dot gain invention white paper

8/2/2019 Dot Gain Invention White Paper

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Dot Gain Tool Invention White Paper (v1.1)

Background

Printing

When printing on printing presses, the process consists of producing a printing plate which is hungon the press. This printing plate is essentially a black and white image of where ink needs to be putdown by the press on the paper. For a black and white page a single plate is used. For a color page,multiple plates are used; typically one for each of cyan, magenta, yellow and black, with possiblyadditional plates if any spot color s are being used.

The process of printing on a printing press is purely a binary process you can either put downsome ink in an area, or not. That means that you can put down 100% of cyan in an area, or 0% of cyan. In order to get a 50% cyan tint, you cant put down 50% of ink. To achieve this, you have toput down 100% cyan in half the area and 0% in the other half. The eye then averages what it seesand views the area as being a 50% cyan tint. For example, a 50% cyan tint could be produced byputting down a checkerboard of cyan ink as follows.

50% Checkerboard

The printing plate that is used on the press to indicate where (or not) to put ink can be produced inseveral ways. It can either be produced by producing a film (which is then chemically processed totransfer (burn) the same image onto a plate), or by directly producing (burning) a plate. Theprocess of putting an image on a film is called Computer to Film and on a plate is calledComputer to Plate (CtP).

Screening

Since the printing process is a binary one (either 0% ink or 100% ink), a method is required forobtaining various shades of gray or color. In the opening section, we suggested a method forachieving a 50% tint. However, to reproduce photos, many tint levels are required; white, black &50% gray are not sufficient.

The solution used to solve this is to take an area composed of several of the smallest reproduciblepixels and replicate this across the image where required. This area is called a Screen Cell (orHalftone Cell) and the process of replicating it across the image is called Screening (orHalftoning).

To achieve a 50% tint, half the area is lit up.

Copyright Hamillroad Software, 2005. Page 1 of 13 Andy Cave. January, 2005


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Single Screen Cell (50%) Screen Cell replicated at 0

The screen has an inherent shape, called the Dot Shape and is replicated a certain number of timesin a given distance, called the Screen Frequency. In general, Round, Elliptical or Euclideanshapes are used, but also shapes such as Line screens are used too.

It was found that replicating a screen at 0 produced a vertical/horizontal pattern that was quitevisible to the eye. However, rotating the screen by 45 produces a pattern than is less obvious.Black and white jobs therefore tend to use screens that are at 45.

Single Screen Cell (50%) Screen Cell replicated at 45

With color work, this gets even more complicated; if all the screens are at the same angle (e.g. 0),then the screen dots sit on top of each other. If there is a slight misregistration on the printing pressand one of the plates shifts slightly, then you can end up with some pages of a job where the screendots are on top and mix a lot, vs other pages of a job where the screen dots are not on top and sodont mix. Given ink mixing characteristics, this can produce a larger color shift where what shouldbe the same color on subsequent pages appears not to be.

It was found that if one rotated the screens on different separations by different amounts, then onedidnt have the problem of color shifts. However, the result of rotating the screens introduced moirpatterns into the output. If was further found that if the screens were put at 30 apart, then for threescreens, the moir was limited to a very small high frequency rosette pattern.

Three screens with moir. Three screens with rosettes.



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One was still left with the problem of what to do with the fourth screen (since we are dealing withfour inks - cmyk). This was dealt with by deciding that one would put the strong inks (cmk) 30apart and then put the fourth light ink (y) in between two of the other inks. Although the fourthscreen does produce some moir, since the yellow ink is light, the visibility of this is small enoughto not be noticed.

Screens are therefore described by referencing their angle, frequency and dot shape.

Typical angles therefore used for four color work are:

Cyan Magenta Yellow Black15 75 0 450 60 15 30

7.5 67.5 22.5 37.5

Accurate Screening

A further problem with screening is achieving the required angle spacing of the screens at 30. If

one takes a screen that has a frequency of 60 lpi (lines per inch) at 300 dpi (dots per inch) androtates it 15, one gets the following.

r2 = 300 / 60 * sin(15)

r1 = 300 / 60 * cos(15)

Single Rational Tangent Halftone Cell

Since the implementation is digital (implemented on a computer), the values for r1 and r2 have tobe integer. They therefore work out at r1 = 5 and r2 = 1. This produces an actual angle of 11.31instead of the requested 15. This type of screening is called rational tangent screening (RTscreening), since the angle we end up producing is a rational tangent.

In order to solve this problem, two solutions have been used in the industry.

