WordProLWP7.a YƤ1*xWord Pro Text File/DFBAc@PPPPP-PPP@James W. Burrows1;C;TQ@@@ @ SmartMasterH@ASMH@James W. BurrowsH@BJWBXP p@@UNIVERSAL_SMARTMASTER_EDITOR@ESMX@@@q pcPP`@@q pcPP` @UNIVERSAL_ALL_OTHERS_EDITOR@FOTRX@@@q pcPP`@@q pcPP` @James W. Burrows@FJWBX@@@q pcPP`@@q pcPP`B@QCB PP p  q@Tp= yqp~ qPHPHPHPH(x qQdIZ+88fxBBp= fA8@FH,p= f@B43Bp= @B>Bp= 8CPHBp= 8!CPBp= !A8@Bz$Bp= A!@B?Bp= APHBPHBgf ( xAQdHHAQdHHq ~APHBgf PHB(e AAk qAy}- ?@E 7 xP@P@@@ P@@@P @@@ X@@@Ppq *@LH @@@d*plC|@@@ p@@@P 7q @P@P@@@ P@@@P @@@PpP@@@ | @@@P *CyEH @ Heading 1 OpEH@EText 1 ?}{ExP : A @P@P@@@ P@@@P @@@ P@@@Pp I "xE7CAJBBx7 A&PHPHZ2)6 3APPP{)AA@L@{UPHHSqU{A@JLUHKIsA2GBA2$DHHPHA$ %A2Ay%]A$Az]A%AHHPHA A]AyZ(*Q|*B*BpBCه |VQz_ fBKCt V |z_ fBMCY  Vz_ fBNBw 6E ffBff3&A6ItB&A3Bz$Bz*'ABBBBRBBB #Cz@ @@P@ J )x@ @@P@@@@@P@"q !@@ @@P@# OC @@@P@c xpp  @@@PppP @@@ qcP`R@d H@dfxHBPHBff (xBHHBff PHB(ZZ Z Z Z pH@PZ  pH@P pH@P pH@P pH@PZZZZ(( /!("(# ($(%(&('Z)Z*Z,Z-fZ.cZ/dZ0eZ17Z3 Z4 IZ5Z6 Z7 OZ8 JZ9Z:Z;ZZZ>H@@ ??X@P`@@P`@@Pp@P`@@Hx``@@Hx``PC q@@P@ A7@A#yC@Hx@Hx@Hx@Hx`%C@@@Q$q%@@@@Q@@@R- }Ex$ lq@@@@P |C@@@P y *CEH@EText 2y O@EH@EText 3{ ?Am@@@@@@@ " !A I@EJa8PP%C@@@R q@AJB7CAHSLSm  A%@p@  ABff4z @@@P@ ) 'A J@@@@P@z@@@@P@A '@@ @@P@ !"A O@@ @@P@ O !A#@@ @@P@ ABffbff€BBB7@-@<@Pc@P c@P c@P ABffbff, Aff,A@Aj|A !@EJa8|mA@EJX s-ExPpAHS m  x@Pp@Pp@Pp@Pp`p@@@R&$ p`@x@& p`@x@&p`A m{|@EJX !A "@EJXPP& p`A pA  'A )@@@@P@&p`A )PqZ%A*QP HBH$@P@P P P  DBlpQEl @QDmqDG@Rl lRs%D@@EBodytBPP@EBody@p F{@ {}yPV uAuxpA@P#AyU@@Default FooterXA@BQJA+AP@EFooter%A@@@Default Footer Styleh$@aAAAyA@ @YAfAdAe@ XQ$@c.Y+u@pA@B PRA=A+P@EFooterI/A#A%Iyy@ @Y XQ@c /*BA,yd@Q. $@FStoryBA,Y0A0AmU AxpA@Pq#yU@@Default HeaderXA@BQJPA#AP@EHeaderA@@@Default Header Styleh$@aAAAyA@ @YAfAdAe@ XQ@c+Xq.yu@pA@B PRPA.A#P@EHeaderI,AAIyy@ @Y XQ@c ,,/Bqd@Q+ $@FStory/BQ-A-Amu .A+AV@@ Default PageQA@JIXA @CPageH@@Default Page Styleh$@@ Default TextIxAA~AyAc@ iAfAdAe@ @Printer Folder SettingH$@@ +y\D'd@Q ,@FStory A4AmT &xpA@PCX=@pH@B PRA&A=P@EFooterIHA#A%Iyy@ @Y XQ@c H.8AByd@QC ,@@FStory8ABB%aID m=WqCy@pH@B PRPACA.P@EHeaderIBAAIyy@ @Y XQ@c B*HA/yd@Q= @@FStoryHA/YKAKAmBq]ACA=AT@iH@IAAuP@CPageIAu+ A p@t q@@PE y@D@ @ @ EP-V vs. @ @ @ DRMSSSEndKPAmTffAB@ASSEnd/d Ax @m}qk@ Default TextP@@@i@@Default Text Style@@@pE A@x`aA D}AF @@@PP@@@  r H@@a I! xZmT AH@CHcSEnd qIB $ZmH@CHH@@SHHD\HH@@SHHE HHG HH2001-08-27 13:26:06HHE TPAlnF SEnd  cr W 8iH{ @@PE  H@Now() %FLISODate2 @F@Xw +@DTitleP@@@i@P@@@pEAm@Dd B}q *A# @@@  ) EAH@[2y@B DefinitionsSSEnd2Z(D @ Heading 1P@@@i@P@@@pEAm@D A ?y OA @@@  EVB@eS H@BThe R@ @ @ RMS (Root Mean Square) deviation of the surface of a mirror is the square root of the area-weighted mean squared deviation from the parabolic surface