Abstract:
A method and apparatus for testing a magnetic medium. The method comprises applying a magnetic field of a time-varying strength; directing a polarized optical beam towards a portion of the medium that is in the magnetic field, wherein the optical beam is reflected by a surface of the medium at a point of incidence in the magnetic field; moving the medium relative to the optical beam so as to cause the point of incidence to repeatedly traverse each of a plurality of sectors along a track on the surface; obtaining a series of Kerr signal measurements of the reflected optical beam; grouping measurements into ensembles such that the measurements in an individual ensemble are those obtained while the point of incidence was in a corresponding one of the sectors; and determining at least one magnetic property of at least one of the sectors from the measurements in the corresponding ensemble.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is the National Stage of International Application No. PCT/SG2008/000299, filed Aug. 13, 2008, entitled “METHOD AND APPARATUS FOR TESTING MAGNETIC PROPERTIES OF MAGNETIC MEDIA,” listing Chengwu An and Kaidong Ye as the inventors, which claims the benefit under 37 U.S.C. 119(e) of U.S. Provisional Application No. 60/935,433, filed Aug. 13, 2007, to An et al., hereby incorporated by reference herein. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to the testing of magnetic media and, in particular, to a method and apparatus for dynamically testing magnetic properties of magnetic media including magnetic disks. 
     BACKGROUND 
     Magnetic media, such as computer hard disks, rely on magnetic properties to store data. To ensure that the disks meet certain standards of quality, these magnetic properties need to be tested from time to time, particularly during the manufacturing process. 
     Two important magnetic properties of interest include remanence and coercivity. Coercivity (typically expressed in oersteds) refers to the intensity of an applied magnetic field required to reduce the magnetization of a sample of ferromagnetic material to zero after the magnetization of the sample has been driven to saturation. For its part, remanence (typically expressed in ampere/m) refers to the magnetization left behind in the sample after an external magnetic field is removed. 
     The coercivity and remanence of a disk can be measured in the following way. A magnetic field is applied to the disk with a certain sweep rate from a positive value to a negative value and then back to its original positive value. A polarized laser beam is shone towards the disk surface at a point of interest that is subjected to the magnetic field. The beam is reflected by the disk surface. Due to what is known as the magneto-optic Kerr effect (MOKE), the reflected beam will undergo an amount of polarization rotation that depends on the magnetic properties of the disk surface. The component of the reflected beam exhibiting a changed polarization angle is known as the “Kerr signal”. The Kerr signal is sampled many times during the sweeping of the magnetic field and a hysteresis loop is plotted from the acquired measurements. From this, the corecivity and remanence of the magnetic disk (at the point of interest) can be determined. To determine the coercivity and remanence of the magnetic disk at a second or subsequent point of interest on the surface of the disk, the disk position is changed and the process is repeated. 
     Since sweeping of the magnetic field takes several seconds, it is clear that testing numerous points of interest (e.g., different sectors of a track) can take minutes if not hours. This length of time for testing a single disk can be considered inefficient. Thus, there is a need in the industry for an apparatus and method for testing the magnetic properties of a magnetic medium by virtue of which multiple regions of the medium can be tested more efficiently. 
     SUMMARY OF THE INVENTION 
     In what will be described below in greater detail, there is provided a method for dynamically mapping magnetic coercivity and remanence of hard disk media using the magneto-optical Kerr effect described above. In this method, the magnetic disk is spun while an applied magnetic field is swept and a Kerr signal is being acquired. The overall effect is that the captured data is not just from one point but from a ring (track) which is subdivided into actual or conceptual sectors. The spin angle, the applied magnetic field and the sampling of the Kerr signal are all synchronized in phase. The acquired Kerr signal data is then segmented on a per-sector basis for each revolution, and the results for the same sector over multiple revolutions forms an ensemble. Each ensemble is then used to determine the coercivity and remanence of the concerned sector, and then a distribution of the coercivity and remanence for various sectors of the track is conveyed (e.g., graphically). The time taken for taking measurements for all sectors on one track (with each track consisting of multiple points along an arc length) is roughly the same time that would be required for taking measurements for just one point on the track in conventional approaches. 
     Accordingly, a first aspect of the present invention seeks to provide an apparatus for testing a magnetic medium, comprising:
         a magnetic field generation sub-system configured to apply a magnetic field of a time-varying strength to a portion of the magnetic medium;   a light generation sub-system configured to direct a polarized optical beam towards the portion of the magnetic medium that is in the magnetic field, wherein the optical beam is reflected by a surface of the magnetic medium at a point of incidence in the magnetic field;   a motion sub-system configured to move the magnetic medium relative to the optical beam so as to cause the point of incidence to repeatedly traverse each of a plurality of sectors along a track on the surface of the magnetic medium;   a measurement sub-system configured to obtain a series of Kerr signal measurements of the reflected optical beam; and   a control sub-system configured to group the series of Kerr signal measurements into ensembles such that the Kerr signal measurements in an individual ensemble are those obtained while the point of incidence was in a corresponding one of the sectors, the control sub-system being further configured to determine at least one magnetic property of at least one of the sectors from the Kerr signal measurements in the corresponding ensemble.       