The first of these is called irrational tangent screening (IRT screening). In this technique theimplementation tries to maintain the repeating structure of r1= 4.82962 and r2 = 1.29409across the page as the screen is replicated. As one can imagine, this is a very intensive and timeconsuming task since it involves lots of complicated floating point (non-integer) math. Because of this, IRT is quite often implemented in custom h/w with custom ASICS as opposed to in s/w.

The second of these is called super-cell screening. In this technique the s/w creates a larger rationalcell into which is fits a number of sub-cells. By making a larger rational cell, the required angle canbe met more accurately.



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2x2 super-cell

r2 = 300 / 60 * sin(15)

r1 = 300 / 60 * cos(15)

Some example numbers for a 133 lpi 15 screen at 1200 dpi are:

super-cell size r1 r2 frequency angle1x1 9 2 130.1582 12.52882x2 17 5 135.4398 16.38953x3 26 7 133.7006 15.06844x4 35 9 132.8218 14.42075x5 44 12 131.5587 15.2551

As can be seen from the numbers above, by going up to a 5x5 super-cell one can determine thatusing a 3x3 super-cell produces a much more accurate frequency and angle. By continuing to check higher dimensions, one can continue the search to find an even more accurate super-cell.

The benefit of this technique is that once the appropriate super-cell has been calculated, the actuallyreplication of the screen across the image is exactly the same as for a normal rational tangent screen(and so can be done with simple integer math).

The screening described above is classified as AM (amplitude modulated) screening, since theamplitude of the screen dot is modified to produce different intensity levels.

In an attempt to produce improved quality with screening, a number of alternative approaches havebeen tried. These include FM (frequency modulated) screening, XM (cross modulated) screening,error diffusion screening, dithered screening and many more.

Of these, FM screening is very popular. An FM screen is one where the size of the screen dotsremain the same (typically the smallest sized pixel that can be produced), but the frequency(number) of screen dots increases as the intensity required increases. There are many companieswho have produced variants of these, including HDS from Harlequin.

20% 40% 60% 80%

HDS Medium



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Although in theory the FM screen should be unbounded, in practice an FM screen is producedinside a cell of a given (large) size and this cell is replicated. This means that effectively, most FMimplementations are a rational tangent screen at 0, albeit one that is large with an extremelycomplicated shape.

One of the benefits of FM screening is that you dont get moir (since there are no repeatedstructures at certain angles), so colors that are difficult to produce with conventional screening, suchas flesh tones (where one has to mix magenta and yellow, producing moir) reproduce better.Additionally, FM screening is supposed to reflect better the detail of what is being reproduced,since the screen dots are smaller.

Dot Gain

When producing a film or plate, the required image is burnt or exposed onto the film/plate usinga laser beam. The laser beam scans across the film/plate and where an on is required the laser isturned on, and where an off is required, the laser is turned off.

The image that is to be exposed is made up of square pixels that define the on and offs.

However, the laser beam that is being used is not square, but typically round, and in order to lightup the whole of an on area so that there are no gaps, it needs to be large enough to cover the wholeof this area. Ideally the laser beam would need to have a radius equal to / (0.5), but more often thannot it is in fact larger than this.

A row of output pixels that are exposed would therefore look like this:

Typically the laser beam on an output device is not turned on for each pixel, but turned on at thestart of a black pixel sequence and remains on until that sequence stops. A row of output pixels thatare exposed therefore usually in fact look like this:

Swept laser-beam

Pulsed laser-beam

0.5

rr r

Beam too small Beam just right Beam too large(r = 0.5) (r = / 0.5) (r > / 0.5)



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As can be seen from the above, with a laser beam that is too large, instead of getting the requestedsquare device pixels exposed, a much larger area is exposed. In some cases this can be asignificantly larger area. For example with a 50% checkerboard image (with alternating on/off pixels), one easily gets a solid 100% image. Even with a smaller amount of overlap, instead of getting a 50% checkerboard image, one can get a density reading of 60% or more. This effect isknown as Dot Gain.

50% checkerboard has become solid due to dot gain.

However, even that is not the end of the story.

When the laser beam is initially turned on, it has to ramp up its power level to one that is sufficientto expose the plate. The exact behavior here depends on the plate type, since some plates exposeonly once a certain power threshold is exceeded, whilst others expose proportionally to the powerlevel. So sometimes a row of output pixels that are exposed can alternatively look like this:

or

Dot gain can be minimized by clumping together subsequent on pixels in a screen as the intensityincreases. This is because a new isolated on pixel will gain in all directions, whereas a new onpixel adjacent to existing on pixels will only gain in directions where it does not overlap anadjacent pixel that is on.

