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12. Synthetic Aperture Radar (SAR)

Synthetic Aperture Radar

Synthetic Aperture Radar
Synthetic Aperture Radars were developed as a means of overcoming the limitations of real aperture radars. These systems achieve good azimuth resolution that is independent of the slant range to the target, yet use small antennae and relatively long wavelengths to do it.
SAR Principle
A synthetic aperture is produced by using the forward motion of the radar. As it passes a given scatterer, many pulses are reflected in sequence. By recording and then combining these individuals signals, a "synthetic aperture" is created in the computer providing a much improved azimuth resolution
It is important to note that some details of the structure of the echoes produced by a given target change during the time the radar passes by. This change is explained also by the Doppler effect which among others is used to focus the signals in the azimuth processor. We will illustrate this point with an analogy.

Let us consider, as in the case of the second figure here, a plunger going up and down in the water, producing circles of radiating waves, each with a constant frequency fZ.
These waves travel at a known speed. The plunger is a source of waves analogous to those from a radar. We are interested in the appearance of this wave field at a certain distance.
Consider a boat is moving along the line. At position B, a passenger on the boat would count the same wave number as emitted, since he is moving neither toward nor away from the waves (source).
However, at position A, the boat is moving towards the waves and the passenger will count a higher number of waves: the travelling speed of the waves is slightly increased by the speed of the ship.
On the contrary, at position C, the boat is moving away from the buoy and the apparent frequency is lower: the waves are moving in the same direction as the boat.
Doppler frequency is the difference between received and emitted frequencies where the difference is caused by relative motion between the source and the observer.
Equivalently, the relative spacing between crests of the wave field could be recorded along the line AC, measured as if the wave field were motionless.
This leads to a phase model of the signals that is equivalent to the Doppler model.
During the movement of the boat from position A to position C, the recording by the observer of the number of waves would look like the curve at the right of the figure.

Instead of a plunger, let us now consider an aircraft emitting a radar signal. The boat corresponds to a target appearing to move through the antenna beam as the radar moves past.
The record of the signals backscattered by the target and received would be similar to the record of the passenger in the boat. Such a record is called the Doppler history (or phase history) of the returned signals.
When the target is entering the beam, the Doppler shift is positive because the source to target distance is decreasing. The phase history is then stored to be used during the SAR processing.
By the time the antenna is abeam relative to the target, the received frequency is nominal, with the Doppler frequency being zero. Late it decreases as the satellite moves away.
The phase history is then stored to be used during the SAR processing.

13. SAR processing

SAR processing The objective of SAR processing is to reconstruct the imaged scene from the many pulses reflected by each single target, received by the antenna and registered in memory.
Resolution describes the minimal discernable spacing between two similar point responses (A and B), but often is applied to the width of one response (C). A weaker response (D) requires a larger separation for detection.
Pixels refer to the discrete sample positions used for digital imagery. There must be at least two pixels within a resolution distance.
SAR processing is a simple process although it requires much computation. It can be considered as a two-dimensional focussing operation.
The first of these is the relatively straightforward one of range focussing, requiring the de-chirping of the received echoes.
Azimuth focussing depends upon the Doppler histories
produced by each point in the target field and is similar to the de-chirping operation used to focus in the range direction.
This is complicated however by the fact that these Doppler histories are range dependent, so azimuth compression must have the same range dependancy.
It is necessary also to make various corrections to the data for sensor motion and Earth rotation for example, as well as for the changes in target range as the sensor flies past it.

It is important to note (see figure) that the pixel of the final SAR image does not have the same dimensions as the resolution cell during the data acquisition, due to the variation of range resolution with incidence angle. Thus it is necessary to perform a pixel resampling with a uniform grid.
Even more fundamental, at least two pixels are required to represent each resolution cell, which is a consequence of digital sampling rules. By convention, pixel spacing in SAR imagery is chosen to conform to standard map scales, hence must be a discrete multiple (or divisor) of 100 metres.
For example, ERS-1 data, having nominal resolution of 28 meters in range and azimuth, is delivered with 12.5 metre pixel spacings.

14. ERS SAR geometric configuration

ERS SAR The spacecraft is flying in its orbit and carries a SAR sensor which points perpendicular to the flight direction.

The projection of the orbit down to Earth is known as the ground track or subsatellite track. The area continuously imaged from the radar beam is called radar swath. Due to the look angle of about 23 degrees in the case of ERS, the imaged area is located some 250 km to the right of the subsatellite track. The radar swath itself is divided in a near range - the part closer to the ground track - and a far range.

In the SAR image, the direction of the satellite's movement is called azimuth direction, while the imaging direction is called range direction.