1. Corso di Dottorato in Ingegneria dei
Sistemi Elettronici
Ciclo XXIII
Advancements on interferometric radar:
studies and applications.
Coordinatore: Prof. Carlo Atzeni
Tutor: Prof. Massimiliano Pieraccini
Candidato: Andrea Barucci
Settore Disciplinare
ING-INF/01
Firenze, 31 Dicembre 2010

2. List of Publications of the author published during the
doctoral course
International journal
1. Barucci, G. Macaluso, D. Mecatti, L. Noferini, D. Fanelli, A. Facchini, M.
Materassi, M. Pieraccini and C. Atzeni, Universal fluctuations in tropospheric
radar measurements, EPL, 89 (2010) 20006, DOI 10.1209/0295-
5075/89/20006
International workshop
1. A. Barucci et al., Universal fluctuations in tropospheric radar measurements –
Geosciences Union General Assembly 2010, Vienna, Austria, 2 - 7 maggio
2010.
2. M. Pieraccini, A. Barucci, D. Mecatti, L. Noferini, G. Macaluso and C.
Atzeni, Attenuation of Large Bandwidth Microwave Signals in Water and Wet
Sand – XIII International Conference on Ground Penetrating Radar, Lecce, 21
- 25 giugno 2010.
3. D. Mecatti, G. Macaluso, A. Barucci, L. Noferini, M. Pieraccini and C.
Atzeni, Monitoring Open-Pit quarries by Interferometric Radar for Safety –
European radar Conference 2010, Parigi, Francia, 30 settembre – 1 ottobre
2010.

3. Table of Contents
CHAPTER 1 SYNTHETIC APERTURE RADAR .......................................................................... 7
1.1 CONTINUOUS WAVE STEPPED-FREQUENCY RADAR ....................................................................7
1.1.1 Mathematical signal description .................................................................................................. 8
1.2 SAR IMAGING .........................................................................................................................................10
1.2.1 Synthetic Aperture: the azimuth direction ............................................................................. 11
1.2.2 SAR projection.................................................................................................................................. 13
1.2.3 SAR processing................................................................................................................................. 13
1.2.4 Implementation................................................................................................................................. 14
1.3 SAR INTERFEROMETRY ......................................................................................................................15
1.3.1 The Interferograms ......................................................................................................................... 16
1.3.2 Phase Unwrapping......................................................................................................................... 17
1.4 REFERENCES ...........................................................................................................................................21
CHAPTER 2 MONITORING OPEN­PIT QUARRIES BY INTERFEROMETRIC RADAR
FOR SAFETY PURPOSES ..............................................................................................................24
2.1 GB-SAR FOR TERRAIN DISPLACEMENT MAPPING ....................................................................24
2.2 MONITORING AN OPEN PIT QUARRIES BY A GB-SAR ...............................................................25
2.2.1 The Radar System........................................................................................................................... 26
2.2.2 The Field Survey .............................................................................................................................. 29
2.2.3 The RCS image ................................................................................................................................. 31
2.3 DATA PROCESSING................................................................................................................................33
2.3.1 Pixels selection as permanent scatterers ............................................................................... 34
2.3.2 Atmospheric phase screen............................................................................................................ 37
2.3.3 Total displacement: cumulative interferogram.................................................................... 38
2.4 RESULTS ...................................................................................................................................................38
2.4.1 Pixels displacements ...................................................................................................................... 38
2.4.2 Interferograms.................................................................................................................................. 40
2.4.3 Simulation of displacement by a Corner Reflector target ............................................... 42
2.4.4 Digital Elevation Model ............................................................................................................... 43
2.5 REFERENCES .............................................................................................................................................47
CHAPTER 3 UNIVERSAL FLUCTUATIONS IN TROPOSPHERIC RADAR
MEASUREMENT .............................................................................................................................50
3.1 THE EFFECT OF THE ATMOSPHERE ON THE GB-SAR.................................................................50
3.1.1 The landslide of Formigal............................................................................................................ 51
3.2 RADAR- ATMOSPHERE INTERACTION..............................................................................................53
3.2.1 Spectrum of the wind...................................................................................................................... 53
3.2.2 A brief description of turbulence............................................................................................... 55
3.2.3 Radar echo as a global quantity................................................................................................ 56
3.3 EXPERIMENTAL TESTS .........................................................................................................................57
3.4 THE EXPERIMENTAL TEST AT THE FACILITY OF THE FACULTY OF ENGINEERING ..........57
3.4.1 Instrumentation ................................................................................................................................ 59
3.4.2 Results.................................................................................................................................................. 61
3.5 THE EXPERIMENT AT FIRENZUOLA ..................................................................................................65
3.5.1 The location ....................................................................................................................................... 66
3.5.2 Instumentation .................................................................................................................................. 66
3.5.3 Data pre-processing....................................................................................................................... 70
3.5.4 Data analysis I.................................................................................................................................. 72
3.5.5 Data analysis II................................................................................................................................ 77
3.5.6 Conclusions ....................................................................................................................................... 81

4. 3.6 ACKNOWLEDGEMENTS ........................................................................................................................81
3.7 REFERENCES ...........................................................................................................................................81

5. Preface
This doctoral thesis was written at the Technologies for Cultural Heritage Laboratory
(TCH Lab) which is part of the Electronic Department of the University of Florence.
It is a multidisciplinary laboratory in the Information Technology area that is dealing
with developing and testing of innovative techniques for conservation and monitoring
of Cultural and Environmental Heritage.
This thesis deals with advanced data processing in Interferometric Synthetic Aperture
Radar for unstable slope monitoring. Mainly the attention of the author is turned to
the data processing algorithms for imaging the meaningful content of the specific
radar observations. The particular acquisition system used in each type of observation
was developed at the TCH Lab and was based on a Continuous Wave Stepped
Frequency radar architecture.
Now GB-SAR interferometry is generally recognized as a powerful tool for detecting
the displacements of large structures such as dams or buildings, but also for the terrain
monitoring, exactly as the space-born SAR interferometry. But, in respect to space-
born systems, for monitoring localized landslide phenomena (of the order of 1 km x 1
km area), GB-SAR seems to be more suitable as it can be specifically set up for a
particular scenario geometry and in according to the dynamic characteristics of the
landslide.
While conventional interferometric synthetic aperture radar is a very effective
technique for measuring surface deformation, almost any interferogram includes large
areas where the signals decorrelate and no measurements are possible. Consequently,
most SAR studies focuses on areas that are dry and sparsely vegetated. A relatively
new analysis technique (PS method) overcomes the decorrelation problem by
identifying resolution elements whose echo is dominated by a single scatterer in a
series of interferograms.
After an introduction on radar and SAR systems, in this Thesis we focused on the
application of GB-SAR to monitor an open pit quarry using the PS method, and on the
influence of the atmospheric disturbances, in particular boundary layer turbulence, on
ground based radar measurements.
As far as the turbulence disturbances concerns, in this thesis an experimental survey
was planned in order to deeply understand how radar signal, and in particular his
statistic, can change in presence of such phenomena. The results obtained by using
these procedures on real data acquired in a experimental facility are discussed too.
The agreement between theoretical and real data confirms the validity of the used
statistic, confirming the “Universal distribution” as a powerful tool to understand
differend kind of complex phenomena.
Chapter 1 deals with Synthetic aperture techniques for imaging and interferometric
applications, while Chapter 2 describes a measurement campaign in an open pit
quarry near Florence, and his results are presented and discussed. Chapter 3 presents
two experiments devoted to the study of the influence of atmospherical turbulence on
radar signals.

