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ard tlrus the residual phase telm 02 approxitnates to a constant r f4. Since p:2nLf lT and (ø-cu6) = 2nn\f 12, the argurne¡t of the Fres¡el i¡teg¡als in Eq. (3.27) becor¡es (3.32) where n is a normalizecl flequeucy par.ameter. The spectra in Eq.(3.26) ale thus functions of the tirne-bandwiclth product "A/ (i.e. cornpressiorr ratio Tlr). Duling clesign of a matchecl filter', weighting is usually incluclecl to recluce sicle lobes. The first, ancl lalgest, siclelobe of an ideal matched filter output signal is only 13 clB below the peak of the complessed pulse and near siclelobes fall off at approxirnately 4 dB per sidelobe intelval, with the siclelol¡e null poilts being spacecl 1/A/ apatt. To reduce the uldesirable siclelobes, ther.e are various apploaches such as weighting the spectrurn by frequency clornaiu fllteling, or arnplitucle rveighting of the envelope of the transrnittecl FM signal il the tirne domain. The frequency dornain weighting is gener.ally adopted (Cook alcl Bemfeld [19]). 4:\Ft¡(#) 3.2.2 Doppler Phase History The azirnuth compression of the SAR signal is basecl on the analysis of Doppler shift along arì arÌay. Thus the irnage formation out of SAR data requires accurate estimation of the expectetl phase histor.ies of scatterels on the Ealth's surface. It is tlte sequence of relative clistances between the tnoving sensol and a scatterer that cletermines its phase histor.y. Fol convenierce, a flat-surface model is assumed first and the or.bital SAR case rvill be 49
cliscussecl later il this sectio¡r. Thlee vectots rvhich clescribe the position, velocity, and acceleration of the sensor are clenoted by R"(¿), Vs(¿), A"(r) respectively. The corr.esponcliug vectols for' ¿ scatterer on the surface ale given by R¡(ú), V¡(l), A¿(f) as displayed in Figule 3.6. Because the lelative lnotion is rrole irnpoltant, the vectors R(l), V(l), A(i) ale clefined by R(r) v(¿) A(¿) R"(f)- Ri(¿) vs(r)- vt(t) as(¿)- Ar(r) (3.33) rvhich descl'il¡e the relative rnotion l:etween the sensol and scatteler'. In a short time iltelval centerecl at l¡, the clistance can be expressecl by R(r) : R(¿o) +v(¿o)(t - to) + ;A(r0)(¿ - ¿o)'? (3.34) The nolr:i of the vector is lR(¿)l : ,nt¿l.Rt¿l R(lo) v(ro)r',-r", - lR(¿o)l* lR(r.)l \" "u/ + (v(¿0) 'v(tol+ R(¿0) A(¿o)) t+ +-\2 /? (Ú Ór/ a,.\ @t'-'ot rvliele lR(f6)l is a magnitucle of R(16) and denotes a clot product. The return signal is tirne clelayed by 2lR(tg)l/c, thus the phase shift due to the signal time clelay is op¡: -lz,r¡n1r¡¡ (3.36) 50
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INVERSION OF SYNTHETIC APERTUR,E R,
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ñr^-- ltoN. J00NG suN '¿i¡r"r os
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I heleby declale that I am tlie sol
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plot of the maximum amplitude of th
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Contents Abstract Acknowledgements
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6.3.1 Introduction ..151 6.3.2 Digi
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5.1 Florv chart fot the proposecl i
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List of Tables 2,1 Seasat SAR senso
Page 17 and 18: List of Notations cr squint angle P
Page 19 and 20: tist of Abbreviatíons SAR Syntheti
Page 21 and 22: The objectives of this thesis rnay
Page 23 and 24: Ground Range l;l 2 sin0 Figure 1.2:
Page 25 and 26: ol'cler to evaluate its full aclvan
Page 27 and 28: algolithrn extlacts the complex bac
Page 29 and 30: successful as expected. Thele ale,
Page 31 and 32: eú ø1. [103]). Similal clevelopme
Page 33 and 34: aerial plìotogl'aphy ovel the area
Page 35 and 36: 2.2 Spaceborne SAR Systems 1) SEASA
Page 37 and 38: tlie basis of a distinctive dlainag
Page 39 and 40: set fol selectecl aleas, useful for
Page 41 and 42: 3) ERS-I The first European rernote
Page 43 and 44: Table 2.4: ERS-I Ðieterle [104]).