     A second aspect of the present invention seeks to provide a method of testing a magnetic medium, comprising:
         applying a magnetic field of a time-varying strength to a portion of the magnetic medium;   directing a polarized optical beam towards the portion of the magnetic medium that is in the magnetic field, wherein the optical beam is reflected by a surface of the magnetic medium at a point of incidence in the magnetic field;   moving the magnetic medium relative to the optical beam so as to cause the point of incidence to repeatedly traverse each of a plurality of sectors along a track on the surface of the magnetic medium;   obtaining a series of Kerr signal measurements of the reflected optical beam;   grouping the series of Kerr signal measurements into ensembles such that the Kerr signal measurements in an individual ensemble are those obtained while the point of incidence was in a corresponding one of the sectors; and   determining at least one magnetic property of at least one of the sectors from the Kerr signal measurements in the corresponding ensemble.       

     A third aspect of the present invention seeks to provide an apparatus for testing a magnetic medium, comprising:
         means for applying a magnetic field of a time-varying strength to a portion of the magnetic medium;   means for directing a polarized optical beam towards the portion of the magnetic medium that is in the magnetic field, wherein the optical beam is reflected by a surface of the magnetic medium at a point of incidence in the magnetic field;   means for moving the magnetic medium relative to the optical beam so as to cause the point of incidence to repeatedly traverse each of a plurality of sectors along a track on the surface of the magnetic medium;   means for obtaining a series of Kerr signal measurements of the reflected optical beam; and   means for grouping the series of Kerr signal measurements into ensembles such that the Kerr signal measurements in an individual ensemble are those obtained while the point of incidence was in a corresponding one of the sectors; and   means for determining at least one magnetic property of at least one of the sectors from the Kerr signal measurements in the corresponding ensemble.       