6. Ringraziamenti
Durante i tre anni di dottorato ho avuto l’onore di lavorare con persone
meravigliose: Alessandro Spinetti, Daniele Mecatti, Devis Dei, Filippo Parrini,
Gilberto Grazzini, Giovanni Macaluso, Linhsia Noferini e Matteo Fratini. Le qualità
lavorative e morali di questo gruppo di persone sono state e saranno per me un
esempio da seguire.
A tutti loro va il mio rispetto e la mia amicizia.
Daniele mi ha aiutato tantissime volte nel corso di questi anni, progettando e
costruendo molta della strumentazione utilizzata per le misure da me svolte, non ho
parole per ringraziarlo. Lavorare con lui è stato un piacere ed un divertimento.
Con Linhsia ho condiviso la maggioranza del mio tempo, discutendo infinite volte dei
problemi che via via ci trovavamo ad affrontare, cercando di capire ed imparare.
Linhsia è stata per me un’insegnante ed un’amica impareggiabile, sostenendomi,
aiutandomi, sopportandomi e consigliandomi, per questo avrà sempre la mia più
grande stima ed il mio più profondo rispetto. A Lei devo moltissimo, senza il suo
prezioso contributo niente di quanto descritto in questa tesi sarebbe stato possible.
Un ringraziamento al Prof. Carlo Atzeni ed al Prof. Massimiliano Pieraccini che mi
hanno dato l’opportunità di lavorare nel Laboratorio di Tecnologie per i Beni
Culturali ed Ambientali, dandomi sempre libertà di ricerca ed ampio spazio di
lavoro, e ricordandosi sempre che sono un fisico.
Infine un ringraziamento alla mia famiglia, che nonostante i tanti problemi che la vita
ci porta ad affrontare, mi ha sempre sostenuto ed incoraggiato a fare ciò che mi
piaceva. A loro devo tutto.

7.
Chapter 1 Synthetic
Aperture Radar
This chapter provides the basic concepts on synthetic aperture radar imaging and
interferometry (InSAR).
The first part presents the essential characteristics of a continuous wave stepped-
frequency radar with a mathematical description of the transmitting waveform.
Section 2 is dedicated to SAR principles and images generation and interpretation
including issues that impact processing algorithms, while Section 3 provides a
consistent mathematical representation of InSAR principles and phenomenology
associated with interferometric phase measurements.
1.1 Continuous Wave Stepped-Frequency Radar
Since 1960’s in developing pulsed radar systems it was evident that the simple pulsed
radar was not suitable for radar applications requiring ultimate performance in both
range (high transmitted pulse power) and resolution (short pulse width). To overcome
the difficulty of combining these requirements, alternative waveforms were
developed.
Pulse compression waveforms are specially coded to allow the transmission of longer
pulse widths which allow higher mean powers, while retaining wide bandwidths for
high resolution. The system used in this thesis exploits a frequency compression
technique known as stepped frequency technique.

8. Figure 1-1: Block diagram of the stepped-frequency radar. The transmitted waveform x(t),
received waveform y(t) and the complex baseband waveform I(t)+jQ(t) are shown.
The stepped-frequency radar technique transmits a sequence of single frequency tones
or pulses stepped in frequency at intervals of Δf across a bandwidth B. The block
diagram of the stepped-frequency radar is shown in Figure 1-1. Each frequency step
received from reflecting targets is mixed with the transmitted waveform for down-
conversion to baseband by means of a quadrature mixer. The quadrature mixer
produces a baseband signal comprising of two orthogonal components to preserve the
magnitude and phase of the received tone. These components, known as the in-phase I
and in-quadrature Q components, are sampled using a high precision, low frequency
(audio) dual channel analog to digital converter. After I and Q were stored, the next
frequency step is transmitted. Once the radar has completed the steps across the
bandwidth an IDFT (Inverse Discrete Fourier Transform) is applied to the digitised I
and Q frequency domain arrays to produce the synthesised time profiles of the targets.
The IDFT is the digital equivalent of the analog matched filter.
1.1.1 Mathematical signal description
The time waveform x(t) transmitted by a stepped-frequency radar can be represented
as a continuous train of N stepped-frequency pulses. Each pulse in the train has a
width of T in time and a carrier frequency which is stepped at increments of Δf from

9. pulse to pulse starting from the lower frequency bound f1 to f 2 = f1 + ( N " 1) # $f .
Generally, there are many cycles of the carrier frequency within each pulse envelope.
It is assumed for a coherent system that the amplitude and phase of each stepped-
!
frequency pulse in the train is constant for all frequency steps. The switching delay
between frequency steps is assumed negligible.
The stepped-frequency pulse train x(t) is mathematically represented by:
[ ]
x ( t ) = & Re exp( j2" ( f1 + i # $f ) t ) rect
N %1
' t % i # T % T /2 )
i=0
( T * Eq. 1-1
! Consider a single point target with a reflection coefficient of A = A exp( j" ) and an
associated delay τ in a lossless medium. It is assumed that the permittivities of the
target and medium are constant with frequency so that A and τ can be treated constant
!
as well. The reflected signal y(t) from this single point target is represented by:
[ ]
y ( t ) = ' Re Aexp( j2" ( f1 + i # $f ) # ( t % & )) # rect
N %1
( t % & % i # T % T /2 *
i=0
) T + Eq. 1-2
A reference version of the transmitted signal is coupled to the quadrature mixer of the
!
receiver. The complex baseband signal generated by the mixing process and low-pass
filtering (it is assumed T >> " ) is:
I ( t ) + j " Q( t ) = ' Aexp(# j2$ ( f1 + i " %f )& ) " rect
N #1
( t # i " T # T /2*
) T + Eq. 1-3
! i=0
The sampling of the baseband signal in Eq. 1-3 produces a complex array C(k) whose
!
elements correspond each to the value taken by the baseband signal at roughly the
middle of the relative pulse interval:
C( k ) = Aexp(" j2# ( f1 + k $ %f )& ) with k = 0,1,2,..,N " 1 Eq. 1-4
The elements of this array can be viewed as the baseband signal content at the
!
specified frequencies. In order to reconstruct the typical time profile of the target a

10. Fourier transformation can be carried out. The limited number of frequencies
considered on the transmitted bandwidth brings with it a limitation on the longest
delay observable by the system after transformation from frequency to time domain.
The support of the Fourier transformed function of Eq. 1-4 is the time interval
[0,1 "f ) , indeed. No target, even if it really is, appear farther than 1/Δf. Aliasing
effects occur when targets so far from the sensor are illuminated by the system.
! In the frequency domain, the resulting function can be supposed to approximate the
analytic function:
⎛ f − fc ⎞
D( f ) = A ⋅ rect exp(− j2πfτ )
⎝ B ⎠ Eq. 1-5
where fc is the centre frequency of the transmitted bandwidth. By applying the inverse
Fourier transform to Eq. 1-5, the time profile of the baseband signal results:
d( t ) = FT −1[ D( f )] = A ⋅ B ⋅ sinc (πB( t − τ )) ⋅ exp( j2πf c ( t − τ )) Eq. 1-6
This function is the synthesised time profile containing the target’s reflection
coefficient and delay time.
The IDFT algorithm is a pulse compression filter which compresses the received time
waveform y(t) to form the high-resolution synthesized time waveform d(t).
Applying the Rayleigh’s criterion to Eq. 1-6 it is obvious that the time resolution of
the stepped-frequency radar is exactly 1/B if the two way path toward and back from
the target is taken into account and the velocity in the medium is known. If there are
multiple targets in the synthesised time profile separated peaks appear in
correspondence of the time bin of those targets that are farther from each another than
the system range resolution.
1.2 SAR Imaging
In synthetic aperture radar (SAR) remote sensing, the region to be imaged is observed
from a sequence of spatial sampling positions and the received signals are combined

11. using SAR algorithms to obtain high resolution along the antenna track direction. The
generated images generally reproduce the location of a target in a two-dimensional
coordinate system, with one axis along the antenna track direction (“azimuth” or
“cross range” direction) and the other orthogonal to the first axis and pointing toward
the radar line of sight direction (“cross-track” or “range” direction).
1.2.1 Synthetic Aperture: the azimuth direction
Generally a radar sensor resolves targets in the range direction by measuring the time
that a radar pulse takes to propagate to the target and return to the radar. Targets that
differ from each other in their azimuth coordinates only, generate overlapping radar
echoes and thus they cannot be distinguished. Conceptually azimuth location can be
achieved by changing the viewing angle of a very directive antenna and processing
the range information relative to each angle separately. SAR techniques just
accomplish the latter task by globally processing the data provided by an antenna that
moves across a defined series of positions.
The antenna motion, realizing a synthetic antenna array, assures the required antenna
directivity since the system is equivalent to a physical antenna twice the length of the
synthetic array. The main lobe of the physical antenna exactly is two times larger than
that of the synthetic aperture of the same length.
The series of antenna positions along track is geometrically limited by the fact that
from each reached position the antenna aperture is assumed to comprise the area to be
investigated. In practice this assumption provide a down limit to the achievable
azimuth resolution. If an azimuth resolution ΔX is required for a target at distance R
from the center of the rail, the synthesized antenna length L must satisfy:
#
L" R
2 $ %X Eq. 1-7
where λ is the transmitted wavelength and the factor 2 is due to the round trip from
!
the radar to the target and back to the radar. The assumption that the physical antenna
aperture effectively comprises the synthesized length from a distance R where the
target is located, means that:

