Tesi ph d_andrea_barucci_small

865 views

Published on

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
865
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
84
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Tesi ph d_andrea_barucci_small

  1. 1. Corso di Dottorato in Ingegneria dei Sistemi Elettronici Ciclo XXIII Advancements on interferometric radar: studies and applications.Coordinatore: Prof. Carlo AtzeniTutor: Prof. Massimiliano PieracciniCandidato: Andrea Barucci Settore Disciplinare ING-INF/01 Firenze, 31 Dicembre 2010
  2. 2. List of Publications of the author published during the doctoral courseInternational 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- 5075/89/20006International 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. 3. Table of ContentsCHAPTER
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. 4. 3.6 ACKNOWLEDGEMENTS ........................................................................................................................81
 3.7 REFERENCES ...........................................................................................................................................81


  5. 5. PrefaceThis 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 dealingwith developing and testing of innovative techniques for conservation and monitoringof Cultural and Environmental Heritage.This thesis deals with advanced data processing in Interferometric Synthetic ApertureRadar for unstable slope monitoring. Mainly the attention of the author is turned tothe data processing algorithms for imaging the meaningful content of the specificradar observations. The particular acquisition system used in each type of observationwas developed at the TCH Lab and was based on a Continuous Wave SteppedFrequency radar architecture.Now GB-SAR interferometry is generally recognized as a powerful tool for detectingthe displacements of large structures such as dams or buildings, but also for the terrainmonitoring, 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 1km area), GB-SAR seems to be more suitable as it can be specifically set up for aparticular scenario geometry and in according to the dynamic characteristics of thelandslide.While conventional interferometric synthetic aperture radar is a very effectivetechnique for measuring surface deformation, almost any interferogram includes largeareas where the signals decorrelate and no measurements are possible. Consequently,most SAR studies focuses on areas that are dry and sparsely vegetated. A relativelynew analysis technique (PS method) overcomes the decorrelation problem byidentifying resolution elements whose echo is dominated by a single scatterer in aseries of interferograms.After an introduction on radar and SAR systems, in this Thesis we focused on theapplication of GB-SAR to monitor an open pit quarry using the PS method, and on theinfluence of the atmospheric disturbances, in particular boundary layer turbulence, onground based radar measurements.As far as the turbulence disturbances concerns, in this thesis an experimental surveywas planned in order to deeply understand how radar signal, and in particular hisstatistic, can change in presence of such phenomena. The results obtained by usingthese procedures on real data acquired in a experimental facility are discussed too.The agreement between theoretical and real data confirms the validity of the usedstatistic, confirming the “Universal distribution” as a powerful tool to understanddifferend kind of complex phenomena.Chapter 1 deals with Synthetic aperture techniques for imaging and interferometricapplications, while Chapter 2 describes a measurement campaign in an open pitquarry near Florence, and his results are presented and discussed. Chapter 3 presentstwo experiments devoted to the study of the influence of atmospherical turbulence onradar signals.
  6. 6. RingraziamentiDurante i tre anni di dottorato ho avuto l’onore di lavorare con personemeravigliose: Alessandro Spinetti, Daniele Mecatti, Devis Dei, Filippo Parrini,Gilberto Grazzini, Giovanni Macaluso, Linhsia Noferini e Matteo Fratini. Le qualitàlavorative e morali di questo gruppo di persone sono state e saranno per me unesempio 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 ecostruendo molta della strumentazione utilizzata per le misure da me svolte, non hoparole per ringraziarlo. Lavorare con lui è stato un piacere ed un divertimento.Con Linhsia ho condiviso la maggioranza del mio tempo, discutendo infinite volte deiproblemi 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 piùgrande stima ed il mio più profondo rispetto. A Lei devo moltissimo, senza il suoprezioso contributo niente di quanto descritto in questa tesi sarebbe stato possible.Un ringraziamento al Prof. Carlo Atzeni ed al Prof. Massimiliano Pieraccini che mihanno dato l’opportunità di lavorare nel Laboratorio di Tecnologie per i BeniCulturali ed Ambientali, dandomi sempre libertà di ricerca ed ampio spazio dilavoro, e ricordandosi sempre che sono un fisico.Infine un ringraziamento alla mia famiglia, che nonostante i tanti problemi che la vitaci porta ad affrontare, mi ha sempre sostenuto ed incoraggiato a fare ciò che mipiaceva. A loro devo tutto.
  7. 7. 