     A fourth aspect of the present invention seeks to provide computer-readable media containing instructions which, when executed by a computing device, cause the computing device to implement a method that comprises:
         receiving a time series of measurements, each measurement potentially representative of a manifestation of a magneto-optic Kerr effect within an individual sector from among a plurality of sectors of a magnetic medium;   grouping the time series of measurements into ensembles of groups of measurements, the groups from different ensembles being time-interleaved, wherein measurements potentially representative of the manifestation of the magneto-optic Kerr effect within an individual one of the sectors are distributed among the groups of measurements from within a same one of the ensembles;   determining at least one magnetic property of plural ones of the sectors from the groups of measurements in the corresponding ones of the ensembles; and   outputting an indication of said at least one magnetic property of said plural ones of the sectors.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  conceptually illustrates the magneto-optic Kerr effect that takes place in a magnetic medium exposed to an externally applied magnetic field. 
         FIGS. 2A through 2C  illustrate different types of magneto-optic Kerr effect depending on polarization direction of the magnetic medium. 
         FIG. 3  is a block diagram of a test bed used to test a magnetic disk having multiple sectors, in accordance with a non-limiting embodiment of the present invention. 
         FIGS. 4A and 4B  conceptually illustrate different orientations of a magnetic pole established by the applied magnetic field. 
         FIG. 5  shows a time series of measurements obtained by the test bed of  FIG. 3  throughout the course of variation of the applied magnetic field. 
         FIG. 6  illustrates identification of an ensemble of measurements corresponding to an individual sector of the magnetic disk. 
         FIG. 7  shows derivation of remanence and coercivity from a hysteresis loop obtained from the ensemble of measurements corresponding to an individual sector of the magnetic disk. 
         FIGS. 8A and 8B  show alternate graphical representations of a particular magnetic property found to be exhibited by the various sectors of a magnetic disk as a result of testing using the test bed of  FIG. 3 . 
         FIG. 9  illustrates a computing unit that can be configured to carry out processing operations and convey the graphical representations of  FIGS. 8A and 8B . 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present invention relate to the testing of magnetic properties of a magnetic medium containing regions on the surface of the medium where data is magnetically written to and read from. Such regions can be referred to as “tracks”, and a “track” can be actually or conceptually subdivided into a plurality of “sectors”. A non-limiting example of a magnetic medium that can be tested using embodiments of the present invention includes a computer hard disk. 
     Before describing an embodiment of the invention in detail, it will be useful to briefly describe the general principle of what is known as the magneto-optical Kerr effect (MOKE), and schematically shown in  FIG. 1 . When an optical beam  10  exhibiting polarization in a “plane of polarization” is incident on a magnetic medium  12  under the influence of an applied magnetic field, the incident optical beam  10  is reflected by the magnetic medium, which results in a reflected optical beam  14  with a polarization in a plane that is rotated an angle of rotation of polarization relative to a reference orientation that would be exhibited in the absence of the applied magnetic field. The angle of rotation of polarization, denoted Φ, is proportional by a factor f to the magnetization of the magnetic medium  12 , where f is dependent on the magnetic medium itself. 
     When the magnetization of the magnetic medium  12  is parallel to the surface of the magnetic medium  12  and in the plane of the incident optical beam  10  (see  FIG. 2A ), this produces a “longitudinal” Kerr effect. When the magnetization of the magnetic medium  12  is parallel to the surface of the magnetic medium  12  but orthogonal to the plane of the incident optical beam  10  (see  FIG. 2B ), this produces a “transverse” Kerr effect. When the magnetization of the magnetic medium  12  is orthogonal to the surface of the magnetic medium  12  and in the plane of the incident optical beam  10  (see  FIG. 2C ), this produces a “polar” Kerr effect. 
       FIG. 3  is a block diagram of an apparatus (a “test bed”)  402  that can be used for testing magnetic properties of a magnetic medium using the aforementioned magneto-optical Kerr effect in accordance with a specific non-limiting embodiment of the present invention. In the present non-limiting example, the magnetic medium being tested is a magnetic disk  404 , however this should not be construed as limiting. The test bed  402  can perform an evaluation of the data recording and storage functionality of the magnetic disk  404 , as characterized by certain magnetic properties (including coercivity and remanence). 
     The test bed  402  can be composed of the following sub-systems that allow the detection and measurement of magnetic properties of a magnetic medium such as the magnetic disk  404 :
         a light generation sub-system for generating an incident optical beam  412  that results in a reflected optical beam  413  upon reflection by the magnetic disk  404 ;   a magnetic field generation sub-system that controls an orientation and a strength of a magnetic field applied at a given time to a portion of a track of the magnetic disk  404  (the “track under test”); and   a motion sub-system that is used to control rotation of the magnetic disk  404  and the track under test;   a measurement sub-system for detecting a Kerr signal indicative of the angle of rotation of polarization Φ of the reflected optical beam  413 ;   a processing sub-system for acquiring the instantaneous values of the applied magnetic field, disk position and Kerr signal, grouping the measurements on a per-sector basis and processing the acquired values in order to obtain the magnetic properties of individual sectors of the track under test.       

