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" @ 'Q"0  `OdWelcome;Readme Working Data"Two Axes ,Module3{,Module1  ;,   ;2   ;, Hb =UQ"BEYܥw@]'+wj@=EYܥw@]'+wj 8oTxVNQ=,`"bBWـ#P ِu L6vV@^A &f7s7j1ws~̬B,y|p\ga`a@?82ޑ%^\3@y{,V  XMT" 31} jTD{.LREbȤ"84RbSHjv3K-RGt}˓dU-/..2[H,M1alf<,ሽ P$cŧ=6g>^i_VVFm/ܪEQ@(%~,hrߞ aS-cѧiVYkjvzӨp%e 9@%a"+%5(/ۤMDܖZTO"Έewg}=u'gøM{H v}_Xp1N?KkW?=ٸEh?b(/Fըe^q牛}^T8ovs-B^dZSG{{O>qg| 4#b{uyIFq';~ӆIsJ?8% DhBlqk_SoF~Фߩ11 }^ϫݛ"6~nȭ vdzSV#S9"M:Nymak+,IzKEx{VvPof/?OBfB~e!򳪲dq V_jabCcDKo>Ɉ;1n2kUEz#vU%*CcDKo>Ɉ;1PNG  IHDRxC`1PLTE{DD”@8G$$$ACCADE,tyAH)dbjfeiu@D`""_刔D#%&af$&t?̑(&GSTQ45=h242礩Iie_zzz8cddXPyDDNSUaٙ*,)swl03e&X\ - d-3Ozgjlh\\_ źD>xz{ #RPDB,LRxxzLLN!$Fpp$7xg)$ttWT$۱ېgd^4wv ZǼW~ԑ)8;xD|0|Xpn丒{רT󙩪QRTR8:،X<:<<|z8rqbHM *,HK^)+gZ[S9;399=Pv t<: A)-MnD/+ Y8WֹN/ Z7N!@"陓}}IJ&V=iRB&czeZS'[ܔc65͡g{[Zʍ}K|$"RW׏O_0N͊NqR1YBg_J# YӧWnvozglnK7ȵLD6MT AIY :Y2(>h61~K$Jf}#Tr###g'-=kW6fۥ#c4 ,<1UP4A[f2vb_@'<(pof2FBM-kZE <I,癚\0Ԡ,#wRLPs]}}d\H"P`X VM 8ɑEeP\jO~9lqTk>d2>ύDUW|xA XcxT PTiEkӍ ^1~ztǿ~3#./>>_h2x9l pT ]z+9.wo쥾ѧ?ʺ\k C2ꜰ"04c@,PCW6Os7.YR\ãP&1"טr-kW/co۰$ptv jh/ Pg6>S~ǶpF@ċwhcGE>w~bZ 5M]=d3jh>:qwE?#u#'Nu|*QvB;N7l!^I1C׭c(#,Z?N A!Kh^!G;JZzvDcW8{46z IR}Lj)GH谈X Y 7׼cO {lxcya E%ÎеLbA3 љvN&_loJ{;c,/⦑-Q%;d_hz6ͅ|YHG5֊7 ɞ º~ᲀ9CY+}\BS2+ϼcE+g &VTBZE/=ɁVX|s:8Ն nZ/_NJB %V@(:Shby^ҝH2fc>pBħ9I[r8R"f@5 "yCHvd\=S 3O^)=-$& ]g3N`ܬ4PKI{;f 5k|p*ّMj!dSuCt2اb2GY (kBf.W>c$/>^ilo~dG?zG-] Ȁksfm@i[r״C7#zI&f"+ąU禅~6kjǏ¦-uiY@O?Fh PVpd@wx*NB>B60. Gtoء{™Bc0P=Y-T_;d{}&6b}$j |yR[Z͔~9>T >',qodjC~.AαO.TSOo}a׽vI|p&ÞgzXdo$j,cu]bjNbH. ~>?:0bR$Qe,e|3l-O\-̓wC2ރ(ժz\z?yr *Hzd&, mqKT?fáŃnzNS&phhdct#l0␌)ֈ:Wƺ~ ]][5-Ӗq0TٯK{&:5.>͇,FF5eMhZ &9g;hmmd{rgzp,ztm❻n=@X Y*bJlq6?itrOa"Rڦέoa_]{_liٜ+S Ҽ!0VB~6AbP&붎P1pZW*TeQ,k6ٸKW/@"~𚞆'(ʺlNoC;;dFX(]@*Ԣ3<'a Z $jcffFjwHm*stZm 5Kj mdK˥t —v\ n,iG:1Vn\(OMrKZn%L%-YϻB46lvOU,,Sj,~"*2U*np8[\NKjJibTT 9?ۄIENDB`$"uݐXƉ~o-Q@=IݐXƉ~o-P 'O#WxVKkA'n"qHJ-!o͒I %! òg /9{[^IaM0RUgVB>~q{guapHIX{<>|?h6 Dh녽F u+]s1=iɞnu#"_Q$1"L4TެĀ8KzfHuCs*ǙeM[K5`yFlfCi]18ZE5dNiIm҈jz[P.ܦNh]'I{_XÚl4R!ʼNl;M6xi֚Vi̲Y$܌}EvPsUU,2+D8UF6ᛌ!%nr;d\֝zކ6hޅG@~DViX1.]J%` L+_&F ecFL +/}98O4~͔cW.Į_*.n@>3ȜTIō24(8Cp>六Vȇ}uE#[6cʯGsbpfJ~>sԉd,g`irIgX:kOy ql{i=Ew6[jh쇻w:`}zaw}%ΰhKswj8M|I\h]V=h}$wM{2GG˿'dߗ䴗hFM5%?OFyc4 sMF1r 7ƂhWGybc9øwɛ;TzJzVsOȜuzýڦySpB Ƴ g095\;R WM-tqKm!Ğv_yOoI9Fb[\Os/oT+"nM {4P:ԁ4El]cޗDŽ\VQkV CvrxFl"3  @@+9GOptical Diameter Focal Lengthf/D Focal RatioRadius of Curvature Mirror RadiusLambdaRhoZones>>> Mask in/out Common Zone First Axis Reading 1 Reading 2 Second Axis Reading 1Axis 1Axis 2 DeviationsFirst Axis AverageMaximumSecond Axis Average1/All Readings AverageAt Zone Axis 1, 1 Parabola a= Axis 1, 2 Parabola c= Axis 2, 1 Intersect at Axis 2, 2 Constant1Average Axis 1Average Axis 2 Ideal ReadingZONEHxHmHm^2/RHm/4fCOMPUTATION FOR FIRST AXISD1 D1-ConstantLamdaCLambda f Variations Lamda f * 1E5MinMax Lamda f / rhoUx10^6Chart "Y" ValuesReference Parabola WavefrontError %WavefrontCalculations of All ParabolasA=C=x0,10,20,30,40,51,21,31,41,52,32,42,53,43,5)Wavefront Calculations For all Parabolas !& Selection of Reference Parabola Rank ALL + / - max deviation Parabola#COMPUTATION FOR SECOND AXISCOMPUTATION FOR ALL READINGS"+/- 1/8 Wave" Axis 1 Error Axis 2 Error Average Error#Charting Data--% of Wavefront ErrorRadiusIdeal +xIdeal -xAverage"Charting Data--Ideal Versus ActualIdeal"-1/8"+1/8Average Deviation Reading 3Average ReadingCorrection FactorCorrected Average ReadingConstantMaximum Wavefront error =at zoneReference Parabola : y=*x^2+Intersecting at ZonesGraph<DO NOT USE THIS SHEET FOR INPUT, CLICK ON "Working Data" TABD1,2,3D1,2,3-Constant CONVENTIONSTitlesBlue fonts are for titles.Computed-Black fonts are computed values