Radar signal contains 2 types of information: intensity and phase intensity lets us discriminate among materials

Transcript

1 Radar signal contains types of information: intensity and phase intensity lets us discriminate among materials Phase is used to measure topography and ground motion Interferometry: interaction between two superimposed wave trains ϕ Two waves are traveling and are offset by an amount ϕ ϕ is the phase difference

2 Interferometry is realized observing the same area from two slightly different positions (A1 and A) separated by a Baseline B A1 B A A 1 Ae i ϕ 1 A Ae i ϕ ϕ A1 is usually called the Master, A the Slave. Difference in distance of antennae from surface ensure that return arrives at one antenna before other, resulting in phase difference ϕϕ -ϕ 1 Single Pass Interferometry : one antenna transmits pulse, but returns received by both simultaneously: Repeat Pass Interferometry: both antennas receive and transmit, but with a time interval:

3 Single pass Repeat pass ρ 1 ρ π ϕ ϕ ϕ 1 ( ρ ρ 1 ) Single Pass: p1 Repeat Pass: p p

4 Single Pass has so far been reserved to airborne campaigns, with the exception of Shuttle Radar Topography Mission (Jan. 000) C-band One receiver in the Shuttle cargo bay, one receiver at the end of a 60m long mast

5 Repeat Pass Interferometry from space Two satellites image the Earth s surface: tandem (ERS1/ sometimes) One satellite takes the images a few days apart: if ground does not move between times when satellite revisits spot the phase should be the same atmospheric/environmental conditions need to remain similar between passes

6 The image representing ϕ is called interferogram. The pixels of an interferogram are produced from two complex SAR images by multiplication of each pixel acquired by the master A1 with the complex conjugate of the corresponding pixel acquired by the slave A ϕ arg[ A 1 A * ] 0 < ϕ < π The interferogram contains the interference fringes, that represent the cycles of ϕ. The fringes are represented by colour cycles blue-green-yellow-red Pixel with the same colour have got the same ϕ. After a cycle in colours, pixels represent a variation of ϕ equal to π

7 Utilizzo dell interferometria per ricostruire le deformazioni della superficie (Interferometria differenziale) Ho una prima misura interferometrica repeat pass che fornisce: ϕ ϕ ϕ 1 Ed una seconda misura interferometrica costruita con un acquisizione effettuata dopo che la superficie osservata ha subito uno spostamento. Questa seconda immagine fornisce: 4 π B II ϕ ' ϕ ' ϕ 1 4 π ( ρ ' + ξ ρ ) ξ è la componente dello spostamento lungo la direzione di osservazione. ϕ ' contiene sia la differenza di fase dovuta alla topografia che quella dovuta allo spostamento.

8 Posso calcolare la differenza di fase ϕ tpg che avrebbe avuto la seconda immagine se non ci fosse stato lo spostamento conoscendo ϕ, B, B', α e α' ξ π ϕ ϕ α ϑ π ρ ρ π ϕ α ϑ π ρ ρ π ϕ + 4 ' ) ' sin( ' 4 ) ' ( 4 ) sin( 4 ) ( 4 tpg tpg B B Dalla prima coppia deduco la differenza di fase dovuta esclusivamente alla topografia, e dalla seconda deduco. (Notare che le due coppie interferometriche hanno in comune la misura effettuata prima del verificarsi dello spostamento). ξ ϕ 1

9

10 Master image Slave image Interferogram Interferogram after flattening

11 Unwrapping Extracting the phase We can get only the wrapped phase ϕ arg[ A 1 A * ] where π < ϕ < π ϕ We would like the continuous phase. This appears simple. Look for π jumps and then add the appropriate multiple of π. If the data are good, phase unwrapping is straightforward Steep topography, large deformations pose the greatest problems

12 If the propagation medium changes between the two SAR acquisition, there are error sources caused by phase delays introduced by the intervening medium. This is the case of the atmosphere: if humidity, temperature, pressure change between the time interval of the SAR images, a phase term, independent of the baseline, appears.