Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm

AbstractIn this article we combine the well-known Ptychographical Iterative Engine (PIE) with the Hybrid Input-Output (HIO) algorithm. The important insight is that the HIO feedback function should be kept strictly separate from the reconstructed object, which is done by introducing a separate feedback function per probe position. We have also combined HIO with floating PIE (fPIE) and extended PIE (ePIE). Simulations indicate that the combined algorithm performs significantly better in many situations. Although we have limited our research to a combination with HIO, the same insight can be used to combine ptychographical algorithms with any phase retrieval algorithm that uses a feedback function

Image formation properties and inverse imaging problem in aperture based scanning near field optical microscopy

Aperture based scanning near field optical microscopes are important instruments to study light at the nanoscale and to understand the optical functionality of photonic nanostructures. In general, a detected image is affected by both the transverse electric and magnetic field components of light. The discrimination of the individual field components is challenging as these four field components are contained within two signals in the case of a polarization resolved measurement. Here, we develop a methodology to solve the inverse imaging problem and to retrieve the vectorial field components from polarization and phase resolved measurements. Our methodology relies on the discussion of the image formation process in aperture based scanning near field optical microscopes. On this basis, we are also able to explain how the relative contributions of the electric and magnetic field components within detected images depend on the chosen probe. We can therefore also describe the influence of geometrical and material parameters of individual probes within the image formation process. This allows probes to be designed that are primarily sensitive either to the electric or magnetic field components of light

Analysis of a model for imaging in photolithography

AbstractThe governing equation of a model for imaging in photolithography is studied. The density p of the photoactive component of the resist, which is a function of time and position, decreases at a rate assumed proportional to the local light intensity. It satisfies a nonlinear differential equation dϱdt (t) = F(ϱ(t)), of which an evaluation of the right-hand side requires solving Maxwell's equations in a periodic 2D-configuration of dielectrics consisting of the resist and the substrate. The electric permittivity of the resist is a function of position which depends on ϱ. The Maxwell problem is studied by applying the limiting absorption principle. It is proved using the contraction mapping theorem that for every exposure time and every initial density (∗) has a unique solution which is a smooth function of time and position when all data are smooth

Rigorous model of the scattering of a focused spot by a grating and its application in optical recording

We describe a rigorous model for the scattering of a three-dimensional focused spot by a one-dimensional periodic grating. The incident field is decomposed into a sum of quasi-periodic fields, and the scattering of each of these is computed inside one unit cell of the grating. The model is applied to the simulation of the readout of a DVD disk. The polarization dependence of the reflected near and far fields is studied, and, for a TM-polarized incident spot, plasmons are observed in the reflected far-field intensity

On the determination of dopant-concentration profiles by grazing emission X-ray fluorescence spectroscopy using the maximum-entropy method

The determination of concentration profiles of impurities in silicon from angle scans of emitted x-ray fluorescence intensities using the maximum-entropy method is studied. Existence and convergence properties of the maxium- entropy method are discussed. The application of the maximum-entropy method to Grazing emission X-Ray Fluorescence Spectromety is compared with an analytical method. It is found that, provided noise levels are sufficiently low, concentration profiles can be reconstructed without using a priori knowledge

A mode expansion technique for rigorously calculating the scattering from 3D subwavelength structures in optical recording

We apply a mode expansion technique to the three-dimensional vectorial diffraction problem of an electromagnetic field that is incident on a perfectly conducting, metallic disc containing a pattern of rectangular pits. The mode expansion technique reduces the three-dimensional diffraction problem to a two-dimensional numerical problem. Furthermore, by choosing a particular numerical discretization, the a priori unknown amplitudes of the propagating and evanescent scattered plane waves in the half space above the metallic plate can be eliminated from the system of equations. The relatively small remaining system of equations for the amplitudes of the propagating and evanescent modes inside the pits, can be solved very rapidly. Some first results are presented. Furthermore, the application of the scanning of an optical beam by a pit structure on a metallic optical disc is discussed

Simulation of polarization effects in diffraction problems of optical recording

The reflection of a focused spot from a digital versatile disk (DVD) depends strongly on the polarization of the light. When the spot is polarized such that the magnetic field is mainly parallel to the tracks on the disk, the reflected near field is very sensitive to the width and depth of the pit. Simulations suggest that also the far-field intensity distribution is sensitive to subwavelength features. Several modifications of the pit geometry of the DVD format are considered with the aim of increasing storage densities