Patent Publication Number: US-2012026273-A1

Title: Focusing a laser on a label surface of an optical disc

Description:
BACKGROUND 
     Some optical disc drives are capable of generating a visible label on an optical disc removably inserted in the disc drive. Optical discs for use with such drives typically have, in addition to a mechanism which allows digital data to be stored on the disc, an internal or external labeling surface that includes a material whose color, darkness, or both can be changed, with the controlled application of a laser beam thereto, in order to form visible markings at the positions on the labeling surface at which the laser beam is applied. The visible markings that constitute the label can collectively form text, graphics, and photographic images on the optical disc. Such a labeling mechanism advantageously avoids the need for additional equipment such as a silk-screener, or for the inconvenience of having to print and attach a physical label to the disc. Many users would also like the visible markings to form a label of high image quality and be produced as quickly as possible. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The features of the present invention and the manner of attaining them, and the invention itself, will be best understood by reference to the following detailed description of embodiments of the invention, taken in conjunction with the accompanying drawings. 
         FIG. 1  is a schematic representation of an optical disc in accordance with an embodiment of the present invention that illustrates features of a label surface. 
         FIG. 2  is a schematic representation of an optical disc drive in accordance with an embodiment of the present invention for marking the label surface of the optical disc of  FIG. 1 . 
         FIG. 3  is a schematic representation of the sweeping of laser focus optics in accordance with an embodiment of the present invention from a baseline position according to a sine wave in one revolution of the optical disc of  FIG. 1 . 
         FIGS. 4A and 4B  are a flowchart in accordance with an embodiment of the present invention of a method of forming a visible label on the optical disc of  FIG. 1 , including determining actuator signals for focusing a laser on the label surface of the optical disc of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     Referring now to the drawings, there are illustrated embodiments of the present invention that determine focus actuator signals for a laser mechanism of an optical disc drive that can be used to form a visible label of a high image quality on an optical disc inserted in the disc drive. The label is formed by the properly-focused laser controllably making visible marks on a label surface of the optical disc, in accordance with label data received by the disc drive. 
     To achieve a high level of image quality, the size, color, and/or darkness of the spots or marks formed by the laser on the optical disc should be consistent. The characteristics of these spots are determined at least in part by the degree of focus of the laser beam, generated by the laser mechanism, on the virtual track on which the marks are being formed. The optical drive has a focus actuator that positions laser focus optics at a z-axis position above the virtual track on the label surface in response to the focus actuator signals. The z-axis position of the laser focus optics determines the degree of focus of the laser beam on the virtual track, at least in part. During labeling, the focus actuator is operated to place the laser&#39;s focus optics at the desired z-axis position relative to the label surface. 
     However, an optical disc may not be perfectly flat. Instead, it may be warped in some manner. Furthermore, the disc may be tilted when it is inserted into the disc drive. As a result, to achieve high quality imaging under such conditions, the z-axis position at which the laser focus optics are positioned by the focus actuator to maintain the desired distance relative to the label surface can vary with both the radial position of a virtual track from the hub of the optical disc, and with the angular position around a virtual track, according to a “surface contour” of the optical disc in the disc drive that results from the warp and the tilt. In order to determine the appropriate actuator signals to apply to the focus actuator at the various radial and angular positions to be labeled on the optical disc, the surface contour of the disc, as it is installed in the disc drive, can be “mapped”, or characterized, before the laser forms the marks. The mapping results may then be used to construct a surface model usable to generate the proper focus actuator signals to focus the laser when the laser marks the various radial and angular positions on the optical disc in a subsequent marking operation. 
     The time to map the surface contour adds to the total amount of time it takes to label the disc. Thus it is advantageous to perform this operation in as short a time as possible. In addition, some multiple-layer optical discs, such as DVDs, can exhibit a warp with higher frequency surface deviations than optical discs of a simpler structure. Thus it is advantageous to construct a surface model that better models these higher frequency surface deviations. 
     As will be described in greater detail subsequently, embodiments of the present invention advantageously reduce the time it takes to map the surface contour, and thus reduce the total time it takes to label the disc. Mapping angular sectors of the surface using a sinusoidal sweep or perturbation of the laser focus optics from a baseline position allows the mapping for a given radial position to be completed in a single revolution of the disk. Sinusoidally sweeping the focus optics reduces overshoot and ringing in their positioning, which in turn allows the number of angular sectors defined on the optical disc to be increased, the disc to be rotated faster, or both. An increased number of angular sectors allows construction of a surface model that better models higher frequency surface deviations. 
     Considering now one embodiment of an optical disc, and with reference to  FIG. 1 , the optical disc  100  may be a CD (compact disc), DVD (digital versatile disc), or other forms of optical discs capable of forming visible markings on or within the disc in response to the application of electromagnetic energy, such as from a laser, to the disc. This includes discs in CD-R, CD-RW, DVD+R, DVD-R, DVD+RW, DVD-RW, DVD-ROM, and Blu-ray formats, and the like. Such discs also typically store digital data that may represent, for example, photographs, videos, music, computer programs, and other various types of information or data. In some discs the data is prefabricated, while in other discs the data may be written to the disc using an optical disc drive. Digital data stored on a disc can be read from the disc using an optical disc drive. 
     Various physical and chemical structures may be used to provide the optical disc with the capability of forming the visible markings in response to the application of a proper amount of electromagnetic energy to the disc. In one embodiment, a labeling layer or coating is applied to at least a portion of a surface of the disc. In one embodiment, the layer is applied to the disc surface on the opposite side of the disc from the surface through which laser energy is impinged to read or write the digital data. In one embodiment, the labeling coating is a laser-sensitive layer that has thermochromic and/or photochromic materials that can be activated at desired locations by the application of laser energy to the desired locations. In some embodiments the materials may be sensitive only to energy within a particular band of frequencies, either visible or invisible. In one embodiment, these frequencies may be in the infrared or near-infrared region. When and where activated, the materials form visible markings having a particular color, darkness, and/or contrast relative to unmarked materials. A coating may enable the generation of markings that are all of a single color, or of multiple colors. The coating may be applied continuously to the surface, or to discrete locations on the surface. 
