# Dot Gain

Dot gain is the difference between the actual printed dot and the ideal digital dot. For example, a pixel may indicate a 50% dot, but after printing, it is measured to be 70%, showing a "dot gain" of 70 - 50 = 20%. Fundamental to this is the ability to meaure the printed dot. The most common method is the Murray-Davies equation, which computes the dot gain ($G$) from density measurements:

$$G = {{1 - 10^{(D_0 - D_N)}} \over {1 - 10^{(D_0 - D_{100})}}} \times 100 - N$$

In this equation, $D_0$ is the measured density of a 0% dot (i.e. unprinted substrate), $D_{100}$ is the density of a 100% dot, and $D_N$ is the density of the sample $N$% dot (typically, $N$ = 50).

At the time this was first used, densitometers were more common and less expensive than colorimeters or spectrophotometers. Today, colorimeters and spectrophotometers are often more available than densitometers, which causes a problem for those people wishing to measure dot gain. I have developed a method of modifying the Murray-Davies equation for use with colorimetric measurements. If you use reflectance ($R$) instead of density ($D$), the Murray-Davies equation simplifies considerably:

$$G = {{R_0 - R_N} \over {R_0 - R_{100}}} \times 100 - N$$

Reflectance is linearly related to energy, and this equation involves ratios of reflectance differences. Therefore, other values that are also linearly related to energy might be used in place of reflectance. The obvious choice is XYZ, which meets this criterion. By choosing the predominant component for the ink color, dot gain can be accurately measured from XYZ measurements. Note that XYZ is easily computed from Lab values, either by using a CIE Color Calculator, or by programming the proper equations yourself. I have also created a couple Excel spreadsheets that can compute dot gain for you from Lab measurements, using this technique.

For CMYK printing, here are the reflectance substitutions you should make:

 Ink Color Substitute for R Cyan X Magenta Y Yellow Z Black Y

The constraints for using this method are the same as for using the normal Murray-Davies equation, namely that all measurements be made from printings of single inks.