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,

ε(t)=E0exp[j(παt2+2πν0t+ϕe(t)+ϕs(t)+ϕ0)],
whereE0is the field amplitude, αis the constant chirp rate term (Hz/s), ν0is the initial optical frequency, and ϕ0 is the initial phase. The residual phase terms include deterministic sweep nonlinearities (ϕe) and the stochastic phase noise (ϕs) intrinsic to the laser. In a typical self-heterodyne FMCW reflectometry system, the light source is split and sent to a reference local oscillator (LO) path and a measurement path (R). There will be separate time delays to the photodetector (PD) through the local path (τLO) and measurement path (τR). Assuming matched polarizations and a perfectly flat target, the intensity at the detector is equal to the square of the electric field sum,
I(t)=|εLO(tτLO)+εR(tτR)|2.
The time domain can be referenced to the LO such that τLO=0, and the time difference can be written asτD=τRτLO. When the return light is mixed with the LO at the photodetector, a time-averaged current is produced that is dependent on the detector bandwidth. The current is converted to voltage and AC coupled, leaving a detectable beat signal,
v(t)=Acos[απτD2+2πατDt+2πν0τD+Δϕe+Δϕs],
where A is an optical power-to-voltage conversion factor (assumed constant), and the remaining phase errors areΔϕ=ϕ(t)ϕ(tτD). If N flat surfaces are encountered, the total signal can be expressed as i=1Nvi(t). For a finite time period of T, the total optical bandwidth swept can be written asB=αTfor a linear sweep, resulting in a signal response of
vB(t)=v(t)rect(tt0T/2T),
wheret0=0is 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,
VB(f)=F[v(t)]F[rect(tt0T/2T)],
whereFis the Fourier transform (FT) operator, anddenotes convolution. For a noiseless, linearly swept laser, Eq. (5) results in a sinc function (defined sinc(x)sin(x)/x) centered at+fD=ατDfor the positive single-sided Fourier transform. The distance to the measurement reflection surface is zD=cfD/2αng, where c is the speed of light andngis 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 isΔzmin=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(B1=B2=B)of the photodiode signal from a single reflector (Fig. 1).

 figure: Fig. 1

Fig. 1 Two adjacent regions containing part of the beat signal.

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

vtot(t)=v(t)[rect(ttc+B1/2αB1/α)+rect(ttcB2/2αB2/α)],
wheretcis the time at the mid-point of the two sections. The Fourier transform of Eq. (6) results in,
Vtot(f)=πBAαexp(jθ)sinc[πBα(ffD)]×{exp[jπα(ffD)(2νcB)]+exp[jπα(ffD)(2νc+B)]},
where θ includes the constant phase terms in v(t) and νc is the optical frequency at timetc. Eq. (7) can be simplified as,

Vtot(f)=2πBAαsinc[2πBα(ffD)]exp{j[θ2πνcα(ffD)]}.

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/4B. Additional swept regions can be concatenated in a similar manner to further widen the bandwidth, and thus improve the resolution (Fig. 2).

 figure: Fig. 2

Fig. 2 (a) Individual laser element frequency sweeps with time, LO (solid line) and delayed return reflection (dashed line). Tn indicates the nth sweep period and τD is the time delay to the target. (b) Combined total bandwidth after resampling at equal optical frequencies and stitching.

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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, 2πτDαit[ki]=2πτDνi[ki],where ki is the chosen sample number for concatenating the ith source to the next source. The individual source chirp rates, αi, must also match, otherwise different beat frequencies would occur, causing a superposition of shifted 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 Δterr for the B2 region. If we assume there is no gap between the regions, Eq. (6) becomes,

vtot(t)=v(t)[rect(ttc+B1/2αB1/α)]+v(tΔterr)[rect(ttcB2/2αB2/α)].
The registration shift error isΔterr=qΔνs/α, withΔνsdenoting the constant optical frequency change between sample points, and 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,
Vtot(f)=πBAαexp(jθ)sinc[πBα(ffD)]×{exp[jπα(ffD)(2νcB)]+exp[jπα(ffD)(2νc+B)jθerr]}.
It is important to note that the error depends on both the sampling step size and the distance to the target. ForΔνs = 100 MHz andτD = 1 ns, the phase error, θerr=2πqΔνsτD, in Eq. (10) is 0.63 radians for a single sample shift (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.

 figure: Fig. 3

Fig. 3 (a) Combined photodiode response regions with a single target and perfect registration at the combination point (vertical line), (b) Correct Fourier transform after combining, (c) Two regions with a shift error 1 sample point in the second section. (d) FFT resulting in a corrupt main lobe due to the shift error.

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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.

 figure: Fig. 4

Fig. 4 Experiment Layout. The dotted line indicates components housed inside the butterfly package. The custom printed circuit-board (PCB) drives each DFB element. The light blue lines indicate PM fiber. A Mach-Zehnder reference arm (MZI) and a HCN gas cell aids in wavelength calibration. The Fresnel back reflection from a wedged window acts as the LO, SOA: Semiconductor optical amplifier, A/D: Analog-to-digital data acquisition, TEC: Thermoelectric cooler, BPF: Bandpass filters for DC blocking and anti-aliasing, PD: Photodecter receiver.

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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.

 figure: Fig. 5

Fig. 5 (a) Current ramp applied to each DFB and (b) resulting response of the DFB module’s 50 GHz etalon wavelength reference from a single element sweep. The shaded section is removed when combining with the previous DFB signal. (c) Custom PCB showing the butterfly package containing the DFB array, current driver, and transistor network. (d) Measurement of linearity for all 12 elements over the 5.5 THz sweep, plotted at the MZI zero-cross points. The dotted line is the approximate standard deviation.

