Patent Publication Number: US-2013249896-A1

Title: Method of displaying three-dimensional stereoscopic image and display apparatus performing the method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority from and the benefit of Korean Patent Application No. 10-2012-0029487, filed on Mar. 22, 2012, which is hereby incorporated by reference for all purposes as if fully set forth herein. 
     DISCUSSION OF THE BACKGROUND 
     1. Field 
     Exemplary embodiments of the present invention relate to a method of displaying three-dimensional stereoscopic image and display apparatus performing the method. 
     2. Discussion of the Background 
     Generally, liquid crystal display apparatuses display two-dimensional planar images. Recently, the demand for liquid crystal display apparatuses that can display three-dimensional stereoscopic images has increased in various industry fields, such as games, movies, etc. 
     Generally, three-dimensional stereoscopic images are displayed by using a principle of binocular parallax through human eyes. For example, images observed from different angles through each eye are input to human brain because human eyes are spaced apart. Stereoscopic image displaying apparatuses use the principle of binocular parallax. 
     There are stereoscopic methods and autostereoscopic methods that use the binocular parallax. The stereoscopic methods include an anaglyph method and a shutter glass method. The anaglyph method uses glasses having blue and red lenses. The shutter glass method uses glasses that selectively prevent light from reaching the left and right eyes of a user in synchronization with when left eye images and right eye images are displayed. 
     The autostereoscopic methods include lens methods and barrier methods. A display apparatus employing the lens method includes lens panel disposed on a display panel. The lens panel displays a three-dimensional stereoscopic image by refracting the three-dimensional stereoscopic image displayed on the display panel to a plurality of viewpoints. A display apparatus employing the barrier method includes a barrier panel disposed on a display panel. The barrier panel displays a three-dimensional stereoscopic image by emitting the three-dimensional stereoscopic image displayed on the display panel to a plurality of viewpoints. 
     Recently, techniques to form the lens panel and the barrier panel as a liquid crystal panel are being developed to selectively display two-dimensional images and three-dimensional images. 
     BRIEF SUMMARY OF THE INVENTION 
     Exemplary embodiments of the present invention relate to a method of displaying three-dimensional stereoscopic images by detecting observers and then selectively driving a multi-viewpoint mode and tracking mode, in order to improve the display quality of the three-dimensional stereoscopic images. Exemplary embodiments of the present invention also provide a display apparatus to perform the method. 
     Exemplary embodiments of the present invention provide a method of displaying three-dimensional stereoscopic image that includes displaying N viewpoint images on N dots, emitting the N viewpoint images through a dynamic conversion panel on which a emission unit is defined, controlling a sub-area to emit the N viewpoint images onto N×M viewpoint positions if multiple observers are detected, moving the emission unit to a position determined according to an observer&#39;s position if the observer is single, and emitting the N viewpoint images to the observer&#39;s position. The dots are consecutive in a row direction of a display panel. The emission unit includes an emission unit including of M sub-areas. M and N are natural numbers. 
     Exemplary embodiments of the present invention provide a display apparatus that includes a display panel to display N viewpoint images on N dots, and a dynamic conversion panel on which an emission unit is defined. The dots are consecutive in a row direction. The emission unit includes an emission unit including M sub-areas. The dynamic conversion panel controls the sub-areas to drive in a multi-viewpoint mode which N viewpoint images are emitted to N×M viewpoint positions if observers are plural. The dynamic conversion panel moves the emission unit to a position determined according to an observer&#39;s position to drive in a tracking mode which N viewpoint images are emitted to the observer&#39;s position if the observer is single. M and N are natural numbers. 
     According to various embodiments, the display quality of three-dimensional stereoscopic images may be improved by detecting the number of observers and then driving in a multi-viewpoint mode or a tracking mode according to the number of the observers. 
     Additional features of the invention will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention, and together with the description serve to explain the principles of the invention. 
         FIG. 1  is a block diagram of display apparatus according to an exemplary embodiment of the present invention. 
         FIG. 2  is a cross-sectional view illustrating an emission unit included in the dynamic conversion panel of  FIG. 1 . 
         FIGS. 3A and 3B  are plan views illustrating shapes of the emission units of the dynamic conversion panel of  FIG. 1 . 
         FIG. 4  is a flow diagram illustrating a method of driving the display apparatus of  FIG. 1 . 
         FIG. 5  is a cross-sectional view illustrating a dynamic conversion liquid crystal lens panel according to another exemplary embodiment of the present invention. 
         FIG. 6  is a cross-sectional view illustrating a liquid crystal lens panel according to is another exemplary embodiment of the present invention. 
         FIGS. 7A and 7B  are cross-sectional views illustrating multi-viewpoint driving of the liquid crystal lens panel of  FIG. 6 . 
         FIG. 8  is a cross-sectional view illustrating a liquid crystal lens panel according to still another exemplary embodiment of the present invention. 
         FIGS. 9A and 9B  are cross-sectional views illustrating multi-viewpoint driving of the liquid crystal lens panel of  FIG. 8 . 
         FIG. 10  is a cross-sectional view illustrating a liquid crystal lens panel according to still another exemplary embodiment of the present invention. 
         FIGS. 11A and 11B  are cross-sectional views illustrating multi-viewpoint driving of the liquid crystal lens panel of  FIG. 10 . 
         FIG. 12  is a cross-sectional view illustrating a liquid crystal lens panel according to still another exemplary embodiment of the present invention. 
         FIGS. 13A and 13B  are cross-sectional views illustrating multi-viewpoint driving of the liquid crystal lens panel of  FIG. 10 . 
         FIG. 14  is a luminance profile of three-dimensional stereoscopic images formed by the liquid crystal lens panel of  FIG. 6 . 
         FIG. 15  is a cross-sectional view illustrating a tracking mode using the liquid crystal lens panel of  FIG. 6 , when an observer is located within an observation distance. 
         FIG. 16  is a cross-sectional view illustrating a tracking mode using the liquid crystal lens panel of  FIG. 6 , when the observer&#39;s position is located beyond the observation distance. 
         FIG. 17  is a plan view of an observer screen according to the tracking mode of  FIG. 16 . 
         FIG. 18  is a timing chart illustrating the control of the position of a lens structure corresponding to the observer screen of  FIG. 17 . 
         FIG. 19  is a timing chart illustrating the control of the position of a lens structure corresponding to an observer screen, according to another exemplary embodiment of the present invention. 
         FIG. 20  is a cross-sectional view illustrating a tracking mode of a liquid crystal lens panel according to still another exemplary embodiment of the present invention when the observer&#39;s position is located beyond the observation distance. 
         FIG. 21  is a plan view of the observer screen according to the tracking mode of  FIG. 20 . 
         FIG. 22  is a timing chart illustrating the control of the position of a lens structure corresponding to the observer screen of  FIG. 20 . 
         FIG. 23  is a timing chart illustrating the control of the position of a lens structure corresponding to an observer screen according to still another exemplary embodiment of the present invention. 
         FIG. 24  is a luminance profile of three-dimensional stereoscopic images according to the liquid crystal lens panel of  FIG. 10 . 
         FIG. 25  is a plan view of the observer screen according to the liquid crystal lens panel of  FIG. 10 . 
         FIG. 26  is a timing chart illustrating the control of the position of a lens structure corresponding to the observer screen of  FIG. 25 . 
         FIG. 27  is a cross-sectional view illustrating a tracking mode of a liquid crystal is lens panel according to still another exemplary embodiment of the present invention when an observer is located within an observation distance. 
         FIG. 28  is a cross-sectional view of a dynamic conversion panel of liquid crystal barrier type according to still another exemplary embodiment of the present invention. 
         FIG. 29  is a cross-sectional view of a liquid crystal barrier panel according to still another exemplary embodiment of the present invention. 
         FIG. 30  is a cross-sectional view illustrating multi-viewpoint driving type of the liquid crystal barrier panel of  FIG. 29 . 
         FIG. 31  is a cross-sectional view of a liquid crystal barrier panel according to still another exemplary embodiment of the present invention. 
         FIG. 32  is a cross-sectional view illustrating multi-viewpoint driving type of the liquid crystal barrier panel of  FIG. 31 . 
         FIG. 33  is a cross-sectional view of a liquid crystal barrier panel according to still another exemplary embodiment of the present invention. 
         FIG. 34  is a cross-sectional view illustrating multi-viewpoint driving type of the liquid crystal barrier panel of  FIG. 33 . 
         FIG. 35  is a cross-sectional view illustrating a tracking mode according to the liquid crystal barrier panel of  FIG. 29  when the observer is located within the observation distance. 
         FIG. 36  is a cross-sectional view illustrating a tracking mode according to the liquid crystal barrier panel of  FIG. 33 , when the observer is located within the observation distance. 
         FIG. 37  is a timing chart illustrating the control of the position of a barrier unit corresponding to the observer screen according to the liquid crystal barrier panel of  FIG. 30  when observed by an observer located far away. 
         FIG. 38  is a timing chart illustrating the control of the position of a barrier unit corresponding to an observer screen according to still another exemplary embodiment of the present invention. 
         FIG. 39  is a timing chart illustrating the control of the position of a barrier unit corresponding to the observer screen according to the liquid crystal barrier panel of  FIG. 33  when observed by an observer. 
         FIG. 40  is a perspective view of display apparatus according to another exemplary embodiment of the present invention. 
         FIG. 41  is a cross-sectional view illustrating a emission unit included in the dynamic conversion panel of  FIG. 40 . 
     
    
    
     DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS 
     The invention is described more fully hereinafter with reference to the accompanying drawings, in which exemplary embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the exemplary embodiments set forth herein. Rather, these exemplary embodiments are provided so that this disclosure is thorough, and will fully convey the scope of the invention to those skilled in the art. In the drawings, the size and relative sizes of layers and regions may be exaggerated for clarity. Like reference numerals in the drawings denote like elements. 
     It will be understood that when an element or layer is referred to as being “on” or “connected to” another element or layer, it can be directly on or directly connected to the other is element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on” or “directly connected to” another element or layer, there are no intervening elements or layers present. 
       FIG. 1  is a block diagram of display apparatus according to an exemplary embodiment of the present invention.  FIG. 2  is a cross-sectional view illustrating an emission unit (viewing unit) included in the dynamic conversion panel of  FIG. 1 .  FIGS. 3A and 3B  are plan views illustrating shapes of the emission units of the dynamic conversion panel of  FIG. 1 . 
     Referring to  FIGS. 1 ,  2 ,  3 A, and  3 B, the display apparatus includes a controller  100 , a display panel  200 , a display driver  300 , a dynamic conversion panel  400 , a conversion driver  500 , a light source  600 , a light source driver  700 , a surveillance part  800 , and a tracker  900 . The controller  100  receives two-dimensional image data and three-dimensional image data, and controls the driving of each component of the display apparatus in a two-dimensional image mode or a three-dimensional image mode, on the basis of the received image data. 
     The controller  100  controls an operating mode of the dynamic conversion panel  400  according to the image modes. For example, the controller  100  drives the dynamic conversion panel  400  in a transmission mode, in order to emit two-dimensional images displayed on the display panel  200  during the two-dimensional image mode. The controller  100  drives the dynamic conversion panel  400  in a conversion mode in order to emit three-dimensional images displayed on the display panel  200  to at least two viewpoint positions in the three-dimensional image mode. 
     In addition, the controller  100  may drive the dynamic conversion panel  400  in a multi-viewpoint mode when there are multiple observers, or in a tracking mode when there is only one observer is single, in the three-dimensional image mode. The dynamic conversion is panel  400  emits the three-dimensional images displayed on the display panel  200  to a plurality of viewpoint positions in the multi-viewpoint mode. The dynamic conversion panel  400  emits the three-dimensional images displayed on the display panel  200  to the position of the observer in the tracking mode. 
     The controller  100  may correct the image data using various correction algorithms. For example, the adaptive color correction (ACC) may be performed to uniformly correct white levels of the image data. Also, the dynamic capacitance compensation (DCC) may be performed to correct the image data of a current frame, on the basis of image data of a previous frame, in order to improve the response speed of the current frame with respect to the previous frame. 
     In addition, the controller  100  may render the three-dimensional image to fit the viewpoint of the observer in the tracking mode, if the observer is located beyond a designed observation distance. 
     The display panel  200  includes a plurality of data lines DL, a plurality of gate lines GL, and a plurality of subpixels SP. The data lines DL extend in a first direction D 1  and are arranged in a second direction D 2  crossing the first direction D 1 . The gate lines GL extend in the second direction D 2  and are arranged in the first direction D 1 . The subpixels SP may be arranged in a matrix including a plurality of pixel rows and columns, and may be an elementary unit of the display panel  200 . Each subpixel SP includes a switching element TR connected to the data lines DL and the gate lines GL, and a pixel electrode PE connected to the switching element TR. The display panel  200  includes a plurality of unit pixels PU including at least one of the subpixels SP. For example, the unit pixel PU may include red R, green G, and blue B subpixels. 
