Talk:Polarization correction

Angle		Adjacent	Opposite	Hypotenuse	Sine = O/H	Cosine = A/H	Tangent = O/A
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi}	Azimuth on detector (relative to $q_{z}$ axis)	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r = \sqrt{x^2 + z^2}}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sin \chi = \frac{x}{r}}	$\cos \chi ={\frac {z}{r}}$	$\tan \chi ={\frac {x}{z}}$
$2\theta$	Full scattering angle (between incident beam and scattering)	$y$	$r={\sqrt {x^{2}+z^{2}}}$	$R={\sqrt {x^{2}+y^{2}+z^{2}}}$	$\sin 2\theta ={\frac {r}{R}}$	$\cos 2\theta ={\frac {y}{R}}$	$\tan 2\theta ={\frac {r}{y}}$
$\gamma$	In-plane angle	$y$	$x$	$h={\sqrt {x^{2}+y^{2}}}$	$\sin \gamma ={\frac {x}{h}}$	$\cos \gamma ={\frac {y}{h}}$	$\tan \gamma ={\frac {x}{y}}$
$\delta$	Elevation angle	$h={\sqrt {x^{2}+y^{2}}}$	$z$	$R={\sqrt {x^{2}+y^{2}+z^{2}}}$	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sin \delta = \frac{z}{R}}	$\cos \delta ={\frac {h}{R}}$	$\tan \delta ={\frac {z}{h}}$

So:

${\begin{alignedat}{2}\tan \gamma &={\frac {x}{y}}\\&={\frac {r\sin \chi }{r/\tan 2\theta }}\\&=\tan 2\theta \sin \chi \\\gamma &=\tan ^{-1}\left[\tan 2\theta \sin \chi \right]\end{alignedat}}$

and:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{alignat}{2} \sin \delta & = \frac{z}{R} \\ & = \frac{r \cos \chi}{r / \sin 2 \theta} \\ & = \sin 2 \theta \cos \chi \\ \delta & = \sin^{-1} \left [ \sin 2 \theta \cos \chi \right ] \end{alignat} }

and so:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{alignat}{2} P_h & = 1 - \cos^2 \delta \sin^2 \gamma \\ & = 1 - \cos^2 \delta \frac{ \left [ \tan 2 \theta \sin \chi \right ]^2 }{ \left [ \tan 2 \theta \sin \chi \right ]^2 + 1 } \\ \end{alignat} }