Directional backlight unit and 3D image display device having the same

A three-dimensional (3D) image display device comprising:

• a directional backlight unit comprising:
• a light guide plate;
• a light source configured to radiate a plurality of color lights toward an incident surface of the light guide plate;
• a plurality of gratings configured to emit the plurality of color lights radiated toward the light guide plate;
• and a color filter comprising a plurality of color filter pixels that respectively correspond to the plurality of color lights emitted from the plurality of gratings;
• and
• a display panel configured to form an image by using the plurality of color lights emitted from the directional backlight unit,
• wherein each of the plurality of gratings comprises a plurality of sub-gratings, and each of the plurality of sub-gratings is configured to react to the plurality of color lights
• wherein the directional backlight unit is configured to satisfy the following formula:
• Ncfp≤Ngu−i*Nsgu-i*Nl
• where Ncfp is a total number of color filter pixels included in the color filter, Ngu-i is a total number of the plurality of gratings, Nsgu-i is a total number of the plurality of sub-gratings in the grating corresponding to index i, and Nl is a number of wavelengths of the plurality of color lights emitted from the light source.