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.

This study focuses on the retrieval of lidar overlap functions at two wavelenghts (355 and 532 nm) for the lidar routinely operated at the EARLINET Granada station, placed in the southeastern Iberian Peninsula. For this aim, aerosol backscatter coefficients retrieved from both Raman and elastic lidar signals were used. The method is based on the fact that aerosol backscatter profiles derived from elastic signals suffer from incomplete overlap effect whereas those retrieved from Raman signals are unaffected. This article reports about the reproducibility of the lidar overlap functions under different atmospheric scenarios and also the impact of some features of the iterative process itself.

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.

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.

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.