A study of calibration technique for side looking Airborne Radar
Principle of ratio calibration method
For the SLAR system, input is return power from target and output is brightness on image or film density. A range limited pulse system can use the pulse integral for the return power.
Where
pt = PtoP(t)
When the beam width and range resolution limits are narrow enough and the antenna pattern varies with CSC
2Y one can assume that the variations in scattering cross-section
s°, distance R and illuminated power P
t are negligible when across the illuminated area. In this case, we have.
After rearrangement, the expression becomes
Where
òAtG
2dA is the illumination integral involving the antenna pattern, sometimes called the illumination integral. The usual practical method is to define a wighted area A
wp associated with
G02Awp = òAtG2dA
Where G
0 is the maximum gain of the antenna. If we define the antenna gain by
G = G0ga(q . j)
The expression for the weighted area Awp may be written as
Awp = òAt ga2(q.j) dA
Scattering cross-section
s° is obtained by measuring the value with this weighted area
Where
l = working wavelength of the SLAR
R = distance from the SLAR to target detected
We can see from above expression that the scattering cross-section is propotional to ration value of the return power and illumination power. Evidently, this is an important practical expression. Ratio method calibration is based on this expression
Analysis of precision
As far as the SLAR is concerned, the same system is used for all the measurement. The value of the scattering cross-section electric field E
S at the receiver is a combination
r°0 is based on P
r/P
to. So that precision of measurement is mainly determined by relative value from scattering cross-section of calibration target to background. According to analysis from F. T. Ulaby the calibration target of scattering cross-section
sc is illuminated by a SLAR antenna, the back scattering electric field E
S at the receiver is a combination of the electric field from the calibration target and the background. We have
As well known, the scattering cross-section
sS is proportional to the received power
Where K is a proportional constant and
z is the relative phase angle between E
b ad E
c. Thus the two limited value of corresponding calibration precision is determined by following formulation. When
z takes a value between 0 and
p