12. #
L" R
! Eq. 1-8
where is the azimuth length of the physical employed antenna. By comparing Eq.
!
1-7 and Eq. 1-8 it results that
!
"X #
2 Eq. 1-9
i.e. the SAR azimuth resolution cannot be better than half the length of the employed
!
antenna no matter the distance.
Once the synthetic length L was chosen, the number N of antenna positions along the
track must guarantee a suitable spatial sampling of the received signal. The spatial
sampling period is provided by the step between two successive acquisitions and is
given by d = L ( N " 1) . To avoid ambiguity in the measured azimuth profile, the
following equation must be satisfied:
!" #
d
4 $ sin(% 0 ) Eq. 1-10
where 2" 0 is the full angular extent of the illuminated scenario. A three-dimensional
!
view of the resolution cell of a conventional SAR system within the physical antenna
elevation aperture indicated in the figure, is shown Figure 1-2.
!

13. Figure 1-2: Three-dimensional view of the resolution cell of a conventional SAR. The red points
depicted in the resolution cell cannot be distinguished in SAR images.
1.2.2 SAR projection
Data backscattered by the illuminated scenario are processed in range and cross range
only. The third dimension is lost and the effect on SAR images depends on the
relative geometry of the SAR aperture and the illuminated surface. Then target
locations are distorted relative to a planimetric view and their identifications could be
very difficult. For many applications, this altitude-dependent distortion adversely
affects the interpretation of the imagery. To obtain the three-dimensional information,
an additional measurement of elevation angle is needed. Interferometry using two or
more SAR images separated by a spatial baseline provides a means of determining
this angle.
1.2.3 SAR processing
The antenna employed in the present work is mounted on a ground based linear rail
and moves along the rail one step further after each signal acquisition. The transmitted
waveform is the stepped frequency continuous wave. So the in-phase ( ) and
quadrature (Q) components of the received signal are measured for each frequency
and for each antenna position on the rail.
The implemented SAR processor provides the range and cross-range synthesis
combining the Fourier transform efficiency with the ultimate resolution obtainable
from the received data. The Fourier transform is used only for getting the range

14. profile from the measurement relative at each antenna position. This is a natural step
and no approximations are needed. The backscattering coefficient of an hypothetic
point scatterer that would be located in a well defined point in the three-dimensional
space within the antenna aperture is estimates first by picking up from the Fourier
transformed data relative to each antenna position the element corresponding to the
distance from the point and the antenna position, then summing all these antenna
contributions each multiplied by a right factor to compensate the phase exactly.
It is worth to outline that, although the SAR processor that will be presented works
with points in the three-dimensional space, the elevation angle has not been resolved
yet. Referring to Figure 1-2 the two point-wise scatterers cannot be distinguished and, if
focused, in the images they appear with the same backscattering coefficient equal to
the sum of their individual coefficient. Anyway the capability of focusing three-
dimensional points is very useful when a DEM (Digital Elevation Model) is available
in order to obtain radar image much more similar to that observed and hence facilitate
image interpretation.
1.2.4 Implementation
Here a detailed description of the used SAR processing is presented. Let E i,k be the
measured signal at frequency and antenna position on the rail. The value of the
( )
complex radar image I(Pn) at point Pn = x x , y n ,zn is obtained by adding all signal
contributions, taking in account their phase history:
np nf 4 "f i
1
# Rnk # E ike !c
j R nk o
I(Pn ) = 2
= I(n) e j$ (n )
n f np k =1 i=1 Eq. 1-11
! where is the number of frequencies, is the number of positions on the rail, c is
the speed of light, Rn,k is the distance between the point and the position on the
rail.
Eq. 1-11 can be evaluated rather fast by remarking that it is the inverse spatial
Fourier transform of the measured data. So for each antenna position, the inverse
discrete Fourier transform (IDFT) of the measured data is calculated versus index i.

15. Samples of the discrete IDFT are regularly spaced in range by step of
"r =
(
c nf #1 )
. In order to avoid further resolution degradation, the signal is
2B n f
generally expanded by zero padding before IDFT is applied.
! The algorithm works considering all the geometric points to be focused for each
antenna position and every time for each point. The sample of the IDFT whose range
distance is the nearest to distance between the point and the antenna position is
selected and added to the image value relative to the point. At the end of iteration a set
of values distributed in the space is obtained. The obtained images are complex
bidimensional images whose amplitude represents the distributed radar cross-section
(RCS) and whose phase is the matter of interferometry.
1.3 SAR Interferometry
Interferometric synthetic aperture radar (InSAR) is potentially a unique tool for low-
cost precise digital elevation models (DEM) generation, and large-coverage surface
deformation monitoring. It has applications for geophysical monitoring of natural
hazards, for example earthquakes, volcanoes and landslides, and also in structural
engineering, in particular monitoring of subsidence and structural stability. The
technique involves interferometric phase comparison of SAR images gathered with
different baselines and at different times and has the potential to provide DEMs with
meter accuracy and terrain deformations with millimetric accuracy.
Being the dimension of the resolution cell of a SAR survey much greater than the
wavelength of the impinging radiation, the signal corresponds to the algebraic
combination of all the reflections from independent scatterers within the cell, with
their proper amplitudes and phases. This superposition of effects is only approximate
as one should consider not only the primary reflections (i.e. radar → target → radar),
but also multiple ones (e.g. radar → tree trunk → ground → radar). Then, the signal is
a combination of many independent reflections, with the possibility that some of them
are much higher than others.

16. 1.3.1 The Interferograms
With the aim of determining the occurred range variations, in SAR interferometry two
radar images of the same surface area are acquired and differenced in phase, forming
a radar interferogram. This is usually implemented by cross multiplying the complex
reflectivity at each point of one image by its corresponding conjugate value in the
second image, so that the interferogram also preserves useful information about the
signal amplitudes. The complex product effectively cancels the common
backscattering phase in each resolution element leaving the phase term proportional to
the difference between the path delays.
Until now the radar echo from the elemental scatterers within a resolution element has
been considered a deterministic quantity as it is calculable from knowledge of the
precise locations of each elemental scatterers. Of course, it is no feasible to go on this
way.
Because the size of the resolution element is typically many wavelengths, many
elemental scatterers can be supposed randomly distributed within the resolution
element and each with its individual backscattering amplitude statistically
independent from its phase. With these assumptions the real and imaginary part of the
resolution element backscattering coefficient are independent, zero-mean, Gaussian
random variables with equal variances. These really are the properties that lead to the
Rayleigh probability density function for the amplitude of SAR image pixels. They
also allow to calculate a probability density function for SAR image phase, and hence
for the interferometric phase itself, in an analytically closed form.
It is worth to introduce another very important quantity, i.e. the interferometric degree
of coherence, or simply coherence.
The interferometric coherence is the amplitude of the correlation coefficient
between the two complex SAR images forming the interferogram:
I1 # I2*
"= = ce j$
I1 # I1 I2 # I2 Eq. 1-12
!

