Abstract:
In an optical disk apparatus for focusing a light beam on a track of an optical disk by using a tracking control loop to perform at least one of recording and reproducing operations upon the optical disk, a loop level calculating unit calculates loop levels of the tracking control loop. A control unit calculates a loop gain of the tracking control loop in accordance with the loop levels of the tracking control loop and compensates for a radial tilt of the optical disk in accordance with the calculated loop gain of the tracking control loop.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an optical disk apparatus, and more particularly, to the improvement of compensation of a radial tilt of an optical disk. 
     2. Description of the Related Art 
     In an optical disk apparatus, when an optical disk is inclined in the radial direction with respect to an objective lens of an optical head, the configuration of focused spots on the optical disk fluctuates due to the coma aberration arising from the inclination of the optical disk in the radial direction thereof which is called a radial tilt, so that the read/write characteristics fluctuate. Therefore, it is required to detect and compensate for the radial tilt of the optical disk. 
     In a first prior art optical disk apparatus (see: JP-A-11-039683 and JP-A-2001-195762), a tilt sensor is provided within an optical head to detect a radial tilt of an optical disk, and an actuator for tilting an objective lens or the optical head in the radial direction of the optical disk in accordance with the output signal of the tilt sensor. As a result, the radial tilt detected by the tilt sensor is brought close to zero. 
     In the above-described first prior art optical disk apparatus, however, since the tilt sensor is large in scale, it is impossible to decrease the size of the optical head including the tilt sensor. If the tilt sensor is forcibly decreased in size, the sensitivity of the tilt sensor deteriorates. 
     In a second prior art optical disk apparatus (see: JP-A-9-007207 and JP-A-2000-057606), the amplitude of a tracking error-signal, the amplitude of an radio frequency (RF) signal or a jitter of a digitalized signal of the RF signal is calculated, so that the radial tilt of an optical head is compensated for in accordance with a relationship between the radial tilt of an optical disk and the above-calculated value. 
     In the above-described second prior art optical disk apparatus, however, since there are a lot of disturbances other than the radial tilt component, a high accuracy of compensation of the radial tilt cannot be expected. 
     In a third prior art optical disk apparatus (see: JP-A-10-222860 and JP-A-2000-195080), at least one tilt sensor is provided outside the optical head to estimate a radial tilt of an optical disk. 
     In the above-described third prior art optical disk apparatus, although the problem of the first prior art optical disk apparatus is dissolved, the estimated value of the radial tilt is not accurate, so that a high accuracy of compensation of the radial tilt cannot be expected. 
     In a fourth prior art optical disk apparatus (see: JP-A-2000-348362), a focus search is carried out to detect periods at inner and outer peripheral sides of an optical disk corresponding to the amount of a radial tilt, and a difference between the periods is calculated to estimate the amount and direction of the radial tilt. 
     In the above-described fourth prior art optical disk apparatus, however, since the above-mentioned difference is affected by the attitude of the optical disk, and there is a rolling per one revolution of the optical disk, a high accuracy of compensation of the radial tilt cannot be expected. 
     In a fifth optical disk apparatus (see: H. Yamaguchi et al., “4.7 GB DVD-RAM Drive”, Matsushita Technical Journal Vol. 45, No. 6, pp. 67-73, Dec. 1999), an offset value of a tracking error signal is detected as a radial tilt signal by centering a focused spot at a track using complementary allocated pit address (CAPA) headers. 
     The above-described fifth prior art optical disk apparatus, however, cannot be applied to optical disks having formats other than the CAPA headers. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide an optical disk apparatus capable of accurately compensating for a radial tilt without a tilt sensor. 
     Another object is to provide a method for accurately compensating for a radial tilt of an optical disk apparatus. 
     According to the present invention, in an optical disk apparatus for focusing a light beam on a track of an optical disk by using a tracking control loop to perform at least one of recording and reproducing operations upon the optical disk, a loop level calculating unit calculates loop levels of the tracking control loop. A control unit calculates a loop gain of the tracking control loop in accordance with the loop levels of the tracking control loop and compensates for a radial tilt of the optical disk in accordance with the calculated loop gain of the tracking control loop. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be more clearly understood from the description set forth below, with reference to the accompanying drawings, wherein: 
         FIG. 1  is a diagram illustrating a first embodiment of the optical disk apparatus according to the present invention; 
         FIG. 2  is a detailed diagram of the optical head of  FIG. 1 ; 
         FIG. 3  is a detailed block diagram of the loop level calculating unit of  FIG. 1 ; 
         FIG. 4  is a flowchart for explaining a first operation of the system control unit of  FIG. 1 ; 
         FIG. 5  is a table stored in the memory of the system control unit of  FIG. 1 ; 
         FIG. 6  is a diagram for explaining the flowchart of  FIG. 4 ; 
         FIG. 7  is a flowchart showing a modification of the flowchart of  FIG. 4 ; 
         FIG. 8  is a diagram for explaining the flowchart of  FIG. 7 ; 
         FIG. 9  is a flowchart for explaining a second operation of the system control unit of  FIG. 1 ; 
         FIG. 10  is a diagram illustrating a second embodiment of the optical disk apparatus according to the present invention; 
         FIG. 11  is a flowchart for explaining the operation of the system control unit of  FIG. 10 ; 
         FIG. 12  is a detailed flowchart of step  1102  of  FIG. 11 ; 
