7# IH H H H H H.JHxHxHxHxHHHHxHxI. IN/I*IH II}III4IIIIII RADAR BACKSCATTER MEASUREMENTS Radar backscatter (also known as radar cross section or RCS) is measured in units of area (i.e. square meters) The radar cross section of an object is often related to its actual size, as seen by the radar. For example, the RCS of a sphere is pr2, where r is the radius of the sphere Normalized radar cross section, s o, is given by: s o = 10log10 (RCS/A) where A is the area of the image pixel Units are decibel (dB) Example: for an object with an RCS of 10m2, and an image pixel size of 10mx10m, s o = -10dB. Typical values of s o for natural surfaces are from + 5dB to - 40 dB + 5dB would be a very bright feature in a radar image - 40 dB would be a very dark feature in a radar image  BACKSCATTER IN RADAR IMAGES When looking at a radar image, there are several explanations for the appearance of high and low backscatter: Very high backscatter - Terrain slopes towards radar (above -5dB) - Radar looking almost straight down - Very rough surface - Flooded forest - Man-made objects High backscatter - Rough surface (-10 to 0dB) - Dense vegetation, e.g. forest Moderate backscatter - Moderately rough surface (-20 to -10dB) - Medium level of vegetation, e.g. shrubs, agricultural crops Low backscatter - Terrain slopes away from radar (below -20dB) - Smooth surface, e.g. water, road surface - Very dry material, e.g. sand in an arid desert Caution: these are just rules-of-thumb Many exceptions are possible and have been found by scientists analyzing radar image data  DIFFERENT POLARIZATIONS With different polarizations on transmit and receive, we can measure different polarizations: sHHo - Horizontal transmit, Horizontal receive sVVo - Vertical transmit, Vertical receive sHVo - Horizontal transmit, Vertical receive fHHVV - Phase difference between HH and VV measurements rHHVV - Correlation between HH and VV measurements The fHHVV phase difference is measured in degrees (i.e. not dB) and is therefore number between -180 and +180 degrees. The rHHVV correlation coefficient is a measure of how alike the HH and VV scatterers are, and is given as a number between 0 and 1. rHHVV = 0 means the HH and VV scatterers are different rHHVV = 1 means the HH and VV scatterers are the same  WHAT CHANGES RADAR BACKSCATTER? Backscatter can change if we use a different: - polarization - frequency - time of observation - track angle (angle of radar track compared to True North)  - incidence angle (angle of radar wave at earth's surface, compared with local vertical)  Note that by Pythagoras cos(q i) = h / R  LEVELS OF RADAR BACKSCATTER Here is a summary, indicating potential explanations for high and low backscatter in a radar image: Backscatter range Possible Explanation Very high backscatter - Terrain slopes towards radar (above -5dB) - Radar looking almost straight down - Very rough surface - Flooded forest - Man-made objects High backscatter - Rough surface (-10 to 0dB) - Dense vegetation, e.g. forest Moderate backscatter - Moderately rough surface (-20 to -10dB) - Medium level of vegetation, e.g. shrubs, agricultural crops Low backscatter - Terrain slopes away from radar (below -20dB) - Smooth surface, e.g. water, road surface - Very dry material, e.g. sand in an arid desert These are, of course, just rules-of-thumb, to which many exceptions are possible and have been found by scientists analyzing radar image data. There is often considerable overlap between the backscatter ranges, so it might be difficult to differentiate between forest and shrubs, using backscatter alone. u@5tD5fD5VC CddPro C Q*Y-t X QYt XP  "Af##### #######  C )e@)e,-.