Simulated diffraction image simulatedreal

SimulatedstatisticReal 5.4%R merge 6.2% 18.9I/sd I/sd (1.4 Ǻ) SDCORR PADFPH mlphare f” FOM FOMDM CC(1H87) R cryst R free 0.231

Program flow overview ano_sfall.com mlfsom.com hkl2XYphi.awk mapman

d = (r 2 +g 2 ) 1/2 Point Spread Function I ~ Ω = g(r 2 +g 2 ) -3/2 g r Ω = g/d 3

Point Spread Function pixel intensity (ADU) distance from “point” (mm) re-sampled sum scaled and shifted I ~ g(r 2 +g 2 ) -3/2 g = 30 μm

Darwin’s Formula I(hkl)- photons/spot (fully-recorded) I beam - incident (photons/s/m 2 ) r e - classical electron radius (2.818x m) V xtal - volume of crystal (in m 3 ) V cell - volume of unit cell (in m 3 ) λ- x-ray wavelength (in meters!) ω- rotation speed (radians/s) L- Lorentz factor (speed/speed) P- polarization factor (1+cos 2 (2θ) -Pfac∙cos(2Φ)sin 2 (2θ))/2 A- absorption factor exp(-μ xtal ∙l path ) F(hkl)- structure amplitude (electrons) C. G. Darwin (1914) P A | F(hkl) | 2 I(hkl) = I beam r e 2 V xtal V cell λ 3 L ωV cell

Background scattering I bg - scattered photons/steradian I beam - incident (photons/s/m 2 ) t- exposure time (s) r e - classical electron radius (2.818x m) N A - Avogadro number (6.02x10 23 ) ρ- density of material (g/m 3 ) Mr- molecular weight (g/mol) V- volume of material (in m3) P- polarization factor (1+cos 2 (2θ) -Pfac∙cos(2Φ)sin 2 (2θ))/2 A- absorption factor exp(-μ xtal ∙l path ) f(s)- molecular structure amplitude (electrons) s- scattering length (sin(θ)/λ) P A | f(s) | 2 I bg = I beam t r e 2 N A ρV Mr R. W. James (1947)

Background scattering Resolution (Ǻ) Photons/s/pixel Se edge with detector at 100 mm 

Diffuse scattering I ds - scattered photons/steradian I beam - incident (photons/s/m 2 ) t- exposure time (s) r e - classical electron radius (2.818x m) V xtal - volume of crystal (in m 3 ) V ASU - asymmetric unit (in m 3 ) P- polarization factor A- absorption factor a- particular atom in the ASU f a (s)- atomic structure amplitude (electrons) s- scattering length (sin(θ)/λ) B a - atomic B factor |f a (s)| 2 (1-exp(-2B a ∙s 2 ))I ds = I beam t r e 2 V xtal V ASU P A Σ a R. W. James (1947)

Compton scattering I compton - scattered photons/steradian I beam - incident (photons/s/m 2 ) t- exposure time (s) r e - classical electron radius (2.818x m) V xtal - volume of crystal (in m 3 ) V ASU - asymmetric unit (in m 3 ) P- polarization factor A- absorption factor a- particular atom in the ASU θ- Bragg angle κ- photon energy (keV) / 511 keV Z a - atomic number f a (s)- atomic structure amplitude (electrons) s- scattering length (sin(θ)/λ) Z a - |f a (s)|I compton = I beam t r e 2 Σ a V xtal P A V ASU 1+κ (1-cos(θ)) 2 R. W. James (1947)

Exposure time exposure time (s) CC to correct model

Crystal Size crystal size (um) CC to correct model

Shutter Jitter rms timing error (% exposure) CC to correct model

Site Decay Gd site half-dose (MGy) CC to correct model

Detective Quantum Efficiency fraction of photons “detected” CC to correct model

read-out noise read-out nosie (“extra” photons) CC to correct model Q315r Q315 Mar 325HE Pilatus