Dot gain

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Dot gain is a phenomenon in printing and graphic arts whereby printed dots are perceived and actually printed bigger than intended. This causes a darkening of the screened images or textures, especially in the mid tones and shadows.

This happens because of the viscosity of ink and its ability to spread through the paper as it is soaked in. Dot gain varies with paper type. Uncoated paper stock like newsprint paper shows the most dot gain.

Mathematically, dot gain is defined as:

$gain=a\_\{print\}-a\_\{form\}$

where $a\_\{print\}$ is the ink area fraction of the print, and $a\_\{form\}$ is the pre-press area fraction to be inked. The latter may be the fraction of opaque material on a film positive (or transparent material on a film negative), or the relative command value in a digital prepress system.

The Yule-Nielsen Effect and "Optical dot gain"

The Yule-Nielsen effect, sometimes known as optical dot gain, is a phenomenon caused by absorption and scattering of light by the substrate. Light becomes diffused around dots, darkening the apparent tone. As a result, dots appear to be larger than their relative absorbance of light would suggest.

The Yule-Nielsen effect is not strictly speaking a type of dot gain, because the size of the dot does not change, just its relative absorbance.

Computing the fractional coverage (area) of a halftone pattern

The inked area fraction of the dot may be computed using the Yule-Nielsen model. This requires the optical densities of the substrate, the solid-covered area, and the halftone tint, as well as the value of the Yule-Nielsen parameter, $n$. Pearson has suggested a value of 1.7 be used in absence of more specific information. However, it will tend to be larger when the halftone pattern in finer and when the substrate has a wider Point Spread Function.

Models for dot gain

Another factor upon which dot gain depends is the dot's area fraction. Dots with relatively large perimeters will tend to have greater dot gain than dots with smaller perimeters. This makes it useful to have a model for the amount of dot gain as a function of prepress dot area fraction.

An early model

Tollenaar and Ernst tacitly suggested a model in their 1963 IARIGAI paper. It was:

$gain\_\{TE\}=a\_\{form\}\; cdot\; (1\; -\; a\_\{vf\})$

where $a\_\{vf\}$, the shadow critical area fraction, is the area fraction on the form at which the halftone pattern just appears solid on the print. This model, while simple, has dots with relatively small perimeter (in the shadows) exhibiting greater gain than dots with relatively larger perimeter (in the midtones).

Haller's Model

Karl Haller, of FOGRA in Munich, proposed a different model, one in which dots with larger perimeters tended to exhibit greater dot gain than those with smaller perimeters.

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The GRL Model

Viggiano suggested an alternate model, based on the radius (or other fundamental dimension) of the dot growing in relative proportion to the perimeter of the dot, with empirical correction the duplicated areas which result when the corners of adjacent dots join. Mathematically, his model is:

$gain\_\{GRL\}=left\{\; begin\{array\}\{ll\}$

a_{form}-a_{wf}, & mathrm{for}, a_{form}leq a_{wf} 2cdotDelta_{0,50}sqrt{a_{form}(1-a_{form})}, & mathrm{for}, a_{wf}

where $Delta\_\{0,50\}$ is the dot gain when the input area fraction is one-half; the highlight critical printing area, $a\_\{wf\}$, is computed as:

$a\_\{wf\}=left\{\; begin\{array\}\{ll\}$

frac{4Delta_{0,50}^{2}}{1+4Delta_{0,50}^{2}}, & mathrm{for,}Delta_{0,50}<0 , & mathrm{for,}Delta_{0,50}geq0end{array}right.

and the shadow critical printing area, $a\_\{vf\}$, is computed according to:

$a\_\{vf\}=left\{\; begin\{array\}\{ll\}$

1, & mathrm{for,}Delta_{0,50}leq0 frac{1}{1+4Delta_{0,50}^{2}}, & mathrm{for,}Delta_{0,50}>0end{array}right.

Note that, unless $Delta\_\{0,50\}=0$, either the highlight critical printing fraction, $a\_\{wf\}$, will be non-zero, or the shadow critical printing fraction, $a\_\{vf\}$ will be not unity, depending on the sign of $Delta\_\{0,50\}$. In instances in which both critical printing fractions are non-trivial, Viggiano recommended that a cascade of two (or possibly more) applications of the dot gain model be applied.

Empirical Models

Sometimes the exact form of a dot gain curve is difficult to model on the basis of geometry, and empirical modeling is used instead. To a certain extent, the models described above are empirical, as their parameters cannot be accurately determined from physical aspects of image microstructure and first principles. However, polynomials, cubic splines, and interpolation are completely empirical, and do not involve any image-related parameters. Such models were used by Pearson and Pobboravsky, for example, in their program to compute dot area fractions needed to produce a particular color in lithography.

External links

• Understanding Yule-Nielsen Factors

References

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Last updated on Saturday January 26, 2008 at 19:48:37 PST (GMT -0800)
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