     Optical disc  100  includes a central hub  102  which mounts and positions the disc  100  in an optical disc drive for data reading and writing, and for marking a label surface  104  of the disc  100 . The label surface  104  typically extends from an inner radius to an outer radius of the disc  100 . In some embodiments, the inner and outer radii of the label surface  104  do not extend completely to the inner and outer radii of the disc  100 . In one embodiment, a ring of disc control features  106  is disposed closer to the hub  102  than the inner radius. The disc control features  106  are usable by the disc drive to determine and control the speed of rotation of the disc  100 , and the angular orientation or angular position of the disc  100  in the disc drive. In one embodiment, the disc control features  106  include an index mark  108  usable to determine a reference position for the angular position of the disc  100  in the drive. For example, angular position  110 A may be defined as an angular position of 0 degrees, angular position  110 B may be defined an as angular position of approximately 45 degrees, and angular position  110 C may be defined an as angular position of approximately 90 degrees. In one embodiment, the disc control features  106  include a plurality of equally-spaced timing features, or “spokes”,  107 . While for clarity timing features  107  are illustrated only as disposed between angular positions  110 B and  110 C, it is understood that timing features  107  are disposed completely around disc  100 . In some embodiments, index mark  108  may also serve as a timing feature  107 , or a timing feature  107  may be coincident with index mark  108 . 
     A plurality of virtual angular sectors may be defined on the label surface  104 . These sectors may be defined in connection with mapping the disk surface contour. A first virtual angular sector  116 A is illustrated as spanning angular positions  110 A to  110 B. Put another way, angular positions  110 A-b are the borders of sector  116 A. A second virtual angular sector  116 B is illustrated as spanning angular positions  110 B to  110 C. Each virtual angular sector  116  spans the same number of degrees of rotation of the disc  100 . Put another way, each virtual angular sector  116  is the same size. These sectors  116  are “virtual” in that they are not physically defined on the disc  100 , but rather are defined by the disc drive into which the disc  100  is inserted. In one embodiment, each of the two angular borders  110  of each virtual angular sector  116  is coincident with a timing feature  107 , and each virtual angular sector  116  contains an equal number of timing features  107 . 
     The disc drive can define a various number of virtual angular sectors  116  on the disc  100 .  FIG. 1  illustrates a total of eight virtual angular sectors, in which every third timing feature  107  (of a total of 24 timing features  107 ) is coincident with a sector border  110 . In another embodiment, the disc  100  includes 400 timing features  107 , the disc drive defines twenty virtual angular sectors  116  on the disc  100 , and every twentieth timing feature  107  is coincident with a border  110  of a sector  116 . 
     The laser beam generated by the optical disc drive can be positioned at a radial position between the inner radius and the outer radius of the label surface  104 . While only exemplary radial positions  112 A and  112 B are illustrated, it is to be understood that a large number of different radial positions  112  may exist on the disc  100 . 
     In one embodiment, locations or positions on the label surface  104  markable by the optical drive are logically organized into virtual concentric or annular rings of individual markable locations or positions  114 . Each annular ring, also known as a “virtual track”, has a corresponding radial position  112 . While the exemplary markable positions  114  are illustrated in  FIG. 1  as circular, it is understood that they may alternatively be oblong, continuous, or have other shapes. An individual markable position  114  can be marked by positioning the laser beam adjacent to the radial position of the desired markable position  114 , properly focusing the beam from the laser on the label surface  104  by appropriately positioning the laser focus optics, and synchronizing the application of laser energy to the angular position of the disc  100  during disc rotation. In some embodiments, the concentric rings of markable positions  114  abut one another throughout the label surface  104 , and thus the radial position  112  of adjacent annular rings of locations  114  may be generally determined by the dimensions of the locations  114 , particularly in the radial direction. 
     Considering now an embodiment of an optical disc drive usable to label the optical disc  100 , and with reference to  FIG. 2 , an optical disc drive (ODD)  200  includes an optical pick-up unit assembly (OPU)  202 . The OPU  202  may include an electromagnetic energy source  204 , which may be a laser source, and an objective lens or focus optics  210 . The OPU  202  may also include a sled  206 , a sensor  208 , and a focus actuator  212 . The focus actuator  212  is configured to respond to an input signal, which may be voltage or current, to cause the focus optics  210  to move the focal point of the electromagnetic energy beam  214  generated by source  204 . The electromagnetic energy beam  214  may be a laser beam. Taken together, the laser source  204  and the focus optics  210  constitute a laser  230 . 
     In an exemplary embodiment, a spindle motor  216  is configured to spin or rotate the optical disc  100  substantially circularly. The optical disc  100  is removably mounted to a spindle  215  by mating the hub  102  of the disc  100  with the spindle  215 . When labeling the label surface  104 , the disc  100  is mounted such that the label surface  104  faces the laser  230 . Where the disc  100  is such that the label surface  104  is on (or is accessed from or through) the opposite side of the disc  100  from a data surface  201  of the disc  100 , the disc  100  may be mounted in the drive  200  upside-down from the orientation used when reading digital data from, or writing digital data to, the disc  100 . 
     A radial actuator  218  may be arranged to move the laser  230 , which is mounted on the sled  206 , to different radial positions along a radial axis  220  with respect to the center of the disc  100 . The radial actuator  218  positions the laser adjacent to particular virtual label tracks  112  on the label surface  104  such as, for example, tracks  112 A-B. The operation of the spindle motor  216  and radial actuator  218  can be coordinated to move the label surface  104  of the disc  100  and the laser  230  relative to each other to permit the laser  230  to create an image on the disc  100  by forming marks on selected ones of the markable locations  114  on the label surface  104 . In some embodiments the radial actuator  218  may include a coarse adjustment mechanism which moves the sled  206  along the radial axis  220 , and a fine adjustment mechanism which moves the laser  230  with respect to the sled  206 . 
     In an exemplary embodiment, the focus optics  210  may mounted on lens supports and configured to travel along a z-axis  222  which is generally perpendicular to the label surface  104  of the disc  100 . In an exemplary embodiment, the focus actuator  212  adjusts the focal point of the laser beam  214  by moving the focus optics  210  toward or away from the label surface  104  of the disc  100 . In an exemplary embodiment, the focus actuator  212  is controlled during a disc marking or labeling operation to place the focus optics  210  at a desired position so that markings of a desired darkness and/or color, and size can be formed on the markable locations  114  of the label surface  104 . 