         FIGS. 13 and 14  are diagrams for explaining the flowchart of  FIG. 12 ; 
         FIG. 15  is a detailed flowchart of step  1104  of  FIG. 11 ; 
         FIG. 16  is a diagram illustrating a third embodiment of the optical disk apparatus according to the present invention; and 
         FIG. 17  is a flowchart for explaining the operation of the system control unit of  FIG. 16 . 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In  FIG. 1 , which illustrates a first embodiment of the optical disk apparatus according to the present invention, when an optical disk  1  is rotated by a spindle motor  2  at a predetermined speed, an optical head  3  performs a read/write operation upon the optical disk  1 . The optical head  3  is mounted on a head carriage  4  which can be moved along the radial direction of the optical disk  1  by a lead screw  5  driven by a carriage motor  6 . 
     The optical head  3  includes an objective lens  31  for generating a light beam for the optical disk  1  and receiving a reflected light beam therefrom. 
     The spindle motor  2  is controlled by a spindle control unit  7 . 
     Disk signals are supplied from the optical head  3  to an RF signal calculating unit  8 , a focus error signal calculating unit  9  and a tracking error signal calculating unit  10 . The RF signal calculating unit  8  calculates an RF signal V rf . The focus error signal calculating unit  9  calculates a focus error signal V f  by a known astigmatism method. The tracking error signal calculating unit  10  calculates a tracking error signal V t  by a known push-pull method and transmits it to a loop level calculating unit  11 . 
     The spindle control unit  7 , the RF signal calculating unit  8 , the focus error signal calculating unit  9  and the tracking error signal calculating unit  10  (the loop level calculating unit  11 ) are connected to a system control unit  12  which is constructed by a central processing unit (CPU), memories and the like. 
     The system control unit  12  also controls a focus servo unit  13  for driving the objective lens  31  along the focus direction of the optical disk  1  in accordance with the focus error signal V f , a radial tilt control unit  14  for driving the objective lens  31  along the radial direction of the optical disk  1 , and a tracking servo unit  15  for driving the objective lens  31  along the radial direction of the optical disk  1  in accordance with the tracking error signal V t  to track the focused spot on a track. In this case, the system control unit  12  controls a carriage control unit  16  in accordance with the tracking error signal V t , so that the carriage motor  6  is driven to move the optical head  3  along the radial direction of the optical disk  1 . 
     A driving current I f  generated from the focus servo unit  13  and a driving current I r  generated from the radial tilt control unit  14  are added by an adder  17  which supplies a driving current I f +I r  to a focus winding  32  provided in the optical head  3  as illustrated in  FIG. 2 . Also, a difference between the driving current I f  generated from the focus servo unit  13  and the driving current I r  generated from the radial tilt control unit  14  is calculated by a subtracter  18  which supplies a driving current I f −I r  to a focus winding  33  provided in the optical head  3  as illustrated in  FIG. 2 . Further, a driving current I t  generated from the tracking servo unit  15  is supplied to a tracking winding  34  in the optical head  3  as illustrated in  FIG. 2 . 
     As illustrated in  FIG. 2 , if the driving currents I f  having the same phase are supplied to the focus windings  32  and  33 , the objective lens  31  is moved along the focus direction. Also, if the driving currents I r  having the opposite phases are supplied to the focus windings  32  and  33 , the objective lens  31  is moved along the radial tilt direction. 
     In  FIG. 3 , which is a detailed block circuit diagram of the loop level calculating unit  11  of  FIG. 1 , the loop level calculating unit  11  is constructed by an adder  111  inserted between the tracking error signal calculating unit  10  and the tracking servo unit  15  via the system control unit  12 , so that a tracking control loop is formed. In order to obtain a loop gain of the tracking control loop, while the tracking servo unit  15  is being operated so that a focused spot follows a track, a periodic wave signal such as a sinusoidal wave signal having a frequency of 2 to 2.5 kHz is generated by a sinusoidal wave generator  112  and is inserted via the adder  111  into the tracking control loop. The input level V in  of the periodic wave signal to the tracking control loop is detected by a level detection unit  113  formed by a bandpass filter  1131 , a full-wave rectifier  1132  and a lowpass filter  1133 . On the other hand, the output level V out  of the periodic wave signal from the tracking control loop is detected by a level detection unit  114  formed by a bandpass filter  1141 , a full-wave rectifier  1142  and a lowpass filter  1143 . In this case, the bandpass filters  1131  and  1141  only pass the frequency component of the periodic wave signal of the sinusoidal wave generator  112  therethrough, so that the frequency component of fluctuation of the tracking error signal is excluded by the bandpass filters  1131  and  1141 . 
     Note that a loop gain G denoted by a ratio of the output level V out  to the input level V in  is calculated by the system control unit  12 (G=V out /V in ). 
     When the loop gain G is maximum, the read/write characteristics are optimal. Therefore, when the radial tilt control unit  14  generates an optimal driving current I r (LPOPT) for the maximal loop gain G, the read/write characteristics are optimal. 
     A first operation of the system control unit  12  for determining the optimal driving current I r (LPOPT) will be explained next with reference to  FIG. 4 . The flowchart of  FIG. 4  is carried out every time the optical head  3  is placed in a new track of the optical disk  1 . 
     First, at step  401 , the sinusoidal wave generator  112  is turned ON. 
     Next, at step  402 , a value i is initialized, i.e., i=0. 
     Next, at step  403 , a driving current I r  of the radial tilt control unit  15  is set by
 