or constants.Comments.Green fonts are for comments and documentation OTHER NOTES: ProtectionFPrint area is set to deliver a one page summary report. for insertion in mirror notebookNotes.Embedded throughout the Readme sheet are NotesCDragging the mouse over these red indicators should call the notes.Monitors,The user should make appropriate adjustments;Worksheet developed by Steve Meyering and Alex McConahay ofHRiverside Astronomical Society/Riverside Amateur Telescope makerS (RATS)Wavefront Error Date/Comments:DataRBlue areas with red font are for input of data that only needs to be entered once.OGray areas with red font are for input of data that changes every test session.ClickComments/TitlesRYellow area with green font is a control box. Click it to start the computations. \White cell with green font indicates cell that must equal 0.000 to make some graphs correct.Workbook Copyright RATS-2000Smoke's 8 incher--PyrexSmoke's 8 incher $3/12/00 Three times around, 1/2 ovalLambda CLambda f * 1E5Lambda f / Rho0Charting Data--Millies-LaCroix--Parabola Removed1Charting Data--Millies-La Croix--Parabola RemovedrAxis 1 readings on June 9 --Axis 2 on June 8--after another session on June 9, readings were flat with no shadows.6/13/00 This follows 20 minutes of 2/3/ Wide W, MOT--Then 10 minutes accented on edge, TOT short w, then 10 minutes full parabolization (1/1, wide W) stroke MOTAlex's 8 incherN6/14/00 This follows 7 minutes of full parabolization (1/1, wide W) stroke MOT6/14/00 This follows 7 minutes of full parabolization (1/1, wide W) stroke MOT. This is the second such session of the evening.3Suggestions and improvements to amcconahay@juno.comWavefront Error ReportlAfter aluminization, Reading one taken one night, reading two and three another night, on two axes 90d apartNOTE: This area can record your progress.Simply highlight the readings and comments section (D6 to H9), right click and copy, move cursor to unoccupied fields in this area, right click and paste. SAMPLE ONLYamcconahay@juno.comCopyright RATS-2000>Copyright 2000. May not be copied or redistributed if altered. Light Source Divisors>>Line 49Line 50MNote: Items at right for adapting sheet to fixed or moving light sources>>>>>FixedMovingETo remove Protection, use Tools-Protection--Unprotect pull down menu.RAll worksheets are protected but may be altered. Please save an unaltered originalP should you inadvertently alter your worksheets and need the original program.Read Me*This "Readme" Worksheet is non-functional.9Differences among monitors may affect graphs and colors. http://www.rivastro.org/^N N9OrOX_PaePrPz\RQx~Q,$Q\AER R{bSSATCNU<xVI_&X xY [< A]<g^0sT0bˆbNH0sT0bbˆbkf H0sT0b@nXo #b  b~c b0b{AB4S0bt00 a @ fyK yK 2http://www.rivastro.org/ Sheet3 I@ $\^j  MbP?_*+%)&&L&D&T&CWorksheet Copyright RATS 2000 MCanon Bubble-Jet BJC-4100@nyyhh@MSUDCanon Bubble-Jet BJC-4100d"Qhh??cU} } m }  }  }  } } $ } m } $  T0  b  b  b  Á    b  @b      ;b  b     E E   bO b b   O  . T0T  b T0  QK           k J~ @ K P M O N   I L ~ M@<lG@  D!@˿@ DD@ D+Gʍq$?aQ?DDH34>  [A?=D= J*$?@@@@  !@=D= J~ %K7)?.S㥛?D% r@.MbX9?D%i@.?D%K7) @.S㥛?D@.D  @ D=  # Mbp?B`"۩?ˡE?~jt?On? 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D.&/{J +@ D.D.&/{/$)@ D.D.&/{ rhI @ D.D.&/{S㥛 @oD.D. /&' ~ 0r@ 0x&,0z7D/D D,0{*`?4D/D D,0{e?4D/D D,0{/娺?4D/D D,0{16"?4D/D D,0{1ݎh?4D/D D 0&' ~ 1r@ 1x'(1z1D/D D(1|`r:::L%:t,0;::rY;::F';::t,0;::7 ;: : ;r ;x5~ ;y!;{zK(< D9D:!;{1RL< D9D:!;{M< D9D:!;{< D9D:!;{:< D9D: ; <r <x6~ <y*<zoabD;D *<z[AbD;D *<z\ȕbD;D *<zbD;D *<zi>9bD;D  < =QQ =Qe#=V[A? %bbB =S=C!