We often see a color shift near the saturated areas of colors sprayed on top of other colors. For example, when white is sprayed over dark backgrounds, a clearly recognizable blue shift occurs. However, a color shift also occurs when some light colors are sprayed over darker colors. In this case a "cold" shift is common. The following experiments try to find out the physical origin of these color shifts.
Titanium White is produced using titanium dioxide (TiO2) and it is very common nowadays in fine arts and in the industry. TiO2 has a polymorphic crystal structure with Rutile and Anatase being the most common forms. The main reasons for its diffusion are that it is chemically inert (it can be used in the food industry also) and it is very opaque thanks to its high refractive index. The Rutile crystal structure has an refractive index of 2.73, while Anatase's is 2.55, letting Rutile's hiding power be 30% higher compared to Anatase. Rutile is the most common form. It has a significant absorption in the violet band between 360 and 400nm, while its spectrum is almost flat on the remaining visible spectrum and it is very close to 1. Even if the spectrum of the saturated pigmented surfaces is flat, the perceived color spectrum depends also on the pigment size.
The optimal pigment size depends on the refractive index difference between pigment and medium, and on the wavelength according to Weber's equation, if the goal is maximizing the light scattering. In order to maximize the scattering (the luminosity of the color), a Rutile pigment should be 0.31 micron for the red color (at 660nm), it should be 0.26 micron for the green color (at 550nm) and it should be 0.21 micron for the blue (at 430nm). A common value used by color manufacturers is 0.25 micron to have a good response all over the visible spectrum , while the most common size is 0.3 for the Anatase crystal structure. A direct consequence of this choice is that single dioxide pigments will scatter better the short wavelength (blue) compared to the reds due to basic electromagnetic coupling, creating a blue cast.
What the airbrush colors is concerned, white is the color which clogs the airbrushes more than any other color. A common idea is that clogging is a consequence of the manufacturing process, where the pigments can not be milled fine enough. This idea is completely wrong: a pigment size of 0.25 micron is 1/400 of the diameter of a 0.1mm nozzle!!! Moreover, there are cases, like coloring the PVC materials, where the final size of 0.25 micron is obtained after a coating of different inert materials to prevent outdoor color changes. The clogging actually is due to the easy flocculation of the titanium dioxide. The flocculation is the origin of pigment grouping, and it depends on the medium, additives and temperature (summer time, for example, whites clog the airbrushes more easily!). However, flocculation represents a very weak bond which can be broken simply shaking the color in the container. The pigment agglomerations easily increase the size even above 100 times that of a single pigment, leading to several consequences. The first is the already mentions clogging of the airbrush; the second is that the hiding power is compromised, as we can see the evident grains on dark backgrounds and not a smooth gradation as with other colors; the third is that on saturated areas the blue halo disappears, leaving the well known and expected bright white. The first two effects can be reduced adding some flow aid to the color because pigment dispersion in the medium must be increased on the path between airbrush and painted surface. The manufacturers know well these things and they balance their whites with medium, solvents, additives to have the best dispersion possible, reducing flocculation as much as they can. Manufacturers, however, try to maximize the hiding power, therefore, also viscosity is high and the flocculation at the end has to be solved by the artists. People often use solvents to reduce the problem (water for acrylics), but it is useful to know that this creates an unbalanced state between dispersers and water and may increase flocculation. The solvent actually is needed by the medium. A flow aid is what we really need in this case, added to the solvent to keep the balance correct. Using additives will always decrease the hiding power, but this is often what we are for. There are also other things people love putting into the paint, like retarders, windex and other liquids, but they can have nasty consequences. The retarder may help to reduce the color drying on the needle and it doesn't create problems when used in the right amount. Windex and similar things, on the other hand, are created as detergents and may alter the color over time. This is not a real problem if an illustrator has to scan the painting immediately, but it may have serious consequences in fine arts.
