Color Space Mathematical Modeling Using Microsoft Excel - Journal of

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Color Space Mathematical Modeling Using Microsoft Excel M. J. Delgado-González, Y. Carmona-Jiménez, M. C. Rodríguez-Dodero, and M. V. García-Moreno* Department of Analytical Chemistry, University of Cadiz, Puerto Real, Cádiz 11510, Spain

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S Supporting Information *

ABSTRACT: Colorimetry allows every color to be defined as a combination of three values, known as color coordinates. Color coordinates allow researchers to universalize and standardize their color measurements, and nowadays, determining the color coordinates of samples is a routine method applied by organic and analytical chemists, students, and specialists like enologists. Although the colorimetry method requires a simple experimental procedure, many students, researchers and teachers might find the mathematical treatment of the data too difficult. In this paper, we introduce two workbooks using Microsoft Excel with Microsoft Visual Basic that simplify the use of colorimetry: one of these workbooks is specifically oriented to students and teachers, and it includes explanations and information about each color model. The second workbook is aimed at researchers, and it allows them to introduce and analyze numerous samples at the same time. Finally, another workbook has been included that contains various sample spectra that teachers can use to improve student comprehension of color coordinates. KEYWORDS: First-Year Undergraduate/General, Graduate Education/Research, Analytical Chemistry, Organic Chemistry, Computer-Based Learning, Acids/Bases, Agricultural Chemistry, Dyes/Pigments

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INTRODUCTION In the fields of chemistry and enology the determination of the color spaces of liquid samples is widely applied. For example, chemists evaluate color using the CIE L*a*b* model of organic dyes and colorants1−5 and pH indicators,6−8 and enologists analyze the color of wine and spirit samples.9−11 This procedure is officially described by the International Organization of Vine and Wine (OIV) as “one of the most important visual features that provide a large amount of information”.12 Numerous papers have been published on the importance of teaching students color evaluation processes.13,14 Although these methods are easily understandable for students, the most general method of determining the color of a sample requires the quantification of three values known as color coordinates. Although the experimental procedure is quite simple, the determination of color spaces of samples involves long and difficult mathematical equations that have been developed by the International Commission on Illumination (CIE) and these are explained in their technical reports.15 For this reason, in this paper we have collected the expressions for some color spaces in Microsoft Excel with the aim of simplifying the mathematical treatment for students, researchers, and teachers, in addition to explaining and facilitating the understanding of color coordinates for students of chemistry and enology.

which are excited by light at different wavelengths of the visible spectrum, i.e, red, green, and blue light, respectively. Therefore, as explained by the trichromatic theory of color vision, human perception of color depends on the wavelengths of the light that interacts with our photoreceptors, and it can be defined as a mixture of three primary light colors: red, green, and blue. CIE defines 3D graphs that represent all colors that humans can see, with each one defined as a combination of three values known as color coordinates, which are determined by mathematical formulas that are expressed considering the absorbance spectra of human cone cells. In this way, each color coordinate is usually related with one of its color properties: for example, in the CIE L*a*b* space model the L* parameter is related to the luminosity of the color, the a* parameter defines the red or green component of the color, and the b* parameter defines the yellow or blue component. Importance of Colorimetry

The fastest and cheapest color-determination method is the simple observation of the sample. This method has two drawbacks: first, two different analysts can observe the same color and obtain different results, and second, the color depends on the illumination of the sample, so if the analysis is carried out under different lighting conditions, e.g., daylight at different hours, the results may change. This effect is represented in Figure 1: under cold lighting conditions, colors are sharper and more brilliant than colors that are observed

What Is a Color Space Model?

Human cone cells are photoreceptors that are responsible for the perception of each color that we observe. There are only three types of human cone cells, namely, long wavelength cones, medium wavelength cones, and short wavelength cones, © XXXX American Chemical Society and Division of Chemical Education, Inc.

Received: September 4, 2017 Revised: July 9, 2018

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DOI: 10.1021/acs.jchemed.7b00681 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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Figure 1. Fruit, wine, and olive oil, photographed under eight different light sources. In the first row, from left to right: candle light, warm light, solar light, and cold light. In the second row, from left to right: red light, orange light, green light, and blue light. Photographs were taken with a Nikon D300 digital camera in manual mode with white balance in the sunlight position, with a focal length of 18 mm, 4.5 diaphragm aperture, and shutter speeds of 1/30 sec for photos in the first row, and 1/15 sec for photos in the second row. A JEDI lighting LED E27 (LTL International, Belgium) color-changing bulb was used as the light source.

