FMCW Differential Synthetic Aperture Ladar for Turbulence Mitigation 18 th Coherent Laser Radar Conference

Transcription

1 FMCW Differential Synthetic Aperture Ladar for Turbulence Mitigation 18 th Coherent Laser Radar Conference June 3, 16 Zeb Barber, Jason Dahl, Ross Blaszczyk

2 Outline Ultra-high resolution (< mm) FMCW sources Active stabilization of chirp rate and center frequency Synthetic Aperture Ladar Imaging Introduction Image based phase correction Differential Synthetic Aperture Ladar DSAL concept and receiver design Comparison with SAL in atmospheric turbulence

3 frequency Ultra-high Resolution FMCW Sources Tunable laser sources Large mode-hop free tuning (1 s of nm possible) Trade-off between tuning bandwidth, coherence length, and tuning speed External-cavity, DFB, integrated photonics? Active Stabilization with improvements Fiber delay generates error signal on chirp rate PLL locks chirp rate Lock around the corner for phase coherence Stabilize center frequency to molecular absorption using digital loop Temp Controller DFB Laser Current Driver 9/1 Splitter Inline Polarizer Amplifiers Servo DPD 9 1 5/5 Splitter 1m Delay AOM DDS 1 Micro Controller 9/1 Chirp Splitter Output DDS 5/5 Splitter 15MHz Ref Detector Amplifier HCN Cell Comparator Detector f Local Oscillator Delayed Signal f beat = κτ D B τ τ D τ c t time 3

4 Residuals Px [mm] Px [m] Relative Distance (mm) microns Relative Power (db) Metrology Applications Transmit x Stabilized Chirp Laser Local Oscillator Return Photodetector Focusing Lens Eight targets at 14. km standoff Computer Reference Plate Sample X-Y Stage Relative Range (m) Precision =.7 mm Time (s) mm 4 mm 6 8 Stabilized Chirped Laser Source Fiber Splitter 9 1 fiber path free path LO Emitter C and mirror for the interferometer Tx Rx Auto-Balanced Detector A D C to interferometer Computer controlled translational stage Scattering Target Emitter B Collimated Emitter /Receiver A Unprocessed Data Post Processing Py [m] Py [m] Measurements Savitzky-Golay smooth 4

5 Synthetic Aperture Radar Proposed in 1951, Carl Wiley First images in 1957 Radar signals recorded on film, processed optically Digital supplanted optical processing in late 7 s Synthetic Aperture Ladar Synthetic Aperture Imaging History Early work in 196 s United Aircraft (Lewis & Hutchins) Re-emergent interest in mid s (NRL, Aerospace Corp) SAR of Venus Magellan Table-top work needs a very large bandwidth (> 1 s of GHz) chirp source In fact, finding a suitable source has been one of the most challenging aspects of the SAIL imaging problem. Generally, tunable sources are not sufficiently stable and stable sources are not broadly tunable. f Local Oscillator Delayed Signal f beat = κτ D B Bashansky et. al Beck, Buck, Buell et. al τ D τ c t 5

6 Coherent Imaging Coherent Illumination Coherent field scattering off diffuse objects creates 3D speckle field Speckle field is a Fourier domain representation of object Size of speckles inversely proportional to size of object Speckles move with object orientation Absolute phase depends on absolute roundtrip distance and laser wavelength Coherent Detection Speckle field phase required to reconstruct image Interference with LO field captures signal field phase Image formed by Fourier transforms and quadratic focusing Provides single photon sensitivity Digital Holography Spatial sampling, no temporal or frequency domain sampling Synthetic Aperture Ladar Frequency/Range domain sampling in one dimension, temporal sampling of spatial degree by motion Combinations of above How do you divide up your resources?

7 meters SAL Imaging Simulation Tx/Rx Plane Object Plane -.5 Synthetic Aperture Scan m propagation meters Frequency Scan 7

8 Crossrange SAL Imaging Demonstrations Post- Processing Unprocessed Data Computer Controlled Stage Shot N N-1 Range ADC Balanced Detector 5/5 Shot 1 Circulator Local Oscillator Path 99/1 EDFA 9/1 Fiber Splitter\Coupler Stabilized Chirped Laser Source HCN Ref Phase of optical field required to form image Motion induced piston error largest phase error source LMCT presented a SAL flight demonstration at CLEO 11 Motion compensation techniques Prominent Point (point target of opportunity or artificial cooperative target) Phase Gradient Autofocus (PGA) Differential Synthetic Aperture Ladar E. A. Stappaerts and E. T. Scharlemann, "Differential synthetic aperture ladar," Opt. Lett. 3, (5). 8

9 Power [db] Phase Correction [rad] Table Top SAL Demos a) b) 13x13 Pixels a) b) c) Range [m] SA index Single Range Profile Image before PGA PGA Estimate Phase Correction 9

10 Phase Gradient Autofocus Algorithmic Steps in PGA Step 1 Input Complex Image Domain Data Step Center Shift Largest Targets Step 3 Determine Window Width and Apply Window Step 4 Fourier Transform in Cross-Range Dimension (to range-compressed domain) Step 5 Estimate Phase Error Function Across Aperture RMS Phase Error < Threshold? No Step 6 Apply Phase Correction Yes Done Step 7 Inverse Fourier Transform Back to Image Domain Step - center shifting chooses strongest targets and removes the linear phase variation from each target Step 3 - windowing attempts to include as much energy from a single target in each range line without including multiple targets - proper choice of window affects efficiency and final image quality Step 5 - phase error estimation accomplished by averaging of all targets to bring common mode phase error above clutter and noise Iteration - algorithm proceeds iteratively with decreasing window width to converge on final processed image - threshold on estimated RMS phase error is used to stop iteration N * m g k, m 1 g k, m k 1 1