Considering the chromatic behavior of titanium white, there are two main cases to take into account. The first is mixing colors with white, which is a color from this point of view as all the others: it will have a cooler or warmer hue according to the crystal structure and to the manufacturing process. This type of color mixing is described by the Kubelka - Munk theory where absorption and scattering is taken into account. The two programs drop2color and color2drop, for example, are based on this theory. The second case to be considered is when white is sprayed over other colors. In this case a blue shift occurs creating a halo around the saturated areas. This blue halo can be a problem some times. The following analysis tries to understand the physical nature of this color shift...
Three samples were prepared to check under a microscope. Schoellershammer 4G strips were used spraying them with color for the background and then spraying titanium white on the left side until saturation, letting the overspray define the color gradation on the right. This samples allow me to check the effect of 0 to 100% coverage of the ground. Since a 1800x magnification is going to be used leading to strong depth of field problems, I didn't use any transparent varnish.
The following image shows the picture of the first sample on the top and the microscope image of the circled area on the bottom. The physical magnification here is 1800x. The background color is the Brown (out of the bottle) by Golden. On the top of the image the blue shift is quite evident at about 1/3 from the left border, where the white spray is close to saturation.
The slightly irregular background structure can be clearly seen in the microscope image. It is the fine grain thick paper's surface texture. The collapsed white drops can be seen also, where the border region contains single pigments while the centers are flocculated. On the other hand, if the drops are assumed to be spheres formed by pigments suspended in the medium, when the drops reach the surface, they are flattened. On this flattened sphere, the pigment density is minimum on the edges and it is maximum in the central areas. When many pigments are squashed together as in the drops' central area, flocculation occurs creating a significant height also which doesn't allow for focusing on both the background and the top of the pigment aggregates. Since the microscope light is white, thus its spectrum is even, the reflected light depends on scattering of the individual wavelengths. The drops' central region with flocculated pigments has a uniform scattering on the visible spectrum, while the border regions with 0.25 micron pigments scatter the short wavelength (blue colors) better compared to the reds. Even if these images are not color correct, the picture shows a very close scenario to the reality where the drops' center regions are bright white and the borders are light blue.
The image below shows the area of the sample identified by the red circle. It is the center of the sample surface where the color shift is most evident. It is manifest from the microscope image that the blue border regions are very significant in this region of the sample.
The following image shows the second sample on the top and the microscope image on the bottom. The color shift here is quite strong.
The following image shows the third sample on the top and the microscope image on the bottom corresponding to the circled area of the sample. The background was sprayed with pure Orange. The color shift here is not too strong.
It is quite easy to understand from the microscope images what happens when white is sprayed over the colored background. The white drop is like a sphere of medium where the TiO2 pigments are evenly distributed. When the drop reaches the surface, it is flattened, and obviously, more pigments are in the center compared to the border regions. Therefore, in the flattened drop flocculation occurs in the center region while single pigments remain in the border areas. Since flocculated areas are bright white while optical filtering occurs in the borders due to single pigment size, the improved scattering of short wavelength in the border regions create a blue cast of these areas only. Using this idea, the following image shows the physical model of the blue shift which seems the most reasonable to me:
The leftmost image shows a black background and a few white drops on it. Therefore, the background color dominates over both blue border and white center areas, showing negligible overall color shift. The maximum color shift is shown in the center of the image where the border area of drops is maximized. From this image it is clear why the maximum color shift occurs near the saturated regions. Keeping on spraying, more white is added to the surface and thanks to flocculation less and less border regions remain. Therefore, the white dominates over both blue border areas and black background, reducing the color shift again.
Since the titanium dioxide is very opaque, the color we see derives from additive mixing of the background, drop border color and drop center, exactly the same what happens with inkjet printers, colors in magazines printing or in some impressionist paintings where adjacent color drops create different colors additively when seen from a distance. Spraying other colors where the opacity is not so strong, a more complicated mixing occurs based on both subtractive and additive mechanisms.
In order to validate the blue shift model, I've created many samples using the base Pen Colors as backgound. The base colors were mixed to white, to prevent the problems arising with the use of masstones and to increase the opacity, and sprayed on paper strips. At the end, pure white was sprayed on one side exactly as for the microscope images to create the color gradation between white and the background color. Once the samples were dried, I made many measurements on the sample surface with the spectrophotometer starting on one side and ending up on the other side of the sample creating the color trajectories. I'm going to show the results in the CIE-L*ab color space on the ab plane where the blue region corresponds to negative values of the b coordinate.
