Abstract:
A method and an apparatus capable of increasing the video depths depending on the video content of each line in order to provide a maximum of color gradation for each given scene shall be proposed. For this purpose there is disclosed an apparatus for driving a display device including input means for receiving a digital value as video level for each pixel or cell of a line of the display device, reference signaling means for providing at least one reference driving signal and driving means for generating a driving signal on the basis of the digital value and the at least one reference driving signal. The apparatus further includes adjusting means for adjusting the at least one reference driving signal in dependence of the digital values of at least a part of the line.

Description:
This application claims the benefit, under 35 U.S.C. §119 of European Patent Application 06/300741.3, filed Jun. 30, 2006. 
     FIELD OF THE INVENTION 
     The present invention relates to a method for driving a display device including the steps of providing a digital value as video level for each pixel or cell of a line of the display device, providing at least one reference driving signal and generating a driving signal on the basis of the digital value and the at least one reference driving signal. Furthermore, the present invention relates to a respective apparatus for driving a display device. 
     BACKGROUND OF THE INVENTION 
     The structure of an active matrix OLED (organic light emitting display) or AMOLED is well known. According to  FIG. 1  it comprises:
         an active matrix  1  containing, for each cell (one pixel includes a red cell, a green cell and a blue cell), an association of several TFTs T 1 , T 2  with a capacitor C connected to an OLED material. Above the TFTs the capacitor C acts as a memory component that stores a value during a part of the video frame, this value being representative of a video information to be displayed by the cell  2  during the next video frame or the next part of the video frame. The TFTs act as switches enabling the selection of the cell  2 , the storage of a data in the capacitor C and the displaying by the cell  2  of a video information corresponding to the stored data;   a row or gate driver  3  that selects line by line the cells  2  of the matrix  1  in order to refresh their content;   a column or source driver  4  that delivers the data to be stored in each cell  2  of the current selected line; this component receives the video information for each cell  2 ; and   a digital processing unit  5  that applies required video and signal processing steps and that delivers the required control signals to the row and column drivers  3 ,  4 .       

     Actually, there are two ways for driving the OLED cells  2 . In a first way, each digital video information sent by the digital processing unit  5  is converted by the column drivers  4  into a current whose amplitude is directly proportional to the video level. This current is provided to the appropriate cell  2  of the matrix  1 . In a second way, the digital video information sent by the digital processing unit  5  is converted by the column drivers  4  into a voltage whose amplitude is proportional to the square of the video level. This current or voltage is provided to the appropriate cell  2  of the matrix  1 . 
     However, in principle, an OLED is current driven so that each voltage based driven system is based on a voltage to current converter to achieve appropriate cell lighting. 
     From the above, it can be deduced that the row driver  3  has a quite simple function since it only has to apply a selection line by line. It is more or less a shift register. The column driver  4  represents the real active part and can be considered as a high level digital to analog converter. 
     The displaying of a video information with such a structure of AMOLED is symbolized in  FIG. 2 . The input signal is forwarded to the digital processing unit that delivers, after internal processing, a timing signal for row selection to the row driver synchronized with the data sent to the column driver  4 . The data transmitted to the column driver  4  are either parallel or serial. Additionally, the column driver  4  disposes of a reference signaling delivered by a separate reference signaling device  6 . This component  6  delivers a set of reference voltages in case of voltage driven circuitry or a set of reference currents in case of current driven circuitry. The highest reference is used for the white and the lowest for the smallest gray level. Then, the column driver  4  applies to the matrix cells  2  the voltage or current amplitude corresponding to the data to be displayed by the cells  2 . 
     In order to illustrate this concept, the example of a voltage driven circuitry will be taken in the rest of this document. The driver of this example uses 8 reference voltages named V 0  to V 7  and the video levels are built as explained in the following table 1. 
     
       
         
               
             
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Gray level table from voltage driver 
               
             
          
           
               
                 Video level 
                 Grayscale voltage level 
               
               
                   
               
               
                  0 
                 V7 
               
               
                  1 
                 V7 + (V6 − V7) × 9/1175 
               
               
                  2 
                 V7 + (V6 − V7) × 32/1175 
               
               
                  3 
                 V7 + (V6 − V7) × 76/1175 
               
               
                  4 
                 V7 + (V6 − V7) × 141/1175 
               
               
                  5 
                 V7 + (V6 − V7) × 224/1175 
               
               
                  6 
                 V7 + (V6 − V7) × 321/1175 
               
               
                  7 
                 V7 + (V6 − V7) × 425/1175 
               
               
                  8 
                 V7 + (V6 − V7) × 529/1175 
               
               
                  9 
                 V7 + (V6 − V7) × 630/1175 
               
               
                 10 
                 V7 + (V6 − V7) × 727/1175 
               
               
                 11 
                 V7 + (V6 − V7) × 820/1175 
               
               
                 12 
                 V7 + (V6 − V7) × 910/1175 
               
               
                 13 
                 V7 + (V6 − V7) × 998/1175 
               
               
                 14 
                 V7 + (V6 − V7) × 1086/1175 
               
               
                 15 
                 V6 
               
               
                 16 
                 V6 + (V5 − V6) × 89/1097 
               
               
                 17 
                 V6 + (V5 − V6) × 173/1097 
               
               
                 18 
                 V6 + (V5 − V6) × 250/1097 
               
               
                 19 
                 V6 + (V5 − V6) × 320/1097 
               
               
                 20 
                 V6 + (V5 − V6) × 386/1097 
               
               
                 21 
                 V6 + (V5 − V6) × 451/1097 
               
               
                 22 
                 V6 + (V5 − V6) × 517/1097 
               
               
                 . . . 
                 . . . 
               
               
                   
                 V1 + (V0 − V1) × 2278/3029 
               
               
                 251  
                 V1 + (V0 − V1) × 2411/3029 
               
               
                 252  
                 V1 + (V0 − V1) × 2549/3029 
               
               
                 253  
                 V1 + (V0 − V1) × 2694/3029 
               
               
                 254  
                 V1 + (V0 − V1) × 2851/3029 
               
               
                 255  
                 V0 
               
               
                   
               
             
          
         
       
     
     Table 1 illustrates the obtained output voltages (gray scale voltage levels) from the voltage driver for various input video levels. For instance, the reference voltages of Table 2 are used. 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Example of voltage references 
               
             
          
           
               
                   
                 Reference Vn 
                 Voltage (V) 
               
               
                   
                   
               
             
          
           
               
                   
                 V0 
                 3 
               
               
                   
                 V1 
                 2.6 
               
               
                   
                 V2 
                 2.2 
               
               
                   
                 V3 
                 1.4 
               
               
                   
                 V4 
                 0.6 
               
               
                   
                 V5 
                 0.3 
               
               
                   
                 V6 
                 0.16 
               
               
                   
                 V7 
                 0 
               
               
                   
                   
               
             
          
         
       
     
     Then, the grayscale voltage levels of following Table 3 depending on video input levels according to Table 1 and Table 2 are obtained: 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Example of gray level voltages 
               
             
          
           
               
                   
                 Video level 
                 Grayscale voltage level 
               
               
                   
                   
               
               
                   
                  0 
                  0.00 V 
               
               
                   
                  1 
                 0.001 V 
               
               
                   
                  2 
                 0.005 V 
               
               
                   
                  3 
                 0.011 V 
               
               
                   
                  4 
                  0.02 V 
               
               
                   
                  5 
                 0.032 V 
               
               
                   
                  6 
                 0.045 V 
               
               
                   
                  7 
                  0.06 V 
               
               
                   
                  8 
                 0.074 V 
               
               
                   
                  9 
                 0.089 V 
               
               
                   
                 10 
                 0.102 V 
               
               
                   
                 11 
                 0.115 V 
               
               
                   
                 12 
                 0.128 V 
               
               
                   
                 13 
                  0.14 V 
               
               
                   
                 14 
                 0.153 V 
               
               
                   
                 15 
                 0.165 V 
               
               
                   
                 16 
                 0.176 V 
               
               
                   
                 17 
                 0.187 V 
               
               
                   
                 18 
                 0.196 V 
               
               
                   
                 19 
                 0.205 V 
               
               
                   
                 20 
                 0.213 V 
               
               
                   
                 21 
                 0.221 V 
               
               
                   
                 22 
                 0.229 V 
               
               
                   
                 . . . 
                 . . . 
               
               
                   
                 250  
                 2.901 V 
               
               
                   
                 251  
                 2.919 V 
               
               
                   
                 252  
                 2.937 V 
               
               
                   
                 253  
                 2.956 V 
               
               
                   
                 254  
                 2.977 V 
               
               
                   
                 255  
                  3.00 V 
               
               
                   
                   
               
             
          
         
       
     
     As can be seen in the previous paragraph current AMOLED concepts are capable of delivering 8-bit gradation per color. This can be further enhanced by using more advanced solutions like improvements on analog sub-fields. 
     In any case, there will be the need in the future of displays having more video-depth. This trend can be seen in the development of transmission standards based on 10-bit color channels. At the same time, various display manufacturers like PDP makers are claiming providing displays with more than 10-bit color-depth. 
     SUMMARY OF THE INVENTION 
     The object of the present invention is to provide a method and an apparatus capable of increasing the video depth depending on the video content of each line in order to provide a maximum of color gradation for a given scene. I.e., a line content picture enhancement shall be provided. 
     According to the present invention this object is solved by a method for driving a display device including the steps of
         providing a digital value as video level for each pixel or cell of a line of said display device,   providing at least one reference driving signal and   generating a driving signal on the basis of said digital value and said at least one reference driving signal, as well as   adjusting said video level and said at least one reference driving signal in dependence of the digital values of at least a part of said line.       

