## Abstract

Swept-wavelength reflectometry is an absolute distance measurement technique with significant sensitivity and detector bandwidth advantages over normal pulsed, time-of-flight methods. Although several tunable laser sources exist, many exhibit short coherence lengths or require mechanical tuning components. Semiconductor distributed feedback laser diodes (DFBs) are advantageous as a swept source because they exhibit a narrow instantaneous linewidth and can be frequency-swept simply via a single injection current. Here, we present a novel bandwidth generation technique that uses a compact, monolithic, 12-element DFB array to create an effectively continuous, gap-free sweep. Each DFB is sequentially swept over 3.5 nm at 1,600 THz/s using a shaped current pulse, ensuring spectral overlap between each element. After combining the self-heterodyned return signatures, the transform-limited resolution of the 43.6 nm sweep is demonstrated to be ~27.4 μm in air with a precision of 0.18 μm at a distance of 1.4 m.

© 2017 Optical Society of America

## 1. Introduction

Coherent frequency-modulated continuous-wave (FMCW) reflectometry is an interferometric distance measurement technique that has been employed in many sensing applications including optical coherence tomography (OCT) of biological tissue [1,2], optical frequency-domain reflectometry (OFDR) for fiber optic sensors and fiber component analysis [3,4], and long-range lidar systems [5–7]. Unlike ranging techniques that use short, high peak power pulses for time-of-flight measurements, FMCW reflectometry relies on the mixing of time-delayed light with a local oscillator (LO) to create a low bandwidth beat frequency that varies with distance. Common spectral analysis tools such as the Fast Fourier transform (FFT) can be used on the beat signal to extract the locations of reflections in the path. Coherent FMCW reflectometry is attractive because it exhibits a significant sensitivity advantage over time-of-flight techniques [8]. In addition, the range resolution can be improved by increasing the optical frequency bandwidth of the sweep. Ideally, a perfectly linear frequency-swept laser source would result in an exact match between beat frequency and distance. In practice, fluctuations in the sweep rate, effects of material dispersion, and laser phase noise can all degrade the beat signal. The sweep rate can be actively linearized by employing an optoelectronic phase-locked loop (OPLL) that uses feedback to synchronize the chirp rate to an external electronic frequency reference [9–11]. Free-running, nonlinear laser sweeps can be tracked externally using an optical frequency comb [12] or a reference interferometer. The known properties of the interferometer can be used to estimate the instantaneous phase using an I/Q demodulation scheme [13] or as part of a “k-clock” that triggers data acquisition on the beat signal zero-crossings, effectively sampling on equally spaced optical frequencies [2, 14]. The nonlinearities in the data also can be corrected in post-processing using a Hilbert transform to acquire the analytic signal, then directly compensating for the phase errors [15,16]. Dispersion effects can be corrected using numerical techniques such as applying a chirp-z transform to the measurement signal [17].

Many types of tunable lasers are viable as sources for coherent FMCW reflectometry. The laser coherence length is a vital characteristic and must be long enough for the desired ranging capability. The frequency sweeping rate also must be taken into consideration, as higher sweep rates can limit the total range depth by exceeding the detector bandwidth while sweep rate nonlinearities can distort the beat signatures. External-cavity lasers can tune over large frequency ranges and exhibit narrow linewidths, but require moving parts and can be subject to mode-hopping [18]. Diode lasers with electrically-tunable elements, such as super-structured-grating distributed Bragg reflector lasers (SSG-DBRs), can be discretely tuned over large frequency ranges, but have limited continuous sweep regions and require complex look-up tables for operation of multiple control sections [19,20]. Vertical-cavity surface-emitting lasers (VCSELs) can be frequency-swept by injection current [21] or by a mechanically-tuned cavity [22], but tend to have linewidths of tens of MHz at best [23]. Distributed feedback lasers (DFBs) can produce a single longitudinal mode, exhibit instantaneous linewidths of 10 MHz or less, and can be continuously tuned several nanometers simply by modulating the injection current [24]. In addition, DFBs can be actively linearized at high speeds using an OPLL [11]. Vasilyev, et al. reported ranging results using sweeps of 300 GHz by combining multiple temperature-shifted DFBs [25], while Dieckmann demonstrated a sweep of 1.4 THz using a refractive index-tunable twin-guide DFB [26].

