A Primer on GCR - Part 2

An Imperfect Process
One problem, however, that becomes very apparent with the three-color process is that CMY process black rarely achieves the density of an actual black ink. In colorimetric terms, the L* of the CMY black will not typically achieve the L* of the K black, which restricts the full dynamic range of the printer (whitest white to blackest black). This is the same for color monitors (referred to as contrast ratio), and film and digital photography (referred to as luminance range).
 
Achieving the maximum dynamic range of the printer helps to ensure the maximum color gamut is reproduced. In most cases, the media itself dictates minimum density, or Dmin. Whatever the media L*, it will define Dmin and any color printed will have a higher density than Dmin (which is why media density is general calibrated to zero). By the same token, the black solid will define the maximum density, or Dmax and any color printed will have a lower density than Dmax. Every printed color should have an L* value somewhere between that of Dmin and Dmax.
 
GCR: Gray Component Replacement
As mentioned before, CMY is the inverse of RGB – take any RGB value as a percentage between zero and one, subtract it from one and the result is CMY. For example, a 20 percent red (0.20) equates to an 80 percent cyan (0.80), a 40 percent green to a 60 percent magenta, or a 30 percent blue to a 70 percent yellow. This assumes, of course, that your CMY (ink plus media) is the colorimetric inverse equivalent of your RGB, but in reality that will likely not be the case. This is why a modern color workflow converts all colors to common colorimetric equivalents, a connection space such as CIELAB. For illustrative purposes, however, and sake of simplicity we will leave that function out for now.
 
Returning to our CMY value, we now need to calculate a K percentage that, when added to the CMY value will produce a colorimetrically equivalent CMYK. For those colors to be equivalent, the K must replace some portion of the CMY that is colorimetrically equivalent to the K we are adding. Any color printed using all three primaries – C, M and Y – will have a gray (achromatic) component and a color (chromatic, or tonal) component. Likewise, any value of K should have a CMY gray equivalent, at least to the maximum density (Dmax) of the CMY grayscale. This should be true of any four-color process printer.
 
The solution to GCR, therefore, is to identify the CMY equivalent of K, and then substitute K for the CMY gray component of the given color. One way to accomplish this is to perform a grayscale calibration of the printer prior to profiling, and the most straightforward way to do that is to calibrate the printer to G7 aims (ANSI/CGATS TR015-2013). G7 defines neutral print density for both K and CMY process grayscale, and process gray balance (the a*, b* component of the CMY grayscale).
 
In the case of print density, G7 employs two relatively simple formulas to determine the print density targets between Dmin and Dmax for both the K and CMY process grayscales. This means that the CMY gray density can be matched to an equivalent K gray density, preserving L* in the original color. G7 also establishes a neutral gray balance, defining by way of formula what constitutes a neutral gray for a given media white point; it compensates for the color cast present in a given ink and media combination. If your magenta was too red, for example (too much yellow) G7 calibration would reduce the yellow channel to pull the gray balance back toward blue. The opposite would be true if your cyan was too blue, pulling it back toward green (or vice versa). The point is that G7 calibration establishes a neutral balance by adjusting the C, M and Y curves to compensate for ink and media differences.
 
Once a neutral gray balance has been established through G7 calibration, the next step is to identify the difference between it and the chromatic bias of your K ink. Optimally, your K ink will have no bias, the a*, b* values will both be very close to zero. If so, it should also be very close to the gray balance of your G7 calibrated process grayscale. In such case, GCR is mainly a matter of substituting CMY gray with an equivalent density (L*) of K.
 
If not, you (or more likely your color management software) will first need to correct for the chromatic bias of the K ink by creating a set of C, M and Y curves that generate a process gray with the same chromatic bias as your K. This operation, or at least the internal mathematics, is identical to matching process gray to the G7 gray balance aims – you simply match to your K ink (a,b) instead. The difference between these three curves (the K bias curves) and your G7 calibration curves will tell you the amount of C, M or Y ink that needs to be added back to the K channel to achieve a neutral grayscale.
 
The amount of C, M or Y that gets added back, if any, will be small, unless the gray balance is deliberately adjusted for a particular bias. For example, in the analog print world press operators sometimes add C, M and Y ink to the K channel to produce rich blacks that appear blacker-the-black, or blacks biased toward blue/cyan (cool black) or red/yellow (warm black). However, these rich black blends do not always translate well to digital inkjet and can be problematic to maintain against color drift on long production runs. This is often referred to as under-color addition, or UCA. The application of UCA (and its closely related cousin under-color removal, or UCR) is not normally applied in conjunction with GCR – and is beyond the scope of this article.
 
So now, by way of G7 calibration, we have established a substitution equivalence between CMY and K, such that we can remove the gray component of any CMY value and replace it with a K that will change neither the hue angle (a*, b*) nor the density (L*) of the original color. We can use the G7 curves to determine the amount of C, M and Y to remove, and we can use the same curves to determine the amount of K to add and the amount of C, M or Y to add back. This also means that many CIELAB values coming out of profile connection space will have two CMYK matches – one with no K (CMY only), and one with K. The one with K, the result of GCR, will be the one we will use.

Coming up, Part 3...