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90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
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rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse
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%%EndProcSet
%%BeginFont: CMR5
%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
/UniqueID 5000788 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 8 /braceleftbig put
dup 9 /bracerightbig put
dup 12 /vextendsingle put
dup 16 /parenleftBig put
dup 17 /parenrightBig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 20 /bracketleftbigg put
dup 21 /bracketrightbigg put
dup 26 /braceleftbigg put
dup 27 /bracerightbigg put
dup 40 /braceleftBigg put
dup 41 /bracerightBigg put
dup 56 /bracelefttp put
dup 57 /bracerighttp put
dup 58 /braceleftbt put
dup 59 /bracerightbt put
dup 60 /braceleftmid put
dup 61 /bracerightmid put
dup 88 /summationdisplay put
dup 90 /integraldisplay put
dup 104 /bracketleftBig put
dup 105 /bracketrightBig put
dup 110 /braceleftBig put
dup 111 /bracerightBig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI5
%!PS-AdobeFont-1.1: CMMI5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{37 -250 1349 750}readonly def
/UniqueID 5087380 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 82 /R put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
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016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
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D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
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364A65B9F1F9C6416198FB016FC8456DEEFED46BF4E1F873527AF52C13078ABF
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96A6D048ACFEF549BBCE51A9EE6CE333704CFD95926DFC740F5A6896D22EBB27
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32E05B3C998C9D89CD66E4DAB5422D01B386769A45984EA2B3250786533E85CB
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cleartomark
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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2DB0E39997F264D408BD076F65A50E7E94C9C88D849AB2E92005CFA316ACCD91
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cleartomark
%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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end
%%EOF

%%EndDocument
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(transducer:)e(\(a\))g(lateral)2143 2191 y(vie)o(w;)23
b(\(b\))f(a)h(pair)h(of)e(elements.)p 2044 2320 V 2143
2567 a Fq(W)-7 b(e)31 b(de\002ne)f(the)g(transducer)e
Fn(f)9 b Fq(-number)27 b(as)k Fn(n)3535 2579 y Fm(f)3619
2567 y Fp(=)40 b Fn(z)3763 2579 y Fj(0)3800 2567 y Fn(=)p
Fp(\(2)p Fn(a)p Fp(\))p Fq(,)2044 2667 y(where)18 b Fn(a)i
Fq(is)g(the)f(transducer)e(aperture)h(radius.)g(In)h(the)g
Fr(F)-5 b(r)m(esnel)20 b(ap-)2044 2766 y(pr)l(oximation)i
Fp(\()p Fn(a)2546 2736 y Fj(2)2612 2766 y Fo(\034)28
b Fn(z)2766 2736 y Fj(2)2762 2787 y(0)2803 2766 y Fp(\))c
Fq(one)e(can)h(sho)n(w)g(that)h(the)f(v)o(elocity)f(po-)2044
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(the)g(pair)f(of)h(ele-)2044 2966 y(ments)20 b(in)g(the)g(sector)g
(array)g(is)h(gi)n(v)o(en)e(by)h(Eq.)f(\(18\).)2143 3067
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y Fq(.)21 b(One)g(can)f(sho)n(w)-5 b(,)20 b(from)g(Eq.)g(\(18\),)g
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4018 y Fe(\022)2812 4079 y Fn(\031)p 2799 4116 76 4 v
2799 4192 a(N)2904 4135 y Fp(+)2997 4079 y(2)p Fn(\031)s(n)p
2997 4116 142 4 v 3030 4192 a(N)3167 4135 y Fo(\000)18
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v 3609 4192 a(N)3718 4043 y Fe(\021)3782 4135 y Fn(:)69