In this paper, we present a novel method for generating a large frequency sweep for laser radar (ladar) measurements by using a compact, commercially available, butterfly-packaged DFB laser array. Each DFB element is swept over 500 GHz in 300 μs using a tailored current pulse, ensuring a spectral overlap between each element. The return signatures are remapped to equal frequency steps using a reference Mach-Zehnder interferometer (MZI) then combined in post-processing, resulting in a 5.5 THz bandwidth stretching over the communications C-band (1525 – 1565 nm). A fiber-coupled HCN gas cell is used as an aid for wavelength calibration and registering the DFB regions. The details of combining each source are discussed, and the resulting resolution capabilities (~27.4 μm in air) are demonstrated on various targets.

## 2. Theory of the proposed ladar system

#### 2.1 Single source analysis

For a frequency-swept laser source, the electric field in free-space can be written as,

*A*is an optical power-to-voltage conversion factor (assumed constant), and the remaining phase errors are$\Delta \varphi =\varphi (t)-\varphi (t-{\tau}_{D})$. If

*N*flat surfaces are encountered, the total signal can be expressed as ${\sum}_{i=1}^{N}{v}_{i}(t)}.$ For a finite time period of

*T,*the total optical bandwidth swept can be written as$B=\alpha T$for a linear sweep, resulting in a signal response ofwhere${t}_{0}=0$is the LO-referenced start time of the frequency sweep and

*rect*is the rectangular function. The Fourier transform of Eq. (4) converts the signal to the beat frequency domain and is written as,

*sinc*function (defined $\mathrm{sinc}(x)\equiv \mathrm{sin}(x)/x)$ centered at$+{f}_{D}=\alpha {\tau}_{D}$for the positive single-sided Fourier transform. The distance to the measurement reflection surface is ${z}_{D}=c{f}_{D}/2\alpha {n}_{g},$ where

*c*is the speed of light and${n}_{g}$is the group refractive index along the light path. The minimum axial resolution is given as the distance between the

*sinc*function’s main lobe peak and first null. For a rectangular window, the free-space resolution is$\Delta {z}_{\mathrm{min}}=c/2B.$ Therefore, the resolution can be improved by increasing the frequency sweep bandwidth.

#### 2.2 Combining ideal sources

We now consider two adjacent, equal length bandwidth regions$({B}_{1}={B}_{2}=B)$of the photodiode signal from a single reflector (Fig. 1).

For a linearly swept source, the signal response of the equal bandwidth regions can be described as,

In this case, the sum of exponential terms in Eq. (7) collapses to a purely real, in-phase “sharpening” cosine function that halves the resolution to *c*/4*B.* Additional swept regions can be concatenated in a similar manner to further widen the bandwidth, and thus improve the resolution (Fig. 2).

#### 2.3 Signal registration error effects

Independent sources with adjacent linear frequency sweeps can be combined if their time-dependent wavelengths are known with sufficient accuracy. The optical frequency at the chosen stitch points must match to ensure beat signal phase continuity. The phase relationship is dictated by the time-dependent term in Eq. (3), or, in discrete form, $2\pi {\tau}_{D}{\alpha}_{i}t[{k}_{i}]=2\pi {\tau}_{D}{\nu}_{i}[{k}_{i}],$where *k _{i}* is the chosen sample number for concatenating the

*i*

^{th}source to the next source. The individual source chirp rates,

*α*, must also match, otherwise different beat frequencies would occur, causing a superposition of shifted

_{i}*sinc*functions after the FT. Each source’s chirp rate can be tracked by comparing the beat signal from a well-characterized reference interferometer to a stable electronic oscillator. Applying the proper feedback can ensure that all sources sweep at the same rate [10, 11].

