Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

An apparatus and method to determine a property of a substrate by measuring, in the pupil plane of a high numerical aperture lens, an angle-resolved spectrum as a result of radiation being reflected off the substrate. The property may be angle and wavelength dependent and may include the intensity of TM- and TE-polarized radiation and their relative phase difference.

Method and apparatus for angular-resolved spectroscopic lithography characterization

Surface topography and light scattering were measured on 15 samples ranging from those having smooth surfaces to others with ground surfaces. The measurement techniques included an atomic force microscope, mechanical and optical profilers, confocal laser scanning microscope, angle-resolved scattering, and total scattering. The samples included polished and ground fused silica, silicon carbide, sapphire, electroplated gold, and diamond-turned brass. The measurement instruments and techniques had different surface spatial wavelength band limits, so the measured roughnesses were not directly comparable. Two-dimensional power spectral density (PSD) functions were calculated from the digitized measurement data, and we obtained rms roughnesses by integrating areas under the PSD curves between fixed upper and lower band limits. In this way, roughnesses measured with different instruments and techniques could be directly compared. Although smaller differences between measurement techniques remained in the calculated roughnesses, these could be explained mostly by surface topographical features such as isolated particles that affected the instruments in different ways.

/pdf/surface-characterization-techniques-for-determining-the-root-1bn2vivtpm.pdf

Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components

Ion beam assisted deposition, the bombardment of a thin film with a beam of energetic particles during deposition, provides a powerful technique for modifying the microstructure and properties of thin films and coatings. Various experimental approaches used for ion beam assisted deposition are described and the physical basis for the effects is examined. Observations on modification of nucleation and growth behaviour, microstructure development, compound synthesis, and applications to the modification of properties such as intrinsic stress, adhesion, surface mechanical properties, corrosion and oxidation resistance, optical properties, and electrical properties, are reviewed.

Use of ion beam assisted deposition to modify the microstructure and properties of thin films

The optical properties of the dielectric oxide films SiO2, Al2O3, TiO2, ZrO2, CeO2 and Ta2O5 produced by ion-based techniques have been reviewed. The influence of ion bombardment during deposition is discussed in some detail and the various production techniques are described. Recent results on the deposition and properties of diamond-like carbon films are also reviewed. Finally, some examples of the practical applications of high quality dielectric oxide films are given.

Ion-based methods for optical thin film deposition

Oxygen ion-assisted deposition of SiO2 and TiO2 has been investigated as a function of ion energy (30–500 eV) and current density (0–300 μA/cm2) at the optic. It is shown that both low and high energy ion bombardment improve SiO2 film stoichiometry, although slightly greater improvement is realized for the low energy case. For TiO2 films, low energy bombardment improves stoichiometry, while high energy bombardment is clearly detrimental. A reduction in H content by a factor of 10 is observed in SiO2 films deposited with high energy ion bombardment. Durable films are produced at low substrate temperatures (50–100°C). Film stress characteristics are discussed.

Ion-assisted deposition of optical thin films: low energy vs high energy bombardment

An optical scatterometer system enables illumination of a sample material at various angles of incidence without rotating or otherwise moving the sample material.

Lens scatterometer system employing source light beam scanning means

During recent years, economic and technological pressures have driven research for higher performance optical fabrication techniques. Among the candidate figuring technologies is ion beam sputtering in which material is removed from the optical surface by the kinetic interaction of ions and atoms or molecules of the surface. The first use of sputtering as a means for optical figuring occurred in the mid 1960's [1,2], and the technique has been investigated by several groups since that time. The prior work was done primarily with ion sources producing high energy (20KeV and above), low current (fraction of a milliampere), narrow (usually less than one millimeter) ion beams. The low current directly translates to low removal rates, while the high energy contributes to radiation damage, ion implantation, and other effects. In the present work the low current, high energy source is replaced with a Kaufman broad-beam ion source[3]. These sources produce higher ion currents at lower energies, thus giving faster removal with minimal surface damage. The ion beam produced by a Kaufman ion source consists of a number of ions traveling in a (typi-cally) slightly diverging beam, along with an equal flux of lower energy electrons. The electrons are injected into the ion beam to reduce electrostatic repulsion in the beam, but also to prevent the charging of dielectric targets.

Surface Figuring Using Neutral Ion Beams

The disclosure relates to a method and apparatus using ion etching and ion assisted deposition to reform a surface of an object, such as a large lens, from its existing topography to a predetermined topography. The method comprises comparing the existing topography of the surface of the object to the predetermined topography. In one embodiment, the comparison can be used to distinguish objects having surfaces which are readily or economically reformable to the predetermined topography from those which are not suitable for such reforming. The method novelly utilizes an algorithm comprising image restoration. The ion etching structure of the apparatus comprises an ion source grid which can be used to provide an ion beam of a preselected spatial distribution. The grid is constructed of a nonconducting, vacuum compatible material, such as a ceramic sheet coated with a conductive layer on each side. Apertures are drilled through the grid in a selected pattern. The ion beam produced from a plasma source when a suitable voltage is applied across the coatings has a spatial distribution in accordance with the aperture pattern. In one embodiment the coatings comprise discrete corresponding areas on each surface and different voltages are appliable to each area to further control beam spatial distribution. Ion assisted deposition may be simultaneously performed under the algorithm to add material to the surface in accordance with the desired predetermined topography.

Method and apparatus for ion etching and deposition

The theory and measurement of angle-resolved scatter are described. Values of rms roughness that were obtained by using this technique to characterize four different materials are compared with values that were obtained by using a total integrated scatter measuring instrument, an optical profiler, and a mechanical profiler. The spatial frequency bandwidths and modulation transfer functions of the four instruments are different, and results are described in light of these differences.

S. R. Wilson

Papers

Ion-assisted deposition of optical thin films: low energy vs high energy bombardment

Lens scatterometer system employing source light beam scanning means

Surface Figuring Using Neutral Ion Beams

Method and apparatus for ion etching and deposition

Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques