# Patent

## Title
Systems and methods for printed-media SSW reference pattern with extra servo bursts used near OD

## Abstract

A printed media self-servowriting process can be utilized whereby each wedge in the printed media pattern can have more than two servo bursts in order to effectively eliminate the high PES noise. A final pattern can be written based on the printed media pattern and eliminate the timing eccentricity suffered by the printed media pattern due to disk mis-centering. A radius can be determined such that more than two servo bursts can be can be used to determine the PES for radii between the radius and the OD, while only one or two servo bursts can be used between the radius and the ID. This description is not intended to be a complete description of, or limit the scope of, the invention. Other features, aspects, and objects of the invention can be obtained from a review of the specification, the figures, and the claims.

## Background
INCORPORATION BY REFERENCE
This application is related to the following patent which is hereby incorporated by reference in its entirety:
U.S. Pat. No. 6,738,205, entitled SELF-WRITING OF SERVO PATTERNS IN DISK DRIVES, Inventors: Patrick Moran, et al., filed Jul. 8, 2001.
FIELD OF THE INVENTION
The present invention relates to the writing of position information to rotatable media.
BACKGROUND
Advances in data storage technology have provided for ever-increasing storage capability in devices such as DVD-ROMs, optical drives, and disk drives. In hard disk drives, for example, the width of a written data track has decreased due in part to advances in read/write head technology, as well as in reading, writing, and positioning technologies. More narrow data tracks result in higher density drives, which is good for the consumer but creates new challenges for drive manufacturers. As the density of the data increases, the tolerance for error in the position of a drive component such as a read/write head decreases. As the position of such a head relative to a data track becomes more important, so too does the placement of information, such as servo data, that is used to determine the position of a head relative to a data track.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram showing components of an exemplary drive system that can be used in accordance with various embodiments of the present invention.
FIG. 2 is a diagram showing an example of a data and servo format for a disk in the drive of FIG. 1.
FIG. 3 is a diagram showing servo information that can be written to the tracks shown in FIG. 2.
FIGS. 4(a)–(f) are diagrams of a servo-burst pattern being written over a progression of servowriting steps.
FIG. 5 is a diagram of a disk stack containing a printed reference pattern that can be used with the system of FIG. 1.
FIG. 6 is a diagram showing various views of portion of a magnetic pattern that can be used with the system of FIG. 1.
FIG. 7 is a diagram showing a phase burst and corresponding read signals that can be used with the system of FIG. 1.
FIG. 8 is a plot showing an exemplary sampling approach that can be used with the signals of FIG. 6 and FIG. 7.
FIG. 9 is a diagram showing relative burst phases that can be used with the system of FIG. 1.
FIG. 10 is a diagram showing a reference pattern in a disk stack that can be used in the system of FIG. 1.
FIG. 11 is a diagram showing a printed reference pattern and a final pattern that can be used with the system of FIG. 1.
FIG. 12 is a flowchart showing a process that can be used with the system of FIG. 1.
FIG. 13 shows an exemplary printed signal pattern with a pair of extra zig/zag bursts inserted in accordance with embodiments of the present invention.
FIG. 14 is a flowchart showing a process that can be used with the system of FIG. 1.
FIG. 15 shows an exemplary printed media self-servowriting process in accordance with embodiments of the present invention.
FIG. 16 is a diagram showing the PES noise at various radius of disk in accordance with embodiments of the present invention.
FIG. 17 shows wedge-related parameters in accordance with embodiments of the present invention.



