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Density has traditionally been used as the primary means to control the printing process. It has been widely held that it correlates well with the amount of colorant that is put on the paper over a limited range of ink film thicknesses. In addition, it is a convenient metric to use in a production environment, since it provides insight through a one-dimensional variable by which press operators can judge whether too much or not enough ink is being laid on a given substrate. This article is going to focus on the theory of density and dot gain. The next article is going to be on the theory of colorimetry. Having the theoretical understanding of these concepts will help in understanding the statistical process control and quality control systems that benefit printing operations. DENSITY Density = log10 1/Reflectance factor Reflectance is calculated by the function: R= Ir/Io. Ir stands for the intensity of the reflected light and Io for the intensity of the light source. For purposes of reflective densitometry, we are using the reflectance factor, which is the ratio of the reflected light from a specimen compared to the reflected light from a surface that would reflect 100 percent of the light. Transmission density follows the same principles as reflective density, dealing, however, with transparent substrates. Density is a logarithmic function of the inverse of reflectance, meaning that the lower the reflectance of light from the ink film—or the higher the absorption—the higher the density. The logarithmic relationship means that equal increases in density do not translate to equal decreases of reflectance; as the reflectance factor decreases, density increases at a decreasing rate until the difference between increases in density values are not observed. For example, a press operator could be adding more black ink on the substrate without achieving an equal amount of increase in the observed “blackness.” The usual range of reflective densities for printing applications is between 0.00 and 3.00 density points.
GRAPH 1 Theoretically, as the ink film doubles, the reflectance is halved, and the density increases by 0.3 points due to the base 10 logarithmic function employed. The implication of this to printing is that by the time an ink film reflects only 0.9 percent of the incident light (and absorbs 99.1 percent), the already significant amount of ink film needs to be doubled in order to make even the slightest increase on the amount of light absorption, which would nevertheless be perceptually negligible. Furthermore, in practice, density reaches a saturation point when values of 1.8 or more are reached. Trying to put more ink on the substrate, in those cases, would result in an improper ink/water balance, increases in dot gain, an uncontrollable press run, ink unnecessarily spent, and possibly curing problems with UV inks. Density is preferred over reflectance, because equal increases in density correlate more closely with human vision (Graph 2). GRAPH 2: Grey Levels of Reflectance & Density
We’ve been talking about reflectance as if we were referring to a single point. This is actually not true. The reflected light from an object is spread over the visual spectrum, which is measured in wavelengths and ranges from 400 to 700 nanometers. If the visible spectrum is reflected in its entirety, the perceived color would be white, including all the wavelengths at approximately equal amounts. If, on the other hand, no light is reflected, the perceived color is black. In other words, white light contains all the colors and black none. Shorter wavelengths—below 480 nanometers—are more intense and result in the perception of blue. Longer wavelengths—more than 680 nanometers—result in the perception of red. Similarly, we perceive the other colors that have their own characteristic spectral reflectance curves. Green is between 480 and 560; yellow between 560 and 590; orange between 590 and 630; and purple by mixing red and blue light from the extremes of the visible spectrum.
FIGURE 1: The visible spectrum In the printing processes, the dyes and pigments selectively absorb wavelengths of the white light and, therefore, the color mixing is called “subtractive.” A yellow ink would absorb the blue wavelengths of the spectrum and allow the rest of the light (green-red) to be reflected. The amount of absorption would define the yellowness of the perceived color, or—more accurately—lack of blueness. Similarly, a cyan ink would absorb the red part of the spectrum and reflect the green and blue, and a magenta ink would absorb the green part and reflect the blue and red. The wavelength that each ink allows most light to be reflected could be described as the ink’s peak reflectance, and it is a determining factor with regard to color perception. Let us examine Graph 3.