     Sensor  208  provides signal data indicative of the degree of focus of the laser beam  214  on label surface  104 . A portion of the laser energy applied to the label surface  104  can be reflected back through the optics  210  to the sensor  208 . In one embodiment, sensor  208  has four individual sensor quadrants, A, B, C and D, that collectively provide a SUM signal. Quadrants A, B, C, and D may be configured to measure reflected light independent of one another. In particular, voltage is generated by the quadrants A, B, C and D in response to reflected light. When the sum of the measured voltage of the quadrants A, B, C and D are at a relative maximum, it is an indication that the focus optics  210  are positioned along the z-axis  222  in a position that places the laser beam  214  at an in-focus position on the label surface  104 . In other embodiments, quadrant outputs of sensor  208  may be added or subtracted in other combinations to provide different signals, such as a focus error signal (FES). 
     In an exemplary embodiment, the disc drive  200  includes a controller  250 . The controller  250  may be connected via a computing device interface  252  to a computing device (not shown) or other data source external to the disc drive  200 . The controller  250  may be implemented, in some embodiments, using hardware, software, firmware, or a combination of these technologies. Subsystems and modules, or portions thereof, of the controller  250  may be implemented using dedicated hardware, or a combination of dedicated hardware along with a computer or microprocessor controlled by firmware or software. Dedicated hardware may include discrete or integrated analog circuitry and digital circuitry such as programmable logic device and state machines. Firmware or software may define a sequence of logic operations and may be organized as modules, functions, or objects of a computer program. Firmware or software modules may be executed by at least one CPU  254  for processing computer/processor-executable instructions from various components stored in a computer-readable medium, such as memory  260 . Memory  260  may be any type of computer-readable medium for use by or in connection with any computer-related system or method. Memory  260  is typically non-volatile, and may be read-only memory (ROM). 
     In one embodiment, the controller  250  may be implemented on one or more printed circuit boards in the disc drive  200 . In other embodiments, at least a portion of the controller  250  may be located external to the disc drive  200 . The disc drive  200  may be included in a computer system, such as a personal computer, may be used in a stand-alone audio or video device, may be used as a peripheral component in an audio or video system, or may be used in a stand-alone disc media labeling device or accessory. Other configurations are also contemplated. 
     In one embodiment, the controller  250  generates control signals for the spindle motor  216 , radial actuator  218 , focus actuator  212 , and electromagnetic energy source  204 . The controller  250  also reads data, where appropriate, from these components, including degree-of-focus data from sensor  208 . 
     In some embodiments, the controller  250  includes a radial position driver  262 , a z-axis position driver  264 , a disc rotation speed driver  266 , and a laser driver  268 . In an exemplary embodiment, the drivers may be firmware and/or software components which may be stored in memory  260  and executable on CPU  254 . The drivers may cause the controller  250  to selectively generate digital or analog control or data signals, and read analog or digital data signals. 
     In an exemplary embodiment, the disc rotation speed driver  266  drives spindle motor  216  to control a rotational speed of optical disc  100  via the spindle  215 . The disc rotation speed driver  266  operates in conjunction with the radial position driver  262  which drives the radial actuator  216  to control at least coarse radial positioning of OPU assembly  202  with respect to disc  100 . In disc surface contour mapping operations, and disc location marking operations, the sled  206  of OPU  202 , including laser  230 , is moved along the radial axis  220  to various virtual tracks  112  of optical disc  100 . In some embodiments, for a given radial position of the laser  230  the disc rotation speed driver  266  rotates the disc  100 , for a given virtual track  112 , at a faster speed during disc surface contour mapping operations than during disc location marking operations. 
     In an exemplary embodiment, the laser driver  268  controls the various components of the OPU  202 . The laser driver  268  controls turning the laser source  204  on and off, and controls the intensity of the laser beam  214  generated by the laser source  204 . In some embodiments, a lower intensity laser beam  214  is generated during disc surface contour mapping operations, while a higher intensity laser beam  214  is generated during disc location marking operations. 
     In an exemplary embodiment, the z-axis position driver  264  controls the focus actuator  212  in order to adjust the position of the focus optics  210  along the z-axis  222 . 
     In an exemplary embodiment, the controller  250  further includes a disc surface contour mapping module  270 , and a disc location marking module  280 . The disc surface contour mapping module  270  maps the contour of the label surface  104  of the disc  100  by determining the position of the laser optics  210  that focuses the laser beam  214  to a desired degree of focus on the virtual angular sectors  116  of a desired virtual track  112  on the label surface  104  of the disc  100 . To prevent the markings from exhibiting undesirable darkness or color variations due to differences in the laser energy absorbed at locations  114  in different virtual angular sectors  116  on the label surface  104  due to differences in surface contour between the sectors, the focus is generally maintained within a few microns of the label surface  104  for all sectors  116  in which locations  114  are marked. 
     The disc surface contour mapping may be performed, prior to labeling the label surface  104 , for any of a variety of reasons. For example, while a conventional disc drive is capable of maintaining the laser in an in-focus position in real-time during reading data from, or writing data to, the data surface  201  of the disc  100  regardless of any tilt or warp in the disc  100 , it cannot do so when forming a visible label to the virtual tracks  112  of label surface  104 . One reason is that the quality of the signal detected by the sensor  208  is inadequate. This occurs where the label surface  104  is not as reflective as the data surface  201 . In such a situation, it is difficult or impossible to extract a reliable signal from the sensor  208  in real-time. In addition, the label surface  104  is typically not as smooth as the data surface  201 . As a result, the signal from the sensor  208  may need to be averaged to eliminate the noise, which prevents real-time focusing during marking. Another reason why disc surface contour mapping is performed is that the desired degree of focus for a marking operation does not correspond to an in-focus position of the laser, but rather to a defocused position of the laser. This defocusing may be accomplished, in one embodiment, by applying a focus offset signal to the focus actuator  212  that offsets the optics  210  a focus offset distance  225  along the z-axis  222  from its actual in-focus distance  223 . One reason for defocusing the laser is to produce a larger spot size, and thus a larger mark, than would be produced with an in-focus laser beam. However, when the laser is defocused to the desired degree for marking, the sensor  208  will typically be operating outside of its usable signal range for providing real-time focus control. 
     Thus because of at least these factors, the disc surface contour is mapped before the laser forms the marks. However, because disc contour mapping is an additional, sequential operation, it increases the total time to label the disc. 
