㔚ሶశቇ㐷
㧙ޓ㔚ሶಽశⵝ⟎ߩℂ⸃ߩߚߦޓ㧙
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ཅ⮮ޓ⺈ ᣣᧄ㔚ሶ (ᩣ) ޥ 196-8558 ᧲੩ㇺᤘፉᏒᱞ⬿㊁ 3-1-2 kato@jeol.co.jp 㧔2008 ᐕ 8 4 ᣣฃℂ㧕 㔚ሶశቇ♽ߦ߅ߡ㧘ߩᕈ⾰ࠍᡰ㈩ߔࠆߩߪኻ‛ࡦ࠭ߢߔ㧚ߎࠇߪ㧘㔚ሶࡆࡓߩ㐿߈ⷺ߇‛ 㕙ߦ߅ߡᦨ߽ᄢ߈ߥ୯ߣߥࠆ߆ࠄߢߔ㧚⚿ࠍߣ߽ߥ߁㔚ሶಽశߩ႐ว㧘ⓨ㑆ಽ⸃⢻ࠃࠅᒝᐲ߇ ఝవߐࠇࠆߎߣ߇ߒ߫ߒ߫ࠅ㧘ߘߩߣ߈ߩߩᕈ⾰ߪኻ‛ࡦ࠭ߩ㕙Ꮕߦࠃߞߡቯߐࠇ߹ߔ㧚 ࿁ߪ㧘㕙Ꮕߩሽߩ߽ߣߢߩࠗࡦࠦࡅࡦ࠻శቇ♽ߩ⚿ࠍ⼏⺰ߒ߹ߔ㧚߹ߚ㧘ߘߩࠃ߁ߥ శቇ♽ߩ⹏ଔߩߚߦലߣߥࠆⓨ㑆ᵄᢙᔕ╵ߩℂ⺰ࠍ⚫ߒ߹ߔ㧚Introduction to Electron Optics
for the Study of Energy Analyzing Systems (12)
M. KatoJEOL Ltd., 3-1-2 Musashino, Akishima, Tokyo 196-8558. kato@jeol.co.jp
(Received: August 4, 2008)
The quality of images of an electron optical system is dominated by the performance of an objective lens. This is because the angle spread of an electron beam becomes largest in an object plane. In electron spectroscopy with imaging, image intensity often has priority over spatial resolution, and then the image quality is determined by the spherical aberration of an objective lens. In this chapter, the imaging process for incoherent illumination under the influence of spherical aberration is discussed. Evaluation of such optical systems using the theory of spatial-frequency response is also described. ޓ
12
ኻ‛ࡦ࠭ߩ⸳⸘ߣߩ⹏ଔ
12.1
ߪߓߦ
㔚ሶ⚿♽ߦࠃߞߡߟߊࠄࠇࠆߩᕈ⾰ߪ㧘߶ߣ ࠎߤኻ‛ࡦ࠭ߩᕈ⢻ߛߌߢࠄࠇ߹ߔ㧚ߎࠇߪ㧘 TEM ߩࠃ߁ߥ౮ဳߩⵝ⟎ߛߌߢߪߥߊ㧘SEM ߩ ࠃ߁ߦ㔚ሶࡊࡠࡉࠍᩏߔࠆⵝ⟎ߦ߅ߡ߽ห᭽ ߢߔ㧚࿁ߪ㧘ߥߗኻ‛ࡦ࠭߇㊀ⷐߦߥࠆ߆ࠍ߹ߕ ㅀߴ㧘ౕ⊛ߥኻ‛ࡦ࠭ߩ᭴ㅧ㧘߅ࠃ߮ᒻᚑߐࠇࠆ ߩ⹏ଔߦ㑐ߒߡ⺑ߒ߹ߔ㧚 ⓨ㑆ಽ⸃⢻ߦ㑐ߒߡߩశቇ♽ߩᦨㆡ᧦ઙߦߟߡ ߪ㧘೨࿁ߒߊㅀߴ߹ߒߚ㧚ⓨ㑆ಽ⸃⢻߇ᦨዊߣߥࠆ ࠃ߁ߥࡆࡓߩ㐿߈ⷺ㧘ߔߥࠊߜᦨㆡ㐿߈ⷺ߇ሽ ߒߡ㧘ߘߎߢߪ࿁᛬Ꮕߣ㕙Ꮕ߇ห⒟ᐲߩነਈ ߣߥࠆߩߢߒߚ㧚TEM ߿ SEM ߩࠃ߁ߦᒻᘒⷰኤ߇ ⋡⊛ߩⵝ⟎ߢߪ㧘ⓨ㑆ಽ⸃⢻߇ᦨ㊀ⷐߩ⹏ଔၮḰߣ ߥࠅ㧘ࠃߞߡಽ⸃⢻ߦ㑐ߒߡߩᦨㆡ᧦ઙߩ߽ߣߢߩേ ߇೨ឭߣߥࠅ߹ߔ㧚 ৻ᣇ㧘㔚ሶಽశߩࠃ߁ߦಽᨆࠍ⋡⊛ߣߔࠆⵝ⟎ߦ ߅ߡߪ㧘ᔅⷐߥᗵᐲࠍᓧࠆߚߦ㧘ⓨ㑆ಽ⸃⢻ࠍ ‶†ߦߖߑࠆࠍᓧߥ⁁ᴫ߇ߒ߫ߒ߫߈߹ߔ㧚ߚߣCopyright (c) 2008 by The Surface Analysis Society of Japan
߃߫ AES ߢߪ㧘৻ᰴ㔚ሶ✢ߩࡊࡠࡉ㔚ᵹ୯ࠍఝవ ߔࠆߎߣߢಽశߩᗵᐲࠍᓧ߹ߔ㧚ࠆߪ㧘⹜ᢱࠍ X ✢ߢᾖߒߡ㧘⹜ᢱ߆ࠄߐࠇࠆశ㔚ሶߢࠗࡔ ࠫࡦࠣࠍⴕ߁ⵝ⟎ߦ߅ߡ߽ห᭽ߢߔ㧚ߎߩࠃ߁ߥ႐ วߪ㧘ߩࠦࡦ࠻ࠬ࠻߇㊀ⷐߣߥࠅ㧘ߤߎ߹ߢ⚦߆ ᭴ㅧ߇߃ࠆ߆ߣ߁ᗧߢߩಽ⸃⢻ߛߌߢߪᕈ ⢻⹏ଔ߇ߢ߈߹ߖࠎ㧚ߎߩ⹏ଔߩߚߦ↪ߥߩ߇㧘 శቇ♽ߩⓨ㑆ᵄᢙᔕ╵ߩᔨߢߔ㧚ߎߩ⇛ߪ೨࿁ ␜ߒ߹ߒߚ߇㧘࿁ߪߘߩ⚦ࠍㅀߴ߹ߔ㧚 ᗵᐲ߇ఝవߐࠇࠆ႐วߦ㧘శቇ♽ߩᕈ⢻ࠍᡰ㈩ߔ ࠆߩߪኻ‛ࡦ࠭ߩ㕙Ꮕߣߥࠅ߹ߔ㧚ߥߗ㕙 Ꮕ߆ߣ߃߫㧘ࡆࡓߩ㐿߈ⷺ߇ᦨㆡ୯ࠃࠅ߽ᄢ߈ ߊขࠄࠇࠆߚߦ㧘࿁᛬Ꮕ߇ήⷞߐࠇ㧘㐿߈ⷺߣ ߣ߽ߦᕆỗߦჇᄢߔࠆ㕙Ꮕ߇ࡔࠗࡦߩነਈࠍߔ ࠆ߆ࠄߢߔ㧚ߘߎߢ㧘೨࿁ㅀߴߚࠃ߁ߥᵄേశቇ⊛ߥ ᛒߪਇⷐߣߥࠅ㧘ᐞశቇ߇ലߣߥࠅ߹ߔ㧚ߎࠇ ߪ㗴ߩᛒࠍኈᤃߦߔࠆ߆ߣᕁ߃߫㧘ታߪߘ߁ߢ ߪࠅ߹ߖࠎ㧚㕙Ꮕ߇ߟߊࠆ․ᓽ⊛ߥ㔚ᵹኒᐲ ಽᏓ߇ᒻᚑߦነਈߔࠆߎߣߦࠃߞߡ㧘නߦޟᏅߦ ࠃߞߡ߇ࡏࠤࠆޠߣߞߚᛠីߢߪᷣ߹ߐࠇߥߊߥ ࠅ߹ߔ㧚ߘߩࠃ߁ߥߩ⹏ଔߩߚߦ㧘ⓨ㑆ᵄᢙ․ ᕈ߇ലߦ߈߹ߔ㧚 ᦨㆡ᧦ઙ߆ࠄ㔌ࠇߚ㧘ᗵᐲࠍఝవߔࠆ⁁ᴫߢߩⓨ 㑆ಽ⸃⢻ߪ㧘߹ࠅ⼏⺰ߐࠇࠆߎߣ߇ࠅ߹ߖࠎ㧚 ࿁ߪ㧘ߘߩࠃ߁ߥ᧦ઙߩ߽ߣߢߩ⚿ࠍ⠨߃߹ߔ㧚ߥ ߅㧘ߩᕈ⾰ߪ‛ߩࠦࡅࡦࠬߦଐሽߒ߹ߔ߇㧘 ࿁ߪࠗࡦࠦࡅࡦ࠻ߩ႐วߦ㒢ࠅ߹ߔ㧚ߔߥࠊ ߜ㧘శ㔚ሶߦࠃࠆࠗࡔࠫࡦࠣ㧘ࠆߪ SEM ߩࠃ ߁ߥᩏဳߩⵝ⟎߇ኻ⽎ߢߔ㧚ࠦࡑ߿ᱡᦛߥߤߩゲᄖ Ꮕߩነਈߦ㑐ߒߡߪ㧘ኻ‛ࡦ࠭ࠃࠅ߽㧘ᓟᲑߦ ⟎߆ࠇࠆࡦ࠭ߩነਈ߇ਥߣߥࠅ߹ߔ㧚ᄙᲑࡦ࠭♽ ߩ⸃ᨆᴺߣߩ⹏ଔߦ㑐ߒߡߪ㧘ᰴ࿁⸃⺑ߔࠆ੍ቯ ߢߔ㧚
12.2
ኻ‛ࡦ࠭ߩ㊀ⷐᕈ
⚿ࠍⴕ߁㔚ሶశቇ♽ߦ߅ߡ㧘ⓨ㑆ಽ⸃⢻ߦ㑐 ߒߡߪኻ‛ࡦ࠭߇߽ߞߣ߽㊀ⷐߥነਈࠍߒ߹ߔ㧚ᧄ ▵ߦ߅ߡߘߩℂ↱ࠍㅀߴ߹ߔ㧚 12.2.1 ࡆࡓߩ㐿߈ⷺߣಽ⸃⢻ 㔚ሶశቇ♽ߢߪ㧘ᔅⷐߣߐࠇࠆ₸ߦᔕߓߡⶄᢙߩ ࡦ࠭߇⚵ߺวࠊߐࠇ߹ߔ㧚৻ߩࡦ࠭ߩ₸ M ߪ㧘‛㕙߆ࠄࡦ࠭߹ߢߩ〒㔌ࠍ a㧘ࡦ࠭߆ࠄ㕙 ߹ߢߩ〒㔌ࠍ b ߣߒߡ㧘M = b/a ߢߔ㧚߽ߒ㧘〒㔌 a ࠍᢙ mm ⒟ᐲߦዊߐߊขࠇࠇ߫㧘㕙߹ߢߩ〒㔌 ࠍߦ 100 mm ߣߒߡ㧘৻ߩࡦ࠭ߢᢙ 10 ߆ࠄ 100 ߩ₸߇ᓧࠄࠇ߹ߔ㧚ߘࠇએߩ₸߇ᔅⷐߢ ࠆ႐วߪ㧘b ࠍᄢ߈ߊߔࠆߩ߇৻ᴺߢߔ߇㧘ߘࠇࠃ ࠅ߽㧘ߩࡦ࠭ࠍਅᵹߦਗߴࠆᣇ߇ోߩ㐳ߐࠍ ᛥ߃ࠆߎߣ߇ߢ߈߹ߔ㧚ో♽ߩ₸ߪ㧘ฦࡦ࠭ߩ ₸ߩដߌ▚ߣߥࠆ߆ࠄߢߔ㧚 ታߦߪ㧘⹜ᢱࠅߩⓨ㑆ࠍ⏕ߔࠆߚߦ㧘a ࠍ 10 mm ⒟ᐲߩᄢ߈ߥ୯ߦߔߴ߈႐ว߇ߒ߫ߒ߫ࠅ ߹ߔ㧚⹜ᢱ߆ࠄࡦ࠭㔚ᭂ㧘ࠆߪ⏛ᭂ߹ߢߩ〒㔌 ߪ㧘േ〒㔌 (working distance : WD) ߣ߫ࠇ㧘⸳ ⸘⠪ߦߪߎߩ୯߇ᜰቯߐࠇ߹ߔ㧚߽ߒᄢ߈ߥ WD ߇ ᔅⷐߢࠇ߫㧘৻ߩࡦ࠭ߢߪචಽߥ₸ߪ߆ߖ ߍ߹ߖࠎ㧚 ⶄᢙߩࡦ࠭߆ࠄᚑࠆశቇ♽ߦ߅ߡ㧘⹜ᢱ߆ࠄ ߡᦨೋߩࡦ࠭߇ኻ‛ࡦ࠭ (objective lens : OL) ߢ ߔ㧚ߘࠇߦ⛯ߊߊߟ߆ߩࡦ࠭ࠍਛ㑆ࡦ࠭♽㧘ߘ ߒߡࠬࠢࡦ㧔Ⱟశ᧼㧘ࡈࠖ࡞ࡓߥߤ㧕ߦࠍߟߊ ࠆᦨᓟߩࡦ࠭ࠍᛩᓇࡦ࠭ (projective lens : PL) ߣ߹ߔ㧚◲නߥߣߒߡ㧘ੑᲑࡦ࠭♽ߦ߅ߌࠆ 㔚ሶ゠ߩ᭽ሶࠍឬߡߺߚߩ߇ Fig.1 ߢߔ㧚ߎߩ࿑ ߢߪਛ㑆ࡦ࠭ߪሽߒߥߩߢ㧘OL ߣ PL ߛߌ߆ ࠄߥࠆ♽ߢߔ㧚OL ߪ⹜ᢱߩᦨೋߩᄢ I1ࠍߟߊ ࠅ㧘ߘࠇ߇ PL ߦߣߞߡߩ‛ߣߥߞߡ㧘PL ߦࠃߞ ߡߐࠄߦ I2ߦᄢߐࠇ߹ߔ㧚OL ߣ PL ߩ₸ࠍߘࠇ ߙࠇ M1㧘M2ߣߔࠇ߫㧘ో♽ߩ₸ߪ M = M1M2 ߢߔ㧚 ࿑ߩ♽ߦ߅ߡ㧘OL ߇࿁᛬ D1ࠍߟߊࠅ㧘PL ߦ ࠃߞߡߘࠇ߇ D2ߦ⚿ߐࠇ߹ߔ㧚⹜ᢱ㕙ߢߩࡆࡓ ߩ㐿߈ⷺࠍ⸳ቯߔࠆߚߦ࿁᛬⛉ࠅ߇ᔅⷐߢߔ߇㧘ߎ ࠇߪ D1߆ D2ߩߤߜࠄ߆ߩ⟎ߢࠇ߫ࠊߌߢ ߔ㧚ߒ߆ߒ㧘ᄙᲑࡦ࠭♽ߦ߅ߡ㧘࿁᛬㕙ߩ⟎ߣ ߘߎߢߩ₸ߪฦࡦ࠭ߩᒝᐲߦࠃߞߡࠈࠈᄌൻ ߒߡߒ߹߹ߔ㧚ߘߎߢ㧘ߥࠆߴߊᄌേߩዋߥ OL ߩ࿁᛬㕙㧘࿑ߢߪ D1ߩ⟎ߦ࿁᛬⛉ࠅ߇⟎߆ࠇࠆߩ ߇᥉ㅢߢߔ㧚 ߐߡ㧘࿑ߦ߅ߡߪ㧘⹜ᢱߩਃὐ߆ࠄߘࠇߙࠇ㧘 ਃߟߩⷺ (0,±αo) ߢ゠ࠍߒߡ߹ߔ㧚ߎߩ ߁ߜ㧘ゲᄖߩ৻ὐ߆ࠄߚਃᧄߩ゠ࠍᄥ✢ߢឬߡ ߹ߔ㧚ߎࠇࠄߩᄥ✢ߩ゠ࠍ߹ߣߡࡆࡓߣߒߡ ⠨߃ࠆߣ㧘OL ࠍㅢࠆߣ߈ߩࡆࡓߩᐢ߇ࠅ㧔ᄥߐ㧕 ߦᲧߴߡ㧘PL ࠍㅢࠆߣ߈ߩᐢ߇ࠅ߇ዊߐߊߥߞߡ ࠆߎߣ߇ࠊ߆ࠅ߹ߔ㧚ߎࠇߪ㧘ⶄᢙߩࡦ࠭ߢࠍ ᄢߔࠆㆊ⒟ߢ㧘ࡆࡓߩ㐿߈ⷺ߇ᷫዋߒߡߊ߆ࠄ ߢߔ㧚ߎߩᄌൻߪ㧘⹜ᢱ㕙ߩߩὐ߆ࠄߐࠇߚࡆFig.1: A lens system consisting of an objective lens (OL) and projective lens (PL). ࡓߦ㑐ߒߡ߽ห᭽ߢߔ㧚 ߎߩ㐿߈ⷺߩᄌൻߪ㧘ߩᄢߦ߁ᔅὼ⊛ߥ߽ ߩߢߔ㧚ࡦ࠭ߦࠃࠆᱜߩടᷫㅦߩߥ႐ว㧘৻ ߩࡦ࠭ߩ₸ M ߣⷺᐲ₸ Mαߩ㑆ߦߪ㧘 M Mα= 1 (1) ߩ㑐ଥ߇ࠅ߹ߔ㧚ߎߩᑼߪ㧘⟎ߣⷺᐲߢᒛࠄࠇࠆ ⋧ⓨ㑆ߦ߅ߌࠆⓍሽ㧘ߔߥࠊߜノᐲਇᄌೣ߆ࠄ ዉ߆ࠇ߹ߔ㧚㧔ⷺᐲ₸ߣノᐲਇᄌೣߦ㑐ߒߡߪ㧘ߘ ࠇߙࠇ╙ 1 ┨ߣ╙ 8 ┨ࠍෳᾖߒߡߊߛߐ㧚㧕ߎࠇߪ ࡦ࠭߇ⶄᢙߞߡ߽㧘ోߣߒߡߩ₸ߣⷺᐲ₸ ࠍ⠨߃ࠆߥࠄ߿ߪࠅᚑ┙ߒ߹ߔ㧚ߎߩ㑐ଥߦࠃߞߡ㧘 ࠍᄢߔࠇ߫ߔࠆ߶ߤ㧘‛㕙ߩછᗧߩ৻ὐ߆ࠄ ߚࡆࡓߪ⚦ߊ⛉ࠄࠇߡ߈߹ߔ㧚 ߐߡ㧘ߎߎߢⓨ㑆ಽ⸃⢻ࠍ⠨߃߹ߒࠂ߁㧚ಽ⸃⢻ߩ ⷰὐ߆ࠄߪ㧘⹜ᢱ㕙ߩ৻ὐ߆ࠄࠈࠈߥⷺᐲߢߚ ゠߇㧘㕙ߢߔߴߡหߓὐߦ㓸᧤ߔࠆߩ߇ℂᗐߢ ߔ㧚Fig.1 ߦ߅ߡ㧘⹜ᢱߩ৻ὐ߆ࠄߐࠇߚࡆ ࡓߪ㧘OL ਛߢߪᄢ߈ߊᐢ߇ߞߡࠆߩߢ㧘߽ߒ OL ߇Ꮕࠍ߽ߡ߫㧘゠ߩߘࠇߙࠇߪᧄ᧪ߣ⇣ߥࠆᣇ ะߦᦛߍࠄࠇ߹ߔ㧚ߟ߹ࠅ㧘゠߇ℂᗐ⊛ߥ⁁ᘒ߆ࠄ ߘࠇߡ㧘ᦨ⚳㕙ߢ৻ὐߦ㓸᧤ߔࠆߪߕߩࡆࡓ߇ ࡃߌߡߒ߹߹ߔ㧚 ห᭽ߩߎߣࠍ PL ߦኻߒߡ⠨߃߹ߒࠂ߁㧚㧔OL ߪ Ꮕࠍ߽ߚߥߣቯߒ߹ߔ㧚㧕PL ਛߩࡆࡓߪ⚦ߊ⛉ ࠄࠇߡࠆߩߢ㧘PL ߇Ꮕࠍ߽ߞߡߡ߽㧘ࡆࡓ ࠍ᭴ᚑߔࠆ゠߇ߞߖߦᧄ᧪ߣߩᣇะߦᝄࠄ ࠇࠆߛߌߢߔ㧚ߟ߹ࠅ㧘ࡆࡓ߇⚦ߊ⛉ࠄࠇߡ৻ᧄߩ ♻ߩࠃ߁ߦߥߞߡࠇ߫㧘゠ࠍࡃߌߐߖࠃ߁ߣߒ ߡ߽ߢ߈߹ߖࠎ㧚ߘߎߢ㧘PL ߦᏅ߇ߞߡ߽ᦨ⚳ ⊛ߥߪࡏࠤߕ㧘߆ࠊࠅߦᱡࠎߛ߇ߟߊࠄࠇ߹ߔ㧚 ߎࠇߪ㧘ᱡᦛᏅߩ⊒↢ࠍᗧߒ߹ߔ㧚㧔ࡦ࠭ߩਇ ቢోߐ߇ߤߩࠃ߁ߥ߮ฬߩᏅߣߒߡ⊒ߔࠆ߆ ߪ㧘ࡦ࠭ߩࠊࠇᣇߦࠃࠅ߹ߔ㧚ߎߩᖱߦ㑐ߒߡ ߪ╙ 5 ┨ࠍෳᾖߒߡߊߛߐ㧚㧕PL ߪߎߩࠃ߁ߦ㧘 ࠍࡏࠤߐߖࠆࠃࠅ߽㧘ࠍᱡ߹ߖࠆߎߣߦᄢ߈ߊነ ਈߔࠆߎߣߦߥࠅ߹ߔ㧚 એߩࠃ߁ߦ㧘OL ߣ PL ߇ห⒟ᐲߩᏅࠍ߽ߞߡ ߚߣߒߡ߽㧘ߘࠇࠄ߇ᦨ⚳ߦਈ߃ࠆᓇ㗀ߪ⇣ߥࠅ ߹ߔ㧚߇ࡏࠤࠆ⒟ᐲ㧘ߔߥࠊࠅⓨ㑆ಽ⸃⢻ߦ㑐ߒߡ ߪ㧘⹜ᢱߦ৻⇟ㄭ OL ߇ਥߥነਈࠍߔࠆࠊߌߢߔ㧚 12.2.2 ฦࡦ࠭ߩነਈ OL ߇ⓨ㑆ಽ⸃⢻ߦ߽ߞߣ߽ᄢ߈ߥነਈࠍߔࠆߣ ߁ᖱߦ㑐ߒߡߪ㧘೨㗄ߩ⼏⺰ߢᧄ⾰ߪዧ߈ߡ߹ ߔ㧚ߒ߆ߒ㧘ߚߣ߃߫ੑ⇟⋡ߩࡦ࠭߇ಽ⸃⢻ߦߤߩ ⒟ᐲነਈߔࠆ߆ࠍ⠨߃ࠆߦߪ㧘߽߁ዋߒቯ㊂⊛ߥ⼏ ⺰߇ᔅⷐߢߔ㧚 ‛㕙ߩశゲߦὐశḮࠍ⟎ߡ㧘㕙ߢߟߊࠄࠇࠆ ࡏࠤߩᓘࠍ᷹ࠇ߫㧘ߘࠇ߇ᄢ㔀ᛠߦߞߡಽ⸃⢻ߦኻ ᔕߒ߹ߔ㧚ߚߛߒ㧘㕙ߢߩࡏࠤߩᄢ߈ߐ߇ߘߩ߹߹ ಽ⸃⢻ߦߥࠆߩߢߪࠅ߹ߖࠎ㧚ಽ⸃⢻ߣߪޟ‛㕙 ߩ৻ὐ߇ߤࠇߛߌࡏࠤࠆ߆ޠߣ߁㊂ߢߔ㧚ߘߎߢ㧘
㕙ߦ߅ߌࠆὐశḮߩᓘࠍశቇ♽ోߩ₸ M ߢ ഀߞߡ㧘‛㕙ߦ߅ߌࠆࡏࠤߩᄢ߈ߐߦ឵▚ߒߥߌࠇ߫ ߥࠅ߹ߖࠎ㧚ߎࠇ߇㧘೨࿁߹ߢߦᐲ߆⺑ߒߚ‛㕙 ឵▚ߢߔ㧚એਅߩ⼏⺰ߦ߅ߡ߽㧘Ꮕ㊂ߪߔߴߡ㧘 ߎߩ‛㕙឵▚ߩ߽ߣߢਈ߃߹ߔ㧚 ೨㗄ߩ Fig.1 ߩ♽ߢ㧘ฦࡦ࠭߇ಽ⸃⢻ߦ߷ߔᓇ 㗀ࠍ⠨߃ߡߺ߹ߒࠂ߁㧚߹ߕ࿁᛬Ꮕߦ㑐ߒߡߪ㧘ߎ ࠇߪࡦ࠭⥄り߇⊒↢ߔࠆ߽ߩߢߪߥߩߢ㧘ߤߩ ࡦ࠭߇ߤࠇߛߌߩ࿁᛬Ꮕࠍߟߊߞߡࠆ߆ߣ߁ ⼏⺰ߪήᗧߢߔ㧚࿁᛬Ꮕߦ㑐ߒߡߪ㧘ోߢ৻ ߩࡦ࠭ߣ⠨߃ߡ㧘࿁᛬Ꮕߦࠃࠆࡏࠤߩᑼࠍㆡ ↪ߔࠇ߫ߩߢߔ㧚ߔߥࠊߜ㧘⹜ᢱ㕙ߢߩࡆࡓߩ 㐿߈ⷺࠍ αo㧘ᵄ㐳ࠍ λoߣߔࠇ߫㧘‛㕙឵▚ߒߚࡆ ࡓߩࡏࠤߪᰴᑼߢਈ߃ࠄࠇ߹ߔ㧚 dD= 0.61 λo αo (2) ᑼߩಽᲣߩ αoߪᱜߒߊߪ sin αoߢߔ߇㧘࿁᛬Ꮕ ߇㊀ⷐߣߥࠆߩߪ αoߩዊߐߥ႐วߥߩߢ㧘ㅢᏱߪߎ ߩᑼߢචಽߢߔ㧚 ᰴߦ㕙Ꮕࠍ⠨߃߹ߔ㧚߹ߕోߢ৻ߩࡦ࠭ ߣ⠨߃ߡ㧘ߘߩ㕙Ꮕଥᢙࠍ CSߣߒ߹ߔ㧚ࡆࡓ ߩࡏࠤࠍᦨዊ㍲ੂ⟎ߢ⹏ଔߔࠆߥࠄ㧘ߘߩ⋥ᓘ ߪᰴᑼߣߥࠆߩߢߒߚ㧚 dS = 1 2 CSαo 3 (3) ߎߎߢ CSߪ㧘‛㕙឵▚ߒߚᏅࠍਈ߃ࠆࠃ߁ߦቯ⟵ ߐࠇߚᏅଥᢙߢࠅ㧘߰ߟ߁㕙Ꮕଥᢙߣ߃߫ ߎߩ㊂ࠍᜰߒ߹ߔ㧚 ߐߡ㧘Fig.1 ߦ߅ߡߪ㧘OL ߣ PL ߩੑߟߩࡦ ࠭ߩ㕙Ꮕࠍޘߦ⠨߃ࠆߎߣ߇ߢ߈߹ߔ㧚OL ߣ PL ߩනߣߒߡߩᏅଥᢙࠍߘࠇߙࠇ CS(1)㧘CS(2) ߣߒ߹ߔ㧚CS(1)ߪ⹜ᢱ㕙ߢߩ㐿߈ⷺ αoߦኻߒߡቯ ⟵ߐࠇ㧘CS(2)ߪਛ㑆 I1ߩ⟎ߢߩ㐿߈ⷺ α1ߦኻ ߒߡߩ߽ߩߢߔ㧚߹ߕ CS(1)ߩነਈߪ㧘(3) ߣห᭽ߢ ߔ߆ࠄ㧘 dS(1)=1 2 C (1) S αo3 (4) ߣߥࠅ߹ߔ㧚߿ߞ߆ߥߩߪ PL ߩነਈߢߔ㧚PL ߇ ߟߊࠆࡏࠤߩᄢ߈ߐߪ㧘PL ߦߣߞߡߩ‛㕙㧔I1ߩ㕙㧕 ߦ឵▚ߒߚᄢ߈ߐߢ (1/2)CS(2)α13ߣߥࠅ߹ߔ㧚ߎߩ ᑼߦ߅ߌࠆ α1ߪ㧘(1) ߩ㑐ଥࠍ↪ࠇ߫ α1= αo/M1 ߣ⟎߈឵߃ࠄࠇ߹ߔ㧚߹ߚ㧘⹜ᢱ㕙ߦ߅ߌࠆࡏࠤߦ឵ ▚ߔࠆߦߪ M1ߢഀࠇ߫ࠊߌߢߔ㧚⚿ዪ㧘㕙 Ꮕߦ㑐ߒߡߩ PL ߩነਈߪᰴᑼߣߥࠅ߹ߔ㧚 dS(2)= 1 2 CS(2) M14 αo 3 (5) ߎࠇࠍ (4) ߣᲧߴࠇ߫㧘PL ߩᓇ㗀ߩᐲวߪ M14 ߩᲧ₸ߢᷫዋߔࠆߎߣ߇ࠊ߆ࠅ߹ߔ㧚CS(1)ߣ CS(2) ߪห⒟ᐲߩᄢ߈ߐߣߔࠇ߫㧘M1߇ߚߣ߃ 2 ߣ߆ 3 ߩ ⒟ᐲߢߞߡ߽㧘PL ߩ㕙Ꮕߩነਈߪήⷞߢ߈ࠆ ߎߣߦߥࠅ߹ߔ㧚ಽ⸃⢻ߩ⸘▚ߦ㓙ߒߡ㧘߰ߟ߁╙ੑ ࡦ࠭એ㒠ߩነਈ߇⠨ᘦߐࠇߥߩߪߎߩᖱߦࠃ ࠅ߹ߔ㧚 ߢߪ㧘ゲᄖᏅߦ㑐ߒߡߩฦࡦ࠭ߩነਈߪߤ߁ߢ ߒࠂ߁߆㧚ߩ㕙Ꮕߩ႐วߦߪ㧘Ꮕ㊂߇㐿߈ⷺ ߩ 3 ਸ਼ߢჇടߔࠆߩߢ㧘ߩᄢߦ߁㐿߈ⷺߩᷫ ዋߩലᨐ߇㗼⪺ߦࠇ߹ߒߚ㧚ߒ߆ߒゲᄖᏅߪ㧘ⷺ ᐲ αoߦ㑐ߒߡߩߴ߈ߪߘࠇࠃࠅਅ߇ࠅ㧘߆ࠊࠅߦ‛ ὐߩశゲ߆ࠄߩ〒㔌 xoߩߴ߈߇߹ࠇߡ߈߹ߔ㧚ߚ ߣ߃߫㧘ࠦࡑᏅߪ xoαo2ߦᲧߔࠆߩߢߒߚ㧚ᱡ ᦛᏅߥࠄ xo3ߦᲧߒ߹ߔ㧚 ߽߁৻ᐲ Fig.1 ࠍࠇ߫㧘OL ਛߩᄥ✢ߩ゠ߪૐ 㧔శゲ߆ࠄߩ〒㔌߇ዊߐ㧕ߩߦኻߒߡ㧘PL ߢߪ 㜞ߊߥߞߡ߹ߔ㧚߇ᄢߐࠇߡߊߩߢᒰὼߢ ߔ㧚ߘߎߢ㧘⟎ߩ 3 ਸ਼ߦᲧߔࠆᱡᦛᏅߪ㧘৻⥸ ߦᓟᲑߩࡦ࠭߶ߤነਈ߇ᄢ߈ߊߥࠅ߹ߔ㧚ߘߩઁߩ ゲᄖᏅߦ㑐ߒߡߪ㧘ߘߩⷺᐲߣ⟎ߩଐሽᕈߦᔕ ߓߡ㧘⇣ߥࠆ⟎ߩࡦ࠭߇ᡰ㈩⊛ߣߥࠅ߹ߔ㧚 એߢ⠨ኤߒߚߩߪ㧘ਗࠎߛࡦ࠭ߦࠃߞߡ߇ න⺞ߦᄢߐࠇߡߊ♽ߢߔ㧚ߚߣ߃߫ TEM ߢߪ㧘 㜞₸ߩ᧦ઙߢߪߘߩࠃ߁ߦߥࠅ߹ߔ㧚ߒ߆ߒ TEM ߢ߽㧘ૐߩ᧦ઙߪᔅⷐߢߔ㧚ૐ᧦ઙߦ߅ߡߪ㧘 ⹜ᢱ㕙ߢࠆ▸࿐߇ᐢ߇ࠅ㧘₸߇ਅ߇ࠆ߶ߤ⹜ᢱ㕙 ߢߩ⟎߇ᄢ߈ߊߥࠅ߹ߔ㧚ߘߎߢ㧘OL ਛߢ߽ ゠ߪ㜞ߊߥࠄߑࠆࠍ߃ߕ㧘߹ߚోߩ₸ࠍᄢ߈ߊ ߒߡߪߌߥߩߢ㧘ห⒟ᐲߩ゠ߩ㜞ߐߩ߹߹ ࡦ࠭♽ࠍㅢㆊߒߡߊߎߣߦߥࠅ߹ߔ㧚 ߎߩࠃ߁ߥૐߩశቇ᧦ઙߢߪ㧘ᓟᲑߩࡦ࠭߶ ߤ㐿߈ⷺ߇ᷫዋߒߡߊߣߪ㒢ࠄߥߊߥࠅ߹ߔ㧚ߘߎ ߢ㧘OL ߛߌ߇ಽ⸃⢻ߦነਈߔࠆߣߪ߃ߥߊߥࠅ߹ ߔ㧚ߣߎࠈ߇㧘ૐߢࠇ߫㜞ಽ⸃⢻ߪⷐ᳞ߐࠇߥ ߩߢ㧘ಽ⸃⢻ߪ߹ࠅ᳇ߦߔࠆᔅⷐߪࠅ߹ߖࠎ㧚 㗴ߪ㧘ᱡᦛࠍᆎߣߒߚゲᄖᏅࠍ㒰ߊߎߣߢߔ㧚 ฦࡦ࠭ਛߩ゠߇ߕࠇ߽㜞ߩߢ㧘ߎࠇߪኈᤃ ߢߪࠅ߹ߖࠎ㧚 㕙Ꮕߣߪ⇣ߥࠅ㧘ゲᄖᏅߪࡦ࠭㑆ߢᛂߜᶖ ߒวࠊߖࠆߎߣ߇น⢻ߢߔ㧚ߒ߆ߒ㧘ゲᄖᏅ߇ᱜ ߐࠇߚ⁁ᴫࠍ㧘₸ߩนᄌ▸࿐ోߢታߔࠆߩߪ ◲නߢߪࠅ߹ߖࠎ㧚㧔TEM ߢߪ㧘࠻࠲࡞₸ M ߣߒߡᢙ 10 ߆ࠄ 106⒟ᐲ߹ߢᔅⷐߢߔ㧚㧕ࡦ࠭ᒝᐲ ߩ⚵ߺวࠊߖࠍࠆ㓙ߦߪ㧘ᔅⷐߥ₸▸࿐ࠍࠞ
ࡃߔࠆߛߌߢߪਇචಽߢࠆࠊߌߢߔ㧚 㔚ሶಽశ♽ߢ↪ࠄࠇࠆࡦ࠭♽ߢ߽㧘ฦࡦ࠭ ߩ↪ߪන⺞ߢߥߩ߇᥉ㅢߢߔ㧚৻ߟߦߪ߿ߪࠅ㧘 ₸ࠍนᄌߦߔࠆ⋡⊛߇ࠅ߹ߔ㧚߹ߚ㧘ࡆࡓߩട ᷫㅦ߇ㅜਛߢⴕࠊࠇࠆ႐วߢߪ㧘ࡆࡓߩ㜞ߐߣ㐿߈ ⷺߪⶄ㔀ߦჇᷫߒߡ߈߹ߔ㧚ߣߊߦ㧘ࡆࡓߩᷫㅦ ߪ㐿߈ⷺߩჇᄢࠍ߁ߩߢ㧘ᷫㅦ₸ߩᄢ߈ߥ♽ߢߪ㧘 ߤߩࡦ࠭㧔ࠆߪࠕ࠽ࠗࠩ㧕߇ಽ⸃⢻ߦነਈߔ ࠆ߆ߪන⚐ߦߪ߹ࠅ߹ߖࠎ㧚ߘߩࠃ߁ߥࡦ࠭♽ ߩ⸃ᨆߦ㑐ߒߡߪᰴ࿁ㅀߴࠆ੍ቯߢߔ㧚
12.3
ኻ‛ࡦ࠭ߩ᭴ᚑߣ߈
