OPTIMAL BEAM FORMING FOR LASER BEAM PROPAGATION ...

the effects of refraction and diffraction. When the sizes of inhomogeneitiesin the object become comparable to or smaller than the wavelength, it is notappropriate to use geometric propagation based ray theory.Tomographicreconstruction approaches based on Fourier diffraction theory are developedwhen the interaction of an object and a field is described by the inhomogeneouswave equation. This method is the so called diffraction tomography.In diffraction tomography, acoustic and electromagnetic waves do not travelalong straight rays and the projections are not line integrals [40]. Diffractionand scattering of optical fields in the inhomogeneous medium must beinvolved.1.2 Research GoalsIt is well known that the propagation of waves in homogeneous media canbe described by the wave equation, which is a second order linear differentialequation. Optical fields in any position inside a homogeneous medium canbe determined by the source fields in the aperture and the wave equation.However, for the problem of wave propagation in an inhomogeneous medium,there is no direct analytic solutions for the wave equation. In practice, approximateformalisms of the homogeneous medium wave propagation arewidely used in the cases of weak inhomogeneities. Born and Rytov approximationsare well known approximate methods [37]. Many other propagationmodels have been developed recently, including linear system representationsand simulation schemes [23, 24].5