 Chapter 1 Synthetic Aperture RadarThis chapter provides the basic concepts on synthetic aperture radar imaging andinterferometry (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 interpretationincluding issues that impact processing algorithms, while Section 3 provides aconsistent mathematical representation of InSAR principles and phenomenologyassociated with interferometric phase measurements.1.1 Continuous Wave Stepped-Frequency RadarSince 1960’s in developing pulsed radar systems it was evident that the simple pulsedradar was not suitable for radar applications requiring ultimate performance in bothrange (high transmitted pulse power) and resolution (short pulse width). To overcomethe difficulty of combining these requirements, alternative waveforms weredeveloped.Pulse compression waveforms are specially coded to allow the transmission of longerpulse widths which allow higher mean powers, while retaining wide bandwidths forhigh resolution. The system used in this thesis exploits a frequency compressiontechnique known as stepped frequency technique.
  8. 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 tonesor pulses stepped in frequency at intervals of Δf across a bandwidth B. The blockdiagram of the stepped-frequency radar is shown in Figure 1-1. Each frequency stepreceived from reflecting targets is mixed with the transmitted waveform for down-conversion to baseband by means of a quadrature mixer. The quadrature mixerproduces a baseband signal comprising of two orthogonal components to preserve themagnitude and phase of the received tone. These components, known as the in-phase Iand 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 nextfrequency step is transmitted. Once the radar has completed the steps across thebandwidth an IDFT (Inverse Discrete Fourier Transform) is applied to the digitised Iand 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 descriptionThe time waveform x(t) transmitted by a stepped-frequency radar can be representedas a continuous train of N stepped-frequency pulses. Each pulse in the train has awidth of T in time and a carrier frequency which is stepped at increments of Δf from
  9. 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. 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. 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. 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. 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 projectionData backscattered by the illuminated scenario are processed in range and cross rangeonly. The third dimension is lost and the effect on SAR images depends on therelative geometry of the SAR aperture and the illuminated surface. Then targetlocations are distorted relative to a planimetric view and their identifications could bevery difficult. For many applications, this altitude-dependent distortion adverselyaffects the interpretation of the imagery. To obtain the three-dimensional information,an additional measurement of elevation angle is needed. Interferometry using two ormore SAR images separated by a spatial baseline provides a means of determiningthis angle.1.2.3 SAR processingThe antenna employed in the present work is mounted on a ground based linear railand moves along the rail one step further after each signal acquisition. The transmittedwaveform is the stepped frequency continuous wave. So the in-phase ( ) andquadrature (Q) components of the received signal are measured for each frequencyand for each antenna position on the rail.The implemented SAR processor provides the range and cross-range synthesiscombining the Fourier transform efficiency with the ultimate resolution obtainablefrom the received data. The Fourier transform is used only for getting the range
  14. 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. 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. 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. 17. where and represent the two SAR images, the brackets mean the average valueof the argument and is the corresponding interferometric phase.The coherence provides an estimation of the achievable quality of an interferogramsince it determines the peak width of the probability density function around that isstrictly related to the measurable phase variance. Physically, a loss of coherencedepends on how the elemental scatterers move within resolution cell. If thedisplacements randomize the positions of each scatterer with respect to others, thepair of echoes will be less well related and the coherence of the interferogram willdecrease 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 inthe interferogram and may be inverted to recover surface topography or displacementfields. However, the phase observables are measured modulo 2π; that is, the integralnumber of phase cycles on each measurement is lost. It is said that the phases linearwith range variation are wrapped in the interval [-π, π) by the measurement process.Consequently, if the surface displacement in a scene determines a phase excursiongreater than one cycle, or if the combination of interferometric baseline and surfacetopography yields more than one fringe of topographic signature, the interferogramcannot be uniquely inverted without a procedure to recover the missing cycles. Werefer to such procedures as phase unwrapping.The aim of phase unwrapping (PU) is to recover the integer number of cycles to beadded to the wrapped phase so that the unambiguous phase value can be finallyobtained 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. noconstraint is given to the solution, PU is an ill-posed problem and therefore an infinitenumber of different solutions can be found, all honouring the data.The most straightforward PU procedure would be a simple integration of the phasedifferences, starting from a reference point. However, because of phasediscontinuities, it is not always accurate.
