2. Theory

2.1 Single DFB signal

The imaging system relies on the coherent mixing of scattered measurement light with a local reference path, or local oscillator (LO) at a photodetector. For a laser chirping at a constant rate of α (rad/s²) and illuminating a single surface, the photodetector beat signature over a sweep period of T is

2.2 Stitching multiple signals

If we now consider N adjacent laser elements sweeping at the same rate, each with a starting frequency, ${\omega }_{n-1},$ and ending frequency, ${\omega }_n,$ the individual bandwidths, b_n, can be written as $b_n={\omega }_n-{\omega }_{n-1}.$ The combined signal is then

The improved axial resolution from multiple sources is only realized by properly phase-aligning each element’s signal (Fig. 1). The optical bandwidth of each element can be determined via $b_n=\Delta {\omega }_s{M}_n,$where M_n is the number of samples acquired per element and $\Delta {\omega }_s$ is the frequency step between samples. The signal described in Eq. (3) can be expressed in sample space (s) as

 

Fig. 1 Example combined measurement signal for n laser elements. The top axis is angular optical frequency, and the bottom axis is the sample number acquired. The registration error for the third DFB (ε₃) is shown.

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3. System configuration

3.1 Experiment layout

A commercially-available, telecommunication 12-element DFB array module (Fitel FRL15TCWB-D86-19610A, ~3 MHz linewidth) was used as the laser source and driven using a custom printed circuit board (PCB) [26]. Each DFB element was sequentially swept 3.6 nm in 240 µs, providing a total useable optical bandwidth of 5.56 THz in 3 ms, with the combined DFBs spanning between 1524 and 1568 nm. This 12-DFB bandwidth afforded a minimum theoretical axial resolution of 26.98 µm. The frequency sweeps were linearized using feedback from an auxiliary 2.066 m fiber Mach-Zehnder interferometer (MZI) with a free spectral range (FSR) of 100.14 MHz. The 20 MHz photodiode beat signature from the “fine” MZI was send back to the PCB and compared to an on-board reference clock to generate an error signal [(Fig. 2(a)]. The error was used to modify the current drive during the sweep to maintain a highly linear sweep rate (<1 ppm from linear) of −2,002.9 THz/s. A complex programmable logic device (CPLD) acted as a phase-frequency detector to provide the error signal, while also routing the current to each DFB via a transistor network. A thermoelectric cooler (TEC) maintained an array base temperature of 10°C, allowing for the DFB active regions to cycle through the full valid thermal range. Each DFB in the module [(Fig. 2(b)] was internally routed via a multimode interference coupler to a semiconductor optical amplifier (SOA). The SOA was driven in a constant power mode using the in-package power monitor to maintain 20 mW of optical power out of the DFB module. The launched power was 12.7 mW, accounting for 1.97 dB of system losses, including the calibration arm tap [(Fig. 2(c)].

 

Fig. 2 (a) Scanning system layout. DFB: Distributed feedback laser, ISO: Optical isolator, PD1: Balanced photodetector (PD) used for distance measurement, PD2/PD3: PDs used for the reference coarse and fine fiber Mach-Zehnder interferometers (MZI), PD4: PD used to track the absolute wavelength via a hydrogen cyanide (HCN) gas cell. The PDs had low-pass filters (not shown) to reduce out of band noise. The dotted line indicates the custom printed circuit board (PCB). A zero-crossing (ZC) circuit monitored PD3 was mixed with a clock reference (XRef) using a complex programmable logic device (CPLD). Semiconductor optical amplifier (SOA) and thermoelectric cooler (TEC) drivers locked the temperature and output power. The “zero-delay” point (r₀) was set to 5 cm beyond the back mirror. µC: Teensy microcontroller, SSD: solid-state hard drive, PC: computer. (b) DFB array module. (c) Normalized output power over all elements.

