Ray tracing - ESRF

Theory II
Physical model: Dynamical Theory of Diffraction
C 1
C 2
=
=
e iϕ – 1t o
e iϕ – 2t o
Manuel Sánchez del Río
z
=
❑ BRAGG case
(Zachariasen 1945)
(Compact, general (thin/thick, Laue/Bragg), with absorption, general expression for τ, F H )
valid for perfect flat crystals
R( θ)
❑ LAUE case R( θ)
ϕ1 2π koδ'o = ----------γ
o
ϕ2 2π koδ''o = ------------γ
o
1 – b b
-----------Ψ
2 o – --τ
2
q = bΨHΨ H
γ o
b ≈ -----γ
H
where
δ'
⎛ o⎞
=
⎝δ''o⎠ τ
1
--
b
IH = ----- =
Io 1
--
b
IH = ----- =
Io Ray tracing simulations for crystal optics (9 of 23)
1
--
b
x1x2 c ( 1 – c2) --------------------------------c2x2
– c1x1 1
--
b
x1x2 c ( 1 – c2) --------------------------------x2
– x1 1
-- ψ
2 o z q z 2
⎛ – ⎛ ± + ⎞⎞
⎝ ⎝ ⎠⎠
2
2
x
⎛ 1⎞
=
⎝x2⎠ 1
---- B
2
ko 2 H 2 ke = ( + ( o ⋅ BH ) ) τ ≈ 2( θ– θB) sin2θ
Ψ H
=
z q z 2
– ⎛ ± + ⎞
⎝ ⎠
----------------------------------ψ
H
e2 mc2 --------- 1
---
V
λ2
----- ( f
π
o + f ' + f '')
e
n 2πi H r ⎛ ( ⋅ n)
⎞
∑
K
⎝ ⎠
n ∈ unitcell
SPIE, July 22, 1998