Transformation techniques from scalar wave fields to polarized optical fields for wide-viewing-angle holographic displays
Although the optical waves are vector-valued electromagnetic waves in nature, in holographic three-dimensional television (3DTV) research, an optical eld to be displayed is usually modeled as a scalar wave eld. In this respect, during the display phase, the scalar wave should be mapped to a polarized optical eld with the intention that the desired scalar results are obtained through the generated polarized waves. This mapping has usually been implemented by directly equating the scalar eld to the transverse eld components of a simply polarized electric eld. Although this conventional method is valid in paraxial elds, it becomes erroneous in wide-angle elds due to the nonnegligibly large longitudinal component of the electric eld. In order to make a quantitative analysis of error arising from this mapping, a 2D linear-shift invariant (LSI) system is derived from Maxwell's equations, where the inputs and the output are the transverse and longitudinal components, respectively. The magnitude responses of the lters used in the system and some discrete simulations also indicate the longitudinal component becomes the dominant term in large propagation angles. In order to obtain desired scalar results in wide-angle elds, we develop two other techniques which can be used for di erent purposes. In the rst technique, we apply a pair of 2D lowpass lters to the scalar eld before mapping it to the transverse components, where the lowpass lters are derived so as to equalize the power spectra of the given scalar eld and the resulting electric eld. It is shown through discrete simulations that the excessive ampli cation of the longitudinal component and the deteriorations in the electric eld intensity in large propagation angles are prevented by the speci ed lowpass lters. In the second technique, we rst impose a constraint on the electric eld vector to be generated such that the amplitude vector of a plane wave has a simple polarization state at plane which is orthogonal to the corresponding propagation direction. Then, the components of the vector amplitude of the plane wave at that locally transverse plane are directly matched with the amplitude of the corresponding plane wave component of the scalar eld. As a result of the second technique, the desired intensity images can be obtained if an imaging sensor captures a locally paraxial segment of the eld on its observation plane; this is the case for common sensors. The validity of the second technique is justi ed through the computer simulation of a holographic display of a computer generated 3D object. In the simulation, the proposed method outperforms the conventional method and ends up with the correct intensity of the scalar eld associated with the object at di erent tilted and rotated planes. In conclusion, use of the scalar theory of optics becomes possible also in wide-angle elds as a consequence of the developed techniques and the prescribed scalar results can be realized by means of wide-viewing-angle holographic displays.