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%!PS-Adobe-3.0 % % ******************************************************************************** % % Figure 3.23 from the book: "The Theory of the Moire Phenomenon, Vol. II" % by I. Amidror, published by Springer, 2007. % % * * * Copyright (c) 2007 EPFL * * * % % Author: I. 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/mT[.24 0 0 -.24 28.081 810.979]def %RBIIncludeStartNup /sD 16 dict def %%IncludeFont: Times-Roman /f14/Times-Roman :mre /f29 f14 50 scf /f42 f14 25 scf {/Courier findfont[10 0 0 -10 0 0]:mf setfont}stopped{$error/newerror F put}if %PostScript Hack by Mike Brors 12/7/90 /DisableNextSetRGBColor { userdict begin /setrgbcolor { pop pop pop userdict begin /setrgbcolor systemdict /setrgbcolor get def end } def end } bind def /bcarray where { pop bcarray 2 { /da 4 ps div def df setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs 0 0 smc da 0 smc da da smc 0 da smc c gray { gl} {1 setgray}ifelse da 2. div dup moveto show }bind put } if % % Used to snap to device pixels, 1/4th of the pixel in. /stp { % x y pl x y % Snap To Pixel, pixel (auto stroke adjust) transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } bind def /snapmoveto { % x y m - % moveto, auto stroke adjust stp moveto } bind def /snaplineto { % x y l - % lineto, auto stroke adjust stp lineto } bind def %%EndSetup %%Page: 1 1 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (lspmac22; page: 1 of 1)setjob %%EndPageSetup gS 0 0 2242 3254 rC 0 0 0 0 rC 0 0 :M 0 setlinecap gR gS 0 0 2242 3254 rC 609 1037 :M f29 sf (\(a\))S 1554 1037 :M (\(b\))S 1 G 260 201 744 744 rF 0 G 2.078 lw 260 201 744 744 rS 267 227 :M f42 sf .012 .001(MOIRE EFFECTS THAT OCCUR IN THE SUPERPOSITION OF PER)J 267 251 :M .014 .001(IODIC LAYERS HAVE BEEN INTENSIVELY INVESTIGATED IN T)J 267 275 :M .012 .001(HE PAST, AND THEIR MATHEMATICAL THEORY IS TODAY FU)J 267 298 :M .009 .001(LLY UNDERSTOOD. THE SAME IS TRUE FOR MOIRE EFFECTS B)J 267 322 :M .008 .001(ETWEEN REPETITIVE LAYERS I.E. BETWEEN GEOMETRIC TRA)J 267 345 :M .017 .002(NSFORMATIONS OF PERIODIC LAYERS. HOWEVER, ALTHOUG)J 267 369 :M .01 .001(H MOIRE EFFECTS THAT OCCUR BETWEEN APERIODIC LAYER)J 267 393 :M .009 .001(S \(GLASS PATTERNS\) ARE KNOWN SINCE THE 1960S, ONLY LI)J 267 416 :M .012 .001(TTLE IS KNOWN TODAY ON THEIR MATHEMATICAL BEHAVIO )J 267 440 :M .01 .001(UR. IN THIS BOOK WE STUDY THE BEHAVIOUR OF SUCH MOI )J 267 463 :M .012 .001(RES, AND COMPARE IT WITH ANALOGOUS RESULTS FROM TH)J 267 487 :M .008 .001(E PERIODIC CASE. WE SHOW THAT ALL CASES, PERIODIC OR)J 267 511 :M .01 .001(NOT, OBEY THE SAME BASIC MATHEMATICAL RULES IN SPIT )J 267 534 :M .01 .001(E OF THEIR DIFFERENT VISUAL PROPERTIES. THIS LEADS US )J 267 558 :M .011 .001(TO A UNIFIED APPROACH WHICH EXPLAINS BOTH THE BEHA )J 267 582 :M .011 .001(VIOUR OF GLASS PATTERNS IN THE APERIODIC CASE, AND T)J 267 605 :M .01 .001(HE WELL KNOWN BEHAVIOUR OF THE MOIRE PATTERNS IN P)J 267 629 :M .012 .001(MOIRE EFFECTS