19th Coherent Laser Radar Conference 200-GHz 8-ms LFM Optical Waveform Generation for High-Resolution Coherent Imaging Kevin W. Holman 19th Coherent Laser Radar Conference 18 – 21 June, 2018 This material is based upon work supported by the Assistant Secretary of Defense for Research and Engineering under Air Force Contract No. FA8702-15-D-0001. 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.

Methods for Resolving Range Direct Detection: Measure Pulse Arrival Time Pulsed Laser Start Stop Resolution ~ (Detector Bandwidth)-1 Coherent Detection: Interferometer to Measure Optical Phase Range Waveform Source Direct detection provides straightforward range measurement: time of flight measurement provides range. Transmit beam scatters from target, focused onto detector, and arrival time of pulse is measured to determine transit time. Range resolution is given by timing resolution, which is limited by pulse duration. However, not sufficient to have short pulse – detector must have equally fast response. This is equivalent to having detector bandwidth = pulse bandwidth. For 0.1-mm resolution, this corresponds to 1.5 – THz detector bandwidth, which is not attainable. Coherent detection requires reference beam (LO), and by combining LO and return signal on receive detector, the resolution is limited only by the optical bandwidth – this allows the use of a much slower detector. Local Oscillator (LO) Resolution ~ (Waveform Bandwidth)-1

Methods for Resolving Range Direct Detection: Measure Pulse Arrival Time Pulsed Laser Start Stop Resolution ~ (Detector Bandwidth)-1 Coherent Detection: Interferometer to Measure Optical Phase Range Waveform Source Direct detection provides straightforward range measurement: time of flight measurement provides range. Transmit beam scatters from target, focused onto detector, and arrival time of pulse is measured to determine transit time. Range resolution is given by timing resolution, which is limited by pulse duration. However, not sufficient to have short pulse – detector must have equally fast response. This is equivalent to having detector bandwidth = pulse bandwidth. For 0.1-mm resolution, this corresponds to 1.5 – THz detector bandwidth, which is not attainable. Coherent detection requires reference beam (LO), and by combining LO and return signal on receive detector, the resolution is limited only by the optical bandwidth – this allows the use of a much slower detector. Local Oscillator (LO) Resolution ~ (Waveform Bandwidth)-1

Wideband Optical Waveform Source Linear Frequency Modulated (LFM) Waveform Optical Waveform Source Stretch Processing Frequency LO fbeat B LO Target return Tsweep Time Photodetector fbeat << B allows low detector bandwidth Frequency of beat (fbeat) between LO and return gives range: Range resolution = c/2B Coherent processing of consecutive sweeps gives Doppler Tsweep < (Doppler Spread)-1 to avoid phase wrapping between sweeps Waveform Parameters Parameter Value Performance Impact Bandwidth (B) 200 GHz 1-mm range res. Duration (Tsweep) 8 ms 122-kHz Doppler BW Sidelobe Level < -20 dB Analogous to Airy diffraction lobes in passive imagery Coherent detection with linear frequency modulated waveform provides high-resolution for range measurement. Beat frequency between reference pulse and return pulse is directly proportional to range. Range resolution is given by chirp bandwidth, but the detector requirement is driven by the dynamic range. This unique waveform greatly relaxes the bandwidth requirements of the detector, since the frequency ramp is optically deramped prior to detection. Since it is a coherent measurement, it is also possible to measure the Doppler shift caused by a moving target, which is useful for improving transverse resolution through SAR techniques. 4

Wideband Optical Waveform Generation 16 Optical Frequencies Frequency Time x16 Frequency Time x16 Modulated Frequencies Frequency Time x16 Swept Optical Waveform 0.5 ms 200 GHz 12.5 GHz 8 ms Frequency Time Swept RF Waveform 12.5 GHz 0.5 ms Challenges Generating 16 phase-coherent optical frequencies Modulating optical source to generate stepped-frequency Creating 12.5-GHz swept RF source Transferring RF waveform onto optical frequencies Maintaining phase continuity between stitching points in optical spectrum We generate a 200-GHz swept-frequency optical waveform by generating a smaller bandwidth waveform, and duplicating this at multiple locations across the optical spectrum. Each of these individual pieces are then phase coherently stitched together to produce a 200-GHz-broad chirp.

Synthesis of Wideband Waveform Frequency Intensity Modulators f 200 GHz CW Laser Swept-Frequency Generator PM AM 16 x Dt PM: Phase Modulation AM: Amplitude Modulation Phase Control Loop 16 Optical Frequencies Frequency Time x16 12.5 GHz Challenges Generating 16 phase-coherent optical frequencies Modulating optical source to generate stepped-frequency Creating 12.5-GHz swept RF source Transferring RF waveform onto optical frequencies Maintaining phase continuity between stitching points in optical spectrum The first step in producing the 200-GHz waveform is to produce 16 phase-coherent frequencies, spaced by 12.5 GHz. These serve as the building blocks of the waveform. These are produced from a single narrow-linewidth cw laser by large-depth phase modulation, followed by amplitude modulation to flatten the intensity across the spectrum.