     Furthermore, there is provided an apparatus for driving a display device including
         input means for receiving a digital value for each pixel or cell of a line of said display device,   reference signaling means for providing at least one reference driving signal and   driving means for generating a driving signal on the basis of said digital value and said at least one reference driving signal, as well as   adjusting means for adjusting said video level and said at least one reference driving signal in dependence of the digital values of at least a part of said line.       

     Preferably, the display device is an AMOLED or a LCD. Especially, these display concepts can be improved by the above described method or apparatus. 
     The reference driving signal may be a reference voltage or a reference current. Each of these driving systems can profit from the present invention. 
     According to a further preferred embodiment, a maximum digital value of at least the part of a line is determined and when adjusting the reference driving signals, they are assigned to digital values between a minimum digital value, which is to be determined or is predetermined, and a maximum digital value. By this way, the whole range of gray scale levels is used for the video input of one line. 
     A further improvement can be obtained when determining a histogram of the digital values of at least the part of a line and adjusting the reference driving signals on the basis of this histogram. This results in an enhanced picture line-dependent gradation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments of the invention are illustrated in the drawings showing in: 
         FIG. 1  a circuit diagram of an AMOLED electronic according to the prior art; 
         FIG. 2  a possible OLED display structure according to the prior art; 
         FIG. 3  a sequence of the movie “Zorro” and a corresponding line analysis diagram; 
         FIG. 4  a sequence of a Colombia movie and a corresponding line analysis diagram; 
         FIG. 5  a histogram of line  303  from the sequence “Zorro”; 
         FIG. 6  a histogram of line  303  with optimized reference voltages and 
         FIG. 7  a block diagram of a hardware embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The main idea behind the inventive concept is based on the fact that in a video scene, the whole video dynamic range is not used on a large part of the scene.  FIGS. 3 and 4  show typical examples for frames of different dynamics.  FIG. 3  shows a dark picture of the movie “Zorro”. The picture has the format 4:3 with 561 lines. On the right hand side of  FIG. 3  the maximum video level of each line is plotted. 
       FIG. 4  shows a picture of a Colombia film. The picture has the format 16:9 with 267 lines. The right hand side diagram of  FIG. 4  illustrates that nearly each line is driven with a maximum video level. 
     Together,  FIGS. 3 and 4  show that for some sequences there are strong differences in the vertical distribution of video levels. The most differences are located in dark scenes with some luminous content as illustrated by the sequence “Zorro”. 
     On the other hand, it is important to notice that in dark scenes the eye is much more sensitive to picture gradation. Therefore, an optimization of picture gradation for dark scenes while keeping luminous scenes quite stable would have a positive effect on the global picture quality. 
     As already explained, the main idea is to perform a picture line-dependent gradation by optimizing the driver reference signaling (voltage or current) to the maximum of video levels available in a line. For instance, in the sequence “Zorro” of  FIG. 3 , the maximum video level for line  303  is  128 . Therefore, if nothing is done, from the 8-bit of available gradations ( 0  to  255 ), only 7 are used for this line ( 0  to  128 ). However, according to the present invention, the 8-bit gradation for video levels between  0  and  128  will be used. In order to do that, the reference signaling of the driver is adjusted to these 129 levels. In the present example of a voltage driven system the maximum voltage level will be adjusted to the  129 / 256  of the original one and all other voltages accordingly. This is illustrated in following Table 4: 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Example of adjusted voltage references for line 303 
               
             
          
           
               
                 Reference Vn 
                 Line 303 Voltage (Vn) 
                 Original Voltage (Vrefn) 
               
               
                   
               
             
          
           
               
                 V0 
                 1.5 
                 3 
               
               
                 V1 
                 1.3 
                 2.6 
               
               
                 V2 
                 1.1 
                 2.2 
               
               
                 V3 
                 0.7 
                 1.4 
               
               
                 V4 
                 0.3 
                 0.6 
               
               
                 V5 
                 0.15 
                 0.3 
               
               
                 V6 
                 0.08 
                 0.16 
               
               
                 V7 
                 0 
                 0 
               
               
                   
               
             
          
         
       
     
     More generally, a complex function can be applied to the reference signaling under the form S n =f(Sref n ;MAX(Line)) where MAX(Line) represents the maximum video level used for a given line and Srefn the reference signaling (either voltage or current). This function can be implemented by means of LUT or embedded mathematical functions. 
     In the example shown in Table 4, all voltages have been modified using the same transformation 
               V   n     =         (       Vref   n     -     Vref   7       )     ⨯       MAX   ⁡     (   Line   )       255       +     Vref   7             
where Vref 0  represents the threshold voltage. This is the simplest transformation that can be used for voltage driven system since the gamma function is applied inside the OLED according to the proportionality L(x,y)∝I(x;y)=k×(V(x;y)−V th ) 2  where L(x;y) represents the luminance of the pixel located at (x;y) and I(x,y) the current provided to this pixel. Indeed in a first approach, it is intended to have L(x,y)∝k×(Video(x;y)) 2  if one could afford to have a gamma of 2 instead of a gamma of 2.2. In this case it is easy to understand that if the Video level dynamic is modified by a factor p, then it is sufficient to modify the voltages by the same factor. In all other cases, like gamma different from 2 or current driven systems where no inherent gamma is existing a more complex transformation is mandatory for the voltage adjustment since the voltages are no more proportional to the video values.
 
     For instance, in a current driven system there is L(x,y)=k×(I−I th ) but ideally it should be L(x,y)∝(Video(x;y)) 2.2 . Then, a gamma transfer function of 2.2 is needed between the video level and the applied intensity. So if the video level is divided by 2, the provided intensity must be divided by 4.59 since 
     
       
         
           
             
               
                 L 
                 ⁡ 
                 
                   ( 
                   
                     x 
                     , 
                     y 
                   
                   ) 
                 
               
               ∝ 
               
                 
                   ( 
                   
                     
                       Video 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           x 
                           ; 
                           y 
                         
                         ) 
                       
                     
                     2 
                   
                   ) 
                 
                 2.2 
               
             
             = 
             
               
                 
                   
                     ( 
                     
                       Video 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           x 
                           ; 
                           y 
                         
                         ) 
                       
                     
                     ) 
                   
                   2.2 
                 
                 
                   2 
                   2.2 
                 
               
               . 
             
           
         
       
     
     The same is true for a voltage driven system and a real gamma of 2.2 is aimed. In this case, there is a transformation of 1.1 between video and voltages under the form V(x,y)∝Video(x;y) 1.1  that is needed in order to have finally:
 
 L ( x,y )∝( V ( x;y )− V   th ) 2 ∝(Video( x;y ) 1.1 ) 2 =Video( x;y ) 2.2  
 
     In that case, if the maximum video is divided by 2, the voltages must be divided by 2 1.1 =2.14. 
     Such a transformation is quite complex and it is often difficult to be computed on-chip. Therefore, the ideal solution is to use a LUT containing 255 inputs, each one dedicated to a maximum value. The output can be on 8-bit or more in order to define the adjusting factor. Ideally, 10-bit is mandatory. 
     Reverting to the example of the current driven system, if the maximum amplitude per line is 128, the output of the 256×10-bit LUT will be 225. Then the voltages will be multiplied by 225 and divided by 1024 to obtain the factor 4.59. Here, it is very difficult to perform a division in hardware excepted if a 2 m  divider is used that is simply a shift register. Indeed, dividing by 1024 corresponds to a shift by 10. Therefore the multiplication coefficients are always based on a 2 p  divider. Some further examples for such a LUT are given in Table 5 below. 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Example of LUT for reference signalling adjustment 
               
             
          
           
               
                   
                 LUT (Voltage 
                 LUT (current 
               
               
                   
                 driven) 
                 driven) 
               
               
                 MAX (Line) 
                 power of 1.1 
                 power of 2.2 
               
               
                   
               
             
          
           
