Multiple-surface interferometry with nanoscale accuracy is important in the precise manufacturing of optically transparent parallel plates. To measure the surface profile and thickness variation of the plates simultaneously, the frequencies of the interferometric signal must be estimated from overlaid interferograms. Traditional algorithms typically suffer from issues such as spectrum leakage, reliance on initial iterative values, and the need for prior knowledge. In this study, the time-domain estimation algorithm for multiple-surface interferometry (MSI-TDe) is introduced based on a difference model to improve the accuracy of frequency estimation. The MSI-TDe algorithm is based on a normal equation that is insensitive to environmental noise. Using the algorithm, the frequencies of an interferometric signal can be estimated without prior knowledge and employed for wavefront reconstruction in multi-surface interferometry. Numerical simulation results indicate that the MSI-TDe algorithm has better frequency estimation performance than the discrete Fourier transform (DFT) algorithm. The relative error of the frequency estimation is on the order of 10-4. Three-surface interferometry was first performed. The root-mean square repeatability standard deviations of 0.07, 0.12 and 0.11 nm for the thickness variation, front surface profile, and rear surface profile, respectively, indicate the stability of the MSI-TDe algorithm. Four-surface interferometry with six frequency components was then performed. The adaptability of the MSI-TDe algorithm is validated by the measurement results.

The commonly used analytic bidirectional reflectance distribution functions (BRDFs) do not model goniochromatism, that is, angle-dependent material color. The material color is usually defined by a diffuse reflectance spectrum or RGB vector and a specular part based on a spectral complex index of refraction. Extension of the commonly used BRDFs based on wave theory can help model goniochromatism, but this comes at the cost of significant added model complexity. We measured the goniochromatism of structual color pigments used for additive color printing and found that we can fit the observed spectral angular dependence of the bidirectional reflectance using a simple modification of the standard microfacet BRDF model. All we need to describe the goniochromatism is an empirically-based spectral parameter, which we use in our model together with a specular reflectance spectrum instead of the spectral complex index of refraction. We demonstrate the ability of our model to fit the measured reflectance of red, green, and blue commercial structural color pigments. Our BRDF model enables straightforward implementation of a shader for interactive preview of 3D objects with printed spatially and angularly varying texture.

Recent advances in pigment production resulted in the possibility to print with RGBW primaries instead of CMYK and performing additive color mixing in printing. The RGBW pigments studied in this work have the properties of structural colors, as the primary colors are a result of interference in a thin film coating of mica pigments. In this work, we investigate the angle-dependent gamut of RGBW primaries. We have elucidated optimal angles of illumination and observation for each primary ink and found the optimal angle of observation under diffuse illumination. We investigated dot off dot halftoned screen printing with RGBW inks on black paper and in terms of angle-dependent dot gain. Based on our observations, optimal viewing condition for the given RGBW inks is in a direction of around 30◦ to the surface normal. Here, the appearance of the resulting halftoned prints can be estimated well by Neugebauer formula (weighted averaging of the individual reflected spectra). Despite the negative physical dot gain during the dot off dot printing, we observe angularly dependent positive optical dot gain for halftoned prints. Application of interference RGBW pigments in 2.5D and 3D printing is not fully explored due to the technological limitations. In this work, we provide colorimetric data for efficient application of the angle-dependent properties of such pigments in practical applications.

Traditional printing relies primarily on subtractive color mixing techniques. In this case, optical color mixing is achieved by one of the established halftoning methods that use Cyan, Magenta, Yellow and Black (CMYK) primaries on a reflective white substrate. The reason behind the subtractive color mixing in printing is the high absorbance of available pigments used in inks. A new type of mica-based pigments that exhibit high reflectivity at Red, Green, Blue and White (RGBW) spectral bands was recently introduced by Merck (SpectravalTM). Printing with RGBW primaries on black background allows additive color mixing in prints. While offering excellent color depth, the reflected spectra of such pigments vary with the angles of incidence and observation. As a result, new approaches in modelling the appearance of prints as well as strategies for color separation and halftoning are needed. The prior optical characterization of the reflective inks is an essential first step. For this purpose, we have used SpectravalTM pigments to prepare acrylic based inks, which we applied on glass slides by screen printing. In this work, we measured the relative spectral bidirectional reflection distribution of Red, Green, Blue and White reflective inks. The measurements were conducted on an experimental set up consisting of a goniometer, spectrometer, and a xenon light source. Based on the measurements, we simulate the reflectance spectra under diffuse illumination and demonstrate ratios of red, green, and blue spectral components for different observation angles of individual inks and their combinations.

People spend most of the time under artificial light sources, so it is important to create a comfortable lighting environment for work and rest. Four-component RGBW systems are the most effective for this. It is needed to create methods for obtaining white light with the specified parameters and choose the most optimal LED components. In this work, the influence of the white LEDs parameters on the resulting white light of the RGBW systems is studied. Two different methods proposed by us earlier for obtaining white light are applied for three RGBW systems with different warm white LEDs. It is shown that the use of white LEDs with a colour rendering index close to 80 is more optimal for most applications. In this case, they provide the resulting white light with the colour rendering index above 90 and luminous efficacy above 130 lm/W.