DETAILED DESCRIPTION
Systems and methods in accordance with various embodiments of the present invention can be used when servowriting, or self-servowriting, a rotatable storage medium in a data storage device, such as a hard disk drive. For example, a typical disk drive 100, as shown in FIG. 1, includes at least one magnetic disk 102 capable of storing information on at least one of the surfaces of the disk(s). A closed-loop servo system can be used to move an actuator arm 106 and data head 104 over the surface of the disk(s), such that information can be written to, and read from, the surface of the disk(s). The closed-loop servo system can contain, for example, a voice coil motor driver 108 to drive current through a voice coil motor (not shown) in order to drive the actuator arm, a spindle motor driver 112 to drive current through a spindle motor (not shown) in order to rotate the disk(s), a microprocessor 120 to control the motors, and a disk controller 118 to transfer information between the microprocessor, buffer memory 110, read channel 114, and a host 122. A host can be any device, apparatus, or system capable of utilizing the data storage device, such as a personal computer or Web server or consumer electronics device. The drive can contain at least one processor, or microprocessor 120, that can process information for the disk controller 118, read/write channel 114, VCM driver 108, or spindle driver 112. The microprocessor can also include a servo controller, which can exist as an algorithm resident in the microprocessor 120. The disk controller 118, which can store information in buffer memory 110 resident in the drive, can also provide user data to a read/write channel 114, which can send data signals to a current amplifier or preamp 116 to be written to the disk(s) 102, and can send servo and/or user data signals back to the disk controller 118.
The information stored on such disk(s) can be written in concentric tracks, extending from near the inner diameter to near the outer diameter of the disk 200, as shown in the example disk of FIG. 2. In an embedded servo-type system, servo information can be written in servo wedges 202, and can be recorded on tracks 204 that can also contain data. In a system where the actuator arm rotates about a pivot point such as a bearing, the servo wedges may not extend linearly from the inner diameter (ID) of the disk(s) to the outer diameter (OD), but may be curved slightly in order to adjust for the trajectory of the head as it sweeps across the disk(s).
The servo information often includes bursts of transitions called “servo bursts.” The servo information can be positioned regularly about each track, such that when a data head reads the servo information, a relative position of the head can be determined that can be used by a servo processor to adjust the position of the head relative to the track. For each servo wedge, this relative position can be determined in one example as a function of the target location, a track number read from the servo wedge, and the amplitudes or phases of the bursts, or a subset of those bursts. A measure of the position of a head or element, such as a read/write head or element, relative to the center of a target track, will be referred to herein as a position-error signal (PES).
For example, a centerline 300 for a given data track can be “defined” relative to a series of bursts, burst edges, or burst boundaries, such as a burst boundary defined by the lower edge of A-burst 302 and the upper edge of B-burst 304 in FIG. 3. The centerline can also be defined by, or offset relative to, any function or combination of bursts or burst patterns. As a non-limiting example, a centerline defined by four bursts can be referred to as “4-burst-centerline” as described for example, in U.S. Pat. No. 5,381,281 entitled “Disk Drive System Using Multiple Embedded Quadrature Servo Fields”, by Louis J. Shrinkle, et al, filed Jun. 24, 1993. The definition of a track centerline can include, for example, a location at which the PES value is a maximum, a minimum, or a fraction or percentage thereof. Any location relative to a function of the bursts can be selected to define track position. For example, if a read head evenly straddles an A-burst and a B-burst, or portions thereof, then servo demodulation circuitry in communication with the head can produce equal amplitude measurements for the two bursts, as the portion of the signal coming from the A-burst above the centerline is approximately equal in amplitude to the portion coming from the B-burst below the centerline. The resulting computed PES can be zero if the radial location defined by the A-burst/B-burst (A/B) combination, or A/B boundary, is the center of a data track, or a track centerline. In such an embodiment, the radial location at which the PES value is zero can be referred to as a null-point. Null-points can be used in each servo wedge to define a relative position of a track. If the head is too far towards the outer diameter of the disk(s), or above the centerline in FIG. 3, then there will be a greater contribution from the A-burst that results in a more “negative” PES. Using the negative PES, the servo controller could direct the voice coil motor to move the head toward the inner diameter of the disk(s) and closer to its desired position relative to the centerline. This can be done for each set of burst edges defining the shape of that track about the disk(s).
The PES scheme described above is one of many possible schemes for combining the track number read from a servo wedge and the phases or amplitudes of the servo bursts. Many other schemes are possible that can benefit from embodiments in accordance with the present invention.
A problem that exists in the reading and writing of servo information such as servo patterns involves the misplacement, or offset, of a read/write head with respect to the ideal and/or actual position of a track. It is impossible to perfectly position a head with respect to a track for each rotation of disk(s), as there is almost always a noticeable offset between the desired position and the actual position of the head with respect to the disk(s). This can cause problems when writing servo patterns, as each portion of the pattern can be slightly misplaced. This can lead to what is referred to as “written-in runout.” Written-in runout can be thought of as the offset between the actual centerline, or desired radial center, of a track and the centerline that would be determined by a head reading the written servo pattern. Written-in runout can lead to servo performance problems, wasted space on disk(s) and, in a worst case, unrecoverable or irreparably damaged data.
Additional servowriting steps can be used when writing servo information. The use of additional servowriting steps for the writing and/or trimming of servo burst patterns, for example, can provide for a low written-in runout in a servo pattern, but at the cost of some time-penalties in the servowriting and/or self-servowriting operations.
FIGS. 4(a)–4(f) depict the progression of several servowriting steps of an exemplary servowriting process. The pattern shown in these figures is commonly referred to in the industry as a 3-pass-per-track, trimmed-burst pattern, for reasons described below. Using the nomenclature of this document, one could refer to the pattern as a “3-servowriting-step-per-track, trimmed-burst” pattern. Each figure depicts a small portion of the surface of disk(s). This portion can contain several servo tracks, extending radially on the disk(s) and vertically in the figures, and can cover the space of a single servo wedge, circumferentially on the disk(s) and horizontally in the figures. A typical drive can have tens of thousands of servo tracks, and over one hundred wedges per revolution. In the figures, the black areas indicate portions of the surface of the disk(s) that have been magnetized in one direction. The white areas have been magnetized in another direction, typically in a direction opposite to that of the patterned areas. For a drive that uses longitudinal recording, the two directions can be in the positive and negative circumferential directions. For a drive that uses vertical recording technology (also sometimes referred to in the industry as “perpendicular recording”), the two directions can be perpendicular to the recording surface, such as would be “in” and “out” of the page for the illustrations of FIGS. 4(a)–(f). These simplified figures do not show effects of side writing of the write element, which can produce non-longitudinal magnetization and erase bands. Such effects are not of primary importance to the discussion herein.
In FIG. 4(a), the result of a single servowriting step is shown. From that step, the servowriting head (passing from left to right in the figure) has written an exemplary servo pattern containing a preamble, followed by a servo-address mark (SAM), followed by an INDEX-bit, and then a track number, as is known in the art. Other information can be written to the servo pattern in addition to, or in place of, the information shown in FIG. 4(a). An INDEX-bit, for example, is one piece of information that can be used to give the servo an indication of which wedge is wedge-number zero, useful for determining circumferential position. The track number, which can be a graycoded track-number, can later be used by the servo to determine the coarse radial position of the read/write (R/W) head (note that the bits representing the track number shown here are for illustration purpose only, a typical drive may have up to 18 or more track number bits). Following the track number, the head writes one of four servo bursts, in this case what will be referred to as a C-burst, which can later be used by a servo to determine the fine (fractional track) radial position of a R/W head. The number of servo bursts used can vary with servo pattern. The burst that is written can be, for example, the one that is in-line with the digital information. The width of the written track can be determined by the magnetic write-width of the write element of the servowriting head.
FIG. 4(b) shows the result of a second servowriting step of the servowriting head. All that has been added in the second step is an additional burst, in this case referred to as an A-burst. The A-burst is displaced longitudinally from both the digital information and the C-burst, to prevent any overlap in the longitudinal direction. The A-burst is also displaced by approximately one-half of a servo-track in the radial direction.
FIG. 4(c) shows the magnetization pattern after three servowriting steps of the servowriting head. The new portion of the pattern has been written with the servowriting head displaced another half servo track radially, for a total displacement of one servo-track, or two-thirds of a data-track, from the position of the head during the first servowriting step. New digital information has been written, including the same preamble, SAM, and INDEX-bit, as well as a new track number. A D-burst was added during the third servowriting step, and the C-burst was “trimmed.” The C-burst was trimmed by “erasing” the portion of the C-burst under the servowriting head as the head passed over the burst on the third servowriting step. As long as the servowriting head is at least two-thirds of a data-track in radial extent, the digital information will extend across the entire radial extent of the servo-written pattern. This trimming of the C-burst and writing of the D-burst created a common edge position or “boundary” between the two bursts.