               
                 96 
                 350 
                 119 
               
               
                 97 
                 354 
                 122 
               
               
                 98 
                 358 
                 125 
               
               
                 99 
                 362 
                 128 
               
               
                 100 
                 366 
                 131 
               
               
                 101 
                 370 
                 133 
               
               
                 102 
                 374 
                 136 
               
               
                 103 
                 378 
                 139 
               
               
                 104 
                 382 
                 142 
               
               
                 105 
                 386 
                 145 
               
               
                 106 
                 390 
                 148 
               
               
                 107 
                 394 
                 152 
               
               
                 108 
                 398 
                 155 
               
               
                 109 
                 402 
                 158 
               
               
                 110 
                 406 
                 161 
               
               
                 111 
                 410 
                 164 
               
               
                 112 
                 414 
                 168 
               
               
                 113 
                 418 
                 171 
               
               
                 114 
                 422 
                 174 
               
               
                 115 
                 426 
                 178 
               
               
                 116 
                 431 
                 181 
               
               
                 117 
                 435 
                 184 
               
               
                 118 
                 439 
                 188 
               
               
                 119 
                 443 
                 191 
               
               
                 120 
                 447 
                 195 
               
               
                 121 
                 451 
                 199 
               
               
                 122 
                 455 
                 202 
               
               
                 123 
                 459 
                 206 
               
               
                 124 
                 463 
                 210 
               
               
                 125 
                 467 
                 213 
               
               
                 126 
                 472 
                 217 
               
               
                 127 
                 476 
                 221 
               
               
                 128 
                 480 
                 225 
               
               
                 129 
                 484 
                 229 
               
               
                 130 
                 488 
                 233 
               
               
                 131 
                 492 
                 237 
               
               
                 132 
                 496 
                 241 
               
               
                 133 
                 500 
                 245 
               
               
                 134 
                 505 
                 249 
               
               
                 135 
                 509 
                 253 
               
               
                 136 
                 513 
                 257 
               
               
                 137 
                 517 
                 261 
               
               
                 138 
                 521 
                 265 
               
               
                   
               
             
          
         
       
     
     In parallel to that the video levels must be modified accordingly to benefit of the enhanced gradation. In that case 
               L   out     =       L   in     ⨯     255     MAX   ⁡     (   Line   )                 
applies. Here also the transformation should be better implemented via a LUT with 256 inputs corresponding to the 256 possible values for MAX(Line) and an output corresponding to a coefficient on 10-bit or more.
 
     In the previous paragraph, a simple solution is shown based on adjusting the reference signaling range to the maximal available video level in a line. A more advanced concept would lead in an optimization of the gradation between the more used video levels. Such enhanced concept of picture line-dependent gradation will be based on a histogram analysis performed on each line. The example of the sequence “Zorro” and the line  303  shall be taken from such histogram analysis with the previous approach for voltage adjustment. 
       FIG. 5  shows in a histogram analysis the repartition of video levels for the line  303  of the sequence “Zorro” ( FIG. 3 ). The vertical lines represent the new adjusted voltages from the first embodiment presented in connection with Table 4. The reference voltages are represented according to the example from Table 1 and the video level is adjusted according to the equation 
     
       
         
           
             
               V 
               n 
             
             = 
             
               
                 
                   ( 
                   
                     
                       Vref 
                       n 
                     
                     - 
                     
                       Vref 
                       0 
                     
                   
                   ) 
                 
                 ⨯ 
                 
                   
                     MAX 
                     ⁡ 
                     
                       ( 
                       Line 
                       ) 
                     
                   
                   255 
                 
               
               + 
               
                 
                   Vref 
                   0 
                 
                 . 
               
             
           
         
       
     
     Now, for all examples simply a gamma of 2 shall be used. For this case, the new correspondence between video levels and voltages is shown in Table 6. 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Adjusted gray level table from voltage driver 
               
             
          
           
               
                   
                 Video level 
                 Grayscale voltage level 
               
               
                   
                   
               
               
                   
                  0 
                 V7 
               
               
                   
                  0.5 
                 V7 + (V6 − V7) × 9/1175 
               
               
                   
                  1 
                 V7 + (V6 − V7) × 32/1175 
               
               
                   
                  1.5 
                 V7 + (V6 − V7) × 76/1175 
               
               
                   
                  2 
                 V7 + (V6 − V7) × 141/1175 
               
               
                   
                  2.5 
                 V7 + (V6 − V7) × 224/1175 
               
               
                   
                  3 
                 V7 + (V6 − V7) × 321/1175 
               
               
                   
                  3.5 
                 V7 + (V6 − V7) × 425/1175 
               
               
                   
                  4 
                 V7 + (V6 − V7) × 529/1175 
               
               
                   
                  4.5 
                 V7 + (V6 − V7) × 630/1175 
               
               
                   
                  5 
                 V7 + (V6 − V7) × 727/1175 
               
               
                   
                  5.5 
                 V7 + (V6 − V7) × 820/1175 
               
               
                   
                  6 
                 V7 + (V6 − V7) × 910/1175 
               
               
                   
                  6.5 
                 V7 + (V6 − V7) × 998/1175 
               
               
                   
                  7 
                 V7 + (V6 − V7) × 1086/1175 
               
               
                   
                  7.5 
                 V6 
               
               
                   
                  8 
                 V6 + (V5 − V6) × 89/1097 
               
               
                   
                  8.5 
                 V6 + (V5 − V6) × 173/1097 
               
               
                   
                  9 
                 V6 + (V5 − V6) × 250/1097 
               
               
                   
                  9.5 
                 V6 + (V5 − V6) × 320/1097 
               
               
                   
                  10 
                 V6 + (V5 − V6) × 386/1097 
               
               
                   
                  10.5 
                 V6 + (V5 − V6) × 451/1097 
               
               
                   
                  11 
                 V6 + (V5 − V6) × 517/1097 
               
               
                   
                 . . . 
                 . . . 
               
               
                   
                 125.5 
                 V1 + (V0 − V1) × 2278/3029 
               
               
                   
                 126 
                 V1 + (V0 − V1) × 2411/3029 
               
               
                   
                 126.5 
                 V1 + (V0 − V1) × 2549/3029 
               
               
                   
                 127 
                 V1 + (V0 − V1) × 2694/3029 
               
               
                   
                 127.5 
                 V1 + (V0 − V1) × 2851/3029 
               
               
                   
                 128 
                 V0 
               
               
                   
                   
               
             
          
         
       
     
     As it can be seen on  FIG. 5 , the maximum of video levels are located between level  15  (V 5 ) and level  95  (V 2 ) but this is not the location where the finest gradation is obtained. However, the finest gradation is obtained when reference voltages are near together. This example shows that the gradation obtained with this driver with voltages computed according to the first embodiment is not optimized to this particular line structure. 
     Therefore, according to a further embodiment there is provided an adaptation of the video transformation and voltage levels to adjust finest gradation where the maximum of video levels are distributed. In order to implement this concept, a first table is needed representing the driver behavior, which means the number of levels represented by each voltage. This is illustrated in Table 7 for the example of Table 1. A full voltage reference table for the driver chosen as example is given in Annex 1. 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Example of voltage references video rendition 
               
             
          
           
               
                   
                 Reference Vn 
                 Amount of levels 
               
               
                   
                   
               
             
          
           
               
                   
                 V7 
                 0 
               
               
                   
                 V6 
                 15 
               
               
                   
                 V5 
                 16 
               
               
                   
                 V4 
                 32 
               
               
                   
                 V3 
                 64 
               
               
                   
                 V2 
                 64 
               
               
                   
                 V1 
                 32 
               
               
                   
                 V0 
                 32 
               
               
                   
                   
               
             
          
         
       
     
     It is generally known that a histogram of a picture represents, for each video level, the number of times this level is used. Such a histogram table is computed for a given line and described as HISTO[n], where n represents the possible video levels used for the input picture (at least 8 bit or more). In order to simplify the exposition, an input signal limited to 8-bit (256 discrete levels) will be taken. 
     Now, the main idea is based on a computation of video level limits for each voltage. Such a limit represents the ideal number of pixels that should be coded inside each voltage. Ideally, this will be based on a percentage of the number of pixels per line. For example, for a display with 720 pixels per lines (720×3 cells) the voltage V 5  should be used to encode at least 720×3×16/255=135 cells. Based on this assumption the following Table 8 is obtained. 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                 Example of voltage references limitation 
               
             
          
           
               
                   
                 Amount of 
                 Limit with 
               
               
                 Reference Vn 
                 levels 
                 320 cells 
               
               
                   
               
             
          
           
               
                 V7 
                 0 
                 0 
               
               
                 V6 
                 15 
                 127 
               
               
                 V5 
                 16 
                 135 
               
               
                 V4 
                 32 
                 271 
               
               
                 V3 
                 64 
                 542 
               
               
                 V2 
                 64 
                 542 
               
               
                 V1 
                 32 
                 271 
               
               
                 V0 
                 32 
                 271 
               
               
                   
               
             
          
         
       
     
     The limits of this table are stored in an array LIMIT[k] with LIMIT[ 0 ]=0, LIMIT[ 1 ]=127, . . . , LIMIT[ 7 ]=271. 
     Now, for each line following exemplary computation is performed: 
     
       
         
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 LevelCount = 0 
               
               
                   
                 Range = 1 
               
               
                   
                 For (l=0; l&lt;255; l++) 
               
               
                   
                 { 
               
               
                   
                   LevelCount = LevelCount + HISTO[l] 
               
               
                   
                   If (LevelCount &gt; LIMIT[Range]) 
               
               
                   
                   { 
               
               
                   
                     LevelCount = 0 
               
               
                   
                     LEVEL_SELECT[Range]=l 
               
               
                   
                     Range++ 
               
               
                   
                   } 
               
               
                   
                 } 
               
               
                   
                   
               
             
          
         
       
     
     From this computation a table of video levels LEVEL_SELECT[k] results that represents the video level at the transition between the voltage k- 1  and k. The results for line  303  are given in Table 9 below, which is based on Annex 2. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 Results of analysis for line 303 
               
             
          
           
               
                   
                 Level 
                 Occurrence 
                 Accumulation 
                 Decision 
               
               
                   
                   
               
             
          
           
               