ࠃߊ↪ࠄࠇࠆኻ‛ࡦ࠭ߩ᭴ᚑߣേࠍᧄ▵ߢ ⺑ߒ߹ߔ㧚ࠍᄢߔࠆߚߩࡦ࠭♽ߦ߅ߌࠆ ኻ‛ࡦ࠭ࠍᗐቯߒߡㅀߴ߹ߔ߇㧘㔚ሶಽశ♽ߩࠗ ࡦࡊ࠶࠻ࡦ࠭ߩࠃ߁ߦ㔚ሶࠍขࠅㄟ⋡⊛ߩ߽ߩ㧘 ࠆߪ㔚ሶࡊࡠࡉࠍᩏߔࠆⵝ⟎ߩኻ‛ࡦ࠭ ߢ߽⠨߃ᣇߪหߓߢߔ㧚 12.3.1 㕒㔚ဳኻ‛ࡦ࠭ߩ࠲ࠗࡊ ᦨೋߪ㕒㔚ဳߩኻ‛ࡦ࠭ߢߔ㧚㕒㔚ࡦ࠭ߩേ ේℂߪ╙ 4 ┨ߢ⺑ߒ߹ߒߚ߇㧘ߎߎߢߪኻ‛ࡦ ࠭ߣߒߡߩᔕ↪ࠍㅀߴ߹ߔ㧚㕒㔚ࡦ࠭ߪ㧘㔚ሶߩട ㅦ߆ᷫㅦ㧘ࠆߪߘߩਔᣇࠍ߁߽ߩߢࠅ㧘ᄢ߈ ߊᰴߩੑߟߦಽ㘃ߐࠇ߹ߔ㧚 (1) ࡦ࠭ߣߒߡߩ㓸᧤↪ࠍ߽ߚߖࠆߚߦടᷫ ㅦࠍⴕ߁߽ߩ㧚 (2) ᱜߩടᷫㅦࠍⴕ߁߽ߩ㧚 ߎߩ߁ߜ (1) ߪ㧘ࡦ࠭ਛߢ㔚ሶߩടᷫㅦࠍⴕ߁ߎ ߣߢ㓸᧤↪ࠍᓧߡ㧘ࡦ࠭ࠍࠆߣ߈ߦߪ߽ߣߩ ࠛࡀ࡞ࠡߦᚯࠆࠃ߁ߥ߽ߩߢߔ㧚ߎߩ࠲ࠗࡊߪ৻⥸ ߦࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ߣ✚⒓ߐࠇ߹ߔ㧚ࡦ࠭ਛߢᷫ ㅦ߇ⴕࠊࠇࠆ႐ว߇ᷫㅦဳࠕࠗࡦ࠷ࠚ࡞ࡦ࠭㧘ടㅦ ߩ႐ว߇ടㅦဳࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ߢߔ㧚ౖဳ⊛ߦߪ 3 ߟߩ㔚ᭂߢ᭴ᚑߐࠇ㧘ᄖߩੑߟߩ㔚ᭂࠍࠕࠬ㔚 ߣߒߡ㧘ਛᄩ㔚ᭂߦടㅦ߆ᷫㅦߩߚߩ㔚ࠍ߆ ߌ߹ߔ㧚 ߹ߚ (2) ߪ㧘ࡦ࠭ߣߒߡߩ㓸᧤↪ࠍ߅ࠃ߷ߔߣ หᤨߦ㧘ࡦ࠭ߩญߣญߢ㔚ሶߩࠛࡀ࡞ࠡ߇ᄌ ൻߔࠆࠃ߁ߥ߽ߩߢߔ㧚ߎࠇߪࠗࡑ࡚ࠫࡦࡦ࠭ߣ ✚⒓ߐࠇ߹ߔ㧚ߎߩ࠲ࠗࡊߢߪ㧘ࡦ࠭ߩਔ┵߇ߣ߽ ߦࠕࠬ㔚ߣ߁ࠊߌߦߪ߆ߕ㧘ญ߆ญߩዋ ߥߊߣ߽৻ᣇߩ㔚ߪᶋߊߎߣߦߥࠅ߹ߔ㧚ㅢᏱߪ㧘 ⹜ᢱࠍ⽶ߩ㔚ߦᶋ߆ߖߡࡦ࠭㔚ᭂߩ৻ㇱߣߒߡ ↪㧘ࡦ࠭ญ߇ࠕࠬ㔚ߣߥࠆࠃ߁ߦߒ߹ߔ㧚 ߎߩߣ߈ߪ⹜ᢱ߇㒶ᭂߣߒߡߊߎߣߦߥࠆߩߢ㧘⹜ ᢱ߹ߢߚࡦ࠭ో߇ࠞ࠰࠼ࡦ࠭ߣ߫ࠇ ߹ߔ㧚 ߐߡ㧘ኻ‛ࡦ࠭ߩ⸳⸘ߩ┙႐߆ࠄߪ㧘⹜ᢱ㕙ߦ߅ ߌࠆ㔚ሶߩㆇേࠛࡀ࡞ࠡߩ୯߇㊀ⷐߢߔ㧚⹜ᢱ߆ࠄ ߐࠇࠆ㔚ሶࠍ⚿ߔࠆⵝ⟎ߢߪ㧘ߎࠇߪ㔚ሶߩ ೋᦼࠛࡀ࡞ࠡ୯ߩߎߣߢߔ㧚ߎߩ୯ߦࠃߞߡ㧘ኻ‛ ࡦ࠭ਛߢᱜߩടᷫㅦࠍⴕ߁ߴ߈߆ߤ߁߆߇߹ߞ ߡ߈߹ߔ㧚 㔚ሶߩೋᦼࠛࡀ࡞ࠡ߇ࠄ߆ߓࠄࠇࠆ ࠍߊߟ߆ߍߡ߅߈߹ߔ㧚߹ߕ XPS ߢߪ㧘⹜ᢱߦ X ✢ࠍᾖߒߡ⹜ᢱ߆ࠄߐࠇࠆశ㔚ሶࠍ㧘ࠗࡦ ࡊ࠶࠻ࡦ࠭ߢ㓸ߡࠕ࠽ࠗࠩߦዉ߈߹ߔ㧚ߎߩ 㓙ߦขࠅㄟߴ߈శ㔚ሶߩࠛࡀ࡞ࠡߪ㧘0 eV ߆ࠄ 1500 eV ⒟ᐲ߹ߢߢߔ㧚ߎߩ♽ߩࠗࡦࡊ࠶࠻ࡦ࠭ߪ ኻ‛ࡦ࠭ߩ৻⒳ߣࠆߎߣ߇ߢ߈㧘శ㔚ሶߢࠗࡔ ࠫࡦࠣ߹ߢⴕ߁႐วߪ߽ߜࠈࠎߘ߁ߢߔ㧚 ߹ߚ㧘⹜ᢱߦ㔚ሶ✢ࠍᾖߒߡ㧘⹜ᢱ߆ࠄߩ㔚 ሶࠍ⚿ߐߖࠆⵝ⟎߇ࠅ߹ߔ㧚ߎߩ႐วߪ㧘⹜ᢱ 㕙ߦᢅᗵߥૐࠛࡀ࡞ࠡߩ㔚ሶࠍᾖߒߡ㧘ᒢᕈᢔੂ ߐࠇߚ㔚ሶࠍࠗࡔࠫࡦࠣߩኻ⽎ߣߒ߹ߔ㧚ߎߩⵝ⟎ ߪૐࠛࡀ࡞ࠡ㔚ሶ㗼ᓸ㏜ (low energy electron microscope : LEEM) ߣ߫ࠇ߹ߔ㧚ߎߩశቇ♽ߪ㧘 㕙ߩ⚿᥏᭴ㅧࠍ⺞ߴࠆ LEED ߦࠗࡔࠫࡦࠣߩᯏ ⢻ࠍㅊടߒߚ߽ߩߣࠆߎߣ߇ߢ߈߹ߔ㧚⚿ߩኻ⽎ ߣߥࠆࠛࡀ࡞߽ࠡ LEED ߣห᭽ߣߥࠅ㧘ᢙ eV ߆ ࠄᢙ 10eV ߩ⒟ᐲߢߔ㧚 ߩߣߒߡ㧘⹜ᢱࠍടᾲߒߡߡߊࠆᾲ㔚ሶߢ ࠗࡔࠫࡦࠣࠍⴕ߁ߎߣ߇ߢ߈߹ߔ㧚ߎߩ႐วߪ㧘⹜ ᢱߩ᷷ᐲߦᔕߓߡᾲ㔚ሶߩࠛࡀ࡞ࠡಽᏓ㧔ࡑ࠶ࠢࠬ ࠙ࠚ࡞ಽᏓ㧕߇ቯ߹ࠅ㧘0 eV ߆ࠄ 1 eV ⒟ᐲ߹ߢߩಽ Ꮣߣߥࠅ߹ߔ㧚 ৻ᣇ㧘TEM ߿ SEM ߢߪ㧘㔚ሶࡆࡓߪ⹜ᢱߩ᭴ ㅧⷰኤߩߚߦ↪ࠄࠇࠆߩߢ㧘⹜ᢱ㕙ߦ߅ߌࠆ㔚 ሶߩࠛࡀ࡞ࠡߣߒߡ․ቯߩ୯߇ⷐ᳞ߐࠇࠆࠊߌߢ ߪࠅ߹ߖࠎ㧚ߎߩࠃ߁ߥⵝ⟎ߢߪ㧘೨࿁ㅀߴߚࠃ߁ ߦ㧘ࠛࡀ࡞ࠡࠍ㜞ߊߔࠇ߫ߔࠆ߶ߤ⦟ⓨ㑆ಽ⸃ ⢻߇ᓧࠄࠇ߹ߔ㧚ߎࠇߪ㧘࿁᛬Ꮕߣ⦡Ꮕ߇ᷫዋߔ ࠆ߆ࠄߢߔ㧚ߘߎߢ㧘ࡆࡓߪ㔚ሶ㌂ࠍࠆᲑ㓏ߢߥ ࠆߴߊ㜞㔚ߢടㅦߐࠇ㧘ߘߩࠛࡀ࡞ࠡ୯ߢ⹜ ᢱ㕙ߦ㆐ߔࠆࠃ߁ߦߒ߹ߔ㧚㧔ߚߛߒ SEM ߢߪ㧘⹜ᢱ ߩ࠴ࡖࠫࠕ࠶ࡊࠍ㒐ߋߥߤߩℂ↱ߢ㧘ૐടㅦߩ㔚ሶ ࡊࡠࡉ߇ᅢ߹ࠇࠆ႐ว߇ࠅ߹ߔ㧚㧕 ߎߩࠃ߁ߦ㧘⹜ᢱ⟎ߦ߅ߌࠆ㔚ሶߩࠛࡀ࡞ࠡ୯߇ࠄ߆ߓᜰቯߐࠇࠆ႐วߣ㧘ߘ߁ߢߥ႐ว ߇ࠅ߹ߔ㧚ᓟ⠪ߢߪ㧘ࡆࡓࠛࡀ࡞ࠡࠍ㜞ߊ⸳ቯ ߔࠆ߶ߤߣߥࠆࠊߌߢߔ㧚ߢߪ೨⠪ߩ㧘ೋᦼࠛࡀ ࡞ࠡ߇ᜰቯߐࠇࠆ႐วߢ߽㧘⹜ᢱ߆ࠄߚߣߩ 㔚ሶࠍടㅦߔࠇ߫ಽ⸃⢻ࠍ⦟ߊߢ߈ࠆߢߒࠂ߁߆㧫ߎ ࠇߪ⚿⺰ߣߒߡߪ Yes ߥߩߢߔ߇㧘ᖱߪዋߒⶄ㔀 ߢߔ㧚 ߹ߕ࿁᛬Ꮕࠍ⠨߃ࠆߣ㧘ߎࠇߪ⹜ᢱ㕙ߢߩᵄ㐳 λoߣขࠅㄟߺⷺ αoߢ߹ߞߡߒ߹߁ߩߢߒߚ߆ࠄ㧘 ߘߩߣߢടㅦߒߡ߽ߒߥߊߡ߽㧘ዋߥߊߣ߽ᑼߩ ߢߪᓇ㗀߇ࠅ߹ߖࠎ㧚ߒ߆ߒ㧘ߣߢࠆࠃ߁ߦ㧘 㔚ሶࠍടㅦߒߥ߇ࠄขࠅㄟߎߣߢ CSߣ CCࠍ⊛ ߦዊߐߊߢ߈߹ߔ㧚ߘߎߢ㧘ᦨㆡ㐿߈ⷺߪᄢ߈߶߁ ߦߕࠇ㧘⚿ᨐ⊛ߦ࿁᛬Ꮕ߇ૐᷫߐࠇ߹ߔ㧚⚿ዪ㧘ߔ ߴߡߩᏅ߇ዊߐߊߥࠆߎߣߢಽ⸃⢻ߪ⦟ᣇะߦ ᄌൻߒ߹ߔ㧚㧔ታ㗴ߣߒߡ㧘ዊߐߥࠛࡀ࡞ࠡߩ ߹߹㐳〒㔌ࠍࠄߖࠆߣᄖੂ⏛႐ߥߤߩᓇ㗀ࠍฃ ߌ߿ߔߩߢ㧘ߥࠆߴߊᣧߊടㅦߒߚߣ߁ᖱ ߽ࠅ߹ߔ㧚㧕 ৻ᣇߢ㧘⹜ᢱ߆ࠄߐࠇߚ㔚ሶࠍടㅦߔࠆߎߣ ߦߪታ㓙ߩߊߟ߆ߩ࿎㔍߇߁ߚ㧘ߟߢ߽ (2) ߩ࠲ࠗࡊߩኻ‛ࡦ࠭߇ណ↪ߐࠇࠆࠊߌߢߪࠅ ߹ߖࠎ㧚ߎߩᖱߦ㑐ߒߡߪ㧘એਅߢౕ⊛ߥࡦ࠭ ߩ᭴ㅧࠍ⚫ߒߥ߇ࠄㅀߴߡ߈߹ߔ㧚 12.3.2 ࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ ᱜߩടᷫㅦߩߥ㕒㔚ဳኻ‛ࡦ࠭ߩౕࠍ ߡߺ߹ߔ㧚߹ߕ Fig.2(a) ߪ㧘ᷫㅦဳߩࠕࠗࡦ࠷ࠚ࡞ ࡦ࠭ࠍኻ‛ࡦ࠭ߣߒߡ↪ࠆߢߔ㧚᭴ㅧߪਃߟ ߩ㔚ᭂ߆ࠄᚑࠅ㧘ਔࠍࠕࠬ㔚㧘ਛᄩߩ㔚ᭂࠍ⽶ ߩ㔚ߣߒ߹ߔ㧚ਛᄩ㔚ᭂߩઃㄭߢ㔚ሶࠍᷫㅦߒߡ㧘 ߹ߚ߽ߣߩࠛࡀ࡞ࠡߦᚯߔㆊ⒟ߢࡦ࠭↪ࠍᓧ ߹ߔ㧚 㔚ᭂ㑆ߦߪ⛘✼ߩߚߩ⎹ሶ㧔ࠟࠗࠪ㧕߇ᔅⷐߢߔ ߇㧘ߎࠇߪ࿑ߦߪ␜ߒߡ߹ߖࠎ㧚ࡦ࠭㔚ߩᄢ ߈ߐߦࠃߞߡߪ㧘㔚ࠍ㒐ߋߚߦ⎹ሶߩ㗔ၞࠍᄢ߈ ߊߣࠆᔅⷐ߇ࠅ߹ߔ㧚⸳⸘⠪߇৻⇟⧰ഭߔࠆߩߪ㧘 ⎹ሶߩᴪ㕙㔚ࠍ㒐ߋߎߣߢߔ㧚⌀ⓨਛߩ㔚ᭂ㑆ߩ 㔚ߦ㑐ߒߡߪ㧘㑆㓒 1 mm ߚࠅ 10 kV ⒟ᐲ߹ߢශ ടน⢻ߣߐࠇߡ߹ߔ߇㧘ታ㓙ߪ߽߁ዋߒ߇ข ࠄࠇ߹ߔ㧚ߥ߅㧘࿑ߩߢߪ㧘⹜ᢱㄝߩⓨ㑆ࠍߥࠆ ߴߊⓨߌࠆߚߦ㧘వ┵㔚ᭂߩᒻ⁁ࠍవ⚦ࠅߦߒߡ ࠅ߹ߔ㧚ߚߣ߃߫㧘ኻ‛ࡦ࠭ߩ⣁߆ࠄ⹜ᢱߦะߌ ߡ X ✢ࠍᾖߔࠆߚߦ㧘ߎߩࠃ߁ߥᒻ⁁ߦߔࠆᔅ ⷐ߇ࠅ߹ߔ㧚 ࿑ߦߪ㧘⹜ᢱ㕙ߩశゲ߆ࠄߐࠇߚ㔚ሶ゠߇ ឬ߆ࠇߡ߹ߔ㧚㔚ሶߩೋᦼࠛࡀ࡞ࠡ Eoߪ㧘శ㔚 ሶࠍᗐቯߒߡ 1000 eV ߣߒߡ߹ߔ㧚ࡦ࠭ࠍᛮߌ ߚߣߩߩࠛࡀ࡞ࠡࠍ Eiߣ⸥ߒ߹ߔ߇㧘ߩ ႐วߪᱜߩടᷫㅦ߇ߥߩߢ Eo= Eiߢߔ㧚࿑ߪ 1 ᰴ゠ࠍឬߡߡ㧘Ꮕߩነਈߪ߹ࠇ߹ߖࠎ㧚 ゠ߩ᭽ሶ߇߿ߔࠃ߁ߦ㧘⹜ᢱ߆ࠄߩⷺ αo ߣߒߡᄢ߈ߩ± 8◦ߣߒߡ߹ߔ߇㧘ታ㓙ߦߤߩࠃ ߁ߥ㐿߈ⷺߢ↪ࠆ߆ߤ߁߆ߪ↪ㅜᰴ╙ߢߔ㧚ⵝ⟎ߦ ߅ߌࠆ㐿߈ⷺߩᓮߪ㧘ኻ‛ࡦ࠭ਛߩ࿁᛬㕙⟎ ߦ࿁᛬⛉ࠅࠍ⟎ߊߎߣߢⴕ߹ߔ㧚߽ߒ႐ᚲ⊛ߦήℂ ߇ࠇ߫㧘h12.2.1 ߢ߽ㅀߴߚࠃ߁ߦ㧘ਅᵹߩᓎ㕙 ߦ⛉ࠅࠍ⟎ߊߎߣ߽น⢻ߢߔ㧚 ਛᄩ㔚ᭂߩ㔚 Vcࠍᄌ߃ࠇ߫㧘㕙⟎߇⒖േߒ ߹ߔ㧚࿑ߢߪ㧘㕙⟎ zi߇⹜ᢱ߆ࠄ 100 mm ߩ〒 㔌ߣߥࠆࠃ߁ߦ Vc߇ࠄࠇߡ߹ߔ㧚ߘߩߣ߈ߩ Ꮕଥᢙ CS㧘CCߩ⸘▚୯߽࿑ߦ⸥ߐࠇߡ߹ߔ㧚 CSߣ CCߪ㔚ሶ゠ߩࠬࠤ࡞ߦᲧߔࠆߩߢ㧘 ߚߣ߃߫ Eo߇ 10 ߦߥߞߚߣ߈ߦ Vc߽ 10 ߦߔ ࠇ߫㧘゠ߩᒻ⁁ߪਇᄌߥߩߢᏅଥᢙߪਇᄌߢߔ㧚 ߽ߜࠈࠎ㧘ᤨ㑆ߩ㑐ᢙߣߒߡߚ㔚ሶߩㆇേߪᄌࠊ ࠅ߹ߔ߇㧘Ꮕଥᢙࠍࠆߩߪ゠ߩᒻ⁁ߢߔ㧚߹ ߚ㧘⹜ᢱߣࡦ࠭㔚ᭂࠍߚో♽ࠍߔߴߡ 1/10 ߩ ࠬࠤ࡞ߦߒߚߣߔࠇ߫㧘Ꮕଥᢙ߽ 1/10 ߣߥࠅ߹ ߔ㧚㧔ࡦ࠭㔚ᭂߩᒻ⁁ߛߌࠍ 1/10 ߦߒߡ߽ߛߢ㧘 ⹜ᢱ߆ࠄߩ〒㔌߽ 1/10 ߦ❗ࠆᔅⷐ߇ࠅ߹ߔ㧚㧕ࠬ ࠤ࡞ࠍ❗ࠆߩߪᏅଥᢙࠍዊߐߊߔࠆߚߩ ᤃߥᣇᴺߢߔ߇㧘㔚ࠍ㒐ߋߩ߇㔍ߒߊߥࠅ㧘߹ߚട Ꮏ♖ᐲ߇ߒߦߊߊߥࠅ߹ߔ㧚ߐࠄߦ㧘⹜ᢱࠅߩ⥄ ↱ᐲ߇㒢ߐࠇࠆߥߤ㧘ઍఘ߇ࠈࠈߡ߈߹ߔ㧚 ৻⥸ߦ㧘ᷫㅦဳࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ߩਛᄩ㔚ᭂߩ 㔚୯ߪ㧘ࡆࡓߩࡈࠜࠞࠬ⟎ߦ߽ଐࠅ߹ߔ߇㧘 ߚߡߪޟࡆࡓࠛࡀ࡞ࠡࠍടㅦ㔚ߦ⺒ߺᦧ ߃ߚߣ߈ߩᢙ୯㧔ߩ╓ภࠍᄌ߃ߚ߽ߩ㧕ޠߦㄭߊߥࠅ ߹ߔ㧚ߩ႐วߢ߃߫㧘Eo= 1000 eV ߥߩߢ㧘Vc ߪߛߚ−1000 V ߣߥߞߡ߹ߔ㧚߽ߒ Vc߇ߜࠂ ߁ߤ−1000 V ߥࠄ㧘ਛᄩ㔚ᭂߦ㔚ሶ߇㆐ߒߚߣߎࠈ ߢㆇേࠛࡀ࡞ࠡ߇ 0 ߣߥߞߡᱛ߹ࠆߎߣߦߥࠅ߹ ߔ㧚ߒ߆ߒ㧘ታ㓙ߦ㔚ሶ߇ㅢࠆߩߪశゲઃㄭߢࠅ㧘 శゲߩ㔚߇ߤߎ߆ߢ−1000 V ߦߥࠆࠊߌߢߪ ࠅ߹ߖࠎ㧚߽ߜࠈࠎ㧘ਛᄩ㔚ᭂߩ㔚ࠍਅߍߔ߉ࠆ ߣ㧘శゲઃㄭࠍㅢࠆ㔚ሶ߇ㅜਛߢᱛ߹ߞߡᒁ߈ߔࠃ ߁ߥߎߣ߇ߎࠅ߃߹ߔ㧚 ࿑ߩฝߩࠣࡈߪ㧘⹜ᢱ㕙ߩశゲߦ⟎߆ࠇߚ ὐశḮߦኻߒߡ㧘ߩࡏࠤߩᓘ d ࠍ㐿߈ⷺ αoߩ㑐ᢙ ߣߒߡ␜ߒߚ߽ߩߢߔ㧚㧔ᧄ▵ߢߪ d ࠍⓨ㑆ಽ⸃⢻ߣ
Fig.2: Three types of electrostatic objective lens: (a) retardation-type einzel lens; (b) accerelation-type einzel lens; (c) cathode lens. The spatial resolution d is assessed by the geometric mean of the diffraction aberration dD, spherical aberration dS, and chromatic aberration dC.