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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, lc, of 33.4 m using lc=c/πσ, 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 byλ=2Λneff, where Λ is the grating period and neff 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 mth crossing can be written asα(m)=γ(m)fz(m) where γ(m)=0.5ΔνFSR(m)Hz/ζ andfz(m)=1/Δt(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 (H13C14N) 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 ith NIST peak-to-peak gap difference (ΔνG,i) was compared to the number of corresponding MZI zero-crossings (Δζi) 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 ith peak-to-peak region was estimated as,

γi(m)ΔνG,iΔζicMLng,i,
where Δζi is the distance in ζ-space between the peaks, ng,i is the MZI group index using the ith 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.

 figure: Fig. 6

Fig. 6 (a) Combined signal using all 12 DFB elements. The HCN absorption peaks (red) and a signal from a 50 μm fused silica etalon (blue) are shown. The vertical lines indicate the combination points between DFB regions. The last peak in each DFB region is listed above the HCN trace. (b) Two adjacent measurement signal regions (blue) registered to the absorption peaks (red) of the HCN gas cell. The peak-to-peak distance in zero-crossing-space is labeled as Δζ. The vertical dotted line is the combination point. (c) 2σ uncertainty of the measured gap values (blue bars). The mean MZI FSR (dotted line) and half-FSR (dashed line) are shown for comparison. (d) Optical spectrum analyzer trace averaged over all 12 elements.

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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, ω0. The angular frequency dependence can be converted to ζ-space via ω(m)=2πmγ(m)+ω0,where m is in units of ζ. The propagation constant can then be approximated to third-order as,

β(m)β0+2πmγ0β1+12(2πmγ0)2β2+16(2πmγ0)3β3,
whereβ0=n0ω0/c andγ0=ΔνFSR(m0)/2. β1 is the inverse group velocity (s/m), β2 is the group velocity dispersion (s2/m), and β3 is the third-order dispersion (s3/m) of the fiber, each evaluated at the starting wavelength (m0 = 0).

 figure: Fig. 7

Fig. 7 (a) Air-fiber phase mismatch of the MZI beat signal in terms of the zero-crossings, referenced to the start of the sweep. The contributions of each Taylor series term are shown. For a 1524.9131 nm wavelength start (ng ≈1.4681), the profile follows: (6.37365e-10)m2 + (4.13137e-16)m3. (b) Single reflector FFT peak before (dotted line) and after (solid line) dispersion compensation using all DFB elements. (c) Dispersion compensated signature from a 100 μm fused silica etalon placed at 1 m. The two main lobes correspond to the front and back glass surfaces.

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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),

vtot[m']=vtot[m+(2πγ0)β22β1m2+(2πγ0)2β36β1m3].

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(m0). 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 vtot[m'] to 221 points. To determine the corresponding free-space equivalent range, the FFT frequency axis was scaled bycM/[2nairNzpΔνFSR(m0)], where M = 2 ζ, nairis the refractive index of air (~1.00027), and Nzp 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.

 figure: Fig. 8

Fig. 8 Signal processing steps. MZI ZC: The Mach-Zehnder interferometer zero-crossings are used as the resampling reference (black arrow). The HCN peaks (red arrows) provide a known wavelength reference for registering the measurement segments (blue arrows).

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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).

 figure: Fig. 9

Fig. 9 (a) Incremental improvement in surface resolution of a 1 mm glass slide using 6 elements. All plots are normalized per trace. The measured physical thickness accounting for the refractive index is denoted by Δz. The thickness measured using a micrometer was 1.02( ± 0.01) mm. (b) Thickness measurement of a 100 μm fused silica etalon using up to 12 elements. The thickness reported by the manufacturer was 100.7 μm.

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 figure: Fig. 10

Fig. 10 (a) Improvement in surface resolution of a 50 μm fused silica etalon using 12 elements. The manufacturer-provided thickness was listed as 47.6 μm. (b) Incremental improvement in surface resolution of a 25 μm fused silica etalon. The actual thickness was not provided.

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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 asΔzmin0.829ΔzFWHMfor a rectangular window [25]. As shown in Fig. 11(a), the main lobe peak width decreases at a 1/BN rate, where BN 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.

 figure: Fig. 11

Fig. 11 (a) Minimum free-space resolution calculated using the main lobe FWHM of the processed signature from a mirror placed at 1.4 m. The mean of 30 trials is shown. (b) Deviation from the 12 DFB mean range value (dotted line) for elements 6-12. (Nominal range = 143.9173 cm, MZI L = 2.06571 m) The error bars indicate the 1σ standard deviation from the mean. The final 12-element standard deviation was ~180 nm.

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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, δz=Δzmin/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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4. D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011). [CrossRef]  

5. C. J. Karlsson, F. Å. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction continuous-wave coherent laser radar at 1.55 µm for range, speed, vibration, and wind measurements,” Appl. Opt. 39(21), 3716–3726 (2000). [CrossRef]   [PubMed]  

6. M. U. Piracha, D. Nguyen, D. Mandridis, T. Yilmaz, I. Ozdur, S. Ozharar, and P. J. Delfyett, “Range resolved lidar for long distance ranging with sub-millimeter resolution,” Opt. Express 18(7), 7184–7189 (2010). [CrossRef]   [PubMed]  

7. A. B. Mateo and Z. W. Barber, “Multi-dimensional, non-contact metrology using trilateration and high resolution FMCW ladar,” Appl. Opt. 54(19), 5911–5916 (2015). [CrossRef]   [PubMed]  

8. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003). [CrossRef]   [PubMed]  

9. K. Iiyama, L. T. Wang, and K. I. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996). [CrossRef]  

10. N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17(18), 15991–15999 (2009). [CrossRef]   [PubMed]  

11. P. A. Roos, R. R. Reibel, T. Berg, B. Kaylor, Z. W. Barber, and W. R. Babbitt, “Ultrabroadband optical chirp linearization for precision metrology applications,” Opt. Lett. 34(23), 3692–3694 (2009). [CrossRef]   [PubMed]  

12. E. Baumann, F. R. Giorgetta, J. D. Deschênes, W. C. Swann, I. Coddington, and N. R. Newbury, “Comb-calibrated laser ranging for three-dimensional surface profiling with micrometer-level precision at a distance,” Opt. Express 22(21), 24914–24928 (2014). [CrossRef]   [PubMed]  

13. O. Y. Sagiv, D. Arbel, and A. Eyal, “Correcting for spatial-resolution degradation mechanisms in OFDR via inline auxiliary points,” Opt. Express 20(25), 27465–27472 (2012). [CrossRef]   [PubMed]  

14. M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001). [CrossRef]  

15. T. J. Ahn, J. Y. Lee, and D. Y. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation,” Appl. Opt. 44(35), 7630–7634 (2005). [CrossRef]   [PubMed]  

16. Z. Ding, X. S. Yao, T. Liu, Y. Du, K. Liu, J. Jiang, Z. Meng, and H. Chen, “Compensation of laser frequency tuning nonlinearity of a long range OFDR using deskew filter,” Opt. Express 21(3), 3826–3834 (2013). [CrossRef]   [PubMed]  

17. C. Lu, G. Liu, B. Liu, F. Chen, T. Hu, Z. Zhuang, X. Xu, and Y. Gan, “Method based on chirp decomposition for dispersion mismatch compensation in precision absolute distance measurement using swept-wavelength interferometry,” Opt. Express 23(25), 31662–31671 (2015). [CrossRef]   [PubMed]  

18. H. Gong, Z. Liu, Y. Zhou, and W. Zhang, “Extending the mode-hop-free tuning range of an external-cavity diode laser by synchronous tuning with mode matching,” Appl. Opt. 53(33), 7878–7884 (2014). [CrossRef]   [PubMed]  

19. D. H. Choi, R. Yoshimura, and K. Ohbayashi, “Tuning of successively scanned two monolithic Vernier-tuned lasers and selective data sampling in optical comb swept source optical coherence tomography,” Biomed. Opt. Express 4(12), 2962–2987 (2013). [CrossRef]   [PubMed]  

20. S. O’Connor, M. A. Bernacil, A. DeKelaita, B. Maher, and D. Derickson, “100 kHz axial scan rate swept-wavelength OCT using sampled grating distributed Bragg reflector lasers,” Proc. SPIE 7168, 716825 (2009). [CrossRef]  

21. K. Iiyama, S. I. Matsui, T. Kobayashi, and T. Maruyama, “High-resolution FMCW reflectometry using a single-mode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 23(11), 703–705 (2011). [CrossRef]  

22. D. D. John, C. B. Burgner, B. Potsaid, M. E. Robertson, B. K. Lee, W. J. Choi, A. E. Cable, J. G. Fujimoto, and V. Jayaraman, “Wideband electrically pumped 1050-nm MEMS-tunable VCSEL for ophthalmic imaging,” J. Lightwave Technol. 33(16), 3461–3468 (2015). [CrossRef]   [PubMed]  

23. B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz-1MHz axial scan rate and long range centimeter class OCT imaging,” in SPIE BiOS (2012), paper 82130M.

24. A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998). [CrossRef]  

25. A. Vasilyev, N. Satyan, S. Xu, G. Rakuljic, and A. Yariv, “Multiple source frequency-modulated continuous-wave optical reflectometry: theory and experiment,” Appl. Opt. 49(10), 1932–1937 (2010). [CrossRef]   [PubMed]  

26. A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994). [CrossRef]  

27. Z. W. Barber, F. R. Giorgetta, P. A. Roos, I. Coddington, J. R. Dahl, R. R. Reibel, N. Greenfield, and N. R. Newbury, “Characterization of an actively linearized ultrabroadband chirped laser with a fiber-laser optical frequency comb,” Opt. Lett. 36(7), 1152–1154 (2011). [CrossRef]   [PubMed]  

28. W. C. Swann and S. L. Gilbert, “Line centers, pressure shift, and pressure broadening of 1530-1560 nm hydrogen cyanide wavelength calibration lines,” J. Opt. Soc. Am. B 22(8), 1749–1756 (2005). [CrossRef]  

29. I. Grulkowski, J. J. Liu, B. Potsaid, V. Jayaraman, J. Jiang, J. G. Fujimoto, and A. E. Cable, “High-precision, high-accuracy ultralong-range swept-source optical coherence tomography using vertical cavity surface emitting laser light source,” Opt. Lett. 38(5), 673–675 (2013). [CrossRef]   [PubMed]  

30. Z. W. Barber, W. R. Babbitt, B. Kaylor, R. R. Reibel, and P. A. Roos, “Accuracy of active chirp linearization for broadband frequency modulated continuous wave ladar,” Appl. Opt. 49(2), 213–219 (2010). [CrossRef]   [PubMed]  

31. M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004). [CrossRef]   [PubMed]  

32. A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002). [CrossRef]   [PubMed]  

33. M. Njegovec and D. Donlagic, “Rapid and broad wavelength sweeping of standard telecommunication distributed feedback laser diode,” Opt. Lett. 38(11), 1999–2001 (2013). [CrossRef]   [PubMed]  

