MVR5 I)plotting=6"%&falseGE\[l5%,coordplot2DGR6&'%&xyeqsG%%listG'%'urangeG<#/%%nameG %&rangeG'%'vrangeGF/'%"nG%(integerG6.%'uplotsG%'vplotsG%%uminG%%umaxG%%vminG%%v maxG%"iG%"UG%"VG%)plotargsG%"xG%"yGF$F$C*>8&-%#opG6$7$""#"""9%>8'-FI6$7$FLFLFN> 8(-FI6$FK9&>8)-FI6$FSFX>8-&9"6#;""&9#?(8*FMFM9'%%trueGC$>8+,&FGFM*(,&F`oFM!""FM FM,&FaoFMFioFMFio,&FPFMFGFioFMFM>&8$6#F`o-%%plotG6$7$-FI6#-%%subsG6$/-%$lhsG6#F NFeo9$FX/%&colorG%%blueG?(F`oFMFMFaoFboC$>8,,&FUFM*(FhoFMFjoFio,&FZFMFUFioFMFM> &8%F_p-Fap6$7$-FI6#-Fgp6$/-F[q6#FXFdqF]qFN/F_q%$redG-&%&plotsG6#%(displayG6&7$- FI6#-%(convertG6$F^pF,-FI6#-Fas6$FjqF,/%(scalingG%,constrainedG/%'labelsG7$Q"xF $Q"yF$FhnF$F$F$%5PlotZernikeWavefrontGR6*'%$opdG%*algebraicG'%(epsilonG<$F1F,'% "cG%&tableG'%(sublistGF,'%&unitsG%'stringG'%%pertG<$%&floatGF,'%-focal_lengthGF cu'%,beam_radiusGFcu6,%"GG%"FGF?%"pGF6%"mG%"kG%&scaleGFB%&tlistGF$F$C0>FP""!?(F GFMFM-%%nopsG6#FaoFboC%>FU&&Fao6#FG6#FM>FZ&Fjv6#FL>FP,&FPFM-%,ZernikeTermG6%FUF ZFXFM@%-%%typeG6$FNF,>Fhn7$-FIF\q%$rhoG>Fhn7$FNF\x>F^p-%(collectG6%,&F]qFMFPFio Fhn%'factorG>F^p-%(combineG6$F^p%%trigG>F^p-Fax6%F^pFhnFdx-%,debug_printG6&9!Q+ wavefront:F$FMF^p@//9(Q#cmF$>FeoFM/FdyQ#mmF$>Feo"#555/FdyQ(micronsF$/FdyQ'micro nF$/FdyQ#umF$>Feo"&++"/FdyQ#nmF$>Feo")+++5/FdyQ#pmF$>Feo",+++++"/FdyQ#fmF$>Feo" /++++++5-%&ERRORG6#Q0~Unknown~units!F$@%Ffw>Fhn7'F\x%$phiGF[x%"fG%"RG>Fhn7'F\xF h[lFNFi[lFj[l>Fjq-%)optimizeG6$-%)makeprocG6$,$*&FeoFMF^pFMFio/%+parametersGFhn %(tryhardG@%Ffw>Fhn7'F\xFh[l-FI6#9)9*9+>Fhn7'F\xFh[lF^]lF_]lF`]l>Fdq7+7%*&F\xFM -%$cosG6#Fh[lFM*&F\xFM-%$sinGFi]lFM-Fjq6#-FI6#Fhn/Fh[l;Fbv,$%#PiGFL/F\x;FbvF`]l /%%gridG7$"#N"#?/%,orientationG7$"$5""#l/%&lightG7'"#g"#!*FLFLFL/%-ambientlight G7%$""%FioFi_lFi_l/F[t7%Q,radius~(cm)F$Q!6"Q%OPD~F$/%&titleG((Q2Wavefront~Error ~(F$FdyQ")6"@$2"")F^o?