RADAR TARGETS IN THE CONTEXT OF EARTH OBSERVATION. Dr. A. Bhattacharya

Transcription

1 RADAR TARGETS IN THE CONTEXT OF EARTH OBSERVATION Dr. A. Bhattacharya 1

2 THE RADAR EQUATION The interaction of the incident radiation with the Earth s surface determines the variations in brightness in a radar image and reveals properties of the Earth s surface of interest. Detection of discrete target by a radar Isotropic radiator 2

3 THE RADAR EQUATION The power density at the target, R meters away p i = P t 4πR 2 Wm 2 ; i incident on the target If instead of an isotropic radiator, the radar uses an antenna that concentrates the power in a preferred direction, the power density at the target is p i = P t G t 4πR 2 Wm 2 ; G t Gain of the transmitting antenna 3

4 THE RADAR EQUATION G t The ratio of power density it produces in the preferred direction compared with the power density produced by an isotropic radiator A target at position R will present an area or cross section to the incoming radiation It may absorb some of the incident energy, but will also reflect/scatter a significant portion of the energy The Radar Cross Section is introduced 4

5 RADAR CROSS SECTION (RCS) RCS has dimensions of area (orthogonal to the incident radiation) Describes how much power the target extracts from the power density of the incoming wave Most of this intercepted power will be scattered Irrespective of its shape, the target is assumed to scatter the intercepted power isotropically (theoretical assumption) RCS is described by σ m 2 Usually not easily related to any physical cross sectional area of the target If the radar rotates w.r.t the incoming radar beam, then it will have a different RCS defined by the implicit area needed at that orientation to account for the energy extracted from the wavefront and re-radiated back to the radar set isotropically 5

6 RADAR CROSS SECTION (RCS) The power received by the target and available for reradiation is P σ = p i σ = P t G t σ 4πR2 W The power density produced back at the platform after scattering from the target is p r = P t G t σ 4π 2 Wm 2 R4 The extra 4πR 2 term in the denominator is caused by the isotropic propagation back to the platform 6

7 RADAR CROSS SECTION (RCS) To find the actual power received, the returned power density is multiplied by a property of the antenna referred to as its aperture A r, having dimension of area The received power is P r = P t G t σa r 4π 2 W R4 The aperture of an antenna can be written in terms of its gain G r = 4π λ 2 A r 7

8 RADAR RANGE EQUATION The power received by the radar system after scattering from the target is P r = P t G t G r λ 2 σ 4π 3 W R4 This is called the radar range equation since it can be used to determine the maximum range of a radar if all the other terms are known and we know the limit of detection of received power One of its main features is the inverse fourth power dependence on the distance to the target 8

9 RADAR RANGE EQUATION If we choose a transmitter power and range, and measure the received power at the wavelength of interest then we can find σ, assuming we know the antenna gains If we take several measurements of received power with different orientations of the target, we would then be able to build up a picture of how the RCS of an object changes with the angle with which it is viewed 9

10 EXPRESSION FOR RCS The transmitted power creates a power density p i incident on the target The RCS of the target σ intercepts σp i Watts of power which it re-radiates isotropically, producing a power density at the receiver of p r = σp i 4πR 2 Wm 2 The average power density is related to electric field by p = E2 η η Free space impedence; E rms value of the field 10

11 EXPRESSION FOR RCS The expression for received power density E r 2 = Thus the definition for RCS σ = lim σ Ei 2 4πR 2 E 4πR 2 Er 2 R i 2 R We need to be far enough away from the target so that near field effects can be ignored 11

12 EXPRESSION FOR RCS The RCS value can extend over an enormous range (less than 0.01 m 2 to 100 m 2 ) It is usual to express RCS in decibels (db) w.r.t some reference level using the definition σ = 10 log 10 σ σ ref ; σ ref = 1m 2 The unit of RCS is then dbm 2 σ σ = 10 log 10 1m 2 dbm2 12

