Transformation techniques from scalar wave fields to polarized optical fields for wide-viewing-angle holographic displays
Author
Külçe, Onur
Advisor
Onural, Levent
Date
2018-07Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
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.
Keywords
Wide-Viewing-Angle Holographic DisplayOptical Field Generation
Scalar-to-Polarized Field Mapping
Optical Signal Processing