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This article represents an analytical formulation for optical properties of absorbing metallic nanoparticles in visible region of electromagnetic spectrum based on Mie theory, in order to find a clear relationship between fundamental characteristics of nanoparticles with their spectral behavior and color coordinate in CIE-LAB color space. Calculations were performed on nanoparticles with various diameters (d 5 50, 100, and 200 nm), as well as complex refractive index with different real (n 5 1.5, 2.0, 2.5, and 3.0) and imaginary (k 5 0.001 and 0.1) parts. Obtained results reveal that scattering phenomena in nanoparticles are strongly linked to the particle size parameter and complex index of refraction. The results indicate that the reflectance and lightness (L*) of nanoparticles increases as a result of increase in their size and real part of complex refractive index and decrease with increasing the imaginary part of complex refractive index. The CIELAB colorimetric system was used for analysis the color of nanoparticles. According to obtained results, all nanoparticles have greenish-blue color, and undergo color change as a result of varying in their size and the complex refractive index.

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Fluorescent materials are now a critical field of research due to their unique excitation and emission properties that can be tailored to specific fluorescence detection technologies. In this work, a procedure is described to approximate the emission spectral data of fluorescent materials of different types from their excitation spectral data using principal component analysis (PCA) technique. First, PCA as a statistical and mathematical method was used to reconstruct the excitation and emission spectra of training dataset and then, the approximation was accomplished by multiple linear regression (MLR).The performance of obtained function was examined on testing dataset. Afterward, CIE tristimulus values of the fluorescent samples were calculated based on ASTM, E2152-12 standard test method. The colorimetric accuracy was then evaluated by calculating the geometric differences in CIE tristimulus values X, Y, and Z for the 1964 standard colorimetric observer under illuminant D65. The obtained results show a good curve fit between the actual emission spectra and recovered emission spectra. In addition, based on cumulative variance and root mean square (RMS), eight principal components were selected as optimum number of principal components for prediction of emission spectra data.

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