                   
                  0 
                 27 
                 27 
                 Range 1 
               
               
                   
                  1 
                 13 
                 40 
                 Range 1 
               
               
                   
                  2 
                 1 
                 41 
                 Range 1 
               
               
                   
                  3 
                 2 
                 43 
                 Range 1 
               
               
                   
                  4 
                 3 
                 46 
                 Range 1 
               
               
                   
                  5 
                 4 
                 50 
                 Range 1 
               
               
                   
                  6 
                 3 
                 53 
                 Range 1 
               
               
                   
                  7 
                 0 
                 53 
                 Range 1 
               
               
                   
                  8 
                 1 
                 54 
                 Range 1 
               
               
                   
                  9 
                 1 
                 55 
                 Range 1 
               
               
                   
                 10 
                 2 
                 57 
                 Range 1 
               
               
                   
                 11 
                 0 
                 57 
                 Range 1 
               
               
                   
                 12 
                 5 
                 62 
                 Range 1 
               
               
                   
                 13 
                 7 
                 69 
                 Range 1 
               
               
                   
                 14 
                 4 
                 73 
                 Range 1 
               
               
                   
                 15 
                 8 
                 81 
                 Range 1 
               
               
                   
                 16 
                 9 
                 90 
                 Range 1 
               
               
                   
                 17 
                 19 
                 109 
                 Range 1 
               
               
                   
                 18 
                 29 
                 138 
                 Range 2 
               
               
                   
                 19 
                 50 
                 188 
                 Range 2 
               
               
                   
                 20 
                 35 
                 223 
                 Range 2 
               
               
                   
                 21 
                 37 
                 260 
                 Range 2 
               
               
                   
                 22 
                 24 
                 284 
                 Range 3 
               
               
                   
                 23 
                 26 
                 310 
                 Range 3 
               
               
                   
                 . . . 
                 . . . 
               
               
                   
                 116  
                 0 
                 2149 
                 Range 7 
               
               
                   
                 117  
                 2 
                 2151 
                 Range 7 
               
               
                   
                 118  
                 1 
                 2152 
                 Range 7 
               
               
                   
                 119  
                 0 
                 2152 
                 Range 7 
               
               
                   
                 120  
                 1 
                 2153 
                 Range 7 
               
               
                   
                 121  
                 0 
                 2153 
                 Range 7 
               
               
                   
                 122  
                 0 
                 2153 
                 Range 7 
               
               
                   
                 123  
                 2 
                 2155 
                 Range 7 
               
               
                   
                 124  
                 0 
                 2155 
                 Range 7 
               
               
                   
                 125  
                 1 
                 2156 
                 Range 7 
               
               
                   
                 126  
                 1 
                 2157 
                 Range 7 
               
               
                   
                 127  
                 2 
                 2159 
                 Range 7 
               
               
                   
                 128  
                 1 
                 2160 
                 Range 7 
               
               
                   
                   
               
             
          
         
       
     
     Table 9 shows that:
         Levels [ 0 - 17 ] are used in Range  1 →voltage V 6 →LEVEL_SELECT[ 1 ]=18   Levels [ 18 - 21 ] are used in Range  2 →voltage V 5 →LEVEL_SELECT[ 2 ]=22   Levels [ 22 - 31 ] are used in Range  3 →voltage V 4 →LEVEL_SELECT[ 3 ]=32   Levels [ 32 - 40 ] are used in Range  4 →voltage V 3 →LEVEL_SELECT[ 4 ]=41   Levels [ 41 - 51 ] are used in Range  5 →voltage V 2 →LEVEL_SELECT[ 5 ]=52   Levels [ 52 - 60 ] are used in Range  6 →voltage V 1 →LEVEL_SELECT[ 6 ]=61   Levels [ 61 - 128 ] are used in Range  7 →voltage V 0 →LEVEL_SELECT[ 7 ]=128
 
LEVEL_SELECT[ 0 ]=0.
       

     The result is illustrated in  FIG. 6  showing a possible optimization of the voltages repartition according to the video levels repartition. The example of algorithm used here for this optimization should be seen as an example since other computations with similar achievements are possible. Indeed, it could be better to reduce a bit more the gap V 1  to V 0  in the above example. This can be achieved by a more complicated system. 
     As soon as the optimal voltages repartition for a given line is defined, two types of adjustment should be performed to display a correct but improved picture:
         First the adaptation of the voltages themselves—this computation is similar to the computation done in the previous embodiment. In that case the following equation applies:       

     
       
         
           
             
               V 
               n 
             
             = 
             
               
                 
                   ( 
                   
                     
                       Vref 
                       n 
                     
                     - 
                     
                       Vrefr 
                       
                         n 
                         - 
                         1 
                       
                     
                   
                   ) 
                 
                 ⨯ 
                 
                   ( 
                   
                     
                       
                         LEVEL_SELECT 
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       - 
                       
                         LEVEL_SELECT 
                         ⁡ 
                         
                           [ 
                           
                             n 
                             - 
                             1 
                           
                           ] 
                         
                       
                     
                     
                       LIMIT 
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                   
                   ) 
                 
               
               + 
               
                 V 
                 
                   n 
                   - 
                   1 
                 
               
             
           
         
       
         
         
           
             with n≧1 
             Then, the modification of the video levels to suit the new voltages distribution. In that case for a level located in Range n the luminance value is: 
           
         
       
    
     
       
         
           
             
               L 
               out 
             
             = 
             
               
                 
                   ( 
                   
                     
                       L 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                     - 
                     
                       LEVEL_SELECT 
                       ⁡ 
                       
                         [ 
                         
                           n 
                           - 
                           1 
                         
                         ] 
                       
                     
                   
                   ) 
                 
                 ⨯ 
                 
                   ( 
                   
                     
                       LIMIT 
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                     
                       
                         LEVEL_SELECT 
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       - 
                       
                         LEVEL_SELECT 
                         ⁡ 
                         
                           [ 
                           
                             n 
                             - 
                             1 
                           
                           ] 
                         
                       
                     
                   
                   ) 
                 
               
               + 
               
                 
 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 TRANS 
                 ⁡ 
                 
                   [ 
                   
                     n 
                     - 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     With the table transition being an accumulation of the LIMIT[k] values so that 
               TRANS   ⁡     [   k   ]       =       ∑     p   =   0       p   =   k       ⁢       LIMIT   ⁡     [   k   ]       .             
Consequently, one gets TRANS[ 0 ]=0, TRANS[ 1 ]=16, TRANS[ 1 ]=32, TRANS[ 2 ]=64, TRANS[ 3 ]=128, TRANS[ 4 ]=192, TRANS[ 5 ]=224 and TRANS[ 6 ]=256.
 
     The results of the previous computations are given in Tables 10 and 11 below: 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 10 
               
             
             
               
                   
               
               
                 Computed new voltages for line 303 
               
             
          
           
               
                   
                 Vref 
                 Vline 303 
               
               
                   
                   
               
             
          
           
               
                 V7 
                 0.00 V 
                 0.00 V 
               
               
                 V6 
                 0.16 V 
                 0.19 V 
               
               
                 V5 
                 0.30 V 
                 0.23 V 
               
               
                 V4 
                 0.60 V 
                 0.32 V 
               
               
                 V3 
                 1.40 V 
                 0.43 V 
               
               
                 V2 
                 2.20 V 
                 0.57 V 
               
               
                 V1 
                 2.60 V 
                 0.68 V 
               
               
                 V0 
                 3.00 V 
                 1.52 V 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 11 
               
             
             
               
                   
               
               
                 Computed new video levels for line 303 
               
             
          
           
               
                   
                 Lin 
                 Lout 
               
               
                   
                   
               
             
          
           
               
                   
                  0 
                 0 
               
               
                   
                  1 
                 0.833333 
               
               
                   
                  2 
                 1.666667 
               
               
                   
                  3 
                 2.5 
               
               
                   
                  4 
                 3.333333 
               
               
                   
                  5 
                 4.166667 
               
               
                   
                  6 
                 5 
               
               
                   
                  7 
                 5.833333 
               
               
                   
                  8 
                 6.666667 
               
               
                   
                  9 
                 7.5 
               
               
                   
                 10 
                 8.333333 
               
               
                   
                 11 
                 9.166667 
               
               
                   
                 12 
                 10 
               
               
                   
                 13 
                 10.83333 
               
               
                   
                 14 
                 11.66667 
               
               
                   
                 15 
                 12.5 
               
               
                   
                 16 
                 13.33333 
               
               
                   
                 17 
                 14.16667 
               
               
                   
                 18 
                 15 
               
               
                   
                 . . . 
                 . . . 
               
