1. Introduction

Endoscopy has undergone substantial advancements, transitioning from basic visual aids to sophisticated tomographic 3D imaging systems. These systems have profound applications in various fields, notably in medical diagnostics and industrial inspections. Among various 3D-imaging modalities, optical coherence tomography (OCT) distinguishes itself due to its ability to offer high-speed, high-resolution 3D images on the micron-scale [1–5]. In recent years, a variety of endoscope designs have been integrated with OCT, ranging from compact fiber-based probes suitable for arterial inspections to larger capsule probes designed for gastroenterology applications [6–9]. A key focus in the latest OCT research has been to increase A-scan rates to several MHz using Swept Source OCT (SS-OCT) [10]. This enhancement facilitates live volumetric OCT imaging [11], which is critical for using OCT as a navigational tool in surgical interventions, enabling surgeons to make real-time decisions. Additionally, real-time OCT endoscopy is highly relevant in preventive medical examinations, such as early cancer detection in the colon or rectum. Real-time imaging allows doctors to identify and potentially remove pre-cancerous tissue during examinations, thus reducing the likelihood of overlooking such tissue and consequently decreasing the risk of cancer development [5,12,13].

Building on the foundational advancements in OCT endoscopy [5–9,12], this study introduces the design and implementation of a rigid circumferential scanning OCT endoscope. The probe features a tip diameter of 25 mm and an adjustable radial distance for the beam waist relative to the endoscope axis, extending to a few centimetres. Specifically tailored for clinical use, particularly in colorectal screening, our OCT probe potentially offers superior diagnostic resolution compared to conventional ultrasound imaging (USI), with a significant emphasis on real-time imaging. In our application, achieving a lateral OCT resolution of approximately 20 $\mathrm{\mu}$m and scan radii spanning a few centimeters necessitates a considerable number of circumferential A-scans, often surpassing tens of thousands. This requirement is largely due to the need for beam spot oversampling to adhere to Nyquist’s theorem. Therefore, achieving high-speed A-scan rates, ideally reaching the multi-megahertz range, is essential for facilitating real-time imaging. MHz OCT has also been successfully integrated into endoscopic probes using either Fourier-Domain-Mode-Locking (FDML) lasers or tunable vertical-cavity surface-emitting lasers (VCSEL), enabling volumetric endoscopes in both clinical and industrial settings [7–9,14–16].

With the design of our OCT endoscope tailored for colorectal screening, we next address critical operational challenges that are pivotal in actualizing its clinical potential. A paramount issue in real-time imaging is the initiation of each 3D frame at a consistent location on the target tissue, crucial for avoiding image jitter, a common impediment that can obscure crucial diagnostic details. Additionally, we must tackle non-uniform rotational distortion (NURD), a phenomenon resulting from asynchronous motor rotation relative to the OCT acquisition speed. NURD can significantly degrade image quality, thus impacting the reliability of diagnostic conclusions [5,7,8,16–20]. Previous efforts to address image jitter and NURD in OCT have often relied on specialized custom motors to maintain constant rotational frequency, probe window markers, or numerical post-acquisition corrections [7,17–19,21–24]. To avoid numerical post-processing, Wang et al. triggered the OCT acquisition using the motor’s driving voltage assuming no lag between motor position and driving voltage to enable endoscopic Doppler-OCT [25]. A more precise method was presented in [15], where an optical motor position sensor was included in the endoscope. However, these approaches, while effective, often introduce complexities in terms of additional equipment inside the probe or computational requirements, and may not fully address the real-time demands of clinical applications.

In this work, to enable motor-position-triggered OCT imaging without the need for costly position sensors, we employed commercially available low-cost brushless direct current (BLDC) drone motors for scanning. For OCT triggering, we leveraged the principle that a voltage is induced in 3-phase BLDC motors due to the motor’s rotation, creating a force that counteracts the rotation (Lenz’s law); commonly known as back electromotive force (BEMF). Since BEMF depends on the motor’s position, it can be utilized for position sensing. We demonstrate that our sensorless approach accurately detects the rotational position of the motor and can be used to trigger image acquisition with our lab-built FDML-based OCT system at almost the same position. Furthermore, we present data validating that the motor used operates with minimal NURD, maintaining an angular position deviation of less than 4 mrad. Additionally, low position jitter and NURD may facilitate the integration of various OCT contrast methods in real-time OCT endoscopy, such as phase-sensitive and dynamic contrast OCT (dOCT) [26,27], which we expect to play a major role in future cancer screening application. While this work focuses on technical aspects, medical results have been obtained and will be presented in follow-up publications.

