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Under consideration is the inverse problem of controlling the deposition of a multilayer coating using optical monitoring. Some new nonlocal algorithm is introduced for data analysis. Using the simulation of deposition process, the errors are compared of the proposed nonlocal algorithm and the traditional local algorithm. Some scheme of correction of the levels of the deposition process termination is considered that allows us to improve the accuracy of deposition monitoring. We show that the nonlocal algorithm is more efficient both for the deposition without correction of the signal level for the deposition interruption and with correction of this level.

The molecular dynamic algorithm for simulation of thin-film growth is reported. The achieved performance of this algorithm is sufficient for detailed investigations of structural effects in thin films with practically meaningful dimensions.

The production of polarizers for high-intensity applications based on a ZrO2/SiO2 pair of thin film materials is discussed. A special approach to accurate determination of a ZrO2 refractive index and the application of direct broadband optical monitoring enable obtaining good manufacturing results.

We deal with design and production of optimal two-component antireflection (AR) coatings for an ultra broadband spectral range from 450 nm to 1800 nm. We demonstrate the whole design-production chain including design selection, choosing monitoring technique, coating production, and reverse engineering of the deposited coatings. At each step of this chain we provide thorough analysis on the basis of theoretical results and adequate computational manufacturing experiments. In order to produce the designed AR coatings we use magnetron sputtering deposition technique and accurate time monitoring.

Two algorithms used for the on-line and off-line characterization of multilayer optical coatings are experimentally compared using test samples produced by two different deposition processes and different monitoring approaches. One of these algorithms, called the triangular algorithm, demonstrates its superiority in all considered situations. We performed experiments with multilayer samples formed by high-density thin films, which allowed us to neglect possible errors in the film refractive indices and concentrate only on errors in the thicknesses of the layers of the produced coatings.

Modern design approaches enable one to construct a series of theoretical designs with excellent spectral properties for almost all optical coating design problems. Selection of a practical optimal design among a variety of possible theoretical designs becomes a key issue. We demonstrate how preproduction estimations of expected production yields can be used for selection of a practical optimal design. The question of reliability of such estimations is also addressed.

A rigorous definition of the error self-compensation effect is provided. An existence of this effect in the case of coating production with broadband optical monitoring of layer thicknesses is investigated for several widely used types of optical coatings.

Optical constants of thin metal films are strongly dependent on deposition conditions, growth mode, and thickness. We propose a universal characterization approach that allows reliable determination of thin metal film optical constants as functions of wavelength and thickness. We apply this approach to determination of refractive index dispersion of silver island films embedded between silica layers.

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.

A new approach to inhomogeneous layer synthesis is proposed that differs from the classical Fourier transform methods. This approach, based on the wave-number discretization of the continuous Q function, is described together with the relationship between the smoothness of the inhomogeneous layer’s refractive-index profile, the complexity of the target reflectance specification, and the total optical thickness of the layer. An iterative procedure is introduced to overcome the inaccuracy connected with the approximate Q-function representation. Some control features of the Q-function phase are studied, and numerical examples are given.

The principal focus of my report is on the theoretical study of the properties of spectral coefficients in a complex wave-number plane. The basic results of the study are described, and their application to the synthesis of a rugate filter and to inhomogeneous layer recognition problems are considered. General results concerning the existence of solutions to synthesis problems are also presented. The close analogy between synthesis problems in thin-film optics and optimal control problems is outlined, and some applications of Pontryagin's maximum principle are considered.

A new method for the design of antireflection coatings is described in which a linearly constrained quadratic programming optimization procedure is used to find an inhomogeneous layer solution that, for a given overall thickness of the layer, corresponds to the global optimum for the problem. The refractive-index profile of this solution is then approximated by a two-material multilayer system that serves as a starting design for further numerical refinement. We present the theoretical basis for this method and discuss the effect of the various approximnations made on the solution. Four different antireflection problems are solved to illustrate this new method.