@ D= =Rf+=D@ D=%bbB@ = >LQL >8g>B&S1zͿ>D >Rh>i> D >Ei>v> hD]D 0,4 ?L7?QL`````v' DlJJ2VA-8@ T0A bB bC bD ÁE F G bH bI J K bL bM N O PhEQERSbOTbUbVWXOYZ.[T0T\]b ^T0 _@L @g8 @g9 @b:@bbbb&' AL;7AewlkۿA!D9@D9@D.@D.@,AfQD9@DAD.@,Ae_[QDAD.@DA,AeR4QDAD.@DA,Ae_`@QDAD.@DA,Ae_[QDAD.@DA,Aed]DQDAD.@DA BL<7Be>{{B!D9@D9@D.@D.@,BfRD9@DBD.@BeqIRB BNALL.@LBeÕRBBeRBBeqIRBBeġp#RB CL=7Ce~]߿C!D9@D9@D.@D.@,CfSD9@DCD.@CeSBCemSBCeCSBCeSBCedvSB DL>7De&S1zͿD!D9@D9@D.@D.@,DfTD9@DDD.@Det,0TBDerYTBDeF'TBDet,0TBDe7 TB EL?7Ee)YҿE!D9@D9@D.@D.@,EfUD9@DED.@EeJ lUBEeqAbEiUBEeq$P\UBEeJ l UBEe0/UB FL@7FeiF!D9@D9@D.@D.@,FfBw?VD9@DFD.@Fe_[VBFeÕVBFe?VBFe"VBFefb'VB GLA7Ge!/$G!D9@D9@D.@D.@,Gfps.9?WD9@DGD.@Ge_[WBGe#*O4WBGeCWBGem5})WBGeoҬ\WB HLB7He{<;ſH!D9@D9@D.@D.@,Hfd8n]XD9@DHD.@He_[XBHef4XBHev5)XBHet,0XBHeFDo XB ILC7Ie?LJ*пI!D9@D9@D.@D.@,If \-YD9@DID.@Ie_[YBIe1&YBIe_\ YBIe:TF YBIe0/YB JLD7Je#4>˿J!D9@D9@D.@D.@,JfZD9@DJD.@Jeߺ T ZBJeÕZBJeCZBJe6<ZBJeZB KLE7Ke ?K!D9@D9@D.@D.@,Kf/&,I[D9@DKD.@Kebr[BKeÕ[BKeހJ;= [BKet,0[BKe^^[B LLF7Le@L!D9@D9@D.@D.@,Lf3S$ \D9@DLD.@Le/l\BLeÕ\BLe \BLe~_@'#\BLe0/\B MLG7Me,n?M!D9@D9@D.@D.@,Mf&OK$$]D9@DMD.@MebG~ ]BMexf]BMeC]BMet,0]BMe062]B NLH7NeA$?N!D9@D9@D.@D.@,NfcE¼^D9@DND.@Ne{X^BNe 7^BNeC^BNe÷ٮ,^BNe0/^B OLI OLa' O'J O''' PLK P'LPa''''' PM P N Qc;Q@RQQ^L-Q^@@BQ%AQQ^TL9@LAQ%0QQ%q= ףp0QQ%ffffff0QQ%Q@0QQ%(\@QQQ9Q QQ^L L L L L L B$WL L L L L L B$ "BQ dY@BQ ^Q^ TL@LALAL@ALAL@ALAB dB Rc<R@SQR%BQR%q= ףp?BQR%BQR%Q?BQR%RQ@BQR%Q@RQR9?R QR dQ@CQ Sc=S@TQS%CQS%q= ףp?CQS%)\(CQS%CQS%(\ @CQS%= ףp= @SQS9S QS dY@DQ Tc>T?UQT%DQT%333333DQT%RQDQT%DQT%DQT%)\(TQT9?T QT dRQ@EQ Uc?U@VQU%EQU%zGڿEQU%QEQU%QEQU%ffffff?EQU%UQU9U QU dY@FQ Vc@V@WQV%q= ףpFQV%FQV%FQV%ףp= ?FQV%Gz@FQV%(\@VQV9V QV dY@GQ WcAW@XQW%ffffffֿGQW%GQW%GzGQW%GQW%Q @GQW%Gz @WQW9W QW dY@HQ XcBX@YQX%?HQX%HQX%QHQX%ffffffHQX%HQX%HzGXQX9X QX dY@IQ YcCY@ZQY%(\?IQY%IQY%QIQY%)\(IQY%Q?IQY%YQY9Y QY dY@JQ ZcDZ@[QZ%(\@JQZ%Gz?JQZ%JQZ%JQZ%Gz@JQZ%p= ף?ZQZ9?Z QZ d(\@KQ [cE[@\Q[%HzG@KQ[%Gz @KQ[%KQ[%ףp= KQ[%KQ[%333333[Q[9[ Q[ dY@LQ \cF\@_Q\%Q @LQ\%Q@LQ\%LQ\%p= ףLQ\%zG?LQ\%\Q\9\ Q\ dY@MQ ]cG]@^Q]%$@MQ]%(\@MQ]%Q@MQ]%MQ]%MQ]%333333 ]Q]9] Q] dY@NQ ] " ] n]  ^cH^@fQ^%Q@NQ^%)\( @NQ^%(\?NQ^%NQ^% ףp= ?NQ^%^Q^9?^ Q^ dQ@QQ ^ " ^ ^  _LO)_9@_%Q^B@+_f:%AND_B+_ft,0:%AND_B+_frY:%AND_B+_fF':%AND_B+_ft,0:%AND_B+_f7 :%AND_B_ " _  _ D%lJi8<Nu%%%%%%%%%%%GK`T0 a,bbb cb dÁef gb hbijkblb mnopEqErsbotbubvwxOyz.{T0T|}b~T0 `UQ `UR `8BR` " ` `  aUQl-a)7pf?oDDD/-a)gd S?aDDD/-a)'?aDDD/-a)טO?aDDD/-a^z"?aDDD/a "~ a a  b,Qmbnoa?_D<Abn[A?_D<Abn\ȕ?_D<Abn_D<Aboi>9?=D<Ab " b 'o b pc,q!ppppp/c " c q c r d,Q d(Vd[\])^&d " d s d teQe-/eeeLeK7)?.ee r@eeei@eeeK7) @eee@eee& e " fQf:efffLf.oafff.[Afff.\ȕfff.fff;i>9lff&f " f uf  gQ,g&&&&/g " g g hQ h(h(***+/, h " iQ i1Wi2K7)?eD/i2J +@iD/i2/$)@iD/i2 rhI @iD/i2S㥛 @iD/ i/, i " i =v i  ijQ j1Xj27pf?fDaj2gd S?jDaj2'?jDaj2טO?jDaj3z"?jDa j/, j " j kQ k1Yk27pfjDak2gd SkDak2'kDak2טOkDak3z"kDa k40 k "> k lQ l5jl6 7v~?lD4l6``YΎ?lD4l6  mQ44 44444 m " m wm nQ n[n44 n >> nxoQokD.oXK7)?ioop LoXJ +@oooX/$)@oooX rhI @oooXS㥛 @oo o44 o > pQp2*`?pop2e?pop2/娺?pop216"?pop31ݎh?qop4 p y p z qQ!q2J׸q DpDa!q22烣?q DpDa!q2׽??q DpDa!q23Bދ5?q DpDa!q3V):?r DpDaq  q { rQ!r2:S?r DpDa!r2Q6(?r DpDa!r2;Э?r DpDa!r2/0)f|ɿ?r DpDa!r3 m%|?s DpDa r  ssfQY?sD ssxVh?sD s/娺?sD sH+?sD s 8缧?sD s tXXXXXXt u4jjjjj u | u v77777v v }w77777x77777y77777z77777 z ~z {77777 { { |77777 | | }4}77777 } ~4~7777777777DlR+BXH@>L 2,888,T0bbbÁbb77777777777777777777777777777777777777777777777777R# EP<:#( @A@A <p < 6NMM? +]`!  I@&A Page &PMCanon Bubble-Jet BJC-4100@nyyhh@MSUDCanon Bubble-Jet BJC-4100d"dhh??3*3d23 M NM4 3QQ ;jjQ ;iiQ3_  NM ] d4E4 3QQ ;kkQ ;iiQ3_  NM ] d4E4 3QQ ;llQ ;iiQ3_  NM ] d4E4D$% M 3O&Q4$% M 3O&Q4FAJ3O3*N43*N4523   43d" 3_ M NM ] d444% O@M:3O&Q F!Millies-LaCroix--Parabola Removed'44eK7)?K7)?K7)?J +@J +@J +@/$)@/$)@/$)@ rhI @ rhI @ rhI @S㥛 @S㥛 @S㥛 @e7pf?7pf 7v~?gd S?gd S``YΎ?'