2. Materials and methods

2.1 OCT system and imaging

Figure 1(a) presents a schematic diagram of the home-built FDML laser-based MHz OCT system used in this study, as detailed in [28,29]. The system’s FDML laser operates at a tuning rate of approximately 410 kHz with eightfold optical buffering, achieving an effective A-scan rate of around 3.28 MHz. The central wavelength is set at 1310 nm, coupled with a bandwidth of 105 nm, which provides an axial resolution of approximately 8 $\mathrm{\mu}$m in air [28,30,31]. The probe’s optical power output is 17 mW. The OCT interference signal is captured using a 1.6-GHz balanced photodetector (Thorlabs, PDB480C-AC, USA) and a data acquisition card with 4 GS/s and 12-bit sampling depth (Alazartech, ATS9373, Canada). The imaging depth range of our OCT system is approximately 5 mm, reflecting the integrated capabilities of the FDML laser, APD, and ADC [29]. Control over both the FDML laser and ADC is managed by an arbitrary waveform generator (AWG, Rigol DG 1062, China). Real-time processing and visualization of OCT data are facilitated by an NVIDIA GPU (NVIDIA, GeForce RTX 3070, USA). The approaches to signal processing and large dataset management in our OCT system align with those previously reported by our research group [14,32,33].

 

Fig. 1. Experimental OCT and Endoscope Setup: (A) Integration of endoscopic probe with FDML-OCT system and trigger components (details of turquois highlighted area are given in Fig. 2); (B) Detailed view of an endoscopic probe with inset highlighting optomechanical elements. Abbreviations: MC, motor controller; C, collimator; FC, fiber coupler; FL, focusing lens; RM, reflective mirror; BM, brushless DC Motor; ADC, analog to digital converter; AWG, arbitrary waveform generator; BPD, balanced photodetector; TC, trigger controller.

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2.2 Endoscope design

Fig. 1(b) illustrates the design and components of the OCT endoscope (rectoscope) developed in this study, with a probe diameter of 25 mm. This includes a schematic of the optical and mechanical components at its distal end. Starting from the distal end, a smoothly profiled alloy end cap was incorporated to ensure easy probe insertion. Within the end cap, a ball-bearing motor (BETAFPV, 1102, China) was centrally mounted using a 3D-printed part fabricated using an SLA printer (Anycubic, Mono 4K). A mirror mount was also fabricated by 3D printing to mount a 3 mm-wide reflective prism mirror (Thorlabs, MRA03) on the motor axle, positioned at a 5-degree angle relative to the optical window to minimize back reflections. A 2 mm-thick polymethyl methacrylate (PMMA) window served as the optical interface, firmly affixed to the end cap. Nevertheless, our exhaustive ray tracing simulation, carried out with the commercial software Zemax, along with subsequent spot size measurements, demonstrated that the plexiglass had minimal impact on the beam profile. For additional information, please refer to the Supplement 1. The opposite end of the PMMA window was connected to a lens holder made of aluminum alloy. This holder encased a focusing doublet lens (Thorlabs, AC080-030-C) with a focal length of $f_{FL}=30$ mm, which resulted in a focal spot size (at $1/e^2$ intensity fall off) of roughly 18 $\mathrm{\mu}$m at a wavelength of $\lambda =1310$ nm, corresponding to a Rayleigh range of about $z_R=191$ $\mathrm{\mu}$m (all values in air). This lens holder was then attached to a collimator (Thorlabs, F260APC) using threads, with a spacer placed between the focusing lens and the collimator. The OCT fiber was attached to the collimator on one side, and its other end was connected to the rear side of the handgrip, which was fabricated using a 3D printer (Prusa, MK4 3D). A stainless-steel casing tube connected one end to the PMMA window and lens holder and the other front end to the handgrip. Additionally, the handgrip accommodated the motor’s control circuitry. During our experiments, the focusing lens was placed at two different locations. This adjustment enabled a focal spot with a radial distance of 500 $\mathrm{\mu}$m and 10 mm to the PMMA window outside the probe.