{/z{0yz1xy2wx3vw5uv6tu7st8rs:qr;pq<op=no>mn?jm@ej "@e## ###P "f##### #######  C eeggjjmmnnooppqqrrs st tu uv vw wxxyyzz{{~~e "e## ###P  "*###########(# C"*#####( Q, X 1i+ 0h," currentpoint /legm_top exch def /legm_left exch def " currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def &/legm_wide legm_wide 2 mul 19 div def %/legm_high legm_high 2 mul 4 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 0 3 lineto 18 3 lineto save_matrix setmatrix clip gsave ddProd6dPro,"- grestore """-,-,-,"<;<;<;"KJKJKJ"ZYZYZY"ihihih"xwxwxw""""""""""ddPro grestore  CpddProP "#### C"#P "###########(# C"#####( A^-p H"W currentpoint /legm_top exch def /legm_left exch def "!_ currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def %/legm_wide legm_wide 2 mul 8 div def %/legm_high legm_high 2 mul 8 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 4 1 lineto 7 2 lineto 7 5 lineto 4 7 lineto 0 7 lineto 0 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4W ^WYY]]^]^ W]"1o grestore "WTTT"X"Y"ZUUUUUU"[***"\"]ddPro grestore  Cp*W ^W[^^ [ WWWddProP "W############ C######""W currentpoint /legm_top exch def /legm_left exch def "*_ currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def %/legm_wide legm_wide 2 mul 8 div def %/legm_high legm_high 2 mul 8 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 4 1 lineto 7 2 lineto 7 5 lineto 4 6 lineto 0 7 lineto 0 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4"W)^"W\#\]$]^(Z^)WZ":o grestore ""WTTT""X""Y""ZUUUUUU""[***""\""]ddPro grestore  Cp*"W)^"W"[$^'^([)W"W"WddProP ""W############ C######" \ currentpoint /legm_top exch def /legm_left exch def "#o currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def ""^ currentpoint )/legm_radius exch legm_top sub 2 div def Llegm_left sub 2 div dup legm_radius gt {/legm_radius exch def} {pop} ifelse gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def 9legm_wide legm_left add legm_high legm_top add translate Alegm_wide legm_left add neg legm_high legm_top add neg translate ,/legm_high legm_high 2 mul legm_top add def -/legm_wide legm_wide 2 mul legm_left add def *legm_left legm_radius add legm_top moveto Hlegm_wide legm_top legm_wide legm_top legm_radius add legm_radius arcto 4 {pop} repeat Jlegm_wide legm_high legm_wide legm_radius sub legm_high legm_radius arcto 4 {pop} repeat Jlegm_left legm_high legm_left legm_high legm_radius sub legm_radius arcto 4 {pop} repeat Hlegm_left legm_top legm_left legm_radius add legm_top legm_radius arcto 4 {pop} repeat save_matrix setmatrix clip gsave ddProd6dPro- \#o"8t grestore " U "U"V&f&f&f"V323232"W???"XLLL"XYYY"Yfefefe"Zs2s2s2"Z"[ˌˌ"\"\eee"]111"^"^"_ٗٗٗ"`ddd"`111"a"bddPro grestore  C @ \#o H"* currentpoint /legm_top exch def /legm_left exch def ". currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def &/legm_wide legm_wide 2 mul 19 div def %/legm_high legm_high 2 mul 4 div def legm_left legm_top translate legm_wide legm_high scale 0 3 moveto 0 0 lineto 18 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4*.