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The output of the butterfly package was sent to a 60 dB isolator and routed to the measurement and calibration arms using polarization-maintaining (PM) fiber. In addition to the fine MZI used for linearization, a “coarse” MZI (l = 0.25 m, 827 MHz FSR) and fiber-coupled 25 Torr hydrogen cyanide (HCN) gas cell (Wavelength References HCN-13-H(5.5)-25-FCAPC) were used to track the relative and absolute wavelength sweeps between elements for subsequent combination in post-processing. A PM circulator was used to send and receive the measurement light.

1. Introduction

High-fidelity 3D imaging of remote surfaces with micron-grade resolution and precision can prove to be a challenging task. One common method used for long-distance, high-resolution ranging relies on a linearly-swept, frequency-modulated continuous-wave (FMCW) laser source arranged in a self-heterodyne configuration, where the measured photodetector beat frequency corresponds to the scatter’s distance [1]. Such sources exhibit long coherence lengths and are typically swept at kilohertz rates or less [2, 3]. Long-distance FMCW ranging has found much use in lidar [4, 5], surface profilometry [6], autonomous navigation [7], and optical frequency-domain reflectometry (OFDR) for fiber optic system measurements [8–10]. Similarly, the medical industry has employed this interferometric technique in swept-source optical coherence tomography (SS-OCT) for biological sub-surface imaging [11, 12]. The laser sources used for SS-OCT are swept over several THz of optical bandwidth at up to megahertz rates. The coherence length requirement of the source is greatly diminished due to the millimeters to centimeters of desired dynamic range.

State-of-the-art laser sources for SS-OCT imaging include micro-electro-mechanically-tuned vertical-cavity surface-emitting lasers (MEMS-VCSELs) [13], Fourier-domain mode-locked (FDML) fiber ring lasers [14], and “akinetic” solid-state semiconductor lasers such as Vernier-tuned distributed Bragg reflector (VT-DBR) lasers [15]. MEMS-VCSELs are perhaps the most promising for fast, long range OCT, since they exhibit narrow instantaneous linewidths, a large tuning range, and 100 kHz sweep rates [16]. The mechanical nature of the sweep, however, is subject to resonances, inertial effects, and nonlinearities. At the current time, such VCSEL sources have a limited availability, and thus, can be prohibitively costly. Fiber ring lasers use a piezoelectrically-tuned intracavity Fabry-Perot filter to sweep more than 100 nm at hundreds of kilohertz [17]. Downsides to this approach include a short coherence length on the order of millimeters, a highly nonlinear sweep rate, and large amplitude variations. The VT-DBR’s tuning method relies on modulating the injection current applied to front and back DBR mirrors. The applied current changes the refractive index of the DBR sections, allowing for tens of nanometers of tuning. The time constant of the index change is at the nanosecond-level, allowing for fast tuning rates [18]. However, the control scheme for a linear wavelength sweep can be complex, as each input current must be carefully calibrated to ensure mode hop-free operation.

All of the discussed laser sources are useful for fast, in vivo imaging over typical biological tissue thicknesses. However, for longer ranges and larger objects, the coherence length requirement increases accordingly. In addition, the electrical bandwidth needed to detect distant objects quickly approaches tens of GHz beyond one meter for nominal SS-OCT sweep speeds. A simple optical delay line can be used to shift the “zero-delay” further out if the target’s general location is known, although the unambiguous range depth remains unchanged. For a longer depth and static zero-delay, e.g., the target distance is unknown, a long coherence length source swept at a slower rate is more practical. Narrow linewidth external-cavity diode lasers (ECLs) are commonly used for distances beyond a meter [4, 6]. The extremely long cavity allows for linewidths down to the kilohertz level, providing up to kilometers of coherence length. The mechanical tuning can be accomplished by a motor (~Hz) or MEMS device (~kHz). Without specialized design, mode hops can occur, causing large discontinuities during the sweep [19]. Fiber lasers with PZT-tuned intracavity Bragg gratings exhibit very narrow linewidths (<10 kHz) and have been used in long range OFDR experiments [20]. The limited tuning range, however, limits the axial resolution to millimeters.