A mathematical model of the identified physical phenomenon is still missing at this point. The idea is to create a mathematical model including the physical model only: the agreement between measurements and the model shows how correct the physical model is. What I need is the spectrum of the background, the spectrum of the drops's center part and the spectrum of the drops' border. The first two spectra can be obtained easily both by measurements or using drop2color, because the background color's composition is known. I'm going to use the program because the algorithms are already done while including the measurements would need more time. The third spectrum is more difficult to get because it is impossible to prevent flocculation while spraying and there is no mathematical way to derive it from the measurements I've done writing drop2color and color2drop. These programs actually are based on completely opaque color mixing where border effects or transparent effects are not included. The only thing I can do is spraying the white on a black background (preventing this way color shifts due to the background) and using the spectrum of the area which has the maximum color shift. Using this spectrum I'll have a mixture of the border color and of the bright center part, but it isn't a problem since I need to add the white spectrum anyway: the only consequence of this is that I'll have to find a parameter to fit the curves. Having these three spectra and knowing that TiO2 is very opaque, I can use an additive mixing formula of the spectra. In particular, I'll need a linear term for the background color and the whites along the trajectory,while I'll have to separate the central part of the drops with a quadratic term (since it is an area) and the border blue region with a linear term (because it is a perimeter). The perceived reflectance spectrum becomes:
(rs is the spectrum at a point on the trajectory defined by d, with d = 0 on the background color and d = 1 on the bright white side; rsMix is the color spectrum of the background, rsWcenter that of the bright white, rsWborder is the measured spectrum of the sample with the black background sprayed with white at maximum color shift; P is the fitting parameter taking into account the bright white component in rsWborder, found later experimentally to be 3)
The following images show with D65 illuminant the computed trajectories with black lines on top of the measurement points. There are no fitting parameters in these curves, once P was set to 3. The images in order refer to the yellows, reds, blues, greens and earth colors + black, respectively.
The agreement between measured and computed trajectories is very good. However, there is some mismatch especially for the yellows, due to insufficient coverage of the background color. The mathematical computation of drop2color, the same used here as well, actually is based on the mixing of completely opaque colors where the background doesn't show through. Therefore, the physical and mathematical models include correctly the phenomenon of the titanium white's blue shift.
Finally, just to check what happens if the effect of the blue borders is neglected, the trajectories were computed using a completely additive mixing of the colors and the white according to the following formula:
In the next image the computed trajectories are shown with black lines on top of the same measured points of the images above.
Neglecting the blue borders no blue-shift occurs. It is interesting to note that some colors, like some greens, connect to the white through a completely straight line with fully additive mixing while others, like some reds, run on strongly curved trajectories.
In the comparison between the mathematical model and measurements emerges that the spectrum of the titanium dioxide in the perimetric regions is correctly estimated by 3 rsWborder. This spectrum is shown in the next figure as Data 1 and black line, with its color under D65 illumination. The strength of the short wavelength, the blue component, is evident, as is the significantly different behavior compared to the flat spectrum of the center areas of the white drops.
The gray line and data 2 show the true complementary color spectrum and coordinates for a D65 illuminant. A possible solution to the blue shift problem is spraying lightly and fully opaque with the complementary color the border regions only. The opaque color is important for the additive mixing. Otherwise, through subtractive mixing of transparent colors the background may show through and another color may result worsening the situation. At this point it is obvious that a simple mixing of the white with some orange will not help because the center parts of the drops are already white and the problem comes from the border regions only...
The blue shift is the titanium white's propriety but also other colors manifest halos in the saturated areas. A well known situation is when light colors are sprayed over dark colors in portraiture. These colors have a cool halo while dark colors sprayed over lighter colors doesn't seem to show a color shift. Therefore, working with opaque colors dark over light is very common. What follows tries to find the physical reason why this technique works...