In FIG. 4(d), a B-burst has been added and the A-burst trimmed in the fourth servowriting step of the servowriter. At a point in time after the servowriting is complete, such as during normal operation of the disk drive, the upper edge of the B-burst and the lower edge of the A-burst can be used by the servo, along with the graycoded track-number whose radial center is aligned with the burst edges, to determine the R/W head position when it is in the vicinity of the center of that servo track. If a reader evenly straddles the A-burst and the B-burst, the amplitude of the signals from the two bursts will be approximately equal and the fractional Position-Error Signal (PES) derived from those bursts will be about 0. If the reader is off-center, the PES will be non-zero, indicating that the amplitude read from the A-burst is either greater than or less than the amplitude read from the B-burst, as indicated by the polarity of the PES signal. The position of the head can then be adjusted accordingly. For instance, a negative PES might indicate that the amplitude read from the A-burst is greater than the amplitude read from the B-burst. In this case, the head is too far above the center position (using the portion of the pattern in the figure) and should be moved radially downward/inward until the PES signal is approximately 0. It should be noted that for other portions of the pattern a B-burst could be above an A-burst, resulting in a smaller amplitude contribution coming from the A-burst when the head is too near the outer diameter of the disk(s).
FIGS. 4(e) and 4(f) show the results of subsequent steps of the servowriting process, which has produced a number of servo tracks. After the first step in this process, each subsequent step writes one servo burst in a wedge and trims another. Every second step also writes digital information, including the SAM and track number. Between servowriting steps, the servowriting head is stepped by one-half servo track radially, either toward the inner diameter (ID) or outer diameter (OD) of the disk(s), depending on the radial direction used to write the servo information. A seek typically takes anywhere from one quarter to one half of the time it takes for the disk(s) to make one revolution. The process of writing the servo pattern for each step typically takes one or two full revolutions to write all of the wedges in that pass. It is possible that completing the burst writing and trimming for a single servowriting step can take more than two revolutions, but a maximum of two revolutions (one to write the new burst, and another to trim a previously-written burst) will be considered for the discussion below.
Using such an algorithm, servowriting can take about 1.25–2.5 revolutions per servowriting step. Since there are two servowriting steps per servo-track in this example, and 1.5 servo tracks per data-track, such a process requires 3 servowriting steps per data-track, or 3.75–7.5 revolutions per data-track. For purposes of subsequent discussion only, it will be assumed that the process takes 4 revolutions per data-track (a relatively low bound).
A disk drive can have tens of thousands of data tracks. With 100,000 data-tracks and a spin-speed of 5400 RPM (90 Hz), for example, the process would take 4,444 seconds, or about 75 minutes. If the process is carried out on an expensive servowriter, this can add substantially to the cost of the drive. Thus, drive manufacturers are motivated to use self-servowriting techniques to reduce or eliminate the time that a drive must spend on a servowriter.
One such technique uses a media-writer to write servo patterns on a stack of disks. Each disk is then placed in a separate drive containing multiple blank disks, such that the drive can use the patterned disk as a reference to re-write servo patterns on all of the other disk surfaces in the drive. The media-writer can be an expensive instrument, and it may still take a very long time to write a reference pattern on the stack of disks. However, if a stack contains 10 blank disks, for example, then the media-writer can write the reference pattern for 10 drives in the time that it would have taken to servowrite a single drive. This scheme is a member of a class of self-servowriting techniques commonly known as “replication” self-servowriting. A typical replication process, in which a drive servos on the reference pattern and writes final servo patterns on all surfaces, can take place while the drive is in a relatively inexpensive test-rack, connected to only a power-supply. The extra time that it takes is therefore usually acceptable.
Another class of self-servowriting techniques is known as “propagation” self-servowriting. Schemes in this class differ from those in the “replication” class in the fact that the wedges written by the drive at one point in the process are later used as reference wedges for other tracks. These schemes are thus “self-propagating”. Typically, such schemes require a R/W head that has a large radial offset between the read and write elements, so that the drive can servo with the read element over previously-written servo wedges while the write element is writing new servo wedges. In one such application, a servowriter is used for a short time to write a small “guide” pattern on a disk that is already assembled in a drive. The drive then propagates the pattern across the disk (as described for example, in U.S. Pat. No. 6,631,046 entitled “Servo Track Writing Using Extended Copying with Head Offset”). In this type of self-servowriting operation, previously written tracks can later serve as reference tracks.
Many self-servowriting techniques require considerably more than four disk revolutions per data-track written, as the drive must spend considerable time before each servowriting step determining the written-in runout of the corresponding reference track, so that the servowriting head can be prevented from following that runout while writing the final servo pattern. Techniques exist which allow tracks of servo information to be made substantially circular, despite the fact that the reference information is not perfectly circular. The information used to remove written-in runout from the track can be calculated in one approach by examining a number of parameters over a number of revolutions. These parameters can include wedge offset reduction field (WORF) data values calculated by examining the measured PES over a number of revolutions of a track, as well as the servo loop characteristics. A measurement can be made to characterize servo loop characteristics, which can be combined with the observed PES in order to determine the written-in runout of the reference track. Because the servo typically suffers both synchronous and non-synchronous runout (sometimes referred to in the industry as “repeatable” runout (RRO) and “non-repeatable” runout (NRRO), respectively), any measurement intended to determine the synchronous runout can be affected by the non-synchronous runout. If many revolutions of PES data are observed and combined (one possible approach to combine is to synchronously average the PES data, another possible approach is outlined in U.S. Pat. Nos. 6,069,764, 6,437,936, 6,563,663 and 6,449,116), the effects of the non-synchronous runout can lessen, leaving substantially only synchronous runout. Observing many revolutions of PES data, however, can add significantly to the time required for determination of the written-in runout. Process engineers may need to balance the cost and benefit of additional revolutions of PES data collection in determination of WORF values.
The computed written-in runout values for each servo wedge can be written into the servo wedges themselves for later use by the servo, or can be kept in drive controller memory for immediate use. During a self-servowriting operation, the drive may use the latter option by measuring the written-in runout on a reference track and applying it to the servo by the use of a table in controller memory. Additional revolutions of PES measurements for the reference track can be used to reduce the effects of non-synchronous runout.
As previously described, techniques for determining and removing written-in runout of a track will hereinafter be referred to as WORF technology. If, for example, a drive spends 5 revolutions to determine the written-in runout of each reference track before writing the corresponding final wedges, that would add 15 revolutions to the writing time of each data-track (5 extra revolutions per servowriting step, times 3 servowriting steps per data-track), bringing the total time per data-track to 19 revolutions.
Even though the self-servowriting time may be as much as about five times as long as the time necessary to servowrite a drive on a servowriter (19 revolutions/data-track, versus 4 revolutions/data-track), self-servowriting is likely to be a less expensive alternative due to the expense of servowriters, as well as the fact that servowriting operations on a servowriter generally must be performed in a clean-room environment. Also, as track-densities get higher it becomes more difficult for an external device such as an actuator push-pin to control the position of the R/W heads accurately enough to produce a servo pattern with sufficiently small written-in runout. The expense of servowriting also rises in proportion to the number of tracks on a drive.
In various embodiments of the present invention, the reference pattern can be, but is not limited to, a printed media servo pattern, or a spiral pattern. The spiral pattern is discussed in detail in U.S. Pat. No. 5,668,679 entitled “System for Self-Servowriting a Disk Drive”, by Paul A Swearingen, et al, filed Dec. 21, 1995. The printed media servo pattern will be utilized to illustrate the present invention in the following discussions.
In a drive system that can be used in accordance with embodiments of the present invention, a surface of a magnetic disk 500 can contain a printed magnetic pattern 502. That magnetic disk can be placed in a drive that may contain other magnetic disks 504, 506 in a disk stack, such as the example stack shown in FIG. 5. The surface of the disk 500 having the printed magnetic pattern 502 can be used as a reference for use while writing final wedges to all disk surfaces in the drive. The printed pattern can be used as a reference for information such as timing information, circumferential position information, and/or radial position information for the disk. The use of a printed media pattern as a reference pattern can allow for a reasonable reduction in any repeatable runout written to the reference pattern by reading the printed signal pattern, perhaps over a number of revolutions at each radial location, and calculating the written-in runout. The drive system can then adjust the read/write head position to compensate for the perceived PES obtained from the reference surface in order to effectively remove the written-in runout when replicating the servo pattern. In some embodiments the runout may not be completely removed, but may be adjusted or modified to a pre-determined amount and/or pattern. Note however that it is not necessary for the printed surface to be at one end or the other of the disk-stack as shown in FIG. 5. In fact, it may be desirable to place the printed surface near to the middle of the stack in order to minimize the maximum offset between the head-radius on the reference-surface and that on other surfaces (due to, for example, tilt and other factors). The same applies to FIG. 10 discussed later.
FIG. 6 shows an exemplary printed signal pattern that can be used in accordance with embodiments of the present invention, such as in the exemplary disk stack of FIG. 5. The pattern may include one or more servo wedges, and FIG. 6 shows a reference signal for servo information corresponding to a servo wedge 602 on a disk 600. The signal is shown in a variety of formats. An expanded view 604 of the exemplary magnetization pattern is shown including information for the wedge 602, followed by a signal 606 that could be generated by reading the pattern for the wedge 602. As shown in the Figure, the printed signal pattern contains a preamble, followed by a servo address mark (SAM), and then some digital information, which may include an Index-mark. Following the digital information is a pattern portion referred to as a “zig,” a portion referred to as a “zag,” and an optional timing burst.
FIG. 7 shows a close-up view of an exemplary “zag” phase burst 700. On a local scale, a read element may pass horizontally (in the Figure) across the burst 700. A read/write channel can read such a burst and return both a sine or “real” value 702 and a cosine or “imaginary” value 704. The phase of the burst can then be calculated as: 



