200-GHz 8-µs LFM Optical Waveform Generation for High- Resolution Coherent Imaging
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1 Th7 Holman, K.W. 200-GHz 8-µs LFM Optical Waveform Generation for High- Resolution Coherent Imaging Kevin W. Holman MIT Lincoln Laboratory 244 Wood Street, Lexington, MA USA Abstract: Linear frequency modulated (LFM) waveforms are commonly used to provide range resolution in coherent imaging applications. Large bandwidth waveforms are needed for high range resolution, while short modulation times are needed to accommodate scene movement. In previous work on wideband swept waveform generation, the fastest reported modulation rates were on the order of 1-10 THz/s. Here we report the generation of a 200 GHz waveform with an unprecedented modulation rate of > 24,000 THz/s. We describe our unique scalable approach of modularly generating smaller-bandwidth waveforms across the optical spectrum, and then phasestitching these sub-components together to form the full-bandwidth 200 GHz waveform in 8 µs. We also describe the use of this waveform for sub-diffraction-limited synthetic aperture imaging. Keywords: Coherent Laser Radar, Coherent Lidar; Laser Radar; Ladar; LFM; Linear Frequency Modulation; Synthetic Aperture Ladar; SAL; Optical Waveform Generation 1. Introduction Wideband optical waveforms are used to provide high range resolution in coherent imaging applications. When a linear frequency modulated (LFM) waveform is used, stretch processing techniques can be employed that provide range resolution commensurate with the full optical bandwidth of the waveform, with modest receiver electronic bandwidth. However, the waveform must be generated sufficiently rapidly to minimize blurring caused by movement of the scene. In previous work on wideband swept waveform generation for coherent imaging, the fastest reported modulation rates were on the order of 1-10 THz/s [1, 2]. The waveform generation technique described here provides a 200 GHz waveform with an unprecedented modulation rate of > 24,000 THz/s. The generation technique involves modularly generating smaller-bandwidth waveforms across the optical spectrum, and then phase-stitching these sub-components together to form the full-bandwidth 200 GHz waveform in 8 μs. This waveform has applications to diffraction-limited 3D imaging with 1-mm range resolution, and sub-diffraction-limited synthetic aperture imaging, as described here. 2. Linear Frequency Modulated Waveform The waveform commonly used for coherent imaging applications is the linear frequency modulated (LFM) waveform. This waveform enables simultaneous range and Doppler measurements, and is illustrated in Fig. 1. It consists of a linear frequency ramp over a bandwidth B, in duration T sweep. It is repeated over a duration T CPI. The time-delayed returned waveform (dashed blue line in Fig. 1) is combined onto a detector with a copy of the transmitted signal (red solid line) to produce the heterodyne beat frequency between these two optical signals. This material is based upon work supported by the Assistant Secretary of Defense for Research and Engineering under Air Force Contract No. FA D Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Assistant Secretary of Defense for Research and Engineering. CLRC 2018, June
2 Figure 1. Linear Frequency Modulated Waveform. The heterodyne beat frequency, F, is directly proportional to the target range, R, according to: FTsweep R = c (1) 2B The phase evolution of this beat signal during time T CPI provides the Doppler measurement for each range resolution cell. The bandwidth of the sweep provides the range resolution, δr, and the total duration, T CPI, provides the Doppler resolution, δf, according to the following equations: c δ R = 1.33 (2) 2B ( T ) 1 δ f (3) = CPI The factor of 1.33 in Eqn. 2 corresponds to a particular choice of windowing function used in computing the Fourier transform during range processing. Note that although the range resolution is determined by the optical bandwidth, the required detector bandwidth is determined by the much lower beat frequency F, which is related to the range to the target. One final consideration for the waveform is that the differential optical phase change of the return light due to differential line-of-sight scene-platform motion across the scene should not exceed 2π from one sweep to the next. This sets a maximum velocity spread across a scene, v max, of: vv mmmmmm = and thus a maximum rotation rate, ω max, for a scene of diameter D : ωω mmmmmm = vv mmmmxx DD = λλ 2TT ssssssssss DD 3. Generation of Broadband Optical Waveform λλ 2TT ssssssssss (5) In generating an LFM