repeatably measured. “Overall” phase correction yielded a consistent and narrow A-line spectral bandwidth over f_OCT corresponding to the axial resolution of the source. Distortion suppression and the -10 dB spectral bandwidth results for uncorrected and overall corrected data (N = 10) over f_OCT are plotted in Figure S2. A fixed set of LO and OCT center frequencies spaced over the bandwidth of the photodetector were used to acquire phase corrections for the data presented herein. Measured phase corrections for a given f_LO setting were applied to OCT signals within ∼±50 MHz of the phase correction f_OCT without significant degradation of the PSF.

3.2 Optical performance

The lateral PSF FWHM along X and Y axes was calculated in Excel using data from a slit scanning beam profiler and 1310 nm diode laser. The PSF was found to be well maintained over the $\Delta z$ range with an average X and Y FWHM of 47.8 and 45.6 µm, respectively, over 20 cm (Fig. S3). This compared well with the Zemax prediction, 40.3 µm, especially when considering that Zemax does not model the expected gravity-sensitive Y-coma aberration of the tunable lens.

The optical system sensitivity for normal OCT was measured using a mirror sample and a neutral density filter to represent the optical attenuation of biological tissue. The SNR was calculated as the ratio of the maximum peak amplitude to the average standard deviation of amplitude for a defined noise region with depth adjacent to the peak, among 5000 A-lines. Optical attenuation due to the filter was added back to the measured A-line to get the sensitivity of the system for a perfect reflector, i.e., the system SNR. Theoretical SNR [19] for a perfect reflector was calculated to be 114.65 dB with 12 mW on the sample. A SNR of 112.03 dB was measured at an $\Delta z$ of 13 mm (f_OCT ∼ 100 MHz).

3.3 Electronic frequency-shifting OCT performance

The addition of frequency mixing hardware to the analog processing of the interferogram was expected to impact the system sensitivity. An ideal mixer results in the division of input amplitude between sum and difference frequencies. As the noise and sources of loss through mixing are difficult to accurately predict and dependent on mixing conditions (see Section 2.2). we only consider the signal loss for the stated theoretical mixing SNR. Therefore, a minimum 6 dB loss in SNR is expected. Based on the measured SNR using normal OCT and without considering the above-mentioned practical sources of loss, the highest attainable SNR was expected to be 106 dB. The SNR and phase noise over a $\Delta z$ range of 30 - 190 mm (f_OCT = 235 -1488 MHz) was measured using Laser 1. The results for SNR are shown in Fig. 3(a). The following approach was used to obtain consistent measures of SNR for each dataset. The noise region was selected at various adjacent depth regions of the acquired baseband to represent the highest possible SNR in Fig. 3. This was necessary because the frequency mixing process also shifted the signal relative to weak fixed pattern noise which might fall in the chosen bands. In practice, this amounted to a 1-2 dB shift in SNR. At low f_OCT, the SNR measured ∼103 dB. With increasing f_OCT, SNR is gradually reduced to 97.2 dB at 190 mm $\Delta z$. At low f_OCT, additional loss beyond the ideal SNR is attributed to added noise from the mixer and LO signal. These noise sources impact SNR at all $\Delta z$ and exhibit some degree of frequency dependence and system dependence (e.g., contributions of out-of-band reflectors). Significant frequency dependent loss observed with increasing $\Delta z$ is primarily attributed to reduced LO power relative to the mixer drive level. Under-driving the mixer can result in changes to performance and product level (see Section 2.2). At maximum output power, the synthesizer was not able to generate a 0 dBm LO drive level for f_LO > ∼1.2 GHz. For the corresponding $\Delta z$, the analog interferogram was attenuated to -5 dBm below the LO output power.

 

Fig. 3. EFS-OCT performance measured over f_OCT. Normal OCT measures are plotted at the corresponding f_OCT of 100 MHz/13 mm $\Delta z$. Extended $\Delta z$, up to 190 mm (f_OCT= 235-1488 MHz), were measured via EFS-OCT. Mean and standard deviation were calculated from N separate acquisitions for each setting. Error bars represent the random error, quantified as the standard deviation, among N acquisitions. (a) Signal-to-noise ratio. (b) Time domain phase noise ${\sigma _{TD,norm}}$. (c-d) Frequency domain phase noise ${\mu _{FD,norm}}$ (c) and ${\sigma _{FD,norm}}$ (d) binned over 1 kHz noise frequency intervals. Representative high frequency noise frequency intervals (9.5-19.5 kHz) are plotted for clarity.

