kappa4ch — Kappa Four-Circle (Laboratory)#

Four-circle kappa diffractometer, horizontal scattering plane. Kappa axis tilted at α = 50° from the outer komega axis (which here is along the −vertical direction) toward the equivalent Eulerian chi axis. Laboratory convention.

Walko (2016) designation: S3D1 (kappa)

Coordinate basis: Busing & Levy (BASIS_BL): transverse=+x, longitudinal=+y, vertical=+z.

Quick start#

import ad_hoc_diffractometer as ahd

g = ahd.presets.kappa4ch()
g.wavelength = 1.0  # Å
print(g.summary())

Pre-built geometry definition#

This geometry is defined by the kappa4ch() factory function — see the source for the complete stage and mode configuration.

Stage layout#

Static fallback (click to expand if the interactive figure above is blank)

kappa4ch stage layout

Sample stages (base first):

Stage

Axis

Handedness

Parent

komega

−vertical (−z BL)

left-handed

base

kappa

−z · cos α + ŷ · sin α (α = 50°)

right-handed

komega

kphi

−vertical (−z BL)

left-handed

kappa

Detector stages (base first):

Stage

Axis

Handedness

Parent

ttheta

−vertical (−z BL)

left-handed

base

The kappa axis is computed by kappa_axis_from_eulerian() from the preset’s actual komega and equivalent Eulerian chi axes:

\[ \hat{n}_{\kappa} \;=\; \cos\alpha \cdot \hat{n}_{\kappa\omega} \;+\; \sin\alpha \cdot \hat{n}_{\chi,\,\text{eq}} \;=\; \cos 50° \cdot (-\hat{z}) \;+\; \sin 50° \cdot (+\hat{y}). \]

This formulation is geometry-aware and is correct for the kappa4ch komega = -VERTICAL orientation. See the kappa4cv documentation and issue #241 for the reasons this differs from the textbook vertical · cos α + transverse · sin α formula.

Virtual Eulerian angles omega, chi, phi are mapped to / from the real motors via the geometry-aware decomposition in eulerian_to_kappa_axes() and kappa_to_eulerian_axes().

Diffraction modes#

Each mode is a ConstraintSet of 1 constraint (N − 3 = 1 for N = 4 DOF). Identical mode set to kappa4cv — Kappa Four-Circle (Synchrotron). See Switch Diffraction Modes for usage and Work with Constraints and Diffraction Modes for changing constraint values at run time.

bisecting (default)#

VirtualBisectConstraint: omega_virtual = ttheta / 2 enforced on the virtual Eulerian omega pseudoangle. Solved via the geometry-aware eulerian_to_kappa_axes() decomposition (issue #241).

Computed

komega, kappa, kphi, ttheta

Constant during forward()

—

fixed_kphi#

SampleConstraint: kphi held at declared value (default 0°) — real stage, no kappa inversion needed.

Computed

komega, kappa, ttheta

Constant during forward()

kphi

fixed_omega#

Fix virtual Eulerian omega at declared value (default 0°) — see kappa4cv — Kappa Four-Circle (Synchrotron) for details.

Computed

komega, kappa, kphi, ttheta

Constant during forward()

omega (virtual)

fixed_chi#

Fix virtual Eulerian chi at declared value (default 90°).

Computed

komega, kappa, kphi, ttheta

Constant during forward()

chi (virtual)

fixed_phi#

Fix virtual Eulerian phi at declared value (default 0°).

Computed

komega, kappa, kphi, ttheta

Constant during forward()

phi (virtual)

fixed_psi#

ReferenceConstraint: azimuthal angle ψ validation filter. Set g.azimuthal_reference = (h, k, l) before calling forward(). Returns bisecting solutions only when the natural ψ for (h,k,l) matches the stored target. See Surface Geometry and the Reference Vector.

Extras (input)

n̂ (reference vector), ψ (target azimuth, degrees)

Extras (output)

psi (computed azimuth)

API reference#

References#