Learning / Height of ambiguity

Height of ambiguity

Two radar passes that see the ground from slightly different positions record slightly different distances to every hill. The difference shows up as fringes. How much height fits inside one fringe depends on the baseline, the wavelength and the viewing geometry. Steer them and watch.

The idea in one equation

The interferometric phase measures the difference in distance from the two antennas, in steps of half a wavelength. For a point at height h above the reference surface, the topographic part of that phase is

φtopo = 4π B⊥ h / (λ R sin θ)

where B⊥ is the perpendicular baseline, λ the wavelength, R the slant range and θ the incidence angle. One full fringe (2π) corresponds to a height change of

ha = λ R sin θ / (2 B⊥)

This is the height of ambiguity. A small ha packs many fringes onto a mountain and makes a sensitive height meter; a large ha makes the interferogram almost blind to topography, which is what you want when you are measuring ground motion instead.

Simulator

add the flat-Earth fringes
show the terrain under the fringes
ha
fringes
slant range R
flat-Earth spacing
Radar looks from the left (ground range increases to the right). Terrain is shown in map geometry, so layover and shadow are ignored.

Try this

  1. On Fuego with Sentinel-1, find the baseline that puts exactly one fringe between the base and the summit. Now switch to NISAR at the same baseline. How many fringes are left, and why is the ratio larger than the ratio of the two wavelengths?
  2. Turn on the flat-Earth fringes and set B⊥ near 100 m. Measure the spacing on the ground and compare it with the readout. Processing chains remove these fringes before anyone looks for topography or motion.
  3. Choose "Kirishima: error from a DEM made in 2000". Lava filled the Shinmoedake crater in 2011, so a DEM built from the Shuttle mission of February 2000 is up to about 100 m too low there. (Elsewhere the two DEMs differ by a few meters to a few tens of meters, mostly over forest, because the two radars saw the canopy differently.) Which baseline turns that error into a full fringe with Sentinel-1? With NISAR? Then see the real Sentinel-1 test at Kirishima.
  4. Set B⊥ to zero. What survives, and what does that tell you about the pairs you would choose to measure millimeters of ground motion?

Read more

Rosen, P.A., et al. (2000). Synthetic aperture radar interferometry. Proceedings of the IEEE 88(3), 333–382. doi:10.1109/5.838084
Bamler, R., Hartl, P. (1998). Synthetic aperture radar interferometry. Inverse Problems 14(4), R1–R54. doi:10.1088/0266-5611/14/4/001
Hanssen, R.F. (2001). Radar Interferometry: Data Interpretation and Error Analysis. Kluwer. doi:10.1007/0-306-47633-9

Built for CIVE 6359, SAR Remote Sensing, University of Houston. Terrain: Copernicus DEM GLO-30, © DLR e.V. 2010–2014 and © Airbus Defence and Space GmbH 2014–2018, provided under COPERNICUS by the European Union and ESA; NASADEM, NASA JPL (2020), from Shuttle Radar Topography Mission data of February 2000. Radar parameters: wavelengths from the Sentinel-1 and NISAR product metadata; slant range computed for a spherical Earth from orbit heights of 693 km (Sentinel-1) and 747 km (NISAR).