Goniospectrometric space curve for coatings with special effect pigments: erratum.

In the original publication [Appl. Opt.55, 122 (2016)APOPAI0003-693510.1364/AO.55.000122], Eq. 5(c) was wrong. The correction for it is given here.

Goniospectrometric space: identifiable presentation of spectral goniometric data for complex diffractive samples.

Optical security takes advantage of complex gonioapparent effects of diffractive samples having strong angular and spectral dependence of reflected light. However, resolving the full angular and spectral properties of these kinds of targets might be a tremendous task. Preferably, one would like to measure a more limited number of illumination-viewing directions, using a multiangle goniometer, and still reveal the complex and unique properties of the target. In this study, we use a method for converting the full angular reflection data into reduced goniospectrometric space and further on into an xDNA graph, which we find to show good potential as a fingerprint for gonioapparent surfaces when limited measurement geometries are available. For the evaluation of the xDNA graph, we use two goniometric devices with a 45° incident angle illumination, a high-resolution bidirectional spectrometer, and a portable multiangle goniometer. This study tests the xDNA graph by evaluating the effects of geometry count and spectral resolution in goniometric measurements and further finds that the xDNA graph indeed works best with a reduced count of geometries and is not sensitive to lowered spectral resolution.

Goniospectrometric space curve for coatings with special effect pigments.

Advanced application of eye-catching effects occurring in coatings with special effect pigments requires controlling their appearance. For this purpose, angular dependent reflectance must be analyzed in terms of the used flakes and their distribution inside the coating; it is important to know the size of the surface area they cover, and the position and precision of their orientation. These properties were varied using our numerical model, which gave an angular dependent reflectance factor for each set of coating parameters. The method was applied to analyze how well the calculated goniometric reflectance factor could characterize the appearance of effect coatings. For this purpose, the spectra were transformed in the goniospectrometric space, and the obtained curve was analyzed. While its shape, position, and orientation in the space reveal the optical makeup of the coating, the goniospectrometric space curve could serve as an appearance fingerprint of the corresponding sample. The applicability of the theoretical predictions was confirmed using a coating with metallic flakes and one with mica-based Fe2O3 coated flakes.

Evaluation of complex gonioapparent samples using a bidirectional spectrometer.

Many applications use gonioapparent targets whose appearance depends on irradiation and viewing angles; the strongest effects are provided by light diffraction. These targets, optically variable devices (OVDs), are used in both security and authentication applications. This study introduces a bidirectional spectrometer, which enables to analyze samples with most complex angular and spectral properties. In our work, the spectrometer is evaluated with samples having very different types of reflection, concerning spectral and angular distributions. Furthermore, an OVD containing several different grating patches is evaluated. The device uses automatically adjusting exposure time to provide maximum signal dynamics and is capable of doing steps as small as 0.01°. However, even 2° steps for the detector movement showed that this device is more than capable of characterizing even the most complex reflecting surfaces. This study presents sRGB visualizations, discussion of bidirectional reflection, and accurate grating period calculations for all of the grating samples used.

Suitability of goniospectrophotometric space curves as appearance fingerprints.

Goniospectrophotometric space curves were obtained by summation of spatially under-sampled bidirectional reflectance distribution function over all directions and repeating this for all wavelengths in the visible spectral region. This gives a 3D goniospectrophotometric curve called an xDNA graph. Systematic analysis applying 19 measurement geometries confirms existence of characteristic shapes of the graph for all optically similar samples. This enables distinguishing between differently rough samples, an interference effect on various transparent layers, and selective spectral absorption of light in differently thick pigmented coatings. Therefore, the considered goniospectrophotometric space curves could serve as an appearance fingerprint of such samples.

Goniospectrophotometric space curves of diffraction gratings and their applicability as appearance fingerprints.

The bidirectional reflectance distribution functions of diffraction gratings were calculated by applying diffraction theory and transformed into goniospectrophotometric space curves. Gratings with parallel sinusoidal grooves having periods of 1-3.5 µm and amplitudes below 0.2 µm were analyzed. The obtained goniospectrophotometric space curves consist of lines with different slopes and possible interconnections. The slope of the lines is directly connected to the grating period and the length to the period and the amplitude. Such curves could be regarded as a simple appearance fingerprint of a diffraction grating. The ability of portable multiangle spectrophotometers to provide them for diffraction gratings is analyzed.