     Further details regarding the individual components comprising these sub-systems, as well as an explanation of the operation of the test bed  402 , are provided below in the context of a specific non-limiting embodiment of the present invention. 
     Light Generation Sub-System 
     The light generation sub-system includes an optical beam generation unit, which includes an optical beam system  411 , an optical mirror  414  and a polarizer  415 . The optical beam system  411  generates the incident optical beam  412 , which is directed by an optical mirror  414  through a polarizer  415  onto a surface of the magnetic disk  404 . The polarizer  415  imparts a polarization in a certain plane to the incident optical beam  412  before this beam reaches the surface of the magnetic disk  404  at a point of incidence  419 . The point of incidence  419  identifies the area on the magnetic disk  404  where the incident optical beam  412  meets the surface of the magnetic disk  404  and is reflected as the reflected optical beam  413 . 
     Magnetic Field Generation Sub-System 
     The magnetic field generation sub-system includes a magnetic field driver  423 , a magnetic coil  422 , magnetic poles  421 A,  421 B and an optional field meter (not shown). Generally speaking, the magnetic field generation sub-system is used to generate a magnetic field that is applied to a region of the magnetic disk  404 . In particular, the magnetic field driver  423  determines the orientation and strength of the magnetic field to be applied for testing sectors on a particular track of the magnetic disk  404 . Accordingly, the magnetic field driver  423  controls the signal imparted to the magnetic coil  422 , thereby resulting in the creation of an magnetic field that is applied through the magnetic poles  421 A,  421 B and whose strength is measured and reported by the field meter, which is optional. 
     The magnetic poles  421 A,  421 B are proximate the surface of the magnetic disk  404  and are separated by a gap  424  of length G m . The magnetic poles  421 A,  421 B may be oriented longitudinally or perpendicularly to the magnetic disk  404  so that the gap  424  is aligned for suitability with the recording properties of the magnetic disk  404 . Reference is made to  FIGS. 4A and 4B , which show two example orientations of the magnetic poles  421 A,  421 B relative to a magnetic medium. In  FIG. 4A , the orientation of the magnetic poles  421 A,  421 B suitable for a longitudinal recording medium (such as a magneto-optical disk) is illustrated. In this case, the magnetic poles  421 A,  421 B are oriented parallel to a given track on one side of the medium so that magnetic field generated by the gap  424  covers several sectors of the given track. In  FIG. 4B , the orientation of the magnetic poles  421 A,  421 B suitable for a perpendicular recording medium are illustrated. In this case, the magnetic poles  421 A,  421 B are oriented perpendicularly to the magnetic medium so that the magnetic field generated by the gap  424  covers part of a given track located on both sides of the medium. 
     Motion Sub-System 
     The motion sub-system includes a motion stage  432  and a spindle  431  The motion stage  432  and the spindle  431  are connected to a controller  433  (in the processing sub-system, to be described later), which directs the spindle  431  to spin or stop and the motion stage  432  to acquire a desired lateral position. The spindle  431  is constructed in such a way that its rotation also rotates the magnetic disk  404 , and contains a control mechanism connected to the processing sub-system that reports the spin angle of the spindle  431  (and hence the magnetic disk  404 ). The motion stage  432  is constructed in such a way that its movement translates the spindle  431  in a lateral fashion, which changes the track onto which the incident optical beam  412  is being shone, i.e., this selects the “track under test”. The motion stage  432  may contain a control mechanism connected to the processing sub-system that reports the position of the track under test. 
     Measurement Sub-System 
     The measurement sub-system includes an analyzer  416 , a photo detector  417  and an amplifier  418 . 
     It will be appreciated that the magneto-optical Kerr effect rotates the polarization plane of the reflected optical beam  413  relative to the polarization plane of the incident optical beam  412 , in dependence upon the magnetization of the sector in which the point of incidence  419  is located. The angle of rotation of polarization impacts how the reflected optical beam  413  travels through the analyzer  416  (which in a non-limiting embodiment may be implemented as a polarizer with a high extinction ratio). It should be noted that the optical axis of the analyzer  416  need not be perfectly aligned vertically to the optical axis of the polarizer  415 . In fact, it is noted that when the applied magnetic field decreases from positive to negative, the angle of rotation of polarization of the reflected optical beam  413  will also decrease from positive to negative. If the polarizer  415  and the analyzer  416  are aligned sharply normal in their optical axes, the signal will become stronger no matter whether the rotation angle is positive or negative (i.e., no matter whether a positive or a negative magnetic field is applied). To reflect negative magnetization, an angle offset to the analyzer axis  416  can be useful, which guarantees that one direction of variation of the applied magnetic field, say positive, makes the signal stronger and another direction of variation of the applied magnetic field makes the signal weaker. This offset angle has an optimal range, which is about 4-10 times the maximal Kerr rotation angle, although offset angles outside this optimal range (or no offset angle) can be used without departing from the scope of the present invention. 
     The photo detector  417  converts the intensity of the signal at the output of the analyzer  416  into an analog electrical signal. The output of the photo detector  417  is then supplied to the amplifier  418 , which increases the signal strength prior to sampling by the processing sub-system. The output of the amplifier  418  is hereinafter referred to as the “Kerr signal” and can be expressed in units of milli-degrees, or thousandths of a degree. 
     Processing Sub-System 