*+,-."B grestore "*"*"*-,-,-,"*<;<;<;"*KJKJKJ"*ZYZYZY"*ihihih"*xwxwxw"*"*"*"*"*"*"*"*"*"*ddPro grestore  Cp*..**.ddProP ".#### C".#"f"-f1!81"$8P "!########  C !####P "########  C$####P "########  C$####P ""########  C$"$"#$####P "$######  C %&####P "'########  C %'####P # 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80/.P@  0@0@@ `@@ pP@  @ `@?@  ?00  ddPro8 XG,  Helvetica .+[Sր) P#) A@ ) C\`) E) B ) O) R ) N`) EA)  %)I `)M) A ) G) I)N) G)  z`)R) A) D ) A`) R) - )C ddProH '= (7S) I)R) -)C) E@) D5tD5fD5VC CddPro C Q*Y-t X QYt XP  "Af##### #######  C )e@)e,-.{/z{0yz1xy2wx3vw5uv6tu7st8rs:qr;pq<op=no>mn?jm@ej "@e## ###P "f##### #######  C eeggjjmmnnooppqqrrs st tu uv vw wxxyyzz{{~~e "e## ###P  "*###########(# C"*#####( Q, X 1i+ 0h," currentpoint /legm_top exch def /legm_left exch def " currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def &/legm_wide legm_wide 2 mul 19 div def %/legm_high legm_high 2 mul 4 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 0 3 lineto 18 3 lineto save_matrix setmatrix clip gsave ddProd6dPro,"- grestore """-,-,-,"<;<;<;"KJKJKJ"ZYZYZY"ihihih"xwxwxw""""""""""ddPro grestore  CpddProP "#### C"#P "###########(# C"#####( A^-p H"W currentpoint /legm_top exch def /legm_left exch def "!_ currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def %/legm_wide legm_wide 2 mul 8 div def %/legm_high legm_high 2 mul 8 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 4 1 lineto 7 2 lineto 7 5 lineto 4 7 lineto 0 7 lineto 0 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4W ^WYY]]^]^ W]"1o grestore "WTTT"X"Y"ZUUUUUU"[***"\"]ddPro grestore  Cp*W ^W[^^ [ WWWddProP "W############ C######""W currentpoint /legm_top exch def /legm_left exch def "*_ currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def %/legm_wide legm_wide 2 mul 8 div def %/legm_high legm_high 2 mul 8 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 4 1 lineto 7 2 lineto 7 5 lineto 4 6 lineto 0 7 lineto 0 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4"W)^"W\#\]$]^(Z^)WZ":o grestore ""WTTT""X""Y""ZUUUUUU""[***""\""]ddPro grestore  Cp*"W)^"W"[$^'^([)W"W"WddProP ""W############ C######" \ currentpoint /legm_top exch def /legm_left exch def "#o currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def ""^ currentpoint )/legm_radius exch legm_top sub 2 div def Llegm_left sub 2 div dup legm_radius gt {/legm_radius exch def} {pop} ifelse gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def 9legm_wide legm_left add legm_high legm_top add translate Alegm_wide legm_left add neg legm_high legm_top add neg translate ,/legm_high legm_high 2 mul legm_top add def -/legm_wide legm_wide 2 mul legm_left add def *legm_left legm_radius add legm_top moveto Hlegm_wide legm_top legm_wide legm_top legm_radius add legm_radius arcto 4 {pop} repeat Jlegm_wide legm_high legm_wide legm_radius sub legm_high legm_radius arcto 4 {pop} repeat Jlegm_left legm_high legm_left legm_high legm_radius sub legm_radius arcto 4 {pop} repeat Hlegm_left legm_top legm_left legm_radius add legm_top legm_radius arcto 4 {pop} repeat save_matrix setmatrix clip gsave ddProd6dPro- \#o"8t grestore " U "U"V&f&f&f"V323232"W???"XLLL"XYYY"Yfefefe"Zs2s2s2"Z"[ˌˌ"\"\eee"]111"^"^"_ٗٗٗ"`ddd"`111"a"bddPro grestore  C @ \#o H"* currentpoint /legm_top exch def /legm_left exch def ". currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def &/legm_wide legm_wide 2 mul 19 div def %/legm_high legm_high 2 mul 4 div def legm_left legm_top translate legm_wide legm_high scale 0 3 moveto 0 0 lineto 18 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4*.