Page 45 and 46: Table 2.6: ERS-1 SAR pelfolmance re
Page 47 and 48: Table 2.7: JtrRS-1 olbit pararnetel
Page 49 and 50: Table 2.9: Chalactelistics of OPS o
Page 51 and 52: Table 2.11: Specifications of Racla
Page 53 and 54: Chapten 3 Review of Digital SAR Pro
Page 55 and 56: ,I Figule 3.1: Raclar' L¡earn geom
Page 57 and 58: I L-=J}"no Figure 3.2: Geouretry fo
Page 59 and 60: vhich is the clistance across the a
Page 61 and 62: vlrere ø6 is a angular center fi'e
Page 63 and 64: à1 äl (a) /1T. or^l - r+ (b) I à
Page 65 and 66: a,pploxirnated by l2p sinl(I - ltl)
Page 67: -s(cu) is rewlitten as s@¡ - !"-,r
Page 71 and 72: Ïon = _2 (V(ro) .V(¿o)+ R(ro) .A(
Page 73 and 74: : Range Walk : Range Curvatule : Ra
Page 75 and 76: olbital SAR is given by Ion = -'#{t
Page 77 and 78: is constant cluling the receiving p
Page 79 and 80: a at f¡r
Page 81 and 82: 'rvith a foulula developed il this
Page 83 and 84: Chapter 4 Theoretical Development 4
Page 85 and 86: developed and cliscussed by several
Page 87 and 88: vhere u (r,ro; u) : I U 1r,ro,t)e-i
Page 89 and 90: wheÌe k':frf a¡cl lc -_ uf us ant
Page 91 and 92: 4) there is relative motion of ante
Page 93 and 94: o =løo, 0, 0) Figure 4.1: Schemati
Page 95 and 96: elorv that sulface. In genetal, sul
Page 97 and 98: 4.4 The Inversion The equation Eq.(
Page 99 and 100: *'here % is a platfolrn velocity an
Page 101 and 102: The trq.(a.36) cannot be used dilec
Page 103 and 104: vhele Àl is a tvavenurnbel collesp
Page 105 and 106: 2-D FFT o(,b,;ø) Intelpolation in
Page 107 and 108: ¡nE 0$r-sEc, ¡3 I IrlÊ [18- 5EC
Page 109 and 110: 5.2 Digital Simulation Digital sirn
Page 111 and 112: Table 5.2: Moclel palametels fol di
Page 113 and 114: signal and the leconstructe
Page 115 and 116: (3 È. e tc o) o -tl a Slant Range
Page 117 and 118: that the inversiol method can accor
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(n t0 Ê) 0c (lr) Figure 5.6: Seasa
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5.3 Processing of Real SAR Data A s
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squâre pixel rvith clir¡ension of
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Aziurutì (n Þ !d !D gc Figule 5.1
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(n 5 F Þ tq Figu.e 5.11: Reconst.u
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over tlìe 2.4 inches as shol¡l i'
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Ø Þ :J m (a) (b) ^a ctl _= a"r ro
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Chapter 6 SAR fmage Enhancement for
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1) hoiv can the tlends of lineament
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6.2 Determination of Geological Str
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Coolclinates for the image space an
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Figure 6.2: Point, lines, and hyper
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scatteter (e.g. coller leflectols,
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Figure 6.5: CCRS's airboure C-band
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C-l¡ancl SAR irnagery ovel this al
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Figure 6.8: Radon transform of ailb
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in the irnage space ancl the Iine i
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ERS- 1 N U 0 rl 0o |lO + ,¡l r.l p
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6.2,3 Correlation Using The Radon T
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Since the inside of the squale blac
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Figule 6.12: Model test for correla
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thlough the Radon tlansfolm is shor
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Figure 6.15: Airborne C-band SAR da
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distinct points can be cliscelnerl
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Figure 6.18: Correlation output thr
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6.3 Merging of Multiple SAR Image D
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in Figure 6.19 tvhich is a clilect
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Figure 6.20: Additive irnages rvith
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Figule 6.22: Subtractive images rvi
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(1) select a clirection to be enhan
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Figure 6.24: Lnage obtained through
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6.3.4 Principal Components Analysis
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Table 6.2: Con'elation coeffrcielt
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Figure 6.27: The PCA frrst componen
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the geological surface lilearrent f
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ackscatte.i'g coefficiert can be cl
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Appendices A. Derivation of Forward
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B. Derivation of Inversion Formula
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C. Derivation using the Method of S
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F[eferences [1] Ahmed, S., \Vallen,
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[20] Curlis, J.D,, Flost, V.S., Del
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[43] Holn, R., 1988, E-SAR - The ex
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[65] Lotrelrl, O., 1990, Dopplel ce
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[87] Pye, 8.G., Nalch'ett,4.J., anc
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[111] \,Vu, C., Balkan,8., I(arplus
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