11 microns spring-loaded stage 1.4m Range [mm] More Demos Range Migration Correction 5 1 (c) (d) Spotlight Motion Control and Bistatic Geometry (a) (b) 15 5 rotation stage below target monstatic Tx\Rx optics bistatic Rx optics (d) (e) Cross-range [mm] 15cm computer controlled stage dθ Fig. 3. a) SAL image of Air Force Bar Resolution Target (negative of chrome pattern on glass) with PGA applied in cross range. b) Same SAL image with PGA applied in cross range and range after CZT-PF processing Colors inverted on both images. (f) Interferometric SAL (d) (e) 11

12 Range [cm] Range Range Extremely Low Return Levels (a) 5 4 (c) (b) 5 4 (d) Cross-Range 5 photons per on pixel Top: Retro phased; Bottom: PGA phased Left: ~ 1 photon per pixel averaged 5 times Right: ~5 photons per pixel no averaging cross-range samples Cross-Range Cross-Range [cm] 1

13 SAL Simulation Results Turbulent phase screen near the aperture plane km C n = 1-14 at Aperture km C n = 1-13 at Aperture km C n = 1-1 at Aperture km C n = 1-11 at Aperture km C n = 1-14 at Aperture w/pga km C n = 1-13 at Aperture w/pga km C n = 1-1 at Aperture w/pga km C n = 1-11 at Aperture w/pga Phase Gradient Autofocus is quite good at removing common mode phase errors -Small aperture means turbulence needs to be very strong to not be common mode

14 Differential SAL E. A. Stappaerts and E. T. Scharlemann, "Differential synthetic aperture ladar," Opt. Lett. 3, (5). Patented by Stappaerts in 5 Use differential phase of two halves of receiver aperture Numerical integration across SA as phase history data Similar to idea behind PGA Phase gradient instantaneous (better for dynamic errors e.g. turbulence) Phase evolution estimated by integrating the differential phase Dynamic piston errors common mode Different piston errors for different range lines scatterer Real Aperture Synthetic Aperture z x d 14

15 [rad] [rad] [rad] Differential SAL Setup Tx Chirp Laser Target Tx/Rx Aperture λ/ f 1& = 5mm PBS f 3 = 15mm λ/ f 4 = mm Wollaston Prism Balanced Quad Detectors λ/4 5mm 35mm 185mm mm DSAL Tx/Rx design Monostatic Balanced homodyne receiver using polarization mixing Auto-balanced quadarture Large magnification to match aperture to 1 mm detector Lab experiment with chirp from DFB laser Real Aperture ~ 5 Gaussian μm soft aperture LO SA mm ( steps); Distance m Chirp Rate 83.3 GHz/ms; Chirp Time 1 ms; 83 GHz; dr ~ mm; dcr ~ 1.5 mm Magnification = 13.5 Single Point Target 1 um steps SA - Absolute Measured Phase Differential Phase Reconstructed Phase SA Position [mm] 15

16 Data collection using strip map mode ~ mm SA 8 m range Turbulence introduced into path using space heater Process data using DSAL or SAL w/pga Comparison w/ PGA w/ turbulence PGA performs better with no turbulence or turbulence near Tx/Rx Soft aperture provided by LO and not enough magnification onto detector low pass filters DSAL phase estimate causing problems with image has larger cross-range extent DSAL seems to degrade more gracefully, but not immune 16

17 Intensity Figure of Merit DSAL Turbulence Analysis E. A. Stappaerts and E. T. Scharlemann make bold statement that, DSAL, unlike SAL, is not affected by turbulence changes near the target. SAL immune to static turbulence near the target, but dynamic turbulence messes with phase evolution of point target DSAL since it is immune to overall phase changes E ±,j = a p exp iφ p (j) exp x j x p p w o exp ik x j x p R exp k x j± d 4 x p j is aperture position, p enumerates point scatterers Problem becomes that the phase angle of a sum of complex numbers is not linear in phase (i.e. a + b a + b) 1D DSAL w/ Turbulence simulation r =. 1 Average Ratio of Peak Height with Turbulence to no Turbulence 1 z, Cross-Range [m] r [m] 1D Simulation shows that DSAL does not provide much improvement over PGA+SAL with dynamic turbulence near the target. SAL DSAL 17

18 Turbulence Characterization Work performed for AFOSR YIP High Resolution Ladar ( mm range resolution) 5 Hz update 4x4 =16 square grid retro targets ~ 5 cm transverse spacing, ~ 1 cm range spacing Distance 8 m Turbulence generated using space heater Ladar processing Capture chirps (4 seconds, every 4 seconds) Resolve peaks, extract peak amplitude, range, & phase Process amplitudes and phases using mutual coherence to generate structure function and fit that to get r and C n Target Ladar Heater 18

19 Turbulence Characterization Mutual coherence and modulus of the complex coherence factor Γ Δr = U r U (r ) = U r U r exp ψ r exp {ψ (r ) μ Δr = Γ(r,r ) Γ r,r Γ r,r 1 -> D Δr = ln μ(δr) 1 Accumulative μ(δr i ) 1 All μ(δr i ) 3 Fitting of D(Δr i ) Cn 1-1 Advantage: Insensitive to fixed phase offsets! time [sec] 19

20 Acknowledgements AFOSR Young Investigator Program (YIP) #FA Bridger Photonics/Blackmore Sensors Analytics Randy Reibel, Pete Roos, Brant Kaylor, Stephen Crouch Other Support DARPA/DSO InPho, NSF GOALI CMMI, AFRL SBIR, Montana Board of Research and Commercialization