Assuming the source chirp rates are equal, proper phase registration of the sampled regions is needed for subsequent spectral analysis. We investigate the issue of registration by introducing a combination shift error of $\Delta {t}_{err}$ for the *B*_{2} region. If we assume there is no gap between the regions, Eq. (6) becomes,

*q*denoting the registration shift error in integers of the sample number. The error breaks the symmetry of the trailing exponential sum term in Eq. (7) resulting in a shift of the overlaying sharpening cosine term with respect to the

*sinc*function,

*q*= 1). This phase error results in a corrupt main lobe as shown in Fig. 3(d). Therefore, it is critical to properly match each sample point with the correct optical frequency during each sweep to register the two regions properly. A phase-matching algorithm can be performed directly on the two adjacent signal regions, however, such techniques will degrade at a low signal-to-noise ratio (SNR). This potential problem can be avoided by feeding a portion of the light to an external optical frequency reference, as described in the experimental section below.

## 3. Ladar experiment

#### 3.1 Experiment configuration

We now present a ladar experiment (Fig. 4) that demonstrates combining multiple sources with proper registration. The DFB array module used (Fitel FRL15TCWB) consists of 12 individual DFB elements (<10 MHz linewidth), a semiconductor optical amplifier (SOA), thermoelectric cooler (TEC), and monitor PDs for wavelength and power tracking. Each DFB is separated by 3.5 nm, giving the array a total span over the communications C-Band (1525 – 1565 nm). The laser elements are multiplexed through a multimode interference coupler into the SOA that is terminated with a 30 dB isolator.

The output of the butterfly package was connected to a 95/5 2x2 polarization-maintaining (PM) fiber coupler. Single-mode PM fiber was used throughout the setup to eliminate polarization fading. The 95% arm was terminated with a transmit/receive aspheric collimating lens (f = 4.5 mm, 0.9 mm outer diameter) for sample interrogation. The 5% arm was fed to a reference Mach-Zehnder interferometer (MZI) with a ~2.066 m arm length difference and coupled to a low-noise 400 MHz avalanche photodiode (APD) detector. The MZI was placed in an isolated enclosure and all components were mounted to a floating optical table to reduce the effects of environmental vibrations. The back reflection from an uncoated fused silica wedged window was used as the LO reference surface. The return light was collected and sent to an 80 MHz InGaAs PIN PD receiver. Each photodiode channel was simultaneously sampled at a rate of 333 Megasamples per second (MS/s) using a 500 MHz bandwidth oscilloscope (Agilent DSOX3054A) and sent to a laptop for processing. The PD signals were bandpass-filtered to remove the DC terms and eliminate aliasing effects. The measurement arm’s PD filter was set to match the 80 MHz bandwidth, allowing for unambiguous ranging out to 7.5 m for a chirp rate of 1,600 THz/s. Unlike short-pulse coherent time-of-flight techniques [6], no temporal range ambiguity is encountered here because the pulse width is much larger than the time-of-flight delays investigated.

A custom printed circuit board, shown in Fig. 5(c), was designed to provide adjustable current control and fire each DFB sequentially. An on-board programmable current source is fed to a NPN/PNP bipolar junction transistor (BJT) network that switches the current drive between elements. The minimum switching time between channels is 100 ns, giving a maximum full sweep repetition rate of ~300 Hz. Digital control of on-board components is provided by a complex programmable logic device and Verilog code.