     With regard to the contour of the label surface  104 , disc  100  is exemplarily illustrated in  FIG. 2  not as being flat, but as having a surface contour that varies with radial and angular position on the disc  100  (the contour variation is exaggerated for clarity of illustration). The laser beam  214  is illustrated as focused at location  114 A on label surface  104 . Location  114 A corresponds to a certain virtual track  112  and angular position  110 , and focus actuator  212  places laser optics  210  in the position illustrated so that the laser beam  214  is focused at location  114 A. However, when disc  100  is rotated so that location  114 B, located on the same virtual track  112  as location  114 A but in a different angular position  110 , is positioned adjacent the laser  230 , the controller  250  instructs the focus actuator  212  to move optics  210  to a different position along the z-axis  222  in order to make the laser beam focus at location  1148 . This is due to the variation in the surface contour of the disc  100  which causes location  114 B to be, for example, closer to the laser source  204  along z-axis  222  than is location  114 A. 
     Similarly, consider location  114 C on label surface  104 , which may be located at the same angular position  110  as location  114 A, but on a different virtual track  112 . When the laser source  204  is moved along the radial axis  220  so that the laser beam  214  impinges location  114 C instead of  114 A, focus actuator  212  moves the optics  210  to a different position along the z-axis  222  in order to make the laser beam focus at location  114 C. This is due to the variation in the surface contour of the disc  100  in the radial direction, which causes location  114 C to be, for example, farther from the laser source  204  along z-axis  222  than is location  114 A. 
     In some embodiments, the disc surface contour mapping module  270  determines gain coefficients  292  of an algorithm that can subsequently be used by a disc location marking module  280  to control the focus actuator  212  to move the focus optics  210  to the proper z-axis position for the corresponding angular position  110  to form marks having consistent image quality when labeling desired markable locations  114  on the disc  100 . In one embodiment, the algorithm is a Fourier series. The gain coefficients and Fourier series can generate signals for the focus actuator  212 , synchronized with the rotation of the disc  100 , that position the focus optics  210  so that the laser beam  214  is focused on the label surface  104  for all angular positions  110  as the disc  100  rotates, regardless of any tilt or warp in the disc  100 . 
     In some embodiments, the disc surface contour mapping module  270  includes a focus measurement module  272 . As will be discussed subsequently in greater detail, the focus measurement module  272  sweeps the focus optics  210  sinusoidally from a baseline position, applies the laser beam  214  to the disc  100  through the focus optics  210 , and measures SUM signals from the sensor  208  that are indicative of the degree of focus of the laser beam  214  on the label surface  104 . A SUM signal measurement is made at multiple locations  114 A within each virtual angular sector  116  of the disc  100  as the focus optics are sinusoidally swept through that sector  116 . For a given radial position  112 , the focus optics sweep, laser beam application, and signal measurements are performed for all sectors  116  of the disc  100  during a single revolution of the disc  100 . 
     In some embodiments, the disc surface contour mapping module  270  includes a gain coefficient generator module  274 . As will be discussed subsequently in greater detail, the gain coefficient generator module  274 , for each virtual angular sector  116 , calculates an error term from the measured SUM signals for that sector  116 , and recalculates (i.e. updates or modifies) the gain coefficients  292  for that sector based on the calculated error term. All of the SUM signal measurements needed for the gain coefficient generator module  274  to calculate the error term and recalculate the gain coefficients  292  for all of the virtual angular sectors  116  of the disc  100  are measured in the single rotation of the disc performed by the focus measurement module  272 . If a calculated error term has not yet converged to a desired value indicative of a sufficiently accurate mapping of the disc surface, the disc surface contour mapping module  270  will repeat (i.e. iterate) the operations of the focus measurement module  272  and gain coefficient generator module  274 , until the error terms converge and a sufficiently accurate mapping is achieved. At least the final version of the gain coefficients  292  are stored in memory  290 . 
     The operation of the disc surface contour mapping module  270  has been described above with reference to a particular virtual track or radial position  112 . The operation is typically repeated for each of a number of different radial positions  112 , for each of which a separate set of gain coefficients  292  is determined, since the surface contour of the disk  100  can vary with radial position  112  as well as angular position  110 , as explained heretofore. During operation in some embodiments, the disc surface contour mapping module  270  rotates the disc  100  at a faster speed for a given radial position  112  than does the disc location marking module  280 . 
     The disc location marking module  280  marks designated ones of the markable locations  114  on the disc  100 , according to label data  294  indicative of the labeling image to be formed on the disc  100 . The label data  294  may be received via computing device interface  252  from a source external to disc drive  200 , such as from a personal computer. In some embodiments, the disc location marking module  280  includes a label data processor module  282  that processes the image data  294  to determine the radial position  112  and angular position  110  on the disc  100  of ones of the markable locations  114  designated by the data  294  to be marked by the laser beam  214 . In some embodiments, the label data processor module  282  may also determine, for the designated locations  114  to be marked, the darkness, contrast, and/or color of the mark. In some embodiments, as will be discussed subsequently in greater detail, the disc location marking module  280  includes a focus actuator signal generator module  284  that calculates, using the gain coefficients  292 , a signal for the focus actuator  212  that positions the focus optics  210  at the desired focus position to form the desired mark at the radial position  112  and the angular position  110  of each location  114  to be marked. As the sled  206  is positioned at a designated radial position  112 , and as the disc  100  is being rotated by the spindle motor  216 , the disc location marking module  280  applies to the focus actuator  212  the calculated focus position signal in sync with the rotation of the disc  100 , so that the laser  230  can form the desired mark on the location  114  as it passes adjacent the laser beam  214 . In some embodiments, the disc location marking module  280  rotates the disc  100  at a slower speed for a given radial position  112  than does the disc surface contour mapping module  270 . 
     In one embodiment, the gain coefficients  292  and the label data  294  are stored in a read-write (RAM) memory  290 . In some embodiments, memory  260  and memory  290  may be the same memory device. In some embodiments, the gain coefficients  292  and the image data  294  may be stored in different memory devices. 
     Considering now in greater detail, with reference to  FIG. 3 , the operation of one embodiment of the focus measurement module  272  of the surface contour mapping module  270 , the focus measurement module  272  sweeps the focus optics  210  in a substantially sinusoidal displacement or motion  330  from a baseline position  340  once per virtual sector  116 . The focus optics  210  are swept by the application of a substantially sinusoidal voltage or current signal to the focus actuator  212 . 
