Geniş görüş açılı holografik ekranlar için sayıl dalga alanlarından kutuplanmış optik alanlara dönüşüm teknikleri

Although the optical waves are vector-valued electromagnetic waves in nature, in holographic three-dimensional television (3DTV) research, an optical field to be displayed is usually modeled as a scalar wave field. In this respect, during the display phase, the scalar wave should be mapped to a polarized optical field 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 field to the transverse field components of a simply polarized electric field. Although this conventional method is valid in paraxial fields, it becomes erroneous in wide-angle fields due to the nonnegligibly large longitudinal component of the electric field. 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 filters 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 fields, we develop two other techniques which can be used for different purposes. In the first technique, we apply a pair of 2D lowpass filters to the scalar field before mapping it to the transverse components, where the lowpass filters are derived so as to equalize the power spectra of the given scalar field and the resulting electric field. It is shown through discrete simulations that the excessive amplification of the longitudinal component and the deteriorations in the electric field intensity in large propagation angles are prevented by the specified lowpass filters. In the second technique, we first impose a constraint on the electric field 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 field. 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 field on its observation plane; this is the case for common sensors. The validity of the second technique is justified 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 field associated with the object at different tilted and rotated planes. In conclusion, use of the scalar theory of optics becomes possible also in wide-angle fields as a consequence of the developed techniques and the prescribed scalar results can be realized by means of wide-viewing-angle holographic displays.