A new model for the determination of group delay (GD) and GD dispersion of dispersive mirrors is presented. The algorithm based on this model enables one to process interferometric data provided by a white-light interferometer and to obtain GD wavelength dependence over a broad spectral range.

The constrained optimization approach is applied to the design of quasi-rugate optical coatings. These coatings are defined as multilayers with no thin layers where refractive index profiles resemble rugate-type refractive index profiles and where spectral properties are typical for rugate filters. It is shown that all design problems that are usually solved using rugate filters can be solved successfully in the frame of quasi-rugate optical coatings. Comparison between quasi-rugate and two-component multilayer designs is provided.

A new optical monitoring system has been developed that allows recording of transmission spectra in the wavelength range between 400 and 920 nm of a growing optical coating during deposition. Several kinds of thin film sample have been prepared by use of a hybrid monitoring strategy that is essentially based on a combination of quartz monitoring and in situ transmission spectra measurements. We demonstrate and discuss the applicability of our system for reengineering procedures of high-low stacks and measurements of small vacuum or thermal shifts of optical coatings.

We develop a new approximation for the amplitude reflection coefficients of a slightly inhomogeneous thin film. This approximation incorporates exactly the interference effects at the substrate and the ambient interfaces. Interference effects inside the inhomogeneous film are incorporated in the Born approximation. We also develop a new approach to the reconstruction of the refractive-index profile from ellipsometric spectra. It is based on a physically sound parameterization of the refractive-index profile. The new approach is tested on the model reconstruction problem.

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.

We demonstrate theoretically and experimentally a band filter with two reflection and broadband transmission ranges, which was obtained with standard two-material technology. The fabricated filter has transmission and reflectivity characteristics better than those achievable with rugate technology.

In this paper, we present our recent studies on raising the quality of optical coating production with an indirect monochromatic monitoring system. Preproduction error analysis and computational manufacturing are used to estimate potential advantages of application of indirect optical monitoring. It is then demonstrated that a key issue for realization of this advantage is accurate specification of tooling factors for layer thicknesses on test glasses. The tooling factors are precalibrated using single layer depositions and then are corrected using results of reverse engineering for the first production run. It is found that a gradual variation of tooling factors of low index layers is the main error factor in the first deposition run. Finally, we redeposit our coating with a modified monitoring strategy, taking into account this factor. The new experimental results show excellent correspondence with the theoretical spectral performance.

We present a theoretical approach enabling one to perform a preproduction investigation of the effect of accumulation of thickness errors in the course of optical coating production using broadband optical monitoring. On the basis of this approach we investigate and compare thickness errors that may be associated with such factors as random and systematic errors in measurement data, instabilities of deposition rates, and inaccuracies of on-line algorithms predicting termination instants for layer depositions.

New optical coating design algorithm with the equivalent layers theory is presented. The algorithm is based on the merit-function-constrained optimization in the accessible domain of equivalent phase thicknesses and equivalent refractive indices. It allows for creation of design coatings with sophisticated narrowband spectral characteristics. (

By comparing multilayer and rugate solutions to a typical rugate synthesis problem we demonstrate that rugate synthesis methods are still of a great importance. The new accurate algorithm for the synthesis of rugate coatings with arbitrary refractive index profiles is discussed. It is shown that this algorithm can be successfully applied for solving such classical rugate synthesis problem as reducing sidelobes accompanying stopbands of rugate filters.

An automated approach to the design of wavelength-division multiplexing (WDM) filters is based on the combination of ideas from classical design approaches with an integer optimization technique. This approach turns out to be extremely efficient from a computational point of view and makes it possible to construct a set of significantly different filter designs with nearly equivalent spectral properties. The sensitivity of WDM filters is analyzed by a computer simulation of the deposition process with turning-point optical monitoring. This analysis enables the designer to compare feasibility properties of various filter designs.

A gain-flattening filter (GFF) for minimum manufacturing errors (12 designs submitted) and dense wavelength-division multiplex (DWDM) filters for low group-delay (GD) variation (9 designs submitted) was the subject of a design contest held in conjunction with the Optical Interference Coatings 2001 topical meeting of the Optical Society of America. Results of the contest are given and evaluated. It turned out that the parameter space for GFFs with optimum performance when manufacturing errors are not considered is much different from that when manufacturing errors are considered. DWDM filter solutions with low GD variation are possible.