Synthesis of Wideband Waveform Frequency Intensity Modulators 200 GHz f CW Laser Swept-Frequency Generator PM AM 16 x Dt f Phase Control Loop Frequency Time x16 Modulated Frequencies 0.5 ms Challenges Generating 16 phase-coherent optical frequencies Modulating optical source to generate stepped-frequency Creating 12.5-GHz swept RF source Transferring RF waveform onto optical frequencies Maintaining phase continuity between stitching points in optical spectrum The next step is to use a wavelength-division multiplexor to separate the frequencies into individual paths. Intensity modulators in each path are sequentially switched, so that each of the frequencies are passed one after the other. After recombining the frequencies with a wavelength-division multiplexor, a stair-step waveform is produced.

Synthesis of Wideband Waveform Frequency Intensity Modulators 200 GHz f CW Laser Swept-Frequency Generator PM AM 16 x Dt f Phase Control Loop Integrated Intensity & Phase Modulators Two 8-channel Variable Attenuators 16-Channel Frequency Splitter 16-Channel Frequency Combiner x8 x8 x16 All of the components for performing the modulation are commercially available devices developed for the telecommunications industry. x16 x8 x8

Synthesis of Wideband Waveform Frequency Intensity Modulators 200 GHz f CW Laser Swept-Frequency Generator PM AM 16 x Dt f Phase Control Loop Integrated Intensity & Phase Modulator 27 in. Two 8-channel Variable Attenuators 16-Channel Frequency Splitter 16-Channel Frequency Combiner x8 x8 19 in. x16 These individual components have been packaged together into a rack-mounted chassis. x16 x8 x8

Synthesis of Wideband Waveform Frequency Intensity Modulators 200 GHz f CW Laser Swept-Frequency Generator PM AM 16 x Dt f Phase Control Loop Frequency Time Swept RF Waveform 12.5 GHz 0.5 ms Challenges Generating 16 phase-coherent optical frequencies Modulating optical source to generate stepped-frequency Creating 12.5-GHz swept RF source Transferring RF waveform onto optical frequencies Maintaining phase continuity between stitching points in optical spectrum The next step is to generate a 12.5-GHz broad swept waveform in the RF domain.

Synthesis of Wideband Waveform 780 MHz sweep Down-mix 13.5 GHz I Arb. Wfm. Gen. DC – 390 MHz RF Single- Sideband Modulator 2 f 2 f 2 f 2 f 4 f Q 58 – 70.5 GHz sweep 4 GHz f 16.5 GHz 4 GHz t 0.5 ms Doubler Chain Frequency Time Swept RF Waveform 12.5 GHz 0.5 ms Challenges Generating 16 phase-coherent optical frequencies Modulating optical source to generate stepped-frequency Creating 12.5-GHz swept RF source Transferring RF waveform onto optical frequencies Maintaining phase continuity between stitching points in optical spectrum The 12.5-GHz RF sweep is produced with a 390-MHz broad sweep generated by an arbitrary waveform generator. This is then multiplied by 32 with a RF single sideband generator and 4 frequency doublers. After pre-compensating for distortions introduced by these components, a 12.5-GHz RF sweeps is produced.

Synthesis of Wideband Waveform Frequency Intensity Modulators 200 GHz f CW Laser Swept-Frequency Generator PM AM 16 x Dt f Phase Control Loop Frequency Time x16 Swept Optical Waveform 200 GHz 8 ms Challenges Generating 16 phase-coherent optical frequencies Modulating optical source to generate stepped-frequency Creating 12.5-GHz swept RF source Transferring RF waveform onto optical frequencies Maintaining phase continuity between stitching points in optical spectrum The next step is to transfer this 12.5-GHz RF waveform onto the 16 optical frequencies.

Synthesis of Wideband Waveform Frequency Intensity Modulators 200 GHz f CW Laser Swept-Frequency Generator PM AM 16 x Dt f Phase Control Loop Optical Single-Sideband Spectrum x16 Optical Frequency Optical Single- Sideband Modulator 12.5 GHz Input Time Cancelled lower sideband Swept Output RF Input This transfer of the RF sweep to the optical frequencies is accomplished with an optical single-sideband generator. The single-sideband generator shifts an optical frequency both the frequency of its RF input. Since the RF input is swept, it imposes this frequency sweep onto each of the optical frequencies. 16.5 GHz Frequency x16 4 GHz Time Time