     The processing sub-system comprises the aforementioned controller  433 , an analog-to-digital A/D converter  434  and a computing control panel  435 . 
     The controller  433  may be configured as a computing unit  1000  of the type depicted in  FIG. 9 , which includes a processing unit  1002 , data  1004  and program instructions  1006 . The processing unit  1002  is adapted to process the data  1004  and the program instructions  1006  in order to implement at least part of the functionality of the test bed  402 . The program instructions  1006  may be written in a number of programming languages for use with many computer architectures or operating systems. For example, in some embodiments, the program instructions  1006  may be implemented in a procedural programming language (such as “V-C” or “V-B”) or an object-oriented programming language (“Lab-view” or “JAVA”, for example). The computing unit  1000  shown in  FIG. 9  may be part of any suitable computing device including, but not limited to, a desktop or laptop computing device. 
     The computing unit  1000  may include an I/O interface  1010  for receiving data from, or sending data to, external components, such the spindle  431 , the motion stage  432 , the optical beam system  411 , the magnetic field driver  423 , the polarizer  415 , the analyzer  416 , the A/D converter  434  and so on. Additionally, the I/O interface  1010  can be used for receiving a control signal and/or information from a user (not shown) via the computing control panel  435 , as well as for releasing a signal that drives a display unit  1012  and causes it to implement a user interface implemented by the program instructions  1006 . 
     Optionally, the computing unit  1000  may include additional interfaces (not shown) for exchanging information with additional devices, such as a computer network connected via a wired or wireless interface (not shown). 
     The A/D converter  434  may have several channels for synchronous signal acquisition. For example, a first channel could produce samples of the instantaneous Kerr signal received from the amplifier  418 , a second channel could produce samples of the instantaneous magnetic field strength reported by the field meter and a third channel could produce samples of the instantaneous spin angle reported by the spindle  431 . The digital samples (measurements) output from the first channel form a “time series of Kerr signal measurements” that will be denoted {K(i)}. The digital samples (measurements) output from the second channel form a “time series of magnetic field strength measurements” that will be denoted {M(i)}. Finally, the digital samples (measurements) output from the third channel form a “time series of spin angle measurements” that will be denoted {A(i)}. The {K(i)}, {M(i)} and {A(i)} are stored in memory by the controller  433 . The controller  433  processes the {K(i)}, {M(i)} and {A(i)} to determine the coercivity and remanence of the various sectors of the magnetic disk  404 , as will be shown in further detail later on. 
     The computing control panel  435  acts as a user interface that allows a user to view and control the overall operation of the test bed  402 . In particular, the computing control panel  435  is connected to the controller  433  and allows a user (not shown) to set and adjust certain parameters that will be used by the controller  433  during testing of the magnetic disk  404 . For example, the user could use the computing control panel  435  to set the sampling rate of the A/D converter  434 , rotation speed of the spindle  431 , significant values and rate of change of the magnetic field (i.e., the magnetic field profile) to be applied by the magnetic field driver  423 , the position of the track under test, the numbers of sectors that make up the track under test (as well as their position and arc length), etc. It is conceivable that the aforementioned parameters could be saved within the controller  433  in the form of a profile for a given type of magnetic medium. The user could recall this profile in order to use the test bed  402  to test similar media without having to set the parameters again. It should be understood that the computing control panel  435  may be implemented as a separate physical component connected to the controller  433  via a wired or wireless connection, or may be implemented as a graphical user interface by virtue of the program instructions  1006  within the controller  433 . 
     Operation of Test Bed  402   
     With continued reference to  FIG. 3 , operation of the test bed  402  to test the magnetic disk  404  can now be described. A user (human or robotic) attaches the magnetic disk  404  to the spindle  431 . The user then interacts with the computing control panel  435  to start the test bed  402 , enters or recalls from memory any required parameters for the test (such as the rotation speed for the magnetic disk  404 , the sampling rate of the A/D converter  434 , the magnetic field profile, the position of the track under test, the number of sectors that make up the track under test, etc.), and initiates testing of the magnetic disk  404 . Once the test is initiated by the user, the controller  433  activates the test bed&#39;s  402  constituent components. 
     Specifically, the controller  433  activates the motion stage  432  to move the spindle  431  and the magnetic disk  404  to the appropriate position for the track under test. In addition, the controller activates the spindle  431  to spin the disk  404 . During testing, the rotation speed of the magnetic disk  404  is normally kept constant, although persons skilled in the art will appreciate that in some embodiments, the speed of rotation could be allowed to vary, as long as the speed versus time relation is known to the controller  433  and data acquisition synchronization is carried out by the program instructions  1006 . 
     In addition, the controller  433  activates the magnetic field generation sub-system to apply a magnetic field to a portion of the track under test. Specifically, the magnetic field driver  423  energizes the magnetic coil  422  based on the strength and orientation of the magnetic field needed to generate a magnetic field. The magnetic field applied via the magnetic poles  421 A,  421 B (over the gap  424  of length G m ) magnetizes a portion of the track under test. During testing, the applied magnetic field is swept in accordance with the magnetic field profile selected by the user or stored in memory. 
