Interferometric Sounder Concept for Ice Sheet Mapping

Review, Simulations, Spaceborne System, Future

E. Rodriguez

Jet Propulsion Laboratory

California Institute of Technology

Talk Outline

• Motivation for examiniming the interferometric sounder concept

• Description of interferometric sounder concept and simulation results

• A possible spaceborne implementation

Conventional Sounding is Insufficient

• Nadir sounding full coverage is not sufficient to meet science requirements:– Beam limited spatial resolution (1km) requires

antenna size beyond current capabilities (420 m at P-band)

– Available bandwidth (and range resolution) insufficient for desired 10m height accuracy: 6MHz gives a range resolution of 13.8 m in ice. Worse at VHF.

– Full spatial coverage requires many years of mission lifetime (and large costs)

Conventional Interferometry is Insufficient

• Coverage, spatial resolution, and height accuracy suggest that a swath SAR interferometer might meet requirements

• However, contributions from ambiguous returns from surface clutter and the opposite side basal layer make this approach not feasible

• An alternate approach: multiple baselines to resolve subsurface/surface. Expensive and hard to implement:– In order to get sufficient number of different

baselines a large number of antennas are required– The technique is very sensitive to calibration and to

having good SNR– Data rate is very large

Range Ambiguities for Sounding

Similar ambiguities exist on the opposite side of the nadir track

Geometry of the two layer scattering model. H is the spacecraft height above a reference surface; h is the ice surface height above the reference surface; D is the average depth of the basal layer; d is the topographic variations of the basal layer; xb is the cross-track coordinate of the basal layer point under observation; and, xs is the cross-track coordinate of the surface point whose two-way travel time is the same as the two-way travel time for xb.

Ground Resolution vs Bandwidth

Clutter Effect on Interferometric Error

Height error as a function of signal to clutter () for a baseline of 45 m and a center frequency of 430~MHz (solid lines) and 130 MHz (dashed lines). The values of () are: 1 (blue), 0.1 (red), and 0.01 (black).

Height Noise vs SNR

Height error as a function of SNR for a baseline of 45m and a center frequency of 430 MHz (solid lines) and 130 MHz (dashed lines). The values of SNR are: 0 dB (blue), -5 dB (red), and -10 dB (black). The number of looks is assumed to be 100.

Scattering Area Ratio: Loss of SNR for Off-Nadir Geometry

Ratio of the basal to surface scattering areas. Notice that away from the nadir direction, this ratio quickly approaches 1.

Interferometric Sounding Concept

• Conventional interferometry uses phase information one pixel at a time

• However, there is additional information contained in the spatial frequency of the phase:– Opposite side ambiguities have opposite interferometric

frequencies: while the phase in one side increases with range, it decreases with range in the opposite side (+/- spatial frequencies of complex interferogram)

– Because of the difference in incidence angles, the near nadir interferometric phase spatial frequency is much larger than the equivalent frequency for surface clutter

• IFSAR sounding concept: spatially filter interferogram to retain only basal returns

Surface x-Track Distance vs Basal x-Track Distance

Surface cross-track distance xs as a function ofbasal cross-track distance xb for a platform height of 600km. Notice that near nadir xs is nearly independent of xb, while for xb > 50 km, the two are close to being linearly dependent.

Surface Ambiguous Incidence Angle

Surface incidence angle s as a function of xb for a platform height of 600 km. As expected, the behavior matches that of xs.

Basal Incidence and Look Angles

Basal layer incidence angle 2 as a function of xb for a platform height of 600km (solid lines). Notice that, since the dependent on depth is of order D/H, the incidence angle is nearly independent of depth.The apparent look angle, 1 is also plotted using dashed lines.

Interferometric Phase and Phase Frequency

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Φb ≈ 2kBθ1

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Φs ≈ 2kBθ s

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κ s ≈ 2kB1

xs−hxH

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κ s ≈ 2kB1

xb−

dxn(H + D /n)

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Surface interferometric phase difference

Basal interferometric phase difference

Surface Interferogram slope as a function of range.hx is the surface topography cross-track slope Basal Interferogram slope

as a function of range.dx is the surface topography cross-track slope

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I =αe iΦ b + βe iΦ s Complex interferogram

UHF Fringe SpectrumNo Antenna Pattern

Interferogram spectra for signal to clutter ratio of 1, radar frequency of 430MHz, bandwidth of 6MHz, for the first 50 km of xb. The basal spectrum is colored orange. The remaining curves show the surface spectra for D = 1 km (black), D = 2 km (red), D = 3 km (green),D = 4 km (blue). Notice that the basal fringe spectrum depends very weakly on depth

What is the Effect of Surface Slopes?

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Δκ s = 2kBσ hxH

Spectral broadening due to surface slopes

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Δκ sκ s

<xsH

<<1 Relative spectral broadening is much less than the spectral peak, as long as the angle of incidence is small: changes in the angle of incidence are dominated by changes in cross-track distance rather than changes in slope. This argument does not hold for higher incidence angles.

Filter Design• In range space, both the basal fringe rate and the surface fringe rate are spatially varying

• The basal layer is hard to model (unknown topography and reflectivity)

• The surface layer is easy to model: smooth topography and small changes in reflectivity. However, the topography may not be totally known

• To narrow the surface spectrum, re-project data from range space to a plane near the surface. In this coordinate system, the surface fringe rate is approximately constant

-Empirically, one can see a significant narrowing of the surface contribution and better separation between the two

• Two algorithms examined:

-Surface contribution is frequency shifted to 0 frequency by applying a phase ramp and the basal return is extracted via a band-pass filter. Problems near antenna pattern nulls or strong gradients

- A fit is made to the surface interferogram, including antenna pattern variations.Band-pass filter design is still being optimized.

