The three-level correlator, in which both the data and the fringe rotation function are quantized to three levels, is another scheme in use. The three-level correlator can be considered as a special case of the four-level correlator where both the inner levels are reassigned a weight of zero. As with the four-level correlator, the conversion function cannot be solved for explicitly. The numerically calculated conversion function is shown in Fig. 3 (click here).
The efficiency of the three-level correlator can be derived from the expression for the four-level correlator efficiency by retaining only the terms in n2. The result is
The efficiency is maximised for (
) where it has a value of 0.389, increasing to
0.778 by virtue of the complex correlator architecture. This compares to
0.81 for a three-level
correlator without digital fringe rotation. In practice (
) is used with virtually no loss in
efficiency.