?' Ideal Versus Actual Parabolas'44eK7)?K7)?K7)?K7)?J +@J +@J +@J +@/$)@/$)@/$)@/$)@ rhI @ rhI @ rhI @ rhI @S㥛 @S㥛 @S㥛 @S㥛 @e*`?J׸:S?fQY?e?2烣?Q6(?sxVh?/娺?׽??;Э?/娺?16"?3Bދ5?/0)f|ɿ?H+?1ݎh?V):? m%|? 8缧?e xp < 6NMM? ]`"  I@&A Page &PMCanon Bubble-Jet BJC-4100@nyyhh@MSUDCanon Bubble-Jet BJC-4100d"dhh??3*9e ~~  < < [ XPP?  p9 p]4 @ [# ,5l 6G <Enter Title or Name of Mirror <$   ~~  < <[ XPP? rG]4 @[@$ ^?$6G )<*Enter Measured Optical Diameter of Mirror<! ) @~~  < <[ XPP?  r 9]4 @[$ ^?$6G ?<@The Wavefront Report is a handy summary of mirror performance. <!L >  ?p~~  < <L\ XPP? rd]4 @L\% ^?$6G D<EEnter distance form Mirror surface to focal point of Foucault Tester<![ D~~  < <\ XPP? r 7]4 @\8& ^?$6G 1<2Computed Information--Half of Radius of Curvature<! 1~~ < <] XPP? r r]4@]& ^?$6G ><?Computed Information--Focal Length divided by mirror diameter.<!F >~~ < <x] XPP? r r]4@x]' ^?$6G .</Computed Information: Half of Mirror Diameter <! .~~ < <] XPP? r d]4@]0( ^?$6G A<BConstant--Wavelength of yellow light. Used later in computations.<!L A~~ < <@^ XPP? r d]4@@^( ^?$6G 9<:Computed Information--theoretical Diffraction Disk Radius<!, 9~~ < <^ XPP? ro;]4@^) ٞ$6G  <This row should contain the Actual Inside and Outside measurements of your Couder Mask. The sheet provides default measurements to guide you if you have not yet cut the mask. Once you have, you should measure and enter your readings. You will over-ride the default computations. < $ "' "$ ~~ < <_ XPP? r U]4@_(* ^?$6G 1<2Enter the raw readings from the various zones. You need not correct to a common point. This sheet allows for three sets of readings. They may be on one or more axes, but will be averaged as if they were one. Another sheet in the workbook (Two Axes) allows you to enter and graph data on two axes at once. <! 0  1 xx < 64UXPP?  P]4@4U* ^?$6GX U<VEnter Date and Comments about what work has been done or needs to be done on mirror. <! U~~ < <U XPP?  ]4@Ux+ ^?$6G r<sComputed Information--A raw average of the above readings. This becomes the input for the Texereau table, line 8. <!E q  r~~ < <U XPP?    U]4@U , (5l 6G <Enter common zone for readings. This is the zone which shall be considered perfect, with all other zones measured +/- from here. <! *~~ < <LV XPP? ]4@LV, ^?$6G <Computed Information--This number must be subtracted from each test reading above to set all readings to a common zone (selected by the entry in I5--Common Zone). <!~~ < <V XPP?   9]4@Vp- ^?$6G f<gComputed Information--These are the corrected readings. All readings above are set to a common point so they can be compared. By definition, all readings will match at the "common zone." How well they then match at other zones is an indication of the accuracy of the readings, or (if the readings are taken on different axes) the astigmatism of the mirror. <!  e  f ~~ < <W XPP?  Q ]4@W. !5l 6G S<TThis must equal 0. To make it so, click yellow box after entering zonal readings. <! R  S@~~ < <xW XPP?  i]4@xW. Ӱ^?$6G <Computed Information--The average of the Corrected Readings. Use them to compare the overall mirror surface to the ideal reading in the line below.<$N~~ < <W XPP?  ]4@Wh/ ԰^?$6G <Reference information--This is a convenient copy of the ideal readings. A quick glance at this line and the one above will tell how close the averaged readings are to the ideal. <! ~~ < <@X XPP?  pr ]4@@X0 հ^?$6G <Computed Information--The maximum deviation of the measured wavefront compared to the ideal wavefront expressed as a percentage of the wavelength of yellow light. <!S  ~~ < <R XPP?  pr]4@R0 ְ^?