Method for measuring PES noise of servo patterned media

1. A method of determining actuator position error in the measurement of servo position error signals (“PES”) from a magnetic disk having pre-patterned sector servo data pattern written into a plurality (“j”) of servo sectors defining substantially circular tracks whose centers are offset from the axis of rotation of a spindle onto which the disk is mounted, each servo sector generating a PES signal in a read-back magnetic transducer that is periodic in the radial, cross track dimension, comprising:

a) stepping a magnetic transducer across a disc in i nominally equal radial increments, each step being offset from a nominal step by an actuator position error, where the number of increments is sufficient to span at least one PES period;

b) at each step, measuring the PES at each of the servo sectors n times, where n is a predetermined number greater than zero;

c) for each PES measurement, calculating an average of the n times measurements at each step to form an i×j matrix of average PES measurements, each set of average measurements for each sector j having substantially identical cross track profiles, each cross track profile offset from the initial cross track profile by a phase difference, Φ[j];

d) computing a radial phase offset Φ[j] of each cross track profile for each sector from the average PES measurements assuming, initially, that each step was of a nominal size;

e) realigning the average PES measurements to have substantially the same phase; and averaging the realigned PES measurements by step;

f) decomposing, using a Fourier transformation, the averaged measurements to determine an average cross track profile;

g) comparing the average cross track profile to the measurements to determine the radial distance between the two for each PES measurement;

h) averaging the distances by step to determine an average radial distance for each step;

i) updating a offset for each step by adding to the offset the average radial distance, the offset initially being set to zero; and

j) repeating steps (d) through (i) by adding the respective offsets to the receptive steps radial measurement locations distance until the largest average radial distance is less than a predetermined number; wherein the resultant offset is the actuator position error at each step.

2. A method for removing random noise from the measurement of position error signals, comprising:

a) measuring PES by steps n times according to steps a and b of claim 1 ;

b) forming a plurality of sets of averaged PES measurements as provided in step c of claim 1 by determining an average PES measurement by varying the number of measurements used to form the average,

c) determining a step offset for each set of averaged PES measurements as provided in steps d through j of claim 1 ,

d) calculating an average standard deviation of the differences between the averaged PES measurements and the average cross track profile from the final realigned average PES measurements;

e) plotting the square of the average standard deviation vs. the inverse of the number of measurements used to form the averaged PES measurements;

f) wherein the square of the actual PES noise is the value of the plot at n=∞.

3. The method of claim 1 wherein said method of realigning the average PES measurements includes determining an interpolation point between respective measurements and further wherein said step of averaging the realigned PES measurements comprises averaging the interpolation points.

4. The method of claim 1 wherein said step of comparing the average track profile to the measurements to determine the radial distance between the two for each PES measurement, comprises:

dividing the difference between the PES measurements and the average track profile by the first differential of the average track profile.

5. A method for determining the written in repeatable runout of the servo pattern, comprising:

a) measuring PES by steps and determining step offsets according to claim 1 ;

b) phase unwrapping the final phase offsets Φ[j] to form a continuous periodic signal having one period.

6. The method for determining the written in repeatable runout according to claim 5 wherein the phase unwrapping step comprises:

determining Φ[j,n]=Φ[j]+2n[j]Π from Φ[j], wherein n[j] is determined by

a) setting n[O]=n[ 1 ]=0;

b) from j=1 to the total number of sectors−1, determining n[j+1]=nearest integer of (2Φ[j,n[j]]−Φ[j−1,n[j−1]]−Φ[j+1, 0 ]/(2Π);

c) determining whether n[ 0 ] derived from nearest integer quotient of (2Φ[total_sectors−1, n[total_sectors−1]]−Φ[total_sectors−2, n[total —sectors− 2]]−Φ[ 0 , 0 ])/(2Π)equals to 0 and n[ 1 ] derived from nearest integer quotient of (2Φ[ 0 , 0 ]−Φ[total_sectors−1, n[total sectors−1]]−Φ[ 1 , 0 ])/(2Π) equals to 0; and if it is not, repeating steps a and b, but starting at n[ 1 ]=n[ 2 ]=0, and beginning the determination of subsequent n[j+1] from j=2; and

d) repeating the incrementation of the starting sector j until Φ[j,n[j]] form a continuous periodic signal having one period.

7. A disk drive servo system, comprising:

a memory for storing repeatable runout compensation values that are the resultant step offset of claim 1 , step j); and

means for feeding forward said compensation values into a disk drive servo system; wherein said compensation values are determined according to the method of claim 5 .

8. Apparatus for measuring servo pattern irregularity, comprising:

means for stepping an actuator across a disc drive disc having a plurality of pre-patterned servo sectors while measuring the PES signal from each servo sector; and

means for removing measurement error from the measurements.

9. Apparatus according to claim 8 wherein said means for removing measurement error comprises means for removing step error from the measurements.

10. Apparatus according to claim 8 wherein said means for removing measurement error comprises means for removing random error from the measurements.

11. Apparatus according to claim 8 further comprising means for determining repeatable runout from the measurements.

12. Apparatus according to claim 11 further comprising a disc drive servo system means for feeding-forward said repeatable runout.

13. A method of determining an actuator position error in a measurement of servo position error signals from a magnetic recording disk having pre-patterned sectors of servo data, comprising determining an average cross track profile by computing a radial phase offset of each cross track profile for each of said sectors, realigning average PES measurements to have substantially the same phase, averaging realigned PES measurements, and decomposing averaged PES measurements using a Fourier transformation.