The determination of optical parameters of thin films from experimental data is a typical task in the field of optical-coating technology. The optical characterization of a single layer deposited on a substrate with known optical parameters is widely used for this purpose. Results of optical characterization are dependent on not only the choice of the thin-film model but also on the quality of experimental data. The theoretical results presented highlight the effect of systematic errors in measurement data on the determination of thin-film parameters. Application of these theoretical results is illustrated by the analysis of experimental data for magnesium fluoride thin films.

Single layers of MgF2 and LaF3 were deposited upon superpolished fused-silica and CaF2 substrates by ion-beam sputtering (IBS) as well as by boat and electron beam (e-beam) evaporation and were characterized by a variety of complementary analytical techniques. Besides undergoing photometric and ellipsometric inspection, the samples were investigated at 193 and 633 nm by an optical scatter measurement facility. The structural properties were assessed with atomic-force microscopy, x-ray diffraction, TEM techniques that involved conventional thinning methods for the layers. For measurement of mechanical stress in the coatings, special silicon substrates were coated and analyzed. The dispersion behavior of both deposition materials, which was determined on the basis of various independent photometric measurements and data reduction techniques, is in good agreement with that published in the literature and with the bulk properties of the materials. The refractive indices of the MgF2 coatings ranged from 1.415 to 1.440 for the wavelength of the ArF excimer laser (193 nm) and from 1.435 to 1.465 for the wavelength of the F2 excimer laser (157 nm). For single layers of LaF3 the refractive indices extended from 1.67 to 1.70 at 193 nm to approximately 1.80 at 157 nm. The IBS process achieves the best homogeneity and the lowest surface roughness values (close to 1 nm(rms)) of the processes compared in the joint experiment. In contrast to MgF2 boat and e-beam evaporated coatings, which exhibit tensile mechanical stress ranging from 300 to 400 MPa, IBS coatings exhibit high compressive stress of as much as 910 MPa. A similar tendency was found for coating stress in LaF3 single layers. Experimental results are discussed with respect to the microstructural and compositional properties as well as to the surface topography of the coatings.

The angular properties of various wideband high reflectors are investigated. The theory is developed for the design of high reflectors based on contiguous quarter-wave stacks for use at one oblique angle or for a range of angles of incidence. Numerical results are presented for several high reflectors designed to have a high reflectance in the 0.4-0.8-mum spectral region for use at 50 degrees and with angles of incidence ranging between 0 degrees and 50 degrees . A random error perturbation analysis shows that such layer systems can be produced experimentally.

An efficient first-order algorithm with an exact calculation of the gradients is described and applied to the refinement of inhomogeneous dielectric thin films. Numerical results calculated at normal and oblique angles of incidence are correlated with an important mathematical theorem. It is shown that, when appropriate conditions are satisfied, the synthesis process generates binary type solutions based on two materials, including classical multilayers.

In the present study we determine the optical parameters of thin metal–dielectric films using two different characterization techniques based on nonparametric and multiple oscillator models. We consider four series of thin metal–dielectric films produced under various deposition conditions with different optical properties. We compare characterization results obtained by nonparametric and multiple oscillator techniques and demonstrate that the results are consistent. The consistency of the results proves their reliability.

Wavelength dependencies of refractive indices of thin film materials differ for various deposition conditions, and it is practically impossible to attribute a single refractive index wavelength dependence to any typical thin film material. Besides objective reasons, differences in the optical parameters of thin films may also be connected with nonadequate choices of models and algorithms used for the processing of measurement data. The main goal of this paper is to present reliable wavelength dependencies of refractive indices of the most widely used slightly absorbing oxide thin film materials. These dependencies can be used by other researchers for comparison and verification of their own characterization results.

