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  1. ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❱✳ ❊✳ ❆s❛❞❝❤✐❦♦✈✱ ❨✉✳ ❖✳ ❱♦❧❦♦✈✱ ■✳ ❱✳ ❑♦③❤❡✈♥✐❦♦✈✱ ❇✳ ❙✳ ❘♦s❤❝❤✐♥✱ ❆✳ ▼✳ ❚✐❦❤♦♥♦✈ ∗ ❙❤✉❜♥✐❦♦✈ ■♥st✐t✉t❡ ♦❢ ❈r②st❛❧❧♦❣r❛♣❤② ❘❆❙ ∗ ❑❛♣✐t③❛ ■♥st✐t✉t❡ ❢♦r P❤②s✐❝❛❧ Pr♦❜❧❡♠s ❘❆❙ ➽❙②♥❝❤r♦tr♦♥ ❛♥❞ ❋❊▲ r❛❞✐❛t✐♦♥✿ ❣❡♥❡r❛t✐♦♥ ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s➾ ◆♦✈♦s✐❜✐rs❦✱ ✹✕✼ ❏✉❧② ✷✵✶✻ ❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶ ✴ ✷✶ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙

  2. ❈❡❧❧ ♠❡♠❜r❛♥❡ ♠♦❞❡❧ ✖ ♣❤♦s♣❤♦❧✐♣✐❞ ❜✐❧❛②❡r ❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✷ ✴ ✷✶ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙

  3. ▼♦❞❡❧ ❧✐♣✐❞s ✶✲st❡❛r♦②❧✲✷✲♦❧❡♦②❧✲s♥✲❣❧②❝❡r♦✲✸✲♣❤♦s♣❤♦❝❤♦❧✐♥❡ ✶✱✷✲❞✐st❡❛r♦②❧✲s♥✲❣❧②❝❡r♦✲✸✲♣❤♦s♣❤♦❝❤♦❧✐♥❡ ✭❙❖P❈✮ ✭❉❙P❈✮ ❚❛❜✉❧❛r ♣r♦♣❡rt✐❡s✿ T c ✱ ◦ ❈ ▲✐♣✐❞ ❋♦r♠✉❧❛ ▼♦❧✳ ✇❡✐❣❤t Γ ❈❆❙ ■♥❞❡① ❉❙P❈ ❈ ✹✹ ❍ ✽✽ ◆❖ ✽ P ✼✾✵✳✶✹✺ ✹✸✽ ✺✺ ✽✶✻✲✾✹✲✹ ❙❖P❈ ❈ ✹✹ ❍ ✽✻ ◆❖ ✽ P ✼✽✽✳✶✷✾ ✹✸✻ ✻ ✺✻✹✷✶✲✶✵✲✹ ❉✳ ▼✳ ❙♠❛❧❧✱ P❤②s✐❝❛❧ ❈❤❡♠✐str② ♦❢ ▲✐♣✐❞s✱ ◆❨✱ P❧❡♥✉♠ Pr❡ss✱ ✶✾✽✾✳ ❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✸ ✴ ✷✶ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙

  4. ❍♦✇ ❝❛♥ ♦♥❡ ♣r❡♣❛r❡ ❛ ♠❛❝r♦s❝♦♣✐❝ ❧✐♣✐❞ ♠✉❧t✐❧❛②❡r❄ ▲❛♥❣♠✉✐r✲❇❧♦❞❣❡tt t❡❝❤♥✐q✉❡ P❘❖ ✿ ✇✐❞❡❧② ✉s❡❞ ❛♥❞ r❡❧❛t✐✈❡❧② ❡❛s② t♦ ✐♠♣❧❡♠❡♥t❀ P❘❖ ✿ ❤✐❣❤❧② ❤♦♠♦❣❡♥❡♦✉s ❧✐♣✐❞ ❧❛②❡rs❀ ❈❖◆ ✿ s♦❧✐❞ s✉❜str❛t❡ ❞♦❡s ♥♦t ❝♦rr❡s♣♦♥❞ t♦ ❛❝t✉❛❧ ❝❡❧❧ ❜♦❞②✦ ❈❖◆ ✿ ❝♦♠♣r❡ss✐♦♥ ❦❡❡♣s ❧✐♣✐❞ ✜❧♠ ❤♦♠♦❤❡♥✐t② ✉♣ t♦ t❤❡ ♠♦♥♦❧❛②❡r ♦♥❧②✳ ✏❋r❡❡✑ ✜❧♠ ♦♥ ❧✐q✉✐❞ s✉❜str❛t❡ ❘❡❧❛t✐✈❡❧② ❧♦✇ ❤♦♠♦❣❡♥✐t② ♦❢ t❤❡ ❧❛②❡rs ♦♥ ❝❧❡❛♥ ✇❛t❡r s✉r❢❛❝❡✳ P♦ss✐❜✐❧✐t✐❡s t♦ ✉s❡ ❞✐✛❡r❡♥t ✇❛t❡r s♦❧✉t✐♦♥s ❛s ❛ s✉❜str❛t❡s❄ ❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✹ ✴ ✷✶ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙

  5. ❳✶✾❈ ❜❡❛♠❧✐♥❡ ❛t ◆❙▲❙✱ ❇r♦♦❦❤❛✈❡♥ Φ = ✶✵ ✶✹ ♣❤♦t♦♥s✴s✱ E = ✶✺✵✵✵ ❡❱✱ ∆ E / E ∼ ✶✵ − ✸ ✶ ✕ t❤♦r♦✐❞❛❧ ❳✲r❛② ♠✐rr♦r❀ ✷ ✕ s✐♥❣❧❡✲❝r②st❛❧ ♠♦♥♦❝❤r♦♠❛t♦r❀ ✸ ✕ ✈✐❜r♦✲❞❛♠♣✐♥❣ ♣❧❛t❢♦r♠ ❛♥❞ s❛♠♣❧❡ ❝❤❛♠❜❡r❀ ✹ ✕ ✷ θ ✲r♦t❛t✐♦♥ ♣❧❛t❢♦r♠❀ ✺ ✕ t✇♦✲s❧✐t ❝♦❧❧✐♠❛t♦r❀ ✻ ✕ β ✲r♦t❛t✐♦♥ ♣❧❛t❢♦r♠ ✇✐t❤ ❞❡t❡❝t♦r s❧✐t✳ ❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✺ ✴ ✷✶ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙

  6. ▼♦❞❡❧✲✐♥❞❡♣❡♥❞❡♥t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❡❧❡❝tr♦♥ ❞❡♥s✐t② ♣r♦✜❧❡ ❊①tr❛♣♦❧❛t✐♦♥ ♦❢ t❤❡ r❡✢❡❝t✐✈✐t② ❛s②♠♣t♦t✐❝ ❇❛s✐❝ ❛ss✉♠♣t✐♦♥s✿ ▲❡t δ ( z ) = ❘❡ ✶ − ε ( z ) ❞✐str✐❜✉t✐♦♥ ❝♦♥t❛✐♥s m s♣❡❝✐❛❧ ♣♦✐♥ts ♦❢ n ✲t❤ ♦r❞❡r✱ ✇❤❡r❡ ❢✉♥❝t✐♦♥ δ ( z ) ❛♥❞ ✐ts n − ✶ ❞❡r✐✈❛t✐✈❡s δ ′ ( z ) . . . δ ( n − ✶ ) ( z ) ❛r❡ ❝♦♥t✐♥✉♦✉s ❜✉t n ✲t❤ ❞❡r✐✈❛t✐✈❡ s✉✛❡rs ❛ st❡♣✲❧✐❦❡ ✈❛r✐❛t✐♦♥✳ ❉✐❡❧❡❝tr✐❝ ♣❡r♠✐tt✐✈✐t✐② ♦❢ ❡①t❡r♥❛❧ ♠❡❞✐✉♠ ❡q✉❛❧s t♦ ✈❛❝✉✉♠ ✭ δ ( z < z min ) ≡ ✵✮ ✇❤✐❧❡ ♣❡r♠✐tt✐✈✐t② ♦❢ s✉❜str❛t❡ ✐s ❝♦♥st❛♥t ✭ δ ( z > z max ) ≡ δ + � = ✵✮✳ ❆❧❧ ❞✐s❝♦♥t✐♥✉✐t② ♣♦✐♥ts z ✶ < z ✷ < · · · < z m ❛r❡ ♦❢ t❤❡ s❛♠❡ ♦r❞❡r✳ ❆❜s♦r♣t✐♦♥ ♦❢ t❤❡ ❳✲r❛②s ✐♥ ❛ ♠❛tt❡r ✐s ♥❡❣❧❡❝t❡❞✿ ■♠ ε ( z ) ≡ ✵✳ ❘❡✢❡❝t✐✈✐t② ❛s②♠♣t♦t✐❝ ✐♥ t❤❡ ❢r❛♠❡s ♦❢ ✜rst✲♦r❞❡r ❇♦r♥ ❛♣♣r♦①✐♠❛t✐♦♥✿ � i � ✷ + n m r ( q ) ∼ = − k ✷ � ∆ ( n ) � � � � z j ❡①♣ ✷ iqz j , ✷ q j = ✶ ≡ d n δ dz n ( z J + ✵ ) − d n δ ∆ ( n ) � � z j dz n ( z J − ✵ ) , ■✳ ❱✳ ❑♦③❤❡✈♥✐❦♦✈✱ ◆✉❝❧✳ ■♥str✉♠❡♥ts ❛♥❞ ▼❡t❤♦❞s ✐♥ P❤②s✳ ❘❡s✳ ❆ ✭✷✵✵✸✮ ✺✵✽✿✺✶✾ ❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✻ ✴ ✷✶ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙

  7. ▼♦❞❡❧✲✐♥❞❡♣❡♥❞❡♥t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❡❧❡❝tr♦♥ ❞❡♥s✐t② ♣r♦✜❧❡ ❙❡❛r❝❤✐♥❣ ❢♦r ❞✐s❝♦♥t✐♥✉✐t② ♣♦✐♥ts ❘❡❣✉❧❛r✐③❡❞ ❋♦✉r✐❡r✲❢r❛♥s❢♦r♠ ♦❢ t❤❡ r❡✢❡❝t✐✈✐t② ❝✉r✈❡ q max ✷ ✷ n + ✹ � q ✷ n + ✹ R ( q ) − C � � F ( x ) = ❝♦s ( ✷ qx ) dq k ✹ ( q max − q min ) q min q max ✶ � q ✷ n + ✹ R ( q ) dq , C = q = k s✐♥ θ q max − q min q min 10 0 8 10 −1 6 10 −2 Reflectivity 4 F(x)*10 15 10 −3 2 10 −4 0 10 −5 10 −6 −2 10 −7 −4 10 −8 −6 10 −9 −8 0 0.1 0.2 0.3 0.4 0.5 0 50 100 150 200 250 300 350 400 450 500 q z , Å -1 x ■✳ ❱✳ ❑♦③❤❡✈♥✐❦♦✈✱ ◆✉❝❧✳ ■♥str✉♠❡♥ts ❛♥❞ ▼❡t❤♦❞s ✐♥ P❤②s✳ ❘❡s✳ ❆ ✭✷✵✵✸✮ ✺✵✽✿✺✶✾ ❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✼ ✴ ✷✶ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙

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