The first hypothesis which comes to my mind is that a darker color containing titanium dioxide sprayed over a lighter color containing TiO2 may not create color shifts because the flocculation already occurred on the background area and single pigments do not exist anymore. In order to check this idea, two samples were prepared. The first one was covered with Permanent Yellow (out of the bottle), while the second sample was covered by a mixture of Indian Yellow, White and a touch of Ultramarine Blue. The first sample doesn't have any TiO2 in the background, while the second is full of it. A mixture of Brown and White was sprayed on the left side of the two samples until saturation and the overspray on the right has created the color gradation toward the yellows.The following plot shows the spectrum of the Permanent Yellow and that of the Brown mixed with White.
The image below shows the trajectories between the yellow backgrounds and the brown color sprayed on the top. There is no qualitative difference between the two curves. Therefore, at least in this experiment, the existence of TiO2 in the background color doesn't influence the color shift. However, there is a red shift for both samples.
The following image shows the sample having Permanent Yellow as background and the circled area under the optical microscope.
The borders of the sprayed brown drops have a red tint. Therefore, the red shift of the brown sprayed over the yellow is due to the border areas, which is exactly the same phenomenon how the titanium white shifts toward blue. The reason why the brown drops have a reddish border may be related to the brown pigments or to the transparency of the border regions.
The next plot shows the spectrum of a green color and that of a brown color. The green was used as background and the brown was sprayed
Measuring the trajectory between the green background and the brown top, the following image is obtained. The curve between the two colors is a straight line. Such a straight line is also found on the purely additive color trajectory of white sprayed on top of other colors, when the border effect is neglected.
Analyzing the sample under an optical microscope, no color difference is found between the center of the brown drops and the border area. This is the reason why no color shift occurs.
Finally, two skin tones were mixed. A light color for the medium skin hue, with Burnt Umber and White, and a darker color for the shadow areas with Orange, Light Gray, Magenta and White. These are two common colors for portraiture where it is known that light over dark shifts toward some cool color, while dark sprayed over light doesn't exhibit any shift. The following plot shows the spectra of the two mixed colors and their RGB version for a D65 illuminant.
Two samples were created using the mixed skin tones. The first sample was sprayed to saturation with the lighter color as background, then the darker color was sprayed on the left edge to create the color transition with the overspray. The second sample was treated exactly the same way swapping the two colors. The center part of the next image shows the picture of the two samples. The color shift on the second sample toward a cooler color is evident in the area next to saturation, where the red circle is drawn. Apparently there is no color shift on the first sample.
Above and below the two samples, the optical microscope images are shown corresponding to the circled areas. A drop border region can be clearly seen on both images. The sample with light background exhibits darker and warmer borders of the drops compared to the drops' center regions, while the sample with dark background has a cooler color in the drops' border area. Moreover, the border region in the sample with light background is significantly smaller compared to the border region of the drops on the darker background. Therefore, the color shift is expected to be bigger for the light color over dark background.
Measuring the color trajectories of the samples with the spectrophotometer, the following image is obtained. The figure is a zoom of the ab plane because the two colors are projected on the color plane very close to each other. The projection of the darker color is shown with the upper red dot, while the lower red dot corresponds to the lighter color. The upper trajectory shown with dark gray belongs to the sample with light background, while the lower trajectory shown with light gray line is measured on the sample with dark background. The colored circles are the measurement points. Both samples, therefore, exhibit a color shift. The sample with light background shifts toward the warmer colors, while the other toward the cooler colors. However, only the second is noticed by a naked eye. It is also evident that the second shift is bigger then the first one, and it is closer to the plane center too. In this region the human eye is more sensible to color changes compared to increasing chroma values. This is the reason why the DE*94 was introduced compared to DE*ab...
The next figure shows what happens on the two samples.