(FG""*FMF^oFbo>Fdq7$-FI6#Fdq&FjnF[w-%'plot3dG6#F_alF$F$F$ %/implicitplot3DGR6&%$eqnG'%)x_limitsGF0'%)y_limitsGF0'%)z_limitsGF0F$F$F$-&Fir 6#%/implicitplot3dG6(F]qFNFXFao/Fh^l7%F[_lF[_lF[_lFinF$F$F$%.tubecurveplotGR6&' %&curveG<$F,%'vectorG'%'radiusGFdt'%)t_limitsGF0'%-theta_limitsGF06&%%tubeG%"tG %&thetaG%"rGF$F$C)>FjqFcr>FG-F[qFfv>F^p-%*tubecurveG6&F]qFjqFPFG>F^p-%$mapG6$%( radsimpGF^p>F^p-Fbdl6%FaxF^p7%FP-Fh]lF[w-F\^lF[w>F^p-Fgp6$/FPFN-%&evalmG6#F^p-F cal6'F^pFXFao/Fh^l7$"$+"FjyFinF$F$F$%(gifplotGR6%'F[v<$%%PLOTG%'PLOT3DG'%&fname GF_u'%%fdirGF_uF$F$F$-%*imageplotG6$%$gifGFjnF$F$F$%.contourplot3DGR6%FhalFialF [blF$F$F$-&Fir6#%.contourplot3dG6)F]qFNFX/%'filledGFbo/%)coloringG7$%'yellowGFf r/%)contoursGFjy&Fjn6#;Fj_lF^oF$F$F$%+scalarplotGR6$'FjblFdtF_clF$F$F$-Fap6&F]q FN/%*numpointsGFfel&Fjn6#;""$F^oF$F$F$%,curveplot3DGR6$FiblF_clF$F$F$-&Fir6#%+s pacecurveG6(7#-FI6#-Fas6$F]qF,FN/Fhs%.unconstrainedG/%+projectionG$Fj`lFioF_hlF ahlF$F$F$%,coordplot3DGR6)'%$xyzGF,'%(uvaleqnG<#/F1%(numericG'%(vvaleqnGF^jl'%( wvaleqnGF^jlF-F3'%'wrangeGF/6/F[v%"qGFgcl%"gG%"XG%"YG%"ZG%"uG%"vG%"wG%%uvalG%%v valG%%wvalGF$F$C*>8.-%$rhsGF\q>8/-Fg[mFdr>80-Fg[mFfv>FP"#I>F^p-%,surfaceplotG6' -Fgp6$/-F[q6#FdyFe[mF]qF^]lF_]l/Fh^l7$FPFP/%(shadingG%%zhueG>Fjq-Fb\m6'-Fgp6$/- F[qF]]lFi[mF]qFdyF_]lFi\mF[]m>FG-Fb\m6'-Fgp6$/-F[q6#F_]lF\\mF]qFdyF^]lFi\mF[]m- Fhr6&7%F^pFjqFGFgs/F[t7%Q"XF$Q"YF$Q"ZF$&Fjn6#;Fj`lF^oF$F$F$%(jpgplotGRFielF$F$F $-Fcfl6$%%jpegGFjnF$F$F$%(myarrowGR6$'%%baseGF[cl'%%vectGF[cl6,%#b1G%#v1G%%stem GFgcl%&hbaseG%'hpointG%#v2G%#v3G%%headG%%optsGF$F$C4>F^p-%&evalfG6#-%$evlG6#F]q >Fjq-Fa`m6#-Fd`mF\q@$50-FevFaelFdhl0-Fev6#FjqFdhl-Fb[l6#Q=points~need~three~dim ensionsF$@$34-Fgw6$F^p7%%)realconsGFjamFjam-Fgw6$FjqFiam-Fb[l6#QGpoints~must~ev aluate~to~real~constantsF$>FU-Fd`m6#,&F^pFMFjqFfil>FZ-Fd`m6#,&FjqFMF^pFM>FhnFah l@$/-%*intersectG6$-%'indetsG6#<#Fhn<$F_q%'colourG<">Fhn6$Fhn/FccmFfr>FG-Fihl6% 7$F^pFU/%*thicknessGFdhlFhn@$/Fjq7%FbvFbvFbv-%'RETURNGF[w>FP-%%sqrtG6#-&%'linal gG6#%%normG6$FjqFL>F`o-Fd`m6#-&Fidm6#%*crossprodG6$7%FMFbvFbvFjq@$2-&Fidm6#%(do tprodG6$F`oF`o,$-Fiem6$FjqFjq$FM!"