1. 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. 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.

2. 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

3. 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

4. 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

5. 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.

6. 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.

7. 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.

8. 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

9. 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

10. 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.

11. 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.

12. 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.

13. 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

14. 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.

15. 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.

16. 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

17. 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)

18. 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

19. 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

20. 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

21. Backup Slides

22. 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