     The display panel  200  displays viewpoint images to an observer. A viewpoint is image is formed by dots DT formed by the display panel  200 . A dot DT may emitted by at least one of the subpixels SP. A dot group includes N dots where N is a natural number greater than one. The dot group is an elementary unit of the display panel  200  displaying N viewpoint images. For example, a dot group is used to form each viewpoint image. 
     The display driver  300  drives the display panel  200  according to the control of the controller  100 . The display driver  300  may include a data driver to drive the data lines DL, and a gate driver to drive the gate lines GL. 
     The dynamic conversion panel  400  forms a plurality of emission units EU that emit three-dimensional images displayed on the display panel  200  to at least two viewpoint positions, in the three-dimensional image mode. Each emission unit EU is an elementary unit through which N viewpoint images are emitted. Each emission unit EU includes N emission areas. Each emission area is an area through which one viewpoint image is emitted. A sub-area is an elementary unit of the emission area. The emission area includes M sub-areas where M is a natural number greater than one. 
     Referring to  FIG. 2 , the emission unit EU includes at least one unit area Sf. The unit area Sf is an area which the emission unit EU is movable. The unit area Sf corresponds to one dot DT. The unit area Sf may be determined by a pitch of the dots DT, a distance df between the dot DT and the emission unit EU, and an observation distance Df set for the emission unit EU. 
         Df:Sf =( Df+Sf ): p   [Equation 1]
 
     Referring to  FIG. 3A , the emission units EU extend in the first direction D 1  and are arranged to the second direction D 2  as a striped structure. In contrast, referring to  FIG. 3B , is the emission units EU may extend in a third direction D 3  crossing the first direction D 1  and the second direction D 2 , and may be arranged in the second direction D 2 , as a tilted structure. 
     The conversion driver  500  provides driving voltages to element electrodes of the dynamic conversion panel  400 , according to the control of the controller  100 . The conversion driver  500  adjusts the viewpoint images to at least four viewpoint positions, by moving the position of the emission unit including M sub-emission units in a multi-viewpoint mode, where M is a natural number. The conversion driver  500  directs the viewpoint images to the observer&#39;s position by moving the emission units to according to the observer&#39;s position. 
     The light source  600  may include an edge-illumination light source or a direct-illumination light source. The edge-illumination light source includes at least one light source is disposed on an edge of a light guide plate, which is disposed under the display panel  200 . The direct-illumination light source includes at least one light source is disposed directly under the display panel  200  and does not include the light guide plate is omitted. 
     The light source driver  700  controls the operation of the light source  600  according to a control of the controller  100 . The surveillance part  800  detects at least one observer and provides surveillance data to the tracking part  900 . In particular, the surveillance part  800  detects the position of the head or eyes of the observer. The surveillance part  800  may be a camera. 
     The tracking part  900  detects the number of observers and information on the observers&#39; positions on the basis of the surveillance data. The tracking part  900  tracks the position of the observers on the basis of the surveillance data provided from the surveillance part  800  in the tracking mode. The tracking part  900  may track the observer&#39;s position by recognizing an angle of the observer with respect to the display apparatus. The tracking part  900  provides the is information on the observer&#39;s position to the controller  100 . 
       FIG. 4  is a flow diagram illustrating a method of driving the display apparatus of  FIG. 1 . Referring to  FIG. 1  and  FIG. 4 , in step S 110 , the controller  100  determines whether the received image data is two-dimensional image data or three-dimensional image data. 
     If the received image data is two-dimensional image data, the controller  100  drives the display apparatus in a two-dimensional image mode. In a step S 120 , the conversion driver  500  drives the dynamic conversion panel  400  in a transmission mode, according to the control of the controller  100 . For example, the conversion driver  500  prevents driving voltages from being applied to the dynamic conversion panel  400 . In step S 130 , the display driver  300  displays two-dimensional images on the display panel  200 , according to the control of the controller  100 . Accordingly, the two-dimensional images displayed on the display panel  200  are transmitted through the dynamic conversion panel  400  during the transmission mode. As a result, an observer may receive two-dimensional images. 
     If the received image data is three-dimensional image data, the controller  100  drives the display apparatus in a three-dimensional image mode. In the three-dimensional image mode, the controller  100  sets the driving mode as a multi-viewpoint mode or a tracking mode, according to the number of observers viewing the display apparatus, in step S 210 . For example, if multiple observers are detected, the controller  100  drives the display apparatus in the multi-viewpoint mode, while if only one observer is detected, the controller  100  drives the display apparatus in the tracking mode. 
     In the multi-viewpoint mode, the conversion driver  500  controls the emission units EU of the dynamic conversion panel  400 , according to the control of the controller  100 , in step S 230 . For example, if the dynamic conversion panel  400  is a liquid crystal lens panel that is includes a lens and M lens electrodes, where M is a natural number greater than one, then the lens structure is moved M times by a unit of one lens electrode, during one frame. That is, the sub-area corresponds to the area on which the lens electrode is formed. The display driver  300  displays the three-dimensional image data on the display panel  200  according to the control of the controller  100 , in step S 400 . 
     In addition, if the dynamic conversion panel  400  is a liquid crystal barrier panel driven as a barrier unit which includes an emission unit (opening) consisting of M sub-areas, then the barrier unit is driven such that a dot is emitted from a corresponding emission unit instep S 400 . Accordingly, at least two observers may receive three-dimensional stereoscopic images. 
     In the tracking mode, the tracking part  900  tracks the position of an observer using the surveillance data provided from the surveillance part  800 , in step S 250 . The tracking part  900  provides information on the observer&#39;s position to the controller  100 . 
     The controller  100  compares the observer&#39;s position with the observation distance, on the basis of the information on the position. If the observer&#39;s position is substantially the same as the observation distance, then the conversion driver  500  controls the position of the emission units by a unit of the sub-areas, according to the control of the controller  100 , in step S 330 . That is, each emission unit is moved in a right-and-left direction by a unit of the sub-area, according to a moving direction of the observer. 
     For example, when the emission unit of the dynamic conversion panel  400  includes M sub-areas, the emission unit is moved according to a moving direction of the observer by one sub-area, if the observer moves more than ±E/(2M) in a row direction, where E is the distance between a left eye and a right eye of the observer. In addition, if the observer moves by E/2 in a row direction, then the emission unit is moved in the moving direction of the observer by one sub-area. The display driver  300  displays the three-dimensional image data on the display panel  200  according to the control of the controller  100 . 
     In step S 350 , if the observer&#39;s position is located beyond the observation distance, the controller  100  analyzes an observer screen approximating an image observed at the observer&#39;s position. The controller  100  divides the dynamic conversion panel  400  into a plurality of areas on the basis of viewpoint images (e.g., left-eye images or right-eye images) included in the observer screen and mixed images, and controls the positions of the emission units of the dynamic conversion panel  400  in each area. In step S 360 , the conversion driver  500  controls the position of the emission units included in each area according to the control of the controller  100 . 
     In step S 400 , the three-dimensional image data are displayed on the display panel  200  according to the control of the controller  100 . 
     Alternatively, the controller  100  divides the dynamic conversion panel  400  into a plurality of areas on the basis of the observer screen, and divides the plurality of areas into two groups. In step S 360 , the controller  100  moves the emission units of a first group of areas corresponding to viewpoint images (e.g., left-eye images or right-eye images) to a first position, and moves the emission units of a second group of areas corresponding to mixed areas, to a second position moved by a distance determined with respect to the first position. In addition, the controller  100  renders image data to display a normal viewpoint image in an area on which another viewpoint image among the first group of areas is displayed, and in an area on which another viewpoint image among the second group of areas is displayed. The conversion driver  500  controls the position of the emission units included in each area, according to the control of the controller  100 . The display driver  300  drives the display panel  200  using the rendered image data provided from the controller  100 , in step S 400 . 
       FIG. 5  is a cross-sectional view illustrating a dynamic conversion liquid crystal lens panel  410 , according to another exemplary embodiment of the present invention. Referring to  FIG. 5  and  FIG. 6 , the liquid crystal lens panel  410  includes a first substrate  411 , a second substrate  412 , and a liquid crystal layer  413 . 
     The first substrate  411  includes a plurality of lens electrodes LE. The second substrate  412  includes a counter electrode OE that faces the lens electrodes LE. The liquid crystal layer  413  forms a plurality of lens structures LS in response to a voltage applied to the lens electrodes LE and the counter electrode OE. Each lens structure LS corresponds to an emission unit EU, as described above. 
     If the liquid crystal lens panel  410  is for N viewpoint images, each lens structure LS may include N lens units LU. Each lens unit LU is an elementary unit used to form a viewpoint image. The lens units LU may include M lens electrodes LE. The area on which each lens electrode LE is formed corresponds to a sub-area SA described above. Thus, each lens unit LU includes M sub-areas SA (i.e., M×SA). 
     In  FIG. 5 , although the first substrate  411  is disposed above the second substrate  412 , the positions of the first and the second substrates  411 ,  412  are not limited thereto. 
       FIG. 6  is a cross-sectional view illustrating a liquid crystal lens panel, according to another exemplary embodiment of the present invention.  FIGS. 7A and 7B  are cross-sectional views illustrating multi-viewpoint driving of the liquid crystal lens panel of  FIG. 6 . 
     Referring to  FIG. 6 , the liquid crystal lens panel includes a plurality of lens structures LS for two viewpoints. Each lens structure LS includes two lens units LU. Each lens c unit LU includes two lens electrodes, for example lens electrodes LE 1 , LE 2 . Accordingly, the lens structure LS may include four lens electrodes LE 1 , LE 2 , LE 3 , and LE 4  to project two is viewpoint images. A unit area Sf includes two sub-areas (i.e., 2×SA) corresponding to the number of lens electrodes included in each lens unit LU. The length Q 2  of the lens structure LS is approximately twice the length of the unit area Sf. 
     The display panel  200  corresponding to the liquid crystal lens panel  420  displays two viewpoint images (i.e., left-eye image L and right-eye image R) for every two subpixels, which are consecutive in a row direction. In a multi-viewpoint mode, the method of driving the liquid crystal lens panel  420  is performed as follows. 
     Referring to  FIGS. 1 ,  7 A, and  7 B, the conversion driver  500  applies a first driving voltage V 1 , a second driving voltage V 2 , a third driving voltage V 3 , and a fourth driving voltage V 4  to the first lens electrode LE 1 , the second lens electrode LE 2 , the third lens electrode LE 3 , and the fourth lens electrode LE 4 , respectively, during a first interval of a frame. Accordingly, the liquid crystal lens panel  420  operates as a first lens structure LS  1 , and emits two viewpoint images displayed on the display panel  200  to a first viewpoint position VW 1  and a second viewpoint position VW 2 , during the first interval of the frame. 
     Then, the conversion driver  500  applies shifted voltages (e.g., the fourth, the first, the second, and the third driving voltages V 4 , V 1 , V 2 , V 3 ) to the first, the second, the third, and the fourth lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , respectively, during a second interval of the frame. Accordingly, the liquid crystal lens panel  420  operates as a second lens structure LS 2 , which is moved by the width of one lens electrode, with respect to the first lens structure LS 1 , and emits two viewpoint images displayed on the display panel  200  to a third viewpoint position VW 3  and a fourth viewpoint position VW 4 , during the second interval of the frame. The liquid crystal lens panel  420  may sequentially operate as the first and the second lens structures LS 1 , LS 2  during a frame, to emit the total of four viewpoint images during the frame. 
       FIG. 8  is a cross-sectional view illustrating a liquid crystal lens panel  430  according to still another exemplary embodiment of the present invention.  FIGS. 9A and 9B  are cross-sectional views illustrating multi-viewpoint driving of the liquid crystal lens panel  430  of  FIG. 8 . 
     Referring to  FIG. 8 , the liquid crystal lens panel  430  includes a plurality of lens structures LS for four viewpoints. Each lens structure LS includes four lens units LU. Each lens unit LU includes two lens electrodes, for example, lens electrodes LE 1 , LE 2  are included in one of the lens units LU. Accordingly, the lens structure LS may include eight lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , LE 7 , LE 8 . A unit area Sf includes two sub-areas (i.e., 2×SA) corresponding to the number of lens electrodes included in the lens unit LU. The length Q 4  of the lens structure LS for four viewpoints is 4 times the length of the unit area Sf. The display panel  200  corresponding to the liquid crystal lens panel  430  alternately displays four viewpoint images  1 ,  2 ,  3 ,  4  on every four consecutive subpixels. 
