Self-compensating angular encoder

A method for self-compensating a method includes the steps of rotating the patterned element relative to the read heads, the rotation about the axis to a plurality of first angles covering a range of at least 360 degrees; obtaining, at each of the plurality of first angles, first angular readings for the m measure read heads and for the reference read head; calculating a first array for each of the m measure read heads, each first array including, for each of the plurality of first angles, a difference in the first angular readings of the measure read head and the first angular reading of the reference read head; calculating, for each of the m measure read heads, at least one first spectral component based at least in part on the first array; calculating, for each of the m measure read heads, at least one second spectral component, the second spectral component based, at least in part, on the at least one first spectral component and on estimates of the second angles of the m measure read heads; and recording, for each of the m measure read heads, the at least one second spectral component.