*+,-."B grestore "*"*"*-,-,-,"*<;<;<;"*KJKJKJ"*ZYZYZY"*ihihih"*xwxwxw"*"*"*"*"*"*"*"*"*"*ddPro grestore  Cp*..**.ddProP ".#### C".#"f"-f1!81"$8P "!########  C !####P "########  C$####P "########  C$####P ""########  C$"$"#$####P "$######  C %&####P "'########  C %'####P # ###################"####  CT&"$%&"################" c"8c" Y currentpoint /legm_top exch def /legm_left exch def "#p currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def 9legm_wide legm_left add legm_high legm_top add translate */x_proportion legm_wide legm_high div def x_proportion 1 scale 0 0 legm_high 0 360 arc save_matrix setmatrix clip gsave ddProd6dPro4 X#q [n!X[nq"X[nq#[n"8q grestore " Y " ZEEE" ["""" \..." ]:.:.:." ^EEE" _QsQsQs" `]]]" ahhh" bt\t\t\" c" d" eDDD" f" g" h---" i" jrrr" k" l" m[[[" n" oddPro grestore  C P Y#p X1!81!#81"$8 1 8 1(* 8P "*o########  C (*n1*o.no1n ####"*|P "o########  C 4mmmnnoo ####"|P "########  C ( ####"P "+########  C (+1+.1 ####"+ 1u${ 8 1z$ 8 1~$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1#u){ 8 1#z) 8 1#~) 8 1#) 8 1#) 8 1#) 8 1#) 8 1#) 8 1#) 8 1ux 8 1wz 8 1z} 8 1| 8 1~ 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1)u+ 8 1)+ 8 1)+ 8Q!XQ"'X UUUU1 # 80/.P@  0@0@@ `@@ pP@  @ `@?@  ?00  ddPro8 XG,  Helvetica .+[Sր) P#) A@ ) C\`) E) B ) O) R ) N`) EA)  %)I `)M) A ) G) I)N) G)  z`)R) A) D ) A`) R) - )C ddProH '= (7S) I)R) -)C) E@) D5tD5fD5VC CddPro C Q*Y-t X QYt XP  "Af##### #######  C )e@)e,-.{/z{0yz1xy2wx3vw5uv6tu7st8rs:qr;pq<op=no>mn?jm@ej "@e## ###P "f##### #######  C eeggjjmmnnooppqqrrs st tu uv vw wxxyyzz{{~~e "e## ###P  "*###########(# C"*#####( Q, X 1i+ 0h," currentpoint /legm_top exch def /legm_left exch def " currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def &/legm_wide legm_wide 2 mul 19 div def %/legm_high legm_high 2 mul 4 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 0 3 lineto 18 3 lineto save_matrix setmatrix clip gsave ddProd6dPro,"- grestore """-,-,-,"<;<;<;"KJKJKJ"ZYZYZY"ihihih"xwxwxw""""""""""ddPro grestore  CpddProP "#### C"#P "###########(# C"#####( A^-p H"W currentpoint /legm_top exch def /legm_left exch def "!_ currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def %/legm_wide legm_wide 2 mul 8 div def %/legm_high legm_high 2 mul 8 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 4 1 lineto 7 2 lineto 7 5 lineto 4 7 lineto 0 7 lineto 0 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4W ^WYY]]^]^ W]"1o grestore "WTTT"X"Y"ZUUUUUU"[***"\"]ddPro grestore  Cp*W ^W[^^ [ WWWddProP "W############ C######""W currentpoint /legm_top exch def /legm_left exch def "*_ currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def %/legm_wide legm_wide 2 mul 8 div def %/legm_high legm_high 2 mul 8 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 4 1 lineto 7 2 lineto 7 5 lineto 4 6 lineto 0 7 lineto 0 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4"W)^"W\#\]$]^(Z^)WZ":o grestore ""WTTT""X""Y""ZUUUUUU""[***""\""]ddPro grestore  Cp*"W)^"W"[$^'^([)W"W"WddProP ""W############ C######" \ currentpoint /legm_top exch def /legm_left exch def "#o currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def ""^ currentpoint )/legm_radius exch legm_top sub 2 div def Llegm_left sub 2 div dup legm_radius gt {/legm_radius exch def} {pop} ifelse gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def 9legm_wide legm_left add legm_high legm_top add translate Alegm_wide legm_left add neg legm_high legm_top add neg translate ,/legm_high legm_high 2 mul legm_top add def -/legm_wide legm_wide 2 mul legm_left add def *legm_left legm_radius add legm_top moveto Hlegm_wide legm_top legm_wide legm_top legm_radius add legm_radius arcto 4 {pop} repeat Jlegm_wide legm_high legm_wide legm_radius sub legm_high legm_radius arcto 4 {pop} repeat Jlegm_left legm_high legm_left legm_high legm_radius sub legm_radius arcto 4 {pop} repeat Hlegm_left legm_top legm_left legm_radius add legm_top legm_radius arcto 4 {pop} repeat save_matrix setmatrix clip gsave ddProd6dPro- \#o"8t grestore " U "U"V&f&f&f"V323232"W???"XLLL"XYYY"Yfefefe"Zs2s2s2"Z"[ˌˌ"\"\eee"]111"^"^"_ٗٗٗ"`ddd"`111"a"bddPro grestore  C @ \#o H"* currentpoint /legm_top exch def /legm_left exch def ". currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def &/legm_wide legm_wide 2 mul 19 div def %/legm_high legm_high 2 mul 4 div def legm_left legm_top translate legm_wide legm_high scale 0 3 moveto 0 0 lineto 18 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4*.*+,-."B grestore "*"*"*-,-,-,"*<;<;<;"*KJKJKJ"*ZYZYZY"*ihihih"*xwxwxw"*"*"*"*"*"*"*"*"*"*ddPro grestore  Cp*..**.ddProP ".#### C".#"f"-f1!81"$8P "!########  C !####P "########  C$####P "########  C$####P ""########  C$"$"#$####P "$######  C %&####P "'########  C %'####P # ###################"####  CT&"$%&"################" c"8c" Y currentpoint /legm_top exch def /legm_left exch def "#p currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def 9legm_wide legm_left add legm_high legm_top add translate */x_proportion legm_wide legm_high div def x_proportion 1 scale 0 0 legm_high 0 360 arc save_matrix setmatrix clip gsave ddProd6dPro4 X#q [n!X[nq"X[nq#[n"8q grestore " Y " ZEEE" ["""" \..." ]:.:.:." ^EEE" _QsQsQs" `]]]" ahhh" bt\t\t\" c" d" eDDD" f" g" h---" i" jrrr" k" l" m[[[" n" oddPro grestore  C P Y#p X1!81!#81"$8 1 8 1(* 8P "*o########  C (*n1*o.no1n ####"*|P "o########  C 4mmmnnoo ####"|P "########  C ( ####"P "+########  C (+1+.1 ####"+ 1u${ 8 1z$ 8 1~$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1#u){ 8 1#z) 8 1#~) 8 1#) 8 1#) 8 1#) 8 1#) 8 1#) 8 1#) 8 1ux 8 1wz 8 1z} 8 1| 8 1~ 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1)u+ 8 1)+ 8 1)+ 8Q!XQ"'X UUUU1 # 80/.P@  0@0@@ `@@ pP@  @ `@?@  ?00  ddPro8 XG,  Helvetica .+[Sր) P#) A@ ) C\`) E) B ) O) R ) N`) EA)  %)I `)M) A ) G) I)N) G)  z`)R) A) D ) A`) R) - )C ddProH '= (7S) I)R) -)C) E@) D, ddPro "^p @@#  wwwwA^|n H@@@ wwwwq\{p\bpj{\ p\{p\bpj{\@ "Fg### ##### f3f3  f3f3GYfkGfhHefIdeJcdKbcLabhiM`aN_`O^_P]^Q\]ijR[\SZ[TYZVYZjkZjk[ij\Z[hi]gh^fg_ef`ceabcb[\abc`ad_`e^_f\^ "Ef# ## "^}########  Y^l}YkmZjkmp[ijpt\hitx]ghx{^fg{}_ef|}`de{|acdz{bbcyzcabxyd`awxe_`vwf^_uvg^_tuh_bstibfrsjfjqrkjmpqlmp "]|### "Fg######## ww  wwFg]}FghGgjHjmImoJoqKqtLhitvMvxPxyQijSyzUz{VjkX{|YkmZmr[rv|}\v{]{} "Ef###"U_@@# wwwwAGAWX H@@@ wwwwqE@YZEELZYUS@EE pE@YZEELZYUS@EE@@@"EE+gg UUUUQ_^g X@@@ UUUUqjSurldmgnmooppqqrrrrsrtruqupunumukuetbtas^r[qXpWpVoUnTmSlSlSjTjUjWjXj[kald pjSurldmgnmooppqqrrrrsrtruqupunumukuetbtas^r[qXpWpVoUnTmSlSlSjTjUjWjXj[kald@@@"ldgg Ar]ug H@@@ qo`xdobpdxbx`ob po`xdobpdxbx`ob@ "ye######## ####@@#`GX{Z@@@p6hSsslSkTiXh\h`hcifjimmqrss@d dPro q:B::>B:"H6ddPro d dPro q4<8<848 "F8"E8"38"!8ddPro ddPro8 kc 0A,  Helvetica .