     In a multi-viewpoint mode, the method of driving the liquid crystal lens panel  430  is performed as follows. Referring to  FIGS. 1 ,  9 A, and  9 B, the conversion driver  500  applies driving voltages V 1 , V 2 , V 3 , V 4 , V 5 , V 6 , V 7 , V 8  to lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , LE 7 , LE 8  lens structure, respectively, during a first interval of a frame. 
     Accordingly, the liquid crystal lens panel  430  operates as a first lens structure LS 1  to emit four viewpoint images displayed on the display panel  200 , to viewpoint positions VW 1 , VW 2 , VW 3 , VW 4 , during the first interval of the frame. Then, the conversion driver  500  applies shifted voltages (e.g., driving voltages V 8 , V 1 , V 2 , V 3 , V 4 , V 5 , V 6 , V 7 ) to lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , LE 7 , LE 8 , respectively, during a second interval of the frame. 
     Accordingly, the liquid crystal lens panel  430  operates as a second lens structure LS 2 , which is moved by on sub-area SA, i.e., by a width of one lens electrode, with respect to the first lens structure LS 1 , to emit four viewpoint images displayed on the display panel  200 , to fifth, sixth, seventh, and eighth viewpoint positions VW 5 , VW 6 , VW 7 , VW 8 , during the second interval of the frame. The liquid crystal lens panel  430  may sequentially operate as the first and the second lens structures LS 1 , LS 2  during a frame, to emit the eight viewpoint images during the frame. 
       FIG. 10  is a cross-sectional view illustrating a liquid crystal lens panel  440  according to still another exemplary embodiment of the present invention.  FIGS. 11A and 11B  are cross-sectional views illustrating multi-viewpoint driving of the liquid crystal lens panel  440  of  FIG. 10 . 
     Referring to  FIG. 10 , the liquid crystal lens panel  440  includes a plurality of lens structures LS to display two viewpoints. Each lens structure LS includes two lens units LU. A lens unit LU may correspond to an emission area as described above. Each lens unit LU includes three lens electrodes LE 1 , LE 2 , LE 3 . Accordingly, the lens structure LS may include six lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 . A unit area Sf has a length approximately three times the length of the sub-area SA of a lens electrode, i.e., corresponds includes three sub-areas (i.e., 3×SA) corresponding to the number of lens electrodes included in the lens unit LU. The length Q 2  of the lens structure LS is twice the length of the unit area Sf. 
     The display panel  200  corresponding to the liquid crystal lens panel  440  for two viewpoints alternately displays two viewpoint images L, R on every consecutive two subpixels. 
     In a multi-viewpoint mode, the method of driving the liquid crystal lens panel is performed as follows. Referring to  FIGS. 1 ,  11 A, and  11 B, the conversion driver  500  is applies driving voltages V 1 , V 2 , V 3 , V 4 , V 5 , V 6  to lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6  included in each lens structure Ls, respectively, during a first interval of a frame. Accordingly, the liquid crystal lens panel  430  operates as a first lens structure LS 1  to emit two viewpoint images displayed on the display panel  200  to viewpoint positions VW 1 , VW 2 , during the first interval of the frame. 
     Then, the conversion driver  500  applies shifted voltages (e.g., driving voltages V 6 , V 1 , V 2 , V 3 , V 4 , V 5 ) to lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , respectively, during a second interval of the frame. Accordingly, the liquid crystal lens panel operates as a second lens structure LS 2 , which is moved by a width of one lens electrode with respect to the first lens structure LS 1 , to emit two viewpoint images displayed on the display panel  200  to viewpoint positions VW 3 , VW 4 , during the second interval of the frame. 
     Then, the conversion driver  500  applies shifted voltages (e.g., driving voltages V 5 , V 6 , V 1 , V 2 , V 3 , V 4 ) to the lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , respectively, during a third interval of the frame. 
     Accordingly, the liquid crystal lens panel  440  operates as a third lens structure LS 3 , which is moved by a width of one lens electrode with respect to the second lens structure LS 2 , to emit two viewpoint images displayed on the display panel  200  to a fifth and a sixth viewpoint positions VW 5 , VW 6 , during the third interval of the frame. The liquid crystal lens panel  440  may sequentially operate as the first, the second, and the third lens structures LS 1 , LS 2 , LS 3 , during a frame, to emit the total of six viewpoint images during the frame. 
       FIG. 12  is a cross-sectional view illustrating a liquid crystal lens panel  450  according to still another exemplary embodiment of the present invention.  FIGS. 13A and 13B  are cross-sectional views illustrating multi-viewpoint driving of the liquid crystal lens panel  450  is of  FIG. 10 . 
     Referring to  FIG. 12 , the liquid crystal lens panel  450  includes a plurality of lens structures LS. Each lens structure LS includes four lens units LU. Each lens unit LU includes three lens electrodes. For example, lens electrodes LE 1 , LE 2 , LE 3  may be included in a first lens unit LU. Accordingly, the lens structure LS may include twelve lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , LE 7 , LE 8 , LE 9 , LE 10 , LE 11 , LE 12 . A unit area Sf includes three sub-areas SA and corresponds to the number of lens electrodes included in the lens unit LU. The length Q 4  of the lens structure LS is 4 times that of the unit area Sf. The display panel  200  corresponding to the liquid crystal lens panel  450  alternately displays four viewpoint images  1 ,  2 ,  3 ,  4  on four consecutive subpixels in a row direction. 
     In a multi-viewpoint mode, the method of driving the liquid crystal lens panel  450  is performed as follows. Referring to  FIGS. 1 ,  12 A,  12 B, the conversion driver  500  applies driving voltages V 1 , V 2 , V 3 , V 4 , V 5 , V 6 , V 7 , V 8 , V 9 , V 10 , V 11 , V 12  to lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , LE 7 , LE 8 , LE 9 , LE 10 , LE 11 , LE 12  included in each lens structure LS, respectively, during a first interval of a frame. 
     Accordingly, the liquid crystal lens panel  450  operates as a first lens structure LS 1  to emit four viewpoint images displayed on the display panel  200 , to viewpoint positions VW 1 , VW 2 , VW 3 , VW 4 , during the first interval of the frame. Then, the conversion driver  500  applies shifted voltages (e.g., driving voltages V 12 , V 1 , V 2 , V 3 , V 4 , V 5 , V 6 , V 7 , V 8 , V 9 , V 10 , V 11 ) to electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , LE 7 , LE 8 , LE 9 , LE 10 , LE 11 , LE 12 , respectively, during a second interval of the frame. 
     Accordingly, the liquid crystal lens panel  450  operates as a second lens structure LS 2 , which is moved by a width of a sub-area SA corresponding to one lens electrode, with respect to the first lens structure LS 1 , to emit four viewpoint images displayed on the display panel  200  to viewpoint positions VW 5 , VW 6 , VW 7 , VW 8 , during the second interval of the frame. Then, the conversion driver  500  applies shifted voltages (e.g., driving voltages V 11 , V 12 , V 1 , V 2 , V 3 , V 4 , V 5 , V 6 , V 7 , V 8 , V 9 , V 10 ) to electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 , LE 7 , LE 8 , LE 9 , LE 10 , LE 11 , LE 12 , respectively, during a third interval of the frame. 
     Accordingly, the liquid crystal lens panel  450  operates as a third lens structure LS 3 , which is moved by a width SA of one lens electrode, with respect to the second lens structure SA 2 , to emit four viewpoint images displayed on the display panel  200  to viewpoint positions VW 9 , VW 10 , VW 11 , VW 12 . The liquid crystal lens panel  450  may sequentially operate as lens structures LS 1 , LS 2 , LS 3 , during a frame, to emit the total of twelve viewpoint images during the frame. 
       FIG. 14  is a luminance profile of three-dimensional stereoscopic images produced by the liquid crystal lens panel of  FIG. 6 .  FIG. 15  is a cross-sectional view illustrating a tracking mode performed using the liquid crystal lens panel of  FIG. 6 , when an observer&#39;s position is within an observation distance. 
     Referring to  FIG. 14 , each of a luminance profile of a left-eye image LI_C and a luminance profile of a right-eye image RI_C each have a sinusoidal shape. The luminance profile of the left-eye image LI_C is delayed by an eye distance E measured between a left eye and a right eye of an observer, with respect to the luminance profile RI_C of the right-eye image. 
     If the left eye L_E of the observer is located at a position corresponding to a peak point of the luminance profile LI_C of the left-eye image, and the right eye R_E of the observer is located at a position corresponding to a peak point of the luminance profile RI_C of the right-eye image, then the observer may receive a stereoscopic image that does not include is crosstalk. 
     Referring to  FIGS. 1 ,  14  and  15 , in a tracking mode, if the observer&#39;s position is located within a set observation distance, the controller  100  analyzes how far the observer moves in a right-and-left direction. For example, if a left eye L_E or a right eye R_E of the observer moves by a distance E/2 of the eye distance E, the controller  100  controls driving voltages applied to the liquid crystal lens panel  420  to move the position of the lens structure LS by a corresponding amount. 
     Referring to  FIGS. 6 ,  7 A, and  7 B, if the left eye L_E and the right eye R_E of the observer are located originally at a first and a second viewpoint positions VW 1 , VW 2 , driving voltages V 1 , V 2 , V 3 , V 4  are respectively applied to lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , to form a first lens structure LS 1 . Two viewpoint images (i.e., a left-eye image L and a right-eye image R) displayed on the display panel  200  are emitted to the first and the second viewpoint positions VW 1 , VW 2 , via the first lens structure LS 1 . Accordingly, the left eye L_E and the right eye R_E of the observer, which are respectively located at the first and the second viewpoint positions VW 1 , VW 2 , receive the left-eye image L and the right-eye image R, respectively. 
     Then, if the tracking part  900  determines that the observer&#39;s eyes move by E/2 in a left-to-right direction from the viewpoint positions VW 1 , VW 2  to viewpoint positions VW 3 , VW 4 , the conversion driver  500  respectively applies driving voltages V 4 , V 1 , V 2 , V 3  to the lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , according to the control of the controller  100 . Accordingly, a second lens structure LS 2 , which is moved by a width of one lens electrode in a left-to-right direction with respect to the first lens structure LS 1 , is formed. A left-eye image L and a right-eye image R, displayed on the display panel  200  are emitted to viewpoint positions VW 3 , VW 4 , via the second lens structure LS 2 . Accordingly, the left eye L_E and the right eye R_E of the observer, which are respectively disposed at viewpoint positions VW 3 , VW 4 , receive the left-eye image L and the right-eye image R, respectively. 
     Although not shown, if the observer&#39;s position moves by E/2 in a right-to-left direction, the observer may receive a left-eye image and a right-eye image at the new positions by forming a second lens structure LS 2 , which is moved by a width of one lens electrode in a right-to-left direction, with respect to the first lens structure LS 1 , in substantially the same way. 
     Again, referring to  FIG. 14 , if the observer&#39;s position moves more than E/4 in a right-and-left direction, the left eye L_E and the right eye R_E of the observer receive the luminance profiles corresponding to adjacent viewpoint positions. Accordingly, if the left eye or the right eye of the observer is beyond a distance of E/4 in a right-and-left direction, then the controller  100  controls the liquid crystal lens panel  420  to form a second lens structure LS 2  lens structure, and the left eye L_E and the right eye R_E of the observer respectively receive a left-eye image L and a right-eye image R. 
       FIG. 16  is a cross-sectional view illustrating a tracking mode of the liquid crystal lens panel  420  of  FIG. 6 , when the observer&#39;s position is located beyond the observation distance.  FIG. 17  is a plan view of an observer screen according to the tracking mode of  FIG. 16 .  FIG. 18  is a timing chart illustrating the control of the position of a lens structure corresponding to the observer screen of  FIG. 17 . 
     Referring to  FIG. 16 , a lens structure or a lens electrode of the liquid crystal lens panel  420  has a striped structure as illustrated in  FIG. 3A . If the observer&#39;s position is beyond an observation distance Df, then the left eye (or the right eye) of the observer may receive a left-eye image (or a right-eye image) and a boundary between the left-eye image and is the right-eye image. For example, an observer screen of the display apparatus observed from the right eye R_E of the observer at the observation distance Df is an right-eye image. 
     However, because a visual field is wide when the observer is located beyond the observation distance Df, the right eye R_E of the observer receives a left-eye image L as well as a right-eye image R. If the observer is located beyond the observation distance, the controller  100  computes an observer screen OVS to approximate a screen view at the observer&#39;s position, by executing an analyzing algorithm. 
