# Dot Gain, Spectrophotometry, and Densitometers

## What is Dot Gain?

Dot gain occurs whenever ink is applied to a substrate in a non-solid ink coverage area. It is defined by the amount a digital raster dot spreads beyond its intended coverage, given in percentage. While mainly a product of paper or substrate absorption rates, there are many other factors that also determine the effective dot gain, such as plate pressure, and ink viscosity, and many ways to mitigate the effects within the printing process.

Verifying dot gain on press is an efficient way to help monitor print color quality. As dot gain increases, the perceived color in that area will often darken or over-saturate, muddying textures and obscuring details. Conversely in highlight areas where dots are very small, images can either wash out if too little dot gain or create a color cast if too much dot gain, depending on the primary color. While the human eye might be able to catch some subtle changes, electronic measurement is the most reliable way to assure that dot gain values are within what is allowed by the job specifications.

### A few notes on Dot Gain:

• Dot gain is also known as tone value increase (TVI), as it is measured based off the deviation from the desired tone, in percent.
• Dot gain is typically the largest in midtones for three main reasons:
1. The volume of ink applied is greater than in highlights
2. The amount of empty space between dots for the ink to absorb into is greater than in shadows
3. The ratio of the dot perimeter to blank substrate is most favorable for the greatest amount of ink spread.
• Optical dot gain is the apparent spreading of color due to the way light diffuses on the substrate surface before hitting your eye. It’s not a direct result of ink and paper; it’s just the nature of light. It can vary based on the reflectivity of the substrate, and is measurable. It can account for 10-35% dot gain.
• Expected dot gain varies based on substrate and tone value, with the smallest values typically being in the darkest print areas, often around 10% (depending on ink and substrate, of course)
• Most design software that is designed for professional print output has settings that will help compensate for expected image quality changes due to dot gain.

## Measuring Dot Gain

Densitometers and spectrophotometers are two tools that can be used to calculate dot gain of a printed sample.  Though neither can be used to measure dot gain directly, both are effectively capable of measuring density, from which dot gain can be calculated. These tools work by focusing characterized light onto a surface. This light is either transmitted through the substrate, reflected to the sensor, or scattered away from the sensor, depending on the type of substrate. The amount and wavelength of light that is reflected to the sensor can be used to determine several attributes about the print at that location, including density and spectral remission data.

For any spectrometer to measure dot area, the spectrophotometer must measure the density of the substrate, the density of the solid ink (SID) and the density of the tint.  These parameters are taken from color bars printed on the edge of the printed web.  There are typically more than just these 3 patch types on a color bar, but these are the most common.  Typically, the most forgotten patch is a substrate only patch. The measurement is necessary for density and dot gain calculations for ink patches, and manual measurements must be taken if they’re forgotten during calibration.

In addition to calculating the actual dot area, it is necessary to compare that to a target value. This target value, as noted above, can vary depending on substrate and other factors.

The two main measurements used to calculate dot gain are the density measurement from the area of interest and the solid ink density measurement from the calibration set. Before the final dot gain calculation is performed, each measurement is adjusted to account for the substrate density. The resulting numbers are plugged into the Murray-Davies formula, shown below:

#### Dot Area Percent= $$100* \frac{1-10^{-DT}}{1-10^{-DS}}$$

Where DT is the measured tone density (adjusted for the substrate density) and DS is the solid ink density from the solid ink patch, (adjusted for the substrate density). The result from this equation shows what percentage of a given area of print is covered by halftone dots. Finally, the ideal tone value percent is subtracted from the actual dot area percent, and that result is the dot gain for that area of interest.

## Glossary of terms

Densitometers
An instrument for measuring the photographic density of an image on a film or photographic print.

Density
Effectively, the percent of an area of the substrate that is covered by in on a given sample. However, as it is a function of light reflectivity, blank substrate can also have a density. This is why it is important to consider a substrate’s density when calculating dot gain.

Dot gain
The difference between actual and the idea percent area coverage for a halftone dot

Highlights
Typically, areas with tone values less than 30%

Midtones
Typically, areas with tone values between 30% and 70% coverage

Optical dot gain
Apparent spreading of color due to light diffusion by ink, substrate, atmosphere, or other factors.

Reflectivity
Tendency for a given surface to reflect light, or how much light that surface reflects

Typically, areas with tone values greater than 70%

Spectral remission data
Collection of data points representing the intensity (power) of light of each nm band at which a measurement is taken

Spectrophotometers
An apparatus for measuring the intensity of light the visible spectrum, especially as transmitted or emitted by particular substances.

Substrate
The material on which ink is applied