A large laser beam and therefore amount of overlap is quite common. For example one knowncomputer-to-plate device has a pixel size of 20 but a laser beam size of 35.

[As well as getting dot gain when producing the film or plate, one also gets dot gain when applyingink to an area of the plate. This occurs because ink flows and spreads when it is applied to paper.]

Calibration/Linearisation

The one thing that all the screening technologies mentioned previously have in common is that theyall suffer from dot gain. As a result, instead of linear output, one gets non-linear output. This is areal problem, especially if a large amount of dot gain is involved. This is because it basically

reduces the range of intensities available and an image might appear too dark (unless the imagewere specifically built to deal with a certain amount of dot gain - which would be unrealistic, sincethe image might be re-used on multiple output devices).



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In a high quality process environment (in fact in probably any environment), output from a film orplate setter therefore needs to be linearised. Since the use of a screen produces non-linear output,some sort of modification needs to be made to requested intensity values such that they map onto alinear range of output intensity values.

Traditionally, this has always been done by using a linearisation (or calibration) curve. The methodemployed is to print out a number of patches, measure them and build a transfer curve which isinstalled on the system and used to modify input intensity values so that the output intensity valueswhen printed are linear. The calibration strip below is one that is used in the Harlequin RIP.

Measurements from it are then entered into the calibration system which produces a calibrationcurve something like the following.

You can see from this that if you request a 40% tint (on the horizontal axis), you actually get a52.6% tint (on the vertical axis). What the calibration system therefore does to produce a particularintensity level, such as 40%, is to find the required intensity on the output axis (that is on thevertical axis) and then use the curve to find out what input level needs to be used to achieve this(that is the corresponding value on the horizontal axis). For the example given, 40%, one can see

from the curve that an input intensity of about 29% is required.



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Soft Proofing

The application of calibration curves to solve the problem of dot gain effectively reduces the outputdensities of a screened image, prior to exposure, thus making it lighter. If one therefore views thescreened image with a soft-proofing system, the overall densities of what is viewed are reduced.This leads to a soft-proof that is too light and which can be washed out in some cases extremelywashed out.

This can clearly be seen in the following two pictures, where the original PDF job viewed inAcrobat is clearly darker when compared to the soft-proof shown of the adjusted output prior toexposure. The latter case is clearly lighter and washed out.

.

Original PDF Job Soft-proof of normal RIP data

The application of calibration curves is therefore a major issue for anyone who wishes to soft-proof post-ripped data.

Invention

As can be seen from the earlier discussions regarding dot gain, the basic problem is that eachexposed pixel does not occupy the square device pixel it is meant to, but a larger gain area; it isthis extra gain area that leads to the dot gain.

The image that is to be exposed on film/plate/press is adjusted (typically reduced) using thecalibration curve that compensates for this dot gain. So effectively the output is produced assumingthat the square device pixel is going to grow by the dot gain. If we therefore physically model thisdot gain and apply it to the output that we intend to view, we should be able to modify the output sothat what we view on screen appears the same as that which is exposed.



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Physical Model

When looking at a single exposed pixel, the total area exposed can be broken down into a numberof different sections:

G1vG2

G0 G1h

Single Exposed Pixel

If we therefore know what G1v, G1h and G2 are, then, when we encounter a single exposed pixel,we can modify the output by adding a contribution from that exposed pixel to the surroundingdevice pixels.

As well as adding the contribution from an individual exposed pixel to the surrounding devicepixels, we also have to concern ourselves in the case where two adjacent exposed pixels exist:

G2

Two Horizontally Adjacent Exposed Pixels

From this we can see that we can ignore the overlap of the two exposed pixels in the middle (thedarker shaded area), and modify the output by adding a contribution from the two exposed pixels tothe surrounding device pixels G1v above and below, G1h to the left and right, and G2 diagonally.

Any two vertical adjacent exposed pixels have the same pattern of overlap, but in a vertical asopposed to horizontal direction.

When one considers all possible arrangements of exposed pixels, one discovers that it is alsopossible to have diagonally adjacent exposed pixels, with a different form of overlap:

G0

G1v

G1h

G1v

G1h G0



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G2 G1v

G0 G1hD2

D1

G3

Two Diagonally Adjacent Exposed Pixels

If we add in the contribution to the surrounding pixels following the earlier rules, then one can seethat the area pointed to by G 3 (in red) ends up being double-counted it will be counted first of allfrom the exposed pixels above when we add in G 1v and then counted a second time from theexposed pixels diagonally to the right and below when we add in G 1h.. It is therefore necessary toremove the area G 3 from the contributions computed.

