Colorimetric properties of fluorescent materials depend on the SPD of the illumination. That is why most standards for evaluating them specify the illuminations, which are often hard-to-realize daylight illuminants. The presented method using commercially available LEDs enables accurate enough colorimetric measurements of FWA-treated papers or prints on them illuminated by the specified illuminant. The total spectral radiance factor of a fluorescent specimen, from which most colorimetric values are derived, consists of the luminescent spectral radiance factor and the spectral reflectance factor. This method separately estimates those of FWA-treated paper to add up to the total spectral radiance factor. The luminescent spectral radiance factor is obtained by estimating the SPD of luminescence excited by the specified illuminant as the weighted sum of the multiple SPDs of luminescence excited by the respective narrow band LED emissions at different wavelengths. The LEDs and their weights are determined optimally for generally used papers. The spectral reflectance factor is derived from the estimated SPD of the radiation with fluorescence excluded from the paper illuminated by visible illumination. The method was applied with five different illumination systems each using two or three narrow band LEDs in the excitation range. They were evaluated by measuring the total spectral radiance factors by D50 of seven FWAtreated papers and CMYK prints on four papers. The derived colorimetric values were compared to the respective references by the ideal D50. K E Y W O R D Sfluorescent spectral radiance factor, FWA-treated paper, multi-wavelength excitation, total spectral radiance factor 1 | I NT ROD UCTI ON Today, paper is nearly always treated with FWA (Fluorescent Whitening Agent) additive, which enhances whiteness of paper by converting ultraviolet and shortwave visible energy of illumination into "blue" fluorescence. Because fluorescence depends on both the spectral quantum yield of the FWA and the SPD (Spectral Power Distribution) of the illumination, the relative spectral nature of the illumination needs to be specified when evaluating the colorimetric properties of FWA-treated paper or prints on the paper. For example, ISO5631-1, 2, and 3 1-3 for evaluating the color of paper require CIE (standard) illuminant C, D65, and D50 respectively and the M0 and M1 irradiation conditions of In this study, the SPDs of total, luminescent, and reflective radiations (total, luminescent, and reflective SPDs hereinafter) caused by a specific illumination I are expressed as E T (I, k), E L (I, k), and E R (I, k) respectively. Similarly the

In this article, a new method for measuring a total spectral radiance factor of a FWA-treated sample illuminated by a specific standard illuminant is introduced. The method replaces an unstable real fluorescent standard by a bi-spectral luminescent radiance factor data, which works as a virtual fluorescent standard (VFS) by knowing spectral intensity distributions of illuminations applied to the sample. The method utilizes two illuminations I 1 and I 2 whose relative spectral intensity distributions are different from each other and synthesizes a virtual illumination presenting the identical fluorescent spectral radiance factor to that presented by the standard illuminant with the VFS of the specific bi-spectral luminescent radiance factor by linearly combining I 1 and I 2 with the suitable weighting factors. The applicability of the method is examined in principle by comparing ISO brightness and CIE whiteness index of fluorescent standard paper as a test sample obtained by this new method to the assigned values.

The virtual fluorescent standard (VFS) method is a new approximation method for the practical measurement of the colorimetric properties of an object treated with fluorescent whitening agent (FWA). The essential requirement of the VFS method is that the bi‐spectral characteristics of the VFS must be similar in curve shape to those of the object to be measured. In the case of an object printed on an FWA‐treated substrate, the bi‐spectral characteristics will vary depending on not only the substrate but also the printed ink films.  In this study, two simplified VFS methods, one using the bi‐spectral characteristics of the substrate and the other using those of typical paper as the VFS instead of those similar to each object, were evaluated. The evaluation was performed using two instrument models for the VFS method with the different illuminations with five sets of 13 samples printed in different colors by five different printer/paper combinations.  In this evaluation, the total spectral radiance factor of each sample was obtained by simulated measurement, that is, it was calculated based on the bi‐spectral radiance factor of the sample and the spectral power distributions of the light source of the instrument. The total spectral radiance factor of each sample under D50 obtained using both VFS models and CIE L*a*b* values derived therefrom were compared with those by the reference model with ideal D50 illumination.  Although the samples are limited, the results shows that both simplified VFS methods remarkably reduce the errors due to fluorescence when compared to the conventional method. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012

Numerical corrections of colorimetric errors caused by positioning error and irregular geometry in multiangle measurements of gonio-apparent coatings are presented. These corrections use a model function approximating the gonio-reflection characteristics of the coating to convert the angular displacement due to those geometric errors to reflectance factor errors to be corrected as well as to estimate the angular displacement conversely from the reflectance factors. The performance of these corrections was evaluated for 11 different gonioapparent coatings using a multiangle geometry conforming to ASTM E2539 consisting of eight subgeometries to which artificial displacements were applied so as to present typical positioning errors or irregular geometries. The results show that both corrections significantly reduce the colorimetric errors for all specimens in all subgeometries sensitive to geometric errors.

Measurements by spectrophotometers more or less suffer from heterochromatic stray light generated in their spectrometers. It is divided into near‐band and off‐band stray lights. While the former appears near the spectral band of the incident flux, the latter distributes broadly across the whole range and is far more problematic from colorimetric point of view. This article presents a practical method for correcting off‐band stray light in dual‐channel array spectrographs often built in modern spectrophotometers. Unlike most correction methods using a line spread function, the presented method estimates the distribution of off‐band stray light across the array as the product of a device‐specific stray light distribution and a total stray light intensity. The latter depends on both the spectral power distribution of an incident flux and a device‐specific rate of change from the incident flux to the off‐band stray light. For further simplification, the method replaces wavelengths by several bands dividing the visible range owing to the moderate spectral dependence of the above rate of change. With those simplifications, the method is practical, effective, and robust enough to work in an inexpensive hand‐held spectrophotometer with the compact spectrograph which often suffers from off‐band stray light. The performance of the method was evaluated with two dual‐channel array spectrographs with and without 2nd‐order‐rejection filter. Specimen lights incident through ten different glass filters were measured and the errors caused by off‐band stray light in the pixel outputs from the array were successfully corrected by the method. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 431–439, 2017