     As illustrated in  FIG. 17 , the observer screen OVS received by the right eye R_E of the observer includes a left-eye image L and a right-eye image R. Each of the left-eye image L and the right-eye image R received at the right-eye R_E of the observer has a width W. 
     The controller  100  divides the observer screen OVS into a left-eye (or a right-eye) image area and mixed image area. The controller  100  determines a central part of the left-eye image LA (or a central part of the right-eye image RA) and a boundary part between the left-eye image area LA and the right-eye image area RA. And the controller  100  divides the area between the central part and the boundary part into M areas (e.g., into two areas). The controller  100  divides the observer screen OVS into a first area A, a second area B, a third area C, and a fourth area D. 
     The first area A is an area in which the right-eye image R is observed. The second area B is an area in which the left-eye image L is observed. The third area C is an area in which a first mixed image C_LR is observed at a position between the second area B and the first area A. The fourth area D is an area in which a second mixed image C_RL is observed at a position between the first area A and the second area B. 
     Each of the left-eye image L and the right-eye image R displayed on a is screen of the display apparatus may have substantially the same width W in principle. The position of a lens structure may be controlled differently in an area of every W/M (e.g., W/2 where M is two) from the boundary between the left-eye (or the right-eye) image area and the mixed area. 
     Thus, the controller  100  controls driving voltages applied to lens electrodes disposed in the liquid crystal lens panel, on the basis of the left-eye (or the right-eye) image and the mixed image received from each area A, B, C, D, to control the position of a lens structure. The right eye R_E of the observer may receive a right-eye image displayed on areas A, B, C, D, according to a movement of the lens structure. 
     For example, referring to  FIG. 14  and  FIG. 18 , the first area A is an area which the right eye of the observer receives the right-eye image R. A first lens structure LS 1  of the first area A of the liquid crystal lens panel is regarded as a standard position, hereinafter. 
     The second area B is an area which the right eye R_E of the observer receives a left-eye image L. The second area B arrives at a peak point of the profile RI_C of the right-eye image, when the right eye R_E moves by twice E/2 in a left-to-right direction, to receive the right-eye image R. Accordingly, a second stereoscopic lens LS 2  of the second area B moves by a distance of twice the width of a lens electrode, in a left-to-right direction with respect to the first lens structure LS 1 . The second area B of the liquid crystal lens panel may operate as the second lens structure LS 2 , for the right eye R_E of the observer to receive the right-eye image R in the second area B. 
     The third area C is an area which the right eye R_E of the observer receives the first mixed image C_LR. The third area C arrives at a peak point of the profile of the right-eye image RI_C, when the right eye R_E moves by 3 times E/2, in a left-to-right direction to is receive the right-eye image R. Accordingly, a third lens structure LS 3  of the third area C moves by a distance of three times the width of a lens electrodes, with respect to the first lens structure LS 1 . The third area C of the liquid crystal lens panel may operate as the third lens structure LS 3  for the right eye R_E of the observer to receive the right-eye image R in the third area C. 
     The fourth area D is an area which the right eye R_E of the observer receives the second mixed image C_RL. The third area C arrives at a peak point of the profile of the right-eye image RI_C, when the right eye R_E moves by E/2 in a left-to-right direction, to receive the right-eye image R. Accordingly, a fourth lens structure LS 4  of the fourth area D moves by a width of one lens electrode, with respect to the first lens structure LS 1  of the first area A. The fourth area D of the liquid crystal lens panel may operate as the fourth lens structure LS 4 , for the right eye R_E of the observer to receive the right-eye image R in the fourth area D. 
     As mentioned above, the left eye or the right eye of the observer located beyond the observation distance may respectively receive a corresponding left-eye image or a corresponding right-eye image by controlling the position of the lens structure of the liquid crystal lens panel. 
       FIG. 19  is a timing chart illustrating the control of the position of a lens structure corresponding to an observer screen, according to another exemplary embodiment of the present invention. Referring to  FIG. 19 , the lens structure or the lens electrode of the liquid crystal lens panel has a striped structure as illustrated in  FIG. 3 . 
     The controller  100  controls a left-eye image (or a right-eye image) displayed on the display panel and the position of the lens structure, on the basis of a left-eye image (or a right-eye image) and a mixed image received at each of areas A, B, C, D. 
     For example, the first area A and the second area B are different viewpoint is areas from which the right eye R_E of the observer receives a right-eye image R and a left-eye image L, respectively. The third area C and the fourth area D area are mixed areas from which the right eye R_E of the observer receives a first mixed image C_LR and a second mixed image C_RL, respectively. 
     Referring to  FIGS. 14 ,  17 , and  19 , the first area A and the second area B are areas which the right eye R_E of the observer receives the right-eye image R and the left-eye image L. The controller  100  sets a first lens structure LS 1  of the first area A and the second area B as a standard position. By this, the right eye R_E of the observer receives the right-eye image R via the first lens structure LS 1  in the first area A. 
     In contrast, in the second area B, the right eye R_E of the observer receives the left-eye image L via the first lens structure LS 1 . Accordingly, the controller  100  renders image data to display the right-eye image R on the portion of the display panel corresponding to the second area B. As a result, the right eye R_E of the observer may receive the right-eye image R via the first lens structure LS 1 , by displaying the right-eye image R on an area of the display panel corresponding to the second area B. 
     The third area C and the fourth area D are areas in which the right eye R_E of the observer receives the first and the second mixed images C_LR, C_RL, respectively. The controller  100  moves a second lens structure LS 2  of the third area C and the fourth area D, with respect to the position of the first lens structure LS 1 . 
     For example, if the second lens structure LS 2  moves by a width of three lens electrodes with respect to the first lens structure LS 1 , the first mixed image C_LR displayed on the third area C is observed as the left-eye image L that is moved by 3 times E/2 in a left-to-right direction, by the second lens structure LS 2 . The controller  100  renders image data to display the is right-eye image R on an area of the display panel corresponding to the third area C. Accordingly, the right eye R_E of the observer may receive the right-eye image R in the third area C. 
     If the second lens structure LS 2  moves by three lens electrodes in a right-to-left direction, with respect to the first lens structure LS 1 , the second mixed image C_RL displayed on the fourth area D is observed as the right-eye image R, which is moved by 3 times E/2 in a left-to-right direction by the second lens structure LS 2 . Accordingly, the right eye R_E of the observer may receive the right-eye image R in the fourth area D. 
     According to the present exemplary embodiment, eyes (a left eye or a right eye) of the observer may receive corresponding viewpoint images by controlling the position of the lens structure according to the different viewpoint area and the mixed area, and by controlling image data on the basis of the two types of lens structure. 
       FIG. 20  is a cross-sectional view illustrating a tracking mode of a liquid crystal lens panel according to still another exemplary embodiment of the present invention, when the observer&#39;s position is located beyond the observation distance.  FIG. 21  is a plan view of the observer screen according to the tracking mode of  FIG. 20 .  FIG. 22  is a timing chart illustrating the control of the position of a lens structure corresponding to the observer screen of  FIG. 20 . 
     Referring to  FIGS. 20 and 21 , the liquid crystal lens panel  420  according to the present exemplary embodiment includes a lens structure including four lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , as illustrated in  FIG. 6 . The lens structure or the lens electrode have a tilted structure as illustrated in  FIG. 3B . 
     If the observer is located beyond the observation distance Df, then the left eye and the right eye of the observer receive a left-eye image, a right-eye image, and a boundary between the left-eye image and the right-eye image. The tilted direction of the boundary is substantially the same as the tilted direction of the lens structures or the lens electrodes. 
     According to the present exemplary embodiment, the control of the position of the lens structures may be performed in substantially the same way as illustrated in  FIG. 18 , according to an observer screen. 
     The controller  100  analyzes the observer screen on the basis of the tracked observer&#39;s position. The observer screen OVS includes a left-eye image area LA and a right-eye image area RA. The observer screen OVS includes a first area A, a second area B, a third area C, and a fourth area D. 
     The first area A is an area in which a right-eye image R is observed. The second area B is an area in which a left-eye image L is observed. The third area C is an area in which a first mixed image C_LR is observed and is located between the second area B and the first area A. The fourth area D is an area in which a second mixed image C_RL is observed and is located between the first area A and the second area B. 
     Thus, the controller  100  controls driving voltages applied to the lens electrodes disposed in the liquid crystal lens panel  420 , on the basis of viewpoint images and mixed images received at each of areas A, B, C, D, to control the position of the lens structure. 
     Referring to  FIGS. 14 and 22 , a first lens structure LS 1  of the first area A, in which the right-eye image R is observed, is regarded as a standard position, hereinafter. A second lens structure LS 2  of the second area B on which the left-eye image L is observed is moved by a distance corresponding to the width of two lens electrodes, in a left-to-right direction with respect to the first lens structure LS 1  of the first area A, for the right-eye image R to be observed. 
     A third lens structure LS 3  of the third area C, in which the first mixed image C_LR is observed, is moved by a distance of three lens electrode widths, in a left-to-right direction with respect to the first lens structure LS 1  of the first area A, for the right-eye image R to be observed. A fourth lens structure LS 4  of the fourth area D, in which the second mixed image C_RL is observed, is moved by a distance corresponding to one lens electrode width, in a left-to-right direction with respect to the first lens structure LS 1  of the first area A, for the right-eye image R to be observed. 
     As mentioned above, the left eye or the right eye of the observer located beyond the observation distance may respectively receive a corresponding left-eye image or a corresponding right-eye image, by controlling the position of the lens structure of the liquid crystal lens panel. 
       FIG. 23  is a timing chart illustrating the control of the position of a lens structure corresponding to an observer screen, according to still another exemplary embodiment of the present invention. Referring to  FIGS. 1 and 23 , the liquid crystal lens panel  420  includes the lens structure including four lens electrodes LE 1 , LE 2 , LE 3 , LE 4  illustrated in  FIG. 6 . The lens structure or the lens electrodes have a tilted structure as illustrated in  FIG. 3B . 
     The controller  100  controls the position of the lens structure and viewpoint images displayed on the display panel, on the basis of viewpoint images and mixed images received at each of the first, the second, the third, and the fourth areas A, B, C, D. The control of the display image and the position of the lens may be performed in substantially the same way illustrated in  FIG. 19 , in accordance with an observer screen. 
     A first lens structure LS 1  of the first area A and the second area B is regarded as a standard position. In the first area A, a right-eye image R is observed by the first is lens structure LS 1 . Because a left-eye image L is observed in the second area B through the first lens structure LS 1 , image data is rendered for the right-eye image R to be displayed on the display panel corresponding to the second area B. 
     A second lens structure LS 2  of the third area C and the fourth area D is moved by a distance corresponding to the widths of three lens electrodes, in a left-to-right direction from the first lens structure LS 1 . Because the left-eye image L is observed in the third area C, on which the first mixed image C_LR is observed by the second lens structure LS 2 , the image data is rendered for the right-eye image R to be displayed on the portion of the display panel corresponding to the third area C. In the fourth area D, on which the second mixed image C_RL is observed, the right-eye image R is observed through the second lens structure LS 2 . 
     According to the present exemplary embodiment, eyes of the observer may receive corresponding viewpoint images by controlling the position of the lens structure according to different viewpoint areas and mixed areas and by controlling image data on the basis of the two lens structures. 
       FIG. 24  is a luminance profile of three-dimensional stereoscopic images according to the liquid crystal lens panel  440  of  FIG. 10 .  FIG. 25  is a plan view of the observer screen according to the liquid crystal lens panel  440  of  FIG. 10 .  FIG. 26  is a timing chart illustrating the control of the position of a lens structure corresponding to the observer screen of  FIG. 25 . 
     Referring to  FIGS. 10 and 24 , the lens unit LU of the liquid crystal lens panel  440  includes first, second, and third lens electrodes LE 1 , LE 2 , LE 3 . And a lens structure LS includes first, second, third, fourth, fifth, and sixth lens electrodes LE 1 , LE 2 , LE 3 , LE 4 , LE 5 , LE 6 . The lens unit LU includes three of the lens electrodes. 
     Each of the luminance profile LI_C of a left-eye image and the luminance profile RI_C of the right-eye image, which are two viewpoint images, have sinusoidal shapes. The luminance profile LI_C of the left-eye image delays by an eye distance E of a left eye LE and a right eye RE of the observer with respect to the luminance profile RI_C of the right-eye image. 
     If the left eye L_E of the observer is located at a position corresponding to a peak point of the luminance profile LI_C of the left-eye image, and if the right eye R_E of the observer is located at a position corresponding to a peak point of the luminance profile RI_C of the right-eye image, the observer may receive a normal stereoscopic image without crosstalk. 