+3 N@@ " =/_^` $CMZ@@@p62&D9D&B&?':)7+6,5-31242729@^P@ ddPro ", @@#::/ wwwwA1H H@@@ wwwwq1J@ J;1@ p1J@ J;1@@ "######## f3f3  f3f34) "!"$"$%%&%&(*&',-'(/01 ()2 $3$'4') "### "2##### ###   %471301/0./-.34,-+,*+)*45()'(&' %&56"%&$67&&'(67)56*'(45+34,23-()12.01//00./1)*-.2,-3+,4*+ "1## # 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H@@@ wwwwq*D*5D :* p*D*5D :*@@@"*% ))J UUUUQ"/C8 X@@@ UUUUq'*??01/2-4+6*9):(;'='='>'?'?(?*?+?,>/=4:6895=1>/?.?-?,?*?*?*>*<*;+:+8,3/01 p'*??01/2-4+6*9):(;'='='>'?'?(?*?+?,>/=4:6895=1>/?.?-?,?*?*?*>*<*;+:+8,3/01@@@"01))J A437= H@@@ q249<258<9;3425 p249<258<9;3425@ "5>######## ####@@#NN2` )?RZ@@@p6&*???*=*:*5+1-0..0+4)7'<&?@ "F######################################################################### "F###########################################################";>ZY#@@##ss`^Z@@@p6r~~|yvtsrrrrs@ ddProHTsʂ u, Symbol .+q ddPro0,  Helvetica + id dPro  q6D%6"D%D"D6""D"ddPro ddPro8Ts2 bt* (ohd dPro  q%""%""r" ddPro --ddPro8{ (lUR ]Pre]Pre]Pre8|;8p Ah5tD5fD5VC CddPro C Q*Y-t X QYt XP  "Af##### #######  C )e@)e,-.{/z{0yz1xy2wx3vw5uv6tu7st8rs:qr;pq<op=no>mn?jm@ej "@e## ###P "f##### #######  C eeggjjmmnnooppqqrrs st tu uv vw wxxyyzz{{~~e "e## ###P  "*###########(# C"*#####( Q, X 1i+ 0h," currentpoint /legm_top exch def /legm_left exch def " currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def &/legm_wide legm_wide 2 mul 19 div def %/legm_high legm_high 2 mul 4 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 0 3 lineto 18 3 lineto save_matrix setmatrix clip gsave ddProd6dPro,"- grestore """-,-,-,"<;<;<;"KJKJKJ"ZYZYZY"ihihih"xwxwxw""""""""""ddPro grestore  CpddProP "#### C"#P "###########(# C"#####( A^-p H"W currentpoint /legm_top exch def /legm_left exch def "!_ currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def %/legm_wide legm_wide 2 mul 8 div def %/legm_high legm_high 2 mul 8 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 4 1 lineto 7 2 lineto 7 5 lineto 4 7 lineto 0 7 lineto 0 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4W ^WYY]]^]^ W]"1o grestore "WTTT"X"Y"ZUUUUUU"[***"\"]ddPro grestore  Cp*W ^W[^^ [ WWWddProP "W############ C######""W currentpoint /legm_top exch def /legm_left exch def "*_ currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def %/legm_wide legm_wide 2 mul 8 div def %/legm_high legm_high 2 mul 8 div def legm_left legm_top translate legm_wide legm_high scale 0 0 moveto 4 1 lineto 7 2 lineto 7 5 lineto 4 6 lineto 0 7 lineto 0 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4"W)^"W\#\]$]^(Z^)WZ":o grestore ""WTTT""X""Y""ZUUUUUU""[***""\""]ddPro grestore  Cp*"W)^"W"[$^'^([)W"W"WddProP ""W############ C######" \ currentpoint /legm_top exch def /legm_left exch def "#o currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def ""^ currentpoint )/legm_radius exch legm_top sub 2 div def Llegm_left sub 2 