1

Sensori per il telerilevamento

SNR, SAR

Anno 2007/2008

Pulse limited

2

∆⋅⋅⋅≅−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+⋅= HH

BcHDPL

c22

22 2

2

<<λλ/8/8

22θθ

FresnelFresnelLsynthLsynth

space free resolution Range 2

=⎟⎠⎞

⎜⎝⎛

⋅=∆

cBc

flight direction

R

- c/(2Bc)- DPLR+c/(2Bc)

2HRAZ

λ≥

2H

4R AZ ∆⋅

⋅λ

=

Per MARSIS SAR non focalizzato

Per SHARAD evitando che vi siaRange Cell Migration

Superficie liscia

3

Raz

Sector of PL Circular Crown

Sector of Pulse LimitedCircle

Satellite Motion Direction

2HRF

λ=

842

222

2HH

RH

LHR

saz

⋅=

⋅⋅=

⋅⋅

⋅=

⋅⋅

=λλ

λλλ

The azimuth resolution, for MARSIS will be limited by non focused SAR constraints while for SHARAD, if the maximum employable synthetic aperture is limited by the first Fresnel circle diameter, the obtainable azimuth resolution will be:

SNR

4

The single-look signal-to-noise ratio for non-coherent surface back-scattering is given by:

KTVH

dDCGP

NS

NKTFLH

dHRGPN

KTFLH

dAGP

NS

H

op

H

AZpA

p

n

23

2

0

32

43

2

00

22

43

022

)4(

)(

)4(

)(2

)4(

)(

π

θθσλ

τπ

θθσλτ

π

θσλ

∫

∫∫

∆

∆

=

==

where DCVHPRF

VL

RNR SAZAZ

λττ == 22 , being PRFDC ⋅= τ the duty cycle.

It is assumed that,

for SARAD case

− 10 dBW peak power can be radiated by the antenna.

− 10 MHz bandwidth for the radar pulse, entailing a 15 meters resolution in free space.

− 5% duty cycle.

For MARSIS case

− 1.8 dBW peak power can be radiated by the antenna at 1.8 MHz

7 dBW peak power can be radiated by the antenna at 5 MHz

SNR

5

− 1 MHz bandwidth for the radar pulse, entailing a 15 meters resolution in free space.

− 3.25% duty cycle.

Taking into account that the surface reflectivity is comprised between –6.5 dB and -9.5 dB for

the I/W scenario, and between -7 dB and -12 dB for the D/I scenario; the wavelength-scale

r.m.s. slope s(λ) ranging between 0.05 and 0.1 we finally obtain the results of tables

It is worth noticing that in this computation the Ionosphere attenuation was not included

And while for SHARAD the maximum Ionosphere attenuation during daytime operation is of

the order of one dB for MARSIS in the worst case scenarios (working at 5 MHz during

daytime with a maximum plasma frequency of the order of 3 MHz or during nighttime

working with 1.8 MHz with a maximum value of the plasma frequency of 1 MHz) can be as

high as 7-8 dB.

SNR MARSIS Rough surface

6

MARSIS BAND I (1.8 MHz) MARSIS BAND IV (5 MHz) H=250 km H=800 km H=250 km H=800 km dB dB dB dB

PpG/L 1.8 dBw 1.8 dBw 7 dBw 7 dBw λ3 66.6 66.6 54 54

(4π)3 -33 -33 -33 -33 H2 107.96 118.06 107.96 118.06

K(1.38 10-23) 228 228 228 228 Te=Cane Mod. -70.4 -70.4 -62.03 -62.03

∫∆

H

d

2

00 )( θθσ -9.7÷8.14 -2.7÷7.44 -9.7÷8.14 -2.7÷7.44

D.C. (3.25%) -14.88 -14.88 -14.88 -14.88 v0 -36.2 -35.8 -36.2 -35.8

Single Look S/N 24.33÷42.13 12.16÷31.77 24.55÷42.38 12.41÷32.02

SNR SHARAD Rough surface

7

SHARAD (20MHz) H=255 km H=320 km dB dB

Pp (10 W) 10 10 λ3 (15m) 35.3 35.3

64π3 -33 -33 H2 108.13 109.54

K(=1.38 10-23) 228.6 228.6 Te= Cane Mod -47 -47

∫∆

H

d

2

00 )( θθσ -14.64÷6.1 -15.15÷5.74

DC (6%) -12.23 -12.23 V0 (3444 m/sec) -35.3 -35.3 Single Look S/N 22.74÷43.48 20.26÷41.15

SNR flat surface

8

In specular surface case the radar cross section is limited by the area of the 1st fresnel circle.