2.3 Motor control and OCT synchronization using BEMF-based virtual Hall sensing

To start OCT image acquisition at the same angular position $\theta _n$ of the motor at each $n$-th revolution, we exploited the BEMF-signal of the BLDC motor inside the endoscope to derive an angular position trigger signal [34]. A schematic of the lab-made motor controller is given in Fig. 2. The target rotational frequency of the BLDC motor is set according to the number of A-scans to be recorded per revolution and is controlled by a commercial electronic speed controller (ESC: Graupner, S3079) comprising a PID speed controller. The ESC was reprogrammed to increase the commutation frequency to 96 kHz. A microcontroller board (PJRC, Teensy 4.1) was used to set the motor frequency on the ESC as well as sending a position trigger signal to the OCT’s ADC, see Fig. 1(a). To ensure that A-scan acquisition is only started at the beginning of an FDML wavelength sweep, a D flip-flop is added in front of the ADC’s trigger input channel. Thus, image acquisition is only started if the ADC has received a motor position trigger as well as an FDML sweep trigger. Note that the FDML is buffered 8 times, and a sweep trigger is only provided every 8th A-scan [35].

 

Fig. 2. Detailed illustration motor controller operation. (A-C) Showcase BEMF voltage and input PWM frequency across the motor phases U, V, and W, respectively. (D) Demonstrates a distorted zero-crossing signal (W-U), derived from the comparison of raw signals from two phases through a comparator after current and voltage regulation. (E) Presents a rectangular wave signal with six pulses per rotation, produced after the signal’s traversal through a low-pass filter and subsequent comparison to a threshold voltage. (F) Displays the final output - the OCT imaging trigger for each mechanical rotation.

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To derive the FDML trigger signal from the motor’s BEMF, we adopted the recently proposed virtual Hall sensing technique [34]. It is a sensorless method that computes the BEMF voltage difference between two of the three motor phases U, V, W over a single electrical revolution step (motor coil passing a magnet) during the commutation cycle, as shown in Fig. 2. By comparing the voltages from two motor phases, for example, U and W, a voltage is obtained that drops to 0 at distinct motor angles. This point is known as the Zero-Crossing-Point (ZCP); for more details, see Fig. 2 in Ref. [34]. The input voltage difference between these two phases coincides with the back EMF voltage. As a result, the zero-crossing points (ZCPs) of the two-phase difference generate a virtual Hall signal that closely resembles an actual Hall sensor signal, if one is available [34,36]. Moreover, this two-phase difference approach for back EMF measurement offers significant advantages, particularly at low speeds, over other back EMF-based methods [37].

The technical realization of the endoscope’s motor controller is shown in Fig. 2. The motor was driven by the ESC using pulse-width-modulation (PWM), with this signal being superimposed on the BEMF across all three phases (U, V, and W), as depicted in parts A, B, and C of Fig. 2. We processed the raw signals from two of the phases (W-U, U-V, W-U) using a comparator (1/2 of LM319). Each of these resulting signals passed through a low-pass filter and was then evaluated by a second comparator (2/2 of LM319) against a threshold voltage ($v_{th}$). This comparison produced a rectangular wave signal characterized by six pulses per rotation. This specific pulse number is attributable to the motor being a six-pole-pair motor, as illustrated in part E of Fig. 2. For this work, we focused on utilizing the W-U signal, converting it into a single rotational trigger signal to initiate OCT image acquisition. Considering additional phases U-V and V-W (similar signals with electrical phase shifts of 120 and 240 degrees, respectively) and a larger number of motor pole pairs (six in this study) would allow for a resolution of up to 20 mechanical degrees or 10 mechanical degrees when considering both rising and falling edges of the BEMF signal. This has the potential to bring about more comprehensive enhancements in image stability, particularly in mitigating jitter and addressing intra-frame NURD, ultimately offering significant benefits to various applications, including distortion-free imaging or laser marking, among others.