  18. 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. 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. 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 ispossible to estimate the neighboring pixel differences of the unwrapped phase whenthese differences are less than π. From these, the unwrapped phase can bereconstructed up to an additive constant. The methods differ in the way theyovercome the difficulty posed by the fact that this hypothesis may be somewherefalse, which cause the estimated unwrapped phase differences to be inconsistent, thatis their "integral" depends on the integration path.Branch cuts methods unwrap by integrating the estimated neighboring pixeldifferences of the unwrapped phase along paths avoiding the regions where theseestimated differences are inconsistent. The problem of building cuts delimiting theseregions is very difficult and the resulting phase unwrapping algorithm is veryexpensive computationally.In least squares methods, unwrapping is achieved by minimizing the mean squaredeviation between the estimated and the unknown neighboring pixel differences of theunwrapped phase. Least squares methods are very efficient computationally whenthey make use of fast Fourier transform techniques. But the resulting unwrapping isnot very accurate, because least squares procedures tend to spread the errors that areinstead concentrated on a limited set of points. To overcome this problem a weightingof the wrapped phase can be useful. However, the weighted least squares algorithmsproposed are iterative and not as efficient as the unweighted ones. Moreover, theaccuracy of the results depends on the weighting mask used.The networking algorithms exploit the fact that the neighboring pixel differences ofthe unwrapped phase are estimated with possibly an error which is an integer multipleof 2π. This leads to formulate the phase unwrapping model as the problem of
  21. 21. minimizing the deviations between the estimated and the unknown neighboring pixeldifferences of the unwrapped phase with the constraint that the deviations must beinteger multiple of 2π. This constraint prevents the errors from spreading, so aweighting of the data is not necessary. In any case, weighting is allowed in thisformulation (without loss of efficiency), and can be useful when there are largeregions of noisy data. Even if minimization problem with integer variables are usuallyvery complex computationally, recognizing the network structure underlying theproblem makes available very efficient strategies for its solution. In fact, the problemcan be equated to the problem of finding the minimum cost flow on a network, for thesolution of which there exist very efficient algorithms.1.4 ReferencesC. Cafforio, C. Prati, F. Rocca, “L’Elaborazione di segnale nel radar ad aperturasintetica”, L’Elettrotecnica, vol. 9, pp. 787–795, Settembre 1989.C. Cafforio, C. Prati, E. Rocca, “SAR Data Focusing Using Seismic Migrationtechniques”, IEEE Trans. on aerospace and electronic systems, vol. 27, no. 2, pp. 194-205, march 1991.C. W. Chen, Statistical – cost network – flow approaches to two-dimensional phaseunwrapping for Radar Interferometry, Ph. D. Thesis, Stanford University, 2001.M. Costantini, “A Novel Phase Unwrapping Method Based on NetworkProgramming”, IEEE Trans. Geosci. Remote Sensing, vol. 36, no. 3, May 1998.J. C. Curlander and R. N. McDonough, “Synthetic Aperture Radar - Systems andSignal Processing”, John Wiley & Sons, Inc., New York, NY, USA, 1991.D. Dei, “Monitoraggio dinamico di strutture architettoniche mediante sensori amicroonde”, Ph. D. Thesis, University of Florence, 2010.J. P. Fitch “Synthetic Aperture Radar”, New York; Springer-Verlag,1988.M. Fratini, “Sistemi RADAR per il monitoraggio di beni artistici ed ambientali”, Ph.D. Thesis, University of Florence, 2005.A. K. Gabriel, R. M. Goldstein, and H. A. Zebker, “Mapping small elevation changesover large areas: differential radar interferometry,” J. Geophys. Res., vol. 94, no. B7,pp. 9183–9191, July 1989.D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweightedphase unwrapping that uses fast transforms and iterative methods”, J. Opt. Soc. Am.,vol. 11, no.1, pp. 107-117, January 1994.
  22. 22. R. M. Goldestein, H. A. Zebker, and C. L. Werner, “Satellite Radar Interferometry:Two-dimensional Phase Unwrapping”, Radio Scienc, vol. 23, no. 4, pp. 713-720, July1988.L. C. Graham, “Synthetic interferometric radar for topographic mapping”, Proc.IEEE, vol. 62, pp. 763–768, June 1974.G. Fornaro, G. Franceschetti, and R. Lanari “Interferometric SAR Phase UnwrappingUsing Green’s Formulation”, IEEE Trans. Geosci. Remote Sensing, vol. 34, no. 3,pp. 720-727, May 1996.D. Leva, G. Nico, D. Tarchi, J. Fortuny, and A. J. Sieber, “Temporal Analysis of aLandslide by Means of a Ground-Based SAR Interferometer”, IEEE Trans. Geosci.Remote Sensing, vol. 41, no. 4, pp 745-752, April 2003.G. Luzi, et al., “Ground-Based radar interferometry for landslides monitoring:atmospheric and instrumental decorrelation sources on experimental data”, IEEETrans. Geosci. Remote Sensing, vol: 42 Issue: 11 , pp: 2454 –2466, Nov 2004.G. Macaluso, Radar interferometrici basati a terra ed integrazione dati in ambienteGIS, Ph. D. thesis, 2007.D. Massonnet et al., “The displacement field of the Landers earthquake mapped byradar interferometry,” Nature, vol. 364, pp. 138–142, July 8, 1993.D. Mecatti, “Radar interferometrici per il monitoraggio da terra di versanti franosi”,Ph. D. Thesis, 2005.D. L. Mensa, “High Resolution Radar Cross-Section Imaging”, Artech House.L. Noferini, Processing techniques of microwave data acquired by Continuous WaveStepped Frequency Radar, Ph. D. thesis, 2005.D. A. Noon, “Stepped-Frequency Radar Design and Signal Processing EnhancesGround Penetrating Radar Performance”, Ph. D. Thesis, University of Queensland,January 1996.M. Pieraccini, D. Tarchi, H. Rudolf, D. Leva, G. Luzi, and C. Atzeni, “Interferometricradar for remote monitoring of building deformations”, in Electronics Letters, vol. 36,no. 6, pp. 569–570, March 2000.M. Pieraccini, D. Mecatti, L. Noferini, G. Luzi, G. Franchioni, and C. Atzeni, “SARinterferometry for detecting the effects of earthquakes on buildings”, inNDT&Intrenational, vol. 35, pp. 615–625, August 2002.M. Pieraccini, N. Casagli, G. Luzi, D. Tarchi, D. Mecatti, L. Noferini, and C. Atzeni,“Landslide Monitoring by Ground-Based Radar Interferometry: a field test inValdarno (Italy)”, Int. J. Remote Sensing, vol 24, no 6, pp 1385-1391, Sept. 2002.P. A. Rosen, S. Hensley, I. R. Joughin, F. K. Li, S. N. Madsen, E. Rodriguez and R.M. Goldstein, “Synthetic Aperture Radar Interferometry”, Proc. IEEE, vol. 88, no. 3;pp. 333–382, March 2000.M. I. Skolnik, “Radar Handbook”, McGrawHill, New York, NY, USA, 1990.