     In addition, the controller  433  causes the light generation sub-system to shine a polarized beam of light onto the currently magnetized portion of the track under test. Specifically, the optical beam system  411  generates the incident optical beam  412  that is directed by the optical mirror  414  to pass through the polarizer  415  before reaching the surface of the magnetic disk  404  at the point of incidence  419 . Naturally, the exact location of the point of incidence  419  within the track under test varies over time as the magnetic disk  404  rotates. Thus, where the track under test is actually or conceptually divided into a plurality of sectors, it will be seen that the point of incidence  419  traverses the various sectors over and over again as the magnetic disk  404  rotates. 
     The amplified output of the photo detector  417  (which captures part of the reflected optical beam  413  admitted by the analyzer  416 ) is sampled by the A/D converter  434 , resulting in the time series of Kerr signal measurements {K(i)}. It is recalled that the Kerr signal is proportional to the magnetization of the magnetic disk  404  at the point of incidence  419 . 
     Meanwhile, the output of the field detector (which indicates the instantaneous strength of the applied magnetic field) is sampled by the A/D converter  434 ; resulting in the time series of magnetic field strength measurements {M(i)}. It is recalled that the applied magnetic field follows a profile that can be user-defined or stored in memory. 
     In addition, the signal received from the spindle  431  (which indicates the instantaneous spin angle of the spindle  431 ) is sampled by the A/D converter  434 , resulting in the time series of spin angle measurements {A(i)}. The spin angle will cycle repeatedly from 0 to 360 degrees as the magnetic disk  404  spins, and allows identification of which actual or conceptual sector contains the point of incidence  419  at a given sampling instant. 
     It should be appreciated that the sampling rate may be controllable and can be synchronized with a trigger signal. Specifically, the trigger signal can be received from the spindle  431  and indicates each new revolution of the magnetic disk  404 . Alternatively, a clock signal can be introduced for timing the sectors. The clock signal is synchronously sampled by another channel of the A/D converter  434 . For the case of 64 sectors, a clock signal of 256 periods per revolution of the spindle  431  could be set. This means that the acquired data in the time of the first 4 periods of the clock signal belongs to the first sector, the data acquired in next 4 periods belongs to the second sector, and so on, up to the 64 th  sector. By tying the clock rate to the spin rate using this alternative approach, one may be able to achieve more reliable results, since measurements taken on the boundary between sectors are less likely to occur. 
     It should be appreciated that by controlling the sampling rate, the speed of rotation of the spindle  431  and the profile of the applied magnetic field, the controller  433  can ensure that at least a set minimum number of Kerr signal measurements K(i) is collected per actual or conceptual sector of the track under test and that the collected Kerr signal measurements K(i) are well distributed over the range of magnetic field strength measurements M(i) for those sampling instants. 
     More specifically, with reference to  FIG. 5 , let the track under test be divided into sixty-four (64) sectors, which can correspond to an actual distribution of sectors or can be a purely conceptual subdivision. The time series of Kerr signal measurements {K(i)} includes “ensembles”  610  of interleaved groups of measurements, where the N th  ensemble (N=1, 2, . . . , 64) is derived from Kerr signal measurements K(i) obtained from the reflected optical beam  413  while the point of incidence  419  was traversing the N th  one of the sectors of the track under test. For example, the ensembles  610  that can be identified from the time series of Kerr signal measurements {K(i)}include an ensemble for sector # 1  (denoted K 1 ), another ensemble for sector # 2  (denoted K 2 ) and another ensemble for sector # 64  (denoted K 64 ). 
     Similarly, the time series of magnetic field strength measurements {M(i)} includes interleaved ensembles  660 , where the N th  ensemble is derived from magnetic field strength measurements M(i) obtained (e.g., from the optional field meter) while the point of incidence  419  was traversing the N th  one of the sectors of the track under test. For example, the ensembles  660  that can be identified from the time series of magnetic field strength measurements {M(i)} include an ensemble for sector # 1  (denoted M 1 ), another ensemble for sector # 2  (denoted M 2 ) and another ensemble for sector # 64  (denoted M 64 ). 
     To identify which measurements in the time series {K(i)} (or {M(i)}) are associated with which of the ensembles  610  (or  660 ), the controller  433  considers the number of sectors of the track under test, the speed of rotation of the magnetic disk  404  and the sampling rate of the A/D converter  434 . Where the sectors (actual or conceptual) are not contiguous and/or are not of equal arc length around the circular track, then adjustments need to be made in order to take these variations into account. 
     Consider now that the magnetic disk  404  turns at forty (40) revolutions per second with an applied magnetic field that sweeps from +10 kOe (ten thousand oersteds) to −10 kOe and back to +10 kOe in a loop lasting 10 seconds (i.e., a sweeping rate of 4 kOe per second). This means that the point of incidence  419  spends 0.390625 milliseconds on each sector, and returns to that sector every 25 milliseconds on a periodic basis. If the desired number of measurements to be taken within a single sector before the point of incidence  419  moves to the next sector is one hundred (100), then the sampling rate needs to be 256,000 measurements per second. It is also noted that the total number of revolutions is 400. 
     Recalling that the individual measurements in the time series of Kerr signal measurements {K(i)} are denoted K(i) (i=0, 1, . . . ), then the average Kerr signal measurement for the p th  traversal (p=1, 2, . . . , 400) of the j th  sector (j=1, . . . , 64) by the point of incidence  419  is denoted K p,j , which is given by: 
     