     The location of the baseline  340  (i.e. the z-axis location  222  of the focus optics  210  above the label surface  104 ) is such that the sensor  208  can generate a usable SUM signal. In some embodiments, a nominal baseline  340  may be established as part of an initial disc detect operation (not shown) performed by the drive  200  when the disc  100  is inserted thereto. While baseline  340  is illustrated in  FIG. 3  as a constant position throughout all sectors  116  of the disc  100 , this typically represents the operating condition of only a first iterative execution of the focus measurement module  272  for a given radial position  112 . In subsequent iterative executions of the module  272  at that given radial position  112 , the baseline  340  may neither be constant nor linear; it may be established, as will be discussed subsequently with reference to the gain coefficient generator  274 , by using gain coefficients  292  that have been previously determined by the gain coefficient generator  274 . The sinusoidal sweep motion  330  may be considered as being superimposed on the baseline  340  in some embodiments. 
     In the exemplary operation of  FIG. 3 , the disc  100  is divided into twenty virtual angular sectors  116 , and thus the focus optics are swept sinusoidally for twenty cycles during a single revolution of the disc  100 . While traversing the first half  352  of each sector  116 , the focus optics  210  are swept further from the label surface  104  of the disc  100  than the baseline  340 . While traversing the second half  354  of each sector  116 , the focus optics  210  are swept closer to the label surface  104  of the disc  100  than the baseline  340 . In an alternate embodiment, the focus optics  210  may be swept closer during the first half, and further during the second half, of the traversal of each sector  116 . Sector boundaries, such as at angular positions  110 A-c, correspond to the zero-crossing point between individual cycles of the sinusoidal motion  330 , where the focus optics  210  are positioned at the baseline  340 . 
     During the rotation, and while the focus optics  210  are being sinusoidally swept, the laser  230  is energized and the laser beam  214  applied to disc  100 , and the SUM signal from sensor  208  is measured at a plurality of angular positions  110  within each sector  116 . In one embodiment, the SUM signal measurements are taken in synchronization with the periodic application of laser beam  214 . A portion of the applied laser beam  214  is reflected from the label surface  104  to the sensor  208  to generate the SUM signals. In one embodiment, the angular positions  110  at which the SUM signal is measured corresponds to the position of timing features  107 . Thus, in an embodiment having 20 sectors  116  on disc  100  and 400 total timing features  107 , the SUM signal is measured 20 times for each sector  116 . 
     At the completion of a single revolution of the disc  100 , for each sector  116 , a plurality of SUM signal measurements corresponding to the sinusoidal displacement of the focus optics  210  that is substantially symmetrical about baseline  340  have been collected. From these measurements, as will be discussed subsequently with reference to the gain coefficient generator  274 , an error term descriptive of the degree of focus of the laser beam  214  on the label surface  104  can be calculated. 
     In one embodiment employing the sinusoidal motion  330 , twenty virtual angular sectors  116  are defined on the disc  100 , and the gain coefficient generator  274  derives nine gain coefficients for a Fourier series having a DC component and first-order through fourth-order sinusoidal and cosinusoidal components. In one embodiment, for a given virtual track  112 , the focus measurement module  272  rotates the disc  100  at a faster speed (i.e. a higher rpm) than the speed at which the disc  100  is rotated by the disk location marking module  280 . In one embodiment, the focus measurement module  272  rotates the disc  100  at greater than 50 rpm. 
     Other focus measurement techniques displace the focus optics  210  in a different manner. For example, one technique displaces the optics  210  in a substantially linear ramp in one direction relative to the label surface  104  (for example, toward the surface) in the first half of the sector, and applies the baseline signal in the second half of the sector to return the focus optics  210  to the baseline. However, in order to obtain a plurality of SUM signal measurements that represent a displacement of the focus optics  210  that is substantially symmetrical about the baseline, during a second revolution of the disc  100 , the optics  210  are displaced in a substantially linear ramp in the opposite direction (for example, away from the label surface  104 ) in the first half of the sector, and the baseline signal applied in the second half of the sector to return the focus optics  210  to the baseline during a second revolution of the disc  100 . Thus, in order to collect a sufficient set of measurements to calculate the error term, two revolutions of the disc  100  are performed, instead of one. Performing this sequence multiple times when iterating at a single radial position  112 , and then doing so at a number of different radial positions  112  in order to map the entire disc  100 , approximately doubles the total amount of time required to perform the disc surface contour mapping operation. The same occurs in another focus measurement technique where a half-sine wave is utilized instead of a ramp. Accordingly, using a sinusoidal displacement  330  in the focus measurement module  272 , such that all the SUM signal measurements for all the sectors  116  are performed in a single revolution of the disc  100 , advantageously reduces the time required to perform the disc surface contour mapping operation, compared to focus measurement techniques requiring two revolutions, for a given disc rotation speed. 
     Sinusoidal displacement  330  applied to an electromechanical system such as the focus optics  210  also provides other benefits relative to these other focus measurement techniques. Due to the mass of the focus optics  210  and associated movable components of the drive  200 , significant overshoot and ringing in the motion of these components can occur when the signal applied to the focus actuator  212  includes high frequency content, such as may occur from an abrupt change in slew rate of the motion of these components. For example, the point at which a ramp signal abruptly changes from its peak value to the baseline value at the midpoint of a sector  116  is a discontinuity that includes high frequency content. Another is the abrupt termination of a half-sine wave when it reaches the baseline value midway through the sector  116 . One adverse effect of such overshoot and ringing is the introduction of noise into the SUM signal measurements, which in turn lowers the signal-to-noise ratio and introduces error into the gain coefficient generation. The error can increase the number of iterations (and thus increase the time) required to obtain optimal gain coefficients  292 , or may yield erroneous gain coefficients  292  which cause reduced image quality in the label marks formed on the label surface  104  by the disc location marking module  280 . 
