Analysis of the colorimetric properties of goniochromatic colors using the MacAdam limits under different light sources

Technological innovation in all areas has led to the appearance in recent years of new metallic and pearlescent materials, yet no exhaustive studies have been conducted to assess their colorimetric capabilities. The chromatic variability of these special-effect pigments may largely be due to the three-dimensional effect of their curved shapes and orientations when they are directionally or diffusely illuminated. Our study examines goniochromatic colors using the optimal colors (MacAdam limits) associated with normal colors (photometric scale of relative spectral reflectance from 0 to 1) under certain conventional illuminants and other light sources. From a database of 91 metallic and interference samples and using a multi-gonio-spectrophotometer, we analyzed samples with lightness values of more than 100 and others with lightness values of less than 100, but with higher chromaticities than optimal colors, which places them beyond the MacAdam limits. Our study thus demonstrates the existence of chromatic perceptions beyond the normal solid color associated with these materials and independent of the light source. The challenge for future research, therefore, is to replicate and render these color appearances in current and future color reproduction technologies for computer graphics.

Number of discernible colors for color-deficient observers estimated from the MacAdam limits

We estimated the number of colors perceived by color normal and color-deficient observers when looking at the theoretic limits of object-color stimuli. These limits, the optimal color stimuli, were computed for a color normal observer and CIE standard illuminant D65, and the resultant colors were expressed in the CIELAB and DIN99d color spaces. The corresponding color volumes for abnormal color vision were computed using models simulating for normal trichromatic observers the appearance for dichromats and anomalous trichomats. The number of colors perceived in each case was then computed from the color volumes enclosed by the optimal colors also known as MacAdam limits. It was estimated that dichromats perceive less than 1% of the colors perceived by normal trichromats and that anomalous trichromats perceive 50%–60% for anomalies in the medium-wavelength-sensitive and 60%–70% for anomalies in the long-wavelength-sensitive cones. Complementary estimates obtained similarly for the spectral locus of monochromatic stimuli suggest less impairment for color-deficient observers, a fact that is explained by the two-dimensional nature of the locus.

Measurement of wide frequency range structural microvibrations with a pocket digital camera and sub-pixel techniques

Analysis of vibrations and displacements is a hot topic in structural engineering. Although there is a wide variety of methods for vibration analysis, direct measurement of displacements in the mid and high frequency range is not well solved and accurate devices tend to be very expensive. Low-cost systems can be achieved by applying adequate image processing algorithms. In this paper, we propose the use of a commercial pocket digital camera, which is able to register more than 420 frames per second (fps) at low resolution, for accurate measuring of small vibrations and displacements. The method is based on tracking elliptical targets with sub-pixel accuracy. Our proposal is demonstrated at a 10 m distance with a spatial resolution of 0.15 mm. A practical application over a simple structure is given, and the main parameters of an attenuated movement of a steel column after an impulsive impact are determined with a spatial accuracy of 4 µm.

Resolution limits to object tracking with subpixel accuracy

Subpixel methods increase the accuracy and efficiency of image detectors, processing units, and algorithms and provide very cost-effective systems for object tracking. Published methods achieve resolution increases up to three orders of magnitude. In this Letter, we demonstrate that this limit can be theoretically improved by several orders of magnitude, permitting micropixel and submicropixel accuracies. The necessary condition for movement detection is that one single pixel changes its status. We show that an appropriate target design increases the probability of a pixel change for arbitrarily small shifts, thus increasing the detection accuracy of a tracking system. The proposal does not impose severe restriction on the target nor on the sensor, thus allowing easy experimental implementation.

Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings

A reduced set of measurement geometries allows the spectral reflectance of special effect coatings to be predicted for any other geometry. A physical model based on flake-related parameters has been used to determine nonredundant measurement geometries for the complete description of the spectral bidirectional reflectance distribution function (BRDF). The analysis of experimental spectral BRDF was carried out by means of principal component analysis. From this analysis, a set of nine measurement geometries was proposed to characterize special effect coatings. It was shown that, for two different special effect coatings, these geometries provide a good prediction of their complete color shift.

Open-access operating algorithms for commercial videokeratographer and improvement of corneal sampling

We present an algorithm to process images of reflected Placido rings captured by a commercial videokeratoscope. Raw data are obtained with no Cartesian-to-polar-coordinate conversion, thus avoiding interpolation and associated numerical artifacts. The method provides a characteristic equation for the device and is able to process around 6 times more corneal data than the commercial software. Our proposal allows complete control over the whole process from the capture of corneal images until the computation of curvature radii.

Vibration frequency measurement using a local multithreshold technique

In this paper, we demonstrate the use of a video camera for measuring the frequency of small-amplitude vibration movements. The method is based on image acquisition and multilevel thresholding and it only requires a video camera with high enough acquisition rate, not being necessary the use of targets or auxiliary laser beams. Our proposal is accurate and robust. We demonstrate the technique with a pocket camera recording low-resolution videos with AVI-JPEG compression and measuring different objects that vibrate in parallel or perpendicular direction to the optical sensor. Despite the low resolution and the noise, we are able to measure the main vibration modes of a tuning fork, a loudspeaker and a bridge. Results are successfully compared with design parameters and measurements with alternative devices.