GRAPH 3: Spectral Reflectance Curve of Process inks, substrate (ISO 2846-1) The data for these graphs were derived from ISO 2846-1 (Graphic technology - Colour and transparency of printing ink sets for four-colour printing - Part 1: Sheet-fed and heat-set web offset lithographic printing) and represent the typical spectral reflectance curves of process inks used in sheet-fed offset lithography around the world. The 2846 series of ISO standards contains documents for coldest offset printing, screen printing, gravure, and flexography. The graph on the left displays the reflectance of cyan, magenta, yellow, black, and the substrate. The graph on the right is the reciprocal of reflectance: density. As you can observe, cyan, magenta, and yellow inks do not only absorb light predominantly over a certain range of wavelengths, but also absorb lesser amounts of light over the other regions of the visible spectrum; they are in that regard “impure,” they have “unwanted absorbencies.” We can see, for example, that the cyan ink absorbs light predominantly at 620 nanometers, but due to the impurity of the pigments it doesn’t perfectly subtract all the light from the other regions of the visible spectrum, allowing certain wavelengths to be reflected and affect its appearance. The same holds true for the other colorants, but less for the yellow, which is less “impure” due to its pigmentation. Therefore, it is important to take into account the unwanted absorptions of the colorants in order to reproduce an image with process inks, since each colorant affects the other two. An important effect of this natural imperfection—natural because we cannot find perfect pigments in nature as much as we cannot find a perfectly straight line—is that inks manufactured with different pigments have slight variations on the perceived color and need to be mixed differently. Moreover, as the thickness of the ink film varies, the color shifts proportionally in intensity. This relationship is described by Beer’s Law, which states that equal amounts of absorbing material cause equal amounts of absorption. This wouldn’t present a problem, if not for the magenta ink. As we can see in the previous graph, the magenta ink reflects light at two regions of the spectrum, but at different amounts. Its color perception depends not only on the peak reflectance, which is around 570 nanometers, but also on the short wavelength range of the spectrum, where we see a small “bump” on Graph 3 (this “bump” actually differentiates magenta from red, which lacks this bump and doesn’t look bluish). If we were to double the ink film thickness of a magenta ink, we would in effect be raising to the power of two both parts of the magenta spectrum. Since the longer wavelengths have higher reflectance values than the shorter ones, the reflection of the longer, reddish, wavelengths would be much stronger. As such, the hue of the ink changes as the film thickness varies. The magenta ink would turn bluish as its ink film thickness decreases. This is termed as “dichroism.” How does a densitometer work?
FIGURE 2: How Does a Densitometer Work? Filters
GRAPH 4: Spectral Reflectance Curve of Different Status Filters GRAPH 4 illustrates the differences between the different status filters by showing their spectral curves and their respective spectrum of reflected light. Using the spectral reflectance curve of the magenta ink, we can see that a densitometer captures the amount of reflected light at its lowest point of absorption, or at the highest density. What happens at the rest of the spectrum for each ink is either not captured, or captured by the other filters. Two magenta inks with different pigmentation laid at equal amounts on a substrate would be measured equally through the green filter, but they would differ at the measurements obtained by the other filters (TABLE 1). Even if we were to assess the readings from the other filters to see, for example, how much blueness is contained in the magenta ink, we wouldn’t be getting accurate information, because the spectral curves of each filter do not fully overlap. Moreover, measurements of special colors that do not have a peak reflectance at the bandwidths of either the cyan, magenta, or yellow inks are not precise. TABLE 1: Density measurement of two magenta inks
Different metrology options Another important aspect of measuring density is whether we subtract the density of the substrate or not. Most instruments provide an option to measure the density of the substrate and then subtract it from the measurement of the ink film on the substrate, reducing in this manner the density reading and eliminating one more variable in the assessment of the ink film itself. If, for example, a substrate has a density of 0.15 points, the relative density measurement would be 0.15 less than the absolute one. A cyan reading of 1.25 density points in relative mode would be 1.40 in absolute. This amount of difference can be misleading when a press operator tries to run at a target density. The surface where we measure a sample—the backing as it usually called—is equally important, because its color interferes with the sample and affects the total reflected light. A white backing reflects more light from the surface, where a black backing reflects less or none; therefore, there is a difference between the two measurements. ISO 13656 (Graphic technology - Application of reflection densitometry and colorimetry to process control or evaluation of prints and proofs) specifies a black backing for density measurements, mainly because the reflection of the backing is mostly interference. There are a number of factors that affect the measurement of the same ink film: the filter status; whether that was measured with colorimetric or densitometric means; the backing; the instrument itself; whether the ink is dry or wet or whether there were polarization filters used; and whether absolute or relative density was used. It would be ideal for everyone to agree on an international standard so that these differences would be eradicated, but until that happens, the measurement parameters need to be clearly communicated.