Narrow linewidth semiconductor lasers, such as VCSELs and distributed feedback lasers (DFBs), have also been used for lidar and OFDR measurements [21–23]. Continuous tuning of up to several nanometers is possible by modulating the injection current. The sweep rate can be actively linearized using an optoelectronic phase-locked loop (OPLL), ensuring a valid beat signal without the need for computationally intensive post-processing linearization [24, 25]. In addition, the ubiquitous nature of diode lasers makes them attractive for low cost, compact ranging systems.

We present the theory and experimental results of a novel 3D tomographic imaging system that provides the axial distance resolution typically associated with medical OCT over FMCW distances. Using an optical bandwidth-combined, actively-linearized DFB array, we demonstrate tomography and profilometry with an axial resolution of 27.1 µm (for a 12 DFB system) over a total unambiguous depth of 6 meters. A novel “dithering” method for stitching the DFB signals using a reference interferometer and gas cell is presented. We use a low-bandwidth approach and simple signal processing that is ideal for compact, inexpensive embedded components. Several diffuse and semi-transparent objects are used as targets to demonstrate the versatility and high dynamic range of this technique.

The return light was mixed with the local oscillator (LO) at a 400 MHz InGaAs auto-balanced avalanche photodetector (PD1, Thorlabs PDB570C, gain set to ~5). The LO was path-length matched to align the zero-delay point, r₀, to 5 cm beyond the back scanning mirror. The MZI channels were sent to biased 150 MHz InGaAs PIN photodetectors, while the HCN line used an amplified 80 MHz InGaAs PIN photodetector. A series of interchangeable focusing lenses and 2D galvanometer scanner (Thorlabs GVS102) provided for lateral scanning of targets. The 2-axis scanning was controlled using a Teensy 3.6 microcontroller board. Two on-board 12-bit digital-to-analog converters (DACs) were scaled to ± 5 V, providing ± 12.5° optical sweeps on each axis for a scanning volume of ~14 m³.

After the photodiode signals were low-pass filtered, 60,000 samples per DFB were acquired by a 4-channel oscilloscope (Tektronix MSO5204) at 250 megasamples per second, or a sample taken every 8.01 MHz swept. At this sampling rate and laser sweep rate, the Nyquist-limited range window was 9.4 m, corresponding to beat frequencies of DC – 125 MHz. Although ranges only up to 6 m were explored here, the phase-noise-limited range of the laser source was at least 16 m, allowing for longer possible interrogation depths.

The acquisition trigger was synchronized with the start of the valid sweep region by using the CPLD to trigger the oscilloscope after OPLL lock. This allowed the acquisition window to start after the DFB drive settling time. The oscilloscope’s sampling time base was phase-locked with the PCB reference clock using the oscilloscope’s “External Reference In” port, ensuring that each sample taken between separate DFB elements remained on the same optical frequency time base. The channel traces were bundled using the oscilloscope’s FastFrame function and transferred to an external solid-state hard drive. A MATLAB script running on a computer was used for signal processing and image creation.

3.2 Wavelength tracking and signal combining

The DFB elements were driven to provide a ~5% spectral overlap between the stitching regions to facilitate combining in post-processing. While both reference MZIs can be used to track the individual DFB sweep rates, the absolute and relative wavenumber differences between the DFBs remained unknown. To alleviate this problem, the absorption peaks of the HCN gas cell were used as calibrated markers to register the sweeps to known wavelengths. A total of 55 peaks were used; the first 54 peaks were NIST-traceable [27] and assigned accordingly to DFBs 1 to 11 [Fig. 3(a)]. The last peak (P28) was not certified, however, its approximate value was used for the 12th DFB. The number of samples between HCN peaks was counted to determine the initial estimate of the stitch point. Photodetector noise on the HCN line as well as the inherent NIST-given uncertainties contributed to inaccuracies in the initial calculated sample shift (ε_HCN). To correct for this, a least-squares fit on adjacent overlapping coarse MZI traces was performed to determine the final stitch point. The amount of signal shift needed for the best fit (dither, ε_D) was determined for each element. The measurement trace from each DFB and reference channel was then concatenated accordingly via shifting the n^th DFB signal by ${\epsilon }_n={\epsilon }_{HCN,n}+{\epsilon }_{D,n}.$ The dithering process can also be performed by phase-matching in the frequency domain [28, 29].