  23. 23. U. Spagnolini, “2-D phase unwrapping and instantaneous frequency estimation”,IEEE Trans. On Geoscience and Remote Sensing, vol. 33, no. 3; pp. 579–589, May1995.H. Takajo and T. Takahashi, “Least-squares phase estimation from the phasedifference”, J. Opt. Soc. Am. A, vol. 5, no. 3, pp. 416-425, March 1988.D. Tarchi, H. Rudolf, G. Luzi, L. Chiarantini, P. Coppo, and A. J. Sieber, “SARinterferometry for structural changes detection: A demonstration test on a dam”, inProc. IGARSS, 1999, pp. 1522–1524.F. T. Ulaby, K. Sarabandi, A. Nashashibi, “Statistical Properties of the Muellermatrix of distributed targets ”, Proc. IEEE, vol. 139, no. 2, pp. 136-142, April 1992.D. R. Wehner, “High Resolution Radar”, Artech House, Norwood, MA, USA, 1995.H. A. Zebker and R. M. Goldstein, “Topographic mapping from interferometric SARobservations”, J. Geophys. Res., vol. 91, pp. 4993–4999, 1986.
  24. 24. Chapter 2 Monitoring Open-Pit Quarries by Interferometric Radar for Safety PurposesThis chapter focuses on a measurement campaign carried out to monitor an open pitquarry 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 andmonitoring methodologies”, founded by the Italian Research and University Ministry.2.1 GB-SAR for Terrain Displacement MappingToday Ground-Based Synthetic-Aperture Radar (GB-SAR) interferometers havebecome powerful and effective tools for remote sensing of movements in manyapplication fields. These sensors have been successfully employed in landslide andglaciers monitoring, as well as in avalanche localization and detection of snow coverchanges.With respect to airborne and spaceborne SAR systems, GB-SAR can offer acontinuous temporal coverage and, because of its versatility, an optimal illuminationgeometry in almost all cases. Usually in applications for ground displacement
  25. 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 fromremote, each image containing phase and amplitude informations of the receivedechoes, at a high time rate (typically more than one image per hour). The phase valuesof each pixel of the image are related to the distance between the sensor and the pixelitself, whereas the phase differences between two images acquired at different timesare 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 adirect measurement of the along of sight displacements. The multiple images acquiredcan be thought of as “time-lapse” imagery.2.2 Monitoring an open pit quarries by a GB-SARSlope failure accidents are nowadays responsible for a large number of fatalities andmachinery damages in open pit quarries. Monitoring of slope stability in excavationareas is then a crucial issue in order to optimize the production efficiency and toensure the safety of the operators.Because large rock collapses may show minor precursor movements starting hours ordays in advance, the early detection of these small deformations could be ofparamount 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. 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 theTechnology for Cultural Heritage Laboratory (TCH Lab), a research group within theDepartement of Electronics and Telecommunications of the University of Florence.The radar system is an evolution of the sensor developed at the University of Florencein collaboration with IDS SpA (Pisa, Italy), working in the licensed Ku band. Thesystem was adapted to this application through several improvements in themechanical and electronical components.The measurement geometry in a quarry is often unfavourable for a standard GB-SARsystem, due to the need of imaging a wide area looking from a close location, thusrequiring a wide viewing angle.For this reason the radar system was improved adding the capability to rotate theantennas around a vertical axis: the system was able to observe a very wide area bysimply acquiring several different SAR images at different viewing angles andcombining them in post processing. With this improvement the view angle of theradar sensor was extended up to 150 degrees (Figure 2-2).
