Polarization correction - Revision history

KevinYager at 01:56, 23 November 2019

2019-11-23T01:56:05Z

KevinYager at 01:46, 23 November 2019

2019-11-23T01:46:05Z

KevinYager at 01:04, 23 November 2019

2019-11-23T01:04:40Z

KevinYager: /* See Also */

2019-11-23T00:39:40Z

‎See Also

KevinYager at 00:37, 23 November 2019

2019-11-23T00:37:28Z

KevinYager at 19:54, 31 October 2019

2019-10-31T19:54:41Z

KevinYager: /* See Also */

2019-10-31T19:48:55Z

‎See Also

KevinYager: Created page with "The x-rays used in scattering experiments are frequently polarized. For instance, undulators sources generate x-rays polarized along a well-defined axis associated..."

2019-10-31T19:47:52Z

Created page with "The x-rays used in scattering experiments are frequently polarized. For instance, undulators sources generate x-rays polarized along a well-defined axis associated..."

New page

The [[x-rays]] used in [[scattering]] experiments are frequently polarized. For instance, [[undulators]] sources generate x-rays polarized along a well-defined axis associated with the oscillation direction. (Some specialized undulators generate elliptically polarized light with control of the ellipticity and/or polarization direction.) The intensity of scattering is modulated by the angle between the incident x-ray polarization and the scattering direction, with the scattering probability (and thus measured scattering intensity) dropping to zero when these are aligned.

In particular, scattering occurs with an amplitude proportional to the sine of the angle between the direction of the electric vector of the incident radiation, and the direction of scattering.

==See Also==
* [http://reference.iucr.org/dictionary/Lorentz%E2%80%93polarization_correction Lorentz–polarization correction] [http://reference.iucr.org/dictionary/Main_Page IUCr Online Dictionary of Crystallography]

@@ Line 34: / Line 34: @@
 | <math>\sin^{-1} \left [ \sin 2 \theta \cos \chi \right ]</math>
 | <math>\tan^{-1} \left[ \tan 2 \theta \sin \chi \right]</math>
-| <math>1 - \cos^2 \delta \sin^2 \gamma</math>
+| <math>1 - \sin^2(2 \theta) \sin^2(\chi)</math>
 |-
 | Purely horizontal

@@ Line 32: / Line 32: @@
 | <math>\chi</math>
+|
+| <math>\sin^{-1} \left [ \sin 2 \theta \cos \chi \right ]</math>
 | <math>\tan^{-1} \left[ \tan 2 \theta \sin \chi \right]</math>
+| <math>1 - \cos^2 \delta \sin^2 \gamma</math>
 |-
 | Purely horizontal

@@ Line 6: / Line 6: @@
 </math>
-where <math>\delta</math> is the inplane angle of scattering, and <math>\gamma</math> is the out-of-plane (elevation) angle of the scattering. More generally for a source polarized to extent <math>\zeta</math> (fraction of radiation polarized in horizontal) one can compute:
+where <math>\gamma</math> is the inplane angle of scattering, and <math>\delta</math> is the out-of-plane (elevation) angle of the scattering. More generally for a source polarized to extent <math>\zeta</math> (fraction of radiation polarized in horizontal) one can compute:
 :<math>
 P_p = \zeta P_h + (1-\zeta) P_v
@@ Line 26: / Line 26: @@
 | <math>90^{\circ}</math>
 | <math>2\theta</math>
-| <math>90^{\circ}</math>
+| <math>0^{\circ}</math>
 | 1
 |-
@@ Line 33: / Line 33: @@
+|
+|
+| <math>\tan^{-1} \left[ \tan 2 \theta \sin \chi \right]</math>
+|
 |-