ߥߒߡ⸥ㅀߒ߹ߔ߇㧘ಽ⸃⢻ߩቯ⟵ߦ㑐ߒߡߩ ߒ⼏⺰ߪᰴ▵એ㒠ߢⴕ߹ߔ㧚㧕ߎߩᓘߪ㧘࿁᛬ Ꮕ dD㧘㕙Ꮕ dS㧘⦡Ꮕ dCߩነਈ߆ࠄߥࠅ߹ߔ㧚 ৻ㇱߪߔߢߦh12.2.2 ߢ↪߹ߒߚ߇㧘߹ߣߡ⸥ߖ ߫ᰴߩࠃ߁ߢߔ㧚 d = dD2+ dS2+ dC2 (6) ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ dD= 0.61 λo αo dS =1 2 CSαo 3 dC= CC∆E Eo αo (7) ࿑ߦ߅ߌࠆ dC ߩࠣࡈߪ㧘ࠛࡀ࡞ࠡ ∆E = 1 eV ࠍᗐቯߒߚ႐วߢߔ㧚ᧄߢߪ Eo߇ 1000 eV ߣዊߐߚߦ㧘࿁᛬Ꮕߣ⦡Ꮕ߇ᄢ߈ߊ㧘ᦨㆡ㐿 ߈ⷺߢߩಽ⸃⢻ࠍࠆߩߪߎߩਔ⠪ߣߥߞߡ߹ ߔ㧚ߎߩⷺᐲߩઃㄭߢߪ㧘㕙Ꮕߪነਈߒߡߥ ߎߣߦᵈᗧߒ߹ߒࠂ߁㧚㧔㜞ടㅦߩ SEM ߿ TEM ߢߪ ㅒߦ㧘ᦨㆡ㐿߈ⷺߢߪ⦡Ꮕࠃࠅ㕙Ꮕ߇ᡰ㈩⊛ ߣߥࠅ߹ߔ㧚㧕ࠣࡈ߆ࠄ㧘ᦨㆡ㐿߈ⷺߪ⚂ 1 mrad㧘 ߘߩߣ߈ߩಽ⸃⢻ߪ 40 nm ߣߥߞߡ߹ߔ㧚 ߎߩኻ‛ࡦ࠭߇㧘ߚߣ߃߫శ㔚ሶߢࠗࡔࠫࡦ ࠣࠍⴕ߁ⵝ⟎ߩ߽ߩߢߞߚߣߒ߹ߒࠂ߁㧚㧔․ቯߩ ࠛࡀ࡞ࠡߩశ㔚ሶࠍㆬ߱ߚߦ㧘ኻ‛ࡦ࠭ߩਅ ᵹߦࠛࡀ࡞ࠡࠕ࠽ࠗࠩࠍ⟎߈߹ߔ㧚㧕ߎߩ႐วߪ㧘 ᦨㆡ㐿߈ⷺ߹ߢࡆࡓࠍ⛉ߞߚߩߢߪಽశ♽ߣߒߡ ߩᗵᐲ߇⿷ࠅ߹ߖࠎ㧚ߘߎߢ㧘ಽ⸃⢻ࠍ‶†ߦߒߡ㐿 ߈ⷺࠍߍࠆᔅⷐ߇ࠅ߹ߔ㧚㐿߈ⷺࠍචಽᄢ߈ߊߔ ࠇ߫㧘࿁᛬Ꮕ߽⦡Ꮕ߽ήⷞߢ߈ߡ㧘㕙Ꮕߛߌ ߇ಽ⸃⢻ߦነਈߔࠆࠃ߁ߦߥࠅ߹ߔ㧚ࠣࡈ߆ࠄࠊ߆ ࠆࠃ߁ߦ㧘αo= 0.1 rad㧔⚂ 6 q㧕ߩ⒟ᐲߢߔߢߦ 㕙Ꮕߛߌߩነਈߣߥࠅ߹ߔ㧚 ߥ߅㧘SEM ߩࠃ߁ߦ㔚ሶࡊࡠࡉࠍᩏߔࠆⵝ⟎ ߩኻ‛ࡦ࠭ߣߒߡ↪ࠆ႐ว㧘㔚ሶࡆࡓߪ࿑ߩฝ ߆ࠄ߿ߞߡ߈ߡ⹜ᢱߦᾖߐࠇࠆߣ⠨߃߹ߔ㧚ߎߩ ႐วߪ㧘(6) ߩ d ߪ㔚ሶࡊࡠࡉᓘࠍਈ߃㧘ߒߚ߇ߞ ߡᩏဳⵝ⟎ߩಽ⸃⢻ߦኻᔕߔࠆ㊂ߣߥࠅ߹ߔ㧚 Fig.2(b) ߪ㧘หߓ㔚ᭂ᭴ㅧࠍടㅦဳߩࠕࠗࡦ࠷ࠚ࡞ ࡦ࠭ߣߒߡ↪ࠆ႐วߢߔ㧚(a) ߣߩ㆑ߪਛᄩ㔚 ᭂߩ㔚୯ Vcߢࠅ㧘ടㅦဳߢߪᱜߩ㔚߇ශടߐ ࠇ߹ߔ㧚ᷫㅦဳߩࠕࠗࡦ࠷ࠚ࡞ߢߪࡆࡓߩടㅦ㔚 ߣหߓߊࠄߩ⛘ኻ୯ߩ㔚ߢߒߚ߇㧘ടㅦဳࠕࠗ ࡦ࠷ࠚ࡞ߢߪ㧘ടㅦ㔚ߩዋߥߊߣ߽ᢙ⒟ᐲߩ୯ ߇ᔅⷐߢߔ㧚࿑ߩ႐วߪ⚂ 5 ߩ୯ߣߥߞߡ߹ߔ㧚 ᷫㅦဳߢߪ㧘㔚ሶࠍᷫㅦߐߖߚᓟߢ㧘ࠁߞߊࠅߞߡ ࠆ㗔ၞߢ㓸᧤↪ࠍ߷ߔߩߢ㧘ᒝ↪߇Ყセ ⊛ኈᤃߦᓧࠄࠇ߹ߔ㧚ടㅦဳߢߪኻߩ⁁ᴫߣߥࠅ㧘 㕖Ᏹߦᄢ߈ߥ㔚ࠍ߆ߌߥߣᚲቯߩ㓸᧤↪߇ᓧ ࠄࠇ߹ߖࠎ㧚 ৻⥸ߦ㧘ࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ࠍ↪ߡ߹ߞߚࠛࡀ ࡞ࠡߩ㔚ሶࠍ㓸᧤ߐߖࠆ႐ว㧘ᷫㅦဳࠃࠅ߽ടㅦဳ ߢേߐߖࠆᣇ߇Ꮕଥᢙߪዊߐߊߥࠅ߹ߔ㧚ᷫㅦဳ ߢߪ㧘㔚ሶߪਛᄩ㔚ᭂߦะ߆߁㗔ၞߢᷫㅦߐࠇ㧘ㅊ ߔะ߈ߦജࠍฃߌ߹ߔ㧚ࠃߞߡ㧘ߘߩ㗔ၞߢࡆࡓ ߇߰ߊࠄࠎߢశゲ߆ࠄ㔌ߐࠇߡߒ߹߹ߔ㧚ടㅦဳߢ ߪㅒߦ㧘ਛᄩ㔚ᭂߦࠃࠆടㅦ႐ߢᒁ߈ㄟ߹ࠇࠆߩߢ㧘 వߦࡆࡓ߇⚦ߊ⛉ࠄࠇ߹ߔ㧚ߘߎߢ㧘ࡦ࠭႐ਛߩ ゠ߩ㜞ߐߪടㅦဳߩᣇ߇ૐߊᛥ߃ࠄࠇ㧘ߘߩ⚿ᨐߣ ߒߡᏅଥᢙ߇ዊߐߊߥࠅ߹ߔ㧚Fig.2(b) ߩฝߩࠣ ࡈ߆ࠄࠊ߆ࠆࠃ߁ߦ㧘ടㅦဳߢߪಽ⸃⢻ߪ⚂ 20 nm ߦ߹ߢਅ߇ࠅ߹ߔ㧚 ৻ᣇߢ㧘ടㅦဳࠕࠗࡦ࠷ࠚ࡞ߢߪ Vcߩ⛘ኻ୯߇ᄢ ߈ߊߥࠆߩߢ㧘㔚߇㗴ߣߥࠅ߹ߔ㧚㔚ሶߩೋᦼࠛ ࡀ࡞ࠡ߇ 1000 eV ⒟ᐲߢߪߥࠎߣ߆น⢻ߢߞߡ ߽㧘ߘࠇࠃࠅᄢ߈ߥೋᦼࠛࡀ࡞ࠡߦኻߒߡ㧘ߘࠇࠍ ߐࠄߦࡦ࠭ਛߢടㅦߔࠆߣ߁ߩߪ⧰ߒߊߥࠅ߹ ߔ㧚ߒߚ߇ߞߡ㧘㔚ሶߩೋᦼࠛࡀ࡞ࠡ߇ዊߐߊߡ㧘 ߆ߟᏅఝవߩ႐วߪടㅦဳ㧘ߘ߁ߢߥߌࠇ߫ᷫㅦ ဳߣ߁ಽߌߣߥࠅ߹ߔ㧚 12.3.3 ࠞ࠰࠼ࡦ࠭ ೨㗄ߩࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ߦ߅ߡ㧘ᷫㅦဳࠃࠅട ㅦဳߩᣇ߇Ꮕ߇⦟ߊߥࠆℂ↱ߪ㧘ᓟ⠪ߩᣇ߇ࡦ ࠭႐ਛߩ゠߇ૐߊᛥ߃ࠄࠇࠆ߆ࠄߢߒߚ㧚゠ࠍ ૐߊߔࠆ⋡⊛ߩߚߦߪ㧘⹜ᢱ㕙ߦᒝടㅦ㔚႐ࠍ ߟߊࠅ㧘⹜ᢱ߆ࠄࠆⷺᐲߢߚ㔚ሶࠍߔߋߦశゲ ߦᒁ߈ᚯߔߩ߇ᦨ߽ലᨐ⊛ߢߔ㧚ߎࠇߦࠃࠆᏅૐᷫ ߩലᨐߪ㧘⹜ᢱ㕙ߦ⏛႐ࠍ߆ߌࠆ႐วࠃࠅ߽㗼⪺ߦ ࠇ߹ߔ㧚ታ㓙㧘Ꮕᱜߩߚߩ․ߥᚻᴺࠍ㒰ߌ ߫㧘⹜ᢱ㕙ߦ⋥ធ㔚႐ࠍ߆ߌࠆߩ߇㧘Ꮕଥᢙࠍዊߐ ߊߔࠆߚߩᦨ߽ലߥᣇᴺߢߔ㧚 ߒ߆ߒߥ߇ࠄ㧘ߎߩᣇᴺࠍណ↪ߢ߈ࠆ߆ߤ߁߆ߪ㔚 ሶߩೋᦼࠛࡀ࡞ࠡ Eoᰴ╙ߢߔ㧚Ꮕߩૐᷫࠍᦸ ߦߪ㧘ࠆ⒟ᐲᄢ߈ߥടㅦ₸߇ᔅⷐߢߔ㧚㧔ടㅦ₸ߣ Ꮕߩ㑐ଥߪߣߢ␜ߒ߹ߔ㧚㧕ߚߣ߃߫㧘Eo= 10 eV ߩ㔚ሶࠍ 103ߩࠛࡀ࡞ࠡߦടㅦߒߡ 10 keV ߦߔ ࠆߎߣߪ㔍ߒߊࠅ߹ߖࠎ߇㧘Eo= 1000 eV ߣߥࠆ ߣ㧘ߣหߓടㅦ₸ࠍᓧࠆߦߪ 106 V ߩ㔚߇ߤߎ ߆ߢᔅⷐߣߥࠅ㧘ታ⊛ߢߪࠅ߹ߖࠎ㧚 ߐߡ㧘ടㅦ႐ߪࡦ࠭↪ߪ߽ߟ߽ߩߩ㧘ߘࠇߛߌ
ߢߪታߪߢ߈ߕ㧘⹜ᢱ㕙ߩ⯯߇⹜ᢱߩᓟࠈߦߟ ߊࠄࠇ߹ߔ㧔╙ 4 ┨ࠍෳᾖߒߡߊߛߐ㧕㧚ߘߎߢ㧘 ታࠍᓧࠆߚߦߪ㧘ടㅦ႐ߩਅᵹߦ㓸᧤ߩߚߩ ࡦ࠭ࠍ⟎ߊᔅⷐ߇ࠅ߹ߔ㧚Fig.2(c) ߪߘߩߢߔ㧚 ߎߩ࿑ߢߪ㧘㓸᧤ߩߚߩࡦ࠭႐ߣߒߡ (a) ߩᷫㅦ ဳࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ࠍߘߩ߹߹↪ߡ߹ߔ㧚ߎߩ ࠃ߁ߥ㧘ޟടㅦ႐㧗㓸᧤ࡦ࠭ޠߣ߁♽߇ࠞ࠰࠼ ࡦ࠭ߣ߫ࠇ߹ߔ㧚 Fig.2(c) ߢߪೋᦼࠛࡀ࡞ࠡࠍ Eo= 10 eV ߣߒߡ㧘 ߎࠇࠍ 10 keV ߹ߢടㅦߒߡ߹ߔ㧚ߎߩߚߦ⹜ᢱ ࠍ−9990 V ߦᶋ߆ߖ㧘ࠕࠬ㔚ߢࠆ╙৻㔚ᭂߣ ߩ㑆ߦടㅦ႐ࠍߟߊࠅ߹ߔ㧚߽ߜࠈࠎ㧘⹜ᢱࠍࠕࠬ 㔚ߦߒߡᓟࠈߩ㔚ᭂߩ㔚ࠍᶋ߆ߖߡ߽หߓ㔚႐ ಽᏓ߇ߟߊࠄࠇ߹ߔ߇㧘ᦨ⚳⊛ߦࡦ࠭ࠍᛮߌߚߣ ߈ߦࠕࠬ㔚ߦߥࠆߩ߇ㇺว߇ߩߢ㧘ㅢᏱߪ ࿑ߩࠃ߁ߦߒ߹ߔ㧚ߎߎߢߪ㓸᧤ߩߚߦᷫㅦဳࠕࠗ ࡦ࠷ࠚ࡞ࡦ࠭ࠍㆡ↪ߒߡࠆࠊߌߢߔ߇㧘ߎࠇࠍ ടㅦဳࠕࠗࡦ࠷ࠚ࡞ߦᄌᦝߔࠆߩߪήℂ߇ࠅ߹ߔ㧚 ╙৻㔚ᭂߩ⟎ߦ㆐ߒߚߣ߈ߦ㧘㔚ሶߩࠛࡀ࡞ࠡ ߪ߶߷ 10 keV ߦߥߞߡࠆߩߢ㧘ਛ㑆㔚ᭂߦߎߩᢙ ߩ㔚୯߇ᔅⷐߥߎߣࠍ⠨߃ࠇ߫ታ⊛ߢࠅ߹ ߖࠎ㧚 ߎߩࠃ߁ߥᒝടㅦߦࠃߞߡ㧘Ꮕଥᢙߪ㕖Ᏹߦ ዊߐߥ୯ߣߥࠅ߹ߔ㧚ߎߩߢߪࡒࠢࡠࡦࠝ࠳ ߩᏅଥᢙߦߥߞߡ߹ߔ㧚࿑ߦ߅ߌࠆ⹜ᢱ㕙ߢߩ㔚 ሶ゠ߩ㐿߈ⷺߪ±60◦ߢࠅ㧘Fig.2 (a) ߣ (b) ߩ႐ วߦᲧߴߡ৻ᩴㄭߊᄢ߈୯ߢࠆߦ߽߆߆ࠊࠄߕ㧘 ゠ߪࠃࠅૐߊߥߞߡ߹ߔ㧚 ߥ߅㧘৻᭽ߥടㅦ႐ߦኻߒߡߪ㔚ሶ゠ߪ‛✢ߣ ߥࠆߩߢ㧘ടㅦ႐ߩ↪ߛߌࠍ⠨߃ࠆߥࠄ⸃ᨆ⊛ߥᛒ ߇น⢻ߢࠅ㧘Ꮕଥᢙߦኻߒߡߩౕ⊛ߥᑼࠍ ዉߊߎߣ߇ߢ߈߹ߔ㧚㧔⯯⟎ߦ㑐ߒߡߩᏅଥᢙ ߢߔ㧚㧕߽ߜࠈࠎ㧘ടㅦ₸ࠍᄢ߈ߊߔࠇ߫ߔࠆ߶ߤ Ꮕଥᢙࠍዊߐߊߢ߈߹ߔ㧚Ꮕଥᢙߦኻߒߡߩౕ⊛ ߥᑼߪ⋭⇛ߒ߹ߔ߇㧘߹ߩߢߪ㧘CSߣ CCߦ ኻߒߡߩടㅦ႐ߩነਈߪߣ߽ߦ 0.003 mm ߣߥࠅ߹ ߔ㧚৻᭽ߥടㅦ႐ߩᏅߪߎߩࠃ߁ߦዊߐ߽ߩߢߔ ߇㧘ߘߩᓟߦઃߌ⿷ߒߚᷫㅦဳࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ߩ ߚߦ㧘ోߣߒߡߩᏅߪߘࠇࠃࠅ߽ഠൻߒ߹ߔ㧚 ߒ߆ߒ㧘㐿߈ⷺߩᄢ߈ߥ゠߇ᦨೋߦടㅦ႐ߢ⛉ࠄ ࠇߡࠆߩߢ㧘Fig.2 (a) ߩ႐วߩᏅଥᢙߦᲧߴࠇ ߫ߪࠆ߆ߦዊߐߥ୯߇ታߐࠇߡ߹ߔ㧚ߟ߹ࠅ㧘ട ㅦ႐ߦ⛯ߊ㓸᧤ࡦ࠭ߩᏅ߇ࠆ⒟ᐲᄢ߈ߊߡ߽㧘 ടㅦ႐ࠍ↪ࠆࡔ࠶࠻߇៊ߥࠊࠇࠆߎߣߪࠅ߹ ߖࠎ㧚 ߐߡ㧘ടㅦ႐ࠍ↪ࠆߎߣߢᏅଥᢙࠍ㕖Ᏹߦዊ ߐߊߢ߈ࠆࠊߌߢߔ߇㧘ಽ⸃⢻߇ߤ߁ߥࠆ߆ߪ߹ߚ ߩߢߔ㧚߹ߕ Eo߇ዊߐߊ㧘ࠃߞߡᵄ㐳 λo߇㐳 ߎߣ߆ࠄ㧘࿁᛬Ꮕߪᄢ߈ߊߥࠄߑࠆࠍ߃߹ߖࠎ㧚 ߹ߚ㧘หߓߊ Eo߇ዊߐߚߦ ∆E/Eo߇ᄢ߈ߊߥ ࠅ㧘ߎࠇߪ⦡Ꮕߦߣߞߡਇߢߔ㧚ߒ߆ߒ㧘㕙 Ꮕߦ㑐ߒߡߪ㧘CS߇ᷫߞߚಽߛߌ dSߪਅ߇ࠅ߹ߔ㧚 ߎࠇࠄߩ⚿ᨐߣߒߡ㧘ಽ⸃⢻ߣߒߡߪ Fig.2(a)㧘(b) ߣห⒟ᐲߩ 17 nm ߦߒ߆ߥࠅ߹ߖࠎ㧚 ߒ߆ߒ㧘ߎࠇߪടㅦ႐ࠍ↪ࠆߎߣߩࡔ࠶࠻ࠍุ ቯߔࠆ߽ߩߢߪࠅ߹ߖࠎ㧚หߓ Eoߦኻߒߡ㧘ടㅦ ࠍⴕࠊߥ Fig.2 (a)㧘(b) ߩࡦ࠭ࠍណ↪ߒߚࠄߤ߁ ߥࠆߢߒࠂ߁߆㧚ߘߩ႐วߪ㧘ࠞ࠰࠼ࡦ࠭ࠃࠅ߽ ߪࠆ߆ߦᄢ߈ߥ CSߣ CCߦᚯࠆߛߌߢߪߥߊ㧘ᵄ㐳 ߇ᄢ߈ߊ㧘߆ߟ ∆E/Eo߇ᄢ߈ߣ߁ᖱߪߘߩ߹ ߹ᱷࠆߩߢ㧘ᭂ┵ߦᖡಽ⸃⢻ߒ߆ᓧࠄࠇ߹ߖࠎ㧚ߚ ߣ߃߫㧘Eo= 10 eV ߦኻߒߡᷫㅦဳࠕࠗࡦ࠷ࠚ࡞ࠍ ㆡ↪ߒߚߣߔࠆߣ㧘ಽ⸃⢻ߪ 1.3 µm ߣߥࠅ߹ߔ㧚ߎ ࠇߪ㧘ࠞ࠰࠼ࡦ࠭ࠃࠅ 2 ᩴᖡ୯ߢߔ㧚ߔߥࠊߜ ࠞ࠰࠼ࡦ࠭ߢߪ㧘ടㅦ႐ࠍ↪ࠆߎߣߢ㧘ᜰቯߐ ࠇߚ Eoߦኻߒߡߢ߈ࠆ㒢ࠅߩ⦟ಽ⸃⢻ࠍᓧࠆߎߣ ߇ߢ߈ࠆߩߢߔ㧚 ߎߩࠃ߁ߥടㅦߦࠃࠆലᨐߪ㧘ടㅦ₸߇ਅ߇ࠇ߫ૐ ᷫߐࠇࠆߪߕߢߔ㧚Fig.2(a) ߢߪ Eo= Ei= 1000 eV ߢߒߚ߇㧘ߎࠇࠍࠞ࠰࠼ࡦ࠭ߦᄌᦝߒߡ㧘หߓ Eo ߦኻߒߡ Ei= 10 keV ߦടㅦߒߡߺ߹ߒࠂ߁㧚ߔߥࠊ ߜടㅦ₸߇ 10 ߢߔ㧚ߎߩടㅦߦࠃߞߡ㧘Eo= 1000 eV ߩ߹߹ߢᱜߩടㅦࠍⴕࠊߥࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ߣ Ყߴߡ㧘ࡔ࠶࠻߇↢ߓࠆߢߒࠂ߁߆㧚ታ㓙ߦᏅଥ ᢙࠍ⸘▚ߒߡߺࠆߣ㧘ߎߩࠞ࠰࠼ࡦ࠭ߩᏅଥᢙ ߪ㧘CS = 29 mm㧘CC= 2.4 mm ߣߥࠅ߹ߔ㧚Fig.2 (a) ߩᷫㅦဳࠕࠗࡦ࠷ࠚ࡞ߣᲧセߔࠇ߫㧘ടㅦߩലᨐ ߪචಽࠅ߹ߔ߇㧘(b) ߩടㅦဳࠕࠗࡦ࠷ࠚ࡞ߩᏅ ଥᢙߣᲧߴߡߘࠇ߶ߤ㆑߁ࠊߌߢߪࠅ߹ߖࠎ㧚ߟ߹ ࠅ㧘ടㅦ₸߇ 10 ⒟ᐲߢࠆߣ㧘ടㅦߩലᨐߪߘࠇ߶ ߤ⊛ߦߪࠇ߹ߖࠎ㧚ࠞ࠰࠼ࡦ࠭ߦߒߡߒ߹߁ ߣ㧘⹜ᢱߩ㔚߇ᶋߊߣ߁࠺ࡔ࠶࠻߇ᱷࠆߩߢ㧘 ߤߜࠄࠍណ↪ߔߴ߈߆ߪ್ᢿߦ⧰ߒߣߎࠈߢߔ㧚 ߥ߅㧘ࠞ࠰࠼ࡦ࠭ߦ߅ߡߪ㧘⹜ᢱߪࡦ࠭㔚 ᭂߩ৻ㇱߣߒߡߊߎߣߦߥࠅ㧘⹜ᢱ㕙ߢ߽ߞߣ߽ ᒝ㔚႐߇ߟߊࠄࠇ߹ߔ㧚ߘߎߢ㧘ಳಲߩࠆ⹜ᢱߩ ႐วߪ㧘⹜ᢱ⒖േߦࠃߞߡࡦ࠭ߣߒߡߩേ߇ᄌ ࠊߞߡߒ߹߁ߎߣ߇ࠅ߹ߔ㧚⹜ᢱࠍߌߚࠅߔࠇ߫ ߥ߅ߐࠄߢߔ㧚߹ߚ⛘✼ߩ⹜ᢱߢߪ㧘⹜ᢱ㕙ߩ㔚 ߇ቯ߹ࠅߦߊߊ㧘ᓸዊ㔚߇ߎࠅ߿ߔߊߥࠆ႐ว߽ ࠆߩߢ㧘ቯߒߚേ߇㔍ߒߊߥࠅ߹ߔ㧚ߒ߆ߒ߽ ߜࠈࠎ㧘Eo߇ዊߐ႐วߩࠞ࠰࠼ࡦ࠭ߩലᨐߪ
⛘ᄢߢࠅ㧘ߎࠇߦᢜߔࠆಽ⸃⢻ߪઁߩ࠲ࠗࡊߩ ࡦ࠭ߢߪਇน⢻ߢߔ㧚 12.3.4 ⏛႐ဳኻ‛ࡦ࠭ ⏛႐ဳࡦ࠭ߪ㧘ၮᧄ⊛ߦߪ㧘ࠦࠗ࡞ߣߘࠇࠍ࿐ ㅘ⏛₸ߩ㜞⏛ᕈ㧔࡛ࠢ㧕߆ࠄᚑࠅ߹ߔ㧚㧔⏛ ႐ဳࡦ࠭ߩ᭴ᚑߦ㑐ߒߡߪ╙ 2 ┨ߢ⇛ࠍㅀߴ߹ ߒߚ㧚㧕࡛ࠢߪࠡࡖ࠶ࡊࠍ߽ߜ㧘ߘߎ߆ࠄ߽ࠇࠆ ⏛႐ࠍࡦ࠭႐ߣߒߡ↪߹ߔ㧚࡛ࠢߩ߁ߜߢ㧘ߘ ߩࠡࡖ࠶ࡊઃㄭߪߣߊߦࡐ࡞ࡇࠬߣ߫ࠇ㧘⏛႐ ࠍ㓸ਛߐߖࠆࠃ߁ߥᒻ⁁ߣߥߞߡ߹ߔ㧚TEM ߩኻ ‛ࡦ࠭ߩࡐ࡞ࡇࠬߪ㧘ಽ⸃⢻ࠍఝవߔࠆߣ߆㧘 ࠆߪ⹜ᢱࠍᄢᢳߐߖࠆߥߤߩⷐ᳞ߦᔕߓߡ㧘 ឵น⢻ߦߥߞߡࠆߩ߇᥉ㅢߢߔ㧚 Fig.3(a) ߪ㧘⏛႐ਛߦ⹜ᢱࠍ⟎ߊ࠲ࠗࡊߩ߽ߩߢ㧘 ߎࠇߪࠗࡦࡦ࠭ߣ߫ࠇ߹ߔ㧚TEM ߢߪߎߩࠃ߁ ߥኻ‛ࡦ࠭߇ㅢᏱߢߔ߇㧘SEM ߩኻ‛ࡦ࠭ߢ߽ 㜞ಽ⸃⢻ߩ߽ߩߪߎߩ࠲ࠗࡊߢߔ㧚࿑ߢߪࠦࠗ࡞߿ ࡛ࠢㇱಽߪ⋭⇛ߒߡ㧘ࡐ࡞ࡇࠬߩవ┵ㇱಽߛ ߌࠍ␜ߒߡ߹ߔ㧚࿑ߩߚߣ߃߫Ꮐ߇ N ᭂ㧘ฝ ߇ S ᭂߣߥࠅ㧘N ᭂ߆ࠄ S ᭂߦะ߆߁⏛ജ✢ߩ৻ㇱ ߇⹜ᢱࠍㅢㆊߒ߹ߔ㧚 ႐ᚲ⊛ߥ⚂ߦ㑐ߒߡ߃߫㧘⏛႐ဳࡦ࠭ߪ࡛ ࠢߣࠦࠗ࡞߇ᔅⷐߥߩߢ㧘㔚ᭂߣ⎹ሶߛߌߢᷣ㕒 㔚ဳࠃࠅ߽႐ᚲࠍߣࠅ߹ߔ㧚߹ߚ㧘ࠦࠗ࡞ߪ⊒ᾲߒߡ ࠟࠬࠍߔߩߢ㧘⹜ᢱ߇⌀ⓨਛߢߞߡ߽㧘ࠦࠗ࡞ߛ ߌߪᄢ᳇ߦ⟎߈ߚߣ߁ᖱ߽ࠅ߹ߔ㧚㕒㔚 ࡦ࠭ߪోࠍ⌀ⓨߦẃߌࠆߎߣ߇ߢ߈ࠆߩߢ㧘ߘߩ ᗧߢ㕒㔚ဳߪଢߢߔ㧚 ⏛႐ဳࡦ࠭ߢߪ㔚ሶߩടᷫㅦߪⴕࠊࠇߥߩߢ㧘 ᱜߩടᷫㅦࠍⴕࠊߥࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ߣห㘃 ߣߥࠅ߹ߔ㧚ߒ߆ߒᏅଥᢙߪ㧘ࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ ࠃࠅ߽⏛႐ဳࡦ࠭ߩᣇ߇৻⥸ߦߪዊߐߊߢ߈߹ߔ㧚 㧔ߚߛߒ㧘Eoߩዊߐߥ㔚ሶࠍടㅦ႐ߢᒁ߈ㄟࠞ࠰ ࠼ࡦ࠭ߦߪ߆ߥ߹ߖࠎ㧚㧕ࠗࡦࡦ࠭࠲ࠗࡊߩ⏛ ႐ဳࡦ࠭ߢߪ㧘CSߣ CCߪ 1 mm ೨ᓟߩ୯߇ౖဳ ⊛ߢߔ㧚 ⏛႐ဳࡦ࠭ߦ߅ߡ㧘Ꮕଥᢙࠍዊߐߊߔࠆߚ ߩ⠨߃ᣇߪ㕒㔚ࡦ࠭ߣห᭽ߢߔ㧚ߔߥࠊߜ㧘⹜ᢱ߆ ࠄࠆⷺᐲߢߚ㔚ሶ゠ࠍߥࠆߴߊߪ߿ߊశゲ ߦᒁ߈ᚯߒߡ㧘゠ࠍૐߊᛥ߃߹ߔ㧚ߘߩߚߦߪ㧘 ࡐ࡞ࡇࠬߩࠡࡖ࠶ࡊਛߩ⏛႐ᒝᐲࠍน⢻ߥ㒢ࠅᄢ ߈ߊߒߡ㧘ゲ⏛႐ಽᏓ B(z) = Bz(0, 0, z) ߩࡇࠢ ⟎ߦ⹜ᢱࠍ⟎߈߹ߔ㧚 ߚߛߒ㧘ᐢ㗔ၞߢ⏛႐ࠍߟߊߞߡߒ߹ߞߡߪߛ ߢߔ㧚ߥߗߥࠄ㧘ࡆࡓߩ⚿⟎ߪ߹ߞߡࠆߩ ߢ㧘⹜ᢱࠍߚ゠߇ߔߋ㓸᧤ߒߡߒ߹ࠊߥࠃ߁ ߦ㧘⹜ᢱ㕙ㄭறߢߛߌᒝߊ㧘ߘߩߣߔߋߦᷫߔࠆ ࠃ߁ߥ B(z) ߢߥߌࠇ߫ߥࠅ߹ߖࠎ㧚ℂᗐࠍ߃߫࠺ ࡞࠲㑐ᢙߩࠃ߁ߥಽᏓߢߔ㧚ߎߩὐ㧘ടㅦ㔚႐ߩ႐ว ߪ㧘ߊࠄടㅦ߇ᒝߊߡ߽㓸᧤↪߇ᒝߊߥࠅߔ߉ࠆ ᔃ㈩ߪࠅ߹ߖࠎ㧚㧔ߟߨߦ⯯ࠍߟߊࠆߩߢߒߚ㧚㧕 ⹜ᢱઃㄭߩ⏛႐ߩ㓸ਛᐲߪࡐ࡞ࡇࠬߩᒻ⁁ߢ ߹ࠅ㧘ࠦࠗ࡞ߩ⟎߿࡛ࠢᒻ⁁ߦߪ߶ߣࠎߤଐሽ ߒ߹ߖࠎ㧚ߘߎߢ㧘⸳⸘⠪߇߽ߞߣ߽ᤨ㑆ࠍ߆ߌࠆߴ ߈ߪ㧘ࡐ࡞ࡇࠬߩᒻ⁁ߩቯߢߔ㧚ၮᧄ⊛ߦߪ㧘 ࡐ࡞ࡇࠬߩవ┵ࠍውࠄߖߡ㧘ࠡࡖ࠶ࡊߦ⏛႐߇㓸 ਛߔࠆࠃ߁ߦߒ߹ߔ㧚ߒ߆ߒ㧘߹ࠅ߿ࠅߔ߉ࠆߣ ⏛ᭂ߇⏛᳇㘻ࠍߎߒߡ㧘߆߃ߞߡ B(z) ߩ߇ᐢ ߇ߞߡߒ߹߹ߔ㧚߹ߚ㧘ࠡࡖ࠶ࡊࠍ⁜ߔ߉ࠆߣ⹜ ᢱࠅߩ⥄↱ᐲࠍ㒢ߔࠆߎߣߦߥࠅ߹ߔ㧚⸘▚ᯏߦ ࠃࠆࡐ࡞ࡇࠬ⸳⸘ߩ⥄േൻߦ㑐ߒߡ㧘ᢥ₂ [5] ߦ ႎ๔߇ࠅ߹ߔ㧚 Fig.3(b) ߪ㧘ࡒࠗࡦࡦ࠭ߣ߫ࠇࠆ࠲ࠗࡊߢ㧘 ࡐ࡞ࡇࠬ߇ਔᭂߣ߽⹜ᢱࠃࠅ㕙ߦࠅ߹ߔ㧚 ࡐ࡞ࡇࠬߩߚߣ߃߫ౝ㧔శゲ㧕߇ N ᭂ㧘ᄖ ߇ S ᭂߣߥࠅ㧘N ᭂ߆ࠄߚ⏛ജ✢ߩ߁ߜߢ㧘࿁ ࠅࠍߒߡ⹜ᢱઃㄭࠍㅢㆊߒߡ߆ࠄ S ᭂߦะ߆߁߽ ߩ߇ࡦ࠭↪ࠍ߷ߒ߹ߔ㧚ߎߩ᭴ㅧߥࠄ⹜ᢱࠅ ߩⓨ㑆߇ᐢߊขࠇࠆߩߢ㧘SEM ߩኻ‛ࡦ࠭ߣߒߡ ߒ߫ߒ߫ណ↪ߐࠇ߹ߔ㧚ߒ߆ߒ㧘⹜ᢱ㕙ߢߩ⏛႐ߩ㓸 ਛᐲߪࠗࡦࡦ࠭࠲ࠗࡊࠃࠅഠࠆߩߪᣇ߇ࠅ߹ ߖࠎ㧚ߎࠇߪゲ⏛႐ಽᏓ B(z) ߩᐢ߇ࠅࠍࠇ߫ ࠄ߆ߢߔ㧚ಽ⸃⢻߽߿ߪࠅഠߞߚ୯ߣߥࠅ߹ߔ㧚 ߹ߚ㧘⸘▚ߪ␜ߒ߹ߖࠎ߇㧘⹜ᢱߩᓟࠈߦࡐ ࡞ࡇࠬࠍ⟎ߊࠪࡘࡁࠤ࡞ࡦ࠭ߣ߫ࠇࠆ߽ߩ ߇ࠅ߹ߔ㧚ߎࠇߪ㧘Fig.3 (b) ߩࡦ࠭ࠍ㧘⹜ᢱ㕙 ߦ㑐ߒߡᏀฝォߒߡ⟎ߚࠃ߁ߥ߽ߩߢߔ㧚ᒻᚑߐ ࠇࠆ⏛႐ಽᏓ߽߿ߪࠅᏀฝォߒߚ߽ߩߦߥࠅ߹ߔ㧚 ߎߩ࠲ࠗࡊߪ㧘ࡆࡓߩㅴⴕߩⓨ㑆ࠍ߹ߞߚߊභ ߒߥߣ߁ὐߢߣߥࠅ߹ߔ㧚ߒ߆ߒ㧘⹜ᢱ߆ࠄ ࡆࡓߩㅴⴕߦ B(z) ߩಽᏓ߇ߔߘࠍᒁߡߒ߹߁ ߩߢ㧘⹜ᢱㄭறߢߩ⏛႐ߩ㓸ਛᐲߣ߁ᗧߢߪ ࡒࠗࡦࡦ࠭ࠃࠅ߽⧯ᐓഠࠅ߹ߔ㧚 Fig.3(c) ߪ㧘వߦㅀߴߚࠞ࠰࠼ࡦ࠭ߩ৻⒳ߢ㧘 ടㅦ႐ߦ⛯ߊ㓸᧤ߩߚߩࡦ࠭ߣߒߡ Fig.3 (b) ߩ ࡒࠗࡦࡦ࠭ࠍ⟎ߚߢߔ㧚ߎߩ᭴ᚑߢߪ㧘ടㅦ ႐ߣ⏛႐߇⹜ᢱ⟎ߦ㊀⇥ߐࠇࠆߎߣߣ㧘߽ߣ߽ߣ ᷫㅦဳߩࠕࠗࡦ࠷ࠚ࡞ࡦ࠭ࠃࠅ߽⏛႐ဳࡦ࠭ߩ ᣇ߇Ꮕଥᢙ߇ዊߐߎߣ߆ࠄ㧘৻᭽ടㅦ႐ߩᏅ ଥᢙߦㄭߠ߈߹ߔ㧚⹜ᢱ߆ࠄࠆⷺᐲߢߚ㔚ሶࠍߥ
Fig.3: Three types of magnetic objective lens: (a) inlens type; (b) semi-inlens type; (c) cathode lens with a magnetic field for fucusing.