It is important to remember to accept the use of macros when using these sheets by clicking the enable content button in the message that appears at the top of the sheet.

under a warmer light source. In fact, in this example, yellowish and reddish lights produce colors that cannot be easily distinguished. Given the drawbacks outlined above, CIE colorimetry methods were developed in order to universalize and standardize color determinations and results independently of the light conditions and/or the analyst. This is possible because colorimetry mathematical color spaces are defined using two standard parameters: a standardized lighting source, which fixes the effect of different lighting conditions over the results, and the observer degree, which removes the human factor from the analysis. In this paper, all equations are expressed for a D65 CIE standardized lighting source, proposed by the CIE to represent mean daylight, with a color temperature of 6500 K16 and an observer degree of 10°. Therefore, the use of these standard parameters in addition to all universal colorimetry formulas was an important improvement to achieve reproducibility of color results.

Obtaining the Spectrum of a Sample

As described by ISO 11664-4,17 all color space determinations must begin by obtaining the transmittance or reflectance spectrum of the sample in the range 380−780 nm. Transmittance spectra must be obtained for liquid samples, and these samples must be transparent and must not contain suspended particles. Reflectance spectra must be obtained for solid samples, and these must have a totally flat surface. Liquid samples must be introduced into a 10 mm cuvette, which is the reference path length, in order to obtain universal color coordinates. If possible, the spectrum should be recorded with a wavelength resolution of 5 nm as the factors and formulas provided are expressed for this resolution. The blank is measured with distilled water if the sample is liquid or with a blank solid standard if the sample is solid (for example, for reflectance analyses commercial standards of CaCO3 are often used). Once the transmittance or reflectance spectra of all the samples have been measured, a mathematical treatment is required to obtain the color coordinates.18 The mathematical expressions employed in the most commonly used color spaces (CIE XYZ, CIE L*a*b*, CIE LCH, and RGB) are defined in the file named Color-spaces-formulas.pdf, which can be found in the Supporting Information.

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DETERMINING THE COLOR SPACES OF THE SAMPLE WITH MICROSOFT EXCEL Several spreadsheet files were designed to carry out the mathematical treatment. These spreadsheets within workbooks allow one to obtain the color coordinates from the transmittance spectra. Specifically, two Excel workbooks were developed: Template-5 nm-for-Students.xlsm and Template-5 nm-for-Researchers.xlsm. The file Template-5 nm-for-Students.xlsm was created for use by teachers and students in their laboratory color practical classes or to facilitate classroom explanation. The spreadsheets in this workbook are protected so that formulas, graphs, or images cannot be accidentally changed or moved. This file contains five sheets that include explanations and recommendations that may be helpful for students. The file Template-5 nm-for-Researchers.xlsm was created for use by researchers in their laboratory color experiments, and 10 sample columns were added. This Workbook is not protected, so, if desired, all columns can be copied and pasted so that the sample list can be as large as the researcher requires. This file, which only has one sheet, does not include as much information and explanation as the Workbook for students, but all color parameters of different samples are automatically determined at the same time when the spectra are pasted in the white columns.

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USING TEMPLATE-5NM-FOR-STUDENTS WORKBOOK

First Sheet: Template 5 nm

In the first sheet, called Template 5 nm, the sample spectrum must be introduced so that all formulas can automatically return the color space coordinates. In order to understand this sheet better, some instructions have been introduced in the student’s file. Second Sheet: CIE L*a*b*

The second sheet, called CIE L*a*b*, automatically returns text with the L*a*b* results and their meaning, and it automatically express the resulting L*, a*, and b* values in two graphs: the a*−b* graph and the L* graph (Figure 2). In addition, some information about this color space and the meaning of its parameters are given. B



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Figure 2. a*−b* graph and L* graph for (a) an orange dye and (b) a violet dye. In the a*−b* graph, the black dot represents the point (a*, b*) of the sample. In the L* graph, the red line represents the L* of the sample.