               
                   
                 116  
                 249.2687 
               
               
                   
                 117  
                 249.7463 
               
               
                   
                 118  
                 250.2239 
               
               
                   
                 119  
                 250.7015 
               
               
                   
                 120  
                 251.1791 
               
               
                   
                 121  
                 251.6567 
               
               
                   
                 122  
                 252.1343 
               
               
                   
                 123  
                 252.6119 
               
               
                   
                 124  
                 253.0896 
               
               
                   
                 125  
                 253.5672 
               
               
                   
                 126  
                 254.0448 
               
               
                   
                 127  
                 254.5224 
               
               
                   
                 128  
                 255 
               
               
                   
                   
               
             
          
         
       
     
     As already explained the complex computations are most of the cases replaced by LUTs. In the situation of the video level adjustment described as: 
     
       
         
           
             
               L 
               out 
             
             = 
             
               
                 
                   ( 
                   
                     
                       L 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                     - 
                     
                       LEVEL_SELECT 
                       ⁡ 
                       
                         [ 
                         
                           n 
                           - 
                           1 
                         
                         ] 
                       
                     
                   
                   ) 
                 
                 ⨯ 
                 
                   ( 
                   
                     
                       LIMIT 
                       ⁡ 
                       
                         [ 
                         n 
                         ] 
                       
                     
                     
                       
                         LEVEL_SELECT 
                         ⁡ 
                         
                           [ 
                           n 
                           ] 
                         
                       
                       - 
                       
                         LEVEL_SELECT 
                         ⁡ 
                         
                           [ 
                           
                             n 
                             - 
                             1 
                           
                           ] 
                         
                       
                     
                   
                   ) 
                 
               
               + 
               
                 
 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 TRANS 
                 ⁡ 
                 
                   [ 
                   
                     n 
                     - 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     A 8-bit LUT takes as input the value LEVEL_SELECT[n]−LEVEL_SELECT[n−1] and delivers a certain factor (more than 10-bit resolution is mandatory) to perform the division. The rest are only multiplications and additions that can be done in real time without any problem. 
     As already said, the example is related to a simple gamma of 2 in a voltage driven system to simplify the exposition. For a different gamma or for a current driven system, the computations must be adjusted accordingly by using adapted LUTs. 
       FIG. 7  illustrates an implementation of the inventive solution. The input signal  11  is forwarded to a line analysis block  12  that performs for each input line the required parameters extraction like the highest video level per line or even histogram analysis. This block  12  requires a line memory to delay the whole process of a line. Indeed, the results of the line analysis are obtained only at the end of the line but the modifications to be done on this line must be performed on the whole line. 
     After the analysis and the delay of the line, the video levels are adjusted in a video adjustment block  13 . Here the new video levels Lout are generated on the basis of the original video levels Lin. The video signal with the new video levels is input to a standard OLED processing unit.  14 . Column driving data are output from this unit  14  and transmitted to a column driver  15  of an AMOLED display  16 . Furthermore, the standard OLED processing unit  14  produces row driving data for controlling the row driver  17  of the AMOLED display  16 . 
     Analysis data of line analysis block  12  are further provided to a voltage adjustment block  18  for adjusting a reference voltages being provided by a reference signaling unit  19 . This reference signaling unit  19  delivers reference voltages Vref n  to the column driver  15 . For adjusting the reference voltages, the voltage adjustment block  18  is synchronized onto the row driving unit  17 . 
     The control data for programming the specific reference voltages are forwarded from voltage adjustment block  18  to the reference signaling unit  19 . The adaptation of the voltages as well as that of the video levels is done on the basis of LUTs and computation. 
     In case of a current driven system, the reference signaling is performed with currents and block  18  takes care of a current adjustment. 
     The invention is not limited to the AMOLED screens but can also be applied to LCD displays or other displays using reference signaling means. 
     
       
         
               
             
               
               
             
               
               
             
           
               
                   
               
               
                 Annex 1 - Full driver voltage table 
               
             
          
           
               
                 Level 
                 Voltage 
               
               
                   
               
             
          
           
               
                 0 
                 V7 
               
               
                 1 
                 V7 + (V6 − V7) × 9/1175 
               
               
                 2 
                 V7 + (V6 − V7) × 32/1175 
               
               
                 3 
                 V7 + (V6 − V7) × 76/1175 
               
               
                 4 
                 V7 + (V6 − V7) × 141/ 
               
               
                   
                 1175 
               
               
                 5 
                 V7 + (V6 − V7) × 224/ 
               
               
                   
                 1175 
               
               
                 6 
                 V7 + (V6 − V7) × 321/ 
               
               
                   
                 1175 
               
               
                 7 
                 V7 + (V6 − V7) × 425/ 
               
               
                   
                 1175 
               
               
                 8 
                 V7 + (V6 − V7) × 529/ 
               
               
                   
                 1175 
               
               
                 9 
                 V7 + (V6 − V7) × 630/ 
               
               
                   
                 1175 
               
               
                 10 
                 V7 + (V6 − V7) × 727/ 
               
               
                   
                 1175 
               
               
                 11 
                 V7 + (V6 − V7) × 820/ 
               
               
                   
                 1175 
               
               
                 12 
                 V7 + (V6 − V7) × 910/ 
               
               
                   
                 1175 
               
               
                 13 
                 V7 + (V6 − V7) × 998/ 
               
               
                   
                 1175 
               
               
                 14 
                 V7 + (V6 − V7) × 1086/ 
               
               
                   
                 1175 
               
               
                 15 
                 V6 
               
               
                 16 
                 V6 + (V5 − V6) × 89/1097 
               
               
                 17 
                 V6 + (V5 − V6) × 173/ 
               
               
                   
                 1097 
               
               
                 18 
                 V6 + (V5 − V6) × 250/ 
               
               
                   
                 1097 
               
               
                 19 
                 V6 + (V5 − V6) × 320/ 
               
               
                   
                 1097 
               
               
                 20 
                 V6 + (V5 − V6) × 386/ 
               
               
                   
                 1097 
               
               
                 21 
                 V6 + (V5 − V6) × 451/ 
               
               
                   
                 1097 
               
               
                 22 
                 V6 + (V5 − V6) × 517/ 
               
               
                   
                 1097 
               
               
                 23 
                 V6 + (V5 − V6) × 585/ 
               
               
                   
                 1097 
               
               
                 24 
                 V6 + (V5 − V6) × 654/ 
               
               
                   
                 1097 
               
               
                 25 
                 V6 + (V5 − V6) × 723/ 
               
               
                   
                 1097 
               
               
                 26 
                 V6 + (V5 − V6) × 790/ 
               
               
                   
                 1097 
               
               
                 27 
                 V6 + (V5 − V6) × 855/ 
               
               
                   
                 1097 
               
               
                 28 
                 V6 + (V5 − V6) × 917/ 
               
               
                   
                 1097 
               
               
                 29 
                 V6 + (V5 − V6) × 977/ 
               
               
                   
                 1097 
               
               
                 30 
                 V6 + (V5 − V6) × 1037/ 
               
               
                   
                 1097 
               
               
                 31 
                 V5 
               
               
                 32 
                 V5 + (V4 − V5) × 60/ 
               
               
                   
                 1501 
               
               
                 33 
                 V5 + (V4 − V5) × 119/ 
               
               
                   
                 1501 
               
               
                 34 
                 V5 + (V4 − V5) × 176/ 
               
               
                   
                 1501 
               
               
                 35 
                 V5 + (V4 − V5) × 231/ 
               
               
                   
                 1501 
               
               
                 36 
                 V5 + (V4 − V5) × 284/ 
               
               
                   
                 1501 
               
               
                 37 
                 V5 + (V4 − V5) × 335/ 
               
               
                   
                 1501 
               
               
                 38 
                 V5 + (V4 − V5) × 385/ 
               
               
                   
                 1501 
               
               
                 39 
                 V5 + (V4 − V5) × 434/ 
               
               
                   
                 1501 
               
               
                 40 
                 V5 + (V4 − V5) × 483/ 
               
               
                   
                 1501 
               
               
                 41 
                 V5 + (V4 − V5) × 532/ 
               
               
                   
                 1501 
               
               
                 42 
                 V5 + (V4 − V5) × 580/ 
               
               
                   
                 1501 
               
               
                 43 
                 V5 + (V4 − V5) × 628/ 
               
               
                   
                 1501 
               
               
                 44 
                 V5 + (V4 − V5) × 676/ 
               
               
                   
                 1501 
               
               
                 45 
                 V5 + (V4 − V5) × 724/ 
               
               
                   
                 1501 
               
               
                 46 
                 V5 + (V4 − V5) × 772/ 
               
               
                   
                 1501 
               
               
                 47 
                 V5 + (V4 − V5) × 819/ 
               
               
                   
                 1501 
               
               
                 48 
                 V5 + (V4 − V5) × 866/ 
               
               
                   
                 1501 
               
               
                 49 
                 V5 + (V4 − V5) × 912/ 
               
               
                   
                 1501 
               
               
                 50 
                 V5 + (V4 − V5) × 957/ 
               
               
                   
                 1501 
               
               
                 51 
                 V5 + (V4 − V5) × 1001/ 
               
               
                   
                 1501 
               
               
                 52 
                 V5 + (V4 − V5) × 1045/ 
               
               
                   
                 1501 
               
               
                 53 
                 V5 + (V4 − V5) × 1088/ 
               
               
                   
                 1501 
               
               
                 54 
                 V5 + (V4 − V5) × 1131/ 
               
               
                   
                 1501 
               
               
                 55 
                 V5 + (V4 − V5) × 1173/ 
               
               
                   
                 1501 
               
               
                 56 
                 V5 + (V4 − V5) × 1215/ 
               
               
                   
                 1501 
               
               
                 57 
                 V5 + (V4 − V5) × 1257/ 
               
               
                   
                 1501 
               
               
                 58 
                 V5 + (V4 − V5) × 1298/ 
               
               
                   