  Phase
  =
  
    arctan
    ⁡
    
      (
      
        
          sin
          ⁢
          
            
          
          ⁢
          φ
        
        
          cos
          ⁢
          
            
          
          ⁢
          φ
        
      
      )
    
  




In the “zag” displayed, the magnetization pattern is slanted relative to both the radial direction (vertical in the Figure) and the circumferential direction (horizontal in the Figure). When a read element passes over the slanted burst, the time at which the element encounters the transitions in the burst can be used to determine the radial position of the element. For instance, the “higher up” the read element is in the Figure, or more toward the outer diameter (OD) of the drive, the later the phase transitions are encountered, or the more delayed the phase of the signal. The phase determination can be simplified using both a “zig” and a “zag,” or regions with different or opposite slants or phases, such that the relative phase between the two can be examined, wherein the angles of the zig and zag do not have to be exactly opposite of one another. In this way, absolute phase is not an issue as the drive system can look at the relative phase of the two bursts and can get the radial position for each cycle. If the drive goes through multiple cycles, the drive can track the number of cycles encountered while traversing the disk surface from a known reference-point, as disclosed in U.S. patent application Ser. No. 10/732,638, entitled “Methods for Improving Printed Media Self-servo Writing”, by Richard Ehrlich, filed Dec. 10, 2003.