13 DISTRIBUTED TARGETS Some targets in radar remote sensing are of the nature of discrete scatterers More common scattering takes place from regions on the Earth s surface that are distributed in nature (area of soil/snow/agricultural field/ocean surface) To accommodate these cover types, the radar equation needs to be modified, commencing with a variation to the definition of RCS 13

14 DISTRIBUTED TARGETS RCS strictly refers only to discrete targets To formulate an alternative suited to distributed cover types, we consider a region composed of an infinite collection of infinitesimal elements of effective area ds, many of which make up an individual pixel Resolving a distributed region (e.g., agricultural field), into a set of discrete incremental areas 14

15 DISTRIBUTED TARGETS Suppose that the RCS of each of those infinitesimal area is dσ On an average the region exhibits a RCS of per unit area dσ ds σ 0 = dσ ds Scattering coefficient (Sigma naught) 15

16 DISTRIBUTED TARGETS The power received back at the platform after scattering from one of the incremental regions will be dp r = P t G t G r λ 2 dσ 4π 3 R 4 W In terms of radar scattering coefficient for the region dp r = P t G t G r λ 2 σ 0 ds 4π 3 R 4 W 16

17 DISTRIBUTED TARGETS We can now find the total power returned to the platform from a particular resolution cell, or pixel by P r = P t G t G r λ 2 σ 0 ds 4π 3 R 4 W pixel If all the quantities inside the integral can be considered constant over pixel, then the received power is P r = P t G t G r λ 2 σ 0 (r a r g ) 4π 3 R 4 W r a and r g are the azimuth and ground range resolutions respectively 17

18 DISTRIBUTED TARGETS The radar equation in terms of the scattering coefficient is most used in radar remote sensing If all other parameters are known through the design of the radar system σ 0 can be determined by measuring P r σ 0 describes the tone of the radar image and is analogous to the reflectance of Earth surface materials at visible and infrared wavelengths used in optical RS It is important to relate σ 0 to the physical properties of the region being imaged its composition, water contents, physical properties and so on. 18

19 DISTRIBUTED TARGETS 19

20 DISTRIBUTED TARGETS Like RCS σ, the scattering coefficient σ 0 is expressed in decibels (db) σ 0 = 10 log 10 σ 0 1m 2 m 2 db Examples : 0 db 1m 2 m 2 3 db 2m 2 m 2 ; 20 db 0. 01m 2 m 2 20

21 DISTRIBUTED TARGETS Conversion of scattering coefficients to db 21

22 POLARIZATION DEPENDENCE OF σ 0 Incident and scattered waves, described in terms of power and power density are composed of electric and magnetic field vectors at right angles to the direction of propagation and to each other Polarization of the wave is described in terms of the orientation of the electric field vector Polarization is a very important parameter in radar RS because the scattering properties of Earth surface materials can be different for different incident polarizations 22

23 POLARIZATION DEPENDENCE OF σ 0 The scattered wave can also have a different polarization from that of the incident wave A mechanism referred to as polarization rotation or sometimes depolarization To account for the fact that the scattering coefficient is polarization dependent σ 0 Signifies the polarization of the incident wave and that of PQ the wave scattered and received by the radar 23

24 POLARIZATION DEPENDENCE OF σ 0 Four relevant scattering coefficients (quad polarization) together form a sigma naught σ 0 matrix σ 0 = σ0 HH σ 0 HV σ 0 VH σ 0 VV For monostatic radar systems σ 0 HV = σ 0 VH σ 0 H, σ 0 V are quite different from each other 24

25 POLARIZATION DEPENDENCE OF σ 0 We can define two measures that are important in polarimetric radar RS studies Co- polarization ratio Cross- polarization ratio p = σ0 HH σ 0 VV q = σ0 HV σ 0 VV or σ0 VH σ 0 HH The cross-polarization ratio implicitly carries information about complex scattering events that may lead to a rotation (depolarization) of the polarization state of the incident radiation 25