Calibration of servo index positions of a magnetic tape employing second order curve fitting

A servo system for calibrating servo index positions of a magnetic tape for track following, said magnetic tape having a plurality of parallel sets of linear servo edges, each said servo edge comprising an interface between two dissimilar recorded servo signals, each said set of servo edges comprising one of said servo edges on each of opposite lateral sides of a middle said recorded servo signal, at least a plurality of said servo index positions laterally offset from said linear servo edges, said servo system comprising:

• at least one servo sensor of a tape head, said tape head movable laterally of said magnetic tape, said at least one servo sensor sensing said servo signals comprising said servo edges of at least one said set of linear servo edges;
• an independent position sensor for determining the mechanical lateral position of said tape head servo sensor with respect to said magnetic tape;
• a servo detector coupled to said at least one servo sensor for determining a ratio of said servo signals sensed by said servo sensor;
• a servo loop coupled to said servo detector for positioning said tape head laterally of said magnetic tape to track follow said sensed servo signals at specific position error signals representing offsets from said linear servo edges in accordance with said ratios of said sensed servo signals as determined by said servo detector;
• and
• logic coupled to said servo detector, said independent position sensor, and said servo loop;
• said logic:
• operating said servo loop to laterally position said at least one servo sensor to sense said servo signals at estimated ratios of said servo detector representing locations comprising said servo edges of at least a set of linear servo edges;
• determining from said independent position sensor, the lateral position of said tape head servo sensor with respect to said magnetic tape at said sensed servo edges;
• operating said servo loop to laterally reposition said tape head servo sensor to a plurality of lateral positions of said tape head at predetermined displacements from said sensed servo edges as determined by said independent position sensor;
• and to track follow said linear servo edges with said servo loop at each of said predetermined displacements;
• determining from said servo detector, said ratio of said sensed servo signals at each of said predetermined displacements;
• and
• curve fitting a two dimensional, second order curve to said ratios of said sensed servo signals with respect to said predetermined displacements for each said linear servo edge to calibrate expected said position error signals for said servo loop at said laterally offset servo index positions with respect to said sensed servo edges of said set of linear servo edges.