Fringe periods of color moirés in contact-type 3-D displays

A mathematical formula of calculating the fringe periods of the color moirés appearing at the contact-type 3-D displays is derived. It is typical that the color moirés are chirped and the period of the line pattern in viewing zone forming optics is more than two times of that of the pixel pattern in the display panel. These make impossible to calculate the fringe periods of the color moirés with the conventional beat frequency formula. The derived formula work very well for any combination of two line patterns having either a same line period or different line periods. This is experimentally proved. Furthermore, it is also shown that the fringe period can be expressed in terms of the viewing distance and focal length of the viewing zone forming optics.