       
         
           
             
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     One can then form the Kerr signal ensemble for the j th  sector, denoted K j , by grouping together the average Kerr signal measurements K p,j  for all 400 revolutions (p=1, 2, . . . , 400) of the magnetic disk  404 . In other words, K j ={K p,j |1≦p≦400}. This is shown conceptually in  FIG. 6  for the Kerr signal ensemble K 1 , i.e., the Kerr signal ensemble for sector # 1 . 
     Recalling also that the individual measurements in the time series of magnetic field strength measurements {M(i)} are denoted M(i) (i=0, 1, . . . ), then the average magnetic field strength measurement for the p th  traversal (p=1, 2, . . . , 400) of the j th  sector (j=1, . . . , 64) by the point of incidence  419  is denoted M p,j , which is given by: 
     
       
         
           
             
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                         ( 
                         
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                           1 
                         
                         ) 
                       
                       × 
                       100 
                     
                     + 
                     99 
                   
                 
               
               ⁢ 
               
                 
                   M 
                   ⁡ 
                   
                     ( 
                     i 
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                 100. 
               
             
           
         
       
     
     One can then form the magnetic field strength ensemble for the j th  sector, denoted M j , by grouping together the average magnetic field strength measurements M p,j  for all 400 revolutions (p=1, 2, . . . , 400) of the magnetic disk  404 . In other words, M j ={M p,j |1≦p≦400}. This is shown conceptually in  FIG. 6  for the magnetic field strength ensemble M 1 , i.e., the magnetic field strength ensemble for sector # 1 . 
     It will be noted that gradually sweeping the applied magnetic field while spinning the magnetic disk  404  creates the effect, within each sector, of stepping the applied magnetic field with an average decrement (or increment) of 100 Oe per step and a duty cycle of G m /πD t  for the case shown in  FIG. 4A  or D m /πD t  for the case shown in  FIG. 4B  (where D m  and D t  are the diameters of, respectively, the magnetic poles  421 A,  421 B and the track under test). To present a simplified, yet realistic representation of the Kerr signal ensemble K 1  and magnetic field strength ensemble M 1  for sector # 1 , only a fraction of the total number of 400 revolutions of the magnetic disk  404  is represented in  FIG. 6 . 
     Next, a magnetic property (such as remanence and/or coercivity) for a particular sector (e.g., sector #J) is determined by plotting the Kerr signal ensemble for the particular sector (namely, K J ) against the magnetic field strength ensemble for the particular sector (namely, M J ). With reference to  FIG. 7 , the Kerr signal measurement in milli-degrees for a particular sector on the track under test (Y-axis  804 ) was plotted against the applied magnetic field measurement in Oe (X-axis  802 ). The resulting plot takes the shape of a hysteresis loop since the Kerr signal measurement may be different at two different samples for which the magnetic field strength has the same value. Specifically, the Kerr signal measurement will depend on whether the applied magnetic field was increasing or decreasing at the time the measurement was taken. 
     Once the hysteresis loop for the particular sector is plotted, its coercivity and remanence may be determined. The coercivity (denoted H C ) for a sector can be determined as the value of the applied magnetic field at a Kerr signal (or magnetization value) of zero, while the remanence (denoted M R ) is determined as the Kerr signal (or magnetization value) at zero applied magnetic field. With respect to the example hysteresis loop illustrated in  FIG. 7 , the coercivity (identified here as HO for this particular sector can be determined to be around 4300 Oe while the remanence (identified here as M R ) as for this sector can be determined to be around 73 milli-degrees. 
     Advantageously, the above technique can be performed for any number of sectors on the track under test, based on the corresponding Kerr signal ensemble and magnetic field strength ensemble for each desired sector. All the ensembles are formed from the same time series of Kerr signal measurements {K(i)} and the same time series of magnetic field strength measurements {(M(i)}. In this way, the single application of a sweeping magnetic field while the magnetic medium rotates can be used to determine magnetic properties of multiple sectors of a track under test. This makes the process more efficient than having to separately apply the sweeping magnetic field to each point in each sector to be measured individually and in sequence. 
     The hysteresis loops for different sectors will be different, meaning that the coercivity and remanence of these sectors are correspondingly different and thus the values will form a distribution. In particular, the set of values representing remanance and coercivity of the sectors of the track under test can be depicted in graphical formats such as, but not limited to, tables, charts and/or graphs. 