div dup legm_radius gt {/legm_radius exch def} {pop} ifelse gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def 9legm_wide legm_left add legm_high legm_top add translate Alegm_wide legm_left add neg legm_high legm_top add neg translate ,/legm_high legm_high 2 mul legm_top add def -/legm_wide legm_wide 2 mul legm_left add def *legm_left legm_radius add legm_top moveto Hlegm_wide legm_top legm_wide legm_top legm_radius add legm_radius arcto 4 {pop} repeat Jlegm_wide legm_high legm_wide legm_radius sub legm_high legm_radius arcto 4 {pop} repeat Jlegm_left legm_high legm_left legm_high legm_radius sub legm_radius arcto 4 {pop} repeat Hlegm_left legm_top legm_left legm_radius add legm_top legm_radius arcto 4 {pop} repeat save_matrix setmatrix clip gsave ddProd6dPro- \#o"8t grestore " U "U"V&f&f&f"V323232"W???"XLLL"XYYY"Yfefefe"Zs2s2s2"Z"[ˌˌ"\"\eee"]111"^"^"_ٗٗٗ"`ddd"`111"a"bddPro grestore  C @ \#o H"* currentpoint /legm_top exch def /legm_left exch def ". currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def &/legm_wide legm_wide 2 mul 19 div def %/legm_high legm_high 2 mul 4 div def legm_left legm_top translate legm_wide legm_high scale 0 3 moveto 0 0 lineto 18 0 lineto save_matrix setmatrix clip gsave ddProd6dPro4*.*+,-."B grestore "*"*"*-,-,-,"*<;<;<;"*KJKJKJ"*ZYZYZY"*ihihih"*xwxwxw"*"*"*"*"*"*"*"*"*"*ddPro grestore  Cp*..**.ddProP ".#### C".#"f"-f1!81"$8P "!########  C !####P "########  C$####P "########  C$####P ""########  C$"$"#$####P "$######  C %&####P "'########  C %'####P # ###################"####  CT&"$%&"################" c"8c" Y currentpoint /legm_top exch def /legm_left exch def "#p currentpoint '/legm_high exch legm_top sub 2 div def (/legm_wide exch legm_left sub 2 div def gsave newpath 0 setlinewidth &/save_matrix matrix currentmatrix def 9legm_wide legm_left add legm_high legm_top add translate */x_proportion legm_wide legm_high div def x_proportion 1 scale 0 0 legm_high 0 360 arc save_matrix setmatrix clip gsave ddProd6dPro4 X#q [n!X[nq"X[nq#[n"8q grestore " Y " ZEEE" ["""" \..." ]:.:.:." ^EEE" _QsQsQs" `]]]" ahhh" bt\t\t\" c" d" eDDD" f" g" h---" i" jrrr" k" l" m[[[" n" oddPro grestore  C P Y#p X1!81!#81"$8 1 8 1(* 8P "*o########  C (*n1*o.no1n ####"*|P "o########  C 4mmmnnoo ####"|P "########  C ( ####"P "+########  C (+1+.1 ####"+ 1u${ 8 1z$ 8 1~$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1$ 8 1#u){ 8 1#z) 8 1#~) 8 1#) 8 1#) 8 1#) 8 1#) 8 1#) 8 1#) 8 1ux 8 1wz 8 1z} 8 1| 8 1~ 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1)u+ 8 1)+ 8 1)+ 8Q!XQ"'X UUUU1 # 80/.P@  0@0@@ `@@ pP@  @ `@?@  ?00  ddPro8 XG,  Helvetica .+[Sր) P#) A@ ) C\`) E) B ) O) R ) N`) EA)  %)I `)M) A ) G) I)N) G)  z`)R) A) D ) A`) R) - )C ddProH '= (7S) I)R) -)C) E@) Dm) ހ_ G ~ >~0 ! wh~ !wh~ !!u`  #wpzu nma m)a)z#ma`* * z z  z z*6  '& u~Qu*a*z#` ^`#ua) `#.z#b#~ -g#z.yz/a$#^^ "{^^Bwpuh -z-`*z/ w77`*~zun#.'eghz|}#%&CEF235RFGK 9 : ? - . 0 T \ ]  @ @t @   @z @E @J  ( ) =:t @ @ &'DEwx01vw  {|})*O~짠n!0!0!0 !0!00!0!0!! !,!!!0!0!D0+:u456QRDEr 4 5 + ,ﾷwk_k_kwkwk !0 !0 !0 ! ! !!0!00!0!0 !0!0 !0# , / 0 1 T U [ \ ^ _   > ? x ʿo^oooo!0!0  !08h!0!D0!!! @ !,!! !, !0!0!!0!0!00$  @ B v 7jklξ!!0!0!0!0 !0!0!0   2 -  :t , HH(FG(HH(d'@=/RBH/ -:LaserWriter TonyF:SanFranc.txt+7 HelveticaSymbol  (4 MeasurementsSIR-CED Tony Freeman Tony Freeman