 

Fig. 3 DFB signature stitching details. (a) Reference traces for two adjacent DFBs. Bottom trace: HCN absorption peaks (inverted and band-pass filtered) used to estimate the first shift, ε_HCN. The grey trace is the original DFB 3 HCN trace before shifting, while the blue trace is after shifting the trace to the left by ε_HCN. This moves the peak to the estimated R15 location relative to R16. Middle trace (red): coarse MZI beat signature, Top trace: detail of the stitch point. After shifting the traces by ε_HCN, the remaining error (ε_D) is corrected via the dithering process. The dotted line is the trace after shifting by ε_HCN, which still has a small phase error. The red line is the phase-matched version after dithering by ε_D. (b) Histogram of the required sample dither for 11,000 stitches. (c) The sampled traces (blue boxes) are collected from the 12 DFB elements, then stitched and processed (green boxes) to generate the final image.

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The distribution of the required dither for a data set of 11,000 stitches is shown in Fig. 3(b). The standard deviation over all DFB regions was ± 4.5 samples, or ± 36.1 MHz of optical frequency uncertainty. The inherent mean two-sigma uncertainty over all peaks as given by NIST at 25°C was ± 12.304 MHz, implying that the majority of the error was associated with the peak location step. The unambiguous optical frequency range of the coarse MZI ( ± 413 MHz, or ± 51 samples) was much larger than the measured worst-case error ( ± 20 samples), eliminating any 2π wrapping uncertainties on the fitting region. Figure 3(c) shows a summary of the image generation process.

3.3 PSF analysis

An evaluation of the system’s axial point spread function (PSF) was performed (Fig. 4). The output was sent through a collimating aspheric lens (f = 11 mm, NA = 0.24) to the 2D scanner. A pair of lenses was used to expand the beam to a 1.4 mm waist with a confocal distance of 8 m. A gold mirror target was placed at points along the total system distance, and measurements were taken with the scanning mirrors stationary. The chromatic dispersion mismatch between the fiber interferometer (silica) and measurement path (air) caused a residual chirp to remain on the measurement signal, resulting in a widening of the point spread function (PSF) [Figs. 4(b)-4(e)]. A 3^rd-order Taylor expansion of the fiber’s propagation constant was used to approximate the dispersion mismatch. The first HCN peak location (R26) was used as the expansion point. The group velocity, group delay dispersion, and third-order dispersion values of the fiber were used as initial expansion coefficients. These values were then iteratively modified to maximize the PSF sharpness to within 1% of the theoretical value. Because the refractive index properties of the fiber do not change greatly over time, the coefficients were measured once and stored. These coefficients were then used to dechirp each subsequent measurement via cubic spline interpolation [26] using MATLAB’s griddedInterpolant function. The final ~700,000 sample points were zero-padded to 2²⁰ points before applying the FFT. The system sensitivity level, defined as the minimum detectable FFT signal level, was −107 dB. However, the sensitivity level increased to −102 dB during the mirror measurements. The strong retroreflected signal created additional scattering within the collection fiber, leading to a decrease of the apparent sensitivity. Because the mirror returns were very strong, the oscilloscope was set to “HiRes” capture mode, increasing the ADC to ~11-bits giving 68 dB of dynamic range. All subsequent measurements used 8-bit sampling (50 dB dynamic range).

 

Fig. 4 PSFs for 12 DFBs. (a) Final 2²⁰-point PSFs up to 6 m. FFTs of measurements using a mirror placed at (b) 0.5 m, (c) 1.5 m, (d) 2 m, and (e) 3 m. The PSFs before (dotted red line) and after (solid black line) the dispersion correction is applied are shown. Note: For smoother visual plots, the data was zero-padded to 2²² points first before the FFTs shown in (b) – (d).