                 1501 
               
               
                 59 
                 V5 + (V4 − V5) × 1339/ 
               
               
                   
                 1501 
               
               
                 60 
                 V5 + (V4 − V5) × 1380/ 
               
               
                   
                 1501 
               
               
                 61 
                 V5 + (V4 − V5) × 1421/ 
               
               
                   
                 1501 
               
               
                 62 
                 V5 + (V4 − V5) × 1461/ 
               
               
                   
                 1501 
               
               
                 63 
                 V4 
               
               
                 64 
                 V4 + (V3 − V4) × 40/2215 
               
               
                 65 
                 V4 + (V3 − V4) × 80/2215 
               
               
                 66 
                 V4 + (V3 − V4) × 120/ 
               
               
                   
                 2215 
               
               
                 67 
                 V4 + (V3 − V4) × 160/ 
               
               
                   
                 2215 
               
               
                 68 
                 V4 + (V3 − V4) × 200/ 
               
               
                   
                 2215 
               
               
                 69 
                 V4 + (V3 − V4) × 240/ 
               
               
                   
                 2215 
               
               
                 70 
                 V4 + (V3 − V4) × 280/ 
               
               
                   
                 2215 
               
               
                 71 
                 V4 + (V3 − V4) × 320/ 
               
               
                   
                 2215 
               
               
                 72 
                 V4 + (V3 − V4) × 360/ 
               
               
                   
                 2215 
               
               
                 73 
                 V4 + (V3 − V4) × 400/ 
               
               
                   
                 2215 
               
               
                 74 
                 V4 + (V3 − V4) × 440/ 
               
               
                   
                 2215 
               
               
                 75 
                 V4 + (V3 − V4) × 480/ 
               
               
                   
                 2215 
               
               
                 76 
                 V4 + (V3 − V4) × 520/ 
               
               
                   
                 2215 
               
               
                 77 
                 V4 + (V3 − V4) × 560/ 
               
               
                   
                 2215 
               
               
                 78 
                 V4 + (V3 − V4) × 600/ 
               
               
                   
                 2215 
               
               
                 79 
                 V4 + (V3 − V4) × 640/ 
               
               
                   
                 2215 
               
               
                 80 
                 V4 + (V3 − V4) × 680/ 
               
               
                   
                 2215 
               
               
                 81 
                 V4 + (V3 − V4) × 719/ 
               
               
                   
                 2215 
               
               
                 82 
                 V4 + (V3 − V4) × 758/ 
               
               
                   
                 2215 
               
               
                 83 
                 V4 + (V3 − V4) × 796/ 
               
               
                   
                 2215 
               
               
                 84 
                 V4 + (V3 − V4) × 834/ 
               
               
                   
                 2215 
               
               
                 85 
                 V4 + (V3 − V4) × 871/ 
               
               
                   
                 2215 
               
               
                 86 
                 V4 + (V3 − V4) × 908/ 
               
               
                   
                 2215 
               
               
                 87 
                 V4 + (V3 − V4) × 944/ 
               
               
                   
                 2215 
               
               
                 88 
                 V4 + (V3 − V4) × 980/ 
               
               
                   
                 2215 
               
               
                 89 
                 V4 + (V3 − V4) × 1016/ 
               
               
                   
                 2215 
               
               
                 90 
                 V4 + (V3 − V4) × 1052/ 
               
               
                   
                 2215 
               
               
                 91 
                 V4 + (V3 − V4) × 1087/ 
               
               
                   
                 2215 
               
               
                 92 
                 V4 + (V3 − V4) × 1122/ 
               
               
                   
                 2215 
               
               
                 93 
                 V4 + (V3 − V4) × 1157/ 
               
               
                   
                 2215 
               
               
                 94 
                 V4 + (V3 − V4) × 1192/ 
               
               
                   
                 2215 
               
               
                 95 
                 V4 + (V3 − V4) × 1226/ 
               
               
                   
                 2215 
               
               
                 96 
                 V4 + (V3 − V4) × 1260/ 
               
               
                   
                 2215 
               
               
                 97 
                 V4 + (V3 − V4) × 1294/ 
               
               
                   
                 2215 
               
               
                 98 
                 V4 + (V3 − V4) × 1328/ 
               
               
                   
                 2215 
               
               
                 99 
                 V4 + (V3 − V4) × 1362/ 
               
               
                   
                 2215 
               
               
                 100 
                 V4 + (V3 − V4) × 1396/ 
               
               
                   
                 2215 
               
               
                 101 
                 V4 + (V3 − V4) × 1429/ 
               
               
                   
                 2215 
               
               
                 102 
                 V4 + (V3 − V4) × 1462/ 
               
               
                   
                 2215 
               
               
                 103 
                 V4 + (V3 − V4) × 1495/ 
               
               
                   
                 2215 
               
               
                 104 
                 V4 + (V3 − V4) × 1528/ 
               
               
                   
                 2215 
               
               
                 105 
                 V4 + (V3 − V4) × 1561/ 
               
               
                   
                 2215 
               
               
                 106 
                 V4 + (V3 − V4) × 1593/ 
               
               
                   
                 2215 
               
               
                 107 
                 V4 + (V3 − V4) × 1625/ 
               
               
                   
                 2215 
               
               
                 108 
                 V4 + (V3 − V4) × 1657/ 
               
               
                   
                 2215 
               
               
                 109 
                 V4 + (V3 − V4) × 1688/ 
               
               
                   
                 2215 
               
               
                 110 
                 V4 + (V3 − V4) × 1719/ 
               
               
                   
                 2215 
               
               
                 111 
                 V4 + (V3 − V4) × 1750/ 
               
               
                   
                 2215 
               
               
                 112 
                 V4 + (V3 − V4) × 1781/ 
               
               
                   
                 2215 
               
               
                 113 
                 V4 + (V3 − V4) × 1811/ 
               
               
                   
                 2215 
               
               
                 114 
                 V4 + (V3 − V4) × 1841/ 
               
               
                   
                 2215 
               
               
                 115 
                 V4 + (V3 − V4) × 1871/ 
               
               
                   
                 2215 
               
               
                 116 
                 V4 + (V3 − V4) × 1901/ 
               
               
                   
                 2215 
               
               
                 117 
                 V4 + (V3 − V4) × 1930/ 
               
               
                   
                 2215 
               
               
                 118 
                 V4 + (V3 − V4) × 1959/ 
               
               
                   
                 2215 
               
               
                 119 
                 V4 + (V3 − V4) × 1988/ 
               
               
                   
                 2215 
               
               
                 120 
                 V4 + (V3 − V4) × 2016/ 
               
               
                   
                 2215 
               
               
                 121 
                 V4 + (V3 − V4) × 2044/ 
               
               
                   
                 2215 
               
               
                 122 
                 V4 + (V3 − V4) × 2072/ 
               
               
                   
                 2215 
               
               
                 123 
                 V4 + (V3 − V4) × 2100/ 
               
               
                   
                 2215 
               
               
                 124 
                 V4 + (V3 − V4) × 2128/ 
               
               
                   
                 2215 
               
               
                 125 
                 V4 + (V3 − V4) × 2156/ 
               
               
                   
                 2215 
               
               
                 126 
                 V4 + (V3 − V4) × 2185/ 
               
               
                   
                 2215 
               
               
                 127 
                 V3 
               
               
                 128 
                 V3 + (V2 − V3) × 31/2343 
               
               
                 129 
                 V3 + (V2 − V3) × 64/2343 
               
               
                 130 
                 V3 + (V2 − V3) × 97/2343 
               
               
                 131 
                 V3 + (V2 − V3) × 130/ 
               
               
                   
                 2343 
               
               
                 132 
                 V3 + (V2 − V3) × 163/ 
               
               
                   
                 2343 
               
               
                 133 
                 V3 + (V2 − V3) × 196/ 
               
               
                   
                 2343 
               
               
                 134 
                 V3 + (V2 − V3) × 229/ 
               
               
                   
                 2343 
               
               
                 135 
                 V3 + (V2 − V3) × 262/ 
               
               
                   
                 2343 
               
               
                 136 
                 V3 + (V2 − V3) × 295/ 
               
               
                   
                 2343 
               
               
                 137 
                 V3 + (V2 − V3) × 328/ 
               
               
                   
                 2343 
               
               
                 138 
                 V3 + (V2 − V3) × 361/ 
               
               
                   
                 2343 
               
               
                 139 
                 V3 + (V2 − V3) × 395/ 
               
               
                   
                 2343 
               
               
                 140 
                 V3 + (V2 − V3) × 429/ 
               
               
                   
                 2343 
               
               
                 141 
                 V3 + (V2 − V3) × 463/ 
               
               
                   
                 2343 
               
               
                 142 
                 V3 + (V2 − V3) × 497/ 
               
               
                   
                 2343 
               
               
                 143 
                 V3 + (V2 − V3) × 531/ 
               
               
                   
                 2343 
               
               
                 144 
                 V3 + (V2 − V3) × 566/ 
               
               
                   
                 2343 
               
               
                 145 
                 V3 + (V2 − V3) × 601/ 
               
               
                   
                 2343 
               
               
                 146 
                 V3 + (V2 − V3) × 636/ 
               
               
                   
                 2343 
               
               
                 147 
                 V3 + (V2 − V3) × 671/ 
               
               
                   