     The controller  100  computes an observer screen OVS including a left-eye image L and a right-eye image R observed by the right-eye R_E of the observer. Alternatively, the controller  100  divides the observer screen OVS into a left-eye (or a right-eye) image area and a mixed image area. For example, the controller  100  determines a central part of the left-eye image LA (or a central part of the right-eye image RA) and a boundary part between the left-eye image area LA and the right-eye image area RA. The controller  100  divides the area between the central part and the boundary part into M areas (e.g., into three areas). As a result, the controller  100  divides the observer screen OVS into a first area A, a second area B, a third area C, a fourth area D, a fifth area E, and a sixth area F. 
     Each area of the left-eye image L and the right-eye image R, which are displayed on a screen of the display apparatus, may have substantially the same width W. The controller  100  may control the position of a stereoscopic lens differently in an area of every W/3 from the boundary of the left-eye (or the right-eye) image area and the mixed image area. 
     For example, referring to  FIGS. 24 ,  25 , and  26 , a first lens LS 1  formed in is the first area A, which the right eye of the observer receives a right-eye image R, is regarded as a standard position. The first area A of the liquid crystal lens panel  440  operates as the first lens structure LS 1 . Accordingly, the right eye R_E of the observer receives the right-eye image R from the first area A. 
     The second area B is an area which the right eye R_E of the observer receives a first mixed image C_RL 1 . A peak point of the luminance profile RI_C of the right-eye image occurs in the second area B when moved by E/3 in a left-to-right direction, to receive the right-eye image R. Accordingly, a second lens structure LS 2  of the second area B moves by the width of one lens electrode, in a left-to-right direction with respect to the first lens structure LS 1 . The second area B of the liquid crystal lens panel  440  operates as the second lens structure LS 2  for the right eye R_E of the observer, to receive the right-eye image R in the second area B. 
     The third area C is an area from which the right eye R_E of the observer receives a second mixed image C_RL 2 . The third area C arrives at a peak point of the luminance profile RI_C of the right-eye image when moved by 2 times E/3, in a left-to-right direction, to receive the right-eye image R. Accordingly, a third lens structure LS 3  of the third area C moves by two lens electrode widths, in a left-to-right direction, with respect to the first lens structure LS 1 . The third area C of the liquid crystal lens panel  440  operates as the third lens structure LS 3  for the right eye R_E of the observer to receive the right-eye image R in the third area C. 
     The fourth area D is an area which the right eye R_E of the observer receives a left-eye image L. The fourth area D arrives at a peak point of the luminance profile RI_C of the right-eye image when moved by 3 times E/3 in a left-to-right direction, to receive the right-eye image R. Accordingly, a fourth lens structure LS 4  of the fourth area D moves by a width of three lens electrodes in a left-to-right direction, with respect to the first lens structure LS 1 . The fourth area D of the liquid crystal lens panel  440  operates as the fourth lens structure LS 4  for the right eye R_E of the observer to receive the right-eye image R in the fourth area D. 
     The fifth area E is an area which the right eye R_E of the observer receives a third mixed image C_LR 1 . The fifth area E arrives at a peak point of the luminance profile RI_C of the right-eye image, when moved by 4 times E/3 in a left-to-right direction, to receive the right-eye image R. Accordingly, a fifth lens structure LS 5  of the fifth area E moves by four lens electrode widths, in a left-to-right direction, with respect to the first lens structure LS 1 . The fifth area E of the liquid crystal lens panel  440  operates as the fifth lens structure LS 5  for the right eye R_E of the observer to receive the right-eye image R in the fifth area E. 
     The sixth area F is an area which the right eye R_E of the observer receives a fourth mixed image C_LR 2 . The sixth area F arrives at a peak point of the luminance profile RI_C of the right-eye image when moved by 5 times E/3 in a left-to-right direction to receive the right-eye image R. Accordingly, a sixth lens structure LS 6  of the sixth area F moves by a width of five lens electrodes in a left-to-right direction with respect to the first lens structure LS 1 . The sixth area F of the liquid crystal lens panel  440  operates as the sixth lens structure LS 6  for the right eye R_E of the observer to receive the right-eye image R in the sixth area F. 
     As mentioned above, the left eye L_E or the right eye R_E of the observer located beyond the observation distance may respectively receive the left-eye image L or the right-eye image R, by controlling the position of the lens structure of the liquid crystal lens panel. 
     According to the liquid crystal lens panels illustrated in above exemplary embodiments, if the left eye or the right eye of the observer is located at a peak of the luminance profile in the observation distance of the luminance profile, the position of a lens structure is is moved by a width of at least one lens electrode, in a direction corresponding to a moving direction of the observer, when the observer moves more than ±E/(2M) in a right-and-left direction at the peak, under a condition that the lens structure has a length of 2M times N where M is the number of sub-areas included in a lens unit and N is the number of viewpoints. That is, M is the number of lens electrodes included in a lens unit LU having a width equal to that of lens area Sf. In addition, if a head of the observer moves by E/M in a right-and-left direction from a standard position, the position of the lens structure moves by a width of one lens electrode. 
     Each of a left-eye image and a right-eye image included in an observer screen which the observer located beyond an observation distance observes may have substantially the same width W. The position of the lens structure may be controlled differently in an area of every W/M from the boundary between the left-eye image area and the right-eye image area, where M is the number of sub-areas included in a lens unit. 
     If the lens structure has a length of 2 times M corresponding to two subpixels, then the observer may receive the left-eye image or the right-eye image in all area of the observer screen by controlling the position of 2×M types of lens structures. 
       FIG. 27  is a cross-sectional view illustrating a tracking mode of a liquid crystal lens panel according to still another exemplary embodiment of the present invention when an observer&#39;s position is located in an observation distance. 
     Referring to  FIG. 27 , the lens structure (or the lens electrode) of the liquid crystal lens panel according to the present exemplary embodiment has a tilted structure as illustrated in  FIG. 3B . 
     If the observer is located closer than the observation distance Df, then the observer receives an observer screen OVS. The observer screen OVS includes a left-eye image L, a right-eye image R, and a boundary B of the left-eye image and the right-eye image. The tilted direction T of the boundary B may be substantially the same as the tilted direction T of the lens structure (or the lens electrode) of the liquid crystal lens panel. 
     Thus, as illustrated in  FIGS. 21 and 22 , the timing controller  100  analyze the observer screen OVS to divide the observer screen OVS into a first area A in which the right-eye image R is observed, a second area B in which the left-eye image L is observed, a third area C in which a first mixed image C_LR is observed, and a fourth area D in which a second mixed image C_RL is observed. The controller  100  controls the position of lens structures disposed in each of the first to fourth area A, B, C, D. Accordingly, if the observer is located closer than the observation distance, one of the eyes of the observer may receive a corresponding viewpoint image. 
     Alternatively, as illustrated in  FIGS. 21 and 23 , the controller  100  may control the positions of lens structures into two types according to a different viewpoint area and a mixed area, and the eyes of the observer may receive corresponding viewpoint images by controlling image data on the basis of the two types of lens structures. 
       FIG. 28  is a cross-sectional view of a dynamic conversion panel of liquid crystal barrier type according to still another exemplary embodiment of the present invention. Referring to  FIG. 28 , the liquid crystal barrier panel  460  according to the present exemplary embodiment includes a first substrate  461 , a second substrate  462 , and a liquid crystal layer. 
     The first substrate  461  includes a plurality of barrier electrodes BE to form a barrier unit BU. The second substrate  462  includes a counter electrode facing the barrier electrode BE. The liquid crystal layer  463  forms the barrier unit BU which includes an opening OP that transmits light and a barrier BP that blocks light in response to a voltage applied to the barrier electrode BE and the counter electrode OE. The opening OP includes M sub-areas (M times SA), and corresponds to the barrier emission unit illustrated above. Referring to  FIG. 2 , the unit area Sf corresponds to one dot DT. The unit area Sf may be determined by a pitch p of the dots DT, a distance between the dots DT and the barrier unit BU, and an observation distance Df from the barrier unit BU designed. 
     Although the first substrate  461  is disposed in upper part and the second substrate  462  is disposed in lower part in  FIG. 28 , the positions in which the first and the second substrates  461 ,  462  are disposed are not limited thereto. 
       FIG. 29  is a cross-sectional view of a liquid crystal barrier panel  470  according to still another exemplary embodiment of the present invention.  FIG. 30  is a cross-sectional view illustrating multi-viewpoint driving of the liquid crystal barrier panel of  FIG. 29 . 
     Referring to  FIG. 29 , the liquid crystal barrier panel  470  defines a barrier unit BU for two viewpoints corresponding to four sub-areas. The barrier unit BU includes an opening OP and a barrier BP. The opening OP is formed on sub-areas SA 1 , SA 2 , and the barrier BP is formed on sub-areas SA 3 , SA 4 . The opening OP transmits light and the barrier BP blocks light. 
     For example, as shown in  FIG. 30 , a first barrier electrode BE 1  and a second barrier electrode BE 2  are disposed in the first and the second sub-areas SA 1 , SA 2  where the opening OP is formed. A third barrier electrode BE 3  and a fourth barrier electrode BE 4  are disposed in the third and the fourth sub-areas SA 3 , SA 4  where the barrier BP is formed. The opening OP is formed by applying a first driving voltage to the first and the second barrier electrodes BE 1 , BE 2 . The barrier BP is formed by applying a second driving voltage to the third and the fourth barrier electrodes BE 3 , BE 4  and is different from the first driving voltage. 
     Referring again to  FIG. 29 , the display panel  200 , on which the liquid crystal barrier panel  470  is disposed, alternately displays two viewpoint images (e.g., a left-eye image L and a right-eye image R) using two subpixels that are consecutive in a row direction. For example, the display panel displays viewpoint images using columns of subpixels that are next to one another in the row direction. However, for convenience, only one subpixel from each column will be described. 
     The left-eye image L is formed by a first subpixel SP 1  and a second subpixel SP 2  of the display panel  200  and is emitted toward the observer&#39;s left eye L_E via the opening OP. The right-eye image R is formed by a third subpixel SP 3  and a fourth subpixel SP 4  of the display panel  200  and is emitted toward the observer&#39;s right eye R_E. As such, the liquid crystal barrier panel  470  may display two viewpoint images. 
     In a multi-viewpoint mode, the method of driving the liquid crystal barrier panel  470  is performed as follows. Referring to  FIGS. 1 and 30 , the conversion driver  500  applies a first driving voltage to electrode BE 1 , and applies a second driving voltage to barrier electrodes BE 2 , BE 3 , BE 4 . Accordingly, an opening OP is formed by the first barrier electrode BE 1 , and an barrier BP is formed by the second, the third, and the fourth barrier electrodes BE 2 , BE 3 , BE 4 . 
     On the other hand, a first, a second, a third, and a fourth viewpoint images  1 ,  2 ,  3 ,  4  are displayed on the first, the second, the third, and the fourth subpixels SP 1 , SP 2 , SP 3 , SP 4  of the display panel  200 , which are consecutive in a row direction. The first, the second, the third, and the fourth viewpoint images  1 ,  2 ,  3 ,  4  are emitted to a first, a second, a third, and a fourth viewpoint positions VW 1 , VW 2 , VW 3 , VW 4 , via the opening OP formed by the first barrier electrode BE 1 . 
     The liquid crystal barrier panel  470  may display the total of four viewpoint images  1 ,  2 ,  3 ,  4 . If the liquid crystal barrier panel  470  for two viewpoints is driven for four viewpoints as the present exemplary embodiment, the opening OP may consist of one sub-area. 
       FIG. 31  is a cross-sectional view of a liquid crystal barrier panel according to still another exemplary embodiment of the present invention.  FIG. 32  is a cross-sectional view illustrating multi-viewpoint driving type of the liquid crystal barrier panel of  FIG. 31 . 
     Referring to  FIG. 31 , the liquid crystal barrier panel  480  of the present exemplary embodiment includes a barrier unit BU for four viewpoints corresponding to eight sub-emission units. The barrier unit BU includes an opening OP and a barrier BP. The opening OP is formed on two sub-areas SA 1 , SA 2 . The barrier BP is formed on six sub-areas SA 3 , SA 4 , SA 5 , SA 6 , SA 7 , SA 8 . 
     For example, a first and a second barrier electrodes BE 1 , BE 2  are disposed in the sub-areas on which the opening OP is formed. Third to eighth barrier electrodes BE 3 , BE 4 , BE 5 , BE 6 , BE 7 , BE 8  are disposed in the sub-areas on which the barrier BP is formed. The opening OP is formed by a first driving voltage applied to the first and the second barrier electrodes BE 1 , BE 2 . The barrier BP is formed by a second driving voltage applied to the third to the eight barrier electrodes BE 3 , BE 4 , BE 5 , BE 6 , BE 7 , BE 8 , which is different from the first driving voltage. 