Therefore, given any particular arrangement of exposed pixels in a bitmap, with various overlaps, itis possible to work out the area occupied by this extra gain area by summing G 0, G 1v, G 1h and G 2 for each device pixel and subtracting G 3 when there is a diagonal overlap.

In fact it works out simpler if one inverts this, and compares the contribution to a device pixel byitself and its surrounding neighbors. By definition, an exposed pixel can only contribute eithernothing (if off) or G 0 to itself (if on). If an exposed pixel contributes G 0 to itself, then there isnothing further that can be contributed - the device pixel is 100% solid. In the case of where theexposed pixel is blank, we have to add in the contribution from its surrounding eight neighbors.This can be computed quite simply using the following rules:

a) A diagonal neighbor exposed pixel only contributes (G 2) if the opposite diagonal exposedpixel (that makes a 2x2 square of exposed pixels) is blank.

b) A vertical or horizontal neighbor exposed pixel always contributes (G 1v or G 1h).c) If two adjacent-diagonal exposed pixels contribute, then we must subtract the double-

counted contribution (G 3).

Given a theoretical laser beam size, one can work out the various mathematical formulae thatrepresent G 0, G 1v, G 1h, G2 and G 3.

The case analyzed above is for the case where the laser beam is modulated on/off for each pixel. If the laser beam is in fact enabled-swept-disabled then the diagrams change slightly as does themath, but the basic principle holds.

The case analyzed above is correct where the radius of the laser beam is less than 1 pixel. If theradius of the laser beam is larger than that, then the basic principle still holds, but the contributionsto surrounding pixels change, as does the number of possible areas that are double-counted.



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Application

Therefore, given a 1-bit image that represents the data to be output to a film/plate/press, one cantake a certain laser beam size, calculate the parameter set {G 0 to G 3} and then apply this to thebitmap. The result is an 8-bit image that represents what the output is actually going to look like onthe film/plate/press.

This 8 bit image can then be displayed on a typical monitor, to show the user what the output isactually going to look like. Instead of getting the washed out image as shown previously, one getsan image that actually looks like what is going to be output.

Soft-proof of adjusted RIP data If one selects a single separation of the image and zooms in, one can see how each of the devicepixels has grown by the dot gain contribution that we calculated from each exposed pixel to itssurrounding device pixels:

Zoom in detail of the adjusted RIP data



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Configuration

There is however one final question to answer. How do we determine the appropriate laser-beamsize to use? Well with some clever thinking, it turns out that there is an easy way to determine this.

Consider the calibration strip that was shown before. Once this has been printed, measured and thedata entered into the RIP, typically a calibrated strip is produced.

This is printed and the result measured so as to check that the patches are correct. This calibratedstrip obeys the same physical laws as any image, and so before output is adjusted by the calibrationcurve that was created.

Calibrated Strip showing the 50% patch has been reduced by the calibration curve

As can be seen from the picture above, the density of the 50% patch is actually 37.8%, since it hasbeen adjusted by the calibration curve in the RIP. When output though, the dot shape that makes upthe 37.8% patch will increase in size and density (due to the dot gain) and should read 50%.

We can apply our invention to this 50% patch image, using an initial value for the laser beam sizeand modifying it until the 50% patch actually reads 50%. When this is achieved, we haveeffectively selected the laser beam size that matches our output device (along with its chemicals,film, plate, paper, inks, etc).



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It can be seen from the example below that in this case we needed to choose an effective laser beamsize of nearly 0.75 to get the 50% patch to actually measure as 50%.

Since our physical model simulates exactly what is happening on the output device, having got the50% patch to read 50%, all the other patches should be correct. These can easily be checked onscreen using a density tool (such as the one that exists in FirstPROOF Plus).

In the example below, all of the patches were measured to be within less than 1% of their targetdensity, with the average being within less than 0.35% of their target density. Most of this error is infact probably due to the basic inaccuracies and variability of measuring with a densitometer

Calibrated Strip showing the 50% patch has been adjusted (corrected) by the Dot Gain Tool

Summary The end result of using the [Inverse] Dot Gain Tool is that a previous soft-proof of the RIPped jobwhich was washed out and could not be compared to the original has been adjusted and can becorrectly viewed. Since this is the actual data that is going to your film/plate/press, one canview & approve it with confidence.

There really is no excuse now for not printing it right first time.

So, before you print it, First PROOF it! ( www.firstproof.com )

http://www.firstproof.com/http://www.firstproof.com/

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