Subtractive Mixing Research Articles

Unmixing and pigment identification using visible and short-wavelength infrared: Reflectance vs logarithm reflectance hyperspaces

Hyperspectral imaging has recently consolidated as a useful technique for pigment mapping and identification, although it is commonly supported by additional non-invasive analytical methods. Since it is relatively rare to find pure pigments in aged paintings, spectral unmixing can be helpful in facilitating pigment identification if suitable mixing models and endmember extraction procedures are chosen. In this study, a subtractive mixing model is assumed, and two approaches are compared for endmember extraction: one based on a linear mixture model, and the other, nonlinear and Deep-Learning based. Two spectral hyperspaces are used: the spectral reflectance (R hyperspace) and the -log(R) hyperspace, for which the subtractive model becomes additive. The performance of unmixing is evaluated by the similarity of the estimated reflectance to the measured data, and pigment identification accuracy. Two spectral ranges (400 to 1000 nm and 900 to 1700 nm) and two objects (a laboratory sample and an aged painting, both on copper) are tested. The main conclusion is that unmixing in the -log(R) hyperspace with a linear mixing model is better than for the non-linear model in R hyperspace, and that pigment identification is generally better in R hyperspace, improving by merging the results in both spectral ranges.

Comparison of Imaging Models for Spectral Unmixing in Oil Painting.

The radiation captured in spectral imaging depends on both the complex light–matter interaction and the integration of the radiant light by the imaging system. In order to obtain material-specific information, it is important to define and invert an imaging process that takes into account both aspects. In this article, we investigate the use of several mixing models and evaluate their performances in the study of oil paintings. We propose an evaluation protocol, based on different features, i.e., spectral reconstruction, pigment mapping, and concentration estimation, which allows investigating the different properties of those mixing models in the context of spectral imaging. We conduct our experiment on oil-painted mockup samples of mixtures and show that models based on subtractive mixing perform the best for those materials.

Printing the light

AbstractThis paper explores the relationship between additive and subtractive mixing for colour printing. Using Spectraval mica pigments (Merck)—marketed as RGB pigments—colour is generated by selective reflection and prints are based on additive colour mixing principles, that when printed onto black paper, create white and a range of colours. Although currently used mostly for decorative effects, they can be the basis of additive 'process' inks, that present new opportunities for and challenges to traditional print markets. The viewing angle dependency of their selective reflection favours applications in security printing similar to the holograms on bank cards for example. Traditional measurement and modelling methods are difficult to apply due to the layering and irregular dispersion of pigments.

Colour Deceives Continually

This paper explores the relationship between additive and subtractive mixing for printing colour. Using mica pigments that are based on additive colour mixing principles, that when combined, create white. Although currently used for decorative effects for printing, can present a challenge to traditional print markets. We describe different plate making and printing methods for photographic and photomechanical processes, and discuss their applications and limitations.

What are we looking at when we say magenta? Quantitative measurements of RGB and CMYK colours with a homemade spectrophotometer

We address some issues in colour theory, which are of relevance from an educational perspective. Spectra of emitted RGB and of transmitted CMYK colours are quantitatively processed and analysed with quite inexpensive homemade instruments, making use of smartphones as affordable digital cameras. LCD monitors and paper sheets with pigments coming from a laser printer are used to point out the basic differences between additive and subtractive colour formation. As an especially relevant aspect, we point out how it is possible to construct a simple model to explain the subtractive mixing process in terms of convolution of primary colour filters. The analysis presented in this work is particularly suited for enhancing the need for a proper understanding of the physiology of human eye–brain action in light acquisition and perception of colours.

Multiport Reflectometer Based on Subtractive Mixing

A compact multiport reflectometer using a new subtractive mixing scheme for the determination of reflection coefficients in the frequency range of 1–10 GHz is proposed. Compared with classical multiport reflectometers, the architecture proposed reduces the design complexity. Comparison between experimental results obtained from the proposed reflectometer and those given by a conventional network analyzer is given.

REPRODUCTION OF MULTI-COLOURED ARTWORK IN WOVEN FORM WITH REDEFINED SUBTRACTIVE COLOUR SYSTEMS

This study enhances the capability to reproduce multi-coloured images in woven Jacquard forms where weave structure and pattern design were considerably involved in fabrication. In modern weaving, great convenience and efficiencies were established in both production and design process through digitalisation, while the colour adoption has been constrained as the applicable number of figuring yarns were limited. The enhancement toward colour realisation is traditionally related to weaving capability. Surface colour display is dominated by additive, subtractive or optical mixing (Mathur, 2007). An additive colour system offers the largest gamut among output models yet, the light mixing principle is not suitable to apply to weave colour creation. Pre-dyed opaque yarns are used and juxtaposed; small particles of yarn colours reflect lights and they were observed as a certain form of colour. The common and crucial criterial pertinent to an optical mixing of weave colours were aligned more with the subtractive mixing principle. A weave pattern was designed by subtractive primary colour classification and a multi-weft figuring method. Secondary colours are theoretically produced when coupled CMY layers are mixed(i.e., cyan + magenta = blue, cyan + yellow = green, magenta + yellow = red) and black is generated when all CMY primaries are mixed (Berns, 2000);however, non-bendable colours of threads are employed for colour reproduction in weaving and there is a limit to adopt a pigment mixing principle in the woven form. Therefore, each weave pattern required a modification to redefine primary colour regions and densities once an original artwork was separated and presented in greyscales levels. The weave patterns in an original subtractive scheme were altered by applying region-based segmentation to maximise the accessible colour gamut. In this study, the weaving application developed for the multi-coloured image was introduced and the design process was explained based on a practical experiment proceeded with a newly developed weaving application.

The effects of coloured base fabric on electrochromic textile

The colour of electrochromic fabric, and its colour transitions, was explored on the basis of variations in underlying fabric colour. A complete understanding of this phenomenon is essential for the fabric’s use in full-colour wearable displays or other applications. Previous work in this area utilised only white-coloured starting materials. Herein, a large colour swathe of fabrics was chosen. They were loaded with the commercially available conducting polymer, PEDOT-PSS, and were coated with an electrochromic polymer. These all-organic substrates were then switched between their two coloured states via reversible oxidation and reduction. At every stage, coordinates in the CIE Lu′v′ colour space were measured. It was found that darker colours decrease the overall contrast of the electrochromic, with black being entirely unobservable. More vibrant colours affected the observed colour through a subtractive mixing effect, as expected, but no adverse contrast effects between the two states of the electrochromic system was observed.

Colour mixing based on daylight

Colour science is based on the sensation of monochromatic light. In contrast to that, surface colours are caused by reflection of wide sections of the daylight spectrum. Non-spectral colours like magenta and purple appear homologous to colours with spectral hue, if the approach of mixing monochromatic light is abandoned. It is shown that a large region of the colour space can be covered by mixing three primary colours derived from lossless spectral decomposition of daylight. These primaries are specified by hue, saturation and luminosity. Duality of additive and subtractive mixing is formulated quantitatively. Experimental demonstrations of calculated results are suggested. This paper is intended for undergraduate optics courses, and advanced interdisciplinary seminars on arts and physics.