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3.4 Scan distortion and tilt

The two-mirror scanning method caused angle-dependent path length differences in the measurement path, resulting in a distorted raw image. In addition, tilts in the mirrors with respect to the target created additional rotational errors. The “measured distance” is defined here as the sum of the fixed zero-delay distance from the first mirror and the distance computed from the FFT peak, or $r_m=r_0+r_{FFT}.$ For post-objective scanning, the position transformation to Cartesian coordinates for the m^th measurement can be written as

 

Fig. 5 Distortion visualization. (a) Post-objective, two-axis, two-mirror scanning. The red line indicates the measured range. The optical scan angle is twice the mechanical angle. 3D scan of a quarter as viewed along its edge, (b) before and (c) after distortion and tilt correction.

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After applying the distortion correction, the object often remained tilted with respect to the Cartesian planes. When possible, a flat reference surface was placed behind objects and normal to the scanning stage. A series of linear fits to the reference surface was performed to determine the relative tilt angles. With this information, a matrix coordinate rotation was then applied to remove the residual tilt [Figs. 5(b) and 5(c)].

4. Experiment results

4.1 Surface profilometry

The scanning system can perform precision non-contact profilometry of opaque surfaces. The experiments performed in this section used a single combined signature from all 12 DFB elements per data point. After performing each FFT, the peak of the strongest return was used to estimate the surface location. No peak thresholding was needed due to the strong signal return from the gauge block. Distortion and tilt correction was performed before the measurement statistics were calculated.

A series of steel gauge blocks (Mitutoyo 516-103-26, Grade 0) were placed at 4.9 m to test the ranging accuracy and precision while scanning a distant target. Eight blocks were placed flush against another gauge block on an optical bench [Fig. 6(a)]. The surfaces of the blocks were then scanned laterally using a ~0.5 mm step increment and a 200 µm spot size beam. Range measurements along the 8.9 mm block width were used to assess the precision, while the mean differential distance between the background block and each test block’s surface was used as the height measurement [Fig. 6(c)]. Table 1 shows the mean and standard deviation of the scan, as well as the results from ten measurements using a 1 µm resolution micrometer. The mean error in absolute height difference was 10.21 µm with a mean standard deviation of 7.85 µm along the blocks’ surfaces. The accuracy errors in the absolute height most likely can be attributed to imperfect contact with the background block.

 

Fig. 6 (a) Eight gauge blocks placed for scanning at 4.9 m. The block heights are labeled above in mm. (b) Monolithic step block placed at 5.18 m. (c) Close-up of individual measurements taken on the 3 mm gauge block. (d) Single lateral scan of a 0.1” step steel block.

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Table 1. Gauge Block Height Measurements.

View Table

A monolithic steel step block was also placed at 5.18 m as an additional test [Fig. 6(b)]. The monolithic nature of the block removed the placement ambiguity experienced with the step blocks. A single lateral scan was performed, with 35 points acquired along each step surface [Fig. 6(d)]. Using the shortest step as the reference, the mean step height of the remaining four 0.1” steps was measured to be 2542.03 ± 7.72 μm. Using the micrometer, the mean step height was measured as 2540.25 ± 0.79 μm using ten measurements per step. As expected, the height measurement accuracy improved, while the precision was consistent with the gauge block measurements.

4.2 Remote 2D tomography

In addition to single-surface mapping, the DFB scanning system can perform remote sub-surface imaging of semi-transparent objects (Fig. 7). Sub-surface features act as scatters along the measurement path, providing a means to image the interior structure. Such imaging capability would prove useful in many research and industrial applications such as defect analysis, multilayer thickness measurement, and interior profilometry.