I r ←I ri 
 
     Note that the driving currents I ri  (i=0 to N) corresponding to tilt angles TA 0 , TA 1 , . . . , TA 6  as shown in  FIG. 2  where N=6 are predetermined and are stored in the memory as a table as shown in  FIG. 5 . 
     Next, at step  404 , the input level V in  and the output level V out  are fetched from the loop level calculating unit  11  and a loop gain G is calculated by
 
G i ←V out /V in 
 
     Steps  405  and  406  repeat the control at steps  403  and  404  until the value i reaches N. As a result, a relationship between the value i(the driving current I ri ) and the loop gain G i  is obtained as shown in  FIG. 6 . 
     Next, at step  407 , a curve such as a quadratic curve QC 1  as shown in  FIG. 6  is approximated by the least square method to the driving currents I ri  and the loop gains G i . 
     Next, at step  408 , an optimal driving current I r (LPOPT) having the maximal loop gain G(MAX) as shown in  FIG. 6  is determined. 
     Next, at step  409 , the driving current I r  is fixed to I r (LPOPT). 
     Next, at step  410 , the sinusoidal wave generator  112  is turned OFF. 
     The routine of  FIG. 4  is completed by step  411 . 
     In  FIG. 7 , which is a modification of the flowchart of  FIG. 4 , steps  407  and  408  are replaced by steps  701  and  702 , respectively. That is, the control at step  406  of  FIG. 4  proceeds to step  701  where two driving currents I r (MAX 1 ) and I r (MAX 2 ) having maximal loop gains are selected. For example, I r2  and I r3  as shown in  FIG. 8  are selected. Next, at step  702 , an optimal driving current I r (LPOPT) is calculated by
 
