  Purpose: To develop a generic radial sampling scheme that combines the
advantages of golden ratio sampling with simplicity of equidistant angular
patterns. The irrational angle between consecutive spokes in golden ratio based
sampling schemes enables a flexible retrospective choice of temporal
resolution, while preserving good coverage of k-space for each individual bin.
Nevertheless, irrational increments prohibit precomputation of the point-spread
function (PSF), can lead to numerical problems, and require more complex
processing steps. To avoid these problems, a new sampling scheme based on a
rational approximation of golden angles (RAGA) is developed.
  Methods: The theoretical properties of RAGA sampling are mathematically
derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to
the corresponding golden ratio sampling schemes. The sampling scheme is
implemented in the BART toolbox and in a radial gradient-echo sequence.
Feasibility is shown for quantitative imaging in a phantom and a cardiac scan
of a healthy volunteer.
  Results: RAGA sampling can accurately approximate golden ratio sampling and
has almost identical PSF and SPR. In contrast to golden ratio sampling, each
frame can be reconstructed with the same equidistant trajectory using different
sampling masks, and the angle of each acquired spoke can be encoded as a small
index, which simplifies processing of the acquired data.
  Conclusion: RAGA sampling provides the advantages of golden ratio sampling
while simplifying data processing, rendering it a valuable tool for dynamic and
quantitative MRI.
