J. A. Dobrowolski

Refinement of optical multilayer systems with different optimization procedures

Ten different optimization methods, representing both local and global minimum seeking algorithms, were applied to the solution of three different optical thin film design problems. Because all methods were incorporated in the same thin film design program, and because a routine was invoked that reads CPU time, the relative efficiencies of the various methods could be compared directly.

Determination of optical constants of thin film coating materials based on inverse synthesis

A versatile method for determination of the optical constants is described that can be applied to a variety of coating materials. It is based on the use of an optical thin film synthesis program to adjust the constants of dispersion equations until a good fit is obtained between measured and calculated spectral transmittance and/or reflectance curves. The sensitivity of the determination can be increased by a suitable combination of measurement quantities. Because more than the minimum amount of data can be used, sensitivity to measurement errors and the chances of obtaining multiple solutions can both be reduced. To illustrate the method optical constants are determined of MgF2, ZnS, MgO, Inconel, and Si films in the visible part of the spectrum and of ITO films in the 0.4–12.0-μm range.

Completely Automatic Synthesis of Optical Thin Film Systems

The various methods for the synthesis of optical thin film systems with prescribed properties are reviewed. One general approach is to refine numerically the properties of an initial system. In many problems, however, the choice of a suitable starting design for refinement is not at all obvious. The present paper describes a computer program for the completely automatic design of optical thin film systems by evolution which does not require a starting design. Apart from the specification of the desired optical properties of the system, the only input data necessary are the refractive indexes of the substrate, the medium, and the thin film materials that may be employed for the construction of the coating. Optical properties that may be specified at present include transmittance, reflectance, phase changes on transmission and reflection, and the first and second derivatives of these quantities, with respect to wavenumber and angle of incidence. Several examples are given to illustrate the performance of this program. Ways are indicated in which this automatic design program can be improved further in the future.

Optimal single-band normal-incidence antireflection coatings.

Mathematical and computational evidence that strongly suggests that optimal solutions exist to single-band, normal-incidence antireflection coating problems is presented. It is shown that efficient synthesis and refinement techniques can quickly and accurately find such solutions. Several visible and infrared antireflection coating examples are presented to support this claim. Graphs that show the expected optimal performance for different representative substrates, refractive-index ratios, wavelength ranges, and overall optical thickness combinations are given. Typical designs exhibit a pronounced semiperiodic clustering of layers, which has also been observed in the past. Explanations of this phenomenon are proposed.

Multivariate optical computation for predictive spectroscopy.

A novel optical approach to predicting chemical and physical properties based on principal component analysis (PCA) is proposed and evaluated using a data set from earlier work. In our approach, a regression vector produced by PCA is designed into the structure of a set of paired optical filters. Light passing through the paired filters produces an analog detector signal that is directly proportional to the chemical/physical property for which the regression vector was designed. This simple optical computational method for predictive spectroscopy is evaluated in several ways, using the example data for numeric simulation. First, we evaluate the sensitivity of the method to various types of spectroscopic errors commonly encountered and find the method to have the same susceptibilities toward error as standard methods. Second, we use propagation of errors to determine the effects of detector noise on the predictive power of the method, finding the optical computation approach to have a large multiplex advantage over conventional methods. Third, we use two different design approaches to the construction of the paired filter set for the example measurement to evaluate manufacturability, finding that adequate methods exist to design appropriate optical devices. Fourth, we numerically simulate the predictive errors introduced by design errors in the paired filters, finding that predictive errors are not increased over conventional methods. Fifth, we consider how the performance of the method is affected by light intensities that are not linearly related to chemical composition (as in transmission spectroscopy) and find that the method is only marginally affected. In summary, we conclude that many types of predictive measurements based on use of regression (or other) vectors and linear mathematics can be performed more rapidly, more effectly, and at considerably lower cost by the proposed optical computation method than by traditional dispersive or interferometric instrumentation. Although our simulations have used Raman experimental data, the method is equally applicable to Near-IR, UV-vis, IR, fluorescence, and other spectroscopies.

