Execution of prepareFairRef proceeds in levels 1..nLevels. At level 1, 2^(nLevels - 1) pairs of randomly chosen individual particles (groups) are aligned and combined. At level 2, these pairs are aligned and combined into 2^(nlevels - 2) groups, and and so on, until, at the final level, the last 2 groups are combined yielding a multiparticle reference in which each of the selcted particles is weighted equally.
Alignment searches performed by prepareFairRef follow the same multi-iteration strategy used for the subsequent main alignment search and defined either in the eTomo gui's Iteration Table or (equivalently) in the correspond parameter file values. Because prepareFairRef can be time consuming, parallel execution is highly recommended. Each group can be processed in a separate thread/chunk, with multiple groups executing simultaneously. For parallel execution, include the optional "level" and "group" parameters in each invocation of prepareFairRef. All of the groups [1 .. 2^(nLevels - level)] at a given level should be allowed to complete before invoking any groups from the subsequent level. The eTomo gui handles these details, using parallel processing automatically when multiple cpus are available
PrepareFairRef should result in less initial reference bias and better final averages than when using a single particle reference. We have not yet found datasets on which it yields a significant improvement, however, and the program is considered experimental as a result. If you find cases where it helps significantly, or where it should help but does not (especially if the reason for the lack of improvement is apparent), please contact the developers immediately!