From celestial to projection plane coordinates

The reverse operation is done with the generic Euler rotation (their equation 5)

$\displaystyle \phi$	$\displaystyle =$	$\displaystyle \phi_p +$ atan2 $\displaystyle (-\cos\delta\sin(\alpha-\alpha_p), \sin\delta\cos\delta_p-\cos\delta\sin\delta_p\cos(\alpha-\alpha_p))$	(23)
$\displaystyle \theta$	$\displaystyle =$	$\displaystyle \sin^{-1}(\sin\delta\sin\delta_p+\cos\delta\cos\delta_p\cos(\alpha-\alpha_p))$	(24)

and the projection specific to SFL (their equations 90 and 91):

$\displaystyle x$	$\displaystyle =$	$\displaystyle \phi \cos \theta$	(25)
$\displaystyle y$	$\displaystyle =$	$\displaystyle \theta$	(26)