XEDS Tools Solid Angle Calculator V-2014091607 Download M&M2014 Paper with calculation details Microsc. Microanal. 20, 1318 - 1326, 2014 doi:10.1017/S1431927614000956

Circular Cross-section
Radial Detector, Tilt Angle (θ) = 0	Parameter Value  units  Distance to Detector (d) mm Detector Active Radius (r) mm Detector Tilt Angle (θ) degrees Fraction Obstructed (f) 0 < f < 1 Nominal Active Area (A) 0 mm2 Radial Detector Solid Angle (Ω) - sR Non-Radial Detector Solid Angle (Ω) - sR	Non-Radial Detector, Tilt Angle (θ) > 0
Rectangluar Cross-section
Radial Detector, Tilt Angle (θ) = 0	Parameter Value  units  Distance to Detector (d) mm Detector Active Height (h) mm Detector Active Width (w) mm Detector Tilt Angle (θ) degrees Fraction Obstructed (f) 0 < f < 1 Nominal Active Area (A) 0 mm2 Radial Detector Solid Angle (Ω) - sR Non-Radial Detector Solid Angle (Ω) - sR	Non-Radial Detector, Tilt Angle (θ) > 0
Annular Cross-section
	- Parameter Value  units  Distance to Detector (d) mm Outer Active Radius (ra ) mm Inner Active Radius (rb ) mm Fraction Obstructed (f) 0 < f < 1 Nominal Active Area (A) 0 mm2 Calculated Solid Angle (Ω) sR
Calculation of Holder Tilt to Minimize Holder and Detector Penumbra
	Parameter Value  units  Holder Side Wall Half-Height (hs ) mm Holder Half-Width (ws ) mm Holder Penumbra Angle ( θp )   degrees Upper Detector Height (HU ) mm Lower Detector Height (HL ) mm Radial Detector Distance (D) mm Detector Upper Elevation Angle ( θEU )   degrees Detector Lower Elevation Angle ( θEL )   degrees Minimum Holder Tilt Angle ( α = θp - θEL ) to mitigate penumbra's of holder and/or detector   degrees	Note: some detector geometries can have HL which is negative ( i.e. below the specimen plane)
Estimation of Detector Fraction Obstructed ( f )
Moxtek Grid            Holder Penumbra Moxtek/Holder/Collimator Penumbra Notes: when Ru = R then there is no shadowing by the specimen holder or collimator when Ru = - R then 100% of the detector is shadowed/obstructed when Ru > R then 0% of the detector is shadowed/obstructed a collimator shadow can also create the same effect as the holder penumbra, except it does not change with holder tilt       Ru ~ R - D tan(θP) if the holder is non-tilted	If the Detector is Windowless and there are no other obstructions then f = 0 If a Detector Window is present and is supported on a Moxtek AP3 Grid then approximately 75% of the window area is open or "not obstructed" hence   fMoxtek ~ 1 - 0. 75 = 0. 25 . If a Circular Detector is used and is shadowed by the Specimen Holder's Penumbra you can use the following to estimate fHolder Penumbra Parameter Value  units  Detector Active Radius (R) mm Unshadowed Radius (Ru ) mm Fraction Obstructed by Holder Penumbra ( fHolder Penumbra ) Note: you must manually enter f into the parameter space above   0 < f < 1 If you have both of the above situations, then multiply the corresponding terms appropriately. Here fTotal = fMoxtek * (1- fHolder Penumbra ) . Notice that when you have 2 or more obstructions you must carefully account for their relationships. Here the Moxtek obstruction only affects the "open" or unobstructed area of the detector caused by the holder penumbra. Other geometries are left to the user to calculate.