The DFB array base temperature was set to a constant 10°C using the built-in TEC. This allowed the active region temperature to increase while maintaining significant optical output into the SOA section, which was driven to provide 5 mW average optical power. The internal 50 GHz etalon reference signal shown in Fig. 5(b) was initially used as a course measurement of the sweep bandwidth linearity. Similar to Ref. 11, the proper current drive shape was determined by observing both the 50 GHz etalon and reference MZI beat frequency responses using a sawtooth pulse, then iteratively adjusting the current ramp accordingly in an open-loop fashion. The DFB current drive profiles were locked to ensure a constant sweep rate of ~1,600 THz/s by comparing the MZI arm’s beat signal to an on-board 16 MHz clock reference. The effective linearity of the sweep was measured by taking the Hilbert transform of the beat signal from the reference interferometer, unwrapping the result, and removing the linear term [27]. As shown in Fig. 5(d), the standard deviation from linear was 2.8596 MHz, indicating an effective coherence length, *l _{c}*, of 33.4 m using ${l}_{c}=c/\pi \sigma ,$ or a ~16.7 m maximum ranging depth in air.

The DFBs were swept far enough in order to ensure a significant frequency overlap between elements, allowing for the signals to be combined without gaps. At this time scale and current levels, the dominant factor on the wavelength sweep is the thermal expansion of the DFB’s Bragg grating due to the non-radiative recombination of carriers in the active region [24]. The expansion of the grating causes a net increase in the output wavelength as described by$\lambda =2\Lambda {n}_{\text{eff}},$ where Λ is the grating period and *n*_{eff} is the active region’s effective refractive index.

#### 3.2 Sweep calibration and combining bandwidths

In order to track the instantaneous wavelength and account for dispersion effects, the HCN and measurement PD signals were resampled at the zero-crossings of the reference MZI. Linear interpolation was performed using the two original sample points straddling each MZI zero-crossing. Both the rising and falling zero-crossings were used as a reference, resulting in two samples generated per MZI free spectral range (FSR). After remapping to zero-crossing space (ζ-space), the effective chirp rate at the *m*^{th} crossing can be written as$\alpha (m)=\gamma (m){f}_{z}(m)$ where $\gamma (m)=-0.5\Delta {\nu}_{FSR}(m)$Hz/ζ and${f}_{z}(m)=1/\Delta t(m)$ζ/s.

Wavelength calibration was performed directly in the time domain by comparing the zero-crossings to the NIST-traceable absorption peaks derived from SRM 2519a [28]. A fiber-coupled, 25 Torr, 5.5 cm path length hydrogen cyanide (H^{13}C^{14}N) gas cell (Wavelength References HCN-13-H(5.5)-25-FCAPC) was used for this purpose. No special temperature maintenance was used for the gas cell because the effects of the ambient temperature variation (22 ± 1 °C) were negligible [28]. Using the HCN oscilloscope trace, the peak extrema were first determined by a least-squares polynomial fitting procedure. The peak locations were then mapped to the corresponding NIST-provided optical frequencies. The *i*^{th} NIST peak-to-peak gap difference $(\Delta {\nu}_{G,i})$ was compared to the number of corresponding MZI zero-crossings (Δζ_{i}) in order to calibrate the MZI arm FSR and register the DFB signal regions. Two combined sections after proper registration are shown in Fig. 6(b). The first peak for the 12th DFB region (P28) is not on the NIST-certified list, however, its location was extrapolated from the given vacuum pressure value and the previous peak locations. The approximate MZI FSR at each zero-cross within the *i*^{th} peak-to-peak region was estimated as,

_{i}is the distance in ζ-space between the peaks, ${n}_{g,i}$ is the MZI group index using the

*i*

^{th}region’s center wavelength, and

*L*is the MZI length. The parameter

*M*is a scalar equal to 2 ζ, accounting for the two samples taken at the rising and falling zero-crossings for each FSR.