     Because the sinusoidal motion  330  is continuous, it minimizes overshoot and ringing, and has lower harmonic content. Furthermore, the sinusoidal motion  330  permits a greater number of virtual angular sectors  116  to be defined on the disc  100  than do discontinuous displacement approaches. To compensate for the overshoot and ringing caused by non-sinusoidal motion, the focus optics  210  and associated components may be moved more slowly, or more settling time provided, to help minimize noise from overshoot and ringing in the measured SUM signal. However, doing so means defining a fewer number of virtual angular sectors  116  on the disc  100 , and/or rotating the disc  100  at a relatively slower speed during the focus measurement operation. Both can be disadvantageous. Rotating the disc  100  more slowly directly adds to the disc surface contour mapping time required. Measuring SUM signals for a fewer number of sectors  116  can be insufficient to accurately model the surface contour, particularly the higher-frequency surface effects often exhibited by multi-layer discs  100 . For example, defining and measuring 8 sectors may not be sufficient to model third-order and fourth-order sinusoidal effects. If these effects are not accounted for during modeling, the focus optics  210  cannot subsequently be positioned to account for them during labeling, which can result in focus errors that decrease the image quality of the label marks formed on these discs  100 . 
     One characteristic of the two-revolution approaches is that the same portion of the disc surface (i.e. the same half-sector) is measured for both directions of the displacement (i.e. both toward and away from the disc). In the sinusoidal motion  330 , two adjacent half-sectors are measured in one revolution. For a given number of virtual angular sectors  116  each having a given angular span, spatial error may be introduced with the one-revolution approach due to variation in the surface contour between the first and second half-sectors. Such spatial error does not occur with the two-revolution approaches that measure the same half-sector for both directions of the displacement. However, the ability provided by the one-revolution, sinusoidal motion  330  approach to significantly increase the number of virtual angular sectors  116  defined on the disc  100 , as described above, can reduce or eliminate such spatial error. For example, consider a two-revolution approach that defines 8 virtual sectors. Each sector spans 45 degrees, thus the focus measurement is performed in a half-sector that spans 22.5 degrees. Now consider a one-revolution approach that defines 20 virtual sectors  116  on the disc  100 . Each sector spans 18 degrees. Therefore, even though both half-sectors  352 , 354  are measured, together they comprise a smaller angular span than the two-revolution approach. The SUM error value is averaged across the sector so if the sector is sufficiently small the effective spatial error is negligible. 
     Before considering the gain coefficient generator  274  of the surface contour mapping module  270 , it is useful to consider the generation of the baseline signal  340  for the focus actuator  212 . In one embodiment, a Fourier series uses gain coefficients and the angle of rotation of the disc  100  to generate the baseline signal  340 , according to the following algorithm: 
       Baseline signal=( A 0 *DC 0)+( A 1 *QS 1)+( B 1 *QC 1)+( A 2 *QS 2)+( B 2 *QC 2)+( A 3 *QS 3)+( B 3 *QC 3)+( A 4 *QS 4)+( B 4 *QC 4). 
     The DC 0  term is a DC component of the signal. The QSn and QCn terms are sinusoidal and cosinusoidal terms respectively. The value of n indicates the order of the term; for example, QS 1  is a first-order sine term, while QC 4  is a fourth-order cosine term, corresponding to the first and fourth harmonic respectively. The order corresponds to a multiplier for the angle of rotation. For example, for a given angle of rotation, theta, the value of QS 1 =sin(theta), while the value of QC 4 =cos(4*theta). 
     A 0  through A 4 , and B 1  through B 4  are the nine gain coefficients for the corresponding nine terms of the Fourier series. On the first iteration performed by the disc surface contour map module  270 , the value of A 0  is selected to set to a nominal value such that the sensor  208  can generate a usable SUM signal during the focus measurement  272  operation, while the values of A 1  through A 4  and B 1  through B 4  are set to zero. This will generate the constant linear baseline signal  340  as illustrated in  FIG. 3 , corresponding to a flat surface  104  of the disc  100 , on which the sinusoidal motion  330  is superimposed. In subsequent iterations of the disc surface contour map module  270  that use the gain coefficients  292  generated by the previous operation of the gain coefficient generator  274 , the baseline signal  340  will typically neither be constant nor linear, and the sinusoidal motion  330  will be superimposed upon that baseline  340 . 
     Considering now in greater detail the operation of one embodiment of the gain coefficient generator  274  of the surface contour mapping module  270 , the gain coefficient generator  274  uses the SUM signal measurements to calculate, for each sector  116 , an error term descriptive of the degree of focus of the laser beam  214  on the label surface  104  of that sector  116 , and uses the error signal, along with gain coefficients  292  from a previously iteration of the generator  274 , to generate updated or modified gain coefficients  292 . The updated or modified gain coefficients  292 , when used in the next iteration of the focus measurement  272  operation, are intended to improve the degree of focus on the sectors  116 . When the disc surface contour map module  270  completes its cycle of iterating the focus measurement  272  and gain coefficient generator  274  operations, the finalized gain coefficients  292  provide a high degree of focus of the laser beam  214  on the label surface  104  for all sectors  116 . 
     In one embodiment, the SUM signal measurements for one half-sector  352  represent sweeping the focus optics  210  further from the label surface  104  of the disc  100  than the baseline  340 , and the SUM signal measurements for the other half-sector  354  represent sweeping the focus optics  210  closer to the label surface  104  of the disc  100  than the baseline  340 . The error term for the sector  116  comprised of the two half-sectors  352 , 354  is generated by adding the SUM signal measurements for the one half-sector  352  and the other half-sector  354 , and then by taking the difference between these two totals. For example, assume that the SUM signal measurement is normalized such that the measured SUM signal has a value between 0 and 1. Further, assume that 10 SUM signal measurements are made during each half-sector  352 , 354 , and that the total of the SUM signal measurements for the first half-sector  352  of sector  116  is 7, and the total of the SUM signal measurements for the second half-sector  354  of sector  116  is 3. Subtracting the total for the second half-sector  354  from the total for the first half-sector  352  results in an error term of +4 for the sector  116 . It can be observed that, because half the SUM signal measurements are made with the focus displaced from the baseline  340  in one direction and the other half in the other direction, the above sum-and-difference operation effectively integrates the error over a sector  116 . It can also be observed that, when a larger number of sectors  116  are defined on the label surface  104  of the disc  100 , fewer measurements are integrated for a given sector  116  and more error terms are generated, allowing a higher accuracy surface model capable of confirming to higher-order surface deviations to be constructed. 
