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Aftel nrultiplying Eq.(8..2) by e-i2,to./" ancl replacing c.r by Eq.(8..8), the trvo-dirnensional inverse Fourier transforrn becomes oi,"@,4) - -4\/2 1 " ll n" " ",",0 # I I ffi.;¡o y/*i4*2" . o Q",irta + *") "i$"c+kan) dk' dtc,, (8..4) Notice that the restoled irnage oi"(2,7) does not provide aly informatiol for less than the urinimuln slant-range 40, and therefor.e that tlie image is leqnilecl to be explessecl by a shift varial¡le q' : n - 46. The final ilversion follnula then becorres oi.@,q') - - nuú;s """hj¡, I I Æ",n0(*,-r/r",+F') . ø (n,,irraa) ";tt""+*nn') dk,'Ik, (8..5) rvhich is Ðq. (+.32) in Sectior 4.4.
C. Derivation using the Method of Stationary Phase The Fouliel tlansforll of Eq.(3.51) il Section 3.2.3 with r.espect to the azirnuth ¿ can l¡e obtainecl througli tlle rnethod of stationaly phase as follorvs. The Fouliel transforrn of Ðq.(3.51) is given as s(k,,t;rt): I u (, -u, - *) "* {-oT (, - J\c #)} "-,n". a, (c 1) The lnethocl of stationat.y phase is surnrnarizecl as I /(O : J t@) ."v {i(eþ:)} h, € > o - "i' I 2r fllz ¡+ tdt6nl e(26) exp{t{p('o)} (c.2) (c..3) wlrele a6 satisfies p'(xo):0 (Car¡ier et al. [15]). Comparing Eq.(C..1) rvith Eq.(C..2), we can set t(¿):ó (,-?,-"\ \ c cn/ p(r): - (T,.+*- -.,) L* ç'(¿):fr"+-a¿ '^n ç"(r\:! ^n The ø6 satisfyirìg p'(r0) :0 is estimatect frorn Eq.(C..6) such as Àn. - 4tr- (c..4) (c..5) (c..6) (c..7) (c..8) 178
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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
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List of Notations cr squint angle P
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tist of Abbreviatíons SAR Syntheti
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The objectives of this thesis rnay
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Ground Range l;l 2 sin0 Figure 1.2:
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ol'cler to evaluate its full aclvan
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algolithrn extlacts the complex bac
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successful as expected. Thele ale,
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eú ø1. [103]). Similal clevelopme
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aerial plìotogl'aphy ovel the area
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2.2 Spaceborne SAR Systems 1) SEASA
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tlie basis of a distinctive dlainag
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set fol selectecl aleas, useful for
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3) ERS-I The first European rernote
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Table 2.4: ERS-I Ðieterle [104]).
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Table 2.6: ERS-1 SAR pelfolmance re
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Table 2.7: JtrRS-1 olbit pararnetel
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Table 2.9: Chalactelistics of OPS o
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Table 2.11: Specifications of Racla
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Chapten 3 Review of Digital SAR Pro
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,I Figule 3.1: Raclar' L¡earn geom
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I L-=J}"no Figure 3.2: Geouretry fo
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vhich is the clistance across the a
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vlrere ø6 is a angular center fi'e
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à1 äl (a) /1T. or^l - r+ (b) I à
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a,pploxirnated by l2p sinl(I - ltl)
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-s(cu) is rewlitten as s@¡ - !"-,r
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cliscussecl later il this sectio¡r
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Ïon = _2 (V(ro) .V(¿o)+ R(ro) .A(
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: Range Walk : Range Curvatule : Ra
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olbital SAR is given by Ion = -'#{t
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is constant cluling the receiving p
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a at f¡r
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'rvith a foulula developed il this
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Chapter 4 Theoretical Development 4
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developed and cliscussed by several
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vhere u (r,ro; u) : I U 1r,ro,t)e-i
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wheÌe k':frf a¡cl lc -_ uf us ant
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4) there is relative motion of ante
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o =løo, 0, 0) Figure 4.1: Schemati
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elorv that sulface. In genetal, sul
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4.4 The Inversion The equation Eq.(
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*'here % is a platfolrn velocity an
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The trq.(a.36) cannot be used dilec
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vhele Àl is a tvavenurnbel collesp
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2-D FFT o(,b,;ø) Intelpolation in
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¡nE 0$r-sEc, ¡3 I IrlÊ [18- 5EC
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5.2 Digital Simulation Digital sirn
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Table 5.2: Moclel palametels fol di
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signal and the leconstructe
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(3 È. e tc o) o -tl a Slant Range
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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,
Page 145 and 146: Figure 6.5: CCRS's airboure C-band
Page 147 and 148: C-l¡ancl SAR irnagery ovel this al
Page 149 and 150: Figure 6.8: Radon transform of ailb
Page 151 and 152: in the irnage space ancl the Iine i
Page 153 and 154: ERS- 1 N U 0 rl 0o |lO + ,¡l r.l p
Page 156 and 157: 6.2,3 Correlation Using The Radon T
Page 158 and 159: Since the inside of the squale blac
Page 160 and 161: Figule 6.12: Model test for correla
Page 162 and 163: thlough the Radon tlansfolm is shor
Page 164 and 165: Figure 6.15: Airborne C-band SAR da
Page 166 and 167: distinct points can be cliscelnerl
Page 168 and 169: Figure 6.18: Correlation output thr
Page 170 and 171: 6.3 Merging of Multiple SAR Image D
Page 172 and 173: in Figure 6.19 tvhich is a clilect
Page 174 and 175: Figure 6.20: Additive irnages rvith
Page 176 and 177: Figule 6.22: Subtractive images rvi
Page 178 and 179: (1) select a clirection to be enhan
Page 180 and 181: Figure 6.24: Lnage obtained through
Page 182: 6.3.4 Principal Components Analysis
Page 185 and 186: Table 6.2: Con'elation coeffrcielt
Page 187 and 188: Figure 6.27: The PCA frrst componen
Page 189 and 190: the geological surface lilearrent f
Page 191 and 192: ackscatte.i'g coefficiert can be cl
Page 193 and 194: Appendices A. Derivation of Forward
Page 195: B. Derivation of Inversion Formula
Page 199 and 200: F[eferences [1] Ahmed, S., \Vallen,
Page 201 and 202: [20] Curlis, J.D,, Flost, V.S., Del
Page 203 and 204: [43] Holn, R., 1988, E-SAR - The ex
Page 205 and 206: [65] Lotrelrl, O., 1990, Dopplel ce
Page 207 and 208: [87] Pye, 8.G., Nalch'ett,4.J., anc
Page 209: [111] \,Vu, C., Balkan,8., I(arplus
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