  27. 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, thusmaintaining a higher signal to noise ratio, instead of using wide angle – low gainantennas. The drawback is a longer acquisition time needed to acquire the sub-imagesat the different angles.A quarry is typically an area subject to morphological changes due to the continuousmining 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, inthe novel GB-SAR system it was added the capability to realize interferometricDEMs, simply allowing the antennas to move up to 30 centimeters along a verticalaxis.In order to be able to operate day and night even where the electric network was notavailable, the radar system was equipped with an autonomous power supply systemusing solar and wind energy (Figure 2-3).
  28. 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 theinstrument and the real time data download. A picture of the system is shown in Figure2-4.
  29. 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 SurveyThe novel radar system described above was tested during a field survey 39 days longfrom 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 detectpossible 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 Figure2-6.
  30. 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, inall weather conditions. Data were uploaded real time to the automatic processingstation located at the University of Florence through a local radio link and the Internetnetwork. Displacement maps were generated automatically and were available half an
  31. 31. hour after the end of each acquisition. The measurement parameters are listed in Table2-1.Central Frequency 16.75 GHzBandwidth 300 MHzTx Power 26 dBm EIRPSAR scan length 2mSAR acquisition time 10 minutes for each sub-imageSAR acquisition rate 2 sub-images every hourRange Resolution 0.50 mCross Range Resolution 0.5°View angle 150°Power consumption < 40 W Table 2-1: measurements parameters.
2.2.3 The RCS imageA RCS SAR image of the quarry is shown in Figure 2-7, with superimposed the map ofthe same area. The reference system is a local system with the origin in the radarlocation. This wide angle map originates from two sub-images acquired sequentiallyat two different angles.
  32. 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, between600 and 700 meters in range, (b) the rocky wall, between 700 and 800 meters inrange, and (c) the ravaneto1 between 450 and 600 meters. The zone (a) wascharacterized by continuous movement of mining machinery, the zone (c) consisted ofrock debris resulting from quarrying operations, and the zone (b) was the area ofinterest 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. 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. 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. 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. 36. temperature variations. This is the reason because these areas are not completelycovered 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 SARimages used. However, using a number of images greater than 50, the number of PSbecomes almost stable, decreasing very slowly. Altough more rigorous and
  37. 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. 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. 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 inFigure 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 selectedpoints in the wall and for two different days during the survey. The fluctuations are
  40. 40. again due to instrumental noise and to residuals of the atmospheric compensationprocedure. However the cumulative displacements are below the 0.1 mm, meaningthat this point must be considered as stable, being the value of 0.1 mm considered as athreshold. Figure 2-12: cumulated displacements versus time for three points in the rock wall during two days of measurement.2.4.2 InterferogramsAimed to a complete interferometric characterization of the scenario, it is interestingto study the interferogram relative to all the pixels, excluding only the dead zone ofthe antennas (shown in red in the Figure 2-13).In zone (a) the interferometric analysis is not significant because of the continuousmovements of machinery for mining activities. In zone (c) sudden and consistentmovements were observed due to discharging of debris into the ravaneto. However inthis area the interferometric analysis cannot be performed meaningfully, as the rapidaccumulation of debris into the ravine is generally a non coherent process and oftenoriginates phase ambiguity. Nevertheless it is interesting to examine theseinterferograms qualitatively, as the areas where the previous phenomena happen canbe clearly identified.
  41. 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 correspondingto a time lapse of 8 hours during a period of intense quarrying activities. The paths ofdebris 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 debrisseems to settle down giving rise to typical interferometric fringes.
  42. 42. 2.4.3 Simulation of displacement by a Corner Reflector targetAs 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 atlong 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 ata 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, asshown 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 highSNR 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. 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 3Displacement of CR 2.00 1.00 0.50(mm)Measured displacement 2.05 0.89 0.53of CR (mm)It is clearly evident that in the short term (few hours) and in optimal SNR conditionsan accuracy of 0.1 millimeters is guaranteed.2.4.4 Digital Elevation ModelA 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, imageswith different viewing angles can be collected.
  44. 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. 45. between the two DEMs are evident, the laser scanner DEM being more detailed (aspatial 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 wrappingerrors, 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 ofabout five meters compared to the laser scanner DEM.In Figure 2-19 an amplitude SAR image is focused using the laser scanner DEM, wherethe red spot represents the Corner Reflector Target observed by the radar. Figure 2-17: DEM generated by the GB-SAR system.