When the light hits a completely opaque region of sprayed colors, the reflected light is formed by a subtractive mixing of the pigments. In this case the background color doesn't play any role in the perceived color because there is no light reaching its surface. When the light reaches the border region of the drops, part of it is reflected and a part is transmitted to the background. The background reflects the already color filtered light, which goes through the transparent drop border area again. The final color of this part of the light derives from subtractive mixing of colors through transparent colored layers with the background showing through. The final overall color, therefore, will have the contribution of the pigmented areas of the drop center and border combined through the additive mixing with the background where it is not covered by any drop. Therefore, the optical paths and the color contributions are completely different for the two samples where the light and dark colors are swapped. This difference results also from the two trajectories which are completely separated. There are several reasons why the drops' border area can have a different color compared to the central region: pigment dimension due to flocculation (as for TiO2), more or less transparent pigments, their density, optical mixing with the background color and so on...
Concluding, at least according to these experiments, the reason why color shift occurs next to saturated areas of colors sprayed on top of some colored backgrounds, is the color difference between the border areas of drops and their central region. A similar effect may also be observed while brushing strongly diluted colors for glazing.
Light scattering (related to opacity and luminosity) increases with the refraction index difference between the pigment and the medium where the pigment is dispersed. For example, if Calcium Carbonate (gesso) with refraction index (RI) around 1.6 is dispersed in water with RI = 1.33, an opaque white results. If the same pigment is dispersed in oil with RI = 1.48, a quite transparent mixture is obtained. Therefore, the use of pigments is strongly influenced by the medium they are mixed in, ranging from colorants to simple extenders.
The following table shows the most common white pigments and their sizes computed using the Weber's equation for a medium with RI = 1.37, even if there are also many other criteria to define the pigment size, especially if the RI difference between the pigment and the medium is small.
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| Titanium White - Rutile | PW 6 | TiO2 | 1939 | blue | 2.73 | 0.26 micron |
| Titanium White - Anatase | PW 6 | TiO2 | 1919 | yellow | 2.55 | 0.30 micron |
| Zinc Oxide White | PW 4 | ZnO | 1834 | blue | 2.02 | 0.54 micron |
| Flake White - Lead Carbonate White | PW 1 | PbCO3Pb(OH2) | 4th cent. bC | yellow | 1.94 | 0.61 micron |
| Calcium Carbonate | PW 18 | CaCO3 | neutral | 1.63 | 1.35 micron |
Notes:
The following table shows several whites available on the market. The first column is for the brand name, the second for the paint type, the third shows the pigment (if it is written on the paint label) and the fourth column shows the color trajectory of the paint starting from the masstone and ending on the black background. The paper samples were covered with black paint in such a way not to create interaction with the white paint (what happens often using common black paper and spraying wet paint on it, ending with reduced color shift and a grayish false masstone). The trajectory starts from the big white circle (the masstone) and overspray generates the trajectory itself. Each image shows exactly the same area on the ab plane of the CIE Lab color space, where both a and b coordinates range from -20 to +20. This allows for a true comparison of the masstone colors and for the blue-shifts. Masstones are yellower for point located in the upper region, and blue-shift is stronger if the trajectory reaches the lower points of the ab plane. For example, Holbein and Talens shift less, JVR and Ferrario shift more. Some white paints are yellower, like Golden, some others more neutral, like Talens. This masstone color depends on several things, like pigments used, their treatment and the binder.
brand |
type |
pigment |
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| Badger - Air Opaque (White 8-02) | acrylics | undefined |
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| E'TAC - EFX500 (502 - Titanium White) | E'TAC | undefined |
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| Ferrario - Pen Color (1 - white) | acrylics | PW6 |
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| Golden - Airbrush Colors (8380-1 Titanium White) | acrylics | TiO2 rutile / PW6 |
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| Hansa - Airbrush pro-color (60023 opaque white) | acrylics | undefined |
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| Holbein - Aeroflash opaque color (E060 White) | acrylics | PW6 |
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| JVR - X prof (white) | acrylics | undefined |
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| Pebeo - Colorex (2 - white) | watercolor | undefined |
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| Talens - Ecoline (100 white) | watercolor | undefined |
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| E'TAC - EFX500 (Plasma White) | E'TAC | undefined |
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I would like to thank Alessandro Rivetti at the Department of Mechanical Engineering for helping me with the optical microscope. I would like to thank also Eddy Wouters and Marissa Oosterlee for the interesting discussions about color.
Link to the main page of Color Experiments.
Updated the 18th May, 2007 by Zsolt