which minimizes this quantity. That parabola will be called the A Obest-fitA O parabola. A convenient unit for the surface @ @ @ ERMS is @ @ @ nanometers@ @ @ C;2 another popular unit is waves, twice the surface @ @ @ ERMS; divided by the reference wavelength of light (usually 550 @ @ @ Fnm). The importance of the @ @ @ ERMS is that the @ @ @ Strehl2 ratio of the mirror can be found in terms of the @ @ @ ERMS by the @ @ @ Mahajan approximationSSEnd H1/@EText 1p@i@Am@D I J V(A EBe `T5y@BA]ASSEnd5i Bl @FEq Para`@@i@@Center tab & right tab@@@pE A@Am@Db"Bx AVIeK H@BCwFithHH surface HB@ @ @ FRMSHHD H HDsHH and reference wavelength @HDLHHDB. A OThe general implication of a good-quality image is that the HB@ @ @ StrehlHH ratio is 0.8.A O Solving HB@ @ @ FMahajanA LsHH$ approximation gives a passing surfaHHFce HB@ @ @ FRMSHH of 20.7 HB@ @ @ EnmHB@ @ @ D.HcSEnd'#AyU@@ Default FrameQ A@IQXAAP@DFrameH@@Default Frame Styleh$@@ Default TextIAAAAc@ @YAfAdAe@ A]@&AyU@ @GEquationQ E@ QJ00AACP@DFrameI'AxH@@Equation Frame StyleI6A7AAyA@ @Y8 A2@]QAyT@i" A@IQXAAP@DFrameI\A&*A7 @RVA8 A)@)\C@Q] @ @GraphicAY @C.texX@F.texf IHZG c E dtc Z  '* 8yd@Q& $@Story 8_88my(AIeK H@BThe R@ @ @ EP-Vp (Peak-Valley) deviation of the surface of a mirror is the maximum deviation minus the minimum deviation from th&e best-fit parabola. Parallel to the @ @ @ FRMS,# a convenient unit for the surface @ @ @ EP-V is @ @ @ nanometers;A it is also popularly given in terms of waves, twice the surface @ @ @ EP-V4 divided by the reference wavelength of light. The @ @ @ Rayleigh Criterion says that the @ @ @ EP-V( should be less than wave, or surface @ @ @ EP-V < 68.8 @ @ @ Dnm.SSEnd('2AIeS2y@BExamplesSSEnd2A(Be "K H@B=These deviation plots are for a 200 mm f/6 mirror. The plot XCx -axis is zone radius in mm, the XCy"-axis is the surface deviation in @ @ @ Enm.4 The first is the worst -wave mirror I could find:DSSEnd[2IK H@B The surface @ @ @ ERMS is 22.9 @ @ @ Dnm and @ @ @ Strehl ratio 0.760, not quite passing.SSEnd2&U@@Default Graphic/OLEQ A@IQ XA]A&P@DFrameIAxH@@Graphic/OLE Frame StyleIAyyx @Y A]@TBkqT@i" A@HYXDkP@DFrameLV @R2Af XSU)jy@R@ @Graphicj\jP@D.bmp4R @@I@A2@A2@H@H@H@A @B`@G.bmp #I,H@C:\temp\bad.bmp ,B qd@Q @FStory\B W{{m[BdJ`J\R H@BThe next example, gotten by flattening the outermost deviations from the above A JbadA O -wave mirror, is a A KgoodA O -wave mirror:AASSEndc[AK H@B With surface @ @ @ ERMS 13.3 @ @ @ DnmF andE @ @ @ Strehl( ratio 0.912, it is an excellent mirror.SSEnd_r[HBA@} }A{AB_ PP  ZHZOZI(RuqyX@@ Default CellQAA@@@R@0@AAP@CCellH@@Default Table Cell Styleh$@ @ Table TextI3AAAA@7Ay[AyX@@Default ColumnQ@H@@@QH0@AAP@CCellX$@@ Default Texty@!