2.4 Motor stability measurement

The rotational stability of the motor, coupled with the ESC controller, plays a pivotal role in achieving NURD-free imaging. Simultaneously, the precision of the virtual Hall sensing method is critical in determining the exact initiation of image acquisition at consistent angular motor positions. This dual aspect of accuracy and stability was evaluated using the experimental setup illustrated in Fig. 3. A 658 nm laser diode (Roithner, SPL650-20-4-PD) was connected to the OCT fiber input of the endoscope, with the beam focused to a point approximately 10 mm from the probe’s exterior. To measure the period length ($T_n^p$) of each full motor rotation, an amplified photodiode (APD: Thorlabs, PDA015A) was used, with a razor blade placed at the endoscope’s focal point to create a sharp, precise interruption of the light path, enhancing the accuracy and consistency of the measurements. A Keysight oscilloscope (DSOS804A) recorded signals from both the APD and the BEMF originating from the motor controller while the motor was in operation.

 

Fig. 3. Motor stability and BEMF-trigger measurements: top left: experimental setup; top right: sketch of the motor indicating angular motor position $\theta$ and related phase error $\varphi$; bottom: schematic of motor position signal measured by APD (red) and provided by MC (blue) compared to a theoretical signal with constant period length (black). Abbreviations: MC, motor controller; APD, amplified photodetector; DSO, digital storage oscilloscope.

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Motor stability assessments were carried out at three distinct rotational frequencies: $F_r=$200 Hz, 667 Hz, and 1000 Hz. These tests were conducted under a static load (mirror) within a controlled environment that maintained a stable ambient temperature of 22.3 $^\circ$C, free of external disturbances, with each measurement spanning five seconds. Motor stability was quantified by $\delta t^{p}$, which represents the discrepancy between the rising edges of a theoretical motor signal with a constant period $T^i$ and the actual position of the motor as measured by the APD signal, as illustrated in Fig. 3. Additionally, $\delta t^{b}$, which represents the discrepancy between the rising edges of a theoretical motor signal with a constant period $T^i$ and the estimated position of the motor as measured by the BEMF signal, was also considered. The APD measurements were considered the ground truth for the measurement of the accuracy of the BEMF signal. Additionally, trigger accuracy was assessed by $\delta t^{pb}$, defined as the difference between the rising edges of the APD signal and the BEMF signal. For each rotation, the periods recorded from the APD and BEMF signals, denoted as $T_n^p$ and $T_n^b$, respectively (where $n$ is an integer counting the rotations), were transformed into frequency using the formula $f_n^{b,p}=(T_n^{p,b} )^{-1}$.

To meet clinical requirements, the probe’s outside temperature was measured using a PT100 thermistor at a rotational frequency of 667 Hz for one hour under two conditions: natural cooling and induced airflow within the probe. Without airflow, the temperature exceeded 40 $^\circ$C after 25 minutes but stayed below 41.5 $^\circ$C after an hour. With airflow at approximately one litre per minute, the temperature remained below 39 $^\circ$C even after an hour. Further details can be found in Supplement 1.

2.5 OCT measurements and NURD quantification

Real-time OCT imaging using our trigger method was demonstrated using a variety of imaging samples, including a human finger and a pipe with distinctive features such as a weld seam and 3D printed profiles, which also emphasizes the system’s utility in non-destructive testing, not only in biomedical imaging. Thus, application scenarios range from medical diagnostics to industrial quality control. In addition, to quantify NURD, we fabricated a cylindrical test target (SLA printer Photon Mono X, Anycubic, China) with an internal diameter of 26 mm and six equally spaced markers. The process of quantifying NURD included the utilization of image processing techniques where an A-scan shift in the entire data set is calculated with respect to the reference frame.