$6G <Computed Information--The maximum deviation of the measured wavefront compared to the ideal wavefront expressed as the denominator of a fraction of the wavelength of yellow light. (As in "1/x wave" mirror.) <!)  ~~ < <|R XPP?  pr 9]4@|R`1 װ^?$6G v<wComputed Information--The zone with the maximum deviation of the measured wavefront compared to the ideal wavefront. <!m u  vr~~ < <R XPP?  pr <]4@R2 ذ^?$6G P<QComputed Information--The value of a in the equation for a parabola x=ay^2 + c. <! O  P~~  < <DS XPP?  px]4 @DS2 ٰ^?$6G P<QComputed Information--The value of c in the equation for a parabola x=ay^2 + c. <! O  P~~ !< <S XPP?  p]4!@SX3 ڰ^?$6G a<bComputed Information--The zones at which the actual parabola touch the ideal--the "zero points." <! `  a~~ "< < T XPP?  p ]4"@ T4 ۰^?$6G Z<[Computed Information--The constant that must be inserted into line 9 of the Texereau table to adjust the actual parabola to get the highest maximum equal in absolute value and opposite in sign to the lowest minimum. This is calculated by clicking on the yellow button in cell "I 12" (or pressing "ctrl-j") after entering the Foucault readings. <! Y  Zr~~ #< <pT XPP? ,,,]4#@pT4 ٞ$6G 1<2Inside/Outside measurements of Couder Mask Zones.< 1act~~ $< <T XPP? ,",<]4$@TP5 ٞ$6G 8<9Effective radius of optical center of Couder Mask Zones.< 8is ~~ %< <(O XPP? ,o,>]4%@(O5 ٞ$6G (<)Theoretical Ideal Foucault measurements.< (~~ &< <O XPP? ,,,t]4&@O6 ٞ$6G <The average zone radius is divided by the focal length times 4 (fixed light source) or 2 (moving). This is used as a convenient constant in later calculations.< ~~ '< <O XPP? ,8",R]4'@OH7 ٞ$6G %<&Averaged readings from Foucault test.< %~~ (< <TP XPP? ,B,]4(@TP7 ٞ$6G <The averaged readings after subtracting a constant that will make the minimums and maximums in line 11 equal in magnitude and opposite in value. < xx )< 6PXPP? ,O",]4)@P8 ٞ$6GX r<sResidual aberration at the center of curvature. This is the corrected measured parabola minus the ideal parabola. < #r~~ *< <Q XPP? ,[,l]4*@Q@9 ٞ$6G  <!Transverse aberration at Focus. <  ~~ +< <Q XPP? ,g,]4+@Q9 ٞ$6G E<FTransverse aberration at Focus (times 100,000 for convenience sake). < VE~~ ,< <PL XPP? ,s,]4,@PL: ٞ$6G 0<1Transverse aberration compared to the Airy Disk.< 0~~ -< <L XPP? ,o,]4-@L8; ٞ$6G <Error in wavefront slope.< xxx .< 6MXPP? ,",]4.@M; ٞ$6GX e<fThis line adds together the slopes of the various line segments to show the "Y" values for the chart.< e~~ /< <|M XPP? ,,]4/@|M< ٞ$6G 6<7The parabola that best fits the readings to the ideal. This parabola is selected by calculating all parabolas and then picking the one that touches the ideal parabola in only two places, and has the rest of the parabola either above or below the ideal. These calculations are performed in lines 65 to 95 below.< 6~~ 0< <M XPP? ,,]40@M0= ٞ$6G 7<8The difference between the ideal and actual wavefronts.< 7nd ~~ 1< <DN XPP? ,2,]41@DN= ٞ$6G s<tThe difference between the ideal and actual wavefronts expressed as a percentage of the wavelength of yellow light.< 8s onxx 2< 6IXPP?  ) 8,]42@I> ^?$6GX Z<[Minimum of parabola. This must be equal in magnitude and opposite in sign to the maximum. <! Y Z~~ 3< <I XPP?  p,g ,]43@I(? ^?$6G Y<ZMaximum of parabola. This must be equal in magnitude and opposite in sign to the minimum.