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Functional extensions of OCT provide valuable clinical information and materials characterization (e.g., blood flow and mechanical properties) by utilizing the precise phase information provided by OCT [1,7,20–24]. It was unclear to what extent electronic frequency shifting and the phase correction noted above would affect the quality of the OCT phase data. To assess the possibility of functional imaging over a large $\Delta z$, time domain and frequency domain phase noise were measured. Consecutive interferograms at a single position were acquired from a mirror. Since the LO was not synchronized with the laser sweep, a phase shift was introduced to each interferogram, constituting a linear phase ramp in time. As a standard part of our post processing, we fit the phase to a line and subtract the result to remove the linear part of the phase drift. Hence the asynchronous LO does not impact our phase measurement. Time domain phase noise was measured as the standard deviation of the OCT phase at the reflector position. Frequency domain phase was calculated as the FFT of the time domain phase at the reflector. The mean and standard deviation of the frequency domain phase was then calculated over several frequency intervals. In order to compare the time and frequency domain phase noise among data with different SNR, the results were normalized by a factor of $\sqrt {SNR} $, to make the results independent of SNR [25].

Time domain phase is utilized in many OCT angiography and elastography algorithms [20–23]. Figure 3(b) shows the time domain phase noise standard deviation, normalized by $\sqrt {SNR} $, ${\sigma _{TD,norm}}$, for normal and EFS-OCT. The EFS-OCT ${\sigma _{TD,norm}}$ is >3X smaller than that observed with normal OCT and decreases with increasing f_OCT. To better understand the origin of the time domain phase noise trend, the frequency domain phase noise was calculated in 1 kHz binned intervals from 0 - 20 kHz for normal OCT and EFS-OCT over a $\Delta z$ of 13-190 mm. The 0-20 kHz noise frequency range was chosen to encompass the human hearing range [26], as well as other biological signal frequencies studied via angiography and elastography [22,27,28]. Figure 3(c) and (d) show the frequency domain phase noise mean, ${\mu _{FD,norm}}$, and standard deviation, ${\sigma _{FD,norm}}$, respectively, plotted by noise frequency interval over f_OCT. The noise frequency bins are labeled by their center frequency. All bins up to 4.5 kHz are shown; subsequently, bins are plotted at 5 kHz intervals. Frequency domain phase noise also decreases over Δz in a manner dependent on the noise frequency band. More importantly, it can be seen that the low frequency contributions to phase noise, in the 0-3 kHz range (shown by the black, blue and cyan curves), are largely responsible for the improved phase noise of EFS-OCT. This result is consistent with the idea that low noise frequency phase noise is attenuated by the electronic mixing process. Following mixing, filtering around the acquisition bandwidth attenuates low frequency flicker noise and environmental noise that has been shifted outside of the acquired frequency band [15]. Between the 0-1 kHz noise frequency interval, ${\mu _{FD,norm}}$ is reduced by greater than an order of magnitude for the highest Δz using EFS-OCT relative to normal OCT, while ${\mu _{FD,norm}}$ between 1-3 kHz in noise frequency is reduced by more than 5X. Higher frequency noise frequency contributions to both ${\mu _{FD,norm}}$ and ${\sigma _{FD,norm}}$ exhibit lower magnitude overall with high similarity across f_OCT. These results indicate that an overall decrease in time domain phase noise may be achieved with increasing $\Delta z$ via EFS-OCT. For applications such as angiography, this implies the possibility of increased sensitivity to motion, as detected low frequency phase contributions are expected to exhibit greater correlation with sample motion. As noted above, the SNR of EFS-OCT decreases with increasing $\Delta z$ (Fig, 3(a)); however, this improved phase noise performance compensates such that the phase-noise statistics are similar between normal and EFS-OCT. Fig. S4 shows the overall frequency domain phase noise calculated over a noise frequency interval of 3-20 kHz, which reflects this conclusion. The interval 3-20 kHz was selected to exclude flicker noise and provide a representative measure of the frequency domain phase noise for each $\Delta z$ setting. These results demonstrate the utility of EFS-OCT for frequency domain phase-based elastography and vibrometry methods [27,29–31].