Figure 3. C*−H* graph and L* graph for (a) an orange dye and (b) a violet dye. In the C*−H* graph, C* is graphically the length of the dotted line, and H* is represented as the angle of the dark sector. In the L* graph, the red line represents the L* value for the sample.

Third Sheet: CIE LCH

The third sheet, called CIE LCH, automatically returns text with the results and a brief explanation of their meaning, and it also automatically expresses the obtained L*, C*, and H* values in two graphs: the C*−H* graph and the L* graph (Figure 3). Fourth Sheet: RGB

As in the previous sheets, the fourth sheet, called RGB, automatically expresses the obtained R, G, and B values in three graphs: the R graph, the G graph, and the B graph (Figure 4), and the values obtained for each parameter are summarized. Fifth Sheet: Formulas

Figure 4. RGB graphs for (a) an orange dye and (b) a violet dye. The white line represents the R, G, and B values of the sample.

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Finally, the sheet called Formulas contains a summary of all equations proposed by the CIE and all formulas used in Microsoft Excel. This sheet was included because teachers may want to introduce some equations to their students, or they may want the students to understand that mathematical treatment of the sample spectrum is not as easy as this spreadsheet file makes it.

EXAMPLES The file Examples.xlsx can be found in the Supporting Information. This file includes four spectra: one spectrum of an orange dye, one of a violet dye, one of a blue dye, and another of a green dye. These four dyes were chosen because C



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they present different a* and b* signs, so teachers can use these examples to improve their explanations. In addition, in order to aid the explanation of the L* parameter, another spectrum of a dark green dye has been included.

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OBTAINED RESULTS WITH STUDENTS These spreadsheet files have been used by chemistry and enology students at our university in order to discuss their experimental results in a laboratory report. Specifically, for chemistry students the color space parameters of different pH indicators (phenolphthalein, bromothymol blue, and methyl orange) were measured at different pH values. Furthermore, enology students determined the color space coordinates of different wine and alcoholic beverage samples. The newly developed Microsoft Excel workbooks described here, which not only offer more information on the results but also allow a cell to be colored with an almost identical color to the real sample, have allowed students to understand better and improve their discussion of the results in their laboratory reports. Two fragments of students’ laboratory reports can be observed in Color-laboratory-reports.pdf, which is included in the Supporting Information. In the first report, the workbook was used in order to better understand the effect of different quantities of polivinylpolipyrrolidone (PVPP) over the color of red wines. In the second report, the workbook was used in order to describe the color of a wood-aged spirit. Both reports have been translated from Spanish to English for better comprehension. The files described here were also used in a classroom explanation as a visual and interactive aid. In all cases, the results were satisfactory, and students commented that the sheets provided an easy way to understand color space.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

M. J. Delgado-González: 0000-0003-3464-2397 M. V. García-Moreno: 0000-0002-5718-3296 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank S. Delgado for use of her laboratory reports. REFERENCES