<! Y~~ 4< <XJ XPP? ,,]44@XJ? m6G L<MThe next fifteen lines calculate various values for all possible parabolas. < [L 5< DJ  @Text 4 9\]5@Jx@ wh<xWelcome to RATDATA Ratdata is an Excel Workbook with several spreadsheets that help you analyze Foucault tests using a five zone Couder Mask. The worksheets display the data graphically and in table format. It is modeled after the work of Jean Texereau in How to Make a Telescope. The user easily enters the data and quickly sees what is needed to figure the mirror. The user may also print a single sheet report to keep in the figuring notebook. Because it uses the standard Windows and Excel interface, the program is easily adapted to individual tastes and needs. This workbook itself contains this "Readme" sheet of instructions and two worksheets. "Working Data" is for day to day figuring. "Two Axes" follows the same program logic, but allows checking for astigmatism on more than one axis. This is Ratdata release 11, which may use both fixed and moving light sources. Instructions and notes for the basic program are below. THIS WORKSHEET IS FOR INSTRUCTIONS ONLY--USE "WORKING DATA" OR "TWO AXES" SHEETS FOR YOUR ENTRIES. CLICK ON THE TABS AT THE BOTTOM OF THE WINDOW TO CHANGE FROM ONE SHEET TO ANOTHER. Directions: 1) Enter requested information in appropriate fields. Entry fields have red fonts. Information in cells with a blue background needs be entered only once. Information in cells with a gray background must be entered with every set of readings. In "Working Data" you may enter three sets of readings. The computer will average them. 2) Determine the appropriate "Constant" by clicking the yellow control box to make the deviation equal "0.". 3) Analyze the Data. How it works: A full analysis of the parabola and its uses is contained in Texereau's How to Make a Telescope. The spreadsheet roughly follows Texereau's methodology through line 5 of the Texereau data table (Row 48 of the worksheet). Lines 3 and 4 are altered to allow moving light sources as well as fixed. The notation on these lines remain Texereau's for a fixed source. Lines 6, 7, and 8 of the Texereau sheet are replaced by the "averaged readings" (of worksheet row 9). Texereau then suggests one determine (for his line 9) a constant to be subtracted from all the readings so that when one calculates line 10 and 11, one finds the two extreme zones are equal in absolute value, but different in sign. The spreadsheet does this by performing the line 10 and 11 calculations, and identifying the minimum and maximum deviations (in I54 and J54). The "Average" of these two values is put into Cell I6. The Maximum and Minimum must then be made to average 0 (because they must be equal in absolute value but opposite in sign). To make this happen, the user calls a subroutine (by clicking the control box) that runs Excel's "Goal Seek" tool. The subroutine changes the constant and re-runs the figures until the average is 0. When the "Average Deviation" in Cell I6 is 0, the proper constant has been selected. The worksheet then returns to Texereau's methodology to the end of his line 13. At this point, Texereau asks the reader to use graph paper, a ruler, and a pencil. The spreadsheet takes over and actually calculates the "Y" values by using the rise and the run of the line segments to determine where each "Y" point will be. Texereau then asks the reader to fit a parabola to these points. The worksheet first calculates parabolas for all possible points of intercept (rows 65 to 78). In the next set of cells (Row 81 to 94), the worksheet calculates the differences between the wavefront and the "best fit" parabola. The best fit requires that the differences are all either positive (or 0) or negative (or 0). So, the worksheet selects those parabolas that meet that criteria (Column I would indicate a 1). It then finds the maximum absolute