One process utilizing the zig/zag phase bursts is shown in the diagram of FIG. 12. In such a process, a magnetic pattern is created on a disk surface, such as by printing or servowriting, which contains phase bursts for each track of servo information at step 1200. The phase bursts can include zig and zag bursts, and can be included for each or any wedge in the magnetic pattern. A read element, such as on a read/write head, can be passed over at least a portion of a track of servo information, such as a portion corresponding to a servo wedge at step 1202. The relative phase of at least two phase bursts, such as a zig and a zag for a wedge along a track, can be examined at step 1204. The radial position of the read element relative to the magnetic pattern can be determined using the relative phase at step 1206. The radial position can be used to adjust the head position(s) when replicating that portion of the pattern, either to the same surface or to any other surface in a drive or disk stack at step 1208. For instance, if the radial position of a burst for a wedge is too far towards the outer diameter of the pattern, that burst can be moved toward the inner diameter of the pattern when replicated. Several passes of the head over the pattern can be taken to reduce the error in the radial position determination.
Certain processes can be executed initially to determine the runout, as it may be desirable to remove the runout, lessen the amount of runout, or alter the runout to a desired amount. Utilizing WORF calculations is one approach that can be used to determine the amount of runout by taking into account the servo characteristics and determining how much runout was present before the servo tried to remove the runout. After the runout is measured, the amount of runout can be determined and removed.
When decoding phase bursts, a drive system can use an algorithm that takes an arc tangent of the real and imaginary parts of a discreet Fourier transform (DFT) of the burst signal. Existing channels are capable of sampling the signal and doing a discreet Fourier transform. One such discreet Fourier transform that can be used is given as follows: 



  
    F
    k
  
  =
  
    
      ∑
      
        n
        =
        0
      
      
        N
        -
        1
      
    
    ⁢
    
      
    
    ⁢
    
      
        f
        n
      
      ⁢
      
        e
        
          
            -
            j2π
          
          ⁢
          
            
          
          ⁢
          k
          ⁢
          
            n
            N
          
        
      
    
  




In this equation, fn is the sequence in time and Fk is the Fourier component in frequency space. This “complex” math can be simplified in at least a few situations. For example, a signal can be examined at one quarter of the sample rate. The signal can also be examined at up to one half the sample rate using a Nyquist theorem-based approach. These samples can be taken at any appropriate location or interval, such as at or between signal peaks, etc. If the signal 800 is examined at one quarter the sample rate, as shown in FIG. 8 with an “x” marking each sample location, the coefficients are either +1, 0, or −1. In this case, the real part of the Fourier transform multiplies the signal by +1, 0, −1, 0, . . . and the imaginary part multiplies the signal by 0, +1, 0, −1 . . . , the imaginary part being offset by one sample from the real part. Therefore, each sample is adding to, subtracting from, or not affecting the result. An alternative approach is to use coefficients of +1, −1, −1, and +1 for the real part, and +1, +1, −1, −1 for the imaginary part, which can provide for greater immunity to noise since all samples will contribute to the sum. The discreet Fourier transform can then be reduced to an “adder” with no multiplication. A discreet Fourier transform of the signal then can be broken down into real and imaginary parts, which can each be squared and added together. The square root of this sum yields the magnitude of the signal. Alternatively, a ratio of the real and imaginary parts can be taken, and an arctangent of the ratio can yield the phase, such as using the arctan equation given above. Using the phase, the system can determine the radial position Note that such DFT-based burst processing does not consider the fact that the frequency of the printed-media signal is very low, and the signal may actually need to be sampled much more often than 4 times per cycle to allow the use of the analog filtering circuitry of the channel (which is designed to deal with much higher-frequency signals). In such a case, additional DSP filtering may be required to filter the signal so that it can be re-sampled at the 4-times-per-cycle rate as described above. A modern disk-drive Read/Write channel can easily include the necessary DSP filtering circuitry as described in U.S. Pat. No. 6,738,205.

In some drives, it may be necessary to erase any pre-existing “final wedges” or any signals in the final-wedge area. Such an erase procedure can be used, for example, on a “virgin” drive or for a re-scan in a self-scan process. In a virgin drive, or a drive to which no data has been written, it may still be desirable to erase the final wedge area to ensure that no signal exists on the surface of the disk(s). An erase final wedge process can be run on all cylinders in a drive.
After running WORF calculations on a reference track, the measured position can be calculated. In one embodiment, as shown in FIG. 9, the phase of the “zig” burst 900 and the phase of the “zag” burst 902 can be measured. The difference between the phases can be multiplied by a number of tracks per cycle to obtain the measured radial position. For example, one way to calculate the measured position from the relative phases of the bursts can utilize a formula such as:

Measured Position=tracksPerCycle*(Φzig−Φzag)

where Φzig and Φzag can be a function of the phase for the “zig” and “zag” bursts, respectively, covering both linear and non-linear uses of the burst-phase. In some embodiments, Φzig (and/or Φzag) may also be functions of the overall radial position. That is, they may vary across the stroke of the drive, according to the parameters of the printed pattern. In other embodiments, Φzig and Φzag may simply be proportional to the phases of their corresponding bursts.