 I   r ( LPOPT )←( I   r (MAX1)+ I   r (MAX2))/2
 
     Then, the control proceeds to step  409  of  FIG. 4 . 
     In the modification as shown in  FIG. 7 , since the approximating step  407  of  FIG. 4  is unnecessary, the speed of determination of the optimal driving current I r (LPOPT) is enhanced although the accuracy thereof deteriorates. 
     A second operation of the system control unit  12  of  FIG. 4  will be explained next with reference to  FIG. 9 . In  FIG. 9 , an optimal driving current I r (LPOPT) is determined from three successive driving currents I r,i−1 , I r  and I r,i+1 . The flowchart of  FIG. 9  is also carried out every time the optical head  3  is placed in a new track of the optical disk  1 . 
     First, at step  901 , the sinusoidal wave generator  112  is turned ON. 
     Next, at step  902 , a value i is initialized, i.e., i=i0. Note that the initial value i0 is not always 0, for example, N/2. 
     Next, at step  903 , a driving current I r  of the radial tilt control unit  15  is set by
 
I r ←I r,i−1 
 
     Next, at step  904 , the input level V in  and the output level V out  are fetched from the loop level calculating unit  11  and a loop gain G i−1  is calculated by
 
G i−1 κV out /V in 
 
     Next, at step  905 , a driving current I r  of the radial tilt control unit  15  is set by
 
I r ←I ri 
 
     Next, at step  906 , the input level V in  and the output level V out  are fetched from the loop level calculating unit  11  and a loop gain G i  is calculated by
 
G i ←V out /V in 
 
     Next, at step  907 , a driving current I r  of the radial tilt control unit  15  is set by
 
I r ←I r,i+1 
 
     Next, at step  908 , the input level V in  and the output level V out  are fetched from the loop level calculating unit  11  and a loop gain G i+1  is calculated by
 
G i+1 ←V out /V in 
 
     Next, at step  909 , it is determined whether or not G i &gt;G i−1  is satisfied, and at step  910 , it is determined whether or not G i &gt;G i+1  is satisfied. That is, steps  909  and  910  determines whether or not G i  is the maximal value of G i−1 , G i  and G i+1 . Only when G i &gt;G i−1  and G i &gt;G i+1 , does the control proceed to step  911  which set an optimal driving current I r (LPOPT) by
 
I r (LPOPT)←I ri 
 
     Next, at step  912 , the driving current I r  is fixed to I r (LPOPT). 
     Next, at step  913 , the sinusoidal wave generator  112  is turned OFF. 
     When it is determined at step  909  that G i ≦G i−1  is satisfied, the control proceeds to steps  914  to  917 . 
     At step  914 , the loop gains G i  and G i−1  are replaced by G i+1  and G i , respectively. 
     Next, at step  915 , the value i is decremented by
 
i←i−1
 
     Next, at step  916 , a driving current I r  of the radial tilt control unit  15  is set by
 
I r ←I r,i−1 
 
     Next, at step  917 , the input level V in  and the output level V out  are fetched from the loop level calculating unit  11  and a loop gain G i−1  is calculated by
 
G i−1 ←V out /V in 
 
     Then, the control returns to steps  909  and  910 , thus determining whether or not G i  is the maximal value of G i−1 , G i  and G i+1 . 
     When it is determined at step  910  that G i ≦G i−1  is satisfied, the control proceeds to steps  918  to  921 . 
     At step  918 , the loop gains G i  and G i+1  are replaced by G i−1  and G i , respectively. 
     Next, at step  919 , the value i is incremented by
 
i←i+1
 
     Next, at step  920 , a driving current I i  of the radial tilt control unit  15  is set by
 
I r ←I r,i+1 
 
     Next, at step  921 , the input level V in  and the output level V out  are fetched from the loop level calculating unit  11  and a loop gain G i+1  is calculated by
 