GRAPH 5: Tonal value increase. There are, nevertheless, efforts to reach international agreement and specify the metrological parameters of density. Which status filter to use, should we use polarization or not, should we prefer density derived from colorimetry or densitometry? Lack of standardization is perhaps more detrimental to the industry than being standardized with parameters that are not optimum. Finally, even if we were to agree on an international standard, or communicate as clearly as possible the different measurement parameters, there is variability in the instrument itself, as well as variability between different instruments. The former is termed as “instrument repeatability.” Every device has some inherent variation that results in slightly different measurements of the same sample. It is important to take this variation into account when we are trying to define the tolerances of acceptable process variation. Instrument repeatability is usually communicated in the manufacturer’s specifications. The latter, inter-instrument variability refers to differences in readings among different devices. Even if the status filters and light sources are standardized, differences in the manufacturing or the optics of each device result in different readings. In order to address these differences, a production environment should ideally be using instruments from the same manufacturer and establish a regular calibration schedule as per the specifications of the manufacturer. A better approach is to use a calibration standard: these are sheets with different patches whose values are known. If a densitometer fails to provide a reading that meets the communicated values, it should be sent to the manufacturer for repair. Finally, certain instruments allow the user to calibrate one to another by applying a correction factor between the two. This solution is effective, but the precision of the correction factor has to be periodically monitored. Effect of Substrate & Ink Rheology Limitations The fact that density doesn’t measure color limits its application for quality control purposes. In a printing environment, it is important to verify the compliance of incoming supplies, either to internal or international standards. Measuring the ink color is perhaps the simplest example. In that, density would be of little help since it wouldn’t provide a value that would indicate differences in the pigmentation of the ink or color of the substrate. It is debatable whether colorimetry would one day totally substitute density for quality control and process control purposes. In fact, it would be reasonable because a linear correlation has been found between density and the colorimetric coordinates, and, therefore, the argument of linearity with ink film thickness cannot be held exclusively for density. The main problem is the adoption a different science, and it can be dealt with through training and technological solutions that make it easier to use. DOT GAIN Process color reproduction is based on a combination of different amounts of cyan, magenta, yellow, and black ink. A red color, for example, can be reproduced using a good deal of yellow and magenta ink; an orange color can be reproduced with more yellow and less magenta; a brown or a grey with a combination of all three colorants. However, the medium that transfers the ink to the substrate doesn’t have the ability to selectively deliver different amounts of ink films for each different area of the image or premix each color before delivering it to the substrate. The solution to this problem lies on the fact that human vision is not able to discern small spatial resolutions and, instead, combines the different signals into a single perception of color. In particular, by separating each image to dots of different sizes that are below the contrast threshold that our eyes can detect from a certain distance, we are able to reproduce different combinations of colors. As such, an image is broken down to a grid of imaginable cells that are filled in with a dot that covers a certain percentage of the cell. The size of the cell is defined by the screen resolution of the image, and it is usually termed as “screen cell.” We do this for all the process colors and lay them in a certain sequence on top of each other and at different angles. Then, each ink is carried selectively over these dots, is transferred to the substrate by direct contact with it, and in this manner the image is made up. The dot area is, therefore, defined by prepress, and it can be described as nominal, or—in the digitized era—a digital dot. This refers to the dot of the medium. However, the ink, being at liquid state, when it makes contact with the substrate, spreads (or gains) and covers a larger percentage of the screen cell. This additional percentage is defined as dot gain or Tonal Value Increase (TVI).