Deposition error compensation for optical multilayer coatings. I. Theoretical description

The manufacture of complicated optical coatings consisting of many layers of different thicknesses can be a challenge, especially if the deposition technique does not produce dense layers. Deposition errors in a layer can affect not only the desired performance of a multilayer, but can also lead to a complete breakdown of the monitoring and control of subsequent layers. The best chance to achieve the desired optical performance of a multilayer involves deposition error compensation. In this process, the construction parameters of a completed layer are evaluated to determine if any deposition errors have occurred and then the remaining layers of the multilayer system are reoptimized to compensate for any errors made. This paper describes a versatile deposition error compensation program developed at the National Research Council of Canada for the simulation and real-time control of the manufacture of multilayers composed of dielectric or absorbing films. To model porous layers, an effective medium theory approach is used to relate the optical constants of the layer in vacuum and air to the microstructure of the layer. In the simulation mode, random errors are applied to the thickness and porosity of the layers and measurement errors are also included. The best monitoring strategy for the manufacture of a given multilayer is established on the basis of statistical information obtained from a number of these simulations. In this paper the results of calculations on the effectiveness of various monitoring strategies are presented for a sharp edge filter produced by three different physical vapor deposition methods. An extensive list of references to previous papers dealing with sources of errors during deposition is also provided.

Research on thin film anticounterfeiting coatings at the National Research Council of Canada

After a brief description of the threats which face the issuers of documents and valuable papers, the concept of thin film anticounterfeiting coatings proposed by the NRCC is explained. The colorimetric considerations which govern the design of such devices are reviewed. Typical coating designs suitable for use in transmission and reflection are discussed. Reflection coatings can be constructed with and without an integral black absorber coating. The need for geometric patterns in the anticounterfeiting coating is explained. Various methods for producing such logos are proposed. Mention is made of the various numerical tools developed for the design and investigation of single films and multilayers, their desensitization to construction errors, and for the investigation of different process control strategies. During the duration of the project, experiments were performed on the optical constants and nonoptical properties of a number of metal and dielectric films considered for use in the anticounterfeiting coatings. These and some of the processes and equipment investigated during the development of a prototype production facility are reviewed. Finally, some security and economic aspects of the devices are considered.

Synthesis of high rejection filters with the Fourier transform method

Although in theory the Fourier transform method is valid only for small rejections, in practice it can be modified for the synthesis of high rejection filters with minimum transmittances as low as 10(-4). Two new spectral functions are proposed for use in the Fourier transforms. An empirical procedure which is much faster than refinement is described for optimization of the spectral performance. The method and optimization are illustrated numerically for several different spectral shapes.

Influence of small inhomogeneities on the spectral characteristics of single thin films

It is well known that the spectral transmittance and reflectance of a thin film can be influenced by even small inhomogeneities or variations in its complex refractive-index profile. Formulas are derived that describe the theoretical variation of the spectral characteristics for small changes in the refractive index and the extinction coefficient of a homogeneous thin film. These formulas, accurate to the first order in the change in the complex refractive index, are compared with exact calculations for a number of different types of inhomogeneities. It is shown that specific qualitative features in the refractive-index profile of a nearly homogeneous thin film frequently can be determined from an examination of the change in the spectral transmittance and reflectance at normal incidence.

Iterative correction process for optical thin film synthesis with the Fourier transform method

Several errors inherent to the Fourier transform method for optical thin film synthesis, including the inaccuracy of the spectral functions Q (sigma) used in the Fourier transforms, are compensated numerically by using successive approximations. We show that the complex phase of Q (sigma) is a key parameter which can be exploited to reduce significantly the thickness of the synthesized films and to control the shape of the refractive index profiles without affecting the spectral performance. This method is compared to other well established thin film design techniques.