3. Results and discussion

3.1 Motor stability measurement using photodetector

Figure 4 depicts the BLDC motor’s rotational frequency fluctuation over time at three preset operational frequencies: $\sim$ $200\,\text {Hz}$, $667\,\text {Hz}$, and $1000\,\text {Hz}$. The plots reveal a trend of decreasing frequency fluctuation with increasing operational frequency. This pattern signifies enhanced stability at higher speeds, vital for precision and reproducibility in OCT measurements. The standard deviation, represented by $\sigma ^p_f$, of this frequency fluctuation diminishes with ascending operational frequency, observed at $173.86\,\text {mHz}$ at $200\,\text {Hz}$, $76.51\,\text {mHz}$ at $667\,\text {Hz}$, and $49.09\,\text {mHz}$ at $1000\,\text {Hz}$. This reduction in frequency fluctuation can be attributed to several factors. At higher speeds, increased angular momentum inherently stabilizes the motor’s rotation. Additionally, in sensorless control, the amplified BEMF at higher speed provides a clearer indication of rotor position, ensuring more accurate and smoother commutation. There are other factors that could also slightly enhance stability at higher speeds. These include the increased damping effect, the onset of thermal stability, reduced interference from a noisy supply voltage, and the reduction of certain harmonics, among others. Alongside the scatter plots, histograms highlight the frequency distribution of motor speeds and the narrowing distribution of errors with increased operational speed, emphasizing the motor’s enhanced stability. Figure 5 showcases the time and phase errors, denoted as $\delta t^p$ and $\theta$, across the three investigated operational frequencies. Accompanying histograms visualize their distribution. Just as with speed fluctuations, there’s a clear trend of decreasing error values as operational speed increases. This trend is substantiated by the standard deviation values for time and phase errors, $\sigma _t^p$ and $\sigma _\theta$ respectively. These values decline from $\sigma _t^p=4.36\,\mu \text {s}$ and $\sigma _\theta =5.47\,\text {mrad}$ at $200\,\text {Hz}$ to $\sigma _t^p=49\,\text {ns}$ and $\sigma _\theta =0.31\,\text {mrad}$ at $1000\,\text {Hz}$. Histograms accompanying these graphs serve to validate these findings, showing a narrowing distribution of errors concurrent with increased operational speed.

 

Fig. 4. APD measurements of the motor’s rotational frequency indicate the following approximate values: (A) 200 Hz, (B) 667 Hz, and (C) 1000 Hz. The dashed line denotes the pre-determined motor speed. On the left, the time series data (in purple) and its 50 ms moving average (in blue) are presented; on the right, the corresponding frequency histogram is shown.

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Fig. 5. Time errors, represented as $\delta t^p$, alongside their corresponding phase errors $\theta$, are displayed for the motor at approximate rotational frequencies of: (A) 200 Hz, (B) 667 Hz, and (C) 1000 Hz. The black dashed line signifies the reference value. To the left, the time series data is portrayed; to the right, the frequency histogram is presented.

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The simultaneous assessment of speed fluctuation and phase error offers a comprehensive overview of the motor’s performance and stability. These parameters are closely interconnected, as irregularities in speed can influence the motor’s phase positioning, and vice versa. Nonetheless, it’s essential to recognize potential sources of these errors. Errors can be caused by changes in motor parameters (like winding resistance, inductance, and magnetic characteristics), mechanical factors (such as bearing friction, rotor misalignment, or imbalance), or an unstable or noisy power supply. Addressing these issues could significantly enhance overall system performance and stability. However, it is crucial to clarify that mitigating these errors is beyond the scope of the current work. Additionally, the optimization of PID parameters for specific operational speeds represents another promising avenue to further enhance motor control. While this aspect is promising, it lies outside the scope of our current research but remains a valuable area for future investigation.

3.2 Accuracy of virtual Hall sensing based on BEMF

In this section, we analyze the accuracy of virtual Hall sensing using the BEMF. Our evaluation includes a cross-correlation analysis between the photodetector (APD) signal and the BEMF signal over different motor speeds as well as a Fast Fourier Transform (FFT) to determine their frequency content. In addition, we investigate the motor speed and phase shifts when the BEMF signal is used as the triggering mechanism at speeds critical for OCT imaging to validate the effectiveness of BEMF as a reliable trigger for imaging processes.

To determine the degree of similarity and any potential time-lag between the APD and BEMF signals, we utilize the normalized cross-correlation matrix (see e.g. [38]). For clearer visualization, we plotted a contour map (Fig. 6), where each 2D matrix segment indicates the correlation coefficient for a specific APD and BEMF frequency pairing. We employed a color spectrum with red indicating values near 1, gray around 0, and blue close to -1. The x-axis of the map represents the frequency derived from the APD, while the y-axis represents the frequency from the BEMF. With a color-coded correlation coefficient for each point, patterns and dominant trends are immediately discernible. Using the APD as our reference, we can measure BEMF’s accuracy. The normalized cross-correlation coefficients highlight the intricate dynamics between the two signals across diverse frequency pairings. A coefficient of 1 (in red) implies perfect BEMF and APD alignment at that frequency. A coefficient of 0 (in gray) suggests no discernible relation. Notably, we didn’t identify any -1 (in blue) coefficients, underscoring that BEMF readings never opposed APD readings. This finding emphasizes the reliability of the BEMF in measuring motor behaviour compared to the APD benchmark. Another salient feature of our contour maps is the diagonal line, which serves a dual purpose: its width ($\Delta w$) reflects the precision of the correlation between the two frequencies, while its length ($\Delta l$) provides insight into the range and variability of observed motor frequencies. Delving into specific observations from our contour maps (refer to Fig. 6), panels A, D, and G unveiled noteworthy trends. For instance, at 200 Hz (panel A), the diagonal line exhibited both greater length and width, indicating a broad range of correlations across the frequency spectrum and implying increased variability or uncertainty. However, as the operating frequency of the probe increased to 667 Hz (panel D) and further to 1000 Hz (panel G), this diagonal began to contract in both dimensions. This reduction in length and width signifies a narrowing of the correlated frequency range, resulting in increased precision. It suggests that at higher operating frequencies, the BEMF signal becomes a more precise reflection of the APD frequency, providing more consistent and reliable data.