17. where and represent the two SAR images, the brackets mean the average value
of the argument and is the corresponding interferometric phase.
The coherence provides an estimation of the achievable quality of an interferogram
since it determines the peak width of the probability density function around that is
strictly related to the measurable phase variance. Physically, a loss of coherence
depends on how the elemental scatterers move within resolution cell. If the
displacements randomize the positions of each scatterer with respect to others, the
pair of echoes will be less well related and the coherence of the interferogram will
decrease resulting in a noise that may mask the underlying phase signature.
1.3.2 Phase Unwrapping
The interferometric phase signatures vary relatively smoothly from point to point in
the interferogram and may be inverted to recover surface topography or displacement
fields. However, the phase observables are measured modulo 2π; that is, the integral
number of phase cycles on each measurement is lost. It is said that the phases linear
with range variation are wrapped in the interval [-π, π) by the measurement process.
Consequently, if the surface displacement in a scene determines a phase excursion
greater than one cycle, or if the combination of interferometric baseline and surface
topography yields more than one fringe of topographic signature, the interferogram
cannot be uniquely inverted without a procedure to recover the missing cycles. We
refer to such procedures as phase unwrapping.
The aim of phase unwrapping (PU) is to recover the integer number of cycles to be
added to the wrapped phase so that the unambiguous phase value can be finally
obtained for each image pixel.
1.3.2.1 Mathematical formulation
In general, if no a priori information about the wrapped phase is available, i.e. no
constraint is given to the solution, PU is an ill-posed problem and therefore an infinite
number of different solutions can be found, all honouring the data.
The most straightforward PU procedure would be a simple integration of the phase
differences, starting from a reference point. However, because of phase
discontinuities, it is not always accurate.

18. Almost all PU algorithms are based on the assumption that the true unwrapped phase
field is “smooth” and varies “slowly”. More precisely, neighbouring phase values are
assumed to be within one-half cycle (π radians) of one another. Though this
hypothesis is often valid for most of the image pixels, the presence of some phase
discontinuities (i.e. absolute phase variation between neighbouring pixels of greater
than π radians) causes inconsistencies, since integration yields different results
depending on the path followed. This feature is evident whenever the sum of the
wrapped phase differences (the integral of the estimated phase gradient) around a
closed paths differs from zero. To be consistent, a gradient field must be irrotational,
i.e. the curl of ∇ϕ should be zero everywhere. Whenever this condition is verified
over the whole interferogram, we have a “trivial PU problem”. Unfortunately, this is
almost never the case in InSAR data processing.
Phase unwrapping algorithms share then this common initial approach: the relative
phases, or gradient, between adjacent pixels in the interferogram are correctly
evaluated, so the obtained connected phase field is adjusted by an overall constant
multiple of 2π. The basic theory of all the unwrapping procedures starts with the
following equation:
∇ϕ ( x, y ) = s( x, y ) + n Eq. 1-13
where ∇ϕ is the gradient of the absolute interferometric phase, that is the value
linearly related to the range variations, s(x,y) is the measurable variable and n is the
noise included in the measurement. For the noise-free state n = 0 , Eq. 1-13 must be
completely observable, meaning that there is a unique solution for ϕ and the value of
ϕ must be derived at every point ( x, y ) if the vector s is known. For the noise free-
!
state a necessary and sufficient condition that s must satisfy for a unique
determination of ϕ from Eq. 1-13 is easily derived from the potential theory. This
!
condition is given by:
# s " d! = 0 $ % & s = 0 Eq. 1-14
C
!

19. The integration is performed along an arbitrary enclosure in the ( x, y ) plane, and
d! = (d! x ,d! y ) is the infinitesimal length element along the path. In other words,
must be conservative.
!
! This formulation can be extended to a generic noisy case by simply assuming that a
correct absolute phase gradient estimation can be accomplished anyway by removing
all the points where the measured gradient doesn’t satisfy irrotational requirement.
These points are generally called residues.
The occurrence of these points lead to an inherent 2π ambiguity in the phase (due to
circulations around them) and, consequently, self-consistent phase-unwrapping
methods do not succeed for most objects.
Obviously residues are located where Eq. 1-14 is not satisfied. In practice the phase
field is measured over a two-dimensional pixel array N " M , so the discrete version
of the above equations must be considered:
%s1 j = # i, j $ # i$1, j i = 2,..,N; j = 1,.., M
! p
' i,
" s = 0, with l = 1,2 and & 2
l
' si, j = # i, j $ # i, j $1 p i = 1,..,N; j = 1,..,N
i, j
C
( Eq. 1-15
! where ψi,j is the principal value on the interferogram rectangular grid and is an
arbitrary enclosure. The minimum enclosure in the discrete system is the set of 2x2
pixels, called a node. Then residues can be located by evaluating the sum of principal
value differences around each node in the interferogram. A residue or inconsistent
node may be either positive or negative, depending on the outcome of the summation
and the chosen integration direction (clockwise or counterclockwise).
1.3.2.1 Phase unwrapping methods
All of the commonly used phase unwrapping algorithms relate the phase values by
first differentiating the phase field and subsequently reintegrating, adding back the
missing integral cycles to obtain a more continuous result. The many algorithms
proposed for phase unwrapping over the past few years fall into three basic classes:

20. • path-following algorithms based on identification of residues in the wrapped
phase field and cuts, or ‘‘trees,’’ connecting a group of residues to limit the
integration paths;
• algorithms that derive a smooth field by integrating the gradient of the
observations subject to smoothness constraints as determined by least-squared-
difference criteria;
• networking algorithms;
Basically all the existing phase unwrapping techniques start from the fact that it is
possible to estimate the neighboring pixel differences of the unwrapped phase when
these differences are less than π. From these, the unwrapped phase can be
reconstructed up to an additive constant. The methods differ in the way they
overcome the difficulty posed by the fact that this hypothesis may be somewhere
false, which cause the estimated unwrapped phase differences to be inconsistent, that
is their "integral" depends on the integration path.
Branch cuts methods unwrap by integrating the estimated neighboring pixel
differences of the unwrapped phase along paths avoiding the regions where these
estimated differences are inconsistent. The problem of building cuts delimiting these
regions is very difficult and the resulting phase unwrapping algorithm is very
expensive computationally.
In least squares methods, unwrapping is achieved by minimizing the mean square
deviation between the estimated and the unknown neighboring pixel differences of the
unwrapped phase. Least squares methods are very efficient computationally when
they make use of fast Fourier transform techniques. But the resulting unwrapping is
not very accurate, because least squares procedures tend to spread the errors that are
instead concentrated on a limited set of points. To overcome this problem a weighting
of the wrapped phase can be useful. However, the weighted least squares algorithms
proposed are iterative and not as efficient as the unweighted ones. Moreover, the
accuracy of the results depends on the weighting mask used.
The networking algorithms exploit the fact that the neighboring pixel differences of
the unwrapped phase are estimated with possibly an error which is an integer multiple
of 2π. This leads to formulate the phase unwrapping model as the problem of

21. minimizing the deviations between the estimated and the unknown neighboring pixel
differences of the unwrapped phase with the constraint that the deviations must be
integer multiple of 2π. This constraint prevents the errors from spreading, so a
weighting of the data is not necessary. In any case, weighting is allowed in this
formulation (without loss of efficiency), and can be useful when there are large
regions of noisy data. Even if minimization problem with integer variables are usually
very complex computationally, recognizing the network structure underlying the
problem makes available very efficient strategies for its solution. In fact, the problem
can be equated to the problem of finding the minimum cost flow on a network, for the
solution of which there exist very efficient algorithms.
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24. Chapter 2 Monitoring
Open-Pit Quarries by
Interferometric Radar for
Safety Purposes
This chapter focuses on a measurement campaign carried out to monitor an open pit
quarry of pietra serena using a Ground-Based SAR.
The work described has been carried out in the framework of the PRIN 2007 project
“Application of advanced technologies to the safety, environmental protection,
optimization of management and yield in quarry: geomining characterization and
monitoring methodologies”, founded by the Italian Research and University Ministry.
2.1 GB-SAR for Terrain Displacement Mapping
Today Ground-Based Synthetic-Aperture Radar (GB-SAR) interferometers have
become powerful and effective tools for remote sensing of movements in many
application fields. These sensors have been successfully employed in landslide and
glaciers monitoring, as well as in avalanche localization and detection of snow cover
changes.
With respect to airborne and spaceborne SAR systems, GB-SAR can offer a
continuous temporal coverage and, because of its versatility, an optimal illumination
geometry in almost all cases. Usually in applications for ground displacement

25. mapping the imaging geometry of all the SAR observations is maintained identical,
avoiding the baseline error.
A GB-SAR interferometer works by acquiring images of the observed scenario from
remote, each image containing phase and amplitude informations of the received
echoes, at a high time rate (typically more than one image per hour). The phase values
of each pixel of the image are related to the distance between the sensor and the pixel
itself, whereas the phase differences between two images acquired at different times
are related to the eventual radial displacements occurred in the observed scenario.
Therefore calculating the differences between the pixel phase values in two images,
the measurement of the range variations in each pixel is directly obtained, providing a
direct measurement of the along of sight displacements. The multiple images acquired
can be thought of as “time-lapse” imagery.
2.2 Monitoring an open pit quarries by a GB-SAR
Slope failure accidents are nowadays responsible for a large number of fatalities and
machinery damages in open pit quarries. Monitoring of slope stability in excavation
areas is then a crucial issue in order to optimize the production efficiency and to
ensure the safety of the operators.
Because large rock collapses may show minor precursor movements starting hours or
days in advance, the early detection of these small deformations could be of
paramount importance in an early warning system.
In this context, the idea was to set up and test the available GB-SAR system for open-
pit quarries monitoring. The field test took place at a stone quarry in Tuscany, Italy
(Figure 2-1) and lasted 39 days.