     The display panel  200  which the liquid barrier panel  480  is applied alternately displays four viewpoint images (e.g., a first viewpoint image  1 , a second viewpoint image  2 , a third viewpoint image  3 , and a fourth viewpoint image  4 ) using two consecutive subpixels. 
     By the liquid crystal barrier panel  480 , the first viewpoint image  1  is emitted is to the first viewpoint position VW 1  via the opening OP. The second viewpoint image  2  is emitted to the second viewpoint position VW 2  via the opening OP. The third viewpoint image  3  is emitted to the third viewpoint position VW 3  via the opening OP. The fourth viewpoint image  4  is emitted to the fourth viewpoint position VW 4  via the opening OP. The liquid crystal barrier panel  480  according to the present exemplary embodiment may display four viewpoint images. 
     In a multi-viewpoint mode, the method of driving the liquid crystal barrier panel  480  is performed as follows. 
     Referring to  FIGS. 1 and 32 , the conversion driver  500  applies a first driving voltage to the first barrier electrode BE 1 , and applies a second driving voltage to the second to the eighth barrier electrodes BE 2 , BE 3 , BE 4 , BE 5 , BE 6 , BE 7 , BE 8 . Accordingly, an opening OP is formed by the first barrier electrode BE 1 . A barrier BP is formed by the second to the eight barrier electrodes BE 2 , BE 3 , BE 4 , BE 5 , BE 6 , BE 7 , BE 8 . 
     On the other hand, a first, a second, a third, a fourth, a fifth, a sixth, a seventh, and an eighth viewpoint images  1 ,  2 ,  3 ,  4 ,  5 ,  6 ,  7 ,  8  are displayed on a first, a second, a third, a fourth, a fifth, a sixth, a seventh, and an eighth subpixels SP 1 , SP 2 , SP 3 , SP 4 , SP 5 , SP 6 , SP 7 , SP 8  of the display panel  200  which are consecutive in a row direction. 
     The first to the eighth viewpoint images  1 ,  2 ,  3 ,  4 ,  5 ,  6 ,  7 ,  8  displayed on the eight consecutive subpixels (i.e., the first to the eighth subpixels SP 1 , SP 2 , SP 3 , SP 4 , SP 5 , SP 6 , SP 7 , SP 8 ) are emitted to a first, a second, a third, a fourth, a fifth, a sixth, a seventh, and an eighth viewpoint positions VW 1 , VW 2 , VW 3 , VW 4 , VW 5 , VW 6 , VW 7 , VW 8  via the opening OP defined by the first barrier electrode BE 1 . 
     The liquid crystal barrier panel  480  according to the present exemplary embodiment may display the total of eight viewpoint images  1 ,  2 ,  3 ,  4 ,  5 ,  6 ,  7 ,  8 . If the liquid is crystal barrier panel  480  for four viewpoints is driven for eight viewpoints, the opening OP may consist of one sub-areas. 
       FIG. 33  is a cross-sectional view of a liquid crystal barrier panel according to still another exemplary embodiment of the present invention.  FIG. 34  is a cross-sectional view illustrating multi-viewpoint driving type of the liquid crystal barrier panel of  FIG. 33 . 
     Referring to  FIG. 33 , the liquid crystal barrier panel  490  of the present exemplary embodiment includes a barrier unit BU for two viewpoints corresponding to six sub-areas. The barrier unit BU includes an opening OP and a barrier BP. The opening OP is formed on three sub-areas SA 1 , SA 2 , SA 3 . The barrier BP is formed on three sub-areas SA 4 , SA 5 , SA 6 . 
     For example, a first barrier electrode BE 1 , a second barrier electrode BE 2 , and a third barrier electrode BE 3  are disposed in the sub-areas on which the opening OP is defined. A fourth barrier electrode BE 4 , a fifth barrier electrode BE 5 , and a sixth barrier electrode BE 6  are disposed in the sub-areas on which the barrier BP is defined. The opening OP is formed by applying a first driving voltage to the first to the third barrier electrodes BE 1 , BE 2 , BE 3 . The barrier BP is formed by applying a second driving voltage to the fourth to the sixth barrier electrodes BE 4 , BE 5 , BE 6 , and is different from the first driving voltage. 
     The display panel  200  on which the liquid crystal barrier panel  490  is disposed alternately displays two viewpoint images (e.g., a left-eye image L and a right-eye image R) on three subpixels which are consecutive in a row direction. 
     The left-eye image L is displayed on a first subpixel SP 1 , a second subpixel SP 2 , and a third subpixel SP 3  of the display panel  200 , which are consecutive, and is emitted toward the observer&#39;s left eye L_E via the opening OP. The right-eye image R is displayed on a fourth subpixel SP 4 , a fifth subpixel SP 5  and a sixth subpixel SP 6  of the display panel  200 , is which are consecutive, and is emitted toward the observer&#39;s right eye R_E. The liquid crystal barrier panel  490  according to the present exemplary embodiment may display two viewpoint images. 
     In a multi-viewpoint mode, the method of driving the liquid crystal barrier panel  490  is performed as follows. The conversion driver  500  applies a first driving voltage to the first barrier electrode BE 1 , and applies a second driving voltage to barrier electrodes BE 2 , BE 3 , BE 4 , BE 5 , BE 6 . Accordingly, an opening OP is formed by the first barrier electrode BE 1 , and a barrier BP is formed by barrier electrodes BE 2 , BE 3 , BE 4 , BE 5 , BE 6 . 
     On the other hand, viewpoint images  1 ,  2 ,  3 ,  4 ,  5 ,  6  are displayed on subpixels SP 1 , SP 2 , SP 3 , SP 4 , SP 5 , SP 6  of the display panel  200 , which are consecutive in a row direction. Viewpoint images  1 ,  2 ,  3 ,  4 ,  5 ,  6  displayed on subpixels SP 1 , SP 2 , SP 3 , SP 4 , SP 5 , SP 6  are respectively emitted to viewpoint positions VW 1 , VW 2 , VW 3 , VW 4 , VW 5 , VW 6 , via the opening OP formed by the first barrier electrode BE 1 . 
     The liquid crystal barrier panel  490  may display the total of six viewpoint images  1 ,  2 ,  3 ,  4 ,  5 ,  6 . If the liquid crystal barrier panel  490  is driven for six viewpoints, the opening OP may include one sub-area. For an ease of illustration, the opening OP is regarded as being formed on M barrier electrodes, each corresponding to M sub-areas, hereinafter. 
       FIG. 35  is a cross-sectional view illustrating a tracking mode using the liquid crystal barrier panel  470  of  FIG. 29 , when the observer&#39;s position is located within the observation distance. Referring to  FIGS. 14 and 35 , each of a luminance profile of left-eye image LI_C and a luminance profile of right-eye image RI_C have sinusoidal shapes. The luminance profile of left-eye image LI_C is delayed by an eye distance E between a left eye and a right eye of an observer, with respect to the luminance profile RI_C of the right-eye image. 
     If the left eye L_E of the observer is located at a position corresponding to a peak point of the luminance profile LI_C of the left-eye image, and the right eye R_E of the observer is located at a position corresponding to a peak point of the luminance profile RI_C of the right-eye image, then the observer may receive a normal stereoscopic image without crosstalk. 
     If the observer&#39;s position is located within an observation distance, then the controller  100  analyzes the movement of the observer in a right-and-left direction. For example, if a left eye L_E or a right eye R_E of the observer moves by a distance E/2 of the eye distance E, then the controller  100  controls driving voltages applied to the liquid crystal barrier panel  470  to move the position of the barrier unit BU formed in the liquid crystal barrier panel  470 . 
     Referring to  FIGS. 29 and 30 , if the left eye L_E and the right eye R_E of the observer are located originally at a first and a second viewpoint positions VW 1 , VW 2 , then the conversion driver  500  applies a first driving voltage to a first and a second barrier electrodes BE 1 , BE 2 , and applies a second driving voltage to a third and a fourth barrier electrodes BE 3 , BE 4 . Accordingly, an opening OP of a barrier unit BU 2  is formed corresponding to the first and the second barrier electrodes BE 1 , BE 2 , and a barrier BP of the barrier unit BU 2  is formed corresponding to the third and the fourth barrier electrodes BE 3 , BE 4 . 
     Two viewpoint images (i.e., a left-eye image L and a right-eye image R) displayed on the display panel  200  are emitted to the first and the second viewpoint positions VW 1 , VW 2 , via the opening OP. Accordingly, the left eye L_E and the right eye R_E of the observer respectively located at the first and the second viewpoint positions VW 1 , VW 2  may respectively observe the left-eye image L and the right-eye image R. 
     If the tracking part  900  tracks the position of the observer&#39;s eyes moving by E/2 in a left-to-right direction, from the first and the second viewpoint positions VW 1 , VW 2 , so as to be located at a third and a fourth viewpoint positions VW 3 , VW 4 , then the conversion driver  500  applies the first driving voltage to the first and the fourth barrier electrodes BE 1 , BE 4 , and applies the second driving voltage to the second and the third barrier electrodes BE 2 , BE 3 , according to the control of the controller  100 . Accordingly, a second opening OP 2  of a second barrier unit BU 2  is formed corresponding to the first and the fourth barrier electrodes BE 1 , BE 4 , and a second barrier BP 2  of the second barrier unit BU 2  is formed corresponding to the second and the third barrier electrodes BE 2 , BE 3 . The second barrier unit BU 2  is moved by a width of one sub-area, which corresponds to one barrier electrode, in a left-to-right direction with respect to the first barrier unit BU 1 . 
     Two viewpoint images (i.e., the left-eye image L and the right-eye image R) displayed on the display panel  200  are emitted to the third and the fourth viewpoint positions VW 3 , VW 4 , via the second opening OP 2 . Accordingly, the left eye L_E and the right eye R_E of the observer, respectively located at the third and the fourth viewpoint positions VW 3 , VW 4 , may respectively observe the left-eye image L and the right-eye image R. 
     Although not shown, if the observer&#39;s position moves by E/2 in a right-to-left direction, the observer may receive a left-eye image and a right-eye image, by forming a second barrier unit BU 2 , which is moved by a width of one barrier electrode in a right-and-left direction, with respect to the first barrier unit BU 1 , in substantially the same way. 
     Again, referring to  FIG. 14 , if the observer&#39;s position moves more than E/4 in a right-and-left direction, the left eye L_E and the right eye R_E of the observer receive the luminance profiles corresponding to adjacent viewpoint positions. Accordingly, if the left eye or the right eye of the observer is beyond a distance of E/4 in a right-and-left direction, then the is controller  100  controls the liquid crystal barrier panel  470  to form a second barrier unit BU 2 , which is moved by a width of one barrier electrode from the first barrier unit BU 1 . The left eye L_E and the right eye R_E of the moved observer respectively receive a left-eye image L and a right-eye image R. 
       FIG. 36  is a cross-sectional view illustrating a tracking mode using the liquid crystal barrier panel of  FIG. 33 , when the observer&#39;s position is located within the observation distance. Referring to  FIGS. 24 and 36 , if the observer is located within an observation distance, the controller  100  analyzes the movement of the observer in a right-and-left direction. 
     For example, if a left eye L_E or a right eye R_E of the observer moves by a distance E/3 of the eye distance E, then the controller  100  controls driving voltages applied to the liquid crystal barrier panel  490  to move the position of a barrier unit BU formed in the liquid crystal barrier panel  490 . 
     Referring to  FIGS. 33 and 36 , if the left eye L_E and the right eye R_E of the observer are located originally at a first and a second viewpoint positions VW 1 , VW 2 , then the conversion driver  500  applies a first driving voltage to barrier electrodes BE 1 , BE 2 , BE 3 , and applies a second driving voltage to barrier electrodes BE 4 , BE 5 , BE 6 . Accordingly, a first opening OP 1  of a first barrier unit BU 1  is formed corresponding to barrier electrodes BE 1 , BE 2 , BE 3 , and a first barrier BP 1  of the first barrier unit BU 1  is formed corresponding to barrier electrodes BE 4 , BE 5 , BE 6 . 
     Two viewpoint images (i.e., a left-eye image L and a right-eye image R) displayed on the display panel  200  are emitted to the first and the second viewpoint positions VW 1 , VW 2 , via the first opening OP 1 . Accordingly, the left eye L_E and the right eye R_E of is the observer respectively located at the first and the second viewpoint positions VW 1 , VW 2  may respectively observe the left-eye image L and the right-eye image R. 
