Appendix E: Convergence of auto-folder solutions as the numbers of included Fourier modes increase

The actual number of modes used for the folding of any given rotation curve is determined by the mode-choosing strategy of Sect. 7, and this strategy assumes that this number has a maximum limit determined by Sect. 6.2. However, we find that the folding solution over the whole set of rotation curves (defined as the $\ln A$ distribution) can be considered converged for all practical purposes when a maximum of only five Fourier modes are included. The illustration of this fact is given in Fig. E1, which displays the solutions for the four cases of the 1-mode solution, the 3-mode solution, the 5-mode solution and the 10-mode solution. It is quite clear that the solution converges extremely rapidly.

In practice, all the Mk II, III and IV auto-folder solutions shown in the earlier figures have been computed using just five Fourier modes.