@@ Line 45: / Line 45: @@
 ==See Also==
-* [http://reference.iucr.org/dictionary/Lorentz%E2%80%93polarization_correction Lorentz–polarization correction] [http://reference.iucr.org/dictionary/Main_Page IUCr Online Dictionary of Crystallography]
+* [http://reference.iucr.org/dictionary/Lorentz%E2%80%93polarization_correction Lorentz–polarization correction] ([http://reference.iucr.org/dictionary/Main_Page IUCr Online Dictionary of Crystallography])
 * Z. Jiang [http://scripts.iucr.org/cgi-bin/paper?S1600576715004434 GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films] ''J. Appl. Cryst.'' '''2015''', 48, 3, 917-926. [http://dx.doi.org/10.1107/S1600576715004434 doi: 10.1107/S1600576715004434]

@@ Line 6: / Line 6: @@
 </math>
-where <math>\delta</math> is the inplane angle of scattering, and <math>\gamma</math> is the out-of-plane (elevation) angle of the scattering.
+where <math>\delta</math> is the inplane angle of scattering, and <math>\gamma</math> is the out-of-plane (elevation) angle of the scattering. More generally for a source polarized to extent <math>\zeta</math> (fraction of radiation polarized in horizontal) one can compute:
 ==See Also==
 * [http://reference.iucr.org/dictionary/Lorentz%E2%80%93polarization_correction Lorentz–polarization correction] [http://reference.iucr.org/dictionary/Main_Page IUCr Online Dictionary of Crystallography]
 * Z. Jiang [http://scripts.iucr.org/cgi-bin/paper?S1600576715004434 GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films] ''J. Appl. Cryst.'' '''2015''', 48, 3, 917-926. [http://dx.doi.org/10.1107/S1600576715004434 doi: 10.1107/S1600576715004434]

@@ Line 1: / Line 1: @@
 The [[x-rays]] used in [[scattering]] experiments are frequently polarized. For instance, [[undulators]] sources generate x-rays polarized along a well-defined axis associated with the oscillation direction. (Some specialized undulators generate elliptically polarized light with control of the ellipticity and/or polarization direction.) The intensity of scattering is modulated by the angle between the incident x-ray polarization and the scattering direction, with the scattering probability (and thus measured scattering intensity) dropping to zero when these are aligned.
-In particular, scattering occurs with an amplitude proportional to the sine of the angle between the direction of the electric vector of the incident radiation, and the direction of scattering.
+In particular, scattering occurs with an amplitude proportional to the sine of the angle between the direction of the electric vector of the incident radiation, and the direction of scattering. Assuming horizontally-polarized incident x-rays (i.e. linear polarization with the E-field horizontal), for an angle <math>\psi</math> between the polarization axis and the scattering direction, one can define a polarization correction of:
+:<math>
 ==See Also==
 * [http://reference.iucr.org/dictionary/Lorentz%E2%80%93polarization_correction Lorentz–polarization correction] [http://reference.iucr.org/dictionary/Main_Page IUCr Online Dictionary of Crystallography]
 * Z. Jiang [http://scripts.iucr.org/cgi-bin/paper?S1600576715004434 GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films] ''J. Appl. Cryst.'' '''2015''', 48, 3, 917-926. [http://dx.doi.org/10.1107/S1600576715004434 doi: 10.1107/S1600576715004434]

← Older revision		Revision as of 19:48, 31 October 2019
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	==See Also==		==See Also==
	* [http://reference.iucr.org/dictionary/Lorentz%E2%80%93polarization_correction Lorentz–polarization correction] [http://reference.iucr.org/dictionary/Main_Page IUCr Online Dictionary of Crystallography]		* [http://reference.iucr.org/dictionary/Lorentz%E2%80%93polarization_correction Lorentz–polarization correction] [http://reference.iucr.org/dictionary/Main_Page IUCr Online Dictionary of Crystallography]
		+	* Z. Jiang [http://scripts.iucr.org/cgi-bin/paper?S1600576715004434 GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films] ''J. Appl. Cryst.'' '''2015''', 48, 3, 917-926. [http://dx.doi.org/10.1107/S1600576715004434 doi: 10.1107/S1600576715004434]