Marktonk,
Thanks for the screening link. I was trying to avoid promoting a specific brand which is why I did not use a Kodak product reference. HD's IS screening in software, as you are aware is based on HQS screening, which is supercell technology. An earlier version of your guide puts it very well: From the Heidelberg "Expert Guide - An Introduction to Screening Technology" Section: 3.4.2 Modern IS Implementation" "The classic hardware IS algorithm cannot be processed quickly enough in software.This is why the software solution is based on completely different algorithms which are basically similar to the HQS process described earlier."
RGPW1700
I think I'm suffering a bit of jet lag (just got off a 16 hour flight from Australia)
I googled supercell screening to try and get you a fairly vendor neutral technical description - but didn't completely check the contents of the PDF. My bad.
I wasn't trying to promote stochastic/FM screening. What I was describing refers to conventional AM screening. The process to get around the gray level limitation suggested by the formula ("number of gray levels = (ouput res / screen freq)² + 1") is called "dithering". Most descriptions of supercell screening also talk about overcoming gray level limitations (which is why I went there in my original post).
Your question, if I understand it correctly, contains a common misconception.
A halftone dot is formed inside a halftone "cell" The cell is a grid of pixels which are turned on to form the dot. The cell begins with no pixels turned on (0% tone) and as pixels are turned on the dot grows until all the pixels within the cell are turned on and the cell is filled (i.e. 100% tone).
For example.
If the cell size is 2 pixels wide by 2 pixels deep the halftone cell will contain a total of 4 pixels. As a result the following halftone dot tone values can be created:
0% = all pixels off
25% = 1 pixel turned on
50% = 2 pixels turned on
75% = 3 pixels turned on
100% = 4 pixels turned on.
So, with a 2x2 pixel halftone cell it is only possible to have 5 tone levels (gray levels). I.e. the total number of tones possible equals the total number pixels available plus one. In this case 2x2=4 4+1 = 5.
If the number of pixels is increased within the cell by making them smaller - i.e. cell size remains the same but the pixels are smaller - then the number of possible gray levels goes up.
For example:
For a 10x10 cell the number of possible gray levels is 101 (10x10=100, 100+1=101)
For a 16x16 cell the number of possible gray levels is 257 (16x16=256, 257+1=257)
In a basic AM screen the dot is formed by turning on pixels starting from the center of the cell. (For a basic FM screen the pixels within the cell are turned on pseudo-randomly.)
So, as resolution increases - graylevels increases. As resolution decreases gray levels decrease.
If the resolution (dpi) is fixed but the number of adjacent cells is increased (i.e. lpi is increased) then the number of pixels available for each dot decreases and therefore the number of gray levels decreases.
This principle is captured by the classic formula: (dpi/lpi) squared + 1 = number of graylevels
Which is the formula you quoted.
So, for a 2400 dpi device:
2400 dpi/200 lpi = 12. 12 squared = 144. 144 plus one = only 145 tones possible. A problem.
And at 400 lpi
2400 dpi/400 lpi = 6. 6 squared = 36. 36 plus one = only 37 tones possible. A big problem.
However, the formula is only true for the tone represented by a single, isolated, halftone dot based on an individual halftone dot cell- something that never occurs in real production environments. Around 1989 a new approach began to be adopted. This approach is based on the fact that we don't care about individual halftone dots. What is important is the tone represented in an area. For example, we want to see a 17% tone patch value in the presswork. If we cannot represent that area with individual 17% dots because of that classic formula limitation we can still create the 17% value by alternating 16% dots and 18% dots (this is called "dithering"). The eye (and instruments) integrate the alternating 16% and 18% dots and the result is the average value - in this example 17% our desired tone value.
Supercell screening gets around the gray level limitations of the classic formula by looking at a tone area (the important criteria) rather than an individual dot. As a result, since about 1995 virtually all AM screens from all vendors adopted variants of supercell screening technology.
Most RIPs are normally shipped with this feature set to 1024 as this meets the tonal needs of the highest quality printers.
Users of systems that do not offer this functionality must resolve gray-level issues by increasing the addressability and resolution of the output device, limiting the screen ruling to a low lpi, or scaling the size and tonal gradation of problematic vignettes. These very high-resolution devices (e.g. 4000 dpi) are unnecessarily costly. Their high-resolution bitmaps are also larger, process more slowly, and impact throughput speed on the imaging device.
The optimal performance-to-quality ratio points to devices that operate in the range of around 2400 dpi. Systems using supercell screening technology to extend gray level generation offer all the resolution, all the screening, and all the throughput speed that most users will ever need. As a result, 2400 dpi has become the defacto standard for imaging resolution in the commercial print industry. Higher resolutions, as far as halftone screening is concerned, provides no additional value while imposing a penalty on imaging time.
The highest lpi on a 2400 dpi device that I'm aware of was 1694 lpi imaged on a Creo/Kodak CtP device in (I believe) 2000 by Metropolitan Fine Printers in Vancouver Canada which won a "They said it can't be done" award at GrapExpo in Chicago.
Where the various vendors distinguish themselves with their individual implementation of supercell screening is how they deal with issues such as rosette drift - the gradual shift from clear centered rosette to dot centered rosette - over the width of the plate, single channel moiré, miniscus effects as dots first touch, e.g. at the 50% point, and other nuances of halftone screening.
Hope this helps. Best, gordo