 G   i+1   ←V   out   /V   in 
 
     Then, the control returns to steps  909  and  910 , thus determining whether or not G i−1  is the maximal value of G i−1 , G i  and G i+1 . 
     Even in  FIG. 9 , since the approximating step  407  of  FIG. 4  is unnecessary, the speed of determination of the optimal driving current I r (LPOPT) is enhanced although the accuracy thereof deteriorates. 
     In the first embodiment as illustrated in  FIG. 1 , every time the optical head  3  is placed on one new of the optical disk, an optical driving current I r (LPOPT) is determined in accordance with the tracking loop gain to compensate for the radial tilt. 
     In  FIG. 10 , which illustrates a second embodiment of the optical disk apparatus according to the present invention, when the optical head  3  is located in an initial track X of the optical disk  1 , an initial optimal radial tilt control operation as shown in  FIG. 12  is carried out, and after that, when the optical head  3  is located in an arbitrary track Y of the optical disk  3 , a radial tilt control operation as shown in  FIG. 15  is carried out. 
     That is, every time the optical head  3  is placed in a new track of the optical disk  1 , a system control unit  12 ′ carries out a flowchart as shown in  FIG. 11 . 
     In  FIG. 11 , first at step  1101 , it is determined whether or not a flag FX is “0”. Note that the flag FX is initially reset (FX=“0”) when the power is turned ON. If FX=“0”, the control proceeds to step  1102  which carries out the operation as shown in  FIG. 12 , and then, at step  1103 , the flag FX is set (FX=“1”). On the other hand, if FX=“1”, the control proceeds to step  1104  which carries out the operation as shown in  FIG. 15 . Then, the routine of  FIG. 11  is completed by step  1105 . 
     Thus, after the operation as shown in  FIG. 12  for the initial track X is carried out, the operation as shown in  FIG. 15  for the arbitrary track Y is carried out. 
     The initial optimal radial tilt control routine as shown in  FIG. 12  will be explained below. Note that steps  401 A through  408 A and  410 A are the same as steps  401  through  408  and  410 , respectively, of  FIG. 4 , steps  1201  through  1205  are added to steps of  FIG. 4 , and step  409  is of  FIG. 4  is modified to step  1206 . 
     That is, at step  1201  the RF signal V rf  is fetched from the RF signal calculating unit  8 , and a jittering value J i  of the RF signal V rf  is calculated by a jittering detecting means (not shown). The jittering detecting means is constructed by a counter for counting a time difference between a regeneration clock signal and a regenerated data signal. 
     After steps  405 A and  406 A repeat the control at step  1201 , at step  1202 , a curve such as a quadratic curve QC 2  as shown in  FIG. 13  is approximated by the least square method to the driving currents I ri  and the jittering values J i . 
     Next, at step  1203 , an optimal driving current I r (RFOPT) having the minimal jittering value J(MIN) as shown in  FIG. 13  is determined. 
     Next, at step  1204 , a correction value ΔI is calculated by
 
ΔI←I r (RFOPT)−I r (LPOPT)
 
     Next, at step  1205 , the correction value ΔI is stored in the memory. 
     Next, at step  1206 , the driving current I r  is fixed to I r (RFOPT). 
     Note that when the axis of the objective lens  31  is not optimum with respect to the optical disk  1 , it is well known that the jittering value of the RF signal is increased. That is, when a radial tilt occurs, pit information recorded in a track adjacent to the track X leaks to invite a so-called crosstalk. Since this crosstalk depends on the pattern of the pit information, a jittering phenomenon in response to the radial tilt occurs. 
     At steps  1201 ,  1202  and  1203  of  FIG. 11 , the amplitude A of the RF signal can be used instead of the jittering value J. In this case, at step  1201 , the RF signal V rf  is fetched from the RF signal calculating unit  8 , and an amplitude of the RF signal V rf  is calculated. Also, at step  1202 , a curve such as a quadratic curve QC 3  as shown in  FIG. 14  is approximated by the least square method to the driving current I ri  and the amplitude A i . Further, at step  1203 , an optimal driving current I i (RFOPT) having the maximal amplitude A(MAX) as shown in  FIG. 14  is determined. 
     The optimal radial tilt control routine as shown in  FIG. 15  will be explained below. Note that steps  401 B through  408 B and  410 B are the same as steps  401  through  408  and  410 , respectively, and step  409  is modified to step  1501 . 
     That is, at step  1501  the driving current I r  is fixed to I r (LPOPT)+ΔI. 
     Thus, in the second embodiment as illustrated in  FIG. 10 , an optimal driving current I r (LPOPT)+ΔI is substantially determined in accordance with the jittering value or amplitude of the RF signal to compensate for the radial tilt. 
     Note that a similar control as shown in  FIG. 7  can be applied to steps  407 A and  407 A and steps  1202  and  1203  of  FIG. 12  and steps  407 B and  408 B of  FIG. 15 . Also, a similar control as shown in  FIG. 9  can be applied to  FIGS. 12 and 15 . 
     In  FIG. 16 , which illustrates a third embodiment of the optical disk apparatus according to the present invention, when the optical head  3  is located in initial tracks X 1  and X 2  of the optical disk  1 , initial optimal radial tilt control operation as shown in  FIG. 4  or  12  is carried out, and after that, when the optical head  3  is located in an arbitrary track Y of the optical disk  3 , a radial tilt control operation using an interpolation method such as a linear interpolation, an interpolation method or an extrapolation method is carried out. 
     That is, every time the optical head  3  is placed in a new track of the optical disk  1 , a system control unit  12 ″ carries out a flowchart as shown in  FIG. 17 . 
     In  FIG. 17 , first, at step  1701 , it is determined whether or not a flag FX 1  is “0”. Note that the flag FX 1  is initially reset (FX 1 =“0”) when the power is turned ON. If FX 1 =“0”, the control proceeds to step  1702  which carries out the operation as shown in  FIG. 4 , so that an optimal driving current I r (LPOPT) at R=r1 is calculated. Then, at step  1703 , the flag FX 1  is set (FX 1 =“1”). 
     When FX 1 =“1”, the control proceeds from step  1701  to  1704  which determines whether or not a flag FX 2  ia “0”. Note that the flag FX 2  is also initially reset (FX 2 =“0”) when the power is turned ON. If FX 2 =“0”, the control proceeds to step  1705  which carries out the operation as shown in  FIG. 4 , so that an optimal driving current I r (LPOPT) at R=r2 is calculated. Then at step  1706  the flag FX 2  is set (FX 2 =“1”). 
     On the other hand, if FX 1 =FX 2 =“1”, the control proceeds via steps  1701  and  1704  to step  1707  which calculates an optimal driving current I r (LPOPT) at R=r by an interpolation method. That is, if, r1&lt;r&lt;r2, 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     R 
                                   