  46. 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. 47. 2.5
 References

G. Antonello, N. Casagli, P. Farina, D. Leva, G. Nico, A. J. Sieber, D. Tarchi,.“Ground-based SAR interferometry for monitoring mass movements”, Landslides, 1,pp. 21–28, February 2004P. Bernardino, G. Fornaro, R. Lanari, and E. Sansosti, “A new algorithm for surfacedeformation monitoring based on small baseline differential SAR interferograms”,IEEE Trans. Geosci. Remote Sensing, vol. 40, n. 11, November 2002.A. Ferretti, C. Prati, and F. Rocca, “Permanent scatterers in SAR interferometry”,IEEE Trans. Geosci. Remote Sensing, vol. 39, pp 8-20, Jan. 2001.A. Ferretti, C. Prati, and F. Rocca, “Nonlinear subsidence rate estimation usingPermanent Scatterers in differential SAR interferometry”, IEEE Trans. Geosci.Remote Sensing, vol. 38, pp 2202-2212, Sept. 2000.A. Ferretti., C. Colesanti, D. Perissin, C. Prati, F. Rocca, “Evaluating the Effect of theObservation Time on the Distribution of SAR Permanent Scatterers”, Proc. FRINGE‘2003 Workshop, Frascati, Italy, 2003.R. F. Hansen, Radar interferometry. Data Interpretation and Error Analysis, KluwerAcademic Publishers, 2001.R.F. Hansen, “Atmospheric heterogeneities in ERS Tandem SAR Interferometry”,Delft Univ. Press, 1998.A. Hooper, Persistent Scatterer Radar Interferometry for crustal deformation studiesand modeling of volcanic deformation, Ph. D. Thesis, Stanford University, 2006.A. Hooper, H. A. Zebker, P. Segall, and B. Kampes, “A new method for measuringdeformation on volcanoes and other natural terrain using InSar persistent scatterers”,Geophysical Research Letters, vol. 31, 31 (23), 5, doi:10.1029/2004GL021737, 2004.D. Leva, G. Nico, D. Tarchi, J. Fortuny, and A. J. Sieber, “Temporal Analysis of aLandslide by Means of a Ground-Based SAR Interferometer”, IEEE Trans. Geosci.Remote Sensing, vol. 41, no. 4, pp 745-752, April 2003.A. Martinez-Vazquez, J. Fortuny-Guasch, “Feasibility of snow avalanche volumeretrieval by GB-SAR imagery,” in Proc. IGARSS 2006, July 31 – August 04 2006,Denver (CO).A. Martinez-Vazquez, J. Fortuny-Guasch and Urs Gruber, “Monitoring of the snowcover with a ground-based synthetic aperture radar,” in Proc. EARSeL eProceedingsvol. 4, n. 2, 2005.G. Macaluso, Radar interferometrici basati a terra ed integrazione dati in ambienteGIS, PhD Thesis, 2007.D. Mecatti, L. Noferini, G. Macaluso, M. Pieraccini, G. Luzi, C. Atzeni, A.Tamburini, “Remote sensing of glacier by ground-based radar interferometry”, inProc. IGARSS 2007, Barcelona, Spain, 23-28 July 2007.
  48. 48. D. Mecatti, Radar interferometrici per il monitoraggio da terra di versanti franosi,PhD Thesis, University of Florence, 2005.D. Mecatti, Monitoraggio di movimenti del terreno e di grandi strutture: sviluppo diprototipi di radar interferometrici, Bachelor Thesis, University of Florence, 2001.L. Noferini, D. Mecatti, G. Macaluso, M. Pieraccini, C. Atzeni, M. Ripepe, A highspeed microwave interferometer used for monitoring Stromboli volcano, IEEEInternational Geoscience and Remote Sensing Symposium, IGARSS, 2009.L. Noferini, T. Takayama, M. Pieraccini, D. Mecatti., G. Macaluso, G. Luzi, C.Atzeni, “Analysis of Ground-Based SAR Data With Diverse Temporal Baselines”,IEEE Trans. Geosci. Remote Sens. Letters, vol. 46, Issue 6, 2008.L. Noferini, M. Pieraccini, D. Mecatti, G. Macaluso, G. Luzi, C. Atzeni, “DEM byGround-Based SAR Interferometry”, IEEE Trans. Geosci. Remote Sens. Letters, vol.4, Issue 4, 2007.L. Noferini, M. Pieraccini, G. Luzi, D. Mecatti, G. Macaluso, C. Atzeni, “Monitoringof Belvedere glacier using a wide angle ground-based SAR interferometer”, Proc.FRINGE 2007 (Advances in SAR Interferometry from ENVISAT and ERS missions),ESA ESRIN Frascati, Roma, Italia.L. Noferini, M. Pieraccini, D. Mecatti, G. Macaluso, G. Luzi, C. Atzeni, Ground-baesd Radar Interferometry for Monitoring Unstable slopes, IEEE Conference onGeoscience and Remote Sensing Symposium, IGARSS 2006, Denver, CO, USA.L. Noferini, M. Pieraccini, G. Luzi, D. Mecatti, C. Atzeni, A. Tamburini, andBroccolato M., “Permanent Scatterers Analysis for Atmospheric Correction inGround-Based SAR Interferometry,” IEEE Trans. on Geosci. Remote Sens., vol. 43,n. 7, pp. 1459–1471, July 2005.M. Pieraccini, M. Fratini, F. Parrini, C. and Atzeni, “Dynamic Monitoring of BridgesUsing a High-Speed Coherent Radar”, IEEE Trans. on Geosci. Remote Sens., vol. 44,n. 11, November 2006, pp. 3284-3288.M. Pieraccini, N. Casagli, G. Luzi, D. Tarchi, D. Mecatti, L. Noferini, and C. Atzeni,“Landslide monitoring by ground-based radar interferometry: A field test in Valdarno(Italy)”, Int. J. Remote Sens., vol. 24, no. 6, pp. 1385–1391, Sep. 2002.M. Pieraccini , G. Luzi and C. Atzeni "Terrain mapping by ground-basedinterferometric radar", IEEE Trans. Geosci. Remote Sens., vol. 39, no. 10, 2001 .L. Pipia, X. Fabregas, A. Aguasca, J. J. A. Mallorqui, “Comparison of differenttechniques for atmospheric artifact compensation in GB-SAR differentialacquisitions”, Proc. IGARSS, Denver, Colorado (USA), pp. 3739 – 3742, August2006.C. Werner, U. Wegmuller, T. Strozzi, and A. Wiesmann, “Interferometric point targetanalysis for deformation mapping”, Proc. IGARSS, Toulouse, France, pp. 4362-4364,July 2003.
