This paper summarizes selected approaches, to generate spectral ray data for different types of spectrally varying light sources including only angular variable as well as spatial and angular variable sources. This includes a description of their general ideas and applications, the required measurements, and their mathematical concepts. Finally, achieved results for an Red/Green/Blue/White-light emitting diode (RGBW-LED) system are shown. Ray tracing simulations of a spatially and angularly spectral varying LED system combined with a spectrally sensitive optical system are qualitatively and quantitatively compared to a colorimetric far-field measurement of the same system. The results demonstrate the potential and benefits of spectral ray files in general.
This appendix explains the application of PMBS to obtain the spectral ray files of the example discussed in this paper in more detail. An even more detailed description and more examples are provided in Ref. .
The first step is the initial basis spectra estimation, which bases on one spectral measurement at main radiance direction. All basis spectra overlapped at the chosen measurement distance.
Figure 12 shows the estimated parametrized basis spectra blue S1(λ, x), red S2(λ, x), green S3(λ, x), and phosphor SP(λ) and compare them to parametrized fits of the basis spectra derived from individual measurements for reference. The resolution of each spectral measurement was 1 nm with a bandwidth of 5 nm. Note that the phosphor reference was derived from a measurement of only the white LED in the lower left corner. While the red and blue basis spectra estimation is very precise, there are slight deviations in the case of the phosphor spectrum and the green LED spectrum due to their large spectral overlap.
However, these spectra are sufficient to choose an appropriate set of filter transmission functions from the standard filters as well as the glass absorption filters shown in Figure 13A and B. Figure 14 shows the four measured ray files using the selected filter set as irradiances in the aperture plane. The angular resolution of each near-field measurement was set to 0.5 deg for both angular dimensions. Each ray file consists of 10 million equally weighted rays. The near-field information is provided by the spatial and angular density of the rays. The numbers above the irradiances in Figure 14 identify the selected glass absorption filters and equal the edge wavelength, where the internal transmission equals 50%.
By utilizing the spectral information from Figures 12 and 13 as well as the projected irradiances in Figure 14, the irradiances of the reconstruction can be estimated and assessed with respect to their spatial separation and their degree of localization . The reconstruction is shown in Figure 15.
While the delocalization of the blue reconstruction occurs because there are two blue LED chips in the system, the delocalization of the red and especially the green LED is a reconstruction artifact. These artifacts can occur due to uncertainties of the spectral transmissions and the basis spectra description.
Finally, the basis spectra can be optimized with respect to the spatial separation and the degree of localization as described above. Figure 16 visualizes the resulting basis spectra and their projected irradiances. They show a clear improvement if they are compared to the reference spectra. Especially, the phosphor spectrum changed significantly, which also reduced the reconstruction artifacts in the projected irradiances. Finally, the spectral ray file can be created utilizing the procedure described in Refs.  and .
This work was supported by the Federal Ministry of Education and Research in the Program Photonics Research Germany (Funder Id: 10.13039/501100002347, contract number 13N13396).
 H.-J. J. Frasch and G. Steinmetz, Proc. SPIE 4769, 54–66 (2002).Search in Google Scholar
 E. H. Adelson and J. R. Bergen, in ‘Computational Models of Visual Processing’, (Vision and Modeling Group, Cambridge, MA, USA, 1991).Search in Google Scholar
 R. Dürr and U. Streppel, in ‘Proceedings of the International Light Simulation Symposium’, Nuremberg, 2012.Search in Google Scholar
 J. Nevoigt, in ‘Licht’, 2018, (Schweizer Licht Gesellschaft, Davos, 2018).Search in Google Scholar
 G. Durinck, F. B. Leloup, J. Audenaert and P. Hanselaer, Light Eng. 25, 103–112 (2017).Search in Google Scholar
 V. Jacobs, J. Audenaert, J. Bleumers, G. Durinck, P. Rombauts, et al., ‘On spectral ray files of light sources using principal component analysis’, in Proceedings of 28th CIE Session (CIE, 2015), 543–547.Search in Google Scholar
 OSRAM Opto Semiconductors GmbH, ‘Application Note: Importing Rayfiles of LED from OSRAM Opto Semiconductors’, (2013).Search in Google Scholar
 D. Hansen, S. Paul and V. Schumacher, in ‘LED Professional Symposium’, (2012).Search in Google Scholar
 Illuminating Engineering Society, ‘IES TM25-13 Ray File Format for the Description of the Emission Property of Light Sources’, (2013).Search in Google Scholar
 I. Rotscholl, K. Trampert, U. Krüger, I. Saynca, F. Schmidt, et al., LED Prof. Rev. 63, 48–56 (2017).Search in Google Scholar
 I. Saynca, K. Trampert and C. Neumann, in ‘Proceedings of the Lux Junior’, Dörnfeld/Ilm, 2017.Search in Google Scholar
 K. Bieske and T. Fiebig, in ‘Licht’, 2014, (NSVV, Den Haag, 2014).Search in Google Scholar
 A. G. Schott, in ‘Optical Filters’, (2014), https://www.schott.com/d/advanced_optics/a81cd277-746f-499d-90d2-38724bd120e5/1.1/schott-optical-filters-2014-catalog-complete-en.pdf (Accessed July 2015).Search in Google Scholar
©2019 THOSS Media & De Gruyter, Berlin/Boston