#>F`o-Fd`m6#-Faem6$7%FbvFMFbvFjq>F`o-Fd`m6#,$ *(FPFMF`oFM-Fhdm6$F`oFLFio$F]oFafm>Feo-Faem6$FjqF`o>Feo-Fd`m6#,$*(FPFMFeoFM-Fhd m6$FeoFLFioF_gm>Fdq-&Fir6#%.polygonplot3dG6%7(FZ-Fd`m6#,&FUFMF`oFM-Fd`m6#,&FUFM FeoFM-Fd`m6#,&FUFMF`oFio-Fd`m6#,&FUFMFeoFioFahm/%&styleG%&patchGFhn-Fhr6#<$FdqF GF$F$F$%'psplotGRFielF$F$F$-Fcfl6$%#psGFjnF$F$F$%(ODEplotGR6&'%%ODEsG<%%"=GF,%$ setG'%(depvarsG<$F,F_jm'%+ivar_rangeGF/'%$ICsGF,F$F$F$-%'DEplotG60F]qFNFX7#-%%e valGFfv/%%axesG%'normalG/%*linecolorG%%navyG/F]dmFMF][n/%*titlefontG7%%&TIMESG% 'ITALICG"#=/%)axesfontG7$%*HELVETICAG"#7/%*labelfontG7%Fg[n%&ROMANG"#9Fbil/%'me thodG%(dverk78GFinF$F$F$%/implicitplot2DGRFhflF$F$F$-&Fir6#%-implicitplotG6)F]q FNFX/F^[n%&frameG/Fh^l7$"#]Fb]nF^qFfglF$F$F$%0curvatureplot3DGR6&Fibl'%*curvatu reGFdtF_cl'%*plottitleGF_u6%Fi[l%#c1G%#c2GF$F$C&>Fjq-Fehl6(7$F^ilFNFX/F[t7%F]tF ^tQ"kF$/Fb`lFaoF\dmFin>FG-%,curveplot2DG6&F]qFX/F_q%&blackG/%*linestyleGFM>F^p- &%*plottoolsG6#%*transformG6#R6$FCFDF$6$%)operatorG%&arrowGF$7%F]qFNFbvF$F$F$-F hr6(Fjq-F^pF[wFdilFb^nFe^nFinF$F$F$Fb\mR6%'%%eqnsGFbjm'%)u_limitsGF0'%)v_limits GF0F$F$F$-Fcal6'F]qFNFX/Fh^l7$F[_lF[_lFfglF$F$F$Fh^nR6$Fibl'F`cl/F1-F26#F`jl6,F [vFhjl%*curvelistGFB%)plotlistG%&cplotG%$varGF]v%#rpGFgclF$F$C*>FG7">FP7#Fahl?& F^pFahlFbo@,/F^p%'radialGC$>FG7$-FIF[wF^p>FP-%'removeG6%%$hasGFPF^bn/F^p%(evolu teGC$>FGFabn>FP-Febn6%FgbnFPFibn/F^p%)involuteGC$>FGFabn>FP-Febn6%FgbnFPF`cn/F^ p%&pedalGC%>FGFabn>FP-Febn6%FgbnFPFgcn?&FjqFahlFbo@$3-Fgw6$Fjq/F1F,/-F[qF`am%)r efpointGC%>Fdq-%$vecG6#-Fg[mF`am>FP-Febn6%FgbnFPFedn%&breakG/F^p%*inversionGC%> FGFabn>FP-Febn6%FgbnFPFaen?&FjqFahlFbo@&F_dnC$>FdqFhdn>FPF]en3-Fgw6$Fjq/F1Fdt/F ddnF^clC$>FhnFhdn>FP-Febn6%FgbnFPF^cl>FZRF[anF$F$F$-Fap6&Fa^nF^]nF_hlFahlF$F$F$ >FU7#-FZ6'F]qFN/F]dmFLFj^n-FI6#FP>F`oFjp?