ERS-1/2 and RADARSAT Synthetic Aperture Radar (SAR) are space-borne
instruments that emit electromagnetic radiation (EMR) and
then record the strength and time delay of the returning signal
to produce images of the ground.
Amplitude
The EMR involved can be imagined as a sine wave. Conventional
SAR images are made up (as a raster) of the amplitude or ‘strength’
of the sine wave - shown in images as grey level intensity
values.
Phase
When the sine wave starts to repeat itself (phase angle >
360 degrees), one cycle of phase has occurred. If we collect
two separate images from exactly the same satellite position
(same range), but at different times with nothing in the target
area changing, one would expect the two sine waves from each
image to be the same and in phase with each other (they would
appear as one if at right-angles to the plane of the signal).
In practice, the position of the satellite between two image
acquisitions is never identical, and the corresponding difference
in the path (distance between satellite and ground) means
there is a difference in phase between the two signals - a
phase shift.
The physical path difference can be expressed as an integer
number of wavelengths plus the fraction of one wavelength.
It can also be expressed as a difference in phase angle between
the two signals.
Interferometry
SAR interferometry makes use of this phase information by
subtracting the phase value in one image from that of the
other, for the same point on the ground. This is, in effect,
generating the interference between the two phase signals
and is the basis of interferometry.
Fringes
The phase difference for any point on the ground will take
a value ranging from zero to 360 degrees. Neighbouring ground
points will yield other values of phase difference owing to
changes in the path difference. For a collection of points
in a given area of ground, the 360 possible degrees of phase
difference can be quantised into 256 grey levels and visualised
as a fringe of differing grey level intensities. An interferogram
image is made up of many such fringes and is discussed in
section 7; here we consider the case of a single fringe.
A fringe can be thought of as a collection of contours where
each unique grey level within and along the fringe corresponds
to a constant phase difference. The constant phase difference
within a fringe is directly related to constant path difference.
In turn, path difference is a function of ground elevation
as this affects the distance to the satellite. Therefore,
constant path difference can be related to constant elevation.
i.e. the phase difference contours within the fringe are indeed
height contours. For example, grey level 168 in the diagram
above represents points on the ground at the same elevation.
As the ground covered by the satellite in the range direction
is many orders greater than one wavelength (100km for ERS),
the phase cycle is repeated many times producing a series
of contiguous fringes, each cycling from 0 to 255 in grey
level intensity.
The spacing and shapes of the fringes depend on both the
observing parameters (wavelength, geometry) and topography.
If the terrain were flat, then a series of regularly spaced,
parallel fringes would result (as in the diagram). Any deviation
from a parallel fringe pattern can be interpreted as topographic
variation as depicted overleaf in an extract from a real interferogram.
Flattening
interferograms
The fringes in an interferogram are not only a result of
the surface topography but also of the Earth's curvature.
An interferogram is said to have been "flattened"
when the fringe and phase effects due to the shape of the
Earth's ellipsoid have been eliminated and only fringes due
to topography remain.
Phase
unwrapping
The phase value or angle (and hence phase differences in
an interferogram) is not known absolutely, but is given in
the range 0-360 degrees, i.e. the phase is wrapped onto a
fixed range of angle of 0-360 degrees. In order to compute
terrain heights and generate a DEM, the interferogram fringes
have to be unwrapped, i.e. the correct multiple of 360 degrees
must be added to the phase difference at each pixel. If the
ground were flat, unwrapping the above interferogram would
produce an image of constant grey level.
If the interferogram were representing part of a mountainside,
unwrapping might produce an image of increasing grey level
corresponding to increasing elevation.
The perpendicular baseline (Bperp,
or across-track separation between the two satellite positions)
means a difference in path to the same point on the ground
as previously described.
Each complete 360 degree fringe cycle represents a specific
elevation interval for all fringes across the interferogram.
This interval is known as the altitude of ambiguity, delta
z, and is a function of radar wavelength, satellite altitude,
incidence angle and Bperp. For ERS,
most of these values are constant except for Bperp
so that the relationship can be reduced to:
(Where delta z and Bperp are expressed
in metres).
For example, if Bperp were 10m, then
the altitude of ambiguity, ?z, would be 941m. In practical
terms, this means that any fringe observed in such an interferogram
could be representing 941m of change in altitude or 941m of
change in altitude plus any displacement that may have occurred.
The graph below shows the relationship between Bperp
and ?z.
For the interferometric process to work successfully, a degree
of similarity, or correlation must exist in the surface properties
between the two image acquisitions. In most parts of the world,
particularly temperate regions, correlation between images
will degrade with time due to changing/moving vegetation,
differing climatic conditions - termed ‘temporal decorrelation’.
Correlation tends to remain good in arid, desert regions where
little change occurs. An output from the processing chain
is a coherence image, and this represents the correlation
that exists between corresponding pixels of the two images
- lighter pixels showing good correlation (e.g. arid, dry
land cover), and darker pixels showing bad correlation (e.g.
water, changing vegetation).
Differential
interferometry
As described so far, the basic use of SAR interferometry
is to estimate topographic height. However, an advancement
on this technique can very usefully be applied to map surface
displacements such as those associated with earthquakes, landslip
or subsidence. Known as differential interferometry, the method
uses SAR images of different dates that might span a surface
displacement event. A first interferogram is created representing
topography before the event and then a second interferogram
created representing topography after the event. By subtracting
one interferogram from the other, fringes that relate to common
topography cancel each other out, so that remaining fringes
should only represent a difference in topography, i.e. a displacement.
Currently, there are two ways of performing differential
interferometry:
3-pass
(or double-difference method)
Three SAR images of the same scene (different times) are
used in this method. One interferogram is made from the phase
differences in the first and the second image, the second
interferogram is made from the phase differences in the second
and the third. The first interferogram is then subtracted
from the second to produce a third, double-difference interferogram.
2-pass +
DEM (or DEM-elimination method)
This method only employs two SAR images, thus producing just
one interferogram. To perform the differencing, another interferogram
has to be created, or synthesised. The synthesised interferogram
is generated from an existing digital elevation model (DEM)
of the area (and from precise knowledge as to the satellite
position at the time of image acquisitions - orbital state
vectors). The method basically reverses the process described
in section 6 and derives an interferogram from elevation data.
The synthesised interferogram is then subtracted from the
original interferogram, thereby removing all fringes that
relate to ground elevation, leaving only fringes that represent
surface displacement.
The phase differences which remain as fringes in the differential
interferogram are a result of range changes of any displaced
point on the ground from one interferogram to the next. In
the differential interferogram, each fringe is directly related
to the radar wavelength (5.6cm for ERS and RADARSAT), i.e.
one phase cycle.
Any surface displacement away from the satellite causes an
increase in the path (and therefore phase) difference. Owing
to the two-way journey of the signal from and back to the
satellite, the increase in distance measured is twice the
displacement in units of wavelength. In the differential interferogram
a fringe cycle of phase differences (0-360 degrees or one
wavelength) actually corresponds to a displacement relative
to the satellite of only half the wavelength, i.e. 2.8cm.
Georeferencing
Georeferencing is the process of assigning pixels within
an image (raster), with ground co-ordinates, e.g. latitude
and longitude. A georeferenced image may then be transformed
to match a particular map projection system where each pixel
represents a specific location and distance on the ground.
Before georeferencing, SAR images consist of arrays of pixels
fixed into a geometry corresponding to the acquisition parameters
of the satellite - the image is said to be in slant range.
The act of georeferencing and transforming into a map projection
puts the image into ground range. The process of georeferencing
is also known as geocoding.