34. W. C. Swann and S. L. Gilbert, “Pressure-induced shift and broadening of 1560-1630 nm carbon monoxide wavelength-calibration lines,” J. Opt. Soc. Am. B 19(10), 2461–2467 (2002). [CrossRef]  

35. H. Ishii, K. Kasaya, and H. Oohashi, “Narrow spectral linewidth operation (< 160 kHz) in widely tunable distributed feedback laser array,” Electron. Lett. 46(10), 1 (2010). [CrossRef]  

36. J. Qin, Q. Zhou, W. Xie, Y. Xu, S. Yu, Z. Liu, Y. Tong, Y. Dong, and W. Hu, “Coherence enhancement of a chirped DFB laser for frequency-modulated continuous-wave reflectometry using a composite feedback loop,” Opt. Lett. 40(19), 4500–4503 (2015). [CrossRef]   [PubMed]  

37. B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

References

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  1. R. Huber, M. Wojtkowski, K. Taira, J. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express 13(9), 3513–3528 (2005).
    [Crossref] [PubMed]
  2. M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300-nm ring laser source,” J. Biomed. Opt. 10(4), 044009 (2005).
    [Crossref] [PubMed]
  3. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
    [Crossref] [PubMed]
  4. D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
    [Crossref]
  5. C. J. Karlsson, F. Å. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction continuous-wave coherent laser radar at 1.55 µm for range, speed, vibration, and wind measurements,” Appl. Opt. 39(21), 3716–3726 (2000).
    [Crossref] [PubMed]
  6. M. U. Piracha, D. Nguyen, D. Mandridis, T. Yilmaz, I. Ozdur, S. Ozharar, and P. J. Delfyett, “Range resolved lidar for long distance ranging with sub-millimeter resolution,” Opt. Express 18(7), 7184–7189 (2010).
    [Crossref] [PubMed]
  7. A. B. Mateo and Z. W. Barber, “Multi-dimensional, non-contact metrology using trilateration and high resolution FMCW ladar,” Appl. Opt. 54(19), 5911–5916 (2015).
    [Crossref] [PubMed]
  8. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
    [Crossref] [PubMed]
  9. K. Iiyama, L. T. Wang, and K. I. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
    [Crossref]
  10. N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17(18), 15991–15999 (2009).
    [Crossref] [PubMed]
  11. P. A. Roos, R. R. Reibel, T. Berg, B. Kaylor, Z. W. Barber, and W. R. Babbitt, “Ultrabroadband optical chirp linearization for precision metrology applications,” Opt. Lett. 34(23), 3692–3694 (2009).
    [Crossref] [PubMed]
  12. E. Baumann, F. R. Giorgetta, J. D. Deschênes, W. C. Swann, I. Coddington, and N. R. Newbury, “Comb-calibrated laser ranging for three-dimensional surface profiling with micrometer-level precision at a distance,” Opt. Express 22(21), 24914–24928 (2014).
    [Crossref] [PubMed]
  13. O. Y. Sagiv, D. Arbel, and A. Eyal, “Correcting for spatial-resolution degradation mechanisms in OFDR via inline auxiliary points,” Opt. Express 20(25), 27465–27472 (2012).
    [Crossref] [PubMed]
  14. M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
    [Crossref]
  15. T. J. Ahn, J. Y. Lee, and D. Y. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation,” Appl. Opt. 44(35), 7630–7634 (2005).
    [Crossref] [PubMed]
  16. Z. Ding, X. S. Yao, T. Liu, Y. Du, K. Liu, J. Jiang, Z. Meng, and H. Chen, “Compensation of laser frequency tuning nonlinearity of a long range OFDR using deskew filter,” Opt. Express 21(3), 3826–3834 (2013).
    [Crossref] [PubMed]
  17. C. Lu, G. Liu, B. Liu, F. Chen, T. Hu, Z. Zhuang, X. Xu, and Y. Gan, “Method based on chirp decomposition for dispersion mismatch compensation in precision absolute distance measurement using swept-wavelength interferometry,” Opt. Express 23(25), 31662–31671 (2015).
    [Crossref] [PubMed]
  18. H. Gong, Z. Liu, Y. Zhou, and W. Zhang, “Extending the mode-hop-free tuning range of an external-cavity diode laser by synchronous tuning with mode matching,” Appl. Opt. 53(33), 7878–7884 (2014).
    [Crossref] [PubMed]
  19. D. H. Choi, R. Yoshimura, and K. Ohbayashi, “Tuning of successively scanned two monolithic Vernier-tuned lasers and selective data sampling in optical comb swept source optical coherence tomography,” Biomed. Opt. Express 4(12), 2962–2987 (2013).
    [Crossref] [PubMed]
  20. S. O’Connor, M. A. Bernacil, A. DeKelaita, B. Maher, and D. Derickson, “100 kHz axial scan rate swept-wavelength OCT using sampled grating distributed Bragg reflector lasers,” Proc. SPIE 7168, 716825 (2009).
    [Crossref]
  21. K. Iiyama, S. I. Matsui, T. Kobayashi, and T. Maruyama, “High-resolution FMCW reflectometry using a single-mode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 23(11), 703–705 (2011).
    [Crossref]
  22. D. D. John, C. B. Burgner, B. Potsaid, M. E. Robertson, B. K. Lee, W. J. Choi, A. E. Cable, J. G. Fujimoto, and V. Jayaraman, “Wideband electrically pumped 1050-nm MEMS-tunable VCSEL for ophthalmic imaging,” J. Lightwave Technol. 33(16), 3461–3468 (2015).
    [Crossref] [PubMed]
  23. B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz-1MHz axial scan rate and long range centimeter class OCT imaging,” in SPIE BiOS (2012), paper 82130M.
  24. A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998).
    [Crossref]
  25. A. Vasilyev, N. Satyan, S. Xu, G. Rakuljic, and A. Yariv, “Multiple source frequency-modulated continuous-wave optical reflectometry: theory and experiment,” Appl. Opt. 49(10), 1932–1937 (2010).
    [Crossref] [PubMed]
  26. A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994).
    [Crossref]
  27. Z. W. Barber, F. R. Giorgetta, P. A. Roos, I. Coddington, J. R. Dahl, R. R. Reibel, N. Greenfield, and N. R. Newbury, “Characterization of an actively linearized ultrabroadband chirped laser with a fiber-laser optical frequency comb,” Opt. Lett. 36(7), 1152–1154 (2011).
    [Crossref] [PubMed]
  28. W. C. Swann and S. L. Gilbert, “Line centers, pressure shift, and pressure broadening of 1530-1560 nm hydrogen cyanide wavelength calibration lines,” J. Opt. Soc. Am. B 22(8), 1749–1756 (2005).
    [Crossref]
  29. I. Grulkowski, J. J. Liu, B. Potsaid, V. Jayaraman, J. Jiang, J. G. Fujimoto, and A. E. Cable, “High-precision, high-accuracy ultralong-range swept-source optical coherence tomography using vertical cavity surface emitting laser light source,” Opt. Lett. 38(5), 673–675 (2013).
    [Crossref] [PubMed]
  30. Z. W. Barber, W. R. Babbitt, B. Kaylor, R. R. Reibel, and P. A. Roos, “Accuracy of active chirp linearization for broadband frequency modulated continuous wave ladar,” Appl. Opt. 49(2), 213–219 (2010).
    [Crossref] [PubMed]
  31. M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
    [Crossref] [PubMed]
  32. A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002).
    [Crossref] [PubMed]
  33. M. Njegovec and D. Donlagic, “Rapid and broad wavelength sweeping of standard telecommunication distributed feedback laser diode,” Opt. Lett. 38(11), 1999–2001 (2013).
    [Crossref] [PubMed]
  34. W. C. Swann and S. L. Gilbert, “Pressure-induced shift and broadening of 1560-1630 nm carbon monoxide wavelength-calibration lines,” J. Opt. Soc. Am. B 19(10), 2461–2467 (2002).
    [Crossref]
  35. H. Ishii, K. Kasaya, and H. Oohashi, “Narrow spectral linewidth operation (< 160 kHz) in widely tunable distributed feedback laser array,” Electron. Lett. 46(10), 1 (2010).
    [Crossref]
  36. J. Qin, Q. Zhou, W. Xie, Y. Xu, S. Yu, Z. Liu, Y. Tong, Y. Dong, and W. Hu, “Coherence enhancement of a chirped DFB laser for frequency-modulated continuous-wave reflectometry using a composite feedback loop,” Opt. Lett. 40(19), 4500–4503 (2015).
    [Crossref] [PubMed]
  37. B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