The estimated DFB combination point uncertainties ( ± 2σ) were calculated using the systematic fitting uncertainties and the NIST-given 2σ peak uncertainties, as shown in Fig. 6(c). The totals were less than 1 MZI FSR (< 2π certainty), allowing for the determination of an unambiguous section-to-section stitch point to within 1 FSR zero-crossing. As shown from the shaded area in Fig. 5(a), the intensity variations and frequency sweep nonlinearities were larger at the beginning of the pulse. Therefore, after registering each DFB region, the beginning section of each DFB signal was removed and replaced with the backend of the preceding region. The resulting continuous signal containing all 12 regions aligned to the HCN peaks is shown in Fig. 6(a).

#### 3.3 Material dispersion mismatch and processing

While using a reference fiber MZI is adequate for measurements made in similar fiber, a residual nonlinearity will remain for distances measured in air due to the dispersion difference. The remaining chirp broadens and shifts the FFT peak by an amount that varies with distance and the bandwidth of the chirp as seen in Fig. 7(b). This mismatch can be corrected by either using an air-gap reference interferometer [29], dispersion compensating fiber [30], or in post-processing [17, 31]. Here, we use the dispersion properties of the MZI fiber as given by the manufacturer to compensate for the mismatch. To approximate the dispersion effects, the propagation constant, *β(ω)*, can be written as a Taylor expansion about the starting frequency, *ω*_{0}. The angular frequency dependence can be converted to ζ-space via $\omega (m)=2\pi m\gamma (m)+{\omega}_{0},$where *m* is in units of ζ. The propagation constant can then be approximated to third-order as,

*β*

_{1}is the inverse group velocity (s/m),

*β*

_{2}is the group velocity dispersion (s

^{2}/m), and

*β*

_{3}is the third-order dispersion (s

^{3}/m) of the fiber, each evaluated at the starting wavelength (

*m*

_{0}= 0).

For this experiment, the fourth-order term was calculated, however, it was small enough to be neglected as shown in Fig. 7(a). The initial wavelength was determined using the number of zero-crossings between the start of the sweep and the R26 HCN peak. The signal then was corrected by interpolating the samples to *m’* using Eq. (13),

The mismatch effects as referenced to the start of the sweep are shown in Fig. 7(a). By the end of the sweep, there were nearly 9 more zero-crossings as compared to a dispersionless case at *ω*(*m*_{0}). The dispersion mismatch causes the main lobe to shift and spread as shown in Fig. 7(b). Applying the correction procedure removes the residual chirp, revealing the proper main lobe shape and location. As another example, the compensated FFT from a 100 μm etalon using 12 DFB elements is shown in Fig. 7(c).

A standard FFT was performed after compensation and zero-padding ${v}_{\text{tot}}[m\text{'}]$ to 2^{21} points. To determine the corresponding free-space equivalent range, the FFT frequency axis was scaled by$cM/[2{n}_{\text{air}}{N}_{\text{zp}}\Delta {\nu}_{\text{FSR}}({m}_{0})],$ where *M* = 2 ζ, ${n}_{\text{air}}$is the refractive index of air (~1.00027), and *N*_{zp} is the total number of samples after zero-padding. The final FFT peaks were fit with a low-order polynomial to estimate the range value. A summary of the signal processing sequence is shown in Fig. 8.

#### 3.4 Experiment results

To assess the resolution capabilities of the system, a 1 mm glass microscope slide and thin fused silica etalons (nominal 100 μm, 50 μm, and 25 μm thickness) were used as targets. Figure 9(a) shows the improvement in FFT resolution on the 1 mm glass slide as the number of DFBs combined is increased from 1 to 6. Finer structures can be resolved by expanding the range to include all 12 DFB elements as shown in Figs. 9(b) and 10. For closely spaced surfaces, it is important to note that the distance between the two main lobe peaks of the resulting FFT are not equivalent to the true thickness of the sample. In addition to the refractive index scaling factor, the coupling of adjacent *sinc* functions alters the main lobe peak position and amplitude. This perturbation can be compensated by apodizing the signal at a cost of widening the main lobe, or calculating the peak shift numerically [32]. The interference of two close superimposed *sinc* functions can cause inaccurate thickness measurements, as evidenced in Fig. 10(b). Without sufficient bandwidth, the 2 DFB case exhibits one main lobe, implying only a single surface. Both the 4 and 8 DFB cases produce two main peaks, however, the distance between the peaks indicate an apparently thicker sample due to interference between the adjacent main lobes. The 12 DFB case produces two peaks corresponding to the actual surface locations, albeit with a small residual bias due to the remaining overlap of the main lobes. This bias is greatly reduced for separations that are greater than a full main lobe width, or twice the minimum resolution, such as the 12 DFB case in Fig. 10(a).

