Ewald sphere viewer

Reciprocal lattice, Ewald sphere cap, excitation error, and idealized detector projection.

Unit cell

a / Å

b / Å

c / Å

alpha / deg

beta / deg

gamma / deg

Beam and reciprocal shell

lambda / Å

|s_g| cutoff / Å^-1

d_min / Å

d_max / Å

HKL safety cap

Excited marker size

HKL bounds are derived from d_min; the cap only prevents accidentally huge scans.

Euler orientation

Align zone axis [u v w] with the beam before applying Euler angles

u

v

w

phi z

theta y

psi x

Convention: first align direct c, or enabled zone axis, to lab +z. Then use R = Rz(phi) Ry(theta) Rx(psi) on reciprocal vectors.

Display

Show all reciprocal-lattice points in the d shell as grey markers Show local Ewald sphere cap as translucent blue surface Show beam direction and reciprocal-space origin Label excited reflections with hkl values

Summary

Scanned HKLs

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In d shell

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Excited

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Detector points

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Ewald radius

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Min |s_g|

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3D reciprocal lattice and Ewald sphere

Å^-1 coordinates

Idealized detector projection

arbitrary camera length units

Geometry notes

Ewald sphere

The incident wavevector is k0 = (0, 0, 1/lambda). The sphere center is -k0 and the radius is |k0|, so the sphere passes through the reciprocal-space origin.

Excitation error

Reflections are highlighted when |s_g| <= cutoff, where s_g = |k0 + g| - |k0|. Darker red means closer to exact Bragg condition.

Detector projection

Only excited reflections are projected. The simplified detector is perpendicular to +z at L = 1, with x = L kout_x/kout_z and y = L kout_y/kout_z.