Análisis de los datos experimentales

prediction of colour and appearance

In this thesis, an understanding of how changes in the colour appearance of materials are related to changes in the processing or physical characteristics of the material is of prime interest. In order for the 3D colour food printer to be able to customise outputs it needs to be able to account for changes in the substrate. The focus in this section therefore, is on effects other than those of added colorants which have been covered earlier in this review.

The degree of light scattering from a material can be altered by changes in the physical properties of the material which, in turn, can affect the perceived intensity of its colour. Such changes are brought about by processing or by deliberate manipulations, or they represent the (usual) variations within a product range. The decrease in scatter causing visual translucency to develop in tomato pericarp in cut fruits with storage time was noted earlier (Section 2.6.2.3). The effects of light scattering from other materials have been quantified and it has been found, for example, that lightness of oil-in-water emulsions increases with increasing droplet concentration and with decreasing droplet size, and decreases the intensity of the colour from the added dye (Chantrapornchai et al., 1998); increasing the surface roughness of chocolate samples (by casting onto sandpaper of decreasing grit size) decreases gloss significantly and exponentially, while values for lightness and for whiteness index (as determined from image analysis) decreased significantly and linearly (Briones et al., 2006). Fabrics made of finer fibres are lighter when dyed with the same amount of dye as fabrics made from coarser fibres (Li et al., 2009). The relative contributions of bulk and surface reflectance, with increasing dye concentration, to measured reflectance differ between fibres of different denier. Coarser fibres have larger diameter providing a longer distance for light to travel meaning more light is absorbed, but as dye concentration increases these fibres display decreasing colour efficiency as

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the contribution of surface reflectance increases; the lower surface curvature of larger diameter fibres results in smoother surfaces compared with finer fibres (Li et al., 2009). The K/S ratio calculated from the reflectance at selected wavelengths of injected-moulded pigmented plastics for automotive parts which differed in their measured gloss, decreased with decreasing gloss; the scattering coefficient increased as the roughness increased (Ariño et al., 2005). In these studies, the only changes made to the samples were to characteristics affecting scattering, such as surface roughness and droplet size and concentration; no other changes, including changes to dye concentration, composition and processing, were made.

A number of studies have gone further than to simply characterise the relationship between changes in light scattering and perceived or measured colour, and have developed mathematical models that show the potential to predict colour from physical measures of surface texture and droplet characteristics. Such models might enable the appearance of food emulsions to be optimised (McClements et al., 1998), increase the performance and efficiency of dye formulations for textile dyeing (Li et al., 2009), and predict the impact of substrate and printer parameters on gloss in xerographic printing (Dalal and Natale–Hoffman, 1999). Some of these models are based on adaptations to the Kubelka-Munk (K-M) equation. In the prediction of food emulsion colour, K-M absorption and scattering coefficients (K and S respectively) were expressed in terms of the absorption and scattering cross-sections of the droplets, and their asymmetry factor, which were calculated by applying diffuse scattering theory (McClements et al., 1998). Predicted and measured reflectance of emulsions that were based on the same concentrations of red food dye, mean droplet size, and droplet concentrations were in good agreement between 380 nm to 600 nm, however predictions overestimated reflectance at higher wavelengths. In the prediction of fabric depth of shade, the ‘colour efficiency’ (equivalent to the dye coefficient relating dye concentration to absorption and scatter) was expressed collectively in terms of fibre diameter, geometric roughness of the fabric, and a dye parameter

(Li et al., 2009). In both cases, surface effects were accounted for – in the emulsions case,

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1998), while in the fabric study surface reflectance constants for each fibre diameter x dye combination were incorporated into the predictions together with predictions of bulk reflectance using K-M Theory (Li et al., 2009).

The distinction between surface and sub-surface effects is also a feature of the model of gloss effects in xerographic printing developed by Dalal and Natale–Hoffman (1999). In this model, measured reflectance is the sum of the portion of total front surface reflectance captured by the detector (with the amount captured in turn depending on both gloss, and on the measurement geometry), and sub-surface ‘intrinsic reflection’. Intrinsic reflection appears to be constant for a given colour, and while not directly measurable, can be derived as the difference between specular included measurements (capturing all light from the sample) and the portion of total front surface reflectance in this measurement mode, which is calculated from the Fresnel equations using normal angle of incidence and refractive index. The portion of total front surface reflectance captured by the detector for use in the predictive model of measured reflectance, for each measurement geometry, was derived using a set of black samples printed on different coated and uncoated papers, and expressed for each geometry as a function of gloss. This model allows measured colour of papers of different colour and gloss to be predicted from the gloss and intrinsic reflection values. The approach used by Dalal and Natale–Hoffman (1999) was used and adapted by Ariño et al. (2005) to model the effect of both gloss and different surface textures on the colour of injection-molded plastics for the automotive industry. Included in this latter study were physical measures of topography (as well as gloss) of injection-molded plaques produced with smooth (glossy), fine and coarse surface textures, and the calculation of absorption/scatter (K-M) ratios based on measured reflectance predicted from the model.

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2.7.1.

Alternative model for print, based on Principal Components

Analysis (PCA)

Having the capability to predict the effect of printing substrate (paper) properties on colour outputs means that time and effort can be saved in not having to profile a printer every time the substrate is changed. As stated earlier (Section 2.5.2), profiles are most often custom generated (Sharma, 2003). For printers, a custom profile will be specific to the printer, paper and ink that were used to build the profile; changes to any of these require the profile to be reconstructed.

Shaw et al. (2003) investigated and compared several methods, including one based on K-M

Theory, for their ability to predict colour on a test substrate, based on the profile for a reference substrate, and a small amount of information about the test substrate. Of these, an empirical method based on Principal Components Analysis (PCA) gave the lowest colour error - the difference between actual and predicted colour - compared to no recalibration. In PCA multivariate data are ‘collapsed’ into orthogonal vectors (or dimensions) which each progressively account for more of the variability in the original data. The reflectance data for a large number of colour patches on the reference substrate were able to be ‘expressed’ in terms of 10 basis vectors. Based on the measured reflectance of the same set of patches on both the reference and test substrates, weights for each spectrum were determined corresponding to the 10 basis vectors. A linear transformation matrix was used to map the reference substrate PCA weights to the test substrate PCA weights. The test substrate PCA weights were then converted back to reflectance spectra.

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Chapter Three:

Literature Review, Part 2 – Customising foods

using 3D colour printing

Part 1 of this Review dealt with the theory and application of coloration techniques used in both food and non-food industries, and which are relevant to the goal of developing a predictive coloration algorithm for a novel 3D colour food printer. Attention now turns, in Part 2, to the specific context of this research, namely the areas of customisation, 3D printing and 3D coloration. As with Part 1, contributions are drawn from various industries, including food. Part 2 ends with conclusions from the entire Review, leading to the aims and objectives of the thesis.