Contrast and visibility of morphological features in OCT imaging are required to provide clinical value in medical applications of OCT. To qualitatively compare normal OCT and EFS-OCT, B-scans of the finger of a healthy volunteer were recorded over $\Delta z$ using Laser 2 to achieve improved axial resolution compared with Laser 1 (Fig. 4(a)-(h)). Figure 4 illustrates example images during normal OCT imaging (Fig. 4(a)) and at extended $\Delta z$ using EFS-OCT (Fig. 4(b)-(h)). Normal OCT processing was performed for all images, replacing dispersion correction with overall phase correction for mixing data. B-Scans are displayed on a log-scale and normalized with the same values across $\Delta z$, without accounting for differences in SNR or dynamic range mismatch. The imaging methods exhibit a similar degree of contrast between epidermis and dermis, with sharp delineation of morphological features such the epidermal surface, dermal papillae and sweat glands. This is most apparent at lower $\Delta z$ which correspond to lower f_OCT and higher SNR. While the mixer performance is slightly altered with $\Delta z$, morphological features are well visualized without additional image processing up to the highest $\Delta z$. To test the optical system to its working distance limit, we switched to Laser 1 and recorded finger images with $\Delta z$ up to 200 mm. Figure 4(i) and 4(j) show example images acquired at 150 mm, near the longest $\Delta z$ achieved within the typical tunable lens range, and at 200 mm $\Delta z$, near the limit of the photodetector bandwidth and beyond the manufacturer’s specifications for the tunable lens. Similar contrast and features can be visualized between Laser 1 and 2.

 

Fig. 4. B-Scans of a human finger from a healthy volunteer acquired with normal OCT (a) and EFS-OCT (b-j) configurations. $\Delta z$ and corresponding f_OCT at which each B-scan was acquired are noted below each image. (a-h) were acquired using Laser 2, while (i,j) were acquired with Laser 1. Image dimensions are 2.2 × 3.26 mm and 2.2 × 3.27 mm for Laser 1 (i,j) and Laser 2 (a-h), respectively. Finger imaging was performed without stabilization; thus, tissue cross-sections displayed and presence of motion artifact in sample images vary.

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4. Discussion

Herein, we demonstrate a novel and highly flexible method to extend imaging range in OCT. In contrast to the majority of recent work in improving depth range, EFS-OCT allows for a varying optical pathlength difference, while maintaining the original Nyquist imaging depth and acquisition bandwidth. As the imaging penetration depth in many samples is limited to several millimeters at most at OCT wavelengths, this method can enable auto-focusing to collect only the band-limited signal, preserving signal quality and sensitivity, and avoiding the need for data compression. By using a tunable lens, high contrast morphological images were acquired over a > 21 cm range. This approach reduces the optical design complexity needed for focusing over a large axial range without requiring custom optical components or complex signal detection. Importantly, we also avoid bulky translation stages (which have limited range and speed), large bandwidth acquisition electronics, increased data size and storage (which would limit real-time imaging and display), and expensive custom lasers and arbitrary waveform generators. Instead, only one set of modulation electronics (sinusoidal function generator and mixer) is required. Relatively inexpensive and established RF technology can be utilized through existing manufacturing processes. Finally, the use of commercially available components implies the potential of EFS-OCT for translation and practical application.

The achievable depth range using EFS-OCT scales with the linearity of the sweep (and the choice of acquisition bandwidth, sweep rate etc.). Although an Insight laser with a high degree of sweep linearization is applied here, other laser sources with a linearized sweep may also achieve extended ranging through our approach. For instance, a high degree of sweep linearization has been demonstrated using MEMS-VCSEL sources [9,32,33]. Although the degree of linearization is lower relative to the Insight laser, EFS-OCT may provide an extended depth range on the centimeter-scale using these sources as well.