 

Fig. 7 Remote 2D tomographic images. The inset number indicates the amount of DFB elements used. Axial resolution per number of DFBs: 1 = 294.2 µm, 2 = 155.3 µm, 4 = 79.0 µm, 8 = 40.6 µm, 12 = 27.1 µm. Yellow bar = 5 mm. (a-f) Egg crate packaging foam located at 5.1 m. The red box indicates a 10 x 5 mm region. (g) Polyethylene packaging slab at 5.1 m, (h-j) 2” laminated medallion at 1 m. Reference photographs: (k) egg crate foam, (l) polyethylene slab, (m) laminated medallion.

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Figure 7 shows 2D tomographic images of various objects obtained using a single lateral scan with varying amounts of DFBs. Convoluted egg crate “open-cell” polyurethane foam [Figs. 7(a)-7(f)] exhibits small voids, which are visible down to 2 mm below the surface. An expanded view of a foam tip is also shown in Figs. 7(a)-7(e). The increased detail and improved image sharpness is evident as the number of DFBs increase. The tomogram of a 1.5 cm-thick “closed-cell” polyethylene slab [Fig. 7(g)] shows 2 - 3 mm voids inside the structure, with 50 - 100 μm-thick plastic walls that act as strong scatter locations. The image of a two-inch diameter embossed plastic medallion with a clear laminated coating shows the front surface, as well as the detail underneath [Figs. 7(h)-7(j)]. The relief profile of the individually stamped letters and symbols below the lamination are clearly visible, with improved resolution as the DFBs increase.

4.3 Large-volume 3D imaging

High dynamic range 3D imaging is also possible with the DFB scanning system. Several objects were placed at various ranges to test the 3D imaging performance. Depending on the size of the target, the beam waist (w₀) and confocal parameter were varied using an appropriate lens configuration. The beam waist was increased for larger objects to keep the data sets at a manageable size. In addition to reducing the lateral resolution, it should be mentioned that larger spot sizes can reduce the effective axial resolution due to multiple backreflections from the varying depths within the spot area, especially for rough surfaces. A peak threshold was set to 6 dB above the noise floor to reduce false peaks. Axial scans without a return above this threshold were replaced using a 3-by-3 pixel median filter. The additional 6 dB threshold buffer effectively set the sensitivity level to −101 dB for the 3D scan. After a valid peak was found, the scanning distortion was corrected by using the range and angle information to create an image in Cartesian coordinates using Eqs. (5)-(7).

A quarter [Fig. 8(b)] was placed at 25 cm and scanned (w₀ = 71 µm). The relief profile in Fig. 8(a) shows imperfections created during the stamping process, as the bottom ridge is visibly higher than the surrounding coin edge. In addition, fine features such as the text and hair can be resolved. A stamped medallion [Fig. 8(d)] was placed at 1.1 m to demonstrate larger surface mapping (w₀ = 230 µm). Figure 8(c) and Visualization 1 show more detail of the surface, as well as a cut-away of the 2” medallion from Fig. 7.

 

Fig. 8 3D images over depths ranging from less than a millimeter to meters. (a) Surface map of a (b) quarter at 25 cm, 400 x 420 pixels. (c) Surface map of a (d) 15 cm diameter medallion at 1.1 m, 700 x 740 pixels. (e) Volume depth map of a (f) potted plant placed at 2.5 m, 408 x 490 pixels. Volume shown = 33.5l x 30d x 40h cm. (g) Reflectivity profile of the plant with a (h) rotated view. (i) 3D mesh of a (j) six-foot ladder starting at 2.5 m, 408 x 370 pixels. The red arrows indicate the illumination direction. (k) 3D point cloud of a (l) room with a variety of objects, 884 x 900 pixels. Volume shown = 2.4l x 1.6d x 2.5h m (9.6m³).