We present an indirect broadband optical monitoring approach based on using several witness substrates that are brought to a measurement position in a special sequence. Different witness substrates are used to monitor not groups of successive design layers but specially chosen design layers. An attractive feature of the presented monitoring approach is the ability to reliably control thin dielectric and metal layers. Considered examples demonstrate a good accuracy of the proposed approach.

We deal with optimal two-material antireflection (AR) coatings for the visible and adjacent spectral regions. It has been shown before that, for a given set of input parameters (refractive indices of the substrate, ambient medium and high- and low-index coating materials, and for a given spectral width of the AR coating), such designs consist of one or more clusters of layers of approximately constant optical thickness and number of layers. We show that, through the analysis of many different optimal coatings, it is possible to derive two parameters for a simple empirical expression that relates the residual average reflectance in the AR region to the number of clusters. These parameters are given for all possible combinations of relative spectral bandwidth equal to 2, 3, and 4; low-index to ambient-medium index ratio equal to 1.38 and 1.45; and high-to-low index ratio equal to 1.4, 1.5, and 1.7. The agreement between the numerically and the empirically calculated values of residual average reflectance is excellent. From the information presented the optical thin-film designer can quickly calculate the required number of layers and the overall optical thickness of an AR coating having the desired achievable residual average reflectance.

We present an algorithm for the automatic generation of a monitoring spreadsheet that enables the most effective application of the termination level correction algorithm proposed in our previous publication. On a whole the presented monochromatic monitoring strategy entirely eliminates a cumulative effect of thickness errors in optical coating production using direct optical monitoring. The effectiveness of the new monitoring strategy is demonstrated by computational manufacturing experiments in which such error factors as instability of deposition rates, errors in measured transmittance data, shutter delays, and variations of layer refractive indices from their theoretical values are simulated.

We propose an algorithm for correcting deposition termination levels that allows elimination of the cumulative effect of errors in previously deposited layers. For the application of this algorithm at least one monitoring signal extremum should be registered during a layer deposition. We also derive a theoretical relation for the estimation of errors in layer refractive indices based on the results of on-line monitoring measurements. At least two monitoring signal extrema are required for its application.

Design approaches for optical thin films that recognize the key role of a design's total optical thickness are presented. These approaches are based primarily on the needle optimization technique but also utilize other optimization procedures. Using the described design approaches, an optical coating engineer can obtain a set of theoretical designs with different combinations of principal design metrics (merit function value, number of layers, and total design optical thickness); this extends opportunities for choosing the most practical and manufacturable design. We also show that some design problems have multiple solutions with nearly the same combinations of principal design metrics.

Computational manufacturing of optical coatings is a research area that can be placed between theoretical designing and practical manufacturing in the same way that computational physics can be placed between theoretical and experimental physics. Investigations in this area have been performed for more than 30 years under the name of computer simulation of manufacturing and monitoring processes. Our goal is to attract attention to the increasing importance of computational manufacturing at the current state of the art in the design and manufacture of optical coatings and to demonstrate possible applications of this research tool.

We introduce two parameters, large-scale and small-scale rms roughness, to take into account the interface properties of thin films and multilayers in the calculation of their specular reflectance and transmittance. A theoretical motivation for the introduction of these two parameters instead of a standard single rms roughness is provided. Experimental power spectral density functions of several samples are used to illustrate ways in which the parameters introduced can be evaluated.

The phase shift upon transmission of a nonabsorbing multilayer is shown to be a monotonically decreasing function of the wave number, with an average slope proportional to the optical thickness of the coating. Two limiting situations of the phase shift upon reflection are examined: In one the phase monotonically increases with wavelength, and in the other the phase oscillates. The phase shift upon reflection is derivable from Kramers–Kronig-type relationships, provided the radiant reflectance and the Blaschke factors are known. Characteristic features of the refractive-index profile related to these factors are discussed.

The authors' experience with the application of the needle optimization technique to the design of optical coating is summarized. A physical interpretation of the technique is provided, and its main features are identified. Guidelines on the application of the needle optimization technique to various types of design problems are given.