     If the tracking part  900  tracks that the observer&#39;s eyes move by E/3 in a left-to-right direction, from viewpoint positions VW 1 , VW 2  to viewpoint positions VW 3 , VW 4 , then the conversion driver  500  applies the first driving voltage to the barrier electrodes BE 1 , BE 2 , BE 6 , and applies the second driving voltage to barrier electrodes BE 3 , BE 4 , BE 5 , according to the control of the controller  100 . 
     Accordingly, a second opening OP 2  of a second barrier unit BU 2  is formed corresponding to barrier electrodes BE 1 , BE 2 , BE 6 , and a second barrier BP 2  of the second barrier unit BU 2  is formed corresponding to barrier electrodes BE 3 , BE 4 , BE 5 . The second barrier unit BU 2  is moved by a width of one sub-area corresponding to one barrier electrode in a left-to-right direction, with respect to the first barrier unit BU 1 . 
     Two viewpoint images (i.e., the left-eye image L and the right-eye image R) displayed on the display panel  200  are emitted to viewpoint positions VW 3 , VW 4 , via the second opening OP 2 . Accordingly, the left eye L_E and the right eye R_E of the observer respectively located at viewpoint positions VW 3 , VW 4  may respectively observe the left-eye image L and the right-eye image R. 
     On the other hand, if the tracking part  900  tracks that the observer&#39;s eyes move by 2 times E/3 in a left-to-right direction, from viewpoint positions VW 1 , VW 2  to viewpoint positions VW 5 , VW 6 , then the conversion driver  500  applies the first driving voltage to barrier electrodes BE 1 , BE 5 , BE 6 , and applies the second driving voltage to barrier electrodes BE 2 , BE 3 , BE 4 , according to the control of the controller  100 . Accordingly, a third opening OP 3  of a third barrier unit BU 3  is formed corresponding to barrier electrodes BE 1 , BE 5 , BE 6  and a is third barrier BP 3  of the third barrier unit BU 3  is formed corresponding to barrier electrodes BE 2 , BE 3 , BE 4 . The third barrier unit BU 3  is moved by a width of two sub-areas corresponding to two barrier electrodes, in a left-to-right direction, with respect to the first barrier unit BU 1 . 
     Two viewpoint images (i.e., the left-eye image L and the right-eye image R) displayed on the display panel  200  are emitted to viewpoint positions VW 5 , VW 6 , via the third opening OP 3 . Accordingly, the left eye L_E and the right eye R_E of the observer respectively located at viewpoint positions VW 5 , VW 6  may respectively observe the left-eye image L and the right-eye image R. 
     Although not shown, if the observer&#39;s position moves by E/3 (or 2 times E/3) in a right-to-left direction, the observer may receive a left-eye image and a right-eye image by forming a second barrier unit BU 2 . The second barrier unit BU 2  is moved by a width of one sub-area corresponding to one barrier electrode (or a third barrier unit BU 3  moved by a width of two sub-areas corresponding to two barrier electrodes), in a right-to-left direction, with respect to the first barrier unit BU 1 , in substantially the same way. 
     Again, referring to  FIG. 24 , if the observer&#39;s position moves more than E/6 in a right-and-left direction, the left eye L_E and the right eye R_E of the observer receive the luminance profiles of adjacent viewpoint positions. Accordingly, if the left eye or the right eye of the observer is beyond a distance of E/6 in a right-and-left direction, then the controller  100  controls the liquid crystal barrier panel  490  to form a second barrier unit BU 2 , which is moved by a width of one sub-area corresponding to one barrier electrode from the first barrier unit BU 1 , and the left eye L_E and the right eye R_E of the moved observer respectively receive a left-eye image L and a right-eye image R. 
       FIG. 37  is a timing chart illustrating the control of the position of a barrier is unit corresponding to the observer screen according to the liquid crystal barrier panel  470  of  FIG. 30 , when observed by an observer located far away. Referring to  FIGS. 17 ,  30 , and  37 , the barrier unit of the liquid crystal barrier panel  470  has a striped structure as illustrated in  FIG. 3A . 
     If the observer is located beyond the observation distance, the controller  100  computes an observer screen OVS received at the observer&#39;s position, by using an analyzing algorithm. For example, the observer screen OVS received at the right eye R_E of the observer includes a left-eye image L and a right-eye image R, as illustrated in  FIG. 17 . 
     The controller  100  divides the observer screen OVS into a first area A, a second area B, a third area C, and a fourth area D. The first area A is an area in which the right-eye image R is observed. The second area B is an area in which the left-eye image L is observed. The third area C is an area in which a first mixed image C_LR is observed at a position between the second area B and the first area A. The fourth area D is an area in which a second mixed image C_RL is observed at a position between the first area A and the second area B. 
     Each of the left-eye image L and the right-eye image R displayed on a screen of the display apparatus may have substantially the same width W in principle. The position of a barrier unit may be controlled differently in an area of every W/2 from the boundary between the left-eye (or the right-eye) image area and the mixed area. 
     Referring to  FIGS. 14 ,  17 , and  37 , the first area A is an area which the right eye of the observer receives the right-eye image R. A first barrier unit BU 1  of the first area A is regarded as a standard position, hereinafter. That is, the first area A of the liquid crystal barrier panel  470  is driven as the first barrier unit BU 1 . In the first barrier unit BU 1 , a first opening OP 1  is defined by a first and a fourth barrier electrodes BE 1 , BE 4 , and a first barrier BP 1  is defined by a second and a third barrier electrodes BE 2 , BE 3 . 
     The second area B is an area which the right eye R_E of the observer receives a left-eye image L. The second area B arrives at a peak point of the profile RI_C of the right-eye image, when the right eye R_E moves by 2 times E/2 in a left-to-right direction and receives the right-eye image R. A second barrier unit BU 2  of the second area B moves by a width of two sub-areas corresponding to two barrier electrodes, in a left-to-right direction, with respect to the first barrier unit BU 1 . In the second barrier unit BU 2 , a second opening OP 2  is formed by barrier electrodes BE 1 , BE 4 , and a second barrier BP 2  is formed by barrier electrodes BE 2 , BE 3 . The second area B of the liquid crystal barrier panel  470  may operate as the second barrier unit BU 2  for the right eye R_E of the observer to receive the right-eye image R of the second area B. 
     The third area C is an area which the right eye R_E of the observer receives the first mixed image C_LR including the left-eye image and the right-eye image. The third area C arrives at a peak point of the profile of the right-eye image RI_C, when the right eye R_E moves by 3 times E/2 in a left-to-right direction, to receive the right-eye image R. A third barrier unit BU 3  of the third area C moves by a width of three sub-areas corresponding to three barrier electrodes, with respect to the first barrier unit BU 1  of the first area A. In the third barrier unit BU 3 , a third opening OP 3  is defined by third and fourth barrier electrodes BE 3 , BE 4 , and a third barrier BP 3  is defined by a first and a second barrier electrodes BE 1 , BE 2 . The third area C of the liquid crystal barrier panel  470  may operate as the third barrier unit BU 3 , for the right eye R_E of the observer to receive the right-eye image R in the third area C. 
     The fourth area D is an area which the right eye R_E of the observer receives the second mixed image C_RL including the left-eye image and the right-eye image. The third area C arrives at a peak point of the profile of the right-eye image RI_C when the right is eye R_E moves by 1 times E/2 in a left-to-right direction, to receive the right-eye image R. A fourth barrier unit BU 4  of the fourth area D moves by a width of one sub-area corresponding to one barrier electrode, with respect to the first barrier unit BU 1  of the first area A. In the fourth barrier unit BU 4 , a fourth opening OP 4  is defined by first and second barrier electrodes BE 1 , BE 2 , and a fourth barrier BP 4  is defined by third and fourth barrier electrodes BE 3 , BE 4 . The fourth area D of the liquid crystal barrier panel  470  may operate as the fourth barrier unit BU 4 , for the right eye R_E of the observer to receive the right-eye image R in the fourth area D. 
     As mentioned above, the left eye L_E or the right eye R_E of the observer located beyond the observation distance may respectively receive the left-eye image L or the right-eye image R, by controlling the position of the barrier unit of the liquid crystal barrier panel. 
       FIG. 38  is a timing chart illustrating the control of the position of a barrier unit corresponding to an observer screen, according to still another exemplary embodiment of the present invention. Referring to  FIG. 38 , a barrier unit or a barrier electrode of the liquid crystal barrier panel has a striped structure as illustrated in  FIG. 3A . The controller  100  controls a left-eye image (or a right-eye image) displayed on the display panel and the position of the barrier unit, on the basis of the left-eye image (or the right-eye image) and a mixed image received at each of the first, the second, the third, and the fourth areas A, B, C, D. 
     For example, the first area A and the second area B are different viewpoint areas in which the right eye R_E of the observer receives a right-eye image R and a left-eye image L, respectively. The third area C and the fourth area D area are mixed areas in which the right eye R_E of the observer receives a first mixed image C_LR and a second mixed image C_RL, respectively. 
     Referring to  FIGS. 14 ,  17 , and  38 , the first area A and the second area B are areas in which the right eye R_E of the observer receives the right-eye image R and the left-eye image L. The controller  100  sets a first barrier unit BU 1  of the first area A as a standard position. In the first barrier unit BU 1 , a first opening OP 1  is defined by a first and a fourth barrier electrodes BE 1 , BE 4 , and a first barrier BP 1  is defined by second and third barrier electrodes BE 2 , BE 3 . The right eye R_E of the observer receives the right-eye image R, via the first barrier unit BU 1  in the first area A. 
     In contrast, in the second area B, the right eye R_E of the observer receives the left-eye image L, via the first barrier unit BU 1 . Accordingly, the controller  100  renders image data to display the right-eye image R on the display panel corresponding to the second area B. As a result, the right eye R_E of the observer may receive the right-eye image R, via the first barrier unit BU 1 , by displaying the right-eye image R in an area of the display panel corresponding to the second area B. 
     The third area C and the fourth area D are areas through which the right eye R_E of the observer receives the first and the second mixed images C_LR, C_RL, respectively. The controller  100  moves a second barrier unit BU 2  of the third area C and the fourth area D, with respect to the position of the first barrier unit BU 1 . 
     For example, if the second barrier unit BU 2  moves by a width of three sub-areas corresponding to three barrier electrodes in a right-to-left direction, with respect to the first barrier unit BU 1 , in the second barrier unit BU 2 , a second opening OP 2  is defined by a first and a second barrier electrodes BE 1 , BE 2 , and a second barrier BP 2  is defined by a third and a fourth barrier electrodes BE 3 , BE 4 . 
     When the first mixed image C_LR displayed on the third area C is moved by 3 times E/2 in a left-to-right direction, by the second barrier unit BP 2 , the right eye R_E of the observer receives the left-eye image L. The controller  100  renders image data to display the right-eye image R in an area of the display panel corresponding to the third area C. Accordingly, the right eye R_E of the observer may receive the right-eye image R in the third area C. 
     If the second barrier unit BU 2  moves by a width of three barrier electrodes in a right-to-left direction, with respect to the first barrier unit BU 1 , the second mixed image C_RL displayed on the fourth area D is observed as the right-eye image R, which is moved by 3 times E/2 in a left-to-right direction by the second barrier unit BU 2 . Accordingly, the right eye R_E of the observer may receive the right-eye image R in the fourth area D. 
     According to the present exemplary embodiment, eyes (a left eye or a right eye) of the observer may receive corresponding viewpoint images by controlling the position of the barrier unit in two ways, according to the different viewpoint areas and the mixed areas, and by controlling image data on the basis of the two methods of controlling the barrier unit. 
       FIG. 39  is a timing chart illustrating the control of the position of a barrier unit corresponding to the observer screen using the liquid crystal barrier panel of  FIG. 33 , when observed by an observer. Referring to  FIGS. 24 ,  25 , and  39 , the liquid crystal barrier panel  490  has a striped structure as illustrated in  FIG. 3A . For example, the controller  100  computes an observer screen OVS including a left-eye image L and a right-eye image R received at the observer&#39;s right eye R_E. 
     In addition, the controller  100  divides the observer screen OVS into a left-eye (or a right-eye) image area and a mixed image area. For example, the controller  100  determines a central part of the left-eye image LA (or a central part of the right-eye image RA) and a boundary part between the left-eye image area LA and the right-eye image area RA. The is controller  100  divides the area between the central part and the boundary part into three parts. As a result, the controller  100  divides the observer screen OVS into a first area A, a second area B, a third area C, a fourth area D, a fifth area E, and a sixth area F. 
     Each area of the left-eye image L and the right-eye image R, which are displayed on a screen of the display apparatus, may have substantially the same width W in principle. The controller  100  may control the position of a barrier unit differently over a distance of every W/3 from the boundary of the left-eye (or the right-eye) image area and the mixed image area. 