2015 (4)

2014 (2)

2013 (4)

2012 (1)

2011 (3)

D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
[Crossref]

K. Iiyama, S. I. Matsui, T. Kobayashi, and T. Maruyama, “High-resolution FMCW reflectometry using a single-mode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 23(11), 703–705 (2011).
[Crossref]

Z. W. Barber, F. R. Giorgetta, P. A. Roos, I. Coddington, J. R. Dahl, R. R. Reibel, N. Greenfield, and N. R. Newbury, “Characterization of an actively linearized ultrabroadband chirped laser with a fiber-laser optical frequency comb,” Opt. Lett. 36(7), 1152–1154 (2011).
[Crossref] [PubMed]

2010 (4)

2009 (3)

2005 (5)

2004 (1)

2003 (1)

2002 (2)

A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002).
[Crossref] [PubMed]

W. C. Swann and S. L. Gilbert, “Pressure-induced shift and broadening of 1560-1630 nm carbon monoxide wavelength-calibration lines,” J. Opt. Soc. Am. B 19(10), 2461–2467 (2002).
[Crossref]

2001 (1)

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

2000 (1)

1998 (1)

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998).
[Crossref]

1996 (1)

K. Iiyama, L. T. Wang, and K. I. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

1994 (1)

A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994).
[Crossref]

Ahn, T. J.

Amann, M. C.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Anderson, G. A.

A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002).
[Crossref] [PubMed]

Andonovic, I.

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998).
[Crossref]

Arbel, D.

Babbitt, W. R.

Barber, Z. W.

Baumann, E.

Behroozpour, B.

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

Berg, T.

Bernacil, M. A.

S. O’Connor, M. A. Bernacil, A. DeKelaita, B. Maher, and D. Derickson, “100 kHz axial scan rate swept-wavelength OCT using sampled grating distributed Bragg reflector lasers,” Proc. SPIE 7168, 716825 (2009).
[Crossref]

Bosch, T.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Boser, B.E.

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

Burgner, C. B.

Cable, A. E.

Chang-Hasnain, C.

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

Chen, F.

Chen, H.

Choi, D. H.

Choi, W. J.

Choma, M.

Choma, M. A.

M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300-nm ring laser source,” J. Biomed. Opt. 10(4), 044009 (2005).
[Crossref] [PubMed]

Coddington, I.

Cornwell, W. D.

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998).
[Crossref]

Dahl, J. R.

DeKelaita, A.