 

Fig. 6. Analysis of APD and BEMF signals across three rotational frequencies: approximately 200 Hz, 667 Hz, and 1000 Hz. Each row represents a specific rotational frequency. (A, D, G) Contour maps display the normalized cross-correlation between motor speeds as measured by APD and BEMF. A diagonal line indicates strong correlation zones: its width ($\Delta w$) denotes precision, and its length ($\Delta l$) captures motor speed variability during observation. The color gradient shifts from blue (-1, inverse correlation) to red (1, perfect correlation). (B, E, H) FFT analyses of BEMF signals uncover the presence of dominant frequencies. (C, F, I) Panels compare the frequency spectra of BEMF and APD signals, with embedded mini-panels showcasing the FFT of the APD signal.

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FFT analyses of the BEMF and APD signals are depicted in panels B, E, H, and the mini panels within C, F, I of Fig. 6. Upon initial observation, the visual similarity of both the BEMF and APD FFTs across various rotational frequencies is evident. Despite the visual congruence, panels C, F, and I, which highlight the differences between the FFTs of the BEMF and APD signals, reveal subtle variances. The deviations are approximately $20 \times 10^{-4}$ at 200 Hz, $3.4 \times 10^{-4}$ at 667 Hz, and $1.2 \times 10^{-4}$ at 1000 Hz. Given that these discrepancies are of the order of $10^{-4}$, it provides an explanation for the visual similarity between the two FFT signals. The pronounced resemblance, especially at 667 Hz and 1000 Hz frequencies, confirms that both approaches capture nearly identical motor operation characteristics. Given our findings from the cross-correlation and FFT analysis, the observed trends and frequency components of BEMF and APD are consistent. This consistency supports our proposal to use BEMF as an efficient, simpler alternative to APD for measuring motor speed, especially in precision-demanding contexts such as synchronized MHz OCT imaging.

Focusing on the key $\sim$ 667 Hz speed, which is critical for our OCT imaging setup, we delve deeper into the accuracy and stability of BEMF-based detection, as shown in Fig. 7. The scatter plot and histogram in Fig. 7 show the normalized frequency jitter at $\sim$ 667 Hz. These visualizations illustrate the fluctuations over time and provide a comprehensive view of the variability in motor speed as detected by the BEMF relative to the APD. In particular, the normalized frequency jitter, on the order of $10^{-4}$, implies that the differences between the frequencies measured by the APD ($F^{p}$) and the BEMF ($F^{b}$) are extremely small relative to the average frequency ($F_{avg} = \frac {1}{2n} \sum _{i=1}^{n} (F^p_i + F^b_i)$), indicating a high degree of agreement between the two measurement methods. Furthermore, in Fig. 7(b) we analyze the phase ($\varphi$) and time ($\delta t^{pb}$) differences at about 667 Hz. These differences are calculated between the APD and BEMF measurements as shown in Fig. 3. The scatter plot shows the phase and time difference over time, both of which have low standard deviations of $\sigma _\varphi =0.84$ mrad and $\sigma ^{pb}_{t} =220$ ns, respectively. This illustrates the accuracy of the BEMF in tracking the motor’s angular position. Complementarily, the distribution spread in the histogram further demonstrates the accuracy and precision of BEMF. The results demonstrate that performance comparable to the APD can be achieved using BEMF as a trigger for stable OCT imaging. However, it is important to note that BEMF is not only an alternative to APD, but also a novel introduction to the field, given the spatial limitations that make the use of photodetectors impractical during live OCT measurements.

