Talk:Polarization correction - Revision history

KevinYager at 01:58, 23 November 2019

2019-11-23T01:58:56Z

2019-11-23T01:46:07Z

2019-11-23T01:42:51Z

2019-11-23T01:29:17Z

2019-11-23T01:21:19Z

2019-11-23T01:18:13Z

@@ Line 73: / Line 73: @@
 \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 } \\
+     & = 1 - \left( 1 - \left[ \sin 2  \theta \cos \chi \right]^2 \right ) \frac{ \left [ \tan 2 \theta \sin \chi \right ]^2 }{ \left [ \tan 2 \theta \sin \chi \right ]^2 + 1 } \\
 \end{alignat}
 </math>

@@ Line 59: / Line 59: @@
 </math>
 and:
-TBD
+:<math>
 and so:

← Older revision		Revision as of 01:42, 23 November 2019
Line 60:		Line 60:
	and:		and:
	TBD		TBD
		+
		+	and so:
		+	:<math>
		+	\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}
		+	</math>

← Older revision		Revision as of 01:29, 23 November 2019
Line 46:		Line 46:
	\| <math>\tan \delta = \frac{z}{h}</math>		\| <math>\tan \delta = \frac{z}{h}</math>
	\|}		\|}
		+
		+
		+	So:
		+	:<math>
		+	\begin{alignat}{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{alignat}
		+	</math>
		+	and:
		+	TBD

@@ Line 42: / Line 42: @@
 | <math>z</math>
 | <math>R = \sqrt{x^2 + y^2 + z^2}</math>
-| <math>\sin \delta = \frac{x}{R}</math>
+| <math>\sin \delta = \frac{z}{R}</math>
 | <math>\cos \delta = \frac{h}{R}</math>
-| <math>\tan \delta = \frac{x}{h}</math>
+| <math>\tan \delta = \frac{z}{h}</math>
 |}

@@ Line 2: / Line 2: @@
 |-
 ! Angle
 ! Adjacent
 ! Opposite
@@ Line 10: / Line 11: @@
 |-
 | <math>\chi</math>
 | <math>z</math>
 | <math>x</math>
@@ Line 18: / Line 20: @@
 |-
 | <math>2\theta</math>
 | <math>y</math>
 | <math>r = \sqrt{x^2 + z^2}</math>
@@ Line 26: / Line 29: @@
 |-
 | <math>\gamma</math>
 | <math>y</math>
 | <math>x</math>
@@ Line 32: / Line 36: @@
 | <math>\cos \gamma = \frac{y}{h}</math>
 | <math>\tan \gamma = \frac{x}{y}</math>
 |}