S. O’Connor, M. A. Bernacil, A. DeKelaita, B. Maher, and D. Derickson, “100 kHz axial scan rate swept-wavelength OCT using sampled grating distributed Bragg reflector lasers,” Proc. SPIE 7168, 716825 (2009).
[Crossref]

Delfyett, P. J.

Derickson, D.

S. O’Connor, M. A. Bernacil, A. DeKelaita, B. Maher, and D. Derickson, “100 kHz axial scan rate swept-wavelength OCT using sampled grating distributed Bragg reflector lasers,” Proc. SPIE 7168, 716825 (2009).
[Crossref]

Deschênes, J. D.

Dieckmann, A.

A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994).
[Crossref]

Ding, Z.

Dong, Y.

Donlagic, D.

Du, Y.

Duker, J.

Eyal, A.

Froggatt, M.

Fujimoto, J.

Fujimoto, J. G.

Gan, Y.

Gerke, S.

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

Gifford, D.

Gilbert, S. L.

Giorgetta, F. R.

Gong, H.

Greenfield, N.

Grulkowski, I.

Harris, M.

Hayashi, K. I.

K. Iiyama, L. T. Wang, and K. I. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

Heim, P. J.

B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz-1MHz axial scan rate and long range centimeter class OCT imaging,” in SPIE BiOS (2012), paper 82130M.

Hsu, K.

Hu, T.

Hu, W.

Huber, R.

Igawa, H.

D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
[Crossref]

Iiyama, K.

K. Iiyama, S. I. Matsui, T. Kobayashi, and T. Maruyama, “High-resolution FMCW reflectometry using a single-mode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 23(11), 703–705 (2011).
[Crossref]

K. Iiyama, L. T. Wang, and K. I. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

Ishii, H.

H. Ishii, K. Kasaya, and H. Oohashi, “Narrow spectral linewidth operation (< 160 kHz) in widely tunable distributed feedback laser array,” Electron. Lett. 46(10), 1 (2010).
[Crossref]

Izatt, J.

Izatt, J. A.

M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300-nm ring laser source,” J. Biomed. Opt. 10(4), 044009 (2005).
[Crossref] [PubMed]

Jayaraman, V.

Jiang, J.

John, D. D.

Kageyama, K.

D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
[Crossref]

Karlsson, C. J.

Kasaya, K.

H. Ishii, K. Kasaya, and H. Oohashi, “Narrow spectral linewidth operation (< 160 kHz) in widely tunable distributed feedback laser array,” Electron. Lett. 46(10), 1 (2010).
[Crossref]

Kaylor, B.

Kim, D. Y.

Ko, T.

Kobayashi, T.

K. Iiyama, S. I. Matsui, T. Kobayashi, and T. Maruyama, “High-resolution FMCW reflectometry using a single-mode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 23(11), 703–705 (2011).
[Crossref]

Kowalczyk, A.

Lee, B. K.

Lee, J. Y.

Lescure, M.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Letalick, D.

Leyva, V.

Liu, B.

Liu, G.

Liu, J. J.

Liu, K.

Liu, T.

Liu, Z.

Lu, C.

Maher, B.

S. O’Connor, M. A. Bernacil, A. DeKelaita, B. Maher, and D. Derickson, “100 kHz axial scan rate swept-wavelength OCT using sampled grating distributed Bragg reflector lasers,” Proc. SPIE 7168, 716825 (2009).
[Crossref]

Mandridis, D.

Maruyama, T.

K. Iiyama, S. I. Matsui, T. Kobayashi, and T. Maruyama, “High-resolution FMCW reflectometry using a single-mode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 23(11), 703–705 (2011).
[Crossref]

Masselon, C. D.

A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002).
[Crossref] [PubMed]

Mateo, A. B.

Matsui, S. I.

K. Iiyama, S. I. Matsui, T. Kobayashi, and T. Maruyama, “High-resolution FMCW reflectometry using a single-mode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 23(11), 703–705 (2011).
[Crossref]

Meng, Z.

Murayama, H.

D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
[Crossref]

Myllyla, R.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Newbury, N. R.

Nguyen, D.

Njegovec, M.

O’Connor, S.

S. O’Connor, M. A. Bernacil, A. DeKelaita, B. Maher, and D. Derickson, “100 kHz axial scan rate swept-wavelength OCT using sampled grating distributed Bragg reflector lasers,” Proc. SPIE 7168, 716825 (2009).
[Crossref]

Ohbayashi, K.

Olsson, F. Å.

Omichi, K.

D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
[Crossref]

Oohashi, H.

H. Ishii, K. Kasaya, and H. Oohashi, “Narrow spectral linewidth operation (< 160 kHz) in widely tunable distributed feedback laser array,” Electron. Lett. 46(10), 1 (2010).
[Crossref]

Ozdur, I.

Ozharar, S.

Piracha, M. U.

Potsaid, B.

Qin, J.

Quack, N.

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

Rakuljic, G.

Reibel, R. R.

Rioux, M.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Robertson, M. E.

Roos, P. A.

Sagiv, O. Y.

Sandborn, P.

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

Sarunic, M.

Satyan, N.

Shalom, H.

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998).
[Crossref]

Smith, R. D.

A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002).
[Crossref] [PubMed]

Soller, B.

Srinivasan, V.

Swann, W. C.

Taira, K.

Tolmachev, A. V.

A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002).
[Crossref] [PubMed]

Tong, Y.

Tur, M.

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998).
[Crossref]

Udseth, H. R.

A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002).
[Crossref] [PubMed]

Uzawa, K.

D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
[Crossref]

Vasilyev, A.

Wada, D.

D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
[Crossref]

Wang, L. T.