A position error signal (PES) then can be calculated for each wedge. PES can be a function of the location of a read/write head or element relative to a disk surface. Once a write element is at the proper radial location, or within acceptable radial boundaries, the final wedges can be written. Wedges can be written using an approach such as a “stagger” approach or a “concurrent” approach. For example, in one such system a pre-amplifier allows concurrent writing to all heads, or some of the heads, in a drive. If the drive system does not contain such a pre-amplifier, a final wedge can be written for one head. The drive can then switch heads and write for another head, or for a group of heads. This “stagger” approach may require the drive system to know, and be able to deal with the fact, that wedges are offset in time for certain heads.
One limitation of existing printed media self-servowrite approaches results from the use of optical lithographic processes to create pattern masters. While such processes are generally cost effective, the minimum feature sizes can be limited. The limitations for such processes are currently around the 0.3 micron feature size, which can be much larger than the space between transitions on a final servo pattern. Therefore, optical lithographic processes are often used to print a single reference pattern instead of each final pattern. Not only is printing a single surface cheaper than printing all surfaces in a drive, but using a reference pattern for self-servowrite avoids the use in final wedges of a low-frequency pattern that does not make efficient use of the space on the disk(s). Low-frequency patterns can be noisy, and servoing on a low-frequency printed reference disk can also increase the likelihood of synchronous runout. While much of this synchronous runout can be removed using WORF technology, there can also be non-synchronous runout due to disturbances such as air turbulence and noise on the position signal. PES noise on the position signal of a final wedge pattern can typically be a very small fraction of the non-synchronous runout, compared with other sources such as air turbulence spindle runout and other disturbances external to the drive.
In a printed media pattern, PES noise can be the dominant source of non-synchronous runout, which can be significantly more difficult to remove than synchronous runout, due to the low frequency of the printed media pattern. While multiple revolutions of WORF calculations can permit the determination and subsequent removal of much of the synchronous runout, the non-synchronous runout can remain. If the PES is very noisy, several revolutions may be necessary to determine the synchronous runout, as the noise can contaminate the signal. The fact that there can be a lot of noise on the position error signal is itself a limitation to printed media self-servowrite. The number of wedges also can be limited in a printed pattern due to the low-frequency aspect of the pattern.
Timing Eccentricity
A printed media pattern can have a substantial frequency variation due to factors such as a mis-centering of the pattern. As a result, the amount of time between printed pattern wedges encountered by a read element can also vary due to the mis-centering, causing a disk in a drive to exhibit so called timing eccentricity in addition to radial runout. It can be desirable to remove any timing eccentricity, as having uniform spacing (and thus equal amount of time) between wedges of a pattern can make it easier to format the drive.
Under the printed-media self-servowriting approach, the final servo pattern is written directly based the printed media pattern. In order to remove timing eccentricity under such approach, ample space should be reserved between the ends of mis-centered and thus non-uniformly-spaced printed pattern wedges so that there would be enough space between them to accommodate both the timing eccentricity and the final servo pattern wedges that should be uniformly spaced (and thus timed). As a result, the timing of the final wedges may vary, relative to that of the printed wedges because the timing eccentricity introduced by the mis-centering of the printed disk on the spindle of the drive has been taken out. Such final-wedge-to-next-printed-wedge timing may vary roughly sinusoidally around the disk(s). Leaving enough room to accommodate such timing variation across the stroke may have several undesirable consequences:

    
    
        It may limit the sample rate of the printed-media pattern (and therefore, the sample rate of the final pattern).
        It may limit the maximum extent (length) of a printed-media wedge, which in turn limits the extent of the zig/zag bursts that can be used to determine the PES noise. As explained in earlier sections, PES noise can be a major determining factor in the quality (RRO) of final wedges.
    
    


Instead of just leaving enough room (unused by printed-media pattern) to accommodate maximum timing variations of final wedges at all radii, one embodiment of the current invention tries to deal with this problem by introducing one or more extra pairs of zig/zag bursts that may be overwritten by final wedges (at certain circumferential locations) near the ID, but may remain unharmed (even after the PM-SSW process is finished) at the OD. Such extra servo bursts insertion approach is based on the following observations:

    
    
        The PES noise of a printed-media pattern tends to vary significantly from the OD (where it is very severe) to the ID (where it is less severe, perhaps by as much as a factor of two). Therefore, a longer extent of a printed-media wedge is often required in order to measure the PES at the OD than is required at the ID.
        Since disk mis-centering usually causes a fixed amount of spatial displacement, the timing variation of final wedges necessary to completely take out the timing eccentricity due to disk mis-centering is roughly inversely proportional to the radius and as the result, is much smaller (by about a factor of two) at the OD than at the ID.

Therefore, by inserting one or more extra pairs of zig/zag bursts near the OD, the proposed approach is capable of effectively measuring the high-noise PES while still reserving enough space there to take out the timing eccentricity due to disk mis-centering at the OD.

    
    