THAT OCCUR IN THE SUPERPOSITION OF PER)J 267 652 :M .014 .001(IODIC LAYERS HAVE BEEN INTENSIVELY INVESTIGATED IN T)J 267 676 :M .012 .001(HE PAST, AND THEIR MATHEMATICAL THEORY IS TODAY FU)J 267 700 :M .009 .001(LLY UNDERSTOOD. THE SAME IS TRUE FOR MOIRE EFFECTS B)J 267 723 :M .008 .001(ETWEEN REPETITIVE LAYERS I.E. BETWEEN GEOMETRIC TRA)J 267 747 :M .017 .002(NSFORMATIONS OF PERIODIC LAYERS. HOWEVER, ALTHOUG)J 267 771 :M .01 .001(H MOIRE EFFECTS THAT OCCUR BETWEEN APERIODIC LAYER)J 267 794 :M .009 .001(S \(GLASS PATTERNS\) ARE KNOWN SINCE THE 1960S, ONLY LI)J 267 818 :M .012 .001(TTLE IS KNOWN TODAY ON THEIR MATHEMATICAL BEHAVIO )J 267 841 :M .01 .001(UR. IN THIS BOOK WE STUDY THE BEHAVIOUR OF SUCH MOI )J 267 865 :M .012 .001(RES, AND COMPARE IT WITH ANALOGOUS RESULTS FROM TH)J 267 889 :M .008 .001(E PERIODIC CASE. WE SHOW THAT ALL CASES, PERIODIC OR)J 267 912 :M .01 .001(NOT, OBEY THE SAME BASIC MATHEMATICAL RULES IN SPIT )J 267 936 :M .01 .001(E OF THEIR DIFFERENT VISUAL PROPERTIES. THIS LEADS US )J 1 G 1205 201 744 744 rF 0 G 1205 201 744 744 rS 1212 227 :M .012 .001(MOIRE EFFECTS THAT OCCUR IN THE SUPERPOSITION OF PER)J 1212 251 :M .014 .001(IODIC LAYERS HAVE BEEN INTENSIVELY INVESTIGATED IN T)J 1212 275 :M .012 .001(HE PAST, AND THEIR MATHEMATICAL THEORY IS TODAY FU)J 1212 298 :M .009 .001(LLY UNDERSTOOD. THE SAME IS TRUE FOR MOIRE EFFECTS B)J 1212 322 :M .008 .001(ETWEEN REPETITIVE LAYERS I.E. BETWEEN GEOMETRIC TRA)J 1212 345 :M .017 .002(NSFORMATIONS OF PERIODIC LAYERS. HOWEVER, ALTHOUG)J 1212 369 :M .01 .001(H MOIRE EFFECTS THAT OCCUR BETWEEN APERIODIC LAYER)J 1212 393 :M .009 .001(S \(GLASS PATTERNS\) ARE KNOWN SINCE THE 1960S, ONLY LI)J 1212 416 :M .012 .001(TTLE IS KNOWN TODAY ON THEIR MATHEMATICAL BEHAVIO )J 1212 440 :M .01 .001(UR. IN THIS BOOK WE STUDY THE BEHAVIOUR OF SUCH MOI )J 1212 463 :M .012 .001(RES, AND COMPARE IT WITH ANALOGOUS RESULTS FROM TH)J 1212 487 :M .008 .001(E PERIODIC CASE. WE SHOW THAT ALL CASES, PERIODIC OR)J 1212 511 :M .01 .001(NOT, OBEY THE SAME BASIC MATHEMATICAL RULES IN SPIT )J 1212 534 :M .01 .001(E OF THEIR DIFFERENT VISUAL PROPERTIES. THIS LEADS US )J 1212 558 :M .011 .001(TO A UNIFIED APPROACH WHICH EXPLAINS BOTH THE BEHA )J 1212 582 :M .011 .001(VIOUR OF GLASS PATTERNS IN THE APERIODIC CASE, AND T)J 1212 605 :M .01 .001(HE WELL KNOWN BEHAVIOUR OF THE MOIRE PATTERNS IN P)J 1212 629 :M .012 .001(MOIRE EFFECTS THAT OCCUR IN THE SUPERPOSITION OF PER)J 1212 652 :M .014 .001(IODIC LAYERS HAVE BEEN INTENSIVELY INVESTIGATED IN T)J 1212 676 :M .012 .001(HE PAST, AND THEIR MATHEMATICAL THEORY IS TODAY FU)J 1212 700 :M .009 .001(LLY UNDERSTOOD. THE SAME IS TRUE FOR MOIRE EFFECTS B)J 1212 723 :M .008 .001(ETWEEN REPETITIVE LAYERS I.E. BETWEEN GEOMETRIC TRA)J 1212 747 :M .017 .002(NSFORMATIONS OF PERIODIC LAYERS. HOWEVER, ALTHOUG)J 1212 771 :M .01 .001(H MOIRE EFFECTS THAT OCCUR BETWEEN APERIODIC LAYER)J 1212 794 :M .009 .001(S \(GLASS PATTERNS\) ARE KNOWN SINCE THE 1960S, ONLY LI)J 1212 818 :M .012 .001(TTLE IS KNOWN TODAY ON THEIR MATHEMATICAL BEHAVIO )J 1212 841 :M .01 .001(UR. IN THIS BOOK WE STUDY THE BEHAVIOUR OF SUCH MOI )J 1212 865 :M .012 .001(RES, AND COMPARE IT WITH ANALOGOUS RESULTS FROM TH)J 1212 889 :M .008 .001(E PERIODIC CASE. WE SHOW THAT ALL CASES, PERIODIC OR)J 1212 912 :M .01 .001(NOT, OBEY THE SAME BASIC MATHEMATICAL RULES IN SPIT )J 1212 936 :M .01 .001(E OF THEIR DIFFERENT VISUAL PROPERTIES. THIS LEADS US )J 609 2052 :M f29 sf (\(c\))S 1554 2052 :M (\(d\))S 1 G 260 1217 744 744 rF 0 G 260 1217 744 744 rS 267 1243 :M f42 sf .012 .001(MOIRE EFFECTS THAT OCCUR IN THE SUPERPOSITION OF PER)J 267 1267 :M .014 .001(IODIC LAYERS HAVE BEEN INTENSIVELY INVESTIGATED IN T)J 267 1290 :M .012 .001(HE PAST, AND THEIR MATHEMATICAL THEORY IS TODAY FU)J 267 1314 :M .009 .001(LLY UNDERSTOOD. THE SAME IS TRUE FOR MOIRE EFFECTS B)J 267 1338 :M .008 .001(ETWEEN REPETITIVE LAYERS I.E. BETWEEN GEOMETRIC TRA)J 267 1361 :M .017 .002(NSFORMATIONS OF PERIODIC LAYERS. HOWEVER, ALTHOUG)J 267 1385 :M .01 .001(H MOIRE EFFECTS THAT OCCUR BETWEEN APERIODIC LAYER)J 267 1408 :M .009 .001(S \(GLASS PATTERNS\) ARE KNOWN SINCE THE 1960S, ONLY LI)J 267 1432 :M .012 .001(TTLE IS KNOWN TODAY ON THEIR MATHEMATICAL BEHAVIO )J 267 1456 :M .01 .001(UR. IN THIS BOOK WE STUDY THE BEHAVIOUR OF SUCH MOI )J 267 1479 :M .012 .001(RES, AND COMPARE IT WITH ANALOGOUS RESULTS FROM TH)J 267 1503 :M .008 .001(E PERIODIC CASE. WE SHOW THAT ALL CASES, PERIODIC OR)J 267 1526 :M .01 .001(NOT, OBEY THE SAME BASIC MATHEMATICAL RULES IN SPIT )J 267 1550 :M .01 .001(E OF THEIR DIFFERENT VISUAL PROPERTIES. THIS LEADS US )J 267 1574 :M .011 .001(TO A UNIFIED APPROACH WHICH EXPLAINS BOTH THE BEHA )J 267 1597 :M .011 .001(VIOUR OF GLASS PATTERNS IN THE APERIODIC CASE, AND T)J 267 1621 :M .01 .001(HE WELL KNOWN BEHAVIOUR OF THE MOIRE PATTERNS IN P)J 267 1645 :M .012 .001(MOIRE EFFECTS THAT OCCUR IN THE SUPERPOSITION OF PER)J 267 1668 :M .014 .001(IODIC LAYERS HAVE BEEN INTENSIVELY INVESTIGATED IN T)J 267 1692 :M .012 .001(HE PAST, AND THEIR MATHEMATICAL THEORY IS TODAY FU)J 267 1715 :M .009 .001(LLY UNDERSTOOD. THE SAME IS TRUE FOR MOIRE EFFECTS B)J 267 1739 :M .008 .001(ETWEEN REPETITIVE LAYERS I.E. BETWEEN GEOMETRIC TRA)J 267 1763 :M .017 .002(NSFORMATIONS OF PERIODIC LAYERS. HOWEVER, ALTHOUG)J 267 1786 :M .01 .001(H MOIRE EFFECTS THAT OCCUR BETWEEN APERIODIC LAYER)J 267 1810 :M .009 .001(S \(GLASS PATTERNS\) ARE KNOWN SINCE THE 1960S, ONLY LI)J 267 1834 :M .012 .001(TTLE IS KNOWN TODAY ON THEIR MATHEMATICAL BEHAVIO )J 267 1857 :M .01 .001(UR. IN THIS BOOK WE STUDY THE BEHAVIOUR OF SUCH MOI )J 267 1881 :M .012 .001(RES, AND COMPARE IT WITH ANALOGOUS RESULTS FROM TH)J 267 1904 :M .008 .001(E PERIODIC CASE. WE SHOW THAT ALL CASES, PERIODIC OR)J 267 1928 :M .01 .001(NOT, OBEY THE SAME BASIC MATHEMATICAL RULES IN SPIT )J 267 1952 :M .01 .001(E OF THEIR DIFFERENT VISUAL PROPERTIES. THIS LEADS US )J 1 G 1205 1217 744 744 rF 0 G 1205 1217 744 744 rS 1212 1243 :M .012 .001(MOIRE