b Fq(\(20\))2143 4357 y(By)20 b(setting)f Fn(r)26 b Fp(=)d(0)c
Fq(in)g(Eq.)g(\(18\),)f(the)h(v)o(elocity)f(potential)h(in)g(the)2044
4457 y(transducer)f(axis)j(\()p Fn(z)t Fq(-direction\))c(can)j(be)g
(written)g(as)2204 4660 y Fp(^)2194 4682 y Fn(\036)2243
4694 y Fm(n)2288 4682 y Fp(\()p Fn(z)t Fp(\))j(=)2521
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4663 76 4 v 3120 4739 a Fn(z)3207 4682 y Fo(\000)18 b
Fp(1)3332 4590 y Fe(\021)3381 4565 y(\025)2414 4898 y
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Fn(j)5 b(k)2846 4910 y Fj(0)2897 4781 y Fe(\024)2941
4898 y Fn(z)22 b Fp(+)3095 4842 y Fn(a)3139 4812 y Fj(2)p
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Fp(\()p Fn(x)p Fp(\))24 b(=)f(sin\()p Fn(\031)s(x)p Fp(\))p
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b(consider)e(a)h(sector)g(array)g(transducer)e(operating)h(with)2044
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g(case,)g(the)g(elements)p eop end
%%Page: 6 6
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b(and)e(\(b\))h(in)f(depth.)p -112 3330 V -112 3528 a
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y Fm(a)252 3628 y Fq(or)i Fn(!)390 3640 y Fm(b)423 3628
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3739 y Fm(a)796 3727 y Fq(the)i(other)g(half)g(is)h(at)g(frequenc)o(y)c
Fn(!)1802 3739 y Fm(b)1835 3727 y Fq(.)-112 3827 y(The)i(amplitude)f
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Fm(a)p Fj(\))827 4223 y(2)p Fm(n)p Fd(\000)p Fj(1)1010
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624 4464 y Fp(^)613 4486 y Fn(\036)662 4443 y Fj(\()p
Fm(a)p Fj(\))662 4495 y Fm(n)788 4486 y Fq(and)951 4464
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4585 y(changing)20 b Fn(!)267 4597 y Fj(0)328 4585 y
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b(in)g(w)o(ater)g(\()p Fn(c)2692 1733 y Fj(0)2782 1721
y Fp(=)52 b(1500)12 b Fq(m/s\).)36 b(The)g(element)g(pairs)g(in)2044
1821 y(the)22 b(transducer)e(are)i(dri)n(v)o(en)f(alternately)g(with)h
(frequencies)f Fn(f)3882 1833 y Fm(a)3948 1821 y Fp(=)2044
1920 y(2)14 b(MHz)23 b(+)g(5)14 b(kHz)28 b Fq(and)e Fn(f)2801
1932 y Fm(b)2871 1920 y Fp(=)35 b(2)14 b(MHz)24 b Fo(\000)f
Fp(5)14 b(kHz)o Fq(.)28 b(The)f(PSF)h(w)o(as)2044 2020
y(numerically)33 b(e)n(v)n(aluated)g(in)j(M)t Ff(A)m(T)t(L)t(A)t(B)h
Fq(6.5.)d(Plots)h(of)f(the)h(PSF)2044 2120 y(absolute)28
b(v)n(alue)f(in)i(lateral)g(direction)e(and)h(in)h(depth)e(are)i(sho)n
(wn)2044 2219 y(in)37 b(Figure)g(4)g(for)f Fn(N)64 b
Fp(=)54 b(8)p Fn(;)14 b Fp(16)p Fq(.)36 b(F)o(or)h Fn(N)63
b Fp(=)54 b(8)37 b Fq(the)g(sidelobes)2044 2319 y(are)26
b(belo)n(w)g Fo(\000)p Fp(15)p Fn(:)p Fp(5)12 b Fq(dB)26
b(and)g(the)h(transv)o(erse)e(resolution)g(is)i(about)2044
2418 y Fp(1)p Fn(:)p Fp(6)15 b Fo(\002)h Fp(1)p Fn(:)p
Fp(6)d Fq(mm.)20 b(The)f(depth-of-\002eld)e(of)i(the)h(system)g(is)g
Fp(13)p Fn(:)p Fp(5)13 b Fq(mm.)2143 2519 y(F)o(or)39
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2045 y Fl(Figure)23 b(5.)g(Theoretical)g(and)g(e)o(xperimental)g(PSFs.)
p -112 2124 V -112 2302 V 712 4799 a @beginspecial 14
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showpage
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end
%%EOF

%%EndDocument
 @endspecial -13 5019 a(Figure)f(6.)h(Ima)o(g)q(e)f(of)g(the)g
(measured)h(PSF)-8 b(.)23 b(The)f(contour)f(lines)i(are)g(the)f
(theoretical)g(PSF)h(at)f Fo(\000)p Fp(40)13 b Fl(dB.)22
b(The)g(angle)-13 5118 y(between)g(the)h(peak)g(of)g(tw)n(o)f
(consecutive)h(sidelobes)g(is)g Fn(\031)s(=)p Fp(4)14
b Fl(radians.)p -112 5250 V eop end
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userdict /end-hook known{end-hook}if
%%EOF