Height Error After Interferometric Filtering: 45m Baseline No Antenna

Assumed clutter to signal ratio (same side): 0dB

Assumed clutter to signal ration (opposite side): -3dB

Assumed SNR: 0dB

Assumed number of spatial looks: 100

Topographic Simulation ResultsResults Similar to Xiaoqing’s

Basal Interferogram Surface InterferogramTopography Weighted by Gain

RangeRange Distance (km)

Antenna Pattern Results: 2 km

Basal Return Surface Return

Before filtering After filtering

Antenna Pattern Results: 3 kmWhat should be done about long wavelength

brightness variations?

Before filtering After filtering

Basal Return Surface Return

Problems with Simple Band-Pass

• Low frequency envelop variations broaden spectrum and cause simple FFT or FIR based algorithms to either extract too much signal or leave too many sidelobes

• The latest filter, still under development, uses least squares fitting of the expected surface signal, including antenna pattern variations

Spaceborne Radar Concept

• Use P-band interferometer with two antennas and 30m - 60m baseline separation

• Use SAR processing to obtain along track resolution

• Use polarimetric radar to remove ionospheric effects

• Align antennas so that conventional nadir sounding is possible at the same time as interferometric sounding– Use conventional sounding for layering studies and as

calibration for interferometer at cross-over points– Use Interferometric sounding from 10 km to 60 km

Key Instrument Parameters

Polarimetric radar (4 channels)center frequency (Hz) = 430.e6bandwidth (Hz) = 6.e6pulse length (sec) = 20.e-6peak transmit power (W) = 5000.system losses (dB) = -3.receiver noise figure (dB) = 4platform height (km) = 600azimuth resolution (m) = 7prf (Hz) = 10000Duty cycle (%) = 20antenna length (m) = 12.5antenna efficiency (dB) = -2. ! 1-wayantenna boresight angle (deg) = 2.5wavelength (m) = 0.7baseline (m) = 45. swath (km) = 50Minimum number of looks = 500.

Sounder Performance 1 km Ice

Sounder Performance 2 km Ice

Sounder Performance 3 km Ice

Sounder Performance 4 km Ice

Ongoing Work at JPL to Support the IIP• For the IIP, it is very likely that platform motion will play a significant role

• Conventional processors which work in the frequency domain, are not very well suited to handle large motion plus ray bending

• Given improvements in computing, one can solve do an exact time-domain back-propagation to achieve optimal focusing

• This is the slowest algorithm, but makes no approximations

• Results from other processors (KU, Vexcel) can be verified against exact results

• JPL simulator makes approximations, but is significantly faster to run than the sophisticated Vexcel simulator (previous secene completed in a few minutes)

• This tool can be used for system engineering studies to assess performance tradeoffs (e.g., antenna pattern design, optimal element combination)

• The clutter removal filter is still being optimized: handle nulls

Backup Slides

Estimated One-Way Absorption

Absorption losses present severe constraints on system design if an SNR > 0dB is desired. Together with pulse length considerations, this leads to a desired peak power of ~5kW, which is technologically feasible at P-Band and VHF.

Radar Frequency Selection• Select P-band (430MHz) to minimize baseline

length, antenna size and range resolution – Antenna length of 12.5 m consistent with demonstrated

space technology (TRL 9)– Baseline range between 30m to 60m consistent with

SRTM mast (TRL9)– 6MHz bandwidth possible at P-band– Higher clutter mitigated by interferometric sounder

technique

• VHF may be feasible using repeat pass interferometry, although antenna size (~40m) may be problematic.– Can one increase VHF bandwidth over the polar regions?

Desired Swath Altitude

• A 50 km swath will enable a mission lifetime < 4 months => cost savings

• A 50 km swath is consistent with the interferometric sounder approach for a height of 600 km and a 6 MHz bandwidth

• Heights lower than 600 km will require a decrease in swath and a consequent increase in mission lifetime (although this is not a strong constraint).

Assumed Antenna Pattern

• Assume uniform circular illumination

• Antenna diameter 12.5m– Consistent with available

space qualified antennas

• Antenna boresight: 1.5deg

• Assumed antenna efficiency: -2dB 1-way

Pulse Length Selection

• In order to minimize contamination from nadir surface return, use short 20musec chirp– Surface nadir return sidelobes stops after

1.7 km of ice depth

• Much longer pulses will contaminate basal returns significantly

• Use high power and high PRF to overcome ice propagation loss

PRF Selection

• Required PRF to for SAR synthetic aperture: ~1KHz

• Use significantly higher PRF (~7Hz - 10Hz) together with onboard presumming to improve signal to noise ratio.

• Instrument duty cycle: ~20%

Model Backscatter Cross Section

• The backscatter model consists of two contributions:– Geometrical optics

(surface RMS slope dependent)

– Lambertian scattering

• assumed Lambertian contribution at nadir: -25dB

Observed Surface Sigma0 Angular Dependence at 120 MHz

• Data obtained with the JPL Europa Testbed Sounder in deployment with the Kansas U. sounder over Greenland

• Angular decay near nadir (>15 dB in 5 degrees) consistent with very smooth ice surface

• Change in behavior at P-band is still unknown, but probably bounded by 1-3 degree slope models