Refraction distortion - Revision history

KevinYager: /* Refraction Correction */

2019-04-16T12:49:30Z

‎Refraction Correction

2015-11-04T19:08:34Z

‎Refraction Correction

2015-11-04T18:48:45Z

‎Refraction Correction

2015-11-04T18:41:51Z

‎Refraction Correction

2015-11-04T18:40:29Z

‎Refraction Correction

2015-11-04T18:27:37Z

‎Refraction Correction

2015-11-04T18:26:42Z

‎Refraction Correction

2015-11-04T18:24:00Z

‎Mathematics

2015-11-04T18:16:08Z

2015-11-04T18:11:10Z

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 * D. W. Breiby, O. Bunk, J. W. Andreasen, H. T. Lemke and M. M. Nielsen [http://scripts.iucr.org/cgi-bin/paper?S0021889808001064 Simulating X-ray diffraction of textured films] ''J. Appl. Cryst.'' 2008, 41, 262-271. [http://dx.doi.org/10.1107/S0021889808001064 doi: 10.1107/S0021889808001064]
 * Lu, X.; [[Yager, K.G.]]; Johnston, D.; Black, C.T.; Ocko, B.M. '''[http://scripts.iucr.org/cgi-bin/paper?S0021889812047887 Grazing-incidence transmission X-ray scattering: surface scattering in the Born approximation]''' ''Journal of Applied Crystallography'' '''2013''', 46, 165–172. [http://dx.doi.org/10.1107/S0021889812047887 doi: 10.1107/S0021889812047887]
 ==See Also==

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 \begin{alignat}{2}
 \Delta \alpha_s & = \alpha_e-\alpha_s \\
-\theta_B_f & = \alpha_i + \alpha
+\theta_{Bf} & = \alpha_i + \alpha_e \\
 \end{alignat}
 </math>

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 If <math>\scriptstyle \alpha_e>0</math>, then scattering is above the [[horizon]] ([[GISAXS]]); if <math>\scriptstyle \alpha_e<0</math>, then it is sub-horizon scattering ([[GTSAXS]]). For GISAXS, the final scattering angle is:
 :<math>
-\Delta \alpha_f = \alpha_f
+\begin{alignat}{2}
 </math>

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 :<math>
 \Delta \alpha_f = \alpha_f
-<math>
+</math>

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 ==Refraction Correction==
-When computing theoretical scattering patterns, one must account for the refraction correction. The correction is essentially an application of Snell's law, where one using the x-ray [[refractive index]] for ambient (<math>\scriptstyle n_a</math>), the thin film (<math>\scriptstyle n_f</math>), and the substrate (<math>\scriptstyle n_s</math>).
+When computing theoretical scattering patterns, one must account for the refraction correction. The correction is essentially an application of Snell's law, where one using the x-ray [[refractive index]] for ambient (<math>\scriptstyle n_a</math>), the thin film (<math>\scriptstyle n_f</math>), and the substrate (<math>\scriptstyle n_s</math>). For an incident angle of <math>\scriptstyle \alpha_i</math>, one computes a refraction of:
 * Byeongdu Lee, Insun Park, Jinhwan Yoon, Soojin Park, Jehan Kim, Kwang-Woo Kim, Taihyun Chang, and Moonhor Ree [http://pubs.acs.org/doi/abs/10.1021/ma047562d Structural Analysis of Block Copolymer Thin Films with Grazing Incidence Small-Angle X-ray Scattering] ''Macromolecules'' '''2005''', 38 (10), 4311-4323. [http://dx.doi.org/10.1021/ma047562d doi: 10.1021/ma047562d]

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 ==Mathematics==
 The GISAXS refraction distortion shifts the data along <math>\scriptstyle q_z</math>, leaving <math>\scriptstyle q_x</math> unaffected. The amount of the shift is given by:
-[[Image:Lu GTSAXS-Figure5.png|center|thumb|300px|Figure from Lu. et al. ([http://dx.doi.org/10.1107/S0021889812047887 doi: 10.1107/S0021889812047887 ''J. of Appl. Cryst.'' '''2013''', 46, 165]) showing the amount of distortion along ''q<sub>z</sub>'', for different conditions.]]
+\end{alignat}
 ==Refraction Correction==

← Older revision		Revision as of 18:11, 4 November 2015
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		+	[[Image:GISAXS refraction distortion.png\|right\|thumb\|400px\|Illustration of GISAXS refraction distortion. The reciprocal-space scattering is a hexagonal array of peaks. However, these peaks are both shifted, and compressed/stretched along ''q<sub>z</sub>'', due to refraction. This effect is especially pronounced near the [[Yoneda]] (orange line).]]
		+
	In [[GISAXS]], [[GIWAXS]], and other grazing-incidence techniques, the [[refractive index]] difference between the film and the ambient causes the incident and [[scattering\|scattered]] [[x-ray]] beams to be refracted. This extent of refraction depends on the incident and exit angles. Thus, the data that appears on an area [[detector]] in a grazing-incidence experiment is non-linearly distorted. This makes [[Tutorial:What_to_do_with_data\|data interpretation]] more problematic.		In [[GISAXS]], [[GIWAXS]], and other grazing-incidence techniques, the [[refractive index]] difference between the film and the ambient causes the incident and [[scattering\|scattered]] [[x-ray]] beams to be refracted. This extent of refraction depends on the incident and exit angles. Thus, the data that appears on an area [[detector]] in a grazing-incidence experiment is non-linearly distorted. This makes [[Tutorial:What_to_do_with_data\|data interpretation]] more problematic.