 

Fig. 7. This figure shows (A) the frequency jitter over time with a 50 ms moving average, and (B) the time and phase differences between the APD and BEMF at $\sim$ 667 Hz motor speed. Each sub-figure includes a scatter plot (left) and its histogram (right).

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3.3 Accuracy and stability of BEMF-triggered OCT imaging

In this section, we present the main results related to the stability and performance of our BEMF-triggered OCT imaging system. Figure 8 provides evidence of the operational stability of the system and the quality of the OCT images that were produced. Figure 8(a) shows the BEMF-monitored motor speed fluctuations compared to the FDML signal, showing slight fluctuations of $\sigma ^{b}_{f}$ = 141.17 mHz. Figure 8(b) shows the angular position of the motor with respect to the FDML signal, noting an SD in phase error of $\sigma _\Phi$ = 1.33 mrad, which translates to a time error of $\sigma ^{b}_{t}$ = 317.57 ns. Supplement 1 provide details on other operating speeds.

 

Fig. 8. Motor characteristics at $\sim$ 667 Hz using BEMF measurements in BEMF-triggered OCT images: (A) A scatter plot demonstrates variations in motor speed, with a 50 ms moving average (blue line); (B) Illustrations of phase (red) and time interval (blue) errors represent the motor’s angular position; (C) A-scan shift in OCT images obtained by aggregating the shifts observed in five distinct fiducial markers.

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Both the BEMF and FDML signals exhibit some jitter. Notably, the FDML signal shows substantially lower jitter, at about four orders of magnitude less than its BEMF counterpart. This minimal relative jitter implies a notable stability in the FDML signal, allowing it to serve as an ideal clock. However, certain limitations in our data acquisition system have led to minor delays in imaging post-triggering. This has, in turn, introduced a slight increase in jitter within the acquired OCT images. The jitter, or A-scan shift due to this delay, is visually represented in Fig. 8(c). This analysis highlights small variations in the post-trigger angular positions within the acquired OCT image. Notably, the majority of these variations occur within $\pm$ 4 A-scans out of a total of 4900, which could be attributed to the optical buffering factor of 8 FDML sweeps and the D-flipflop used in the OCT’s trigger controller. Triggering image acquisition at every A-Scan was not possible with the current OCT system but would result at significant lower jitter. This will be addressed in future work. A more detailed NURD assessment for individual fiducial markers is presented in Supplement 1. Additionally, Supplementary Visualization 1 provides further insight into the performance and stability of the system.

Figure 9 showcases the potential applications and accuracy of our OCT imaging system. This figure provides insights into multiple applications. For instance, Fig. 9(A) portrays images acquired for NURD quantification using fiducial markers. Figure 9(b) offers an in-depth look at the en-face and 3D visualization of an internal welded seam, highlighting the system’s capacity to reveal intricate structural details, especially in industrial environments. The adaptability of the system is evident in panels C to F of Fig. 9, with 3D visuals ranging from internal thread structures to fingerprint imaging. Supplementary Visualization 2, Visualization 3, Visualization 4, Visualization 5 and Visualization 6 offer more detailed 3D views of these structures. A notable feature of our system, shown in Fig. 9, is its ability to produce detailed images across different settings without the need for post-processing enhancements. The OCT images suggest that deviations are negligible, even at the highest magnifications. This finding is further supported by the calculated NURD ($\sigma _{NURD}$ < 4 mrad) for the entire dataset.

 

Fig. 9. Exemplary Raw OCT images: (A) average of 20 images; this dataset was used for NURD quantification using fiducial markers, (B) en face (left) and 3D visualizations (right) of the internal weld structure, (C-F) illustrate 3D internal views of threads, constant and varying frequency profiles, and fingerprints. See the Supplement 1 for 3D visualization.