                 2343 
               
               
                 148 
                 V3 + (V2 − V3) × 706/ 
               
               
                   
                 2343 
               
               
                 149 
                 V3 + (V2 − V3) × 741/ 
               
               
                   
                 2343 
               
               
                 150 
                 V3 + (V2 − V3) × 777/ 
               
               
                   
                 2343 
               
               
                 151 
                 V3 + (V2 − V3) × 813/ 
               
               
                   
                 2343 
               
               
                 152 
                 V3 + (V2 − V3) × 849/ 
               
               
                   
                 2343 
               
               
                 153 
                 V3 + (V2 − V3) × 885/ 
               
               
                   
                 2343 
               
               
                 154 
                 V3 + (V2 − V3) × 921/ 
               
               
                   
                 2343 
               
               
                 155 
                 V3 + (V2 − V3) × 958/ 
               
               
                   
                 2343 
               
               
                 156 
                 V3 + (V2 − V3) × 995/ 
               
               
                   
                 2343 
               
               
                 157 
                 V3 + (V2 − V3) × 1032/ 
               
               
                   
                 2343 
               
               
                 158 
                 V3 + (V2 − V3) × 1069/ 
               
               
                   
                 2343 
               
               
                 159 
                 V3 + (V2 − V3) × 1106/ 
               
               
                   
                 2343 
               
               
                 160 
                 V3 + (V2 − V3) × 1143/ 
               
               
                   
                 2343 
               
               
                 161 
                 V3 + (V2 − V3) × 1180/ 
               
               
                   
                 2343 
               
               
                 162 
                 V3 + (V2 − V3) × 1217/ 
               
               
                   
                 2343 
               
               
                 163 
                 V3 + (V2 − V3) × 1255/ 
               
               
                   
                 2343 
               
               
                 164 
                 V3 + (V2 − V3) × 1293/ 
               
               
                   
                 2343 
               
               
                 165 
                 V3 + (V2 − V3) × 1331/ 
               
               
                   
                 2343 
               
               
                 166 
                 V3 + (V2 − V3) × 1369/ 
               
               
                   
                 2343 
               
               
                 167 
                 V3 + (V2 − V3) × 1407/ 
               
               
                   
                 2343 
               
               
                 168 
                 V3 + (V2 − V3) × 1445/ 
               
               
                   
                 2343 
               
               
                 169 
                 V3 + (V2 − V3) × 1483/ 
               
               
                   
                 2343 
               
               
                 170 
                 V3 + (V2 − V3) × 1521/ 
               
               
                   
                 2343 
               
               
                 171 
                 V3 + (V2 − V3) × 1559/ 
               
               
                   
                 2343 
               
               
                 172 
                 V3 + (V2 − V3) × 1597/ 
               
               
                   
                 2343 
               
               
                 173 
                 V3 + (V2 − V3) × 1635/ 
               
               
                   
                 2343 
               
               
                 174 
                 V3 + (V2 − V3) × 1673/ 
               
               
                   
                 2343 
               
               
                 175 
                 V3 + (V2 − V3) × 1712/ 
               
               
                   
                 2343 
               
               
                 176 
                 V3 + (V2 − V3) × 1751/ 
               
               
                   
                 2343 
               
               
                 177 
                 V3 + (V2 − V3) × 1790/ 
               
               
                   
                 2343 
               
               
                 178 
                 V3 + (V2 − V3) × 1829/ 
               
               
                   
                 2343 
               
               
                 179 
                 V3 + (V2 − V3) × 1868/ 
               
               
                   
                 2343 
               
               
                 180 
                 V3 + (V2 − V3) × 1907/ 
               
               
                   
                 2343 
               
               
                 181 
                 V3 + (V2 − V3) × 1946/ 
               
               
                   
                 2343 
               
               
                 182 
                 V3 + (V2 − V3) × 1985/ 
               
               
                   
                 2343 
               
               
                 183 
                 V3 + (V2 − V3) × 2024/ 
               
               
                   
                 2343 
               
               
                 184 
                 V3 + (V2 − V3) × 2064/ 
               
               
                   
                 2343 
               
               
                 185 
                 V3 + (V2 − V3) × 2103/ 
               
               
                   
                 2343 
               
               
                 186 
                 V3 + (V2 − V3) × 2143/ 
               
               
                   
                 2343 
               
               
                 187 
                 V3 + (V2 − V3) × 2183/ 
               
               
                   
                 2343 
               
               
                 188 
                 V3 + (V2 − V3) × 2223/ 
               
               
                   
                 2343 
               
               
                 189 
                 V3 + (V2 − V3) × 2263/ 
               
               
                   
                 2343 
               
               
                 190 
                 V3 + (V2 − V3) × 2303/ 
               
               
                   
                 2343 
               
               
                 191 
                 V2 
               
               
                 192 
                 V2 + (V1 − V2) × 40/1638 
               
               
                 193 
                 V2 + (V1 − V2) × 81/1638 
               
               
                 194 
                 V2 + (V1 − V2) × 124/ 
               
               
                   
                 1638 
               
               
                 195 
                 V2 + (V1 − V2) × 168/ 
               
               
                   
                 1638 
               
               
                 196 
                 V2 + (V1 − V2) × 213/ 
               
               
                   
                 1638 
               
               
                 197 
                 V2 + (V1 − V2) × 259/ 
               
               
                   
                 1638 
               
               
                 198 
                 V2 + (V1 − V2) × 306/ 
               
               
                   
                 1638 
               
               
                 199 
                 V2 + (V1 − V2) × 353/ 
               
               
                   
                 1638 
               
               
                 200 
                 V2 + (V1 − V2) × 401/ 
               
               
                   
                 1638 
               
               
                 201 
                 V2 + (V1 − V2) × 450/ 
               
               
                   
                 1638 
               
               
                 202 
                 V2 + (V1 − V2) × 499/ 
               
               
                   
                 1638 
               
               
                 203 
                 V2 + (V1 − V2) × 548/ 
               
               
                   
                 1638 
               
               
                 204 
                 V2 + (V1 − V2) × 597/ 
               
               
                   
                 1638 
               
               
                 205 
                 V2 + (V1 − V2) × 646/ 
               
               
                   
                 1638 
               
               
                 206 
                 V2 + (V1 − V2) × 695/ 
               
               
                   
                 1638 
               
               
                 207 
                 V2 + (V1 − V2) × 745/ 
               
               
                   
                 1638 
               
               
                 208 
                 V2 + (V1 − V2) × 795/ 
               
               
                   
                 1638 
               
               
                 209 
                 V2 + (V1 − V2) × 846/ 
               
               
                   
                 1638 
               
               
                 210 
                 V2 + (V1 − V2) × 897/ 
               
               
                   
                 1638 
               
               
                 211 
                 V2 + (V1 − V2) × 949/ 
               
               
                   
                 1638 
               
               
                 212 
                 V2 + (V1 − V2) × 1002/ 
               
               
                   
                 1638 
               
               
                 213 
                 V2 + (V1 − V2) × 1056/ 
               
               
                   
                 1638 
               
               
                 214 
                 V2 + (V1 − V2) × 1111/ 
               
               
                   
                 1638 
               
               
                 215 
                 V2 + (V1 − V2) × 1167/ 
               
               
                   
                 1638 
               
               
                 216 
                 V2 + (V1 − V2) × 1224/ 
               
               
                   
                 1638 
               
               
                 217 
                 V2 + (V1 − V2) × 1281/ 
               
               
                   
                 1638 
               
               
                 218 
                 V2 + (V1 − V2) × 1339/ 
               
               
                   
                 1638 
               
               
                 219 
                 V2 + (V1 − V2) × 1398/ 
               
               
                   
                 1638 
               
               
                 220 
                 V2 + (V1 − V2) × 1458/ 
               
               
                   
                 1638 
               
               
                 221 
                 V2 + (V1 − V2) × 1518/ 
               
               
                   
                 1638 
               
               
                 222 
                 V2 + (V1 − V2) × 1578/ 
               
               
                   
                 1638 
               
               
                 223 
                 V1 
               
               
                 224 
                 V1 + (V0 − V1) × 60/3029 
               
               
                 225 
                 V1 + (V0 − V1) × 120/ 
               
               
                   
                 3029 
               
               
                 226 
                 V1 + (V0 − V1) × 180/ 
               
               
                   
                 3029 
               
               
                 227 
                 V1 + (V0 − V1) × 241/ 
               
               
                   
                 3029 
               
               
                 228 
                 V1 + (V0 − V1) × 304/ 
               
               
                   
                 3029 
               
               
                 229 
                 V1 + (V0 − V1) × 369/ 
               
               
                   
                 3029 
               
               
                 230 
                 V1 + (V0 − V1) × 437/ 
               
               
                   
                 3029 
               
               
                 231 
                 V1 + (V0 − V1) × 507/ 
               
               
                   
                 3029 
               
               
                 232 
                 V1 + (V0 − V1) × 580/ 
               
               
                   
                 3029 
               
               
                 233 
                 V1 + (V0 − V1) × 655/ 
               
               
                   
                 3029 
               
               
                 234 
                 V1 + (V0 − V1) × 732/ 
               
               
                   
                 3029 
               
               
                 235 
                 V1 + (V0 − V1) × 810/ 
               
               
                   