waveform, a large bandwidth is desirable to provide high range resolution, and a short sweep time is desirable to support large velocity spreads across a scene. The waveform generation technique described here provides an LFM waveform with 200 GHz bandwidth, swept in 8 µs. This corresponds to a modulation slope of 25 THz / ms, as compared to modulation slopes of 1.25 GHz / ms and 10 GHz / ms reported in prior work [1, 2]. In addition to bandwidth and sweep time, another important consideration in waveform generation is linearity and phase distortion of the waveform, which would result in range and Doppler sidelobes for coherent imaging applications. Previous approaches to generating optical LFM waveforms for coherent imaging utilized a matched reference path to compensate nonlinearities in the sweep [1] or digital processing techniques to remove the effect of these nonlinearities [2]. The technique described here relies on an intrinsically low-noise approach to produce broad bandwidth sweeps over a sufficiently short duration, eliminating the need for a matched reference arm or digital post-processing. (6) CLRC 2018, June
3 Figure 2. High-Bandwidth LFM Waveform Generation. Our waveform generation technique relies on producing relatively small bandwidth waveforms across the optical spectrum, and then phase-stitching these sub-components together to form the full-bandwidth 200 GHz waveform. The general approach, summarized in Fig. 2, is scalable to even larger bandwidth waveforms. The building blocks of the waveform are the components of an optical frequency comb. This comb contains 16 frequency components, spanning 200 GHz and spaced by 12.5 GHz. It is generated by strong sinusoidal phase modulation of a single-frequency 1.55-µm fiber laser, followed by amplitude modulation to balance the amplitude across the comb [3]. These modulations are applied with LiNbO3 modulators external to the laser cavity. The frequency components of the comb are separated with an arrayed waveguide grating (AWG) demultiplexer, sending each frequency along a separate optical fiber. Each frequency then passes through an electro-optic intensity modulator, which passes each frequency for 0.5 µs, and then extinguishes that frequency for the remainder of the waveform generation time. The timing of the modulators is adjusted so that each of the frequency components is sequentially transmitted through the array of modulators. Upon recombination of the frequencies by an AWG multiplexer, a stair-step waveform of frequency vs. time is produced. An electro-optic phase modulator immediately after each intensity modulator provides phase control of the frequencies for compensating any relative drifts of the path lengths, as described later. The stair-step waveform is then transmitted through an optical single sideband modulator that is driven with a repetitive RF frequencyswept waveform. The RF waveform produces a 12.5-GHz sweep, centered at 10 GHz, in 0.5 µs. This introduces a sideband on each optical frequency (the transmitted carrier is nulled) that sweeps 12.5 GHz, and matches up with the beginning of the sweep of the next optical frequency's sideband. These GHz frequency-swept waveforms are phase-coherently stitched together using the phase modulators following the intensity modulators to produce a total chirp of GHz = 200 GHz in µs = 8 µs. The two significant challenges in implementing this scheme are the generation of the 12.5 GHz RF LFM waveform in 0.5 µs, and the phase coherent stitching of the individual sub-chirps. The 12.5-GHz RF sweep is produced by first generating a MHz broad sweep at baseband in 0.5 µs using an arbitrary waveform generator. Two such sweeps are produced on independent channels of the arbitrary waveform generator with the appropriate relative phase to drive an I/Q modulator, resulting in a 390.6MHz x 2 = MHz sweep centered at 4.2 GHz. This waveform is then passed through 4 frequency doublers, resulting in a 12.5-GHz sweep bandwidth. Finally, a mixer is used to bring the center frequency of the sweep down to 10 GHz. A calibration procedure measures the amplitude and phase aberrations CLRC 2018, June
