Dual-angle, spectral reconstruction imaging method for the determination of dielectric thin-film thickness.

The thickness of optical thin films, such as dielectrics, can be determined by the use of a profilometer or by a spectrophotometer. Both of these standard methods have coated area size limitations. Converting a digital camera to a spectrophotometer eliminates these size limitations. This work reviews a simple method for determining the physical thickness of a dielectric film on a silicon wafer using two images from a digital camera.

Nonpolarizing color mirrors on a high-reflecting metal base.

Optically variable devices made from optical-interference coatings create chromatic color mirrors that have minimal polarization differences with increasing incidence angle. These metal-dielectric-metal designs produce narrowband, high reflectance in the visible wavelength region. Broader-band reflectance regions, similar to those created by multilayer dielectric stacks, can be replicated on a high-reflecting metal base such as aluminum, maintaining the same nonpolarizing effects of the narrowband designs. These designs are intended for reflective systems used for display where reduced angle sensitivity is paramount. However, these designs can also be adapted for large angular-dependent color shift, such as in effect pigments. Design examples and layer material suggestions are given depending on the application requirements.

First-order goniospectrophotometric spectral modeling of isotropic and anisotropic colorant mixtures.

Color modeling of translucent and opaque media commonly uses two-constant Kubelka-Munk (KM) turbid media theory. KM theory is designed for isotropic color systems that rely on absorption and scatter to produce an overall reflected color. KM theory has previously been considered inadequate to use with interference pigments (IPs) due to their specular reflected, angle-dependent color and anisotropic behavior. If, however, an IP's reflected color is considered to contribute to the background reflectance and not as a colorant in a mixture with a conventional colorant, KM theory can be used. KM theory was successfully implemented to predict the goniospectrophotometric, normalized spectral reflectance of conventional colorants and IP mixtures.

Computation of optimal metamers.

A fast, accurate model for computing Logvinenko's optimal metamers is introduced. The spectral reflectance of an optimal metamer is uniquely determined from a class of metamers with common tristimulus values. A set of optimal metamers is useful for evaluating the color reproduction and gamut of object colors under different illuminants. In conventional methods, optimal metamers are calculated by interpolating the coordinates of precomputed optimal colors. This model optimizes the spectral reflectance parameters efficiently without switching between bandpass (Type I) and bandstop (Type II) optimal metamers, or requiring any stored optimal-color datasets. Some optimal metamer loci computed using MATLAB are presented.

Number of discernible object colors is a conundrum.

Widely varying estimates of the number of discernible object colors have been made by using various methods over the past 100 years. To clarify the source of the discrepancies in the previous, inconsistent estimates, the number of discernible object colors is estimated over a wide range of color temperatures and illuminance levels using several chromatic adaptation models, color spaces, and color difference limens. Efficient and accurate models are used to compute optimal-color solids and count the number of discernible colors. A comprehensive simulation reveals limitations in the ability of current color appearance models to estimate the number of discernible colors even if the color solid is smaller than the optimal-color solid. The estimates depend on the color appearance model, color space, and color difference limen used. The fundamental problem lies in the von Kries-type chromatic adaptation transforms, which have an unknown effect on the ranking of the number of discernible colors at different color temperatures.

Paramer mismatch-based spectral gamut mapping.

A spectral agreement between the original scene and a printed reproduction is required to achieve an illuminant-invariant visual match. This is usually impossible since the spectral gamut of typical printing systems is only a small subset of all natural reflectances. Out-of gamut reflectances need to be mapped into the spectral gamut of the printer minimizing the perceived error between original and reproduction for more than one illuminant. In this paper, we propose an algorithmic framework for spectral gamut mapping to achieve a reproduction that is as visually correct as a colorimetric reproduction for one illuminant and is superior for a set of other illuminants. A sequence of hierarchical mappings in 3-D color spaces are performed utilizing the observer's color quantization to increase the spectral variability of subsequent transformations: For the most important illuminant a traditional colorimetric gamut mapping is performed. For any additional illuminants colors are mapped onto pixel-dependent paramer mismatch gamuts preserving the visual equivalence of previous transformations. We present a separation method for investigating the spectral gamut mapping framework and show that hue shifts and chroma gains cannot be always avoided for the second and subsequent illuminants and that the order of illuminants has a large impact on the final reproduction.

