Biquadratic surface fits for two-dimensional interferometric head/tape spacing

A biquadratic surface-fit technique to provide the “calibration envelopes” for monochromatic interference fringe patterns is described. The fringe patterns are recorded using an analog camera and an 8 bit frame grabber. The least-squares method is used to fit biquadratic surfaces to selected intensity extrema. The surfaces then serve as the calibration envelopes needed to calculate the head/tape spacing over a two-dimensional area. The spacing is determined with a one standard deviation uncertainty of ±5 nm. The method is compared to the “unloading” technique on a linear drive using a cylindrical head with the result that the surface-fit spacing is on average 5 nm higher due to differences in the lower envelopes. Sample spacing results for a longitudinally slotted quarter-inch cartridge (QIC) tape head are given, showing tape spacing variations of approximately 15 nm amplitude between the slots at a tape speed of 3 m/s