Empirical BRDF model for goniochromatic materials and soft proofing with reflective inks.

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.

Iridescence Mimicking in Fabrics: A Ultraviolet/Visible Spectroscopy Study.

Poly(styrene-methyl methacrylate-acrylic acid) photonic crystals (PCs), with five different sizes (170, 190, 210, 230 and 250 nm), were applied onto three plain fabrics, namely polyamide, polyester and cotton. The PC-coated fabrics were analyzed using scanning electronic microscopy and two UV/Vis reflectance spectrophotometric techniques (integrating sphere and scatterometry) to evaluate the PCs' self-assembly along with the obtained spectral and colors characteristics. Results showed that surface roughness of the fabrics had a major influence on the color produced by PCs. Polyamide-coated fabrics were the only samples having an iridescent effect, producing more vivid and brilliant colors than polyester and cotton samples. It was observed that as the angle of incident light increases, a hypsochromic shift in the reflection peak occurs along with the formation of new reflection peaks. Furthermore, color behavior simulations were performed with an illuminant A light source on polyamide samples. The illuminant A simulation showed greener and yellower structural colors than those illuminated with D50. The polyester and cotton samples were analyzed using scatterometry to check for iridescence, which was unseen upon ocular inspection and then proven to be present in these samples. This work allowed a better comprehension of how structural colors and their iridescence are affected by the textile substrate morphology and fiber type.

Full-color holographic display with increased-viewing-angle [Invited].

Among the important features of holographic displays are the wide viewing angles and the full color of the reconstructed images. The present work focuses on achievement of both features. We propose an increased-viewing-angle full-color holographic display using two tiled phase-only spatial light modulators (SLMs), a 4f concave mirrors system, and a temporal-spatial multiplexing method. The 4f optical system consists of two concave mirrors and serves to increase the viewing angle. A temporal-spatial multiplexing synchronization control (TSMSC) method is developed to achieve a full-color image and to remove the color crosstalk of the image. We calculate RGB phase-only holograms of a computer-generated color pyramid by using a slice-based Fresnel diffraction algorithm. The experimental results indicate that the proposed display system is feasible to reconstruct a full-color holographic 3D image with a viewing angle of 12.8°, which is about 3.8 times wider than the viewing angle formed by a single SLM.

Modeling of light interaction with exoskeletons of scarab beetles.

Some beetles of the family Scarabaeidae produce brilliant metallic-looking colors by their pure dielectric exoskeletons and reflect light with a high degree of circular polarization. In the present work, we discuss three models for simultaneously describing scattering, spectral, and polarization characteristics of scarab beetles. Each model consists of three slabs: an outer thin epicuticle, an exocuticle having a helicoidal structure, and a thick uniform slightly absorbing endocuticle. Scattering features are defined by rough interfaces of the epicuticle and/or nonuniformities of the exocuticle. As an example, a slightly modified model of an earlier study of Chrysina aurata is considered. The modification is aimed at including surface and volume nonuniformities that affect not only spectral and polarization properties but also scattering. Another example of using the proposed models is based on the analysis of image formations of a specimen of the species Mimela chinensis, which was studied in a polarizing microscope at different magnifications. The results show that the proposed models can be applied for explanation of light interaction with the exoskeletons of scarab beetles.

Simulation of light scattering from exoskeletons of scarab beetles.

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.

Assessment of minimum permissible geometrical parameters of a near-to-eye display.

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 µm, 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 eye's 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.

Curved-lattice epitaxial growth of In(x)Al(1-x)N nanospirals with tailored chirality.

Chirality, tailored by external morphology and internal composition, has been realized by controlled curved-lattice epitaxial growth of In(x)Al(1-x)N nanospirals. The curved morphology of the spiral segments is a result of a lateral compositional gradient while maintaining a preferred crystallographic growth direction, implying a lateral gradient in optical properties. Individual nanospirals show an asymmetric core-shell structure with curved basal planes. Mueller matrix spectroscopic ellipsometry shows that the tailored chirality is manifested in the polarization state of light reflected off the nanospirals.