K. Iiyama, L. T. Wang, and K. I. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

Wojtkowski, M.

Wolfe, M.

Wu, M.C.

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

Xie, W.

Xu, S.

Xu, X.

Xu, Y.

Yang, C.

Yang, W.

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

Yao, X. S.

Yariv, A.

Yilmaz, T.

Yoshimura, R.

Yu, S.

Zadok, A.

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998).
[Crossref]

Zhang, W.

Zhou, Q.

Zhou, Y.

Zhuang, Z.

Appl. Opt. (6)

Biomed. Opt. Express (1)

Electron. Lett. (2)

A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994).
[Crossref]

H. Ishii, K. Kasaya, and H. Oohashi, “Narrow spectral linewidth operation (< 160 kHz) in widely tunable distributed feedback laser array,” Electron. Lett. 46(10), 1 (2010).
[Crossref]

IEEE Photonics Technol. Lett. (2)

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photonics Technol. Lett. 10(12), 1709–1711 (1998).
[Crossref]

K. Iiyama, S. I. Matsui, T. Kobayashi, and T. Maruyama, “High-resolution FMCW reflectometry using a single-mode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 23(11), 703–705 (2011).
[Crossref]

J. Am. Soc. Mass Spectrom. (1)

A. V. Tolmachev, C. D. Masselon, G. A. Anderson, H. R. Udseth, and R. D. Smith, “Frequency shifts due to the interference of resolved peaks in magnitude-mode Fourier-transform ion cyclotron resonance mass spectra,” J. Am. Soc. Mass Spectrom. 13(4), 387–401 (2002).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300-nm ring laser source,” J. Biomed. Opt. 10(4), 044009 (2005).
[Crossref] [PubMed]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Opt. Eng. (1)

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Opt. Express (10)

R. Huber, M. Wojtkowski, K. Taira, J. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express 13(9), 3513–3528 (2005).
[Crossref] [PubMed]

E. Baumann, F. R. Giorgetta, J. D. Deschênes, W. C. Swann, I. Coddington, and N. R. Newbury, “Comb-calibrated laser ranging for three-dimensional surface profiling with micrometer-level precision at a distance,” Opt. Express 22(21), 24914–24928 (2014).
[Crossref] [PubMed]

O. Y. Sagiv, D. Arbel, and A. Eyal, “Correcting for spatial-resolution degradation mechanisms in OFDR via inline auxiliary points,” Opt. Express 20(25), 27465–27472 (2012).
[Crossref] [PubMed]

Z. Ding, X. S. Yao, T. Liu, Y. Du, K. Liu, J. Jiang, Z. Meng, and H. Chen, “Compensation of laser frequency tuning nonlinearity of a long range OFDR using deskew filter,” Opt. Express 21(3), 3826–3834 (2013).
[Crossref] [PubMed]

C. Lu, G. Liu, B. Liu, F. Chen, T. Hu, Z. Zhuang, X. Xu, and Y. Gan, “Method based on chirp decomposition for dispersion mismatch compensation in precision absolute distance measurement using swept-wavelength interferometry,” Opt. Express 23(25), 31662–31671 (2015).
[Crossref] [PubMed]

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17(18), 15991–15999 (2009).
[Crossref] [PubMed]

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
[Crossref] [PubMed]

B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
[Crossref] [PubMed]

M. U. Piracha, D. Nguyen, D. Mandridis, T. Yilmaz, I. Ozdur, S. Ozharar, and P. J. Delfyett, “Range resolved lidar for long distance ranging with sub-millimeter resolution,” Opt. Express 18(7), 7184–7189 (2010).
[Crossref] [PubMed]

M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
[Crossref] [PubMed]

Opt. Lett. (5)

Proc. SPIE (1)

S. O’Connor, M. A. Bernacil, A. DeKelaita, B. Maher, and D. Derickson, “100 kHz axial scan rate swept-wavelength OCT using sampled grating distributed Bragg reflector lasers,” Proc. SPIE 7168, 716825 (2009).
[Crossref]

Smart Mater. Struct. (1)

D. Wada, H. Murayama, H. Igawa, K. Kageyama, K. Uzawa, and K. Omichi, “Simultaneous distributed measurement of strain and temperature by polarization maintaining fiber Bragg grating based on optical frequency domain reflectometry,” Smart Mater. Struct. 20(8), 085028 (2011).
[Crossref]

Other (2)

B. Behroozpour, N. Quack, P. Sandborn, S. Gerke, W. Yang, C. Chang-Hasnain, M.C. Wu, and B.E. Boser, “Method for increasing the operating distance of MEMS LIDAR beyond Brownian noise limitation,” in CLEO: Appl. and Tech. (2014), paper AW3H–2.

B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz-1MHz axial scan rate and long range centimeter class OCT imaging,” in SPIE BiOS (2012), paper 82130M.