FIG. 13 shows an exemplary printed signal pattern with a pair of extra zig/zag bursts inserted in accordance with embodiments of the present invention. The pattern may include one or more servo wedges such as wedge 1302 and 1304, each containing a preamble, a SAM, an Index-mark followed by a pair of zig/zag bursts 1306 as described earlier. In addition, an extra pair of zig/zag bursts 1308 is inserted to wedge 1302. 1310 and 1312 mark the earliest possible extent of the final wedge at the ID and the OD respectively, indicating that the inserted pair of bursts may be overwritten by the final wedge near the ID. 1314 marks the latest possible extent of the wedge across all radii.
An exemplary printed media self-servowriting process using extra pair(s) of servo bursts is shown in FIG. 14. Printed servo pattern wedges can be printed to a disk surface at step 1400, which due to the mis-centering, can be non-uniformly spaced. One or more extra pair of servo bursts can be inserted for each wedge in the printed pattern at step 1402. Once the pattern printed, step 1404–1408 can be executed repeatedly. The printed pattern can be read by the read element of a read/write head at step 1404 and the position of the read/write head can be adjusted at step 1406 based on the measured PES. Final wedges of a final pattern can then be written between the printed wedges at step 1408, wherein the final wedges are uniformly spaced among themselves and non-uniformly spaced with the printed wedges in order to taken out the timing eccentricity suffered by the printed media pattern. Since the timing eccentricity is small near the OD, there should be enough space to write the final wedges without damaging the inserted extra pair of bursts near the OD. However, the extra pair of bursts near the ID may be over-written by the final wedges in order to completely take out the severe timing eccentricity near the ID.
In some embodiments, the printed media self-servowriting process can switch from using the extra bursts to not using them as shown in FIG. 15. The self-servowriting process is started at step 1500 from OD towards ID. A read element of a read/write head can read both pairs of the servo bursts in the printed pattern at step 1502 near the OD and adjust the head position based on measured PES at step 1504. The process can then decide when to switch from servoing on both pairs of the servo bursts to servoing the original pair of servo bursts only at step 1506. The point (radius) of switching can be determined on a disk-by-disk basis as discussed below, and the decision should be made long before the process gets to the point where the extra pair of bursts is overwritten by the final wedges (For some disks with low eccentricity for example, the switch may not be necessary since both pairs of servo bursts can be preserved and servoed upon across the entire stroke). The process can then switch to read on the original pair of servo bursts only at step 1508. If the SSW process starts at the ID, then the servo would start out using only one pair of bursts, and switch to using two pairs of bursts when it is determined to be safe to do so.
The objective of the self-servowriting processes described above is to minimize the maximum PES noise encountered at any radius by arranging the extra bursts in such a way that the PES noise starts out at its lowest point at the ID, goes up until it reaches a maximum value, then drops (because of the extra bursts used at that radius and beyond), and rises again until it reaches that same maximum value exactly at the OD, as shown in FIG. 16. In situations for which the PES noise of the printed-media pattern is not the dominant factor in determining the written-in runout of the final wedge pattern, a more complex optimization may be necessary. Such an optimization would need to balance the variations of PES noise and other major TMR sources with radius. There is still likely to be a radius beyond which it makes sense to use extra bursts and below which it makes sense to allow them to be overwritten.
Measured in angular displacement, the maximum amount of space ΘPM0 allowed for the base printed media (PM) wedge without the extra servo bursts can be constrained by the wedge-to-wedge space ΘWW, the final-wedge space ΘFW, the maximum allowed eccentricity DE, and the ID radius RI, by the following formula:

Ri*[ΘPM0+ΘFW]+DE=ΘWW*RI 

As shown in FIG. 17 the maximum space ΘPME allowed for a PM wedge with the extra pair of bursts is related to the radius RX beyond which where the extra pair of bursts will not be overwritten by final wedges even with maximum allowed eccentricity by the following formula:

RX*[ΘPM0+ΘPME+ΘFW]+DE=ΘWW*RX 

When ΘPM0 is constrained, this formula yields a relationship between RX and ΘPME.

In some embodiments, the following simplifying assumptions can be made to predict how the PES noise may vary with total burst-length and radius for a conservative estimate of the benefits of using these extra bursts near the OD.

    
    
        With all other parameters being equal, the PES noise at a given radius is proportional to that radius.
        The space occupied by printed-media preamble, SAM, INDEX, etc. are negligible compared to printed-media bursts.
        At a given radius, the PES noise drops in inverse proportion to the square-root of the total burst-length (i.e., if the total burst-length is doubled by extra bursts that are as long as the original bursts, the PES noise can be cut by a factor of √{square root over (2)}).
        The radius at OD RO is exactly twice the radius at ID: RO=2*RI. 
        ΘFW is very small and negligible.
        DE is exactly equal to half of the wedge-to-wedge space at ID, so that ΘPM0=0.5* ΘWW. 

Under these assumptions, the PES noise at radius r, PESNOISE(r), can be calculated as: 



  
    PESNOISE
    ⁡
    
      (
      r
      )
    
  
  =
  
    {
    
      
        
          
            
              K
              ⁢
              
                r
                
                  R
                  I
                
              
            
            ;
          
        
        
          
            r
            ≤
            
              R
              X
            
          
        
      
      
        
          
            K
            ⁢
            
              r
              
                R
                I
              
            
            ⁢
            
              
                
                  Θ
                  
                    PM
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                
                
                  
                    Θ
                    
                      PM
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                  +
                  
                    Θ
                    PME
                  
                
              
            
          
        
        
          
            r
            >
            
              R
              X
            
          
        
      
    
    }
  




i.e., the PES noise rises in proportion to the radius (with constant of proportionality, K), until it gets to radius, RX, when it suddenly drops by the inverse of the square-root of the factor by which the overall bursts are lengthened by the extra bursts inserted. From that point on, the PES noise continues its rise in proportion to the radius. To minimize the maximum PES noise value, PESNOISE(RX) should be equal to PESNOISE(RO), and the constraint ends up being: 



  
    
      
        (
        
          
            R
            O
          
          
            R
            X
          
        
        )
      
      2
    
    +
    
      
        1
        2
      
      ⁢
      
        (
        
          
            R
            O
          
          
            R
            X
          
        
        )
      
    
    -
    2
  
  =
  0




which is solved by 



  
    (
    
      
        R
        O
      
      
        R
        X
      
    
    )
  
  =
  
    
      
        -
        
          1
          4
        
      
      ±
      
        
          8
          +
          
            1
            4
          
        
      
    
    ≈
    1.186
  




or (RX/RO) ̃0.84, i.e., about 70% of the way from the ID to the OD. At this radius, the extra bursts add about 40% to the total PM-pattern length and reduce the worst-case PES noise by about a factor of √{square root over (1.4)} (i.e., an 18% reduction) by using the extra bursts, which is a significant improvement.