(FeoFMFM-&Fidm6#%(vectdimGF[wFbo@,/&FG 6#FeoF^bn>FU7$-FI6#FU-FZ6'-F^bn6$F]qF`oFNFc[n/F_q%'siennaGF_gn/FignFibn>FU7$F]h n-FZ6'-FibnFbhnFNFc[nFerF_gn/FignF`cn>FU7$F]hn-FZ6'-F`cnFbhnFNFc[nF^qF_gn/FignF gcn>FU7$F]hn-FZ6'-Fgcn6%F]qF`oFdqFNFc[n/F_q%(magentaGF_gn/FignFaen>FU7$F]hn-FZ6 '-Faen6&F]qF`oFdqFhnFNFc[n/F_q%+aquamarineGF_gn-Fhr6%FUFgsF_gnF$F$F$%+surfarrow sGR6&%$fldG%%surfG%#r1G%#r2G64F]`m%&gspecG%#p1G%#p2G%#s2G%#f2GFf_mFj_m%#a1G%#a2 GFe_m%#b2G%#n1G%#n2G%#h1G%#h2GF?%"jGF$F$C5>F^pFin>F`o-FI6$FMFX>Feo-FI6$FMFao>Fd q-FI6$FM-FI6$FLFX>Fe[m-FI6$FLFe\o>Fhn-FI6$FM-FI6$FLFao>Fi[m-FI6$FLF]]o>Fjq-F_cm 6$<#F^p/-%*identicalG6#.%*arrowgridGF,@%/FjqFdcm>Fjq/F[^o7$Fj`lFj`lC$>F^p-FI6#- %&minusG6$Fe]oFjq>Fjq&FjqF\w>FG-Fcal6&FNFXFaoF^p>F^p-FI6#-Ff^o6$Fe]o-F_cm6$Fe]o /-Fh]o6#.Fh^lF,>F\\m,&&-FI6$FLFjqF\wFMFioFM>81,&&F[`oF_wFMFioFM>82*&,&Fe[mFMFdq FioFMF\\mFio>83*&,&Fi[mFMFhnFioFMF^`oFio@'Ffw>FUFN-Fgw6$FNF\cl>FUFi`m>FU7%F`oFe oFN@%-Fgw6$F]q%*procedureG>FZ-F]q6#F]hn>FZFc`m>FP-%$seqG6$-Fjao6$-F]_m6$-FI6#-F gp6%/F`o,&FdqFM*&Fb`oFM84FMFM/Feo,&FhnFM*&85FMFf`oFMFM7$FUFZF^p/Fgbo;FbvF\\m/F[ co;FbvF^`o-Fhr6$<$FPFGF^pF$F$F$F^dlR6&Fibl'FeclF1'FgclFdt'FfclFdt6%%(normvecG%' binormGFdclF$F$C&>F^p-%+UnitNormalG6$F]qFN>Fjq-%)BinormalGF`do@$5-Fgbn6$F]q-F\^ lF\q-Fgbn6$F]q-Fh]lF\qC$>F^p-Fbdl6%%)simplifyGF_elFix>Fjq-Fbdl6%F`eo-F`elF`amFi x>FG-F`el6#,&F]qFM*&FXFM,&*&-Fh]lFfvFMF^pFMFM*&-F\^lFfvFMFjqFMFMFMFMF$F$F$FcflR 6&'%$devGF1FjelF^flF`fl6%Fi[l%+pltoptionsG%&ftypeGF$F$C'@)/F]q.FgimC$>FjqQRport rait,noborder,color=cmyk,width=8in,height=8inF$>FGQ$.psF$/F]q.FeflC$>FjqQ@heigh t=600,width=600,colors=256F$>FGQ%.gifF$/F]q.F\_mC$>FjqQ5height=600,width=600F$> FGQ%.jpgF$-Fb[l6#QAdev~must~be~one~of:~gif,~jpg,~psF$@$2Fj_lF^oC%@$2F]oF^o-Fb[l 6#Q4Too~many~arguments!F$@$4-Fgw6$&Fjn6#F]oF_u-Fb[l6#QNPlot~options~must~be~in~ the~form~of~a~string!F$>Fjq-%$catG6%FjqQ",Fg`lF\io-%*plotsetupG6%F]q/%+plotoutp utG-Fcio6%FaoFXFG/%,plotoptionsGFjq-%&printGF\q-Fgio6#%(defaultGF$F$F$F$