Synthesis of Wideband Waveform Frequency Intensity Modulators 200 GHz f CW Laser Swept-Frequency Generator PM AM 16 x Dt f Phase Control Feedback Loop (250 Hz BW) Frequency Time x16 Swept Optical Waveform 200 GHz 8 ms Challenges Generating 16 phase-coherent optical frequencies Modulating optical source to generate stepped-frequency Creating 12.5-GHz swept RF source Transferring RF waveform onto optical frequencies Maintaining phase continuity between stitching points in optical spectrum The final step in generating the 200-GHz optical waveform is to detect the phase discontinuity at each of the stitching points, and control the phases of the individual optical frequencies to ensure phase continuity across the waveform. The beat signal from a delayed self-heterodyne measurement is digitized and demodulated to determine the phase discontinuity between the individual subchirps. Phase correction is applied to the optical frequencies to eliminate this discontinuity.

Demonstration of 1-mm Range Resolution Single Target Range Profile; No Phase Stabilization Range Profile; Phase Stabilized 1-mm range resolution 200 GHz stabilized 200 GHz theory (Hamming) Goal Goal Multiple Targets LOS Adjustable Range Separation d = 1.0 mm d = 1.2 mm Increasing range spread Resolved range separation d The range profile of a single planar target illustrates the importance of maintaining phase continuity across the waveform. Without optical phase control, there are significant sidelobes on the range profile. When the phase contro is activated, the sidelobes are better than 25 dB below the signal. The linewidth of the peak is consistent with a range resolution of 1 mm. The resolution is further verified by imaging two planar surfaces, with adjustable separation. These 2 surfaces are clearly resolved with a separation of 1.2 mm.

Synthetic Aperture Ladar (SAL) Object rotation Object rotation provides relative motion Same processing as for moving platform Inverse Synthetic Aperture Ladar (ISAL) Synthetic Aperture Range-Resolved Doppler-Resolved Front View Side View

ISAL Image Equivalent to View Along Spin Axis 1-mm ISAL Imagery ISAL Image Equivalent to View Along Spin Axis Spin axis Laser flood illumination Down-range Cross-range ISAL Image Cross-Range Profile 1-mm -5 Initial ISAL images were performed by rotating a test target in the laboratory. The ISAL image is equivalent to viewing in along the spin axis. The image confirms that 1-mm range and cross-range resolution has been achieved. -10 Down-range (cm) Power (dB) Power (dB) -15 -20 Cross-range (cm) Cross-range (cm)

ISAL Image Equivalent to View Along Spin Axis ISAL Imaging of Mask Spin axis, 11 °/s ISAL Image Equivalent to View Along Spin Axis 4-cm Laser Illumination Down-range The first ISAL face images were collected on a pirate mask. The mask was oriented such that a horizontal laser beam path would be equivlaent to illumination from below. It was rotated at 11 deg. / s, while a 4-cm spot was raster scanned across the face. For each revolution, one spot was collected for 128-ms. Cross-range 4-cm diffraction-limited spot raster scanned across mask to form 6x4 array 1 spot collected / revolution to simulate simultaneous collection

4-cm real-aperture resolution Mask ISAL Image Close-up Image ISAL Image Real-Aperture Image Down-range Cross-range ISAL processing of the 24 4-cm spots produces a synthetic aperture imaging with 1-mm resolution. This required 4-ms coherent processing for each spot, and 128-ms incoherent averaging for each spot. The equivalent real-aperture image with 4-cm resolution is also shown. 1 mm synthetic aperture resolution 4-ms coherent processing time for each spot 128-ms incoherent averaging for each spot 4-cm real-aperture resolution

Summary Coherent ladar with wideband LFM waveform enables high range resolution with modest detector bandwidth Demonstrated high-speed wideband LFM waveform with compensated phase 200-GHz in 8 ms; scalable to higher bandwidths Demonstrated 1-mm range resolution and 1-mm x 1-mm ISAL imaging

Backup Slides

SAL Processing with LFM FFT Processing LFM Source Detector Signal Time Rearrange into 2D array Signal ‘Fast’ Time ‘Slow’ Time Optical Freq. Time 2D-FFT Detector Signal The beat signals detected from the LFM waveform beating with its delayed copy are processed to provide both the range and Doppler information for a scatterer. The frequency of this beat (the oscillation of the signal occurring during a single chirp) provides the range, as described before. The phase evolution from chirp-to-chirp is caused by the scatterers motion shifting the optical phase of the scattered light. The frequency of this ‘slow-time’ oscillation provides the Doppler information. A single time-series of data can be rearranged into a 2-variable function of ‘fast-time’ and ‘slow-time’. A 2D FFT of this function directly provides the range-Doppler map for the target. Appropriate scaling of the Doppler axis provides the velocity, and thus cross-range information. ‘Fast-time’ oscillation: Range Time ‘Slow-time’ oscillation: Doppler