  49. 49. H. A. Zebker, P. A. Rosen, and S. Hensley, “Atmospheric effects in interferometricsynthetic aperture radar surface deformation and topographic maps”, Journal ofGeophysical Research, vol. 102(B4), pp 7547-7563, April 10,1997.H. A. Zebker, J. Villasenor, and S. Hensley, “Decorrelation in Interferometric RadarEchoes”, Trans. Geosci. Remote Sens., vol. 30, no. 5, pp. 950–959, Sept. 1992.
  50. 50. Chapter 3 Universal Fluctuations in Tropospheric Radar Measurement
This chapter deals with the influence of the atmospherical turbulence on the radarsignal, focusing on the statistical description of the amplitude and phase informationas a function of the air turbulence. Using the radar described in Chapter 2 anexperimental study was realized and the results, interpreted using the complexsystems theory, confirm a strong connection between turbulence and the radar signalfluctuations and statistic.3.1 The effect of the atmosphere on the GB-SARAs the state-of-art in SAR interferometry moves toward a more quantitative andlocalized 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 sourcesof external disturbances, which could significantly alter the measurements response.In the last decades many geophysical applications based on SAR Interferometry werepresented. Even if SAR systems work at frequencies minimizing the atmosphericabsorption, the interferometric phase is affected by a delay due to the propagation inthe tropospheric layer. An increase in the amount of atmospheric water vapourfraction between the acquisition times affects the atmospheric index of refractionwhich induces an increase in the propagation time of microwave radar pulses. All thisappears as an increase in the distance to the ground surface, indistinguishable from
  51. 51. topography or real ground deformation. However, a comprehensive approache tomitigate atmospheric artefacts in InSAR data is still lacking.3.1.1 The landslide of FormigalFrom 2005 to 2008 the TCHLAB was involved within the activities of theGALAHAD project, with the opportunity to monitor many different natural scenariosin different weather conditions and for a long time. A large collection of ground basedradar data was then recorded and processed. In particular a landslide in Spain (Figure3-1) 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 aunique opportunity for studying the temporal behaviour of the radar signal.
  52. 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 windyconditions, the radar interferograms were affected by an overall decorrelation thatcould not be explained by the recorded weather conditions (no rainy events). Focusingthe 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 theradar propagation even over short ranges, an observation which however rested onpurely qualitative ground.
  53. 53. No further experimental realizations were in fact subsequently developed to scrutinizethe process and reach an unambiguous proof of concept.3.2 Radar- atmosphere interactionConscious of the experimental results on Formigal we developed the idea thatatmospheric turbulence might be the process behind the radar signal anomalies. Alittle introduction on this topic is given here.When an electromagnetic wave propagates through the troposphere its amplitude andphase are distorted by a number of mechanisms. These distortions may be placed intothree 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 turbulenceLong trend fluctuations can be well understood and recreated by the many models ofthe air index of refraction presents in literature.However atmospheric turbulence remains the best candidate to try to explain whatobserved in the Formigal images, this phenomena having time and spatial featurescomparable with those of the images generated by a ground-based radar.3.2.1 Spectrum of the windDifferent scale processes occur within the atmosphere, generally referred to assynoptic-scale processes (dozen of days), meso-scale processes (from day to hour)and micro-scale processes (less than an hour). Turbulent phenomena interest themicro scale, corresponding to distances shorter than 1 km.Among the atmospheric phenomena interacting with microwaves, the turbulence has asignificant impact on radar system. By creating time-varying inhomogeneities of theatmospheric refractive index, turbulence induces amplitude scintillations and phasedelays on the propagating signals.