                 3029 
               
               
                 236 
                 V1 + (V0 − V1) × 889/ 
               
               
                   
                 3029 
               
               
                 237 
                 V1 + (V0 − V1) × 969/ 
               
               
                   
                 3029 
               
               
                 238 
                 V1 + (V0 − V1) × 1050/ 
               
               
                   
                 3029 
               
               
                 239 
                 V1 + (V0 − V1) × 1133/ 
               
               
                   
                 3029 
               
               
                 240 
                 V1 + (V0 − V1) × 1218/ 
               
               
                   
                 3029 
               
               
                 241 
                 V1 + (V0 − V1) × 1304/ 
               
               
                   
                 3029 
               
               
                 242 
                 V1 + (V0 − V1) × 1393/ 
               
               
                   
                 3029 
               
               
                 243 
                 V1 + (V0 − V1) × 1486/ 
               
               
                   
                 3029 
               
               
                 244 
                 V1 + (V0 − V1) × 1583/ 
               
               
                   
                 3029 
               
               
                 245 
                 V1 + (V0 − V1) × 1686/ 
               
               
                   
                 3029 
               
               
                 246 
                 V1 + (V0 − V1) × 1794/ 
               
               
                   
                 3029 
               
               
                 247 
                 V1 + (V0 − V1) × 1907/ 
               
               
                   
                 3029 
               
               
                 248 
                 V1 + (V0 − V1) × 2026/ 
               
               
                   
                 3029 
               
               
                 249 
                 V1 + (V0 − V1) × 2150/ 
               
               
                   
                 3029 
               
               
                 250 
                 V1 + (V0 − V1) × 2278/ 
               
               
                   
                 3029 
               
               
                 251 
                 V1 + (V0 − V1) × 2411/ 
               
               
                   
                 3029 
               
               
                 252 
                 V1 + (V0 − V1) × 2549/ 
               
               
                   
                 3029 
               
               
                 253 
                 V1 + (V0 − V1) × 2694/ 
               
               
                   
                 3029 
               
               
                 254 
                 V1 + (V0 − V1) × 2851/ 
               
               
                   
                 3029 
               
               
                 255 
                 V0 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
               
                 Annex 2 - Histogram of line 303 from sequence “Zorro” 
               
             
          
           
               
                   
                 Level 
                 Occurrence 
               
               
                   
                   
               
             
          
           
               
                   
                 0 
                 27 
               
               
                   
                 1 
                 13 
               
               
                   
                 2 
                 1 
               
               
                   
                 3 
                 2 
               
               
                   
                 4 
                 3 
               
               
                   
                 5 
                 4 
               
               
                   
                 6 
                 3 
               
               
                   
                 7 
                 0 
               
               
                   
                 8 
                 1 
               
               
                   
                 9 
                 1 
               
               
                   
                 10 
                 2 
               
               
                   
                 11 
                 0 
               
               
                   
                 12 
                 5 
               
               
                   
                 13 
                 7 
               
               
                   
                 14 
                 4 
               
               
                   
                 15 
                 8 
               
               
                   
                 16 
                 9 
               
               
                   
                 17 
                 19 
               
               
                   
                 18 
                 29 
               
               
                   
                 19 
                 50 
               
               
                   
                 20 
                 35 
               
               
                   
                 21 
                 37 
               
               
                   
                 22 
                 24 
               
               
                   
                 23 
                 26 
               
               
                   
                 24 
                 19 
               
               
                   
                 25 
                 23 
               
               
                   
                 26 
                 12 
               
               
                   
                 27 
                 24 
               
               
                   
                 28 
                 26 
               
               
                   
                 29 
                 23 
               
               
                   
                 30 
                 25 
               
               
                   
                 31 
                 31 
               
               
                   
                 32 
                 56 
               
               
                   
                 33 
                 54 
               
               
                   
                 34 
                 64 
               
               
                   
                 35 
                 61 
               
               
                   
                 36 
                 78 
               
               
                   
                 37 
                 42 
               
               
                   
                 38 
                 59 
               
               
                   
                 39 
                 61 
               
               
                   
                 40 
                 75 
               
               
                   
                 41 
                 78 
               
               
                   
                 42 
                 61 
               
               
                   
                 43 
                 41 
               
               
                   
                 44 
                 55 
               
               
                   
                 45 
                 52 
               
               
                   
                 46 
                 43 
               
               
                   
                 47 
                 48 
               
               
                   
                 48 
                 42 
               
               
                   
                 49 
                 42 
               
               
                   
                 50 
                 46 
               
               
                   
                 51 
                 45 
               
               
                   
                 52 
                 28 
               
               
                   
                 53 
                 29 
               
               
                   
                 54 
                 27 
               
               
                   
                 55 
                 26 
               
               
                   
                 56 
                 28 
               
               
                   
                 57 
                 25 
               
               
                   
                 58 
                 25 
               
               
                   
                 59 
                 33 
               
               
                   
                 60 
                 39 
               
               
                   
                 61 
                 38 
               
               
                   
                 62 
                 38 
               
               
                   
                 63 
                 25 
               
               
                   
                 64 
                 23 
               
               
                   
                 65 
                 12 
               
               
                   
                 66 
                 11 
               
               
                   
                 67 
                 22 
               
               
                   
                 68 
                 13 
               
               
                   
                 69 
                 5 
               
               
                   
                 70 
                 4 
               
               
                   
                 71 
                 5 
               
               
                   
                 72 
                 6 
               
               
                   
                 73 
                 13 
               
               
                   
                 74 
                 8 
               
               
                   
                 75 
                 3 
               
               
                   
                 76 
                 7 
               
               
                   
                 77 
                 6 
               
               
                   
                 78 
                 4 
               
               
                   
                 79 
                 2 
               
               
                   
                 80 
                 2 
               
               
                   
                 81 
                 2 
               
               
                   
                 82 
                 4 
               
               
                   
                 83 
                 5 
               
               
                   
                 84 
                 3 
               
               
                   
                 85 
                 3 
               
               
                   
                 86 
                 6 
               
               
                   
                 87 
                 2 
               
               
                   
                 88 
                 1 
               
               
                   
                 89 
                 3 
               
               
                   
                 90 
                 2 
               
               
                   
                 91 
                 0 
               
               
                   
                 92 
                 3 
               
               
                   
                 93 
                 0 
               
               
                   
                 94 
                 1 
               
               
                   
                 95 
                 1 
               
               
                   
                 96 
                 0 
               
               
                   
                 97 
                 1 
               
               
                   
                 98 
                 0 
               
               
                   
                 99 
                 1 
               
               
                   
                 100 
                 0 
               
               
                   
                 101 
                 0 
               
               
                   
                 102 
                 0 
               
               
                   
                 103 
                 1 
               
               
                   
                 104 
                 1 
               
               
                   
                 105 
                 1 
               
               
                   
                 106 
                 0 
               
               
                   
                 107 
                 2 
               
               
                   
                 108 
                 0 
               
               
                   
                 109 
                 0 
               
               
                   
                 110 
                 1 
               
               
                   
                 111 
                 1 
               
               
                   
                 112 
                 0 
               
               
                   
                 113 
                 1 
               
               
                   
                 114 
                 0 
               
               
                   
                 115 
                 0 
               
               
                   
                 116 
                 0 
               
               
                   
                 117 
                 2 
               
               
                   
                 118 
                 1 
               
               
                   
                 119 
                 0 
               
               
                   
                 120 
                 1 
               
               
                   
                 121 
                 0 
               
               
                   
                 122 
                 0 
               
               
                   
                 123 
                 2 
               
               
                   
                 124 
                 0 
               
               
                   
                 125 
                 1 
               
               
                   
                 126 
                 1 
               
               
                   
                 127 
                 2 
               
               
                   
                 128 
                 1 
               
               
                   
                 129 
                 0 
               
               
                   
                 130 
                 0 
               
               
                   
                 131 
                 0 
               
               
                   
                 132 
                 0 
               
               
                   
                 133 
                 0 
               
               
                   
                 134 
                 0 
               
               
                   
                 135 
                 0 
               
               
                   
                 136 
                 0 
               
               
                   
                 137 
                 0 
               
               
                   
                 138 
                 0 
               
               
                   
                 139 
                 0 
               
               
                   
                 140 
                 0 
               
               
                   
                 141 
                 0 
               
               
                   
                 142 
                 0 
               
               
                   
                 143 
                 0 
               
               
                   
                 144 
                 0 
               
               
                   
                 145 
                 0 
               
               
                   
                 146 
                 0 
               
               
                   
                 147 
                 0 
               
               
                   
                 148 
                 0 
               
               
                   
                 149 
                 0 
               
               
                   
                 150 
                 0 
               
               
                   
                 151 
                 0 
               
               
                   
                 152 
                 0 
               
               
                   
                 153 
                 0 
               
               
                   
                 154 
                 0 
               
               
                   
                 155 
                 0 
               
               
                   
                 156 
                 0 
               
               
                   
                 157 
                 0 
               
               
                   
                 158 
                 0 
               
               
                   
                 159 
                 0 
               
               
                   
                 160 
                 0 
               
               
                   
                 161 
                 0 
               
               
                   
                 162 
                 0 
               
               
                   
                 163 
                 0 
               
               
                   
                 164 
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