ࠆߴߊᣧߊశゲߦᒁ߈ᚯߔߣ߁ᗧߢߪ㧘৻᭽ട ㅦ႐ߣ⏛႐ࠍหߓ႐ᚲߦ㊀⇥ߐߖߚߎߩ᭴ᚑ߇㧘ࠞ ࠰࠼ࡦ࠭ߣߒߡᦨ߽ℂᗐ⊛ߥ߽ߩߢߔ㧚 ߎߎߢ␜ߒߚ⸘▚ߪ㧘ߕࠇ߽⹜ᢱ㕙ߦ⏛႐ࠍ ߟߊࠆ߽ߩߢߔ߇㧘ߘࠇ߇⸵ߐࠇߥ႐ว߽ࠅ߹ ߔ㧚ߚߣ߃߫㧘⹜ᢱ߇⏛ᕈߢࠆߣ߈ߢߔ㧚ࠆ ߪ AES ߩࠃ߁ߦ㧘㔚ሶᾖ♽ߩኻ‛ࡦ࠭ߩ⣁ߦಽ శ♽ߩࠗࡦࡊ࠶࠻ࡦ࠭߇⟎߆ࠇࠆࠃ߁ߥ႐ว߽ߘ ߁ߢߔ㧚ߘߩߣ߈ߪ㧘⹜ᢱ߆ࠄ㔌ࠇߚ⟎ߦ⏛႐߇ߟ ߊࠄࠇࠆࠃ߁ߦࡐ࡞ࡇࠬࠍ㈩⟎ߔࠆᔅⷐ߇ࠅ ߹ߔ㧚᳢↪ߩ SEM ߢߪ㧘ߘߩࠃ߁ߥኻ‛ࡦ࠭߇৻ ⥸⊛ߢߔ㧚
12.4
ߩ⹏ଔ
ᧄ▵߆ࠄ㧘ኻ‛ࡦ࠭ߦࠃߞߡߟߊࠄࠇࠆߣߘ ߩ⹏ଔߦ㑐ߒߡㅀߴ߹ߔ㧚ߎࠇࠍ⠨߃ࠆߦ㓙ߒߡߪ㧘 ᰴߩੑߟߩ࠹ࡑࠍᷙหߒߥࠃ߁ߦᵈᗧߔࠆᔅⷐ ߇ࠅ߹ߔ㧚ߔߥࠊߜ㧘ߩ⦟ߒᖡߒࠍߤߩࠃ߁ߦ⹏ ଔߔࠆ߆ߣ߁㗴ߣ㧘ߘߩࠃ߁ߥ߇ࡦ࠭ߩᕈ ⢻ߤ߁㑐ଥߔࠆ߆ߣ߁㗴ߢߔ㧚ᧄ▵ߢߪ㧘ߩᚑ ࠅ┙ߜߣ⹏ଔᣇᴺߦ㑐ߒߡㅀߴ㧘ᰴ▵h12.5 ߦ߅ ߡశቇ♽ߩౕ⊛ߥነਈࠍ⼏⺰ߒ߹ߔ㧚 12.4.1 ࡦ࠭ߦࠃࠆߩᒻᚑ ޓ ᐔ㕙ߦࠬ࠻ࠗࡊ⁁ߩࡄ࠲ࡦ߇ਗߴࠄࠇߡ ߡ㧘ߘࠇࠍࡦ࠭ߢ⚿ߐߖࠆߣߒ߹ߔ㧚⹜ᢱߣߘ ߩߩ㑐ଥߪ㧘ߚߣ߃߫ Fig.4 ߩࠃ߁ߦߥࠅ߹ߔ㧚⹜ ᢱߪ㧘శḮߣߒߡࠗࡦࠦࡅࡦ࠻ߢࠆߣቯߒ ߹ߔ㧚ߔߥࠊߜ㧘߆ߢᾖߐࠇߡࠆߩߢߪߥߊ㧘 ࡄ࠲ࡦߩฦὐ߇ߘࠇߙࠇ⁛┙ߦ㔚ሶࠍ⊒↢ߐߖ ࠆ⁁ᴫߢߔ㧚ߚߣ߃߫㧘⹜ᢱߦ X ✢ࠍᾖߒߡߡ ߊࠆశ㔚ሶ߇ߘ߁ߢߔ㧚࿑ߢߪ㧘‛㕙㧔ߔߥࠊߜ⹜ᢱ 㕙㧕ߣ㕙ߦ߅ߌࠆᒝᐲߩࠗࡦࡊࡠࡈࠔࠗ࡞߽ឬ߆ ࠇߡ߹ߔ㧚 Fig.4 ߦ߅ߡ㧘㔚ሶ߇ߐࠇࠆࡄ࠲ࡦߩ㗔 ၞߪ㧘⁛┙ߥὐశḮߩ㓸߹ࠅߣߥߔߎߣ߇ߢ߈߹ ߔ㧚ߘࠇࠄߩὐశḮߪ㧘㕙ߦ߅ߡߘࠇߙࠇࡏࠤߚ ᒝᐲಽᏓࠍߟߊࠅ߹ߔ㧚ߣߊߦゲశḮ㧘ߟ߹ࠅశゲ ߦ⟎ߚὐశḮ߇ߟߊࠆߪὐಽᏓ㑐ᢙ㧔point spread function㧕ߣ߫ࠇ㧘೨࿁ߘࠇࠍ PSF(ri) ߣ ⸥ߒ߹ߒߚ㧚ߎߎߢri= (xi, yi) ߪ㕙ߩᐳᮡߢߔ㧚 ὐಽᏓ㑐ᢙ PSF ߪ㧘ⓨ㑆ಽ⸃⢻ߦ⋥ធߦ㑐ਈߔ ࠆ߽ߩߢߔ㧚h12.2.2 ߩᦨೋߦㅀߴߚࠃ߁ߦ㧘ಽ⸃⢻ߣ ߪޟ‛㕙ߩ৻ὐ߇ߤࠇߛߌࡏࠤࠆ߆ޠߣ߁㊂ߢߔ㧚 ߘߎߢ㧘㕙ߢߩࡏࠤ㊂ࠍ₸ M ߢഀߞߡ‛㕙឵▚ ߒߚߩߣห᭽ߦ㧘ὐశḮࠍߔ㑐ᢙ⥄り߽‛㕙឵▚ ߒߡ⠨߃ࠆߴ߈ߢߔ㧚ߔߥࠊߜ㧘₸ࠍ⠨ᘦߒߡὐ ಽᏓ㑐ᢙࠍ‛㕙ߦᒁ߈ᚯߒߡ㧘ߘࠇࠍ PSF(ro) ߣߒ ߹ߔ㧚㧔ro= (xo, yo) ߪ‛㕙ߩᐳᮡߢߔ㧚㧕ߎࠇ߇㧘‛ 㕙ߩ৻ὐ߇ߤߩࠃ߁ߦࡏࠤࠆ߆ࠍਈ߃ࠆ㑐ᢙߢߔ㧚 એਅߢߪ◲නߩߚߦ㧘㕙⥄ࠍ‛㕙ߣหߓࠬ ࠤ࡞ߦᒁ߈ᚯߒߡ㧘‛㕙ߣ㕙ࠍ㊀ߨวࠊߖߡ⠨ ߃߹ߔ㧚㧔Fig.4 ߩࠃ߁ߦ㧘㕙ࠍ‛㕙ߣหߓᄢ߈ߐߦ ߒߡਗߴߡ⠨߃ࠆߣ߁ߛߌߩߎߣߢߔ㧚㧕ߎߩ⚂᧤ ߩ߽ߣߢ㧘PSF(ri) ߪ PSF(ro) ߣหߓ㑐ᢙߣߥࠅ߹ ߔ㧚᳇ᜬߜߣߒߡߪ㧘PSF(ro) ߣᦠߚߣ߈ߪ‛㕙ߩ ৻ὐߩࡏࠤࠍᗐቯߒߡߡ㧘PSF(ri) ߣᦠߌ߫ὐశḮ ߢߔ㧚ߒ߆ߒ㧘ਔ⠪ࠍⓍᭂ⊛ߦߔߴ߈ℂ↱ߪ ࠅ߹ߖࠎ㧚એਅߢߪ㧘ᒁᢙ߇㊀ⷐߢߥߣ߈ߪ㧘නߦ PSF ߣ⸥ߒ߹ߔ㧚 ᵈᗧὐߣߒߡ㧘㑐ᢙ PSF ߪ⋧߹ߢࠎߛⶄ⚛ᝄ ߢߪߥߊ㧘ߘߩ⛘ኻ୯ߩ⥄ਸ਼ߣߒߡߩᒝᐲಽᏓ㧘ߔ ߥࠊߜ㔚ሶߩ㔚ᵹኒᐲಽᏓࠍਈ߃ࠆ߽ߩߢߔ㧚ࠃߞߡ PSF ߪታᢙ㑐ᢙߢ㧘ߒ߆߽ߟߨߦᱜߢߔ㧚ߎߩ㑐ᢙ ߪࡦ࠭ߩᏅߛߌߢߪߥߊ㧘⹜ᢱߢߩขࠅㄟߺ ⷺ߿㧘ࡦ࠭ߩ࠺ࡈࠜࠞࠬ୯ߦ߽ଐሽߒ߹ߔ㧚PSF ߇ߘࠇࠄߩ᧦ઙߦࠃߞߡቯߐࠇࠆ᭽ሶߪᰴ▵h12.5 ߢ⼏⺰ߒ߹ߔ߇㧘ߘࠇ߹ߢߪ㧘PSF ߇ਈ߃ࠄࠇߚ߽ ߩߣߒߡ⠨߃߹ߔ㧚 ߐ ߡ 㧘 ࠍ ⸘ ▚ ߔ ࠆ ߦ ߪ 㧘⹜ ᢱ 㕙 ߩ ฦ ὐ ࠍ PSF(ro) ߩࠃ߁ߦࡏࠤߐߖࠇ߫ࠊߌߢߔ㧚ߚߛ ߒ㧘PSF(ro) ߪߊ߹ߢゲὐߩࡏࠤࠍਈ߃ࠆ߽ߩ ߢࠅ㧘߽ߒࡦ࠭߇ゲᄖᏅࠍ߽ߡ߫㧘ࡏࠤߪశゲ ߆ࠄ㔌ࠇࠆ߶ߤᄢ߈ߊߥߞߡ߈߹ߔ㧚ߒ߆ߒ㧘‛㕙 ߢߩⷞ㊁߇චಽ⁜ߌࠇ߫㧘ߔߥࠊߜశቇ♽ోߣߒ ߡߩ₸߇චಽᄢ߈ߌࠇ߫㧘ߘߩᄌൻߪήⷞߢ߈߹ ߔ㧚ᧄ┨ߦ߅ߌࠆਥ㗴ߪኻ‛ࡦ࠭ߥߩߢ㧘߇ᦨ⚳ ⊛ߦⶄᢙߩࡦ࠭ߢᄢߐࠇࠆ႐วࠍᗐቯߒߡ㧘ゲ ᄖᏅߩነਈߪήⷞߒ߹ߔ㧚 ゲᄖᏅ߇ߥߌࠇ߫㧘ゲᄖὐߩࡏࠤߪ㧘PSF(ro) ࠍ නߦᐔⴕ⒖േߔࠆߛߌߢᷣߺ߹ߔ㧚ߎߩ႐วߪ㧘㕙 ߢߩᒝᐲಽᏓ Ii(ri) ߪ㧘‛㕙ߢߩᒝᐲಽᏓ Io(ro) ߣ PSF(ro) ߣߩࠦࡦࡏࡘ࡚ࠪࡦߣߒߡਈ߃ࠄࠇ߹ ߔ㧚ߔߥࠊߜᰴᑼߢߔ㧚 Ii(ri) = PSF(ri− ro)Io(ro)dro (8) PSF(ro) ߐ߃ਈ߃ࠄࠇࠇ߫㧘ᑼࠍߞߡ㧘છᗧߩ ⹜ᢱߦኻߔࠆ߇⸘▚ߢ߈߹ߔ㧚ࠗࡦࠦࡅࡦ࠻శFig.4: Imaging of a series of white rectangular bars (stripes) by a lens. The image is blurred by the limit of spatial resolution of the lens.
Ḯߦኻߒߡߩᒻᚑߪ㧘ߎߩᑼߢዧߊߐࠇߡ߹ߔ㧚 ࠦࡦࡏࡘ࡚ࠪࡦߣ߁ᠲߪ㧘‛ℂ߿Ꮏቇߩߐ ߹ߑ߹ߥಽ㊁ߢࠇ߹ߔ㧚ታߦⴕࠊࠇࠆ‛ℂ⊛ߥ᷹ ቯߪ㧘ߘࠇ߇ߤࠎߥ߽ߩߢࠇ㧘᷹ቯⵝ⟎ߩಽ⸃⢻ ߦࠃߞߡ⚂ࠍฃߌ߹ߔ㧚ߘߩ⚂ࠍౕ⊛ߦߔ ࠆߩ߇ࠦࡦࡏࡘ࡚ࠪࡦߢߔ㧚ࠆߪ㧘Ⓧᭂ⊛ߦ ޟᐔṖൻޠࠍᗧߔࠆ႐ว߽ࠅ߹ߔ㧚 ৻⥸ߦ㧘ࠦࡦࡏࡘ࡚ࠪࡦߣߒߡߐࠇࠆ⽎ߩ ᧄ⾰ߪ㧘ޟฦὐ߇หߓࡏࠤᣇࠍߔࠆޠߣ߁ߎߣߣ㧘ߘ ࠇࠄߩࡏࠤ߇⿷ߒ▚ߣߒߡ㊀ߨวࠊߐࠇࠆߣ߁ߎ ߣߢߔ㧚శቇ♽ߩ႐วߦ㧘ฦὐ߇หߓࠃ߁ߦࡏࠤࠆߩ ߪ㧘ゲᄖᏅࠍήⷞߒߚ⚿ᨐߢߔ㧚߽߁৻ߟߩ㊀ߨว ࠊߖߦ㑐ߒߡߪ㧘శቇ♽ߢߪᒰߚࠅ೨ߩࠃ߁ߦᕁ߃ ߹ߔ߇㧘ߒ߆ߒߘ߁ߢߪࠅ߹ߖࠎ㧚߇ᒝᐲߩ㊀ ߨวࠊߖߦߥࠆߩߪ㧘⹜ᢱ㕙߇ࠗࡦࠦࡅࡦ࠻ߢ ⋧ߩ⋧㑐ߩߥ႐วߛߌߢߔ㧚߽ߒ㕙ߦ߅ߡ㧘 ᵄߣߒߡߩ㊀ߨวࠊߖ㧔ߔߥࠊߜⶄ⚛ᝄߩ㊀ߨวࠊ ߖ㧕߇߈ࠇ߫㧘ᐓᷤߦࠃߞߡᒝวߞߚࠅᒙวߞ ߚࠅߔࠆߪߕߢߔ㧚ߘߩࠃ߁ߥലᨐߪ㧘ᒝᐲߩ⿷ߒว ࠊߖߢࠆ (8) ߦߪ߹ࠇߡ߹ߖࠎ㧚‛ߣߩᒝ ᐲಽᏓߩ㑐ଥߪ㧘ࠗࡦࠦࡅࡦ࠻ߩ႐วߛߌࠦࡦ ࡏࡘ࡚ࠪࡦߣߥࠅ㧘ࠦࡅࡦ࠻ߩ႐วߪߘ߁ߥ ࠅ߹ߖࠎ㧚ߎߩታߪ㧘శቇ♽ߣ߁߽ߩࠍℂ⸃ߔࠆ ߢ㕖Ᏹߦ㊀ⷐߢߔ㧚 ߐߡ (8) ߦ߅ߡ㧘Io(ro) ߣ Ii(ri) ߩ㑐ଥ߇ᱜߒ ߊਈ߃ࠄࠇࠆߚߦߪ㧘PSF(ro) ߦኻߒߡߥࠎࠄ߆ ߩⷙᩰൻ߇ᔅⷐߩߪߕߢߔ㧚(8) ߦ߅ߡ㧘ὐశḮࠍ Io(ro) = δ(ro) ߣߒߡਈ߃ࠆߣ㧘Ii(ri) = PSF(ri) ߇ ᓧࠄࠇ߹ߔ㧚࠺࡞࠲㑐ᢙ δ(ro) ࠍ‛㕙ߢⓍಽߔࠇ߫ 1 ߢߔ㧚ࠃߞߡ㧘PSF(ri) ߩቯߩߚߦᗐቯߐࠇࠆ ὐశḮߪ㧘㕙ߩඨⓨ㑆ߦߐࠇࠆో㔚ᵹ୯߇ 1 㧔නߪછᗧ㧕ߢࠆࠃ߁ߥ߽ߩߢߔ㧚 ߎ ߩ ⚂ ᧤ ߩ ߽ ߣ ߢ PSF(ri) ߇ ቯ ߐ ࠇ ࠇ ߫ 㧘 PSF(ri) ࠍ㕙ߢⓍಽߒߚ୯ߪߪߞ߈ࠅߒߚᗧ ࠍ߽ߜ߹ߔ㧚ߔߥࠊߜ㧘㔚ᵹ߇ 1 ߩὐశḮߦኻߔࠆ ߩో㔚ᵹ୯㧔㕙ߦࠬࠢࡦࠍ⟎ߚߣ߈ߩๆ 㔚ᵹ୯㧕ߢߔ㧚߽ߒߎߩ୯߇ 1 ࠃࠅዊߐߌࠇ߫㧘ߘࠇ ߪ㔚ᵹ߇ߤߎ߆ߢᄬࠊࠇߚߎߣࠍᗧߒ߹ߔ㧚㧔ᄙߊ ߩ႐ว㧘࿁᛬⛉ࠅߦࠃߞߡ㐿߈ⷺ߇㒢ߐࠇࠆߎߣߦ ࠃࠆ߽ߩߢߔ㧚㧕ߘߎߢ㧘PSF(ri) ߩⓍಽ୯ߪ㧘‛㕙 ߆ࠄ㕙߳ߩ㔚ᵹߩ㆐Ყ₸ࠍਈ߃ࠆߎߣߦߥࠅ߹ ߔ㧚ߎࠇߪὐశḮߩ႐วߛߌߢߪߥߊ㧘ࠃࠅ৻⥸ߩ⚿ ߦ߅ߡ߽ߘ߁ߢߔ㧚㧔(8) ߆ࠄ␜ߐࠇ߹ߔ㧚㧕
12.4.2 ಽ⸃⢻ߣࠦࡦ࠻ࠬ࠻ ೨㗄ߩ Fig.4 ߩࠃ߁ߥࠬ࠻ࠗࡊ⁁ߩࡄ࠲ࡦߩ⚿ ࠍ߽߁ዋߒߒߊ⠨߃߹ߒࠂ߁㧚శቇࡦ࠭㧘ߚߣ ߃߫ࠞࡔࡦ࠭ߢߪ㧘ⓨ㑆ಽ⸃⢻ߩ᷹ቯߩߚߦߎ ߩࠃ߁ߥ⸃࠴ࡖ࠻߇↪ࠄࠇ߹ߔ㧚ࠬ࠻ࠗࡊߩ ࡇ࠶࠴㧔ᦼ㧕ࠍ⚦߆ߊߒߡߞߚߣ߈ߦ㧘ߚߣ߃߫ 1000 ᧄ/mm ߹ߢ❋ᮨ᭽߇⸃น⢻ߢࠆߣߞߚ⹏ ଔ߇ⴕࠊࠇ߹ߔ㧚㧔శߩಽ㊁ߢߪޟⓨ㑆ಽ⸃⢻ޠࠃࠅ ߽ޟ⸃ᐲޠߣ߁↪⺆߇৻⥸⊛ߢߔ㧚㧕 Fig.5 ߪ㧘PSF ࠍ࿕ቯߒߚߢ㧘ࡄ࠲ࡦߩࡇ࠶࠴ ࠍᓢޘߦ⚦߆ߊߒߡߞߚߣ߈ߩࠗࡦࡊࡠࡈࠔࠗ ࡞ߢߔ㧚࿑ߩ (a) ߪ㧘PSF ߩࡏࠤߦᲧߴߡࠬ࠻ࠗ ࡊߩࡇ࠶࠴߇චಽᄢ߈႐วߢߔ㧚ߎߩ႐วߪᒰὼߥ ߇ࠄ㧘⹜ᢱߩࡊࡠࡈࠔࠗ࡞ࠍࠃߊౣߒߚ߇ᓧ ࠄࠇ߹ߔ㧚ࠬ࠻ࠗࡊߩࡇ࠶࠴ࠍ⚦߆ߊߒߡߊߣ࿑ ߩ (b)㧘(c) ߩࠃ߁ߦᄌൻߒߡ߈߹ߔ㧚ฦὐߩࡏࠤ PSF ߇৻ቯߢࠇ߫㧘ࡇ࠶࠴߇⚦߆ߊߥࠆ߶ߤߩ ᔘታᐲ߇ഠൻߔࠆߩߪᒰὼߢߔ㧚ฦࡄ࠲ࡦߩࡏࠤ߇ ߔߘࠍᒁߡㄭ㓞ߩࡄ࠲ࡦߦ㘩ㄟߎߣߢ㧘ᒝ ᐲಽᏓ߇ߥࠄߐࠇߡ߈߹ߔ㧚
Fig.5: Contrast σ = b/a of the image diminishes as the width of the stripes on the object plane is made smaller.