Although the advantages of the EFS-OCT system design are tied to an (effectively) linear-in-k laser source, the system design is convenient to implement and tune to suit applications requiring various optical designs, $\Delta z$ ranges, and bandwidths. As the proposed system uses a typical Mach Zehnder interferometer, sample arm optics can freely be adapted for various field-of-view and resolution requirements. Using commercial RF components offers a wide range of frequencies and bandwidths which can be chosen to suit specific application needs. A common drawback of this technology can be the frequency-dependent nature of the circuit performance. The circuits used herein are specified with much larger RF bandwidths than was used (mixer: ∼6 GHz, synthesizer: ∼9.8 GHz), allowing for greater frequency range expansion. While achievement of a flat frequency response with increasing RF bandwidth becomes increasingly difficult to design, performance in this study was seen to be primarily impacted by frequency-dependent variation in maximum LO power generated with the RF synthesizer. Both SNR and dynamic range could be improved by re-designing the RF synthesizer and mixer circuits to use an appropriate LO drive level and implementing calibration of LO level across f_LO for equivalent image contrast and SNR. While frequency-dependent corrections across the $\Delta z$ range are required in our approach, only a simple post-processing step, similar to dispersion correction, is required. Likewise, laser phase corrections are expected to be stable over long periods of time; hence, only infrequent updates are needed.

The proposed system presents strong potential for convenient workflow integration through an auto-focusing scheme. All components involved in $\Delta z$ variation in the EFS-OCT system are programmatically controlled, with a demonstrated variable working distance approaching the range of microscopes commonly used for medical procedures in ENT. Although we do not implement autofocusing in this study, autofocusing software for real-time imaging has been previously demonstrated [6,7,34]. This paradigm also limits the cost of reduced Nyquist depth as the system design is altered for various applications. With the tuning speed of the RF synthesizer and tunable lens on the order of several milliseconds, periodic autofocusing can be designed to suit the application (e.g., expected motion artifact). Sparsity and compressed imaging techniques are also compatible with EFS-OCT. Further, image stitching routines [35,36] could be used with this system to reconstruct high resolution, large field-of-view volumes of samples with irregular topology, as image depth is pre-determined. Thus, EFS-OCT can offer efficient and customized integration of OCT in clinical and industrial processes.

Larger $\Delta z$ range beyond that demonstrated here is possible via EFS-OCT. In order to fully meet the needs of the ENT clinic and other applications, alternative designs can be explored. For instance, multiple tunable lenses can be used to increase the focusing range. The increased fringe frequency could be accommodated by tuning the Insight laser to use a smaller dk, thereby reducing the fringe frequency for a given $\Delta z$ and sacrificing imaging speed. Alternatively, unbalanced photodetectors with multi-gigahertz bandwidths are available to detect higher frequencies than shown here. As the mixer was broadband, the maximum $\Delta z$ demonstrated was constrained by our choice of the above-mentioned components.

While EFS-OCT shows potential for commercial translation and adoption by other research groups, future advances in technology can further improve the approach. Limitations due to photodetector and mixer bandwidths stemming from mixing in the electronic domain, as well as reduced SNR, may be addressed by implementation of frequency mixing in the optical domain while preserving the benefits of the demonstrated technique. To date, efforts toward optical mixing primarily take an optical aliasing approach using comb sources. While these sources and systems specifically customized for OCT are not yet commercially available, further development of standard comb sources, optimized driving electronics and simplified triggering and post-processing schemes will likely lead to reduced cost and may provide a practical low-cost long-distance ranging solution in the future. However, at the current date, this technique is relatively complex to implement. Alternatively, a single broadband optical modulator could be used to achieve optical mixing prior to photodetection. Such an approach could take advantage of a large variety of laser sources and with benefits and implementation similar to the technique presented here while achieving enhanced SNR. This requires the development of fast optical modulation components with large modulation bandwidths (i.e. in the GHz range) to relieve the requirements for large bandwidth in successive components. Currently, commercially available frequency shifting electro-optic or acousto-optic modulators are primarily limited to small modulation bandwidths or specific spectral bands (i.e. telecommunication bands) [14,37]. However, these components also exhibit frequency-dependent performance - a challenge in broadband applications across domains. Down-conversion could also be approached through spatial mixing strategies in spectrometer-based systems (i.e., spectral-domain OCT).