The work is devoted to the development of a smart lighting system that is able to change correlated colour temperature and consists of tunable 4-components RGBW clusters controlled via three channels. It is shown that fixing a ratio between the intensities of white and red LEDs at a level of 100:9 enables obtaining high values of colour rendering in a wide range of correlated colour temperatures. The control of 3 from 4 channels simplifies the system. The influence of the red LED on CRI and luminous efficiency is analysed.

An approach for simulation of light scattering from beetles exhibiting structural colors originating from periodic helicoidal structures is presented. Slight irregularities of the periodic structure in the exoskeleton of the beetles are considered as a major cause of light scattering. Two sources of scattering are taken into account: surface roughness and volume non-uniformity. The Kirchhoff approximation is applied to simulate the effect of surface roughness. To describe volume non-uniformity, the whole structure is modeled as a set of domains distributed in space in different orientations. Each domain is modeled as an ideal uniformly twisted uniaxial medium and differs from each other by the pitch. Distributions of the domain parameters are assumed to be Gaussian. The analysis is performed using the Mueller matrix formalism which, in addition to spectral and spatial characteristics, also provides polarization properties of the scattered light. (C) 2016 Optical Society of America

Light weight and small dimensions are some of the most important characteristics of near-to-eye displays (NEDs). These displays consist of two basic parts: a microdisplay for generating an image and supplementary optics in order to see the image. Nowadays, the pixel size of microdisplays may be less than 4 mu m, which makes the supplementary optics the major factor in defining restrictions on a NED dimensions or at least on the distance between the microdisplay and the eye. The goal of the present work is to find answers to the following two questions: how small this distance can be in principle and what is the microdisplay maximum resolution that stays effective to see through the supplementary optics placed in immediate vicinity of the eye. To explore the first question, we consider an aberration-free magnifier, which is the initial stage in elaboration of a real optical system. In this case, the paraxial approximation and the transfer matrix method are ideal tools for simulation of light propagation from the microdisplay through the magnifier and the human eyes optical system to the retina. The human eye is considered according to the Gullstrand model. Parameters of the magnifier, its location with respect to the eye and the microdisplay, and the depth of field, which can be interpreted as the tolerance of the microdisplay position, are determined and discussed. The second question related to the microdisplay maximum resolution is investigated by using the principles of wave optics. (C) 2015 Optical Society of America

Chirality, tailored by external morphology and internal composition, has been realized by controlled curved-lattice epitaxial growth (CLEG) of uniform coatings of single-crystalline In_xAl_1-xN nanospirals. The nanospirals are formed by sequentially stacking segments of curved nanorods on top of each other, where each segment is incrementally rotated around the spiral axis. By controlling the growth rate, segment length, rotation direction, and incremental rotation angle, spirals are tailored to predetermined handedness, pitch, and height.  The curved morphology of the segments is a result of a lateral compositional gradient across the segments while maintaining a preferred crystallographic growth direction, implying a lateral gradient in optical properties as well. Left- and right-handed nanospirals, tailored with 5 periods of 200 nm pitch, as confirmed by scanning electron microscopy, exhibit uniform spiral diameters of ~80 nm (local segment diameters of ~60 nm) with tapered hexagonal tips.  High resolution electron microscopy, in combination with nanoprobe energy dispersive X-ray spectroscopy and valence electron energy loss spectroscopy, show that individual nanospirals consist of an In-rich core with ~15 nm-diameter hexagonal cross-section, comprised of curved basal planes. The core is surrounded by an Al-rich shell with a thickness asymmetry spiraling along the core. The ensemble nanospirals, across the 1 cm² wafers, show high in-plane ordering with respect to shape, crystalline orientation, and direction of compositional gradient. Mueller matrix spectroscopic ellipsometry shows that the tailored chirality is manifested in the polarization state of light reflected off the CLEG nanospiral-coated wafers. In that, the polarization state is shown to be dependent on the handedness of the nanospirals and the wavelength of the incident light in the ultraviolet-visible region.

Inline quality control of liquid crystal (LC) cells is usually associated with a real-time noncontact characterization of moved LC cells. Such a characterization enables inspection of the products quality and helps to find in time defects. In the paper, we analyze an approach for fast evaluation of LC cell gap uniformity. The approach is based on detecting interference patterns formed by the quasi-monochromatic light reflected from a tested LC cell. To speed up the data treatment, a simple analytic expression describing the intensity of light interacting with the multilayered structure of an LC cell is derived. The results of the simplified model are compared with rigorous simulations. Two experimental setups are discussed. A CCD camera is used for detecting the interference patterns.