A study of calibration technique for side looking Airborne Radar

A study of calibration technique for side looking Airborne Radar

Duan Lei Liang
Radar and Remote Sensing Research Lab Shangshai Jiao
Tong University Shanghai, China

Abstract
With the development and wide application of microwave remote sensing technique, Specially imaging radar is used in estimation of crop, survey of natural resources, using of land, forecast and monitoring of flood, classification of plants and tactical target, etc. These applications are all determined by the image that converts magnitude of scattering cross-section into difference of brightness. For this, one expects to establish quantitative corresponding relationship between target and its image so that one can develop qualitative remote sensing technique. While the former is mainly determinate by the place, shape, veins and relative variance of brightness of target that the are provided by radar image. To realize this, it is necessary to calibrate the imaging radar first.

This paper is a experimental study of calibration technique on side looking airborne radar.

Introduction to calibration technique
The Calibration of technique are of two types, that is relative calibration used in precise measurement and absolute calibration used in accurate measurement and the latter is not only repeatable, but also the accurate absolute value. Internal calibration permits determination of relative scattering cross-section. While, external calibration permits determination of absolute scattering cross section because side looking airborne radar is an active microwave imaging radar.

External calibration is obtained by return power of known SLAR scattering cross-section. It is often desirable to know scattering cross-section with homogeneous extended target. The azimuth and range dimension of the extended target should be much larger than the corresponding spatial resolution of the SLAR, so that the sufficient average can be performed to reduce the effects of signal fading, dielectric properties and surface roughness. It needed remaining constant over a measurement period of time and known scattering cross-section. All of above mentioned should. be a slowly varying function of theta over the antenna elevation beam width. And the most difficult thing is to account the inherent biases and absolute gain is to account the inherent biases and absolute gain of the antenna and receiver. Therefore, there is a certain restriction in the actual application. Generally, two different methods for internal calibration can be used, the is for the methods of independent or separate calibration in different parts of the system and ratio methods. The latter is a superior approach because that is less error and can process at very frequent intervals. The separate calibration requires interrupting the measurement series. Furthermore, the calibration of different parts results in many errors, which add up to decrease the precision of the overall calibration.

For the SLAR, a system error is same in all time and spatial because the same system is used for all the measurement. Thus, good relative calibration still allows precise distinction to be made between the characteristic of target at different time and place. Sometimes, the output needs to express in terms of the volts, watts, indication on oscilloscopes and film density rather than scattering cross-section.

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

p_t = P_toP(t)

When the beam width and range resolution limits are narrow enough and the antenna pattern varies with CSC²Y 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 ò_AtG²dA 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

G₀²A_wp = ò_AtG²dA

Where G₀ is the maximum gain of the antenna. If we define the antenna gain by

G = G₀g_a(q . j)

The expression for the weighted area Awp may be written as

A_wp = ò_At g_a²(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 s_c 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

Experiment
As has been obtained above s° is proportional p_r/p_t0. Further more is no need for separate measurement of transmitter power and receiver characteristics, and it needs only the direct measurement of it's value when a sample of the transmitted signal is used to calibrate the receiver. As far as the SLAR is concerned, it is very easy to realize. The experimental block diagram and data is shown in Fig. 1

Where

Working wavelength	l = 3.2cm
Antenna type	Slot array antenna with pattern of CSC²j
peak power	P_tc>50KW
Pulse width	t = mS
Pulse repeating frequency	F_r = 1Kc
Receiver characteristics	F_I = 60MC, G_IF>80db. N_f<9db
Photographical instrument	Device changed electricity into light width optical optical fiber revcording tube
Flying altitude	H = 3000m

A directional coupler C_t is set between transmitter and antenna feline and another C_r between antenna and receiver feed line. And an attenuator between the C_t and C_r is a known attenuator of L_c, so that a sample of transmitter signal may be feed through the receiver. Assuming that the value of the transmitter power at the directional coupler C_t is P_t and received power at the another C_r is P_r. As long as the transmission line loses L_t and L_r and the antenna gains remain constant, the calibration using the sample of the transmitted signals gives a complete relative calibration of the SLAR system.

The value for calibration signal P'_rc at the output of the receiver direction coupler is given by

P'_rc = P'_to/L_cC_tC_r

The out put power for the calibration signal with receiver gain si given by

P_oc = g_rP_rc

The output indication for the received signal is given by

P_er = g_rP'_r

With systemization above expression it is obtained by

P_or / P_oc = P'_r / P'_rc = ( P'_r / P_rc )L_cC_tC_r

Since

P_to =P'_to/L_t

P_r = P_r L_r

When this is substituted in above expression, the scattering cross section becomes

s° = [(4p)³R⁴ / G²₀l²Aop] . [L_rL_t / L_cC_tC_r] . [(P_or/P_oc)

Thus under the trigger pulse from synchronizator with a definitive width, the cycial radio frequency power illuminates the area passing through the directional coupler C_t, and antenna Duplexer Tr/ATR. When the antenna duplexer TR/ATR is open to receiving channel, the samples from transmitter signal feed into receiver and there si change from electricity into light by photographical instrument and is sensed automatically on film. After the pulse, antenna duplexer is automatically opened from transmission channel and is insulated to receiving channel. Simultaneously with this, the value of transmission sample is equivalently opened to receiving channel as well.

Thus, as long as return power form calibration target going to the receiver and change electricity into light pass through photographical instrument and is sensed on film as well as. Finally, one can obtain proportional value of two output indication by micro densityer or density cut instrument.

Evidently, the s° of any calibration target is obtained by following expression for the SLAR imaging swath width, and the aim of quantitiative remote sensing technique can be obtained.

s° = [(4p)³R⁴/G²_ol²A_wp] . [L_tL_r/L_cC_tC_r] . (P_orp/P_oc]

When R_n is easily counted by geometry relationship as shown in Fig 2

Where

R_n = [H²+(r_o+r_dn)²]^½

Where

H	Altitude of the SLAR platform
r₀	The width of blind area of the SLAR
r_dn	Distance between the boundary of the SLAR blind area and calibration target to be detected.

References

Meng Kan, Microwave Remote Sensing, Inter Chinese Institute of Technology Publishing House, 1982.
Fawwas T. Ulaby, Richard K. Moore, Adrian K. Fung, Microwave Remote Sensing : Active and Passive, Vol.2, Addison-Welsley Publishing Company in USA 1982
Robert G. Reeves, Manual of Remote Sensing American Society of Photogrammetry, Volume 3m, 1975.
H.D. Brunfeldt, F.T Ulbay, Performance Analysis of the Microwave Remote Sensing Active Spectrometer systems : Calibration, precision and accuracy" Remote Sensing Lab, University of Kasas, 1979.