26. Figure 2-1: a picture of the pit, it is located about 50 km north of Florence.
2.2.1 The Radar System
The employed ground based radar instrumentation was entirely developed at the
Technology for Cultural Heritage Laboratory (TCH Lab), a research group within the
Departement of Electronics and Telecommunications of the University of Florence.
The radar system is an evolution of the sensor developed at the University of Florence
in collaboration with IDS SpA (Pisa, Italy), working in the licensed Ku band. The
system was adapted to this application through several improvements in the
mechanical and electronical components.
The measurement geometry in a quarry is often unfavourable for a standard GB-SAR
system, due to the need of imaging a wide area looking from a close location, thus
requiring a wide viewing angle.
For this reason the radar system was improved adding the capability to rotate the
antennas around a vertical axis: the system was able to observe a very wide area by
simply acquiring several different SAR images at different viewing angles and
combining them in post processing. With this improvement the view angle of the
radar sensor was extended up to 150 degrees (Figure 2-2).

27. Figure 2-2: a detail of the radar system showing the capability to rotate the antennas along the
vertical axis, in order to be able to image all the very wide area of interest.
This solution allows to perform the measurements using high gain antennas, thus
maintaining a higher signal to noise ratio, instead of using wide angle – low gain
antennas. The drawback is a longer acquisition time needed to acquire the sub-images
at the different angles.
A quarry is typically an area subject to morphological changes due to the continuous
mining activity. Therefore, when the interferometric measurements were performed,
an updated Digital Elevation Model (DEM) of the area was not available.
As the Digital Elevation Model is necessary to correctly generate the SAR image, in
the novel GB-SAR system it was added the capability to realize interferometric
DEMs, simply allowing the antennas to move up to 30 centimeters along a vertical
axis.
In order to be able to operate day and night even where the electric network was not
available, the radar system was equipped with an autonomous power supply system
using solar and wind energy (Figure 2-3).

28. Figure 2-3: the power supply of the GB-SAR system using solar and wind energy.
Finally, a GPRS or long range WIFI radio link allows the remote control of the
instrument and the real time data download. A picture of the system is shown in Figure
2-4.

29. Figure 2-4: the GB-SAR system for open pit quarries monitoring. In foreground the rail with the
radar head and the antennas, behind the boxes of electronics and in background the wind
generator for the power supply of the system.
2.2.2 The Field Survey
The novel radar system described above was tested during a field survey 39 days long
from February 16 to March 25, 2009.
The test site was located at a stone (‘pietra serena’) quarry in Firenzuola (Firenze,
Italy). The aim of the survey was to check the capabilities of the system to detect
possible small displacements across the steep slope, overlooking the excavation area.
The radar was installed over a hill in front of the quarrying area, 800 meters faraway,
at about the same quote. The measurement scenario is shown in Figure 2-5 and Figure
2-6.

30. Figure 2-5: the radar sensor was located at a distanc of 800 meters over a hill in front of the area
of interest.
Figure 2-6: the stone (“pietra serena”) quarry in Firenzuola (Firenze-Italy) where the radar
system was tested.
At the test site the GB-SAR system worked in the site automatically day and night, in
all weather conditions. Data were uploaded real time to the automatic processing
station located at the University of Florence through a local radio link and the Internet
network. Displacement maps were generated automatically and were available half an

31. hour after the end of each acquisition. The measurement parameters are listed in Table
2-1.
Central Frequency 16.75 GHz
Bandwidth 300 MHz
Tx Power 26 dBm EIRP
SAR scan length 2m
SAR acquisition time 10 minutes for each sub-image
SAR acquisition rate 2 sub-images every hour
Range Resolution 0.50 m
Cross Range Resolution 0.5°
View angle 150°
Power consumption < 40 W
Table 2-1: measurements parameters.
2.2.3 The RCS image
A RCS SAR image of the quarry is shown in Figure 2-7, with superimposed the map of
the same area. The reference system is a local system with the origin in the radar
location. This wide angle map originates from two sub-images acquired sequentially
at two different angles.

32. Figure 2-7: RCS SAR image of the quarry area with superimposed the topographic map. The
reference system is a local system with the origin in the radar location.
In Figure 2-7 three different zones can be distinguished: (a) the mining area, between
600 and 700 meters in range, (b) the rocky wall, between 700 and 800 meters in
range, and (c) the ravaneto1 between 450 and 600 meters. The zone (a) was
characterized by continuous movement of mining machinery, the zone (c) consisted of
rock debris resulting from quarrying operations, and the zone (b) was the area of
interest with a limited extension in range due to its prevalent vertical slope.
1 In quarries ravaneto is an area of accumulation of quarrying debris, usually a ravine.

33. 2.3 Data Processing
Displacement maps were generated, all over the survey period, processing more than
five hundred SAR acquisitions.
One of the main difficulties in interferometric data processing is the mix of several
different types of information in a given signal. Dielectrical, atmospherical and
displacement informations are all wrapped together in the same signal. Consequently,
the measurement accuracy is not driven by the characteristics of the radar system
(power, resolution, etc.) as much as by the possibility of separating the various
component of the signal.
A short review is here presented of the main results to establish notation and to
discuss the different physical signals that contribute to the interferometric phase. For
the sake of simplicity, phase term due to noise, image misregistration, wrong focusing
parameters, etc. will be neglected. The analysis outlines the rationale behind a multi-
image approach for surface displacements estimation.
The phase of a pixel in a SAR image can change due to:
1. changing in the radar-scatterer relative position
2. possible temporal changes of the target
3. atmospheric variations
Considering K+1 SAR images of the same area, the phase of the pixel x=[x,y] (x and
y being cross-range and range coordinates respectively) of the k-th focused SAR
image is the sum of different contributions:
4#
" k (x) = % r (x) + & k (x) + ak (x)
$ k Eq. 2-1
! where r is the radar-target distance, σ is the scatterer reflectivity phase, and a is the
atmospheric phase contribution.

34. Let us now consider one of the K+1 images as the “master” acquisition m. The phase
difference of the generic “slave” image k with respect to the master will be indicated
with φk(x):
' [ rk (x) $ rm (x)] + [( k (x) $ ( m (x)] + [ ak (x) $ am (x)]
4% Eq.
" k (x) = # k (x) $ # m (x) =
& 2-2
In GB-SAR interferometry, we can express rk as follows:
!
rk = rm + Δµ k Eq. 2-3
where Δµk is the possible target motion in the direction of the radar line-of-sight,
occurring during the time interval between the two acquisitions, the order of
magnitude of this term usually being of millimeters.
The interferometric phase is then a blend of several signals that depends on the
acquisition geometry (radar postion and topography), terrain motion, scattering
changes and atmospheric inhomogeneities:
" k (x) = " µk (x) + " ak (x) + "#k (x) Eq. 2-4
where we posed
!
) 4#
+" µk (x) = $ % &µ k
+
+ 4#
*" ak (x) = %[ak (x) ' am (x)]
+ $
+" (x) = 4# %[( (x) ' ( (x)]
+ (k
, $ k m
Eq. 2-5
2.3.1 Pixels selection as permanent scatterers
!
The main drawback of the InSAR technique is that it is limited to the estimation of the
signals relative to only a restricted ensamble of points scatterers which are
caracterized by long-term stable backscattering properties and extremely good signal
to noise ratio. Pixels in the radar image, that are supposed to represent these stables
and coherents scattereres over the entire observation interval, are called permanent
scatterers (PSs).