GRAPH 6: Optical dot gain Dot gain is both mechanical and optical. Mechanical dot gain is the physical ink spread and is mainly affected by the amount of ink emulsification, its viscosity and tack, the pressure involved during the transfer, and the substrate properties. Environmental temperature and press speed also affect dot gain since they impact the rheological characteristics of the ink. A more fluid ink would spread more, and, thus, the dot gain would be higher. Finally, the amount of ink film thickness is another important factor. Increasing ink film thickness results in having more ink covering the nominal dot area, and when that is squeezed it spreads more. The absorbency of the substrate also affects dot gain, with more absorbent substrates having more dot gain, since they allow the ink to spread more through their pores. Optical dot gain tries to describe the interaction of light with the ink and paper and is, therefore, more difficult to assess. As the light penetrates the ink film and reaches the substrate, a certain amount of it is diffused. The diffused light may exit the edge of the dot in such a way as to reflect some light beyond the dot’s physical dimensions or it gets trapped underneath the dot. As such, the dot appears bigger, even if it physically isn’t. The consequence of this is that the edges of the printed dot are viewed with a shadowing effect like a halo. The first measurement of dot gain was provided in the 1930s by Murray, who related the three quantities—dot area (A), density of the tint (Dt), and solid density (Ds)—in the following equation, known as the Murray-Davies Equation: A = (1-10-Dt) / (1-10-Ds) The total dot area is represented by A, but dot gain involves subtracting the actual digital dot area from the total dot area (A). For example, if we measure 72 percent total dot area on a 50 percent digital dot area, the dot gain would be 22 percent. There are three assumptions involved in this formula. The first is that the densitometer is zeroed on an area without dots, the second that the density of the dots is uniform and receives the same amount of ink film as the solid, and the third that the measured dot area includes both mechanical and optical dot gain. The first assumption means that we have to measure the density of the paper (we are in fact using relative density). The second means that we have to measure both the solid and the tint at an area where both receive the same amount of ink. The third means that we are in effect measuring the apparent tonal value and not the physical dot. Using the Murray-Davies formula, it is possible to calculate the gain for all digital dot area percentages and see what the gain of each is. Usually, during production, the 50 percent or 40 percent dot areas are measured since the gathered value provides an overall insight for the whole reproduction scale (1 percent - 99 percent dot areas). However, the areas of the quartertones and three quartertones (25 percent and 75 percent respectively) are also important. As a rule of thumb, the ¼-tone provides insight into the balance of ink and water. An excessive dot gain value—one that is close to the value of the 50 percent dot area measurement—could mean that the ink is more fluid than it should since it contains more water. The reason we are able to get this information from the ¼-tone is simply that the ink has more room to spread within its imaginary cell. The ¾-tone area provides information on whether there is less or excessive spread of the dots due to pressure. We gather this because on the 75 percent or 80 percent dot areas the spread of the ink due to water is less than the spread due to an irregular transfer of the dot to the substrate. The effect of optical dot gain is accounted for by the Yule-Nielsen formula that introduces the empirical n factor. A = (1-10-Dt/n) / (1-10-Ds/n) The n factor defaults at a value of 1 (no effect) and can be adjusted to account for differences of different substrates. However, a relationship for all the substrates, or a constant for different ones hasn’t been established: the factor is empirical. Since the objective in printing is mainly to provide a visually accurate reproduction and the effect of optical and mechanical gain are both incorporated in the measured value, the Murray-Davies equation has been considered sufficient. Moreover, for purposes of process control the variation of dot gain does not need to separate optical from mechanical; if it is more or less, there is an unknown variable that impacts the process. The substrate has a major effect on the amount of dot gain. Table 2 is useful in illustrating the relationships. The same amount of magenta ink was laid down on a coated and an uncoated substrate and the 40 percent and 80 percent nominal dot areas were measured. From these measurements and calculations, we can understand that the same amount of ink is absorbed at a greater extent by the uncoated stock, and, thus, the solid value decreases. In the same time, though, it spreads through the pores of the uncoated stock at a greater degree and, therefore, the dot gain increases. Another important consideration based on Table 2 is that, in fact, dot gain is based on a density measurement of a tint and a solid and is expressed as a percentage. We can observe that the difference in density between the two stocks is less in the 40 percent and 80 percent dot areas than the solid dot area, where the difference becomes disproportionally larger. Moreover, the density of the tints is higher for the coated stock than the uncoated one at the 80 percent dot area and less at the 40 percent dot area, but the dot gain values are always more for the uncoated stock, regardless of the density of the tint. This happens because the coated substrate at some point, probably before the 80 percent dot area and after the 40 percent dot area, is reaching the limits of its absorbency, and even if we lay down more ink, it stays on the surface of the stock. TABLE 2: The effect of substrate on dot gain.
Finally, it is possible to calculate dot gain from colorimetric means, and this is the preferred method for the latest calibration technologies. The calculation involves a conversion of the CIELAB color space to XYZ and then calculation of dot gain. The values derived from either of these measurements are different, and the user should be cautious and not try to correlate between them. However, as an answer to which one would be more appropriate, we should consider that even if the industry has been using mainly densitometric dot gain, the promise of a calculation that correlates better with human vision is a lucrative prospect, and when the technology and instrumentation is able to provide the conversions at a timely and cost-effective manner, it is likely to predominate. Conclusion About the Author: Please, submit any comments, questions, or topics you would like to discuss on printcolor.blogspot.com under the post of the respective article. Dimitri can also be contacted on dxp3756@gmail.com.
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