Spectral image reconstruction using an edge preserving spatio-spectral Wiener estimation.

Reconstruction of spectral images from camera responses is investigated using an edge preserving spatio-spectral Wiener estimation. A Wiener denoising filter and a spectral reconstruction Wiener filter are combined into a single spatio-spectral filter using local propagation of the noise covariance matrix. To preserve edges the local mean and covariance matrix of camera responses is estimated by bilateral weighting of neighboring pixels. We derive the edge-preserving spatio-spectral Wiener estimation by means of Bayesian inference and show that it fades into the standard Wiener reflectance estimation shifted by a constant reflectance in case of vanishing noise. Simulation experiments conducted on a six-channel camera system and on multispectral test images show the performance of the filter, especially for edge regions. A test implementation of the method is provided as a MATLAB script at the first author's website.

Performance of recent advanced color-difference formulas using the standardized residual sum of squares index.

The standardized residual sum of squares (STRESS) index was used to reevaluate four experimental datasets employed during the development of CIEDE2000, the current CIE recommended color-difference formula. This index enables statistical inferences not achievable by other metrics used commonly for performance evaluation. It was found that CIEDE2000 was statistically superior at a 95% confidence level to either CIE94, the previous recommended equation by the CIE, or the simple Euclidean distance in CIELAB, DeltaE*ab. Recent formulas based on the CIECAM02 color-appearance space and chroma-compressed variants of CIELAB were also evaluated and found to have only slightly reduced performance compared with CIEDE2000. These formulas have the advantage of simplicity and easier interpretation when used for quantifying color accuracy. Finally, each experimental dataset was evaluated separately rather than weight averaged as used during the development of CIEDE2000. Significant differences were found between datasets, suggesting that combining datasets may obscure important differences and that the practice of parameter optimization during formula development using combined data is likely suboptimal.

Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement.

Isometric embedding of non-Euclidean color spaces into Euclidean color spaces is investigated. Owing to regions of nonzero Gaussian curvature within common non-Euclidean color spaces, we focus on the determination of transformations into Euclidean spaces with minimal isometric disagreement. A computational method is presented for deriving such a color space transformation by means of a multigrid optimization, resulting in a simple color look-up table. The multigrid optimization is applied on the CIELAB space with the CMC, CIE94, and CIEDE2000 formulas. The mean disagreement between distances calculated by these formulas and Euclidean distances within the new spaces is far below 3% for all investigated color difference formulas. Color space transformations containing the inverse transformations are provided as MATLAB scripts at the first author's website.

Relative significance of the terms in the CIEDE2000 and CIE94 color-difference formulas.

CIELAB-based color-difference formulas are used to improve the prediction of visually perceived color differences through the introduction of various corrections to CIELAB. In our study we analyze the relative importance of these corrections. From the combined dataset employed for the development of CIEDE2000, we found that the improvement of CIE94 over CIELAB was considerably greater than that of CIEDE2000 over CIE94. Chroma-difference correction was the most important correction in both CIE94 and CIEDE2000. With an arbitrary value of 100 assigned to this correction, the score of the hue-difference correction in CIE94 was 21, and the scores of the four remaining corrections in CIEDE2000 were as follows: hue difference, 29; rotation term, 8; lightness difference, 8; and gray correction, 6. At 95% confidence level each of the corrections introduced in CIEDE2000 or CIE94 was statistically significant for the whole combined dataset, in agreement with the results reported by CIE TC 1-47 and 1-29. For the combined dataset, the differences between CMC and CIEDE2000 were found to be statistically significant at 95% confidence level, but the differences between CMC and CIE94 were not. From subsets of the combined dataset it was concluded that further analyses of the lightness-difference and gray corrections proposed by CIEDE2000 would be desirable, using new experimental data.