Correction Implementations#

The mathematical implementations and the academic reference of each of the implemented corrections are tabulated below for the convenience of those utilizing the package.

In all of the below operations, $I_{j}$ denotes the uncorrected photon count of detector pixel $j$ whilst $I_{j, c}$ denotes the corrected photon count.

Correction Implementations#
Correction	Operation	Parameters	Reference
`correct_deadtime`	$\begin{aligned} I_{j, c} & = \frac{W_{0} (- I_{j} T)}{T} \\ T & = \frac{τ_{1} + τ_{2}}{δ t} \end{aligned}$	$δ t$ : Count time $τ_{1}$ : Minimum pulse separation $τ_{2}$ : Minimum arrival separation	Everything SAXS: small-angle scattering pattern collection and correction
`correct_dark_current`	$I_{j, c} = I_{j} - D_{a} - D_{b} δ t - D_{c} I_{j}$	$δ t$ : Count time $D_{a}$ : Base dark current $D_{b}$ : Temporal dark current $D_{c}$ : Flux dependant dark current	Everything SAXS: small-angle scattering pattern collection and correction
`normalize_frame_time`	$I_{j, c} = \frac{I_{j}}{δ t}$	$δ t$ : Count time	Everything SAXS: small-angle scattering pattern collection and correction
`normalize_transmitted_flux`	$I_{j, c} = \frac{I_{j}}{∯ I_{j}}$		The modular small-angle X-ray scattering data correction sequence
`correct_self_absorption`	$\begin{aligned} I_{j, c} & = I_{j} \frac{1 - T^{\sec 2 θ - 1}}{\ln T (1 - \sec 2 θ)} \\ T & = e^{- μ t} \\ {2 θ}_{j} & = \arctan \frac{\sqrt{{δ x}_{j}^{2} + {δ y}_{j}^{2}}}{Δ z} \end{aligned}$	$μ$ : Absorption coefficient $t$ : Sample thickness ${δ x}_{j}$ : Horizontal pixel beam separation ${δ y}_{j}$ : Vertical pixel beam separation $Δ z$ : Detector sample separation	Everything SAXS: small-angle scattering pattern collection and correction
`average_all_frames`	$I_{j, c} = \sum I_{n, j}$	$I_{n, j}$ : Intensity of pixel $j$ at frame $n$	The modular small-angle X-ray scattering data correction sequence
`subtract_background`	$I_{j, c} = I_{j} - I_{j, b}$	$I_{j, b}$ : Background frame intensity of pixel $j$	Everything SAXS: small-angle scattering pattern collection and correction
`correct_flatfield`	$I_{j, c} = I_{j} F_{j}$	$F_{j}$ : Flatfield correction factor of pixel $j$	The modular small-angle X-ray scattering data correction sequence
`correct_angular_efficiency`	$\begin{aligned} I_{j, c} & = \frac{I_{j}}{1 - e^{\frac{- μ t}{\cos 2 θ}}} \\ {2 θ}_{j} & = \arctan \frac{\sqrt{{δ x}_{j}^{2} + {δ y}_{j}^{2}}}{Δ z} \end{aligned}$	$μ$ : Absorption coefficient $t$ : Sample thickness ${δ x}_{j}$ : Horizontal pixel beam separation ${δ y}_{j}$ : Vertical pixel beam separation $Δ z$ : Detector sample separation	The modular small-angle X-ray scattering data correction sequence
`correct_solid_angle`	$\begin{aligned} I_{j, c} & = \frac{I_{j}}{\cos {2 θ}^{3}} \\ {2 θ}_{j} & = \arctan \frac{\sqrt{{δ x}_{j}^{2} + {δ y}_{j}^{2}}}{Δ z} \end{aligned}$	${δ x}_{j}$ : Horizontal pixel beam separation ${δ y}_{j}$ : Vertical pixel beam separation $Δ z$ : Detector sample separation	Everything SAXS: small-angle scattering pattern collection and correction
`correct_polarization`	$\begin{aligned} I_{j, c} & = I_{j} [P K_{v} + (1 - P) K_{h}] \\ K_{v} & = 1 - (\sin ψ \sin 2 θ)^{2} \\ K_{h} & = 1 - (\cos ψ \sin 2 θ)^{2} \\ {2 θ}_{j} & = \arctan \frac{\sqrt{{δ x}_{j}^{2} + {δ y}_{j}^{2}}}{Δ z} \\ ψ & = \arctan \frac{δ x}{δ y} \end{aligned}$	$P$ : Horizontal polarization ${δ x}_{j}$ : Horizontal pixel beam separation ${δ y}_{j}$ : Vertical pixel beam separation $Δ z$ : Detector sample separation	Everything SAXS: small-angle scattering pattern collection and correction
`normalize_thickness`	$I_{j, c} = \frac{I_{j}}{t}$	$t$ : Sample thickness	Everything SAXS: small-angle scattering pattern collection and correction
`correct_displaced_volume`	$I_{j, c} = I_{j} (1 - v_{d})$	$v_{d}$ : Displaced volume	The modular small-angle X-ray scattering data correction sequence