# 5013- Banding and Halftone Theory

Banding looks very similar to steps across a fountain fill and
is the result of abrupt changes between various shades or
colors.  There are several things which affect the amount of
banding on an object: 

          The size of the object.
          The number of fountain stripes or bands as set in the
     CorelDRAW Print Menu.
          The percentage of gray change from one color to
     another in the Fountain Fill.
          The resolution of the print job.
          The Screen Frequency as set in the CorelDRAW
     Print Menu. 

The value for Screen Frequency will be different depending on the PostScript output device, the
color being used and the print job.  Your Service Bureau can provide the correct value.

Halftones
In the past, Laser Printers and Offset Printing Presses could print only two tones of any color,
solid, where all of the ink  is laid down in one spot and no ink coverage at all.  This process is
referred to as Black and White printing and was useful when newsletters, newspapers and books
were the only things being printed.  Its largest limitation, being unable to accurately reproduce
photographs, was quickly surpassed by using Halftones.  

Halftones are the result of the output device using a small grid made up of device pixels being
grouped together and treated as one.  The size of the pixels depends on the resolution, in dpi,
currently being used for printing, where as the size of the grid is dependent on the lines per inch,
lpi, used by the output device.  These grids are used to create halftone dots which emulate shades
of gray throughout the image.  By using halftones, the human eye registers shades of gray when in
fact, we are looking at a fine pattern of black and white dots.   

To demonstrate this, create an object defined as 50% gray.  When printed, half of the dots within
one cell of this grid will be turned on, black, while the other half of the dots will remain off, white. 
The pattern is then replicated throughout the object making it appear to be gray in color. 

Diagram 1-1.
A typical halftone dot created by  a printer. The small grid represents the device pixels, and the
large dot created by filling the grid is the halftone dot.



PostScript Printing
With current PostScript technology, the output device is limited to 256 shades total on a single
color or a grid that is based upon 16 by 16 halftone cells, 162=256.  In contrast, by dividing the
desired resolution of your output by 16, you can determine the maximum screen frequency that
the device can use to achieve 256 shades of gray.   The printer will accept other values but the
grid may be limited.  Using a lower number may cause the image to be more coarse than desired. 
Similarly, using a number to high may cause the banding to be more prominent in the document.



300

1270

2540
2540
2540
DPI


%
60
90
120
133
120
133
150
LPI


10
2
19
11
9
44
36
28



20
5
39
22
18
89
72
57



30
7
59
33
27
134
109
86



40
10
79
44
36
179
145
114



50
12
99
56
45
224
182
143



60
15
119
67
54
268*
218
172



70
17
139
78
63
313*
255*
200



80
20
159
89
72
358*
291*
229



90
22
179
100
82
403*
328*
258*



100
25
199
112
91
448*
364*
286*



max
0.75
5.97
3.36
2.73
7.5
7.5
7.5




Where,
% = % gray change & max = maximum length of object to be Fountain Filled in inches.

Example:  300 dpi laser printer prints out at 60LPI.  Using the above formula, 300 dpi /
16=18.75 lpi.  Although grouping 16 device pixels together at 300 dpi will force the printer to
produce a coarse image, this value of 18.75LPI will result in a smooth gradation between colors
within the size limitations.  Using 60 lpi will produce a reasonable image but the printer will be
limited to as many shades of gray as it can actually print (see chart below).  Whether this will be
noticeable or not depends on the fountain fills in the document,  how they were created and the
quality of output desired.

Note:     The current PostScript technology limits the maximum number of bands to 256 making all
values with an asterisk (*) not possible.

By using the method below, you can determine how many shades of gray or bands in a fountain
fill are available to the printer based upon the current dpi and lpi, it is then possible to determine if
banding will be noticeable in certain objects.  Once the file has been sent to the printer, the
PostScript interpreter will make the changes to the values that you have specified.

The human eye can see objects as small as .03 inches (1/32") in size, bands in the fountain fill as
small or smaller than this will usually appear smooth. To determine the size of a band, divide the
number of bands by the length of the object containing the fountain fill.  
If the size of the band is smaller that .03 inches, than banding will not be noticeable, however the
opposite is true if the size is greater than .03 inches.

# of Bands=[(DPI/LPI)2 x (% gray change)]/100 where,   
dpi = resolution in dots-per-inch, and lpi =  Screen Frequency 

The Adobe PostScript(r) Language Reference Manual (the "Red Book") reads: "...the best choice
of screen parameters is often dependent on specific physical properties of the output device itself
(e.g., pixel shape, overlap between pixels, and effects of electronic or mechanical noise). ...The
setscreen operator may make slight adjustments to the requested frequency and angle so as to
ensure that the patterns of enclosed pixels remain constant as the screen cells are replicated over
the entire page."1

If you are creating black and white fountain fills only, the above seems fairly straightforward,
however when using color, it is necessary to calculate the gray equivalent.  The following
formula2 is from the Adobe PostScript(r) Language Reference Manual:
% gray = .30 x (% red) + .59 x (% green) + .11 x (% blue)
CorelDRAW can show you the RGB (Red, Green, Blue) equivalents of the colors you are using,
as explained in the following steps:

1.  Use the Uniform Fill tool to fill an object with a color.
2.  Click the Custom Fill tool from the flyout.
3.  Using the CMYK (Cyan, Magenta, Yellow, blacK) color model, the color is defined as a
combination of cyan, magenta, yellow and black..
By changing to the RGB color model, you will see that the color is now defined as a combination
of red, green and blue.
4.  Use the formula below to calculate the percentage of gray.  We are using the color Orange in
this  example: 
      %gray = .30 x (100% R) + .59 x (40% G) + .11 x (0% B)   This works out to be 53.6% 
     gray.
5.  Then using the same formula, calculate the % of gray for the destination color. 
6.  With these two values, you would be able to determine the percentage of gray change between
the two colors, and apply the original formula to decide the number of stripes or bands for your
fountain fill.

Note:     This information is meant to act as a general guide only, and should not be considered as
the definitive solution to a particular problem.


1.2  Postscript(r) Language Reference Manual (c) 1985 Adobe Systems Incorporated
Addison-Wesley Publishing Company Inc