calc_spiral_trajectory

calc_spiral_trajectory#

pypulseqpp.calc_spiral_trajectory()[source]#

Return one spiral-out interleaf, from the centre to kmax.

The pitch between neighbouring turns is set so that design_interleaves rotated copies of this path sample the disc at the Nyquist rate for fov. The caller may acquire a different number.

Parameters:

  • fov (float) – Field of view, in m. Isotropic.

  • matrix (int) – Matrix size, which with fov sets the reach matrix / (2 fov).

  • design_interleaves (int) – Interleaf count the pitch is designed for. One is a single-shot spiral of matrix / 2 turns.

  • density ({"constant", "variable", "dual"}, default='constant') – How the local pitch changes with radius: not at all, as radius ** variable_density_power, or between two plateaus joined by a logistic transition.

  • inner_design_interleaves (float, default=None) – Local interleaf count at the centre and at the edge. The inner one defaults to design_interleaves; the outer one to twice the inner for a variable-density spiral, and is required for a dual-density one. A larger count is a coarser pitch, so a variable-density spiral undersamples the edge.

  • outer_design_interleaves (float, default=None) – Local interleaf count at the centre and at the edge. The inner one defaults to design_interleaves; the outer one to twice the inner for a variable-density spiral, and is required for a dual-density one. A larger count is a coarser pitch, so a variable-density spiral undersamples the edge.

  • variable_density_power (float, default=2.0) – Exponent of the variable-density ramp.

  • transition_radius (float, default=0.5) – Where between the centre (0) and the edge (1) a dual-density spiral changes pitch, and how abruptly.

  • transition_speed (float, default=12.0) – Where between the centre (0) and the edge (1) a dual-density spiral changes pitch, and how abruptly.

  • num_points (int, default=1024) – Samples along the polyline. Sets how finely the curve is described, not how many ADC samples the readout takes.

Returns:

(num_points, 2), in 1/m, starting at the origin.

Return type:

numpy.ndarray

Raises:

ValueError – If density is not one of the three, a dual-density spiral has no outer interleaf count, or any count or shape parameter is out of range.

Examples

>>> import numpy as np
>>> import pypulseqpp as pp
>>> arm = pp.calc_spiral_trajectory(0.256, 128, 8)
>>> bool(np.allclose(arm[0], 0.0)), round(float(np.hypot(*arm[-1])), 6)
(True, 250.0)