                                   = 
                                   r1 
                                 
                                 ) 
                               
                             
                             ) 
                           
                           · 
                           
                             
                               ( 
                               
                                 r 
                                 - 
                                 r2 
                               
                               ) 
                             
                             / 
                             
                               ( 
                               
                                 r2 
                                 - 
                                 r1 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The driving current I r  is fixed to I r (LPOPT) at R=r. 
     Then, the routine of  FIG. 17  is completed by step  1708 . 
     Thus, after the operation as shown in  FIG. 4  for the initial tracks X 1  and X 2  is carried out, the operation at step  1707  for the arbitrary track Y is carried out. 
     In  FIG. 17 , the first embodiment as shown in  FIG. 4  is applied; however, the second embodiment can be applied. In this case, at step  1702 , an optimal driving current I r (LPOPT) at R=r1 is calculated, and also, a correction value ΔI at R=r1 is calculated. Also, at step  1705 , an optimal driving current I r (LPOPT) at R=r2 is calculated, and also, a correction value ΔI at R=r2 is calculated. Further, at step  1707 , an optimal driving current I r (LPOPT) at R=r+I at R=r is calculated by an interpolation method. That is, if r1&lt;r&lt;r2, 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           I 
                           r 
                         
                         ⁡ 
                         
                           ( 
                           LPOPT 
                           ) 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       at 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       R 
                     
                     = 
                     
                       
                         r 
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           I 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           at 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           R 
                         
                       
                       = 
                       
                         r 
                         ← 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           
                                             I 
                                             r 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             LPOPT 
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         at 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         R 
                                       
                                       = 
                                       r1 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       r 
                                       - 
                                       r1 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           
                                             I 
                                             r 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             LPOPT 
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         at 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         R 
                                       
                                       - 
                                       r2 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       r2 
                                       - 
                                       r 
                                     
                                     ) 
                                   
                                 
                               
                               ) 
                             
                             / 
                             
                               ( 
                               
                                 r2 
                                 - 
                                 r1 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   I 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   at 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   R 
                                 
                                 = 
                                 r1 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 r 
                                 - 
                                 r1 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   I 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   at 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   R 
                                 
                                 = 
                                 r2 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 r2 
                                 - 
                                 r 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   ) 
                 
                 / 
                 
                   ( 
                   
                     r2 
                     - 
                     r1 
                   
                   ) 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               Also 
             
             , 
             
               
                 if 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 r1 
               
               &lt; 
               r2 
               &lt; 
               r1 
             
             , 
             
               
                 