Colorimetry: fundamentals and applications

About the Authors. Series Preface. Preface. Introduction. 1 Light, Vision and Photometry. 1.1 Light. 1.2 Mechanism of the Human Eye. 1.3 Adaptation and Responsivity of the Human Eye. 1.4 Spectral Responsivity and the Standard Photometric Observer. 1.5 Definition of Photometric Quantities. 1.6 Photometric Units. 1.7 Calculation and Measurement of Photometric Quantities. 1.8 Relations Between Photometric Quantities. Note 1.1 Luminous Exitance, Illuminance, and Luminance of a Perfect Diffusing Plane Light Source. Note 1.2 Luminance and Brightness. 2 Color Vision and Color Specification Systems. 2.1 Mechanism of Color Vision. 2.2 Chemistry of Color Vision. 2.3 Color Specification and Terminology. 2.4 Munsell Color System. 2.5 Color System Using Additive Color Mixing. Note 2.1 Colorfulness, Chroma and Saturation. 3 CIE Standard Colorimetric System. 3.1 RGB Color Specification System. 3.2 Conversion into XYZ Color Specification System. 3.3 X10Y10Z10 Color Specification System. 3.4 Tristimulus Values and Chromaticity Coordinates. 3.5 Metamerism. 3.6 Dominant Wavelength and Purity. 3.7 Color Temperature and Correlated Color Temperature. 3.8 Illuminants and Light Sources. 3.9 Standard and Supplementary Illuminants. Note 3.1 Derivation of Color Matching Functions from Guild and Wright's Results. Note 3.2 Conversion between Color Specification Systems. Note 3.3 Conversion into XYZ Color Specification System. Note 3.4 Imaginary Colors [X] and [Z]. Note 3.5 Photometric Quantities in the X10Y10Z10 Color System. Note 3.6 Origin of the Term 'Metamerism'. Note 3.7 Simple Methods for Obtaining Correlated Color Temperature. Note 3.8 Color Temperature Conversion Filter. Note 3.9 Spectral Distribution of Black-body Radiation. 4 Uniform Color Spaces. 4.1 Uniform Chromaticity Diagrams. 4.2 Uniform Lightness Scales (ULS). 4.3 CIE Uniform Color Spaces. 4.4 Correlates of Perceived Attributes. 4.5 Comparing CIELAB and CIELUV Color Spaces. 4.6 Conversion of Color Difference. 4.7 Color Difference Equations Based on CIELAB. Note 4.1 Calculation of Munsell Value V from Luminous Reflectance Y. Note 4.2 Modified CIELAB and CIELUV Equations for Dark Colors. Note 4.3 Other Color Difference Formulas. Note 4.4 Direct Calculation of Hue Difference &delta H. 5 Measurement and Calculation of Colorimetric Values. 5.1 Direct Measurement of Tristimulus Values. 5.2 Spectral Colorimetry. 5.3 Geometrical Conditions for Measurement. 5.4 Calculation of Colorimetric Values. 5.5 Colorimetric Values in CIELAB and CIELUV Uniform Color Spaces. Note 5.1 Spectral Colorimetry of Fluorescent Materials. Note 5.2 Reference Standard for Reflection Measurements. 6 Evolution of CIE Standard Colorimetric System. 6.1 Additive Mixing. 6.2 Subtractive Mixing. 6.3 Maximum Value of Luminous Efficacy and Optimal Colors. 6.4 Chromatic Adaptation Process. 6.5 von Kries' Predictive Equation for Chromatic Adaptation. 6.6 CIE Predictive Equations for Chromatic Adaptation. 6.7 Color Vision Models. 6.8 Color Appearance Models. 6.9 Analysis of Metamerism. Note 6.1 Color Mixing Rule. Note 6.2 Lambert-Beer Law. Note 6.3 Method for Calculating the Maximum Value of the Luminous Efficacy of Radiation. Note 6.4 Method for Calculating Optimal Colors. Note 6.5 Method for Obtaining Fundamental Spectral Responsivities. Note 6.6 Deducing von Kries' Predictive Equation for Chromatic Adaptation. Note 6.7 Application of von Kries' Equation for Chromatic Adaptation. Note 6.8 Application of CIE 1994 Chromatic Adaptation Transform. Note 6.9 Theoretical Limits for Deviation from Metamerism. 7 Application of CIE Standard Colorimetric System. 7.1 Evaluation of the Color Rendering Properties of Light Sources. 7.2 Evaluation of the Spectral Distribution of Daylight Simulators. 7.3 Evaluation of Whiteness. 7.4 Evaluation of Degree of Metamerism for Change of Illuminant. 7.5 Evaluation of Degree of Metamerism for Change of Observer. 7.6 Designing Spectral Distributions of Illuminants. 7.7 Computer Color Matching. Note 7.1 Computation Method for Prescribed Spectral Distributions. Appendix I Basic Units and Terms. AI.1 SI Units. AI.2 Prefixes for SI Units. AI.3 Fundamental Constants. AI.4 Greek Letters. Appendix II Matrix Algebra. AII.1 Addition and Subtraction of Matrices. AII.2 Multiplication of Matrices. AII.3 Inverse Matrix. AII.4 Transpose Matrix. Appendix III Partial Derivatives. Appendix IV Tables. References. Bibliography. Index.

How Well Can People Predict Subtractive Mixing?

How Well Can People Predict Subtractive Mixing?

Examples of interference and the color pigment mixtures green with red and red with green

AbstractIn industrial paint formulations, interference pigments are usually mixed with color pigments. Transparent interference pigments mix together according to the laws of additive mixing and color pigments to the laws of subtractive mixing. The behavior of both types differs depending on whether similar colors such as pearl green and green or contrasting colors such as pearl green and red are mixed. In this article examples of these differences for color measurement are discussed, along with showing the resulting charts. © 2001 Wiley Periodicals, Inc. Col Res Appl, 27, 276–281, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10063

Predicting the colour of trichromatic prints

AbstractThe colour resulting from the partial overlap of tiny dots of cyan, magenta, and yellow inks in a matrix is difficult to predict. A method of simulating it on the macro‐scale has been devised by measuring discs with coloured sectors using a spectrophotometer. Here the separate colours are mixed within the integrating sphere of the instrument. Although subtractive mixing occurs where colours overlap, the overall result to the eye/brain is interpreted by additive means. The result of mixing known areas of coloured surfaces additively was predicted successfully by Maxwell in the last century. His method, combined with the use of the CIE System, has been successfully used to predict the coordinates of the mixture of coloured sectors measured on the spectrophotometer. The theoretical model developed applies to trichromatic or polychromatic printing, whatever the substrate. © 1995 John Wiley & Sons, Inc.

Applications of Colour Physics to Textiles

Both additive and subtractive mixing of colours are discussed, leading to the C.I.E. system of colour specification, which is based on three primary colours and additive mixing. Measuring instruments and some types of illuminants are considered. Applications include examples of metameric matches, dichroism, quality control, and some problems in the blending of coloured fibres.