Diffraction & Resolution — teaching applet

Crystal

diffracting power 0.8 1.80 Å

anisotropy level 0 0.00

anisotropy angle 0 0°

Experiment

distance 50 200 mm

Data

beam intensity 0.05 1.00×

background 0 1.00×

I/σ threshold 0 2.0

res circles

scenarios

isotropic

anisotropic, 0°

anisotropic, 45°

enclosed enclosed enclosed slightly beyond slightly beyond slightly beyond way beyond way beyond way beyond

crystal limits (intrinsic)

diffraction limit of the crystal— Å

The highest resolution the crystal could produce — purely a property of the crystal. Set by the diffracting-power slider (and reshaped by anisotropy). Beam, background, and threshold do not move this number; nothing diffracts past it.

diffraction limits of the crystal— / — Å

Two values along the principal axes of the anisotropic ellipse — strong and weak. With anisotropy = 0 they're equal, and the ellipse is a circle.

data limits (after detector clipping)

diffraction limit of the data— Å

The highest resolution that also lands on the detector (and rises above noise). Geometrically: the furthest-reaching point on the cutoff ellipse that still fits inside the detector rectangle — independent of unit-cell size or how densely the reciprocal lattice is sampled.

diffraction limits of the data along principal axes— / — Å

The diffraction limits along the principal axes of the crystal's cutoff ellipse, each clipped by the detector edge in that direction. The two arrows are always perpendicular — they point exactly along the strong and weak crystal axes. In a clipped direction the arrow ends at the detector edge, not at the crystal's own limit.

diffraction limits of the data at crossings— / — Å

Along each principal axis, walk along the cutoff ellipse until you reach the detector boundary — that crossing point is the data limit in that direction. When clipping occurs the two arrows are no longer perpendicular: both still lie on the crystal's cutoff ellipse, but at points where the ellipse meets the detector edge (visible only in the bottom view).

the punchline

"the resolution"— what do you mean? —

When someone says "the resolution is 1.8 Å", they may mean any of these things — and they often shift between them mid-sentence. That's why using diffraction limit(s) is a much better and more accurate term — especially in conjunction with "of the crystal" or "of observations".

crystal limit— observed— observable—

— %

observable defined as

full crystal ellipse Everything the crystal can diffract — regardless of whether it reaches the detector. Ignores that parts of the ellipse may miss the detector entirely. circle at crystal tip (strong axis) Treat the crystal as isotropic at its best (strongest) direction. Overestimates completeness for anisotropic crystals. circle to detector corner Everything within the circle passing through the detector corner. Common software default for the high-resolution shell — but includes space that lies past the detector edge. circle to short detector edge (inscribed) Inscribed circle — radius equals the shorter half-dimension of the detector. Fits entirely within the detector; excludes all corners. circle to long detector edge Radius equals the longer half-dimension. Touches the longer edges but extends outside the shorter edges of the detector. circle at best data limit Circle through the highest-resolution point actually on the detector (the singular data limit). This is the nominal resolution shell reported for the experiment. crystal ellipse ∩ circle at best data limit Intersection of the crystal's diffraction ellipse and the circle at the best data limit. Along the strong axis the circle clips the ellipse; along the weak axis the ellipse clips the circle. This is the physically correct observable when the nominal resolution is defined by the singular data limit.