     The first area A is an area in which the right eye of the observer receives a right-eye image R. A first barrier unit BU 1  is regarded as being in a standard position. In the first barrier unit BU 1 , a first opening OP 1  is defined by first, second, and third barrier electrodes BE 1 , BE 2 , BE 3  of the first area A. A first barrier BP 1  is defined by fourth, fifth, and sixth barrier electrodes BE 4 , BE 5 , BE 6  of the first area A. The first area A of the liquid crystal barrier panel  490  operates as the first barrier unit BU 1 . Accordingly, the right eye R_E of the observer receives the right-eye image R in the first area A. 
     The second area B is an area in which the right eye R_E of the observer receives a first mixed image C_RL 1 . The second area B arrives at a peak point of the luminance profile RI_C of the right-eye image, when moved by 1 times E/3 in a left-to-right direction, to receive the right-eye image R. A second barrier unit BU 2  of the second area B moves by a width of one sub-area corresponding to one barrier electrode in a left-to-right direction, with respect to the first barrier unit BU 1 . In the second barrier unit BU 2 , a second opening OP 2  is defined by the first, the second, and the sixth barrier electrodes BE 1 , BE 2 , BE 6 , and a second barrier BP 2  is defined by the third, the fourth, and the fifth barrier electrodes BE 3 , BE 4 , BE 5 . The second area B of the liquid crystal barrier panel  490  operates as the second barrier unit BU 2 , for the right eye R_E of the observer to receive the right-eye image R in the second area B. 
     The third area C is an area in which the right eye R_E of the observer receives a second mixed image C_RL 2 . The third area C arrives at a peak point of the luminance profile RI_C of the right-eye image, when moved by 2 times E/3 in a left-to-right direction to receive the right-eye image R. A third barrier unit BU 3  of the third area C moves by a width of two sub-areas corresponding to two barrier electrodes in a left-to-right direction, with respect to the first barrier unit BU 1 . In the third barrier unit BU 3 , a third opening OP 3  is defined by the first, the fifth, and the sixth barrier electrodes BE 1 , BE 5 , BE 6 , and a third barrier BP 3  is defined by the second, the third, and the fourth barrier electrodes BE 2 , BE 3 , BE 4 . The third area C of the liquid crystal barrier panel  490  operates as the third barrier unit BU 3  for the right eye R_E of the observer to receive the right-eye image R in the third area C. 
     The fourth area D is an area in which the right eye R_E of the observer receives a left-eye image L. The fourth area D arrives at a peak point of the luminance profile RI_C of the right-eye image, when moved by 3 times E/3 in a left-to-right direction, to receive the right-eye image R. A fourth barrier unit BU 4  of the fourth area D moves by a width of three sub-areas corresponding to three barrier electrodes in a left-to-right direction, with respect to the first barrier unit BU 1 . In the fourth barrier unit BU 4 , a fourth opening OP 4  is defined by the fourth, the fifth, and the sixth barrier electrodes BE 4 , BE 5 , BE 6 , and a fourth barrier BP 4  is defined by the first, the second, and the third barrier electrodes BE 1 , BE 2 , BE 3 . The fourth area D of the liquid crystal barrier panel  490  operates as the fourth barrier unit BU 4 , for the right eye R_E of the observer to receive the right-eye image R in the fourth area D. 
     The fifth area E is an area in which the right eye R_E of the observer is receives a third mixed image C_LR 1 . The fifth area E arrives at a peak point of the luminance profile RI_C of the right-eye image when moved by 4 times E/3 in a left-to-right direction to receive the right-eye image R. A fifth barrier unit BU 5  of the fifth area E moves by a width of four sub-areas corresponding to four barrier electrodes in a left-to-right direction with respect to the first barrier unit LS 1 . In the fifth barrier unit BU 5 , a fifth opening OP 5  is defined by the third, the fourth, and the fifth barrier electrodes BE 3 , BE 4 , BE 5 , and a fifth barrier BP 5  is defined by the first, the second, and the sixth barrier electrodes BE 1 , BE 2 , BE 6 . The fifth area E of the liquid crystal barrier panel  490  operates as the fifth barrier unit BU 5  for the right eye R_E of the observer to receive the right-eye image R in the fifth area E. 
     The sixth area F is an area in which the right eye R_E of the observer receives a fourth mixed image C_LR 2 . The sixth area F arrives at a peak point of the luminance profile RI_C of the right-eye image when moved by 5 times E/3 in a left-to-right direction to receive the right-eye image R. A sixth barrier unit BU 6  of the sixth area F moves by a width of five sub-areas corresponding to five barrier electrodes in a left-to-right direction with respect to the first barrier unit BU 1 . In the sixth barrier unit BU 6 , a sixth opening OP 6  is defined by the two, the third, and the fourth barrier electrodes BE 2 , BE 3 , BE 4 , and a sixth barrier BP 6  is defined by the first, the fifth, and the sixth barrier electrodes BE 1 , BE 5 , BE 6 . The sixth area F of the liquid crystal barrier panel  490  operates as the sixth barrier unit BU 6  for the right eye R_E of the observer to receive the right-eye image R in the sixth area F. 
     As mentioned above, the left eye L_E or the right eye R_E of the observer located beyond the observation distance may respectively receive the left-eye image L or the right-eye image R by controlling the position of the barrier unit of the liquid crystal barrier panel. Although not shown in figures, if a barrier unit of the liquid crystal barrier panel has a tilted structure illustrated in  FIG. 3B , the eyes of the observer may receive corresponding viewpoint images by controlling image data and the position of the barrier unit in substantially the same way as the liquid crystal lens panel illustrated above. 
     According to the liquid crystal barrier panels of the exemplary embodiments above, the opening rate of a unit barrier is 1/N, when N viewpoint images are displayed be every M consecutive subpixels, and an opening is defined corresponding to 2×Sf on every barrier unit having a length of M×N×Sf. 
     In a multi-viewpoint mode, an opening having a length of M×N converts M minus 1 unit areas (or sub-areas) into blocking states, and at the same time, displays M×N viewpoint images on consecutive M×N subpixels to increase the number of viewpoints. In a tracking mode, an opening having a length of M×N moves the position of an opening having a length of M×Sf in consecutive M×N unit areas (M×N×Sf), divided according to the observer&#39;s moving direction, with respect to the display panel for N viewpoints that alternately displays a left-eye image and a right-eye image on every N subpixels. 
     If an opening has a length of M×N, the position of the opening moves by a width of one sub-areas according to the observer&#39;s moving direction as one eye (a left eye or a right eye) of the observer moves more than ±E/(M×N) in a right-and-left direction from a peak point, when the eye of the observer located within an observation distance is positioned at a peak point of the luminance profile. In addition, if the observer moves by E/M in a right-or-left direction from a standard position, the position of the opening moves by a width of one unit (one sub-area). 
     Each of a left-eye image L and a right-eye image R, included in an observer screen for an observer located beyond an observation distance, may have substantially the same width W. The position of the opening may be controlled differently in an area of every W/M from the boundary between the left-eye image area and the right-eye image area. If the opening has a length of M×N corresponding to M×N subpixels, then the observer may receive the left-eye image or the right-eye image in all areas of the observer screen, by controlling the position of M×N-type openings. 
       FIG. 40  is a perspective view of display apparatus according to another exemplary embodiment of the present invention.  FIG. 41  is a cross-sectional view illustrating an emission unit included in the dynamic conversion panel of  FIG. 40 . Referring to  FIG. 40 , all elements are substantially the same as those of  FIGS. 1 and 2 , except for the position of a dynamic conversion panel. Thus, a description of similar elements is omitted. 
     The display apparatus includes a display panel  200 , a dynamic conversion panel  400 A, and a light source  600 . The dynamic conversion panel  400 A is disposed on a light-emitting side of the light source  600  and is disposed between the display panel  200  and the light source  600 . 
     The dynamic conversion panel  400 A operates in a transmission mode to transmit the light from the light source  600  and in a conversion mode to convert the direction of light emission. For example, in a two-dimensional image mode, in which the display apparatus displays two-dimensional images, the dynamic conversion panel  400 A operates in a transmission mode to provide the light to the display panel  200  to display a two-dimensional image. In addition, in a three-dimensional image mode, in which the display apparatus displays three-dimensional images using at least two viewpoint images, the dynamic conversion panel  400 A operates in a conversion mode to provide the light emitted toward at least two viewpoint positions, for the display panel  200  to display a three-dimensional image. 
     The dynamic conversion panel  400 A includes an emission unit to emit the light emitted toward at least two viewpoint positions in a three-dimensional image mode. The emission unit may be operated by at least one element electrode. For example, if the dynamic conversion panel  400 A is a liquid crystal lens panel, the emission unit may be a lens structure, and the element electrode may be at least two lens electrodes. Alternatively, if the dynamic conversion panel  400 A is a liquid barrier panel, the emission unit may be a barrier unit, and the element electrode may be at least one barrier electrode. 
     Referring to  FIG. 41 , a unit area Sb is a moveable area within an emission unit EU. The unit area Sb may be determined by a pitch of the dots DT, a distance between the dots DT and the emission unit EU, and an observation distance Db of the emission unit EU. 
     The method of driving the display apparatus according to the present exemplary embodiment is substantially the same as the exemplary embodiments illustrated in  FIGS. 1 to 39 , except that the unit area Sf is changed to the unit area Sb. Thus, a detailed description of similar elements is omitted. 
     According to the liquid crystal lens panels of the present exemplary embodiments, if the left eye or the right eye of the observer is located at a peak of the luminance profile and within the observation distance of the luminance profile, the position of a lens structure is moved by a width of at least one lens electrode corresponding to a moving direction of the observer, when the observer moves more than ±E/(2M) in a right or left direction with respect to the peak, under a condition that the lens structure has a length of 2M times N, where M is the number of sub-areas included in a lens unit and N is the number of viewpoint images. That is, M is the number of lens electrodes formed in an area of the lens unit. In addition, if an observer moves by E/M in a right-or-left direction from a standard position, the position of the is lens structure moves by a width of one lens electrode. If the liquid crystal lens panel is disposed between the display panel and the light source part, the position of the lens structure moves in an opposite direction to that of the case where the liquid crystal lens panel is disposed in an upper part of the display panel. 
     Each of a left-eye image L and a right-eye image R, included in an observer screen observed by an observer located beyond an observation distance, may have substantially the same width W. The position of the lens structure may be controlled differently in an area of every W/M, from the boundary between the left-eye image area and the right-eye image area. 
     If the lens structure has a length of 2 times M corresponding to two subpixels, then the observer may receive the left-eye image or the right-eye image in all area of the observer screen by controlling the position of 2×M types of lens structures. According to the liquid crystal barrier panels of the present exemplary embodiments, the opening rate of the barrier unit is 1/N when N viewpoint images are displayed on every M consecutive subpixels and an opening is defined corresponding to 2×Sb on every barrier unit having a length of M×N×Sb. 
     In a multi-viewpoint mode, an opening having a length of M×N converts M minus 1 unit area (sub-areas) into blocking states, and at the same time, displays M×N viewpoint images on consecutive M×N subpixels to increase the number of viewpoint images. In a tracking mode, an opening having a length of M×N moves the position of an opening having a length of M×Sb in consecutive M×N distances (M×N×Sb) divided according to the observer&#39;s moving direction with respect to the display panel for N viewpoints, which alternately displays a left-eye image and a right-eye image on every N subpixels. 
     If an opening has a length of M×N, the position of the opening moves by a width of one sub-area according to the observer&#39;s moving direction as one eye (a left eye or a is right eye) of the observer moves more than ±E/(M×N) in a right-and-left direction from a peak point when the eye of the observer located in an observation distance is positioned at a peak point of the luminance profile. In addition, if a head of the observer moves by E/M in a right-and-left direction from a standard position, the position of the opening moves by a width of one unit (or a sub-areas). If the liquid crystal barrier panel is disposed between the display panel and the light source part, the position of the barrier unit moves in an opposite direction to that of the case where the liquid crystal barrier panel is disposed in an upper part of the display panel. 
     Each of a left-eye image L and a right-eye image R included in an observer screen which the observer located beyond an observation distance observes may have substantially the same width W. The position of the opening may be controlled differently in an area of every W/M from the boundary between the left-eye image area and the right-eye image area. 
     If the opening has a length of M×N corresponding to M×N subpixels, then the observer may receive the left-eye image or the right-eye image in all area of the observer screen by controlling the position of M×N types of openings. 
     It will be apparent to those skilled in the art that various modifications and variation can be made in the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.