Zn 1-x Mn x O (x = 0, 0.02, 0.06, 0.10, 0.15) nanopowders were synthesized by the sol–gel technique calcinated at low temperatures. By decreasing the grain size in ZnO , the solubility of magnetic impurity has been increased and no detectable secondary phases were observed even in the high Mn -doping samples. The phase formation, size and morphology of nanoparticles were investigated using X-ray diffraction and SEM observations. The samples were ferromagnetic and the Curie point was found in the range 150–170 K for Zn0.94Mn0.06O and 135–150 K for Zn0.98Mn0.02O . Optical characterization and the effect of doping were carried out by means of Fourier transform infrared (FTIR) spectroscopy. Kramers–Kronig analysis was employed to evaluate the optical constants of pure ZnO and ZnO:Mn nanopowders.

The band structure, the dielectric function, the reflectivity, the refractive index and the oscillator strength sum rule were calculated for pure In2O3 and alloyed In1.5T0.5O3 (where T represents Sc, Y, La and Ac) using density functional theory (DFT). The full potential linearized augmented plane wave (FP‐LAPW) method was used with the local density approximation (LDA + U). Calculations of the optical spectra were performed for the energy range 0–30 eV. The calculated results indicate that the upper valance bands of In2O3 show a small dispersion and the value of the band gap increases for Sc and Y dopants and decreases for Ac and La dopants. The calculations indicate that there are two band gaps for In2O3. The first shows a strong optical absorption, as a direct band gap occurs from a 0.81 eV energy level below the top of valence band. The second shows a much weaker absorption from the top of the valence band to the bottom of the conduction band. The refractive index for In2O3 is 1.69 nm at 800 nm, near the visible region. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The structure, the band structure, the total density of states, the dielectric function, the extinction coefficient and the refractive index have been calculated for lead zirconate (PbZrO3) using density functional theory (DFT). The full potential linearized augmented plane wave (FL‐LAPW) method was used with the generalized gradient approximation (GGA). Calculations of the optical spectra have been performed for the energy range 0–28 eV. It is shown that the orthorhombic PbZrO3, which is optically negative, exhibits a biaxial birefringence and its refractive index is smallest along the a‐axis (na (0) = 2.32, nb (0) = 2.36 and nc (0) = 2.34) which is close to the experimental value. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Orthogonal polynomials can be used for representing complex surfaces on a specific domain. In optics, Zernike polynomials have widespread applications in testing optical instruments, measuring wavefront distributions, and aberration theory. This orthogonal set on the unit circle has an appropriate matching with the shape of optical system components, such as entrance and exit pupils. The existence of noise in the process of representation estimation of optical surfaces causes a reduction of precision in the process of estimation. Different strategies are developed to manage unwanted noise effects and to preserve the quality of the estimation. This article studies the modeling of phase wavefront aberrations in third-order optics by using a combination of Zernike and pseudo-Zernike polynomials and shows how this combination may increase the robustness of the estimation process of phase wavefront aberration distribution.

Pure ZnO and Zn1‐xMnxO (x = 0, 0.02, 0.06, 0.10, 0.15) nanopowders have been synthesized by sol gel technique at low temperatures. XRD results indicate that the powder has a hexagonal polycrystalline structure without secondary phases. The nanopowders were characterized using the X‐ray diffraction (XRD) and transmission electron microscopy (TEM) observation. Kramers‐Kronig's analysis of mid‐IR reflectance spectra were employed to determine the doping effect on the optical constants and optical phonon modes frequencies. The optical band gap energy decreases from 3.22 eV to 3.12 eV for pure ZnO and Zn0.9Mn0.1O dispersed powders, respectively (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)