Development of a Method to Assess the Color Parameters Spatial Distribution in the MacAdam Steps

Abstract

The paper presents a method to assess uniformity of the chromaticity coordinates spatial distribution in the light-emitting diodes. The method differs by introducing mathematical apparatus of the MacAdam ellipses and makes it possible to numerically assess spatial distribution of these parameters. It includes the following phases: 1) manufacture of the luminiferous composition; 2) luminiferous composition application and production of the LED models; 3) measuring luminous flux, luminous efficiency and color rendering index; 4) regression analysis of the results obtained and samples selection; 5) measuring the selected samples chromaticity in the coordinate space; 6) obtaining the approximating expression and finding the approximation errors; 7) color deviation computation in the MacAdam steps. The developed method was tested on LEDs with three luminiferous samples. Chromaticity coordinates spatial deviations in the MacAdam ellipses steps amounted to 4 units, which corresponds to the visual discrimination boundary in color and suggests further research to increase the color spatial uniformity. It was established that for the LEDs based on the GaN/InGaN crystals in the SMD 5030 housing, approximation by a fourth-degree polynomial of the chromaticity coordinates dependence on the emission angle allowed an error of no more than 4.5 %. The method could be useful to developers and manufacturers of the LEDs

Please cite this article in English as:

Andreeva M.V., Soldatkin V.S., Tuev V.I., et al. Development of a method to assess the color parameters spatial distribution in the MacAdam steps. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2024, no. 1 (146), pp. 4--18 (in Russ.). EDN: AUMIYI

References

[1] Fairchild M.D. Color appearance models. Wiley, 2005.

[2] Domasev M.V., Gnatyuk S.P. Tsvet. Upravlenie tsvetom, tsvetovye raschety i izmereniya [Color. Color management, color calculations and measurements]. St. Petersburg, Piter Publ., 2009.

[3] Bergh A.A., Dean P.J. Light-emitting diodes. Oxford, Clarendon Press, 1976.

[4] Klyushnikov S.V. Svetodiody v osveshchenii [LEDs in lighting]. Moscow, MIEE Publ., 2014.

[5] Trotsiuk L.L., Ton E.S., Tsvirko V.I., et al. Photoluminescent properties of phosphor based on perovskite CsPbBr₃ nanocrystals combined with violet leds. J. Appl. Spectrosc., 2022, vol. 89, no. 5, pp. 869--873. DOI: https://doi.org/10.1007/s10812-022-01440-3

[6] Kazankin O.N., Markovskiy L.Ya., Mironov I.A. Neorganicheskie lyuminofory [Inorganic phosphors]. Moscow, Khimiya Publ., 1975.

[7] Devyatykh E.V., Dadonov V.F. Lyuminestsentnye lampy. Lyuminofory i lyumi-nofornye pokrytiya [Fluorescent lamps. Phosphors and phosphor coatings]. Saransk, MRSU Publ., 2007.

[8] Narukawa Y., Ichikawa M., Sanga D., et al. White light emitting diodes with super-high luminous efficacy. J. Phys. D: Appl. Phys., 2010, vol. 43, no. 35, art. 354002. DOI: https://doi.org/10.1088/0022-3727/43/35/354002

[9] Tuev V.I., Soldatkin V.S., Andreeva M.V., et al. Investigation of phosphor compositions for led filament bulb. J. Phys.: Conf. Ser., 2018, vol. 1115, no. 5, art. 052012. DOI: https://doi.org/10.1088/1742-6596/1115/5/052012

[10] Stokes G.G. Uber die Veranderung der Brechbarkeit des Lichts. Ann. Phys. B, 1852, vol. 163, iss. 11, pp. 480--490. DOI: https://doi.org/10.1002/andp.18521631109

[11] Lisitsyn V.M., Soshchin N.P., Yang yang Y., et al. Photoluminescence characteristics of Yag:Ce, Gd based phosphors with different prehistories. Russ. Phys. J., 2017, vol. 60, no. 5, pp. 862--869. DOI: https://doi.org/10.1007/s11182-017-1150-3

[12] Schubert E.F. Light-emitting diodes. Cambridge Univ. Press, 2006.

[13] Soshchin N.P. Light-emitting diode + powder phosphor = new quality of light. Svetodiody i lazery, 2002, no. 1-2, pp. 60--63 (in Russ.).

[14] Ivchenko G.I., Medvedev Yu.I. Vvedenie v matematicheskuyu statistiku [Introduction to mathematical statistics]. Moscow, LKI Publ., 2009.

[15] Yulaeva Yu.V., Khomyakov A.Yu., Tuev V.I. [Mathematical modeling of the spatial distribution of the luminous intensity of a filamentous emitter for LED lamps]. Elektronnye sredstva i sistemy upravleniya. Mater. dokl. XVI Mezhdunar. nauch.-prakt. konf. Ch. 1 [Electronic Means and Control Systems. Proc. XVI Int. Sci.-Pract. Conf. P. 1]. Tomsk, V-Spektr Publ., 2020, pp. 241--245 (inRuss.).

[16] MacAdam D.L. Visual sensitivities to color differences in daylight. J. Opt. Soc. Am., 1942, vol. 32, iss. 5, pp. 247--274. DOI: https://doi.org/10.1364/JOSA.32.000247

[17] Shaw M., Fairchild M.D. Evaluating the 1931 CIE color-matching functions. Color Res. Appl., 2002, vol. 27, iss. 5, pp. 316--329. DOI: https://doi.org/10.1002/col.10077

[18] Galochkin V.T. Ekonometrika [Econometrics]. Moscow, Yurayt Publ., 2017.

[19] Brown W.R.J., MacAdam D.L. Visual sensitivities to combined chromaticity and luminance differences. J. Opt. Soc. Am., 1949, vol. 39, iss. 10, pp. 808--834. DOI: https://doi.org/10.1364/JOSA.39.000808

[20] Wyszecki G., Fielder G.H. New color-matching ellipses. J. Opt. Soc. Am., 1971, vol. 61, iss. 9, pp. 1135--1152. DOI: https://doi.org/10.1364/JOSA.61.001135