35. In this thesis the method used to identify possible PS points is based on the analysis of
the time series of their amplitude values. This approach is due to the fact that an exact
evaluation of the phase stability is possible only after estimation and removal of the
atmospheric contribution, while amplitude values are almost insensitive to the
atmospheric phenomena. Consequently, pixels showing a stable time sequence of
amplitude values will be considered PSs.
The PS extraction procedure starts with the estimation of the amplitude dispersion
index, which is in turn a measure of the phase stability, relative to a temporal
sequence of SAR images. For each image pixel, the dispersion index is defined by:
"A
DA =
mA Eq. 2-6
! where mA and are the mean and the standard deviation of the pixel amplitude
value A trough the sequence of images. PSs are then selected by computing the
dispersion index of the amplitude values relative to each pixel in the area of interest
and considering only those pixels exhibiting DA values under a given threshold
(typically DA ≤ 0.25).
At the test site, the area of interest for the safety of people and machinery was the
rocky wall, being the mining activities in progress just below it. In order to perform a
robust interferometric analysis over a long time, not all the pixels were considered,
but a selection based on double criterion was made. The first selection was based on a
PS approach, analyzing amplitude variation of the pixels, choosing a threshold of 0.2.
The second criterion was a threshold on SNR, selecting only pixels showing a SNR
greater than 30 dB. Beginning with an image with about 900000 pixels, about 50000
pixels were selected as permanent scatterers after the first selection. The second
selection further reduced the number of pixels available for the elaboration to about
20000 (Figure 2-8). Most of the pixels were selected in the wall, being it rock without
vegetation (Figure 2-9). It is however to be noted that the wall was not perfectly
vertical, being there a sort of terraces delimited by a metallic net, dug out in order to
keep possible fall of debris. This fact was certainly a problem for radar measurements,
because this net was not fixed very well and it moves with the wind and with

36. temperature variations. This is the reason because these areas are not completely
covered by PSs.
Figure 2-8: Dispersion Index of a restricted area of the pit near the wall.
Figure 2-9: the wall on the left and a detail of the net on the right.
It’s worth to outline that the number of PS depends strongly on the number of SAR
images used. However, using a number of images greater than 50, the number of PS
becomes almost stable, decreasing very slowly. Altough more rigorous and

37. computationally intensive statistical analyses can be adopted, this very simple
approach turns out to be enough for our purposes.
2.3.2 Atmospheric phase screen
Selected points were then processed in order to remove the atmospheric effects. A
brief discussion on how this step was performed is given here.
Due to the morphology of the area under investigation and to the seasonal
characteristics, frequents, suddens and severe meteorological changes occurred (sun,
rain, fog, snow and so on) during the survey. Therefore interferometric phases must
be compensated for atmospheric effects.
Atmospheric inhomogeneities create an atmospheric phase screen (APS)
superimposed on each SAR image that can seriously compromise accurate
deformation monitoring. APS exhibits a low-wavenumber spectral behavior
(according to th atmospheric water vapor distribution in the troposphere).
The APS mean effect is usually approximated as a phase ramp:
" ak (x) = Ak # x + Bk # y + Ck Eq. 2-7
where Ak, Bk and Ck are the parameters of the atmospheric plane of the k-th
!
interferogram.
Specifically given H pixels is possible to define the functional Γk determining the
APS as follows:
(
*
1 H
{ [
"k = # & exp j # $ kh (x) % ( Ak # x h + Bk # y h )
H h =1
]}
*
{ }
){Ak , Bk } = argmax A k ,B k "k
* ˜ ˜
*˜
*Ck = '"k
˜
*
+ Eq. 2-8
where φkh is the interferometric phase relative to the h-th pixel selected in the k-th
!
interferogram.

38. 2.3.3 Total displacement: cumulative interferogram
For our purpose it results advantageous to calculate the cumulative interferogram
instead of the standard interferogram. Let I1,I2 ,I3 ,...,IN be a set of radar images
acquired at t1< t 2 < t 3 ,... < t N times respectively. The cumulative interferogram of this
set is defined as:
!
"1,N = % #( Ii+1(&)Ii* (&)) = % #(e j(" i +1 (&)$" i (&)) )
N $1 N $1
!
i=1 i=1 Eq. 2-9
!
where “*” is the complex operator and " Ik = # k . ( )
This approach offers the advantage that considering phase changes between two
consecutive SAR images, phase wrapping is most unlikely. By assuming that the
!
dielectric characteristics of the pixel point n-th are the same at each observation,
supposing having removed the atmospheric contribution, the displacement Δrn of this
point at the time of the nth observation can be recovered from the cumulative
interferogram by the following equation:
#1,n
"rn = %
4$ Eq. 2-10
! where is the central wavelength.
2.4 Results
2.4.1 Pixels displacements
As long as the GB-SAR system was working at the quarry, interferometric
measurements did not detect significant movement in zone (b).
Figure 2-10 reports the measured displacement of a selection of 50 pixels located across
the wall over a time period of 23 days. It is worth to outline that in the period a
maximum displacement of 0.2 millimeters was observed. The trend which is visible in
the graph probably depends on a residual error of the meteorological correction. The
gaps are due to the lack of energy of the system when the system switched off.

39. Figure 2-10: cumulative displacements for 50 pixels in the wall during a time period of 23 days.
A zoom relative to a 3 days long period taken from the previous figure is shown in
Figure 2-11. Here it is well evident that none of the selected pixels was really moving.
Figure 2-11: a zoom of the cumulative displacements graph over a period of 3 days.
In Figure 2-12 the measured displacements versus time are shown for three selected
points in the wall and for two different days during the survey. The fluctuations are

40. again due to instrumental noise and to residuals of the atmospheric compensation
procedure. However the cumulative displacements are below the 0.1 mm, meaning
that this point must be considered as stable, being the value of 0.1 mm considered as a
threshold.
Figure 2-12: cumulated displacements versus time for three points in the rock wall during two
days of measurement.
2.4.2 Interferograms
Aimed to a complete interferometric characterization of the scenario, it is interesting
to study the interferogram relative to all the pixels, excluding only the dead zone of
the antennas (shown in red in the Figure 2-13).
In zone (a) the interferometric analysis is not significant because of the continuous
movements of machinery for mining activities. In zone (c) sudden and consistent
movements were observed due to discharging of debris into the ravaneto. However in
this area the interferometric analysis cannot be performed meaningfully, as the rapid
accumulation of debris into the ravine is generally a non coherent process and often
originates phase ambiguity. Nevertheless it is interesting to examine these
interferograms qualitatively, as the areas where the previous phenomena happen can
be clearly identified.

41. Figure 2-13: (a), (b) and (c) cumulative interferometric maps corresponding to daytime during quarrying
and (d) to night time without quarrying (dimensions in meters).
Figure 2-13 shows a sequence of four cumulative interferometric maps corresponding
to a time lapse of 8 hours during a period of intense quarrying activities. The paths of
debris along the ravine are well evident in interferograms (a), (b) and (c).
Interferogram (d), corresponding to the evening when quarrying was just finished,
shows a different phenomenon: in all the upper part of the ravaneto fresh debris
seems to settle down giving rise to typical interferometric fringes.

42. 2.4.3 Simulation of displacement by a Corner Reflector target
As no significant movement was detected in the wall during the 39 days long survey,
in order to check the capabilities of the instrument to detect small displacements at
long distance, a simulation of rock movement was set up as shown in Figure 2-14.
A trihedral corner reflector (CR), 50 cm side, was installed on a micrometric device at
a distance of 800 meters from the radar, on the top of the vertical wall.
The reflector has been moved along the radar line of sight in three small steps, as
shown in Table 2-2. For each position of the CR one single SAR image was acquired,
and the interferograms were calculated. Results, shown in Table 2-2 and Figure 2-15,
prove a good accuracy in the measurement of displacements, but this is with a high
SNR due to the high RCS of the CR and with a quite stable atmosphere.
Figure 2-14: trihedral corner reflector and micrometric device for the simulation of rock
movement.