It is well known that a flat surface of area S illuminated by e.m. radiation propagating in the

normal direction with respect to it behaves like an antenna and the radar cross section is:

22

4 As λπσ Γ=

It should be considered that for the duality of the cases of spherical wave and flat surface and

plane wave on a spherical surface and considering that the flat surface backscattering area

equivalent, from the backscattering point of view, to the smooth spherical surface is given by

a circle of radius equal to πλ

2H (colored area), neglecting for the moment the synthetic

aperture processing, the area is given by:

πλπ

2HAA eq ==

(a) (b)

Fresnel area, equivalent scattering area and azimuth resolution proportions in:

(a) MARSIS case and (b) SHARAD case

Area FresnelRaz Area FresnelRaz

SNR flat surface

9

Considering now the Doppler processing and the consequent azimuth resolution it can be

easily obtained that in MARSIS case the area can be still approximated by equation:

22λ

πλπ HHAA eqMARSIS ==≈

In SHARAD case the azimuth resolution is at least one half of the equivalent area diameter,

therefore:

πλ

πλλ

πλ 1

2282

22 HHHHRA azSHARAD ==≈ 2

2

2 24 HH

ssMARSIS πλλπσ Γ=⎟

⎠⎞

⎜⎝⎛Γ=

2

2

2

12

4 HHssSHARAD Γ=⎟⎟

⎠

⎞⎜⎜⎝

⎛Γ=

πλ

λπσ

The signal to noise ratio in case of coherent scattering, specular surface becomes in MARSIS

case:

..128

..64)4( 0

2

32

022

22

43

222

CDVHKTFLR

GPCD

KTFLVHLGP

NKTFLH

HGPNS

az

spsspc

sp

πλ

πλ

τπ

πλ Γ=

Γ=

Γ=

While for the SHARAD case

..128

..64)4( 0

3

32

023

22

43

222

CDVHKTFLR

GPCD

KTFLVHLGP

NKTFLH

HGPNS

az

spsspc

sp

πλ

πλ

τπ

λ Γ=

Γ=

Γ=

SNR MARSIS flat surface

10

BAND I (1.8 MHz +/- 0.5 MHz)

BAND IV (5 MHz +/- 0.5 MHz)

H=250 km H=800 km H=250 km H=800 km dB dB dB dB

Pp G / L (Radiated Power)

1.8 1.8 7 7

λ3 66.6 66.6 54 54 Γs -12÷-6.5 -12÷-6.5 -12÷-6.5 -12÷-6.5

128π2 -31 -31 -31 -31 H -54 -59 -54 -59

K(1.38 10-23) 228 228 228 228 Te=TF -70.4 -70.4 -62.03 -62.03

V0 -36.2 -35.8 -36.2 -35.8 RAZ -36.6 -39.11 -34.37 -36.6

D.C.(3.25%) -14.88 -14.88 -14.88 -14.88 S/N 41.35 ÷ 46.86 34.22 ÷ 39.72 43.83 ÷ 49.32 36.68 ÷ 42.18

SNR SHARAD flat surface

11

SHARAD (20MHz) H=255 km H=320 km dB dB

Pp G / L (Radiated Power) 10 10

λ3 35.3 35.3 Γs -12÷-6.5 -12÷-6.5

128π3 -36 -36 H 54.06 55.05

K(1.38 10-23) 228.6 228.6 Te=TF -47 -47

V0 -35.3 -35.3 RAZ -28.4 -28.9

D.C.(3.25%) -12.23 -12.23 S/N 48.06 ÷ 53.56 46.58 ÷ 52.08

Signal to Clutter Ratio evaluation

In presence of rough surfaces the useful dynamic range can be strongly reduced by the surface clutter, in fact due to the orbital sounding geometry the off-nadir surface echoes may happen to hide weak subsurface features and the detection of discontinuities in the crust could be then hindered by surface clutter As more the surface is smooth as more rapidly the returns from the surface at off-nadir angles will drop off.The Signal to Clutter ratio is the evaluation of the superposition of the interface echo with the surface clutter echo tail where the incoherent contribution prevails. A scatterer located offnadir can be still received in the RX window, provided that its height and offnadir displacement are such that the radar-scatterer distance R(x) respects the following equation:

12

( ) kmRhRxHxhxR Mars

Mars

5.33932

,22

2 =⎟⎟⎠

⎞⎜⎜⎝

⎛−++=

Signal to Clutter Ratio evaluation

13

R

H

θ

R

RXcTε2

2RXcT

z

xh

Signal to Clutter Ratio evaluation

14

Taking into account the observation geometry it is easy to understand how such echo will be

synchronous with an hypothetical subsurface echo at a depth equal to

( )( )HhxRzmr

−≈ ,1ε

where εmr is the real part of the dielectric constant of the crust, and H is the S/C altitude

After some algebra, for small values of θ we can easily relate the values of off nadir angle(ϑ)

and the penetration dept (z) for respectively surface and subsurface synchronous echoes by:

HHz

Hz

mr

mr

δε

εθ 22

1

1cos 1 =≈

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+= −

By supposing as a worst case that the surface and the subsurface interfaces have the same

roughness, we can write

)()()( 0 θσθσθσ == sss

Signal to Clutter Ratio evaluation

15

Recalling the following parameters:

• Pulsed Limited radius:

HR PL ∆= 2

where ∆ is the Radar range resolution

• Cross-track range displacement, from nadir pointing, of the surface clutter region

referred to subsurface normalized depth: mrz εδ = (the dielectric constant of the

first layer will be taken into account in δ.)

depthiHR →∆== δδδ 2

Including the Doppler processing it is possible to obtain (∆=range resolution, z=depth K=

azimuth resolution):

∫∫∫

∆∆

===HH

Ass dKHdy

HyKdAf

n

2

00

2

000 )(2)(2)()0( θθσσθσ

( ) )2)(2()2(2)( 00 δδδσθσδ HHH

KdAfonA

s −∆+⋅≈= ∫

here σ0 is the backscattering without the fresnel reflectivity term.

Signal to Clutter Ratio evaluation

16

Finally when the penetration depth>>∆

( )δ

δσ2

)2(2 0H

HKzfss ⋅∆⋅≈

therefore

)2)(2()2(

)(

)(

)(

)()(

0

2

00

0

0

δδδσ

θθσ

θσ

θσ

δδ

HHH

dH

dA

dA

ff

H

A

A

s

ss

on

n

−∆+⋅⋅

==∫

∫

∫∆

therefore when the penetration depth>>r(radar range resolution):

HH

dH

ff

H

s

ss δδσ

ϑϑσ

δδ 2

)2(

)(

)()(

0

2

00∫

∆

∆≈

Signal to Clutter Ratio evaluation

17

Signal to Clutter Ratio evaluation (specular surface)

18

The effective detection dynamic will indeed be limited by the noise and surface clutter. The maximum penetration depth in the two boundary scenarios of very rough surface and flat surface is shown in the following graphs. (a) frequency= 1.8 Mhzwithout Ionosphere attenuation (b) frequency= 1.8 Mhz with Ionosphere attenuation fp=1MHz © frequency= 5 Mhz without Ionosphere attenuation (d) frequency= 5 Mhz with Ionosphere attenuation fp=3MHz

Signal to Clutter Ratio evaluation (rough surface)

19

In this case the detection dynamic can be limited by both factors noise and clutter. The penetration depth are shown in the following figures for MARSIS and SHARAD cases for different values of RMS slope and H and in the worst case and best case material attenuation

Signal to Clutter Ratio evaluation (rough surface)

20

(a) best case material, frequency= 1.8 Mhzwithout Ionosphere attenuation (b) best case material frequency= 1.8 Mhz with Ionosphere attenuation fp=1MHz (c) worst case material, frequency= 1.8 Mhzwithout Ionosphere attenuation

(d) best case material, frequency= 5 Mhz without Ionosphere attenuation (e) best case material frequency= 5 Mhz with Ionosphere attenuation fp=3MHz (f) worst case material, frequency= 5 Mhz without Ionosphere attenuation

SHARAD

(a) best case material

(b) worst case material