    
    


Although embodiments described herein refer generally to systems having a read/write head that can be used to write bursts on rotating medium (magnetic media), similar advantages can be obtained with other such data storage systems or devices. For example, a laser writing information to an optical media can take advantage of additional passes when writing position information. Any media, or at least any rotating media in a single and/or multi-headed disk drive, upon which information is written, placed, or stored, may be able to take advantage of embodiments of the present invention.
The foregoing description of preferred embodiments of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to one of ordinary skill in the relevant arts. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications that are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalence.

## Claims

1. A method for printed media self-servowriting, comprising:
printing a printed media pattern on a surface of a rotatable medium having a plurality of servo tracks, wherein the printed media pattern includes one or more wedges and each of the one or more wedges includes at least one of a preamble, a SAM, an index-mark, and includes one or more zig/zag bursts;
positioning a read/write head relative to the surface of the rotatable medium;
servoing on different numbers of the one or more zig/zag bursts near OD versus near ID in each of the one or more wedges in the printed media pattern via the read/write head;
writing a final pattern based on the printed media pattern via the read/write head.

2. The method according to claim 1, wherein:
the printed media pattern can have higher PES noise and/or lower timing eccentricity near the OD than near the ID.

3. The method according to claim 1, wherein:
the one or more wedges in the printed media pattern can be non-uniformly spaced and/or have timing eccentricity.

4. The method according to claim 1, further comprising:
adjusting the position of the read/write head after servoing on at least one of the one or more zig/zag bursts in each of the one or more wedges in the printed media pattern.

5. The method according to claim 1, further comprising:
determining a radius such that:
more than two of the one or more zig/zag bursts in each of the one or more wedges in the printed media pattern can be used to determine the PES for radii between the radius and the OD; and
only one or two of the one or more zig/zag bursts in each of the one or more wedges in the printed media pattern can be used to determine the PES for radii between the ID and the radius.

6. The method according to claim 5, further comprising:
writing a wedge on the one or more wedges in the final pattern in place of at least one of the one or more zig/zag bursts in each of the one or more wedges in the printed media pattern between the radius and the ID.

7. The method according to claim 1, further comprising:
writing the one or more wedges in the final pattern to be uniformly spaced.

8. The method according to claim 1, further comprising:
writing each of the one or more wedges in the final pattern to be separated from an adjacent wedge in the printed media pattern at non-fixed spacing and timing.

9. The method according to claim 1, further comprising:
writing each of the one or more wedges in the final pattern to be smaller in size than a wedge in the one or more wedges in the printed media pattern.

10. The method according to claim 1, further comprising:
writing the final pattern to have essentially the same or higher number of wedges than the printed media pattern.

11. The method according to claim 1, further comprising:
writing the final pattern to have essentially the same or higher sample rate than the printed media pattern.

12. A system for printed media self-servowriting, comprising:
a rotatable medium including a surface having a plurality of servo tracks operable to store at least a printed media pattern and a final pattern, wherein the printed media pattern includes one or more wedges and each of the one or more wedges includes at least one of a preamble, a SAM, an index-mark and includes one or more zig/zag bursts;
a read/write head including:
a read element operable to read one of the printed media pattern and the final pattern; and
a write element operable to write one of the printed media pattern and the final pattern; and

one or more controllers operable to:
position the read/write head relative to the surface of the rotatable medium;
servoing on different numbers of the one or more zig/zag bursts near OD versus near ID in each of the one or more wedges in the printed media pattern via the read/write head;
write the final pattern based on the printed media pattern via the read/write head.

13. The system according to claim 12, wherein:
the rotating medium can be a magnetic disk, an optical disk, laser-recordable disk, a disk in a single and/or multi-headed disk drive, or a rotating data storage device.

14. The system according to claim 12, wherein:
the zig burst and the zag burst in the one or more zig/zag bursts can have different phases.

15. The system according to claim 12, wherein:
the printed media pattern can have higher PES noise and/or lower timing eccentricity near the OD than near the ID.

16. The system according to claim 12, wherein:
the one or more wedges in the printed media pattern can be non-uniformly spaced and/or have timing eccentricity.

17. The system according to claim 12, wherein:
the one or more controllers are further operable to adjust the position of the read/write head after servoing on at least one of the one or more zig/zag bursts in each of the one or more wedges in the printed media pattern.

18. The system according to claim 12, wherein:
the one or more controllers are further operable to determine a radius such that:
more than two of the one or more zig/zag bursts in each of the one or more wedges in the printed media pattern can be used to determine the PES for radii between the radius and the OD; and
only one or two of the one or more zig/zag bursts in each of the one or more wedges in the printed media pattern can be used to determine the PES for radii between the ID and the radius.

19. The system according to claim 18, wherein:
the one or more controllers are further operable to write a wedge in the one or more wedges in the final pattern in place of at least one of the one or more zig/zag bursts in one of the one or more wedges in the printed media pattern between the radius and the ID.

20. The system according to claim 12, wherein:
the one or more wedges in the final pattern can be uniformly spaced.

21. The system according to claim 12, wherein:
each of the one or more wedges in the final pattern can be separated from an adjacent wedge in the printed media pattern at a non-fixed spacing and timing.

22. The system according to claim 12, wherein:
a wedge in the one or more wedges in the final pattern can be smaller in size than a wedge in the one or more wedges in the printed media pattern.

23. The system according to claim 12, wherein:
the final pattern can have essentially the same number of wedges and the same sample rate as the printed media pattern.

24. A system for printed media self-servowriting, comprising:
means for printing a printed media pattern on a surface of a rotatable medium having a plurality of servo tracks, wherein the printed media pattern includes one or more wedges and each of the one or more wedges includes at least one of a preamble, a SAM, an index-mark and includes one or more zig/zag bursts;
means for positioning a read/write head relative to the surface of the rotatable medium;
means for servoing on different numbers of the one or more zig/zag bursts near OD versus near ID in each of the one or more wedges in the printed media pattern via the read/write head;
means for writing a final pattern based on the printed media pattern via the read/write head.