43.
Figure 2-15: corner reflector actual displacement versus measured displacement.
Table 2-2: Results of the simulation of rock movement.
Step n. 1 2 3
Displacement of CR 2.00 1.00 0.50
(mm)
Measured displacement 2.05 0.89 0.53
of CR (mm)
It is clearly evident that in the short term (few hours) and in optimal SNR conditions
an accuracy of 0.1 millimeters is guaranteed.
2.4.4 Digital Elevation Model
A Digital Elevation Model of the terrain can be addressed using the developed GB-
SAR. By raising the antenna at different levels along the vertical direction, images
with different viewing angles can be collected.

44. Because the same antenna is moved firmly, the achieved baseline exactly corresponds
to the geometric shift of the antenna along the vertical direction.
Referring to the measurement geometry depicted in the Figure 2‐16, the relationship
between the unwrapped interferometric phase ϕ and the quote z along the axes
defined by the antenna vertical motion is
4# 4# 2zB B 2
"= (r % r(B)) = r(1% 1% 2 + 2 )
$ $ r r Eq. 2‐11
where λ is the central transmitted wavelength, B is the baseline, and r and r(B) are the
ranges to a target on the illuminated slope when the antenna is positioned at z = 0 and
! z = B, respectively.
Because the GB-SAR generally works in a configuration such that B /r is smaller
than 1, the Taylor’s expansion of the square root in terms of B /r can be truncated to
the linear term and converted into the elevation z:
!
" r !
z= $
4# B Eq. 2‐12
The latter equation provides the basic phase-to-elevation conversion.
!
Figure 2­16: GB-SAR measurement geometry to DEM generation.
A Digital elevation Model of the open pit was generated. Figure 2-17 shows the result,
where a little portion of the all scenario observed was reconstructed. Figure 2-18 shows
instead all the open pit quarries as reconstructed by a laser scanner. The discrepancy

45. between the two DEMs are evident, the laser scanner DEM being more detailed (a
spatial resolution of 0.25 m x 0.25 m compared with the 4 m x 1 m of the GB-SAR)
and more similar to the optical image. Some differences are due to the wrapping
errors, specially in the GB-SAR reconstruction of the wall area due to the high slope.
However in the waste area and in the working area accuracy is better, with an error of
about five meters compared to the laser scanner DEM.
In Figure 2-19 an amplitude SAR image is focused using the laser scanner DEM, where
the red spot represents the Corner Reflector Target observed by the radar.
Figure 2-17: DEM generated by the GB-SAR system.

46. Figure 2-18: DEM of the open pit quarry generated with a laser scanner.
Figure 2-19: an example of an amplitude SAR image focused using the laser scanner DEM of the
open pit quarry. The red spot represents the Corner Reflector Target observed by the radar.

47. 2.5 References
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A. Martinez-Vazquez, J. Fortuny-Guasch, “Feasibility of snow avalanche volume
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Denver (CO).
A. Martinez-Vazquez, J. Fortuny-Guasch and Urs Gruber, “Monitoring of the snow
cover with a ground-based synthetic aperture radar,” in Proc. EARSeL eProceedings
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48. D. Mecatti, Radar interferometrici per il monitoraggio da terra di versanti franosi,
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D. Mecatti, Monitoraggio di movimenti del terreno e di grandi strutture: sviluppo di
prototipi di radar interferometrici, Bachelor Thesis, University of Florence, 2001.
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L. Noferini, T. Takayama, M. Pieraccini, D. Mecatti., G. Macaluso, G. Luzi, C.
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ESA ESRIN Frascati, Roma, Italia.
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50. Chapter 3 Universal
Fluctuations in
Tropospheric Radar
Measurement
This chapter deals with the influence of the atmospherical turbulence on the radar
signal, focusing on the statistical description of the amplitude and phase information
as a function of the air turbulence. Using the radar described in Chapter 2 an
experimental study was realized and the results, interpreted using the complex
systems theory, confirm a strong connection between turbulence and the radar signal
fluctuations and statistic.
3.1 The effect of the atmosphere on the GB-SAR
As the state-of-art in SAR interferometry moves toward a more quantitative and
localized approach, the influence of error budgets becomes more and more important.
It is therefore of paramount importance to have a clear control on all possible sources
of external disturbances, which could significantly alter the measurements response.
In the last decades many geophysical applications based on SAR Interferometry were
presented. Even if SAR systems work at frequencies minimizing the atmospheric
absorption, the interferometric phase is affected by a delay due to the propagation in
the tropospheric layer. An increase in the amount of atmospheric water vapour
fraction between the acquisition times affects the atmospheric index of refraction
which induces an increase in the propagation time of microwave radar pulses. All this
appears as an increase in the distance to the ground surface, indistinguishable from

51. topography or real ground deformation. However, a comprehensive approache to
mitigate atmospheric artefacts in InSAR data is still lacking.
3.1.1 The landslide of Formigal
From 2005 to 2008 the TCHLAB was involved within the activities of the
GALAHAD project, with the opportunity to monitor many different natural scenarios
in different weather conditions and for a long time. A large collection of ground based
radar data was then recorded and processed. In particular a landslide in Spain (Figure
3-1) was monitored continuously for 45 days, gathering one image about every hour.
The collected data set consisted of more than 1000 SAR images and provided a
unique opportunity for studying the temporal behaviour of the radar signal.

52.
Figure 3-1: Formigal, Spain. GB-SAR monitoring of a landslide. In the top part of the figure the
RCS is projected onto a DEM of the landslide. In the low part of the figure the radar system is
showed with in background the observed scenario.
It was in particular observed that occasionally, but in coincidence with hard windy
conditions, the radar interferograms were affected by an overall decorrelation that
could not be explained by the recorded weather conditions (no rainy events). Focusing
the analysis on rocky areas without vegetation, the behavior was the same.
Considering the coincidence between abrupt decorrelation and hard windy conditions,
it was hypothesized that the atmospheric turbulence could drastically influence the
radar propagation even over short ranges, an observation which however rested on
purely qualitative ground.

53. No further experimental realizations were in fact subsequently developed to scrutinize
the process and reach an unambiguous proof of concept.
3.2 Radar- atmosphere interaction
Conscious of the experimental results on Formigal we developed the idea that
atmospheric turbulence might be the process behind the radar signal anomalies. A
little introduction on this topic is given here.
When an electromagnetic wave propagates through the troposphere its amplitude and
phase are distorted by a number of mechanisms. These distortions may be placed into
three groups:
1. absorption, which causes a direct attenuation of the wave
2. long trend fluctuations due to the slow variations of the meteorological
variables, as pressure, temperature and specially humidity
3. fast fluctuations due to the turbulence
Long trend fluctuations can be well understood and recreated by the many models of
the air index of refraction presents in literature.
However atmospheric turbulence remains the best candidate to try to explain what
observed in the Formigal images, this phenomena having time and spatial features
comparable with those of the images generated by a ground-based radar.
3.2.1 Spectrum of the wind
Different scale processes occur within the atmosphere, generally referred to as
synoptic-scale processes (dozen of days), meso-scale processes (from day to hour)
and micro-scale processes (less than an hour). Turbulent phenomena interest the
micro scale, corresponding to distances shorter than 1 km.
Among the atmospheric phenomena interacting with microwaves, the turbulence has a
significant impact on radar system. By creating time-varying inhomogeneities of the
atmospheric refractive index, turbulence induces amplitude scintillations and phase
delays on the propagating signals.