4 introduced by the 4 frequency-doubling stages, which are then pre-compensated by the arbitrary waveform generator. The optical phase modulators are needed to control the relative optical phases of the 16 partial sweeps, such that the phase across the full bandwidth is continuous. Since the optical comb source produces components with a well-defined phase relationship, there is very little high-frequency phase noise. The dominant source of relative noise is due to differential path length fluctuations during the time when each frequency component is traveling on separate optical fibers. The phase modulators in each path are used to eliminate this relative fluctuation, and to set the phase offset of each component to be consistent with a continuous frequency-swept signal (i.e. a quadratic phase evolution). The phase deviations are measured by coupling a portion of the optical waveform into a monitor channel. This monitor channel consists of an unbalanced Mach-Zehnder interferometer, resulting in a beat signal. Digitizing and phasedemodulating the beat signal enables the generation of real-time correction signals to apply to the phase modulators. This feedback loop currently operates at 250 Hz, which is sufficient to suppress most of the path length fluctuations. 4. Imaging Performance of Waveform The resolution performance of the system is verified by imaging a flat, stationary surface. The optical LFM waveform is repeated continuously, enabling the arbitrary selection of T CPI for any given measurement. For this measurement, T CPI was chosen to be 32 ms. Fig. 3(a) shows the range-doppler image resulting from this measurement. Also shown are cuts through the Doppler and range peak locations, yielding the (b) range and (c) Doppler profiles, respectively. The range resolution is 1-mm, as expected for the 200-GHz waveform according to Eqn. 2. The sidelobes are nearly 20 db down, and are understood to be caused by a finite reset time of the RF sweep generator of approximately 20 ns. The Doppler resolution is (T CPI) -1 = 31 Hz, also as expected. One coherent imaging application we have been exploring is inverse synthetic aperture ladar (ISAL) imaging of rotating objects. Fig. 4 illustrates the geometry for obtaining an ISAL image. In such an image, one dimension of resolution is provided by the range resolution of the waveform. The other dimension of image resolution is provided by resolving the Doppler frequency of the return light. According to Eqn. 5, a sweep time of 8 µs enables a maximum velocity spread across the rotating object of 10 cm / s for operation at λ = 1.55 µm. For a 20-cm diameter object, this corresponds to a maximum rotation rate of 500 mrad / s. (30 deg. / s). Inverse synthetic aperture imaging of a face mask is demonstrated by rotating the mask while illuminating it with the wideband waveform. The mask is tilted backward at approximately 45 deg. enabling the range resolution of the waveform to provide the vertical resolution of the image. Rotation of the mask at 11 deg. / s provides horizontal resolution of the mask of 1 mm by resolving the different Doppler frequencies of the light scattered from the different horizontal regions of the mask. A T CPI of 4 ms provides Doppler resolution of 250 Hz, according to Eqn. 3. For a rotation of 11 deg. / s, this corresponds to a horizontal displacement of 1 mm. Fig. 5(a) shows the mask being imaged, along with the reference spot indicating the size of the illumination beam. The 4-cm illumination beam is scanned across the mask, and the resulting series of range-doppler images are summed to produce a single inverse synthetic aperture image, as shown in Fig. 5(b). The image in Fig. 5(b) is the result of 32 fullframe averages, thus reducing the speckle noise that would be evident in a single synthetic aperture image. CLRC 2018, June
5 Figure 3. Range-Doppler Image of Stationary Surface. Figure 4. Inverse Synthetic Aperture Imaging Geometry Figure 5. Inverse Synthetic Aperture Ladar Image 5. Summary We have demonstrated an optical waveform generation technique that provides LFM waveforms suitable for making coherent images of moving objects. The 200-GHz waveform generated with a sweep rate of 25 THz / ms has sufficient bandwidth and speed to produce synthetic aperture images of rotating objects with line-of-sight velocity spreads of up to 10 cm / s, with a range resolution of 1 mm. The scalable waveform generation approach can be extended to larger waveform bandwidths while maintaining the sweep rate with the use of additional optical channels. 6. References [1] M. Bashkansky, R.L. Lucke, E. Funk, L.J. Rickard, and J. Reintjes, Opt. Lett (2002). [2] S.M. Beck, J.R. Buck, W.F. Buell, and R.P. Dickinson, Applied Optics. 44, 7621 (2005). [3] K. Mandai, D. Miyamoto, T. Suzuki, H. Tsuda, K. Aizawa, and T. Kurokawa, IEEE Photon. Tech. Lett. 18, 679 (2006). CLRC 2018, June
o Conclusion and future work. 2
Robert Brown o Concept of stretch processing. o Current procedures to produce linear frequency modulation (LFM) chirps. o How sparse frequency LFM was used for multifrequency stretch processing (MFSP).
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