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Figures (11)

Fig. 1
Fig. 1 Two adjacent regions containing part of the beat signal.
Fig. 2
Fig. 2 (a) Individual laser element frequency sweeps with time, LO (solid line) and delayed return reflection (dashed line). Tn indicates the nth sweep period and τD is the time delay to the target. (b) Combined total bandwidth after resampling at equal optical frequencies and stitching.
Fig. 3
Fig. 3 (a) Combined photodiode response regions with a single target and perfect registration at the combination point (vertical line), (b) Correct Fourier transform after combining, (c) Two regions with a shift error 1 sample point in the second section. (d) FFT resulting in a corrupt main lobe due to the shift error.
Fig. 4
Fig. 4 Experiment Layout. The dotted line indicates components housed inside the butterfly package. The custom printed circuit-board (PCB) drives each DFB element. The light blue lines indicate PM fiber. A Mach-Zehnder reference arm (MZI) and a HCN gas cell aids in wavelength calibration. The Fresnel back reflection from a wedged window acts as the LO, SOA: Semiconductor optical amplifier, A/D: Analog-to-digital data acquisition, TEC: Thermoelectric cooler, BPF: Bandpass filters for DC blocking and anti-aliasing, PD: Photodecter receiver.
Fig. 5
Fig. 5 (a) Current ramp applied to each DFB and (b) resulting response of the DFB module’s 50 GHz etalon wavelength reference from a single element sweep. The shaded section is removed when combining with the previous DFB signal. (c) Custom PCB showing the butterfly package containing the DFB array, current driver, and transistor network. (d) Measurement of linearity for all 12 elements over the 5.5 THz sweep, plotted at the MZI zero-cross points. The dotted line is the approximate standard deviation.
Fig. 6
Fig. 6 (a) Combined signal using all 12 DFB elements. The HCN absorption peaks (red) and a signal from a 50 μm fused silica etalon (blue) are shown. The vertical lines indicate the combination points between DFB regions. The last peak in each DFB region is listed above the HCN trace. (b) Two adjacent measurement signal regions (blue) registered to the absorption peaks (red) of the HCN gas cell. The peak-to-peak distance in zero-crossing-space is labeled as Δζ. The vertical dotted line is the combination point. (c) 2σ uncertainty of the measured gap values (blue bars). The mean MZI FSR (dotted line) and half-FSR (dashed line) are shown for comparison. (d) Optical spectrum analyzer trace averaged over all 12 elements.
Fig. 7
Fig. 7 (a) Air-fiber phase mismatch of the MZI beat signal in terms of the zero-crossings, referenced to the start of the sweep. The contributions of each Taylor series term are shown. For a 1524.9131 nm wavelength start (ng ≈1.4681), the profile follows: (6.37365e-10)m2 + (4.13137e-16)m3. (b) Single reflector FFT peak before (dotted line) and after (solid line) dispersion compensation using all DFB elements. (c) Dispersion compensated signature from a 100 μm fused silica etalon placed at 1 m. The two main lobes correspond to the front and back glass surfaces.
Fig. 8
Fig. 8 Signal processing steps. MZI ZC: The Mach-Zehnder interferometer zero-crossings are used as the resampling reference (black arrow). The HCN peaks (red arrows) provide a known wavelength reference for registering the measurement segments (blue arrows).
Fig. 9
Fig. 9 (a) Incremental improvement in surface resolution of a 1 mm glass slide using 6 elements. All plots are normalized per trace. The measured physical thickness accounting for the refractive index is denoted by Δz. The thickness measured using a micrometer was 1.02( ± 0.01) mm. (b) Thickness measurement of a 100 μm fused silica etalon using up to 12 elements. The thickness reported by the manufacturer was 100.7 μm.
Fig. 10
Fig. 10 (a) Improvement in surface resolution of a 50 μm fused silica etalon using 12 elements. The manufacturer-provided thickness was listed as 47.6 μm. (b) Incremental improvement in surface resolution of a 25 μm fused silica etalon. The actual thickness was not provided.
Fig. 11
Fig. 11 (a) Minimum free-space resolution calculated using the main lobe FWHM of the processed signature from a mirror placed at 1.4 m. The mean of 30 trials is shown. (b) Deviation from the 12 DFB mean range value (dotted line) for elements 6-12. (Nominal range = 143.9173 cm, MZI L = 2.06571 m) The error bars indicate the 1σ standard deviation from the mean. The final 12-element standard deviation was ~180 nm.

Equations (13)

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ε(t)= E 0 exp[ j( πα t 2 +2π ν 0 t+ ϕ e (t)+ ϕ s (t)+ ϕ 0 ) ],
I(t)= | ε LO ( t τ LO )+ ε R ( t τ R ) | 2 .
v(t)=Acos[ απ τ D 2 +2πα τ D t+2π ν 0 τ D +Δ ϕ e +Δ ϕ s ],
v B (t)=v(t)rect( t t 0 T/2 T ),
V B (f)=F[ v(t) ]F[ rect( t t 0 T/2 T ) ],
v tot (t)=v(t)[ rect( t t c + B 1 /2α B 1 /α )+rect( t t c B 2 /2α B 2 /α ) ],
V tot (f)= πBA α exp( jθ )sinc[ πB α ( f f D ) ] ×{ exp[ j π α ( f f D )( 2 ν c B ) ]+exp[ j π α ( f f D )( 2 ν c +B ) ] },
V tot (f)= 2πBA α sinc[ 2πB α ( f f D ) ]exp{ j[ θ 2π ν c α ( f f D ) ] }.
v tot (t)=v(t)[ rect( t t c + B 1 /2α B 1 /α ) ]+v(tΔ t err )[ rect( t t c B 2 /2α B 2 /α ) ].
V tot (f)= πBA α exp( jθ )sinc[ πB α ( f f D ) ] ×{ exp[ j π α ( f f D )( 2 ν c B ) ]+exp[ j π α ( f f D )( 2 ν c +B )j θ err ] }.
γ i (m) Δ ν G,i Δ ζ i c ML n g,i ,
β(m) β 0 +2πm γ 0 β 1 + 1 2 (2πm γ 0 ) 2 β 2 + 1 6 (2πm γ 0 ) 3 β 3 ,
v tot [m']= v tot [ m+ (2π γ 0 ) β 2 2 β 1 m 2 + (2π γ 0 ) 2 β 3 6 β 1 m 3 ].

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