  54. 54. Working in the surface boundary layer, the GB-SAR are especially interested fromthese disturbances. It is worth to note that the time scale of turbulence phenomena introposphere 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-SARapplications. 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. 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. Thisrange is called the “spectral gap”, which separates the two different frequency rangesof the wind fluctuation. The wind fluctuation in the micrometeorological peak shouldbe taken into account in evaluating the effects in the GB-SAR images.3.2.2 A brief description of turbulenceThe physical mechanisms generating turbulence in the the atmospheric surfaceboundary layer are numerous and complex, being related to the atmospheric mixingand vertical transfer processes. The irregularities of the terrain and the proximity offorest or water can have a strong influence on the generation of turbulence, as welldifferences in solar illumination conditions.The atmosphere is an inhomogeneous medium, altough mean values of refractiveindex usually have some horizontal homogeneity. The inhomogeneities are producedand supported by turbulent motion. Turbulence may be defined as an irregular motionwhich in general makes its appearance in fluids, when they flow over solid surfaces orwhen thermal instability is present. While the wind has a mean speed and a meandirection which are reasonably constant for periods of hours, the instantaneous speedand direction at a particular point may differ widely from the mean values. There is noclear idea of how or why turbulence arises, or of the exact nature of the eddies whichform in a fluid in turbulent flow, but it’s known that the local variations of velocity ina fluid are associated with the variations of static pressure which travel downstreamwith the mean velocity of the stream.When a current of air moves over uneven ground we might be tempted to think of theeddies which form in it as cylindrical eddies having their axes in the horizontal planeperpendicular to the direction of the mean wind. However investigations indicate thatthe mean-square fluctuations of wind speed are approximately equal for the threecordinates components. It is usual to define turbulent velocity at a point as thedifference between the instantaneous velocity at the point and the slowly varying
  56. 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 vx, vy and vz, revealed by an anemometer: K t = v2 + v2 + v2 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. 57. state of the crossed medium, and turbulence can be thought as the binder between theneighboring volume cells, creating the correlation in the behaviour of the cells.A comprehensive interpretative framework for such phenomena is however stilllacking, following the inherent difficulties to accommodate for the intimate, highlycomplex nature of radar-air interactions.3.3 Experimental testsAimed to a deeper understanding of the radar-turbulence interaction and aware of ourresults in many survey campaigns, we arranged two outdoor experiments, bothrealized in controlled environments. The first experiment was arranged in a facility ofthe Faculty of Engineering at the University of Florence, but it showed manyproblems that will be discussed later, so we planned a second experiment in the openpit quarry described in Chapter 2.The second experimental test has given very interesting results, suggesting that thefootprint 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 toacquire radar image with an high rate (up to 100 images for second), furtherneglecting the problems related to the SAR images construction.3.4 The experimental test at the facility of the Faculty of EngineeringThe first experiment was arranged in a facility of the Faculty of Engineering at theUniversity 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 thescenario observed from the system, trying to understand the temporal and spatialevolution of atmospheric disturbances, the test site was equipped with twelve targetsconstituted by nine corner reflector, two metallic discs and a small concrete wall. It’s
  58. 58. worth to outline that every target was strongly connected to the ground in order toprevent oscillations.An ultrasonic anemometer and seven weather stations were installed too, in order tomeasure wind velocities, temperature, pressure and humidity. The radar and sixtargets were equipped with a weather stations.The observed scene was essentially a meadow ending with a thick wood, where theonly manmade targets present in the scene were the radar targets, which weredistributed over a range distance from 10 to 120 m (Figure 3-3). On the test site, ifvegetation is ruled out, there are no uncontrolled moving targets, so supposinginstrumentation errors are reduced to negligible values by the autocalibrationprocedure, any amplitude and phase change eventually detected can be related toatmospheric 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. 59. 3.4.1 InstrumentationThe Ku radar described in Chapter 3 was installed on a tripod in the facility. The radardidn’t work in SAR configuration, allowing a fast sampling (1 Hz) of the scenariomonitored 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 issupplied by battery and data are stored in a SD card (Figure 3-5).The WindMaster 3D sonic anemometer was programmed to acquire datasynchronously with the weather stations, but with a 4 Hz rate, saving them in a SDcard (Figure 3-5).
  60. 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. 61. 3.4.2 ResultsIn this section are exposed the results about the relationships between atmosphericturbulence and the oscillations of the signals from the targets. • The RCS imageThe RCS of the observed scenario is shown in Figure 3-6, where 13 peaks are wellevidents above the threshold of -20dB. Twelve peaks representing the manmadetargets in the scenario (Figure 3-3), while the peak labeled with “T“ in the image (at adistance 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 treesin 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. 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.

×