Fig.5 ߦ߅ߌࠆࠗࡦࡊࡠࡈࠔࠗ࡞ߩᄌൻࠍ㧘߽߁ ዋߒߒߊߡߺ߹ߒࠂ߁㧚⹜ᢱ㕙ߢߩࠬ࠻ࠗࡊߩ ࡄ࠲ࡦߪ㧘ᄢ㔀ᛠߦࠇ߫ᱜᒏ⊛ߥᒝᐲᄌൻࠍᜬߞ ߡ߹ߔ㧚ߘࠇ߇⚿ߐࠇߡߚߣ߃߫࿑ (c) ߣߥߞߡ ߽㧘ᱜᒏ⊛ߥᒝᐲᄌൻߪߘߩ߹߹ᱷߐࠇߡࠆߎߣ ߦᵈ⋡ߒ߹ߒࠂ߁㧚ߟ߹ࠅ㧘ᒝᐲᄌൻߩᦼߪਇᄌߢ ߔ㧚߇ᄌࠊߞߚ߆ߣ߃߫㧘ߘࠇߪᒝᐲᄌൻߩᝄ ߢߔ㧚ߔߥࠊߜᱜᒏ⊛ߥ‛ߪ㧘⚿ߦࠃߞߡࡏࠤࠆ ߣ߁ࠃࠅ߽㧘ᝄ߇ᷫߔࠆߣ߁ᣇࠍߔߴ߈ ߢߔ㧚 ߦ߅ߌࠆᒝᐲᄌൻߩᝄߪ㧘ࠦࡦ࠻ࠬ࠻ (con-trast) ߣ߫ࠇ߹ߔ㧚ࠆߪᄌ⺞ (modulation) ߣ ߁ߎߣ߽ࠅ߹ߔ㧚Fig.5 ߩߢߪ㧘࿑ߦ␜ߐࠇߡ ࠆᒝᐲಽᏓߩᐔဋ୯ b ߣᄌൻߩᝄ a ߩᲧ߇㧘ࠦ ࡦ࠻ࠬ࠻ߣߒߡቯ⟵ߐࠇ߹ߔ㧚ߔߥࠊߜ㧘ࠦࡦ࠻ ࠬ࠻ σ ߇ᰴᑼߢਈ߃ࠄࠇ߹ߔ㧚 σ = a b (9) ࠦࡦ࠻ࠬ࠻ߩขࠅ߁ࠆ୯ߪ 0 ߆ࠄ 1 ߹ߢߢࠅ㧘࿑ (a) ߇ᦨᄢ୯㧝ࠍߣࠆ႐วߢߔ㧚ߥ߅ (9) ߩቯ⟵ߪ㧘 ߛߌߢߪߥߊ㧘⹜ᢱ㕙ߦ߅ߚࡄ࠲ࡦߦኻߒߡ߽ㆡ ↪ߐࠇ߹ߔ㧚ߩ႐วߪ㧘⹜ᢱ㕙ߩࡄ࠲ࡦߩࠦࡦ࠻ ࠬ࠻ߪ߽ߣ߽ߣ 1 ߢࠅ㧘ߘࠇ߇⚿ߐࠇࠆߎߣ ߢ σ ߦᄌൻߒߚߣ߁ࠊߌߢߔ㧚 ߥ߅㧘ᢥ₂ߦ߅ߌࠆࠦࡦ࠻ࠬ࠻ߩᑼߪ㧘σ = (Imax− Imin)/(Imax + Imin) ߩᒻ߇ᄙࠃ߁ߢߔ㧚 ߎߎߢ㧘Imaxߣ IminߪߘࠇߙࠇᒝᐲಽᏓߩᦨᄢ୯ߣ ᦨዊ୯ߢߔ㧚ߩ႐วߪ a = (Imax− Imin)/2㧘b = (Imax+ Imin)/2 ߣߥࠅ㧘ࠃߞߡ (9) ߩቯ⟵ߣ৻⥌ߒ ߹ߔ㧚 (9) ߦ߅ߌࠆ b ߪ㧘㔚᳇࿁〝ߩ↪⺆ࠍ↪ߡ㧘⋥ᵹ ᚑಽࠆߪ DC ᚑಽߣ߫ࠇࠆߎߣ߇ࠅ߹ߔ㧚 ࠆߪ㧘⢛᥊㧘ࡃ࠶ࠢࠣ࠙ࡦ࠼㧘ࡌࠬߣ߁ߎߣ ߽ࠅ߹ߔ㧚ߚߣ߃߫శቇ㗼ᓸ㏜߿ TEM ߩⷞ㊁ ߩࠃ߁ߦ㧘৻᭽ߥࠆ⢛᥊ߦኻߒߡߩᥧߢ߇ᒻ ᚑߐࠇߡࠆ႐วߪ㧘b ࠍ⢛᥊ߣ߱ߩ߇⥄ὼߢߔ㧚 ߒ߆ߒ㧘৻⥸ߦߪ b ߪනߦᐔဋ୯ߢߞߡ㧘⢛᥊ߣ ߁࠾ࡘࠕࡦࠬߣߪ⇣ߥࠅ߹ߔ㧚ߘߎߢએਅߢߪ㧘b ࠍ ࡌࠬ୯ߣ߱ߎߣߦߒ߹ߔ㧚ᒝᐲಽᏓߪߟߨߦᱜߢ ࠅ㧘ߘߩߚߦߪ b≥ a ߢߥߌࠇ߫ߥࠅ߹ߖࠎ㧚 ࠦࡦ࠻ࠬ࠻ߣ߁↪⺆ߪ㧘ᄢ߹߆ߦߪޟ↹ߩ ᥧߩᏅޠߣ߁ᗧวߢ↪ࠄࠇ߹ߔ㧚ߚߣ߃߫㧘 (9) ߩ σ ߇ߊࠄᄢ߈ߊߡ߽㧘↹␜ⵝ⟎ߩ࠳ࠗ࠽ ࡒ࠶ࠢࡦࠫߩ৻ㇱߒ߆↪ߒߡߥߌࠇ߫㧘ᥧߩ Ꮕߩߥ৻᭽ߦᥧߦߒ߆߃߹ߖࠎ㧚ߘߩࠃ߁ ߥߦኻߒߡ㧘ޟࠦࡦ࠻ࠬ࠻߇ૐޠߣ߁ᣇ
ࠍㅢᏱߒ߹ߔ㧚ߒ߆ߒߎߎߢߪ㧘␜ᣇᴺߦଐሽߔࠆ ㊂ߪ⠨߃ߕߦ㧘ߣߒߡߩ⚐☴ߥࠦࡦ࠻ࠬ࠻ࠍਈ ߃ࠆ (9) ࠍቯ⟵ߣߒߡ↪߹ߔ㧚శቇ♽ߩ⹏ଔߩߚ ߦߪ㧘ߎߩ┙႐߇ㆡߒߡ߹ߔ㧚 ߐߡ㧘ᧄ㗄ߢᦨೋߦㅀߴߚశቇ♽ߩಽ⸃⢻ߪߤ߁ ߥߞߚߩߢߒࠂ߁߆㧫 ࠬ࠻ࠗࡊ⁁ߩࡄ࠲ࡦߩࡏ ࠤࠍ⠨߃ࠆߪߕ߇㧘ታ㓙ߦߪࠬ࠻ࠗࡊߪࡏࠤࠆߩߢ ߪߥߊ㧘ࠦࡦ࠻ࠬ࠻߇ഠൻߔࠆߎߣ߇ࠊ߆ߞߚࠊߌ ߢߔ㧚ಽ⸃⢻ߩቯ⟵ߩ৻ߟߩน⢻ᕈߣߒߡ㧘ޟ⼂น ⢻ߥࠦࡦ࠻ࠬ࠻߇ᓧࠄࠇࠆࠃ߁ߥࡇ࠶࠴ߩᦨዊ୯ޠ ߣ߁ቯ⟵߇ߒ߫ߒ߫↪ࠄࠇ߹ߔ㧚⼂น⢻ߥࠦࡦ ࠻ࠬ࠻ߣߪ৻ߊࠄߥߩ߆ߪ⼏⺰ߩ߇ࠅ ߹ߔ߇㧘ߚߣ߃߫ߘࠇࠍ σ = 0.05 = 5% ߣߒߡ㧘 ߊࠄߩࡇ࠶࠴߹ߢߎߩࠦࡦ࠻ࠬ࠻߇ᜬߐࠇࠆ߆ࠍ ⺞ߴ߹ߔ㧚శቇࡦ࠭ߦኻߒߡߪ㧘ߘߩࠃ߁ߥᬌᩏߦ ࠃߞߡ㧘㧝 mm ߚࠅᧄ߹ߢ⸃น⢻ߣ߁ࠃ߁ ߥ⹏ଔ߇ⴕࠊࠇ߹ߔ㧚㧔ࠦࡦ࠻ࠬ࠻ߣ߁㊂ࠍߒ ߡಽ⸃⢻߇ቯ⟵ߐࠇߡࠆߎߣߦᵈ⋡ߒ߹ߒࠂ߁㧚㧕
Fig.6: The quality of an image is affected by the trans-fer ratio of the Fourier components of an object. Image (a) containes higher-order harmonics correctly as com-pared with image (b). On the other hand, image (c) is superior to image (a) with regard to the contrast of the fundamental frequency. ߦㅀߴߚಽ⸃⢻ߩቯ⟵ߪᅷᒰߥ߽ߩߢߔ߇㧘ߒ߆ ߒ㧘ߎߩ㊂ߛߌߢ♽ߩ⦟ߒᖡߒࠍ್ቯߔࠆߎߣߪߢ߈ ߹ߖࠎ㧚ߣߒߡ㧘Fig.6 ߩ (a) ߣ (b) ࠍᲧߴߡߺ߹ ߒࠂ߁㧚ߎࠇࠄߪࠦࡦ࠻ࠬ࠻ߩ୯ߣߒߡߪห⒟ᐲߢ ߔ߇㧘ߒ߆ߒ⾰߇หߓߣ߁ࠊߌߦߪ߈߹ߖࠎ㧚 ࿑ߩ (a) ߩᣇ߇㧘(b) ࠃࠅ߽ࠬ࠻ࠗࡊߩᒝᐲಽᏓࠍ ᔘታߦᤋߒߡߡ㧘ࠛ࠶ࠫߩ┙ߜ߇ࠅ߇ࠃߊౣ ߐࠇߡ߹ߔ㧚ࠃߞߡ㧘࿑ (a) ߩᣇߦ⦟ಽ⸃⢻ࠍ ਈ߃ࠆߴ߈ߢߒࠂ߁㧚ࠆߪ㧘࿑ (c) ߩࠃ߁ߥߢ ߪߤ߁ߢߒࠂ߁߆㧚ߎߩߪ㧘࿑ (a) ࠃࠅ߽ࠦࡦ࠻ ࠬ࠻ߩ㕙ߢߪఝࠇߡ߹ߔ߇㧘ߒ߆ߒࠬ࠻ࠗࡊᒻ ⁁ߩᔘታᐲߣߒߡߪഠߞߡ߹ߔ㧚ߘߎߢ㧘࿑ (a) ߣ (c) ߩߤߜࠄ߇ࠃߢࠆ߆ߪ㧘৻ߦߪ߃ߥ ߢߒࠂ߁㧚 ߎࠇࠄߩߪ㧘ࠬ࠻ࠗࡊߩࡇ࠶࠴ߣࠦࡦ࠻ࠬ࠻ ߩ㑐ଥߛߌߢߪశቇ♽ࠍᱜ╬ߦ⹏ଔߢ߈ߥߎߣࠍ ␜ߒߡ߹ߔ㧚ࠬ࠻ࠗࡊߩࡄ࠲ࡦࠍࡈࠛዷ㐿 ߒߡ⠨߃ࠆߥࠄ㧘ၮᧄᵄᢙߣ㧘ߘߩᢛᢙߣߥࠆ 㜞⺞ᵄᚑಽࠍࠎߢ߹ߔ㧚ߘߎߢ㧘Fig.6 ߩ (a) ߣ (b) ߩ㆑ߪ㧘㜞⺞ᵄᚑಽߩౣߩᐲวߦࠃߞߡ⺑ ߐࠇࠆߴ߈߽ߩߢߒࠂ߁㧚 ߎߩ⼏⺰ߦࠃߞߡ␜ໂߐࠇࠆߎߣߪ㧘ࠦࡦ࠻ࠬ࠻ ߣ߁㊂ߪ㧘ࠬ࠻ࠗࡊ⁁ߩࡄ࠲ࡦߣߦኻߒߡ ਈ߃ࠆߩߢߪߥߊ㧘ᱜᒏ⊛ߥᒝᐲಽᏓߩᦼߏߣߦਈ ߃ࠆߴ߈ߢࠆߣ߁ߎߣߢߔ㧚ߔߥࠊߜ㧘ࡄ࠲ࡦ ߩᒝᐲಽᏓࠍࡈࠛᚑಽߦಽ⸃ߒߡ㧘ߘߩᚑಽߏ ߣߦ㧘‛㕙߆ࠄ㕙߳ߩࠦࡦ࠻ࠬ࠻ߩવ㆐ࠍ⠨߃ ࠆߴ߈ߢߔ㧚ߚߣ߃߫㧘ࠆࡈࠛᚑಽߩࠦࡦ࠻ ࠬ࠻߇‛㕙ߢ 1 ߢࠆߣ߈㧘㕙ߢߩࠦࡦ࠻ࠬ࠻ ߇ߊࠄߦߥࠆ߆ࠍ⺞ߴࠆߎߣ߇ߢ߈ࠆߢߒࠂ߁㧚ߎ ߩᠲࠍߔߴߡߩࡈࠛᚑಽߦኻߒߡⴕ߃߫㧘ߘ ߩ⚿ᨐߪశቇ♽ࠍ․ᓽߠߌࠆ߽ߩߣߥࠆߪߕߢߔ㧚 ߎߩࠃ߁ߦ㧘ࠦࡦ࠻ࠬ࠻ߩવ㆐ࠍࡈࠛᚑಽ ߏߣߦᛒ߁ߎߣߪ㧘శቇ♽ߩⓨ㑆ᵄᢙᔕ╵ࠍ⠨߃ ࠆߎߣߦઁߥࠅ߹ߖࠎ㧚ᵄᢙ․ᕈࠍਈ߃ࠆߎߣߢ㧘 శቇ♽ߩᕈ⢻߇ቢోߦ⸥ㅀߐࠇ߹ߔ㧚ߎࠇߪ㧘ಽ⸃⢻ ߣ߁৻ߟߩᢙ୯ߢశቇ♽ࠍ⹏ଔߒࠃ߁ߣߔࠆᓥ᧪ ߩ┙႐ߦઍࠊࠈ߁ߣߔࠆ߽ߩߢߔ㧚ᰴ㗄ߦ߅ߡ㧘ⓨ 㑆ᵄᢙᔕ╵ߦ㑐ߔࠆቯᑼൻࠍⴕ㧘ಽ⸃⢻ߩቯ⟵ ߦ㑐ߒߡߪh12.5.3 ߢ⼏⺰ߒ߹ߔ㧚 12.4.3 ⓨ㑆ᵄᢙ․ᕈ శቇ♽ߩⓨ㑆ᵄᢙᔕ╵ߪ㧘㖸㗀ⵝ⟎߿㔚᳇࿁〝 ߩᤨ㑆⊛ߥᔕ╵ߣኻᔕߠߌߡ⺑߇ߥߐࠇࠆߎߣ߇ ࠅ߹ߔ㧚ᵄᢙᔕ╵ߦࠃߞߡ․ᓽߠߌࠄࠇࠆ♽ߪ㧘
ߘߩޟᵄᢙޠ߇ⓨ㑆⊛ߥ߽ߩߢࠇᤨ㑆⊛ߥ߽ߩ ߢࠇ㧘৻⥸ߦ✢ᒻᔕ╵ᕈߣ߫ࠇࠆᕈ⾰ࠍ߽ߞߡ ߹ߔ㧚 ߚߣ߃߫㧘ࠝ࠺ࠖࠝࠕࡦࡊࠍ⠨߃ߡߺ߹ߒࠂ߁㧚 ࠕࡦࡊߩᓎഀߪ㧘ജߐࠇߚ㖸㗀ߩାภࠍ߆ߦ Ⴧߔࠆߎߣߢࠅ㧘ജᵄᒻࠍߥࠆߴߊߞߚ߹߹ ߢജߐߖࠆߎߣ߇ⷐ᳞ߐࠇ߹ߔ㧚ᱜᒏᵄߩജߦኻ ߒߡ㧘ജ߇߭ߕࠎߛᵄᒻߦߥߞߡࠇ߫㧘ߘࠇߪ ജߦ߹ࠇߥ߆ߞߚᵄᢙᚑಽ߇ജߢ↢ߓߚߣ ߁ߎߣߢߔ㧚ߘߩࠃ߁ߥࠕࡦࡊߢߪ㧘ේ㖸ߩ㖸⾰ࠍౣ ߢ߈߹ߖࠎ㧚㧔ߎߩࠃ߁ߥᔘታᕈࠍᤄߪޟࡂࠗࡈࠔ ࠗޠߣߞߡ߹ߒߚ߇㧘ᦨㄭߪߘࠇ߇ߚࠅ߹߃ߦ ߥߞߡߒ߹ߞߚߖ߆㧘߹ࠅ⡞߈߹ߖࠎ㧚㧕 ജߣหߓᵄᢙߛߌ߇ജߦࠇࠆߩߪ㧘৻⥸ߦ ✢ᒻᔕ╵♽ (linear response system) ߣ߫ࠇࠆ߽ߩ ߩᕈ⾰ߢߔ㧚㧔Ꮏቇߩಽ㊁ߢߪޟ✢ᒻࠪࠬ࠹ࡓޠߣ ߁ߎߣ߇ᄙࠃ߁ߢߔ㧚㧕ߎࠇߪ㧘♽ࠍࡉ࠶ࠢࡏ࠶ ࠢࠬߣߒߡᝒ߃ߚߣ߈㧘߽ߞߣ߽ߔߥ߅ߥᔕ╵ࠍ␜ߔ ࠃ߁ߥ߽ߩߢߔ㧚ାภߩવ㆐ࠆߪಣℂߩߚߩᄙ ߊߩ♽߇㧘ㆡᒰߥㄭૃߩ߽ߣߢ✢ᒻᔕ╵♽ߣߒߡᝄ ⥰߹ߔ㧚✢ᒻᔕ╵♽ߢߪ㧘ജߣหߓᵄᢙᚑಽߒ ߆ജߦࠇߥߩߢ㧘ᵄᢙߏߣߦᝄߣ⋧ߩ ᄌൻߩߒ߆ߚࠍ⺞ߴࠇ߫㧘ߘࠇߢ♽ߩᕈ⾰߇߹ࠅ ߹ߔ㧚ߎࠇ߇ࠊࠁࠆᵄᢙ․ᕈߢߔ㧚 ✢ᒻᔕ╵♽ߪ㧘৻⥸ߦᰴߩࠃ߁ߦቯ⟵ߐࠇ߹ߔ㧚 ജ f1(t)㧘f2(t) ߦኻߒߡߩജ߇ߘࠇߙࠇ g1(t)㧘g2(t) ߢࠆߣ߈㧘ജ f1(t) + f2(t) ߦኻߒߡߩജ߇ g1(t) + g2(t) ߣߥࠆࠃ߁ߥ♽ߢߔ㧚߆߃ࠇ߫㧘㊀ ߨวࠊߖߩේℂ߇ᚑࠅ┙ߟࠃ߁ߥ♽ߢߔ㧚 ✢ᒻᔕ╵♽ߩ߁ߜ㧘ᔕ╵ߩᣇ߇ᄌᢙ t ߦࠃࠄߥ ߣ߈㧘ផ⒖ਇᄌ (shift invariant) ߢࠆߣࠊࠇ߹ ߔ㧚ߣߊߦ t ߇ᤨ㑆ߩ႐วߪ㧘ޟᤨਇᄌᕈޠߢߔ㧚ߎߩ ⷐ᳞ࠍߺߚߔ✢ᒻᔕ╵♽ߦ߅ߡߪ㧘ജ f (t) ߣ ജ g(t) ߩ㑐ଥߪ㧘ࠦࡦࡏࡘ࡚ࠪࡦߣߒߡᰴᑼߩ ߆ߚߜߢਈ߃ࠄࠇ߹ߔ㧚 g(t) = h(t− t)f (t)dt (10) ᑼߦ߅ߌࠆ㑐ᢙ h(t) ߪ㧘♽ߩࠗࡦࡄ࡞ࠬᔕ╵ߣ ߒߡߩᗧࠍ߽ߜ߹ߔ㧚ߔߥࠊߜ㧘࠺࡞࠲㑐ᢙ δ(t) ߇ ജߐࠇߚߣ߈ߩᔕ╵߇ h(t) ߢߔ㧚છᗧߩ㑐ᢙߪ࠺ ࡞࠲㑐ᢙࠍ⿷ߒวࠊߖߡ᭴ᚑߢ߈ࠆߩߢ㧘࠺࡞࠲㑐ᢙ ߦኻߒߡߩᔕ╵߇ࠊ߆ࠇ߫㧘છᗧߩജߦኻߒߡߩᔕ ╵ߪ㊀ߨวࠊߖߩේℂ߆ࠄ᳞ࠆߎߣ߇ߢ߈߹ߔ㧚ផ ⒖ਇᄌᕈߦࠃߞߡ㧘છᗧߩᤨೞߦ߅ߌࠆᔕ╵ߪ㧘h(t) ࠍᐔⴕ⒖േߔࠆߎߣߢਈ߃ࠄࠇ߹ߔ㧚ㅒߦ㧘ജߩ 㑐ଥ߇ (10) ߢਈ߃ࠇࠄࠇ߫㧘㊀ߨวࠊߖߩේℂ߇ᚑ ┙ߒ㧘߆ߟផ⒖ਇᄌᕈࠍߺߚߔߎߣߪࠄ߆ߢߔ㧚ߘ ߎߢ㧘♽߇ផ⒖ਇᄌߥ✢ᒻᔕ╵♽ߢࠆߎߣߣ㧘 ജߩ㑐ଥ߇ (10) ߢਈ߃ࠄࠇࠆߎߣߪห୯ߢߔ㧚 ߩ⼏⺰ࠍ⛯ߌࠆ೨ߦ㧘శቇ♽ߩ⸒⪲ߦᚯߒߡ߅߈ ߹ߒࠂ߁㧚శቇ♽ߦ߅ߌࠆ‛ߣߩ㑐ଥߪ㧘h12.4.1 ߩ (8)㧘ߔߥࠊߜ㧘 Ii(ri) = PSF(ri− ro)Io(ro)dro (11) ߢਈ߃ࠄࠇ߹ߒߚ㧚ߎߩᑼߢ‛ Io(ro) ࠍജ㧘 Ii(ri) ࠍജߣࠇ߫㧘(10) ߩ߆ߚߜࠍߒߡ߹ߔ㧚 ✢ᒻᔕ╵ᕈߪ㧘㕙ߦ߅ߡᒝᐲߩ㊀ߨวࠊߖ߇ⴕ ࠊࠇࠆߎߣߦኻᔕߒ߹ߔ㧚ὐశḮ PSF ߇ࠗࡦࡄ࡞ ࠬᔕ╵ߢࠅ㧘ផ⒖ਇᄌᕈߪ㧘PSF ߇శḮߩ⟎ߦ ࠃࠄߥߎߣ㧘ߟ߹ࠅゲᄖᏅࠍήⷞߔࠆߎߣߦኻ ᔕߒ߹ߔ㧚 శቇ♽ߦኻߒߡ㧘ജߣหߓᵄᢙᚑಽߛߌ߇ജ ߦࠇࠆߎߣࠍ⏕ߒߡߺ߹ߔ㧚߹ߕജ Io(ro) ࠍ ࡈࠛᚑಽߦಽ⸃ߒ߹ߔ㧚ߔߥࠊߜ㧘ᰴᑼߢቯ⟵ߐ ࠇࠆ Io(ro) ߩࡈࠛᄌ឵ࠍ⠨߃߹ߔ㧚 ˆ Io(k) = Io(ro)e−i2πk·rodr o (12) ߎߩ ˆIo(k) ߪ㧘‛߇߽ߟࡈࠛᚑಽ ei2πk·roߩᝄ ߣ⋧ࠍਈ߃߹ߔ㧚 ‛ߩ৻ߟߩࡈࠛᚑಽߦᵈ⋡ߒߡ㧘ߘߩᔕ╵ ࠍ⺞ߴߡߺ߹ߒࠂ߁㧚(11) ߦ߅ߡ Io(ro) = ei2πk·ro ߣ߅߈㧘ࠦࡦࡏࡘ࡚ࠪࡦߩኻ⒓ᕈ f∗ g = g ∗ f ࠍ↪ࠇ߫㧘 Ii(ri) = PSF(ro)Io(ri− ro)dro = ei2πk·ri PSF(ro)e−i2πk·ridr o = ei2πk·riF{PSF(r o)} (13) ߣߥࠅ߹ߔ㧚ߎߎߢF ߪࡈࠛᄌ឵ߩᠲࠍߒ ߹ߔ㧚ߎߩ⚿ᨐߪ㧘ᵄᢙk ߩᱜᒏᵄജߦኻߒߡ㧘 ജ߇หߓᵄᢙk ߩᱜᒏᵄߣߥࠆߎߣࠍ␜ߒߡ ߹ߔ㧚 ߎߩࠃ߁ߦ㧘ᱜᒏᵄߩᔕ╵߇ᱜᒏᵄߢࠆߎߣߪ㧘 ജߩ㑐ଥ߇ࠦࡦࡏࡘ࡚ࠪࡦߢਈ߃ࠄࠇࠆߣ ߁ታߛߌ߆ࠄዉ߆ࠇ߹ߔ㧚ߎࠇߪ㧘㔚᳇࿁〝ߥߤߢ ߪᒰߚࠅ೨ߩࠃ߁ߦᕁ߃߹ߔ߇㧘ߒ߆ߒశቇ♽ߢߪߘ ߁ߢߪߥߢߒࠂ߁㧚ฦὐ߇หߓࠃ߁ߦࡏࠤࠆߣ߁ ߎߣ߇ࠦࡦࡏࡘ࡚ࠪࡦߢߔ߇㧘ߘߩ⚿ᨐߣߒߡᱜ ᒏ‛ߪࡏࠤߡߩᒻߦߥࠆߩߢߪߥߊ㧘߽ᱜᒏ⊛ ߢࠆߎߣ߇⸽ߐࠇࠆࠊߌߢߔ㧚ߎࠇߪ㧘PSF ߩ
ಽᏓߦߪࠃࠄߕ㧘ߒߚ߇ߞߡࡦ࠭ߩᕈ⢻ߣߪή㑐ଥ ߢߔ㧚 ߐߡ㧘ᱜᒏᵄߩᔕ╵߇ᱜᒏᵄߢࠆߩߢ㧘ߎߩ♽ ߩᵄᢙᔕ╵․ᕈࠍ⠨߃ࠆߎߣ߇ߢ߈߹ߔ㧚ߎࠇࠍ ਈ߃ࠆ㑐ᢙߪ㧘ߔߢߦ (13) ߢࠇߡ߹ߔ㧚ߔߥࠊ ߜ (13) ߩᗧߔࠆߣߎࠈߪ㧘k ᚑಽߩജ߆ࠄജ ߳ߩવ㆐Ყ₸ ˆIi(k)/ˆIo(k) ߇㧘PSF ߩࡈࠛᄌ឵ F{PSF} ߢਈ߃ࠄࠇࠆߣ߁ߎߣߢߔ㧚ߎߩ㑐ᢙߪ
శቇવ㆐㑐ᢙ (optical transfer function : OTF) ߣ ߫ࠇ㧘㑐ᢙ⥄り߽ߒ߫ߒ߫ OTF ߣ⸥ߐࠇ߹ߔ㧚OTF ߩቯ⟵ߣᕈ⾰ࠍ৻✜ߦᦠߌ߫㧘ᰴᑼߣߥࠅ߹ߔ㧚 OTF(k) = F{PSF(ro)} = ˆ Ii(k) ˆ Io(k) (14) ߢዉߚ OTF ߪ㧘ᒻᑼ⊛ߦߪ (11) ߩਔㄝߩࡈ ࠛᄌ឵ࠍߣࠇ߫⋥ߜߦᓧࠄࠇ߹ߔ㧚೨࿁߽↪߹ ߒߚ߇㧘৻⥸ߦੑߟߩ㑐ᢙߩࠦࡦࡏࡘ࡚ࠪࡦߩ ࡈࠛᄌ឵ߪ㧘ߘߩੑߟߩ㑐ᢙߩࡈࠛᄌ឵ߩ Ⓧߣߥࠅ߹ߔ㧚ߔߥࠊߜ㧘ੑߟߩ㑐ᢙ f 㧘g ߦኻߒߡ㧘 F(f ∗ g) = ˆf· ˆg ߢߔ㧚ߎߩቯℂࠍ (11) ߦㆡ↪ߔࠆߣ ᰴᑼ߇ᓧࠄࠇ߹ߔ㧚 ˆ Ii(k) = OTF(k) ˆIo(k) (15) ߎࠇߪ㧘‛㕙߆ࠄ㕙߳ߩࡈࠛᚑಽߩવ㆐߇৻ ኻ৻ߢࠅ㧘OTF(k) ߇ᵄᢙࡈࠖ࡞࠲ߣߒߡߊߎ ߣࠍ⋥ធߦ␜ߒߡ߹ߔ㧚 OTF ߇ PSF ߩࡈࠛᄌ឵ߢਈ߃ࠄࠇࠆߎߣߪ㧘 PSF ߇ࠗࡦࡄ࡞ࠬᔕ╵ߢࠆߎߣ߆ࠄߩᏫ⚿ߢߔ㧚࠺ ࡞࠲㑐ᢙߪߔߴߡߩᵄᢙᚑಽࠍห╬ߦߩߢ㧘ߘ ߩᔕ╵ߢࠆ PSF ࠍ⺞ߴࠇ߫㧘ߤࠎߥࡈࠛᚑಽ߇ ߤࠎߥᲧ₸ߢવ߃ࠄࠇߚ߆߇ࠊ߆ࠆߣ߁ࠊߌߢߔ㧚 PSF(ro) ߪᱜߩታ㑐ᢙߢߔ߇㧘ߎࠇߪゲశḮ ߩࡏࠤࠍਈ߃ࠆߩߢ㧘ߟߨߦ㑐ᢙߢߔ㧚ߟ߹ࠅ PSF(−ro) = PSF(ro) ߢߔ㧚৻⥸ߦ㧘ታߢߩ㑐ᢙ ߩࡈࠛᄌ឵ߪ㧘ታߢߢߔ㧚ߟ߹ࠅ㧘OTF(k) ߪ ߟߢ߽ታߢߩ㑐ᢙߣߥࠅ߹ߔ㧚㧔ߒ߆ߒᱜߣߪ㒢 ࠅ߹ߖࠎ㧚㧕OTF(k) ߇ታߢࠆߎߣߪ㧘‛㕙ߢߩᱜ ᒏ‛ߩ⋧߇㕙ߢߚࠇ㧘ᮮߕࠇߒߥߎߣࠍ ᗧߒ߹ߔ㧚ߎࠇߪ PSF ߩኻ⒓ᕈࠍ⠨߃ࠇ߫ᒰὼߩ ߎߣߢߔ㧚OTF(k) ߪ㧘k ᚑಽߩᝄߩᄌൻࠍਈ߃ࠆ ߽ߩߣߥࠅ߹ߔ㧚 శ ቇ ♽ ߩ ᵄ ᢙ ․ ᕈ ߪ 㧘ߔ ߴ ߡ ߩ k ߦኻߒߡ OTF(k) = 1 ߢࠆߎߣ߇ℂᗐߢߔ㧚ߒ߆ߒߎࠇߪ㧘 PSF ߇߹ߞߚߊࡏࠤߕߦ㧘‛ߣ߇৻⥌ߔࠆߎߣ ࠍᗧߒߡ߹ߔ㧚৻⥸ߦߪ㧘ߣߊߦ㜞ᵄᚑಽߩવ ㆐߇ਇ⿷ߔࠆߎߣߢ㧘ࠪࡖࡊߐ߇ᄬࠊࠇߚߦߥࠆ ߢߒࠂ߁㧚ߘߩࠃ߁ߥᄌൻߩᣇࠍ㧘‛ߩㆬ߮ᣇߦ ଐሽߒߥ߆ߚߜߢਈ߃ࠆ߽ߩ߇ OTF ߢߔ㧚 ߐߡ㧘(14) ߇ਈ߃ࠆ OTF ߪ㧘‛㕙߆ࠄ㕙߳ߩ ࡈࠛᚑಽߩવ㆐Ყ₸ࠍਈ߃߹ߔ㧚ߒ߆ߒ㧘ࠊࠇࠊ ࠇߦ⥝߇ࠆߩߪࡈࠛᚑಽߩ୯⥄ߢߪߥߊ㧘 ߘߩࠦࡦ࠻ࠬ࠻ߢߔ㧚ߔߥࠊߜ㧘ฦࡈࠛᚑಽߩ ࠦࡦ࠻ࠬ࠻߇ߤߩࠃ߁ߦવ㆐ߐࠇࠆ߆ࠍਈ߃ࠆ㑐 ᢙ߇᰼ߒࠊߌߢߔ㧚 ࠦࡦ࠻ࠬ࠻ߩવ㆐ࠍ⠨߃ࠆߚߦ㧘৻ߟߩࡈ ࠛᚑಽߛߌࠍᜬߟ‛ࠍ⠨߃ߡ㧘⚿ߦࠃࠆࠦࡦ ࠻ࠬ࠻ߩᄌൻࠍ⺞ߴߡߺ߹ߒࠂ߁㧚ߚߛߒ㧘ࠦࡦ࠻ ࠬ࠻ࠍ⼏⺰ߔࠆߦߪࡌࠬ୯㧘ߟ߹ࠅk = 0 ߩᚑ ಽ߇หᤨߦሽߒߥߌࠇ߫ߥࠅ߹ߖࠎ㧚ߘߩࠃ߁ߥ ‛ࠍ㧘ᰴᑼߩࠃ߁ߦ߅߈߹ߔ㧚 Io(ro) = 1 + σ cos(2πk · ro) (16) ᑼߢߪࡌࠬࠍ 1 ߣߒߡࠆߩߢ㧘k ߣ߁ࡈ ࠛᚑಽߩࠦࡦ࠻ࠬ࠻߇ σ ߢߔ㧚ᱜ⏕ߦ߃߫㧘 cos(2πk · ro) = (ei2πk·ro+ e−i2πk·ro)/2 ߢࠆߎߣ ߆ࠄ㧘ߎߩ㗄ߪk ߣ −k ߩੑߟߩࡈࠛᚑಽ߆ࠄ ᚑࠆߣ߁ߴ߈ߢߔ㧚ߒ߆ߒ㧘OTF(k) ߪ㑐ᢙߥߩ ߢ㧘ߎࠇࠄੑᚑಽߪߟ߽߹ߣߡᛒ߁ߎߣ߇น⢻ ߢߔ㧚 ‛ (16) ߦኻߒߡߩߪ㧘OTF(k) ߇߽ߟᗧߛߌ ߆ࠄᰴߩࠃ߁ߦᓧࠄࠇ߹ߔ㧚߹ߕ㧘(16) ߩࡌࠬ୯ߪ k = 0 ߩᚑಽߢࠅ㧘ߎߩવ㆐Ყߪ OTF(0) ߢਈ߃ࠄ ࠇ߹ߔ㧚ߪ‛ߩࡌࠬ߇ 1 ߥߩߢ㧘㕙ߢߩࡌ ࠬ߇ OTF(0) ߣߥࠅ߹ߔ㧚ᰴߦ㧘k ߣ߁ࡈࠛᚑ ಽߩવ㆐Ყߪ OTF(k) ߥߩߢ㧘(16) ߩ cos(2πk · ro) ߩᝄ߇㕙ߢ OTF(k) ߦߥࠅ߹ߔ㧚⚿ዪ㧘‛ (16) ߩߪᰴᑼߢਈ߃ࠄࠇ߹ߔ㧚 Ii(ri)
= OTF(0) + σOTF(k) cos(2πk · ri) = OTF(0) 1 + σOTF(k) OTF(0)cos(2πk · ri) (17) (17) ߩ⚿ᨐ߆ࠄ㧘k ᚑಽߩࠦࡦ࠻ࠬ࠻ߪ㧘߽ߣߩ σ ߆ࠄ㧘ߘߩ OTF(k)/OTF(0) ߦᄌൻߒߡࠆߎ ߣ߇ࠊ߆ࠅ߹ߔ㧚ߘߎߢ㧘ࠦࡦ࠻ࠬ࠻ߩવ㆐Ყࠍਈ ߃ࠆ㑐ᢙࠍᰴߩࠃ߁ߦቯ⟵ߢ߈߹ߔ㧚 CTF(k) = OTF(k) OTF(0) (18) ߎࠇߪ㧘శቇߢߪޟⷙᩰൻߐࠇߚ OTFޠߣ߱ߎߣ ߇ᄙࠃ߁ߢߔ߇㧘ᧄⓂߢߪࠦࡦ࠻ࠬ࠻વ㆐㑐ᢙ
(contrast transfer function) ߣ߱ߎߣߦߒ߹ߒࠂ߁㧚 ᑼߦ߅ߌࠆ OTF(0) ߪ㧘PSF(ro) ߩࡈࠛᄌ឵ ߩ0 ᚑಽ㧘ߔߥࠊߜ㧘 OTF(0) = PSF(ro)dro (19) ߣߒߡਈ߃ࠄࠇ߹ߔ㧚ߎࠇߪh12.4.1 ߢㅀߴߚࠃ߁ߦ㧘 ‛㕙ߣ㕙ߩ㔚ᵹᲧ₸ࠍᗧߒ߹ߔ㧚ߎߎߢߩ⸒⪲ߢ ߃߫㧘ࡌࠬߩવ㆐Ყ₸ߢࠅ㧘ߩࠆߐࠍ ߹ߔ㧚 ߥ߅㧘㔚ሶశቇߦ߅ߡߪ㧘ࠗࡦࠦࡅࡦ࠻శ Ḯߦኻߒߡߩࠦࡦ࠻ࠬ࠻ࠍ⼏⺰ߔࠆߎߣߪ߹ࠅ ࠅ߹ߖࠎ㧚㔚ሶశቇߢࠦࡦ࠻ࠬ࠻ߩવ㆐ߣ߃ ߫㧘TEM ߩࠦࡅࡦ࠻ᾖߩ႐วࠍᜰߔߩ߇᥉ㅢ ߢߔ㧚೨࿁◲නߦㅀߴ߹ߒߚ߇㧘ࠦࡅࡦ࠻ᾖߩ ߽ߣߢߪ㧘⹜ᢱߦኻߒߡᒙ⋧‛ㄭૃ߇ᚑࠅ┙ߟ ߣ߈ߛߌ✢ᒻᔕ╵♽ߣߥࠅ㧘ࠃߞߡߘߩߣ߈ߛߌᵄ ᢙ․ᕈࠍ⠨߃ࠆߎߣ߇ߢ߈߹ߔ㧚