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As a longer distance test, a potted plant [Figs. 8(e)-8(h)] was placed at 2.5 m and scanned using 50 µrad steps (w₀ = 430 µm). As seen from Fig. 8(g), the individual leaves and stems are clearly defined throughout the plant. A rotated view is shown in Fig. 8(h), and a 360° movie is presented in Visualization 2. Although not performed here, additional scans can be taken from multiple angles to create a full 3D profile. A six-foot ladder [Fig. 8(j)] was imaged to create a 3D mesh [Fig. 8(i)] using a 0.68 mrad angle step size over ± 8° (~3.2 m³ volume scanned, w₀ = 430 µm). The point cloud used to generate the mesh is shown as a rotating animation in Visualization 3. Finally, a 6 meter-deep room containing several objects [Fig. 8(l)] was scanned as a demonstration of the system’s large volume capability (w₀ = 750 µm). An intensity-shaded point cloud is shown in Fig. 8(k) and Fig. 9, where the brighter spots indicate stronger returns. A rotating view of the 3D-mapped room is shown in Visualization 4.

 

Fig. 9 Detailed view of the room scan, colored by depth and shaded by signal strength.

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5. Discussion and conclusions

We have presented a novel 3D FMCW imaging system that combines 12 DFB elements for precision surface interrogation with significant stand-off, depth, and volume. Both sub-surface tomography and diffuse surface profilometry have been demonstrated on a variety of objects at different ranges. The actively linearized source greatly reduces the amount of signal processing required, while a simple stitching process allows for improved axial resolution with minimal processing overhead. The processing can further be reduced by using a properly chirped voltage-controlled oscillator for the OPLL reference clock, dispersion-compensating fiber, or air-gap MZIs for the signal mixing arm to eliminate the dispersion correction step. Because the reference fiber MZIs are sensitive to vibrations and temperature swings, they must be environmentally isolated to ensure consistent measurements over time. An optical frequency comb [30, 31] or laser velocimeter [3] in the calibration arm could be used to account for the effects of the environment, further improving the accuracy and precision. The maximum range can be greatly increased by using post-amplification, higher bandwidth photodetectors, and phase-noise compensation [25].

One limitation of the imaging system is the scanning speed, which is slow compared to its SS-OCT counterparts. The scanning rate is limited by the thermal cycling speed of the DFBs and bandwidth of the OPLL that maintains the linear sweep. One potential increase in speed, at a cost of higher electrical bandwidth, shorter ranging depth, and lack of active linearization would be to use a larger, but shorter current pulse [32]. Another method would rely on sweeping a fraction of each DFB’s available bandwidth, then applying compressive sensing techniques [33], or other sparse sampling methods to extract the range information. Simply using half of the DFB elements would cut the scanning time in half. Although this would also reduce the axial resolution by half, the ranging performance could still be acceptable for large objects.

The data processing of the presented experiments was not performed in real-time. The data acquisition took up to several hours because the measurements needed to be saved to an external hard drive for off-line processing. Without the bottleneck of the oscilloscope and data saving, the total scan time would be greatly reduced. The per-pixel scan time was ~5 ms, including 3 ms for sweeping the 12 DFBs and 1.5 ms to move the mirror. For example, a 12-DFB, 400-by-400 pixel image (84 gigavoxels) would take 13 minutes to scan. While the raster scan was slow compared to typical OCT speeds, the image processing time (sample-for-sample) was greatly reduced by the active linearization of the laser sweep. A free-running laser would require a linearization algorithm to be run on every sweep, which would add significant extra processing time. For a sample-to-sample comparison, a series of 12-DFB 3D range measurements were downsampled to 200,000 points and processed. Each 3D pixel took ~34 ms to process in MATLAB using an Intel Core i7-6700 CPU, as compared to a reported 84 ms [16] for a free-running laser, using the same number of samples. The per-pixel processing time on 2²⁰ samples, including the stitching (11 ms), dispersion compensation (15 ms), and FFT (21 ms) steps, took under 50 ms. The processing time can be sped up further by using specialized spectral analysis tools, such as the Chirp-Z transform [34, 35]. These techniques can readily be applied for diffuse objects which typically only have one surface along the axial direction.

It is important to note that water is highly absorptive within the wavelength sweep range of the laser source [36]. For imaging through water or biological material, another wavelength band, such as near 1.3 μm, would be more appropriate. Therefore, our system is best used for sub-surface imaging of non-biological materials such as plastics, glasses, fabrics, and ceramics.