calc_golden_angles

pypulseqpp.calc_golden_angles()

Return golden-angle rotations in radians, accumulated modulo 2*pi.

For diametric spokes the increment is pi / phi; for full-circle arms it is 2*pi / phi**2, where phi is the golden ratio.

Parameters:

• n (int) – Number of angles.

• full_circle (bool, default=False) – False (the default) is the pi-periodic radial/blade golden angle pi / phi; True is the full-turn spiral golden angle 2 * pi / phi**2. Default is False.

Returns:

Angles (rad), length n, accumulated modulo 2 pi.

Return type:

numpy.ndarray

Examples

>>> import numpy as np
>>> import pypulseqpp as pp
>>> np.rad2deg(pp.calc_golden_angles(4)).round(2)
array([  0.  , 111.25, 222.49, 333.74])

>>> np.rad2deg(pp.calc_golden_angles(3, full_circle=True)).round(2)
array([  0.  , 137.51, 275.02])

References

Winkelmann et al., golden-ratio profile order, DOI 10.1109/TMI.2006.885337.

See also

calc_tiny_golden_angles

smaller increments with the same uniformity.

calc_raga_angles

rational, exactly repeatable approximation.