Generation of a polarized optical field from a given scalar field for wide-viewing-angle holographic displays

Although the scalar wave theory does not fully describe the nature of the light, which is a vector wave field, it is common to characterize the optical field propagated from an object as a scalar wave in 3DTV research. A given scalar wave field is usually directly mapped to the transverse field components of a simply polarized optical field during the generation of the optical field by a holographic 3D display; this procedure gives accurate results in terms of the optical intensity if the field is paraxial. However, due to the nonnegligibly large longitudinal component of the vector field, this method fails in wide-angle fields. In order to generate a polarized optical field which has the same resultant effect as prescribed by a wide-angle scalar field, we extend this simple polarization approach to tilted and rotated planes. That is, we first put a constraint on the generated vector wave field such that each plane wave component has a simple polarization relation at its locally transverse plane. Then, we map the complex plane wave amplitudes of a given scalar field to the plane wave amplitudes of locally transverse field components of the polarization-constrained optical field. As a consequence of the developed mapping, for an observer which is located at a tilted and rotated plane and captures a locally paraxial segment of the incoming wave field, the intended scalar intensity results can also be obtained in wide-viewing-angle 3D holographic displays. The developed model is valid if the chosen local coordinate frames of the locally transverse planes of the propagating plane waves vary slowly as the propagation direction changes. For a 3DTV setup where the display is located at a z-plane and the observers are located away from the z-axis, an analytical representation for appropriate coordinate frames is developed. For the same setup, computer simulation results showed that the excessive amplification of the longitudinal component due to the conventional mapping does not arise in the proposed method and the desired scalar results are observed. Moreover, since the determined polarization state is preserved at each tilted and rotated plane, the new model can also be used in an optical setup where the polarization information is important. As a result, the proposed mapping enables the scalar wave theory to be used in wide-viewing angle holographic display applications under the given constraints.