       FIGS. 8A and 8B  illustrate two sample graphical formats that could be used to depict the remanence and coercivity of a set of 64 sectors. In  FIG. 8A , a possible distribution of the coercivity for each of the 64 sectors of a given track are plotted in a columnar graph. Specifically, a sector&#39;s coercivity in Oe (Y-axis  904 ) is plotted against the sector&#39;s ordinal number (X-axis  902 ). In a non-limiting example, this type of graph could be used to compare the coercivity found for sectors on a given track of a magnetic medium against a baseline to see if there is a difference relative to the baseline. In the affirmative, further investigations could be made to identify the reason for the disparity between the anomalous observed coercivity values and the baseline. 
       FIG. 8B  shows the same distribution of the coercivity for plural sectors in a graphical format that schematically represents a track  906  of sectors  908 A,  908 B,  908 C on a circular disk. In this format, ranges of values for the coercivity are associated with a specific color. For example, a coercivity between 3000 Oe and 3200 Oe (such as in sector  908 A) may be set to be displayed in light blue, while a coercivity between 3201 Oe and 3500 Oe (such as in sector  908 B) may be set to be displayed in green. In this way, the coercivity for multiple sectors of the track  906  can be viewed simultaneously, and anomalies can be identified based on the appearance of a specific color, hue or shading. This technique advantageously allows the rapid identification of sectors that are fall outside of predetermined maximum or minimum values. For example, the color red could be used to flag sectors on a track whose coercivity is either less than 2000 Oe or is greater than 6000 Oe, such as in sector  908 C. Certain colors or shadings may be used to identify sectors whose coercivity may fall outside of the operational parameters necessary for equipment to properly effect read and write operations on the sectors in question. 
     While  FIG. 8B  shows the distribution of coercivity for a single track on a magnetic medium such as a disk, the same format could also be used to show the distribution of coercivity for multiple tracks on the medium. 
     It should be appreciated that the remanence can be converted from units of milli-degrees into units of ampere/m. More specifically, the relationship is M=f·Φ, where f is a factor dependent on the magnetic medium and Φ is the Kerr signal in milli-degrees, which is dependent on the magnetic medium and the optical configuration. It should be noted that calibration may be required to determine which precise value of f to use. However, relative values can be used to compare the remanence among different sectors of a track without necessarily having to compute the true values, thus avoiding the need for calibration. 
     As described previously, the optical beam system  411  generates the incident optical beam  412  continuously during a test, regardless of whether a measurement is currently being performed on the magnetic disk  404 . In a variant of the method and apparatus described above, the optical beam system  411  generates the incident optical beam  412  only when a measurement is needed to be performed by the controller  433 . The intermittent nature of the optical beam generated in this variant may reduce power consumption or extend the life of the components in the optical beam system  411 . 
     As described previously, the time series of measurements {K(i)}, {M(i)}, {A(i)} received by the controller  433  during a test undergoes post-processing to generate ensembles of measurements. Proper execution of this post-processing depends on knowledge of variables such as the number of sectors per track of the magnetic medium, the rotation speed of the magnetic medium, and the profile of the applied magnetic field. It is conceivable that many or all of these variables will be known well in advance, such as for a test bed that is pre-configured to only test disks used in a particular type of hard drive. In such a case, the various ensembles  610  can be built up from measurements taken in real-time, while the magnetic medium rotates. 
     Moreover, it should be appreciated that the magnetic field strength measurements M(i) can be predicted rather than measured. That is to say, the magnetic field driver  423 , which has control over the magnetic field applied by the magnetic coil  422  via the gap  424 , can estimate the applied magnetic field that it expects should exist across the gap  424  at various sample times and can feed this information (in digital form, for each sample “i”) directly to the controller  433 , without the need for a separate channel in the A/D converter  434 . 
     Similarly, it should be appreciated that the spin angle measurements A(i) can be predicted rather than measured. That is to say, the controller  433 , which has control over the spinning of the magnetic disk  404  by the spindle  431 , can estimate the spin angle that it expects should be applied by the spindle  431  at various sample times and can feed this information (in digital form, for each sample “i”) directly to the controller  433 , without the need for a separate channel in the A/D converter  434 . 
     In such a scenario, where both the magnetic field strength and the spin angle are predicted rather than measured, the only measurements taken by the test bed  420  would be the Kerr signal measurements K(i). 
     While specific embodiments of the present invention have been described and illustrated, it will be apparent to those skilled in the art that numerous modifications and variations can be made without departing from the scope of the invention as defined in the appended claims.