(1) Crews, P. C. The fading rates of some natural dyes. Stud. Conserv. 1987, 32 (2), 65−72. (2) Grabchev, I.; Meallier, P.; Konstantinova, T.; Popova, M. Synthesis of some unsaturated 1,8-naphthalimide dyes. Dyes Pigm. 1995, 28 (1), 41−46. (3) Chen, C. C.; Wang, I. J. Synthesis of some pyridone azo dyes from 1-substituted 2-hydroxy-6-pyridone derivatives and their colour assessment. Dyes Pigm. 1991, 15 (1), 69−82. (4) Vankar, P. S.; Shanker, R. Ecofriendly ultrasonic natural dyeing of cotton fabric with enzyme pretreatments. Desalination 2008, 230 (1−3), 62−69. (5) Senthilkumar, M. Modelling of CIELAB values in vinyl Sulphone dye application using feed-forward neural networs. Dyes Pigm. 2007, 75 (2), 356−361. (6) Barbosa, J.; Bosch, E.; Roses, M. Neutralisation indicators in 2methylpropan-2-ol: their pKa values and chromatic parameters of transition ranges. Analyst 1987, 112 (2), 179−184. (7) Fernandez, A. M. C.; Chozas, M. G. Colour specification of pyridine-2-aldehyde and 6-methylpyridine-2-aldehyde p-nitrophenylhydrazones as indicators for pH determination. Talanta 1987, 34 (7), 673−676. (8) Kim, M. J.; Jung, S. W.; Park, H. R.; Lee, S. J. Selection of an optimum pH-indicator for developing lactic acid bacteria-based timetemperature integrators (TTI). J. Food Eng. 2012, 113 (3), 471−478. (9) Gil-Muñoz, R.; Gómez-Plaza, E.; Martínez, A.; López-Roca, J. M. Evolution of the CIELAB and other spectrophotometric parameters during wine fermentation. Influence of some pre and postfermentative factors. Food Res. Int. 1997, 30 (9), 699−705. (10) Delgado-González, M. J.; Sánchez-Guillén, M. M.; GarcíaMoreno, M. V.; Rodríguez-Dodero, M. C.; García-Barroso, C.; Guillén- Sánchez, D. A. Study of a laboratory-scaled new method for the accelerated continuous ageing of wine spirits by applying ultrasound energy. Ultrason. Sonochem. 2017, 36, 226−235. (11) Pérez-Magariño, S.; González-Sanjosé, M. L. Application of absorbance values used in wineries for estimating CIELAB parameters in red wines. Food Chem. 2003, 81 (2), 301−306. (12) OIV. Determination of Chromatic Characteristics According to CIELab (Resolution Oeno 1/2006), Method OIV-MA-AS2-11:2006. In Compendium of International Methods of Wine and Must Analysis; Paris, 2014; Vol. 1; pp 1−16. (13) Chaloupka, K.; Varanka-Martin, M.; Pringle, D. L. Crepe Paper Colorimetry. J. Chem. Educ. 1995, 72 (8), 722. (14) Campos, A. R.; Knutson, C. M.; Knutson, T. R.; Mozzetti, A. R.; Haynes, C. L.; Penn, R. L. Quantifying Gold Nanoparticle

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IN CONCLUSION Two Microsoft Excel workbooks have been included and described in this paper, These sheets, based on the transmittance spectrum of a sample, enable the values of the color coordinates to be obtained in four different color spaces (CIE XYZ, CIE L*a*b*, CIE LCH, and RGB). The first Excel sheet was developed so that students can understand the most relevant color spaces, as well as to facilitate the work of teachers when offering explanations for this topic. This sheet has previously been used in enology and chemistry lectures at the University of Cádiz, and it has been an improvement on the previous teaching methods. The second Excel sheet was developed so that researchers working in the laboratory can easily obtain the coordinates of the color spaces most commonly applied in the scientific community. For this reason, this sheet provides less information that the first sheet, although it can be used to introduce several spectra and thus obtain the color parameters of several samples at the same time.

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mathematical treatment and explanations for students and teachers (Template-5 nm-for-Students.xlsm), Microsoft Excel workbook with examples of sample spectra (Examples.xls), and file summarizing the formulas and explanations of all related color spaces (Color-spacesformulas.pdf) (ZIP)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00681. Two extracts from students’ laboratory reports (PDF) Microsoft Excel workbook for colorimetric mathematical treatment for researchers (Template-5 nm-for-Researchers.xlsm), Microsoft Excel workbook for colorimetric D



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Concentration in a Dietary Supplement Using Smartphone Colorimetry and Google Applications. J. Chem. Educ. 2016, 93 (2), 318− 321. (15) CIE. Colorimetry CIE 15:2004, 3rd ed.; Vienna, Austria, 2004. (16) ISO. ISO 11664-2:2007/CIE S 014-2/E:2006. Joint ISO/CIE Standard: ColorimetryPart 2: CIE Standard Illuminants; Switzerland, 2007. (17) ISO. ISO 11664-4:2008/CIE S 014-4/E:2007. Joint ISO/CIE Standard: ColorimetryPart 4: CIE 1976 L*a*b* Colour Space; Switzerland, 2008. (18) ISO. ISO 11664-3:2012/CIE S 014-3/E:2011. Joint ISO/CIE Standard: ColorimetryPart 3: CIE Tristimulus Values; Switzerland, 2012.

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Color Space Mathematical Modeling Using Microsoft Excel - Journal of

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