value of the differences in that row (Column J), and looks for the smallest of the maximum differences of those parabola that qualify (Column B shows the ranking). The information about the selected parabola is then transferred to row 95, and subsequently to row 59. The worksheet then calculates the remaining datapoints, the difference between the best fit and the actual parabola, and the percentage of difference between the ideal wavefront reading and the actual. This information is transferred into the various report and graph sections. The workbook also contains a sheet called "Two Axes" that allows a more sophisticated approach, with two sets of data, entered on different axes so that the mirror maker can check astigmatism. It uses the same logic as the Working Data sheet. By watching the differences between the graphs on various axes, the mirror maker may see astigmatism in the mirror. This workbook was designed by Steve Meyering and Alex McConahay of the Riverside Astronomical Telescope Makers, part of the Riverside Astronomical Society. If you have suggestions, or bugs, please contact Alex at amcconahay@juno.com. This workbook is distributed free of charge for the use of amateur mirror makers. You may copy and redistribute the original template, but may not distribute an altered version of the template or workbook. While this worksheet is distributed free of charge, we would appreciate a contribution of $10 or more to the Riverside Astronomical Society so that we may develop the Landers Observatory Site. All contributions are tax deductible. Please mail a check to Riverside Astronomical Society, 8300 Utica Avenue, Suite 105, Rancho Cucamonga, CA 92730.<h c#Go G#QT?T ,x w~~ 6< < K XPP? :<>]46@ K4A ^?$6G <This section calculates the differences between the actual parabola and all the possible parabolas. Then, in column I, it assigns a "1" to those parabola which are on one side or the other of the actual, And, in column "J" it selects the largest difference between the candidate parabola and the actual. Finally, in row 96, it selects the candidate parabola which has the smallest maximum deviation. <! ~~ 7< <pK XPP? ,-<]47@pKA ^?$6G <Computed Information--The maximum deviation of the measured wavefront compared to the ideal wavefront expressed as a percentage of the wavelength of yellow light. <! ~~ 8< <`G XPP? , @-<]48@`GB ^?$6G <Computed Information--The maximum deviation of the measured wavefront compared to the ideal wavefront expressed as the denominator of a fraction of the wavelength of yellow light. (As in "1/x wave" mirror.)<!~~ 9< <G XPP? , -]49@G,C ^?$6G u<vComputed Information--The zone with the maximum deviation of the measured wavefront compared to the ideal wavefront.<!u~~ :< <H XPP? ,,]4:@HC ^?$6G P<QComputed Information--The value of a in the equation for a parabola x=ay^2 + c. <!O Pxx ;< 6xHXPP? , -]4;@xH|D ^?$6GX P<QComputed Information--The value of c in the equation for a parabola x=ay^2 + c. <! O  P~~ << <H XPP?  f, @-]4<@H$E ^?$6G `<aComputed Information--The zones at which the actual parabola touch the ideal--the "zero points."<! `~~ =< <@I XPP? ;<?x]4=@@IE ^?$6G p<qThis column ranks all parabolas as to which is closest to the ideal--that is, which has the smallest deviation. <!\o p~~ >< <E XPP?  ;< A]4>@EtF ^?$6G <In this column, the sheet selects which parabolas do not cross the "0" line, These are either all positive or all negative. This is necessary because the ideal parabola must be on one side or the other of the actual. <!~~ ?< <E XPP?  p;< E]4?@EG ^?