The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

CeO2 nanocubes (and nanorods) enclosed by six {200} planes with controlled sizes have been prepared through a facile one-pot method. The nanocubes have a strong tendency to assemble into 2D and 3D arrays with regular patterns on a substrate, which is probably driven by the dipole−dipole interaction of polar {200} planes. The possible formation mechanism of the nanocubes has been put forward as the oriented aggregation mediated precursor growth. It is possible to use the synthesized nanocubes as building blocks to achieve {200}-perfect-oriented monolayers or thickness-controlled films and to apply the preparative method in the incorporation of heterogeneous atoms or nanoparticles for semiconductor doping or heterogeneous nanostructures.

Controlled synthesis and self-assembly of CeO2 nanocubes.

We investigate the electronic properties of nanocrystalline cerium oxide $({\mathrm{CeO}}_{x})$ films, grown by various techniques, and we establish universal relations between them and the film structure, composition, and morphology The nanocrystalline ${\mathrm{CeO}}_{x}$ films mainly consist of ${\mathrm{CeO}}_{2}$ grains, while a considerable concentration of trivalent ${\mathrm{Ce}}^{3+}$ is distributed at the ${\mathrm{CeO}}_{2}$ grain boundaries forming amorphous ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ A small portion of ${\mathrm{Ce}}^{3+}$ is also located around O-vacancy sites The optical properties of the ${\mathrm{CeO}}_{x}$ films are considered, taking into account the reported band-structure calculations The fundamental gap ${E}_{g}$ of ${\mathrm{CeO}}_{x}$ is due to the indirect $\mathrm{O}2\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{Ce}4f$ electronic transition along the L high-symmetry lines of the Brillouin zone and it is correlated with the $[{\mathrm{Ce}}^{3+}]$ content, explaining the redshift of ${E}_{g}$ in nanostructured ${\mathrm{CeO}}_{x},$ which is due to the ${\mathrm{Ce}}^{3+}$ at the grain boundaries and not due to the quantum-size effect itself We also correlate the energy position of the $\mathrm{O}2\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{Ce}4f$ electronic transition, which varies up to 160-meV wide, with the lattice constant of the ${\mathrm{CeO}}_{2}$ grains We also show that the higher-order transitions are more sensitive to film composition The refractive index, far below ${E}_{g},$ is explicitly correlated with the film density, independently of the ${\mathrm{Ce}}^{3+}/{\mathrm{Ce}}^{4+}$ and O concentrations, grain size, and lattice parameter The density is also found to be the major factor affecting the absolute value of the ${\ensuremath{\varepsilon}}_{2}$ peak, which corresponds to the $\mathrm{O}2\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{Ce}4f$ electronic transition

Structure-dependent electronic properties of nanocrystalline cerium oxide films

Synthesis of cerium oxide nanoparticles using Gloriosa superba L. leaf extract and their structural, optical and antibacterial properties

Ce3+ and oxygen vacancy mediated tuning of structural and optical properties of CeO2 nanoparticles

A stable multilayer IR optical filter is designed based on the porous silicon technology The filter stability is achieved based on the mechanical properties of porous silicon that are used to tailor the stresses inside the mutilayer structure The filter, working at the wavelength of 155 µm, have been designed to be matched with spot sizes of 7 µm and 85 µm which makes it compatible with single mode fiber used in optical communications

Stable optical filter using porous silicon technology

Laser altimetry is a technique whereby reflections of a laser beam are used to measure the altitude of an aircraft above the ground based on a round trip delay measurement. With current improvements in short laser pulse generation and high resolution time and amplitude measurements, the same technique is now used to measure topographical features of the ground surface. In addition to surface elevations obtained from high resolution delay measurements, information on the nature of coverage of a target surface can be obtained from high resolution intensity measurements of the returned echo signal. In this technique, global positioning and navigation guidance are needed to provide reference on the position and pointing attitude of the measuring equipment. Both aspects of the altimeter system, namely, echo signal measurements and position referencing, determine the accuracy and resolution of the technique. This paper reviews the principles and basic aspects of a pulsed laser altimeter, and discusses the utilization of data provided by laser altimetry in geographic scanning for urban and environmental studies.

https://ieeexplore.ieee.org/iel5/6758/18070/00838966.pdf

Ahmed Hisham Morshed

Papers

Stable optical filter using porous silicon technology

Laser altimetry and its application in geographic scanning

Multimode optical fiber strain monitoring for smart infrastructures