     Next, the gain coefficients  292  for the sector are updated using the error term, in one embodiment according to the following formulas: 
         A 0(updated)= A 0(prior)+( DC 0 *Ek*Mu ) 
         A 1(updated)= A 1(prior)+( QS 1 *Ek*Mu ) 
         B 1(updated)= B 1(prior)+( QC 1 *Ek*Mu ) 
         A 2(updated)= A 2(prior)+( QS 2 *Ek*Mu ) 
         B 2(updated)= B 2(prior)+( QC 2 *Ek*Mu ) 
         A 3(updated)= A 3(prior)+( QS 3 *Ek*Mu ) 
         B 3(updated)= B 3(prior)+( QC 3 *Ek*Mu ) 
         A 4(updated)= A 4(prior)+( QS 4 *Ek*Mu ) 
         B 4(updated)= B 4(prior)+( QC 4 *Ek*Mu ) 
     The DC 0  term, the QSn and QCn terms, and the gain coefficients A 0  through A 4  and B 1  through B 4  are as defined heretofore. The prior gain coefficients are those used when making the SUM signal measurements used to derive the error term, Ek. Mu is a coefficient that weights the effect of the error terms as they are used to modify the updated coefficients. If the error term were allowed to overly influence a present value of the focus actuator signal, the focus optics  210  might swing too wildly, resulting in excessive iterations of the focus measurement  272  and gain coefficient generation  274  operations, or might not allow the surface model to converge to a stable set of gain coefficients  292 . Conversely, if the error term is overly suppressed from influencing the focus actuator signal, the focus optics  210  might not respond quickly enough to changing conditions, thus also resulting in excessive iterations of the focus measurement  272  and gain coefficient generation  274  operations. Accordingly, the value of Mu input  208  should be selected according to the specific characteristics of the drive  200  and other factors, in order to allow the surface model to converge to a stable set of gain coefficients  292  in an optimal time. In one embodiment, the gain coefficients  292  are determined to have converged if the error term is below a threshold. In another embodiment, the gain coefficients  292  are determined to have converged if the change in gain coefficients between iterations is below a threshold. 
     It is noted that the above operation of the gain coefficient generator  274  was described for one sector  116 . The gain coefficient generator operation is repeated, in some embodiments, for all of the sectors  116  that are defined on the label surface  104  of the disc  100 , generating a set of gain coefficients  292  for each sector  116 . In some embodiments, the values of the individual gain coefficients  292  for the sectors  116  are averaged in order to derive overall gain coefficients  292  usable to generate the baseline signal  340  for the next iteration. 
     For example, for a disc  100  having 20 sectors  116 , the value of the 20 individual B 1 (updated) gain coefficients is averaged to derive an overall B 1 (updated) gain coefficient. 
     Considering now in greater detail the operation of the focus actuator signal generator module  284 , in one embodiment the overall gain coefficients resulting from the final iteration are also used in the operation of the signal generator module  284  during a disk location marking  280  operation. Similar to the generation of the baseline signal  340  during the operation of the disc surface mapping module  270 , a Fourier series uses gain coefficients and the angle of rotation of the disc  100  to generate the control signal for the focus actuator  212  that accurately positions the focus optics  210 , in synchronization with the rotation of the disc, at the proper distance from the label surface  104  to produce marks of high image quality, according to the following algorithm: 
       Actuator signal=( A 0 *DC 0)+( A 1 *QS 1)+( B 1 *QC 1)+( A 2 *QS 2)+( B 2 *QC 2)+( A 3 *QS 3)+( B 3 *QC 3)+( A 4 *QS 4)+( B 4 *QC 4). 
     The various terms are the same as have been described heretofore. It is noted that no sinusoidal signal is superimposed thereon during the disk location marking  280  operation although, in some embodiments, a constant focus offset value may be added as described previously. 
     In some embodiments, the disc surface mapping  270  operation is performed for the entire disc  100  before the disc location marking  280  operation is performed for any of the positions  114  on the disc  100 . In some embodiments, the disc  100  is rotated at a slower rotational speed during the operation of the disc location marking module  280  than during the operation of the disc surface mapping module  270 . This may occur where characteristics of the laser  230  and label surface  104  are such that a slower rotation during marking is used to ensure that a sufficient amount of laser energy be delivered to the positions  114  being marked to form marks of the proper color or darkness. Due to the inertia of the focus actuator  212 , focus optics  210 , and related components, the mechanical response to a signal to the focus actuator  212  is not instantaneous, and thus while the disc  100  is rotating, the response of the focus actuator  212  to a signal applied at a given angular position  110  will not mechanically occur until the disc  100  has already rotated to a different angular position  110 . This effect may be represented as an angular phase shift equal to the difference between the angular position  110  when a signal is applied, and the angular position  110  when the focus actuator  212  mechanically completes its movement. The drive controller  250  may compensate for this phase shift by applying actuator signals earlier in the rotation such that when the mechanical response of the focus actuator  212  does occur, it occurs at the desired angular position  110 . Since the actuator response time remains constant, the magnitude of angular phase shift will depend on the speed of rotation of the disc  100 . At a slower rotational speed the phase shift angle will be smaller, while at a higher rotational speed the phase shift angle will be greater. During the operation of the disc location marking module  280 , this phase shift is compensated for by applying a phase offset between the mapping  270  and marking  280 , to ensure that the focus optics  210  are properly positioned for positions  114 . In one embodiment, the phase offset may be derived from the ratio of the two speeds of rotation used for mapping  270  and marking  280 . 
     In one embodiment, the disc location marking module  280  rotates the disc  100 , for a given radial position  112 , at a slower speed than the disc surface mapping module  270 . In one embodiment, the disc location marking module  280  rotates the disc  100  at less than 6 rpm during the marking operation. 
     Considering now in greater detail one embodiment of a method of forming a visible label on an optical disc, and with reference to  FIGS. 4A-4B , the method  400  can be considered as having a mapping phase that encompasses steps  404  through  424  and a marking phase that encompasses steps  426  through  428 . In some embodiments, the method may be implemented in the disc drive  200  and performed by controller  250 , where some or all of the steps are stored as instructions in memory, such as memory  260 , and are computer-executable by CPU  254 . Disc surface mapping module  270  may perform the mapping phase, while disc location marking module  280  may perform the marking phase. 
     At  402 , a plurality of virtual angular sectors  116  are defined on a label surface  104  of an optical disc  100 . In some embodiments at least 16 sectors are defined. In another embodiment, 20 sectors are defined. 
     At  404 , the optical disc is rotated at a first speed. In some embodiments, the first speed is greater than 50 rpm. In some embodiments, for a given radial position  112 , the first speed is faster than a second speed at which the disc is rotated during the marking phase. 