                   I 
                   r 
                 
                 ( 
                 
                     
                 
                 ⁢ 
                 LPOPT 
                 ) 
               
               ⁢ 
               
                   
               
               ⁢ 
               at 
               ⁢ 
               
                   
               
               ⁢ 
               
                   
                 
                   
                     R 
                     = 
                     
                       
                         
                             
                           
                             r 
                             ← 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             
                                               I 
                                               r 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               LPOPT 
                                               ) 
                                             
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           at 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           R 
                                         
                                         = 
                                         r2 
                                       
                                       ) 
                                     
                                     - 
                                     
                                       ( 
                                       
                                         
                                           
                                             
                                               I 
                                               r 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               LPOPT 
                                               ) 
                                             
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           at 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           R 
                                         
                                         = 
                                         r1 
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                                 · 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       - 
                                       r1 
                                     
                                     ) 
                                   
                                   / 
                                   
                                     ( 
                                     
                                       r2 
                                       - 
                                       r1 
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 ( 
                                 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     I 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     at 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     R 
                                   
                                   = 
                                   r2 
                                 
                                 ) 
                               
                               - 
                               
                                 ( 
                                 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     I 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     at 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     R 
                                   
                                   = 
                                   r1 
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                         · 
                         
                           
                             ( 
                             
                               r 
                               - 
                               r1 
                             
                             ) 
                           
                           / 
                           
                             ( 
                             
                               r2 
                               - 
                               r1 
                             
                             ) 
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Further 
                     
                   
                   , 
                   
                     
                       if 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       r 
                     
                     &lt; 
                     r1 
                     &lt; 
                     r2 
                   
                   , 
                   
                     
                       
                         
                           I 
                           r 
                         
                         ⁡ 
                         
                           ( 
                           LPOPT 
                           ) 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       at 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       R 
                     
                     = 
                     
                       r 
                       ← 
                       
                         
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         I 
                                         r 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         LPOPT 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     at 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     R 
                                   
                                   = 
                                   r2 
                                 
                                 ) 
                               
                               - 
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         I 
                                         r 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         LPOPT 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     at 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     R 
                                   
                                   = 
                                   r1 
                                 
                                 ) 
                               
                             
                             ) 
                           
                           · 
                           
                             
                               ( 
                               
                                 r 
                                 - 
                                 r2 
                               
                               ) 
                             
                             / 
                             
                               ( 
                               
                                 r2 
                                 - 
                                 r1 
                               
                               ) 
                             
                           
                         
                         + 
                         
                             
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     I 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     at 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     R 
                                   
                                   = 
                                   r2 
                                 
                                 ) 
                               
                               - 
                               
                                 ( 
                                 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     I 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     at 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     R 
                                   
                                   = 
                                   R1 
                                 
                                 ) 
                               
                             
                             ) 
                           
                           · 
                           
                             
                               ( 
                               
                                 r 
                                 - 
                                 r2 
                               
                               ) 
                             
                             / 
                             
                               ( 
                               
                                 r2 
                                 - 
                                 r1 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The driving current I r +ΔI is fixed to I r (LPOPT) at R=r+ΔI at R=r. 
     In the third embodiment as illustrated in  FIG. 16 , only two initial tracks are provided; however, three or more initial tracks are provided. 
     Also, in the above-described embodiments, the compensation of a radial tilt is carried out by directly driving the objective lens  31 ; however, this compensation can be carried out without driving the objective lens  31 . For example, a liquid crystal optical element is provided within the optical head  3 , so that voltages are applied to the liquid crystal optical element. As a result, the radial tilt signal is brought close to zero. In this case, since the liquid crystal optical element is divided into a plurality of regions, the voltages applied to the regions change the coma aberration for the transmission light beam therethrough, so that the coma aberration due to the radial tilt of the optical disk  1  can be compensated for by the changed coma aberration. This liquid crystal optical element is disclosed in Sakashi Ohtake et al., “The Application of a Liquid Crystal Panel for the 15 Gbyte Optical Disk Systems”, Jpn. J. Apple. Phys. Vol. 38, pp. 1744-1749, 1999. 
     As explained hereinabove, according to the present invention, a radial tilt can be accurately compensated for without a tilt sensor.