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To contextualize our findings within the broader scientific landscape, Table 1 provides a comparative analysis. Evaluating distortion metrics from various OCT imaging studies. Our BEMF-based FDML-OCT system excels at producing images with insignificant NURD in real-time preview mode, eliminating the need for additional post-processing. Our findings compare favourably with other studies that utilize custom motors and extensive numerical correction. In scenarios involving high-speed rotation, where jitter typically becomes less pronounced, the performance of our system in near-ideal motor conditions still reveals significant potential advantages. Despite the apparent stability of motor operations at these speeds, there remains a risk of drift and speed inconsistencies, potentially arising from unexpected loads or operational changes. Traditional systems without triggering, though adequate in stable conditions, may overlook these subtle variations, impacting the accuracy of real-time imaging. In contrast, our BEMF-based system excels at constantly monitoring, providing feedback, and adjusting for these fluctuations. This approach significantly elevates image quality and operational reliability. To illustrate the effectiveness of our approach, we compare data acquired without triggering to that obtained with BEMF triggering under conditions where the motor operates nearly stably. This comparison, detailed in Supplementary Visualization 7, underscores the critical role of position triggering in achieving precise real-time 2D or 3D visualization.

Table 1. This table compares distortion metrics in various OCT studies, considering study type, probe diameter, and B-scan rate. It also evaluates standard deviation speeds ($\sigma _f$), angular positions ($\sigma _\theta$), and OCT image distortions ($\sigma _{NURD}$). Experimental studies are labeled "Exp.", and numerical correction studies as "Num. Corr.".

View Table

This capability is particularly vital in multimodal systems, such as those combining OCT imaging with precision laser surgery, where integrating additional hardware for feedback is often challenging. The incorporation of our BEMF-based OCT probe with FDML lasers marks a notable technological leap. This combination is poised to transform real-time visualization in high-speed, multi-megahertz OCT imaging, greatly reducing the dependency on extensive post-processing. Therefore, our system could mark a major advancement in OCT imaging technology, maintaining high precision and efficiency.

4. Conclusion

In this study, we have demonstrated the feasibility of an OCT imaging system triggered by a BEMF-based virtual Hall sensor. This system offers distinct advantages for circumferential scanning in endoscopic applications. One notable aspect of our work is the utilization of commercially available BLDC motors, similar to those commonly found in drones. This choice proves to be more cost-effective than the specialized motors typically used in OCT endoscopic probes. This strategic decision significantly reduces the development costs of OCT probes, potentially bringing them down to as low as USD 200 with further optimization. The novelty of our study lies in the application of a sensorless technique that utilizes the BEMF signal generated by a BLDC motor to trigger a multi-Mz OCT system, effectively addressing common challenges such as image jitter and NURD in real-time OCT procedures.

Our BEMF-triggered OCT imaging system demonstrates a notable decrease in both synchronization error and NURD, with a standard deviation of approximately 317 ns, equivalent to an angle of less than 1.33 mrad (or < 4 mrad NURD in OCT images due to post-trigger error). Remarkably, this level of precision is achieved without the need for external components to provide an output trigger to the OCT system. Furthermore, our study illustrates how integrating this BEMF-based OCT probe with FDML lasers opens up new possibilities for real-time visualization in high-speed, multi-megahertz OCT imaging scenarios, effectively reducing the need for extensive post-processing.

The unique and highly precise rotational trigger offered by our OCT probe possesses the possibility to drive advancements in high-speed multi-megahertz dynamic OCT, particularly in scenarios like dOCT, where minimizing revisitation errors is crucial. Harnessing this innovative triggering mechanism can significantly reduce such errors. The implications of our study may extend beyond the realm of medical diagnostics and surgical guidance, including potential applications in non-destructive industrial testing and real-time monitoring. This approach could effectively overcome the spatial limitations encountered by traditional profiling methods, excelling in 3D profiling and diagnosing complicated internal structures. Moreover, our findings hold relevance across a range of disciplines, encompassing medical, engineering, and industrial applications, such as OCT-guided surgery, gastrointestinal endoscopy, quality assessment, and more.

In conclusion, our work represents a significant advancement in the field of OCT endoscopy by introducing a novel, simplified, and cost-effective method for achieving high-resolution, real-time multi-megahertz imaging. This advancement not only holds promise for enhancing current medical diagnostic and therapeutic procedures but also opens up new avenues for research and application in various other fields. Furthermore, we acknowledge the potential of utilizing back EMF from various phases for enhanced NURD performance. While our current approach focuses on frame-to-frame jitter, exploring back EMF’s role in intra-frame NURD in future studies could lead to comprehensive improvements in image stability and quality, thereby addressing both jitter and intra-frame NURD.