Next, a 1 inch mounted gold mirror was placed 1.4 m away at the edge of the optical table for use as a stable single reflector target. The full-width at half-maximum (FWHM) of the resulting FFT main lobe’s amplitude was measured after combining each DFB element. From this width, the minimum range resolution can be approximated as$\Delta {z}_{\text{min}}\approx 0.829\Delta {z}_{\text{FWHM}}$for a rectangular window [25]. As shown in Fig. 11(a), the main lobe peak width decreases at a 1/*B*_{N} rate, where *B*_{N} is the combined bandwidth of 1 to *N* DFBs. The final amount of bandwidth excursion for this data set was 5.47247 THz, indicating a transform-limited resolution of 27.39 μm. The measured FWHM in Fig. 11(a) agrees well with this predicted value.

The improvement in axial precision (*δz*) as the elements are combined is shown in Fig. 11(b). For a FMCW laser source with a given signal-to-noise ratio (SNR), the precision is determined by, $\delta z=\Delta {z}_{\mathrm{min}}/\sqrt{SNR}$ [12]. For the 12 DFB case, the SNR using the specular mirror target was 45 dB (−110 dB noise floor), agreeing well with the measured ~180 nm precision. For non-specular targets, the precision is expected to degrade due to lower return light levels and spatial interference effects from speckle.

## 4. Conclusion

We have demonstrated a novel method to generate and combine the individual bandwidths of a DFB array to increase the resolution of FMCW ladar measurements. The main advantages of this approach are scalability, long stand-off range, and ease of implementation. Unlike mechanically-tuned external cavity lasers, which can be slow and have large unusable sweep regions, nearly all of the available bandwidth of the array is utilized in this technique. Temperature tuning of separate elements is not required; a constant base temperature is provided by a single TEC. The modulation is provided with a single current pulse, while a constant output power can be maintained using the integrated SOA. Wavelength monitoring is provided by the HCN gas cell which is a well-calibrated, compact, and passive component.

If faster modulation is required, a shorter and higher current pulse may be applicable [33]. Although not tested here, the DFB elements could also be fired simultaneously with the returns spectrally separated and sent to a photodetector array, increasing the overall cycle rate [25]. This method can be extended into the L-Band (1565 – 1625 nm) by adding another DFB array module with the proper multiple quantum well design. Wavelength calibration can be accomplished by using a multi-gas cell that includes HCN as well as carbon monoxide [34].

In addition, since the ranging capability is limited by the coherence length, applying our technique to a DFB source with better phase noise characteristics would improve the maximum ranging depth. DFB arrays with linewidths on the order of 100 kHz have been demonstrated [35], which would theoretically allow for ranging depths of hundreds of meters. External phase noise reduction techniques [36] can also be implemented to extend the range even further. Other limitations to the unambiguous range window include the available photodetector bandwidth and DAQ sampling rate. Since the beat frequency linearly increases with both range and sweep rate, the electrical bandwidth requirements can quickly reach several GHz. The bandwidth restriction can be relaxed by using cascaded MZI’s for the signal mixing, essentially scaling the beat frequency down to a detectable level [37].

## Funding

Night Vision and Electronic Sensors Directorate, U.S. Army.

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