54. Working in the surface boundary layer, the GB-SAR are especially interested from
these disturbances. It is worth to note that the time scale of turbulence phenomena in
troposphere and the acquisition rate of usually GB-SAR applications are comparable,
the same is true for the spatial scale.
Figure 3-2: power spectrum of wind speed (R. B. Stull, 1988).
Figure 3-2 shows the power spectrum of the wind speed near the ground (dotted line)
and in the free atmosphere, the former being of interest for its influence on GB-SAR
applications. In the graph five peaks are evident:
1. between 1 and 10 minutes: micrometeorological peak, associated with turbulent
phenomena;
2. 12 hours: half-day cycle;
3. 1 day: daily cycle related to the solar heating;

55. 4. 4 days: macrometeorological peak, it is related to movement of a large-scale
weather system due to global circulation;
5. 1 year: annual cycle;
The frequency range between the first two peaks contains almost no energy. This
range is called the “spectral gap”, which separates the two different frequency ranges
of the wind fluctuation. The wind fluctuation in the micrometeorological peak should
be taken into account in evaluating the effects in the GB-SAR images.
3.2.2 A brief description of turbulence
The physical mechanisms generating turbulence in the the atmospheric surface
boundary layer are numerous and complex, being related to the atmospheric mixing
and vertical transfer processes. The irregularities of the terrain and the proximity of
forest or water can have a strong influence on the generation of turbulence, as well
differences in solar illumination conditions.
The atmosphere is an inhomogeneous medium, altough mean values of refractive
index usually have some horizontal homogeneity. The inhomogeneities are produced
and supported by turbulent motion. Turbulence may be defined as an irregular motion
which in general makes its appearance in fluids, when they flow over solid surfaces or
when thermal instability is present. While the wind has a mean speed and a mean
direction which are reasonably constant for periods of hours, the instantaneous speed
and direction at a particular point may differ widely from the mean values. There is no
clear idea of how or why turbulence arises, or of the exact nature of the eddies which
form in a fluid in turbulent flow, but it’s known that the local variations of velocity in
a fluid are associated with the variations of static pressure which travel downstream
with the mean velocity of the stream.
When a current of air moves over uneven ground we might be tempted to think of the
eddies which form in it as cylindrical eddies having their axes in the horizontal plane
perpendicular to the direction of the mean wind. However investigations indicate that
the mean-square fluctuations of wind speed are approximately equal for the three
cordinates components. It is usual to define turbulent velocity at a point as the
difference between the instantaneous velocity at the point and the slowly varying

56. mean velocity of the stream, and the intensity of turbulence as the ratio of turbulent
velocity to mean velocity. Experimental results show that the intensity of turbulence
may be as large as 2/5, with root-mean-square values of the order of 1/10 or 1/20. The
intensity results essentially independent from mean wind speed above about 5 meters
per second, with the turbulent velocities distributed Gaussianly. Generally turbulent
velocities occurring in the lower troposphere vary from a few tens of meters per
second down to a few centimeters per second.
Concluding, the atmosphere near the ground may therefore be pictured as subject to
accidental fluctuations in refractive index, these fluctuations being autocorrelated only
over distances which can varies from hundreds meters to less than centimeters,
depending on the stability conditions.
In this study turbulence intensity is quantified by the Turbulent Kinetic Energy
(TKE), which is defined in fluid dynamics as the mean kinetic energy per unit mass
associated with eddies in a turbulent flow. Physically, the TKE is characterised by the
measured root-mean-square velocity fluctuations. This latter is calculated from the
fluctuations of the three wind velocity components v'x, v'y and v'z, revealed by an
anemometer:
K t = v'2 + v'2 + v'2
x y z Eq. 3-1
where the symbol <…> stands for a time average over the inspected time window.
!
3.2.3 Radar echo as a global quantity
The fluctuations of the air refractive index due to the turbulence in the boundary layer
can then materialize in a recorded imprint on radar signal, which could therefore
encode an indirect signature of turbulence.
Indeed, the embedding medium can be ideally segmented in neighboring volume
cells, each contributing to the signal according to an overall trend and its own statistic.
The signal impinging on the junction between two adjacent cells is partly reflected
and partly transmitted and the data collected at the receiver is sensitive to the
sequence of scattering events occurred along the propagation path. In this sense, the
radar echo can be thought as a global quantity, indirectly representing the specific

57. state of the crossed medium, and turbulence can be thought as the binder between the
neighboring volume cells, creating the correlation in the behaviour of the cells.
A comprehensive interpretative framework for such phenomena is however still
lacking, following the inherent difficulties to accommodate for the intimate, highly
complex nature of radar-air interactions.
3.3 Experimental tests
Aimed to a deeper understanding of the radar-turbulence interaction and aware of our
results in many survey campaigns, we arranged two outdoor experiments, both
realized in controlled environments. The first experiment was arranged in a facility of
the Faculty of Engineering at the University of Florence, but it showed many
problems that will be discussed later, so we planned a second experiment in the open
pit quarry described in Chapter 2.
The second experimental test has given very interesting results, suggesting that the
footprint of atmospheric turbulence be really encoded in the radar signal statistics.
Both the experiments were performed using the radar system described in Chapter 2,
but not in SAR configuration. Working in simple radar configuration permits to
acquire radar image with an high rate (up to 100 images for second), further
neglecting the problems related to the SAR images construction.
3.4 The experimental test at the facility of the Faculty of Engineering
The first experiment was arranged in a facility of the Faculty of Engineering at the
University of Florence, from December 30 2008 to January 5 2009.
In order to follow the temporal evolution of the radar signal in different places of the
scenario observed from the system, trying to understand the temporal and spatial
evolution of atmospheric disturbances, the test site was equipped with twelve targets
constituted by nine corner reflector, two metallic discs and a small concrete wall. It’s

58. worth to outline that every target was strongly connected to the ground in order to
prevent oscillations.
An ultrasonic anemometer and seven weather stations were installed too, in order to
measure wind velocities, temperature, pressure and humidity. The radar and six
targets were equipped with a weather stations.
The observed scene was essentially a meadow ending with a thick wood, where the
only manmade targets present in the scene were the radar targets, which were
distributed over a range distance from 10 to 120 m (Figure 3-3). On the test site, if
vegetation is ruled out, there are no uncontrolled moving targets, so supposing
instrumentation errors are reduced to negligible values by the autocalibration
procedure, any amplitude and phase change eventually detected can be related to
atmospheric disturbances.
Figure 3-3: the test site at the Faculty of Engineering of the University of Florence. In foreground
the radar system, in background the targets.

59. 3.4.1 Instrumentation
The Ku radar described in Chapter 3 was installed on a tripod in the facility. The radar
didn’t work in SAR configuration, allowing a fast sampling (1 Hz) of the scenario
monitored for 7 days. The range resolution was 37.5 cm.
Figure 3-4: the radar system installed on a tripod along with a weather station the power supply
battery and the electronic of control of all the system.
Each weather station was projected and realized in our laboratory. The energy is
supplied by battery and data are stored in a SD card (Figure 3-5).
The WindMaster 3D sonic anemometer was programmed to acquire data
synchronously with the weather stations, but with a 4 Hz rate, saving them in a SD
card (Figure 3-5).

60. Figure 3-5: Top: a corner reflector target along with the wind anemometer and a wheather
station. Bottom: details of the electronic of the weather station.

61. 3.4.2 Results
In this section are exposed the results about the relationships between atmospheric
turbulence and the oscillations of the signals from the targets.
• The RCS image
The RCS of the observed scenario is shown in Figure 3-6, where 13 peaks are well
evidents above the threshold of -20dB. Twelve peaks representing the manmade
targets in the scenario (Figure 3-3), while the peak labeled with “T“ in the image (at a
distance of about 73 m from the radar) represents a tree presents in the scenario.
Instead, the small peaks in the range between 100 and 120 meters are due to the trees
in the wood at the end of the observed scenario.
Figure 3-6: radar test site scenario, 13 targets are evidents. Each targets has a label: CR – corner
reflector, D – metallic disc, A – corner reflector equipped with the anemometer, T is a tree, W -
concrete wall. The labels with the “*” mark the targets integrated with the weather stations.

62. The targets equipped with the weather stations are shown in Figure 3-7.
Figure 3-7: the six manmade targets equipped with the weather stations.

63. Looking at the Figure 3-7 it’s possible to estimate the level of signal-to-noise ratio for
the manmade targets. The level of noise is at about -30 dB from the maximum of the
signal (0 dB, normalizing the y axis with the value coming from the target CR9).
Then the SNR ranging from about -10 dB (target CR1) to -30 dB (target CR9).
Due to a low level of SNR it’s then impossible to observe the effects of the
atmospherical turbulence in the fluctuations of the radar signal, being these
fluctuations expected at about -50 dB.
• Time series analysis
In order to find a connection between turbulence and the fluctuations in the radar
signal coming from a target we focused on the time series of amplitude and phase of
the corner reflector target equipped with the WindMaster 3D anemometer. We plot
the time series of the standard deviation of amplitude and phase along with the
Turbulent Kinetic Energy time series (Figure 3-8).
Figure 3-8: time series of the standard deviation of amplitude and phase of the corner reflector
target equipped with the anemometer, compared with the TKE time series.