`AyX@@Default Left ColumnQ@H@@@QH0@AAP@CCellX$@@ Default Texty@!_X@@Default Right ColumnQ@H@@@QH0@AAP@CCellX$@@ Default Texty@!mqW@@ Default TableQH@@RB0PAAP @ SuperTableH@@Default Table StyleAy@. A@A&yU@@Default Drop CapQ A@IQXAAP @FDropCapIAxH@@Default Drop Cap Styleh$@@ Default TextI&AAAyA@!AfAdAe@ X@Dzb%@@T]BqT@i" A@HYXD]P@DFrameIA  @U[f XScE nR H@BFinally, a 1-wave mirror:DkSSEndkV&qT@i" A@I@QXE&H@DFrameLj| @Ucf XS{'4E *K H@B&These three examples show the general @ @ @ EP-V vs. @ @ @ ERMSM situation, which is illustrated by the usual A OintersectionA O diagram:D&SSEnd&Nk T@i" A@qXzkH@DFrameL'Q @R'A8 XSP\^W AxpA@P_`abX AxpA@P(iZ  Zd4"q'B JI  HT23+A@BBThe yellow region represents mirrors that are both -wave and 0.8 @ @ @ Strehl@ @ @ C, green 0.8 @ @ @ Strehlh but not -wave, and the red sliver is the small number of -wave mirrors that donA It A KpassA J.SSEnd?q4B BA@@ @qAB? 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Burdell832882267FA ljmYA@H@@P@@P@@PPpPP`@p@P P tݬ;BlOowtJxOp|v~}qrsyz{u HAH pcP`@@Times New Roman Js@James W. Burrows884393539njYA@H@@P@@P@@PPpPP`@p@P P tݬ;BOJO HAH dP@QUUH cpcP@QHdP@QUUH cpcP@QHdP@QTT cpcP@Q cpc@ @CG TimesHWhWHGoJs@James W. Burrows884393558giaA@H@@P@@P@@PPpPP&@$C:\Allmine\work\wordpro\EQUATION.MWPH@p@P P pAOHP LaserJet 5L PCL@CH@C@H@AH?(BX@PP(IfH@H@????T۝@  @@@@@C@ BXJ@@d@PB@@@ELPT1:@HP LaserJet 5L PCL @GHPPCL5GP@E1-9999XPDUVerO@P@Original Version@James W. Burrows1;C; `@@ASMH@BJWBlݬ;,AQA A Q QAA AAAAAAAAAAAAAAAAAAAA !A"A#A A$A%A&A'(A)A*A+A,A-A.A/A0A1A2A3A4A5A6A7A8A9A:A;@ AAAQAAQ>A?AAAB@@James W. Burrows998519263A DYƤ1:.P@@CHH@sh PIHBJM  JGQv1YDmIfI III I I II I III I I P I? I- IQ Ic I I$ I~ Iu I- I I I I I I I I I I I& I/ I8 IIA IN II[ Ih It I I I II I I I I I I I I IH IW I HLQI IIhI|II I )I)I7I7I6I97IW0I)I6I!7I$)I.7II^IIf.I.IL0I6I7IP.I|7I[.I.I.I.I.IR7II2IG7I]7Ih7I.Is7I7Im II ?I7IIII IIIIaIpII2IYII>II[I%CIOII+IM3I':IU9I@I|3I;I$@IAIIxI IIpI4 IAI/)I| II1I BI)IBBI*IIdBI*IBI*IIIh IBIf+IhI IuBI3I3ILI2I III@I@I3I=I9IAI I1II"1I:IIIIIICIYII!IAI/IILIII II4I I.I0II IIjIITEIjCICIDIDIDI|CIDICIsCICIDIDIDICICICICIDICICI>DI3DI,EI7EI!EIIDITDI_DIjDIuDIDIDIDIDIDIEIEIEIBEIZ+:;(D 3c'@AA2@@AA F.f;'F;4@AH@Eݬ;H@A(YIbfIdHIII,IsILIHILIKILIIIM ILIJILIKILIkKIbLIJIKISIfITIgIUI]IVII!hIWIxgIYXIfIXIQfIlWI>cII.IrII4I>I>?I#I5]I`I@I>I@II8 IIITIbI]IaI!_I`cIh^I^I]IT_IVI\IdI0PfIc0IcI^II%I!'I>I,IZI I I5I I II(IIIII II II IAIAIAIIISI7IIVII I I$ II I, I8I-I:!I#I#IAI%Ig2I15I,II I(I&I5&I8IIIU'I9I(I9Iv,I5I,I%9III2I!-I+I.I-IS6I49I0I,0I@IL2IC9IIIBIBICICII6DQv1E4|A IVIoIfrIluHYƤ1.f;:;J.54M4]1Qv1&/20/2վ4?5g5ݬ;{2;ߧc1E72 5a5V521;e1CG Times,18,12,0,0,0,0,0 TCIformat{2}SR $=\exp \left( -\left( 4\pi \sigma /L\right) ^2\right) $`J    . 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