     At  406 , the laser  230 , and consequently the laser beam  214 , is positioned at a radial position  112  at which the contour of the label surface  104  is to be characterized. 
     At  408 , initial values of the current overall gain coefficients are established. The overall gain coefficients are used to generate the signal to the focus actuator  212  to position the focus optics  210  at the baseline  340  during the mapping phase, and to generate the signal to the focus actuator  212  to position the focus optics  210  at the desired focus position when marking disc locations  114  during the marking phase. In some embodiments, the initial gain coefficient for the DC term equals 1, and the initial gain coefficients for the sinusoidal and cosinusoidal terms equals 0. 
     At  410 , a baseline focus position for focus optics  210  of the laser  230  for the sectors  116  is determined. In some embodiments, a signal for the focus actuator  212  is derived to set the baseline  340  by using the current overall gain coefficients  292  in an algorithm. In some embodiments, the algorithm is a Fourier series algorithm. 
     At  412 , the focus optics  210  of the laser  230  are sinusoidally swept from the baseline  340  once per sector  116  during a single revolution of the disc  100 . In some embodiments, a sinusoidal signal  330  is superimposed on the actuator signal for the baseline  340 . The signal applied to the focus actuator  212  is a continuous sinusoid  330  during the single revolution of the disc  100 . 
     At  414 , while sweeping the focus optics  210  during the single rotation of the disc  100 , the laser beam  214  from the laser  230  is impinged on the label surface  104 , and a SUM signal indicative of a degree of focus of the impinged laser beam  214  on the label surface  104  is measured at multiple angular positions  110  of each sector  116 . In some embodiments, the laser beam  214  is periodically impinged on the label surface  104  at a time, and for a duration, that allows the SUM signal to be measured at the particular multiple angular positions  110  of each sector  116 . In some embodiments, each of the multiple angular positions  110  corresponds to one of the timing features  107 , which may be on the disc  100  or alternatively in the drive  200 . All of the SUM signal measurements needed to modify the gain coefficients  292  for one iteration of the mapping phase are measured during a single rotation of the disc  100 . 
     The disc drive  200  typically continues to rotate the disc  100  at the first speed throughout the mapping phase, in order to minimize or eliminate start-up and settling times associated with starting and stopping disc rotation. However, the operation of steps  412  and  414  are performed during a single revolution of the disc  100 . 
     At  416 , updated gain coefficients for each sector  116  are derived from the measured SUM signals for that sector  116 . In some embodiments, an error term is generated from the measured SUM signals for each sector  116 , and updated gain coefficients for that sector  116  are derived from the error term for that sector  116 . Typically, the updated gain coefficients for the individual sectors  116  are averaged over all sectors  116  to derive updated overall gain coefficients  292 . 
     At  418 , it is determined whether or not the overall gain coefficients have converged. In some embodiments, convergence is determined if the error terms are below a threshold. In some embodiments, convergence is determined if the change in overall gain coefficients between iterations is below a threshold. If the gain coefficients have not converged (“No” branch of  418 ), the mapping phase loops back to  410  and the new baseline focus position is determined using the updated gain coefficients. 
     If the gain coefficients have converged (“Yes” branch of  418 ), then at  422  the converged overall gain coefficients  292  for the radial position  112  are stored, such as, for example, in memory  290 . 
     At  424 , it is determined whether the label surface  104  of the disc  100  is to be characterized at another radial position  112 . Typically, the disc  100  includes a large number of virtual radial tracks  112  between the inner and outer radii of the disc  100 . However, in some embodiments the overall gain coefficients  292  determined for one radial position  112  will also be used for a number of adjacent radial positions. In some embodiments, the overall gain coefficients  292  are only determined at or near radial positions  112  of locations  114  at which the label data  294  indicates marks will be made. If the label surface  104  of the disc  100  is to be characterized at another radial position  112  (“Yes” branch of  424 ), the mapping phase continues at  406  by positioning the laser  230  at the next radial position  112  to be characterized. 
     If the characterization of all radial positions  112  has been completed (“No” branch of  424 ), the method enters the marking phase. At  426 , the disc  100  is rotated at a second speed. In some embodiments, the second speed is less than 6 rpm. In some embodiments, the second speed is slower than a first speed at which the disc  100  is rotated during the mapping phase. 
     At  428 , selected locations  114  on the label surface  104  are marked by controlling the laser  230  to impinge the laser beam  214  at the desired radial  112  and angular  110  positions on the label surface  104  that correspond to the locations  114 , while applying signals to the focus actuator  212  which position the focus optics  210  to focus the laser beam  214  on the locations  114  on the label surface  104 . In some embodiments, the signals for the focus actuator  212  are derived by using the overall gain coefficients  292  for the radial position  112  of the location(s)  114  in an algorithm to generate the signals. In some embodiments, the algorithm is a Fourier series algorithm. In some embodiments, the Fourier series comprises a DC component and first-order through fourth-order sinusoidal and cosinusoidal components, where one of the overall gain coefficients  292  for the radial position  112  is associated with each of the components. In some embodiments, a constant focus offset is added to the signal generated by the algorithm. 
     From the foregoing it will be appreciated that the disc drive and methods provided by the present invention represent a significant advance in the art. Although several specific embodiments of the invention have been described and illustrated, the invention is not limited to the specific methods, forms, or arrangements of parts so described and illustrated. For example, the invention is not limited to an optical disc drive. Rather, the invention also applies to other devices which mark optically-labelable material having a varying surface contour, regardless whether the motion between the labelable material and the source of electromagnetic energy is rotational or translational. This description of the invention should be understood to include all novel and non-obvious combinations of elements described herein, and claims may be presented in this or a later application to any novel and non-obvious combination of these elements. The foregoing embodiments are illustrative, and no single feature or element is essential to all possible combinations that may be claimed in this or a later application. Unless otherwise specified, steps of a method claim need not be performed in the order specified. The invention is not limited to the above-described implementations, but instead is defined by the appended claims in light of their full scope of equivalents. Where the claims recite “a” or “a first” element of the equivalent thereof, such claims should be understood to include incorporation of one or more such elements, neither requiring nor excluding two or more such elements. Terms of orientation and relative position (such as “top”, “bottom”, “side”, and the like) are not intended to require a particular orientation of embodiments of the present invention, or of any element or assembly of embodiments of the present invention, and are used only for convenience of illustration and description.