$6G <This column lists the maximum deviations for all parabolas that are either all positive (or zero), or all negative (or zero). If a parabola is neither, (i.e., it crosses the "0" line) it is assigned a maximum deviation of 100 so it can be effectively ignored in the ranking.<! ~~ @< <`F XPP? J"M]4@@`FG ^?$6G <<=This cell tells which parabola from the list is ranked #1. <!@; < ~~ A< <F XPP? JP]4A@FlH ^?$6G `<aThese are the various values for the parabola that has the smallest deviations from the ideal. <!_ `xx B< 6CXPP? K O]4B@CI ^?$6GX P<QCalculation used for 1/8th wave--used for showing acceptable limits for graphs. <!O P<xx C< 6CXPP? OK SZ]4C@CI ^?$6GX< Z<[Pulls data from other parts of the sheet so that all graphing information is in one place.<! Z<xx D< 6`DXPP? S WZ]4D@`DdJ ^?$6GX< Z<[Pulls data from other parts of the sheet so that all graphing information is in one place.<! Z<xx E< 6DXPP? Y ]]4E@D K ^?$6GX< [<\Pulls data from other parts of the sheet so that all graphing information is in one place. <! Z  [ <~~ F< <B XPP?  ldpm]4F@BK ^?$6G< <This is a note <!I   @A <xx H< 6xBXPP? dz-]4H@xB\L 3aQ{6GX< c<dThis worksheet is for directions only. After reading, go to "Working Data" or "Two Axes" to use. <!b ca<xx J< 6BXPP?  r 8 r]4J@BM p6GX< N<OChoose Fixed or Moving Light Source. This changes line 49 and 50 calculations.<! N<ll N< s *,C+9 i ]N`,CM< "<# Click to make average Deviation=0<4 5 "# Judy and Alex McConahay0# Judy and Alex McConahay0# Judy and Alex McConahay0# Judy and Alex McConahay0# Judy and Alex McConahay0#Judy and Alex McConahay0#Judy and Alex McConahay0#Judy and Alex McConahay0#Judy and Alex McConahay0# Judy and Alex McConahay0# Judy and Alex McConahay0-!A satisfied Microsoft Office user# Judy and Alex McConahayf#HJudy and Alex McConahayf#Judy and Alex McConahayf# Judy and Alex McConahayf# Judy and Alex McConahayf# !Judy and Alex McConahayf#Judy and Alex McConahayf# "Judy and Alex McConahayf# Judy and Alex McConahayf# Judy and Alex McConahayf# Judy and Alex McConahayf# Judy and Alex McConahayf# JJudy and Alex McConahayf# Judy and Alex McConahayf# Judy and Alex McConahayf#Judy and Alex McConahayf-.#!A satisfied Microsoft Office user-/$!A satisfied Microsoft Office user-0%!A satisfied Microsoft Office user-1&!A satisfied Microsoft Office user-2'!A satisfied Microsoft Office user-3(!A satisfied Microsoft Office user-4)!A satisfied Microsoft Office user-5*!A satisfied Microsoft Office user-6+!A satisfied Microsoft Office user#62Judy and Alex McConahayf#6 3Judy and Alex McConahayf-7,!A satisfied Microsoft Office user-8-!A satisfied Microsoft Office user-9.!A satisfied Microsoft Office user-:/!A satisfied Microsoft Office user-;0!A satisfied Microsoft Office user-<1!A satisfied Microsoft Office user#=7Judy and Alex McConahayf#=8Judy and Alex McConahayf#=9Judy and Alex McConahayf#>:Judy and Alex McConahayf#>;Judy and Alex McConahayf#> <Judy and Alex McConahayf-?4!A satisfied Microsoft Office user#O6Judy and Alex McConahayf#P=Judy and Alex McConahayf#P>Judy and Alex McConahayf#P ?Judy and Alex McConahayf#_@Judy and Alex McConahayf#_AJudy and Alex McConahayf#`BJudy and Alex McConahayf#dCJudy and Alex McConahayf#hDJudy and Alex McConahayf#nEJudy and Alex McConahayf#p FJudy and Alex McConahayf>@2  jyK yK 6mailto:amcconahay@juno.comAq Light Source8Is light source FIXED, or is it MOVING with knife edge?  j%m  Sheet6 I@ $׭*  MbP?_*+%&A*'&L&D &T&CWorksheet Copyright RATS 2000(Gz?)ףp= ?MCanon Bubble-Jet BJC-4100@nyyhh@MSUDCanon Bubble-Jet BJC-4100d"T hh??cU}  } m  }   }   } $  }  } $  } m  } $ } $  Column NhT0@ b@ @b @b Á@ @ @b@ W@b  @m  @  @b  b@  @b @ b@E E b 0 E  O Q   S㥛? rh? 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