Considerations on the electromagnetic flow in Airy beams based on the Gouy phase

We reexamine the Gouy phase in ballistic Airy beams (AiBs). A physical interpretation of our analysis is derived in terms of the local phase velocity and the Poynting vector streamlines. Recent experiments employing AiBs are consistent with our results. We provide an approach which potentially applies to any finite-energy paraxial wave field that lacks a beam axis.

Engineered surface waves in hyperbolic metamaterials

We analyzed surface-wave propagation that takes place at the boundary between a semi-infinite dielectric and a multilayered metamaterial, the latter with indefinite permittivity and cut normally to the layers. Known hyperbolization of the dispersion curve is discussed within distinct spectral regimes, including the role of the surrounding material. Hybridization of surface waves enable tighter confinement near the interface in comparison with pure-TM surface-plasmon polaritons. We demonstrate that the effective-medium approach deviates severely in practical implementations. By using the finite-element method, we predict the existence of long-range oblique surface waves.

Nondiffracting Bessel plasmons

We report on the existence of nondiffracting Bessel surface plasmon polaritons (SPPs), advancing at either superluminal or subluminal phase velocities. These wave fields feature deep subwavelength FWHM, but are supported by high-order homogeneous SPPs of a metal/dielectric (MD) superlattice. The beam axis can be relocated to any MD interface, by interfering multiple converging SPPs with controlled phase matching. Dissipative effects in metals lead to a diffraction-free regime that is limited by the energy attenuation length. However, the ultra-localization of the diffracted wave field might still be maintained by more than one order of magnitude.

Left-handed metamaterial coatings for subwavelength-resolution imaging

We report on a procedure to improve the resolution of far-field imaging by using a neighboring high-index medium that is coated with a left-handed metamaterial. The resulting plot can also exhibit an enhanced transmission by considering proper conditions to retract backscattering. Based on negative refraction, geometrical aberrations are considered in detail since they may cause a great impact in this sort of diffraction-unlimited imaging by reducing its resolution power. We employ a standard aberration analysis to refine the asymmetric configuration of metamaterial superlenses. We demonstrate that low-order centrosymmetric aberrations can be fully corrected for a given object plane. For subwavelength-resolution imaging, however, high-order aberrations become of relevance, which may be balanced with defocus. Not only the point spread function but also numerical simulations based on the finite-element method support our theoretical analysis, and subwavelength resolution is verified in the image plane.

Effects of high-color-discrimination capability spectra on color-deficient vision

Light sources with three spectral bands in specific spectral positions are known to have high-color-discrimination capability. W. A. Thornton hypothesized that they may also enhance color discrimination for color-deficient observers. This hypothesis was tested here by comparing the Rösch–MacAdam color volume for color-deficient observers rendered by three of these singular spectra, two reported previously and one derived in this paper by maximization of the Rösch–MacAdam color solid. It was found that all illuminants tested enhance discriminability for deuteranomalous observers, but their impact on other congenital deficiencies was variable. The best illuminant was the one derived here, as it was clearly advantageous for the two red–green anomalies and for tritanopes and almost neutral for red–green dichromats. We conclude that three-band spectra with high-color-discrimination capability for normal observers do not necessarily produce comparable enhancements for color-deficient observers, but suitable spectral optimization clearly enhances the vision of the color deficient.

Color representation and interpretation of special effect coatings

A representation of the color gamut of special effect coatings is proposed and shown for six different samples, whose colors were calculated from spectral bidirectional reflectance distribution function (BRDF) measurements at different geometries. The most important characteristic of the proposed representation is that it allows a straightforward understanding of the color shift to be done both in terms of conventional irradiation and viewing angles and in terms of flake-based parameters. A different line was proposed to assess the color shift of special effect coatings on a*,b*-diagrams: the absorption line. Similar to interference and aspecular lines (constant aspecular and irradiation angles, respectively), an absorption line is the locus of calculated color coordinates from measurement geometries with a fixed bistatic angle. The advantages of using the absorption lines to characterize the contributions to the spectral BRDF of the scattering at the absorption pigments and the reflection at interference pigments for different geometries are shown.

Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

Measurement of wide frequency range structural microvibrations with a pocket digital camera and sub-pixel techniques

Analysis of vibrations and displacements is a hot topic in structural engineering. Although there is a wide variety of methods for vibration analysis, direct measurement of displacements in the mid and high frequency range is not well solved and accurate devices tend to be very expensive. Low-cost systems can be achieved by applying adequate image processing algorithms. In this paper, we propose the use of a commercial pocket digital camera, which is able to register more than 420 frames per second (fps) at low resolution, for accurate measuring of small vibrations and displacements. The method is based on tracking elliptical targets with sub-pixel accuracy. Our proposal is demonstrated at a 10 m distance with a spatial resolution of 0.15 mm. A practical application over a simple structure is given, and the main parameters of an attenuated movement of a steel column after an impulsive impact are determined with a spatial accuracy of 4 µm.