EFFECTS THAT OCCUR IN THE SUPERPOSITION OF PER)J 1212 1267 :M .014 .001(IODIC LAYERS HAVE BEEN INTENSIVELY INVESTIGATED IN T)J 1212 1290 :M .012 .001(HE PAST, AND THEIR MATHEMATICAL THEORY IS TODAY FU)J 1212 1314 :M .009 .001(LLY UNDERSTOOD. THE SAME IS TRUE FOR MOIRE EFFECTS B)J 1212 1338 :M .008 .001(ETWEEN REPETITIVE LAYERS I.E. BETWEEN GEOMETRIC TRA)J 1212 1361 :M .017 .002(NSFORMATIONS OF PERIODIC LAYERS. HOWEVER, ALTHOUG)J 1212 1385 :M .01 .001(H MOIRE EFFECTS THAT OCCUR BETWEEN APERIODIC LAYER)J 1212 1408 :M .009 .001(S \(GLASS PATTERNS\) ARE KNOWN SINCE THE 1960S, ONLY LI)J 1212 1432 :M .012 .001(TTLE IS KNOWN TODAY ON THEIR MATHEMATICAL BEHAVIO )J 1212 1456 :M .01 .001(UR. IN THIS BOOK WE STUDY THE BEHAVIOUR OF SUCH MOI )J 1212 1479 :M .012 .001(RES, AND COMPARE IT WITH ANALOGOUS RESULTS FROM TH)J 1212 1503 :M .008 .001(E PERIODIC CASE. WE SHOW THAT ALL CASES, PERIODIC OR)J 1212 1526 :M .01 .001(NOT, OBEY THE SAME BASIC MATHEMATICAL RULES IN SPIT )J 1212 1550 :M .01 .001(E OF THEIR DIFFERENT VISUAL PROPERTIES. THIS LEADS US )J 1212 1574 :M .011 .001(TO A UNIFIED APPROACH WHICH EXPLAINS BOTH THE BEHA )J 1212 1597 :M .011 .001(VIOUR OF GLASS PATTERNS IN THE APERIODIC CASE, AND T)J 1212 1621 :M .01 .001(HE WELL KNOWN BEHAVIOUR OF THE MOIRE PATTERNS IN P)J 1212 1645 :M .012 .001(MOIRE EFFECTS THAT OCCUR IN THE SUPERPOSITION OF PER)J 1212 1668 :M .014 .001(IODIC LAYERS HAVE BEEN INTENSIVELY INVESTIGATED IN T)J 1212 1692 :M .012 .001(HE PAST, AND THEIR MATHEMATICAL THEORY IS TODAY FU)J 1212 1715 :M .009 .001(LLY UNDERSTOOD. THE SAME IS TRUE FOR MOIRE EFFECTS B)J 1212 1739 :M .008 .001(ETWEEN REPETITIVE LAYERS I.E. BETWEEN GEOMETRIC TRA)J 1212 1763 :M .017 .002(NSFORMATIONS OF PERIODIC LAYERS. HOWEVER, ALTHOUG)J 1212 1786 :M .01 .001(H MOIRE EFFECTS THAT OCCUR BETWEEN APERIODIC LAYER)J 1212 1810 :M .009 .001(S \(GLASS PATTERNS\) ARE KNOWN SINCE THE 1960S, ONLY LI)J 1212 1834 :M .012 .001(TTLE IS KNOWN TODAY ON THEIR MATHEMATICAL BEHAVIO )J 1212 1857 :M .01 .001(UR. IN THIS BOOK WE STUDY THE BEHAVIOUR OF SUCH MOI )J 1212 1881 :M .012 .001(RES, AND COMPARE IT WITH ANALOGOUS RESULTS FROM TH)J 1212 1904 :M .008 .001(E PERIODIC CASE. WE SHOW THAT ALL CASES, PERIODIC OR)J 1212 1928 :M .01 .001(NOT, OBEY THE SAME BASIC MATHEMATICAL RULES IN SPIT )J 1212 1952 :M .01 .001(E OF THEIR DIFFERENT VISUAL PROPERTIES. THIS LEADS US )J endp /inch {72 mul} def 2 inch 3.8 inch translate gsave -0.25 inch -1.5 inch translate 0 inch 0 inch moveto /Times-Bold findfont 12 scalefont setfont (Figure 3.23) show /Times-Roman findfont 12 scalefont setfont ( from the book: ) show /Times-Italic findfont 12 scalefont setfont (The Theory of the Moire) show -0.06 inch 0 inch rmoveto (\302 Phenomenon) show -0.1 inch -0.25 inch moveto (Vol. II: Aperiodic Layers,) show /Times-Roman findfont 12 scalefont setfont ( by I. Amidror, published by Springer, 2007.) show 1.7 inch -0.65 inch moveto ((First layer only.)) show grestore showpage %%PageTrailer %%Trailer end %%EOF