Screen Ruling, Print ResolutionAM, FM and Hybrid Halftoning

Sasan Gooran

Linköping University

LiU-Norrköping

DIGITAL IMAGES (pixel based)

Scanning

Photo Digital image

ppi (pixels per inch): Number of samples per inch

ppi (pixels per inch)

• ppi (scanning resolution): Number of samples per inch

• The higher ppi the better the representation of the con-tone image (Photo)

• Higher ppi requires more memory

• ppi should not be unncessarily high

• Choice of ppi????

ppi = 72

ppi = 36

ppi = 18

DIGITAL IMAGES Memory

• Grayscale 8 256 tones

• RGB 3*8=24 256^3=16.7

bits/pixel

million colors

DIGITAL HALFTONING

• Since most printers and image setters are not able to reproduce different shadows of gray the original digital image has to be transformed into an image containing white (0’s) and black (1’s)

Halftoning

DIGITAL HALFTONING

Prepress Halftoning PrintCon-tone

Image

Halftoned

Image

DIGITAL HALFTONING Example

Periodic and clustered dots

DIGITAL HALFTONING Example

Non-periodic and dispersed dots

HALFTONE CELL Pixel (/a number of pixels)

Halftone cell

The fractional area covered by the ink corresponds to the value of the pixel (or the area)

HALFTONE CELL

Original image Halftoned image

Halftone cell

SCREEN RULING/FREQUENCY

• lpi (lines per inch): Number of halftone cells per inch

• The higher lpi the better the print (?!)

• High lpi requires more stable print press etc.

• Does a higher lpi always lead to a better print? (to be answered later)

RULE OF THUMB

lpisizeOriginalsDppi *2* ize esired

Ex. A 10 x 15 cm2 photo that is supposed to be 20 x 30 cm2

when printed at 150 lpi has to be scanned with a ppi about 2*2*150 = 600.

HALFTONE CELLMicro dot

dpi: Number of micro dots per inch

This halftone cell represents at most 82 + 1= 65 gray tones

HALFTONE CELL

Halftone cellHalftone cell Resolution: number of micro dots per inch (dpi)Resolution: number of micro dots per inch (dpi)

Micro dotMicro dot

In this case:17 gray tonesIn this case:17 gray tones

Screen ruling: number of halftone cells per inch (lpi)Screen ruling: number of halftone cells per inch (lpi)

lpi & dpi

• lpi: Number of halftone cells per inch

• A halftone cell consists of micro dots

• dpi: Number of micro dots per inch

• The ratio dpi/lpi decides the size of the halftone cell

lpi & dpi

gray tones of n12

lpidpi umber

lpi & dpi (Example)

• Assume that dpi is fixed at 600

• lpi = 150 only gives 17 gray tones

• lpi = 100 only gives 37 gray tones

• lpi = 50 gives 145 gray tones

• Does a higher lpi always lead to a better print? Not necessarily!

High lpi, few gray tones

Lower lpi, more gray tones

Low lpi, more gray tones but large halftone dots, (not satisfying)

AM & FM HALFTONING

• AM (Amplitude Modulated)– The size of the dots is variable, their frequency

is constant

• FM (Frequency Modulated) 1st generation– The size of the dots is constant, their frequency

varies

• FM (Frequency Modulated) 2nd generation– The size of the dots and their frequency vary

AM & FM (1st & 2nd Generation) Halftone

AM FM, 1st FM, 2nd

AM & FM Halftone

AM FM

FM Halftone, 1st and 2nd generation

First Second

Hybrid Halftoning

AMFM_1FM_2

THRESHOLDING

),(),( if ,0

),(),( if ,1),(

nmtnmg

nmtnmgnmb

g and b are the original and the halftoned image, respectively.

t is the threshold matrix.

THRESHOLDING

0.6

0.1

1

0.3

0.2 0

Original Image Halftoned imageThreshold matrix

This threshold matrix represents 10 gray tones

THRESHOLD MATRIXExample: Line

1 2 3 4 1 2 3 4 5 6 7 8 5 6 7 8 9 10 11 12 9 10 11 12 13 14 15 1613 14 15 16

THRESHOLD MATRIXExample: Spiral

1 2 3 4 1 2 3 4 12 13 14 5 12 13 14 5 11 16 15 6 11 16 15 6 10 9 8 710 9 8 7

THRESHOLD MATRIX Clustered & Dispersed, 45 degrees

14 12 13 16 19 21 20 1714 12 13 16 19 21 20 17 5 4 3 10 28 29 30 23 5 4 3 10 28 29 30 23 6 1 2 11 27 32 31 22 6 1 2 11 27 32 31 22 9 7 8 15 24 26 25 18 9 7 8 15 24 26 25 1819 21 20 17 14 12 13 1619 21 20 17 14 12 13 1628 29 30 23 5 4 3 10 28 29 30 23 5 4 3 10 27 32 31 22 6 1 2 1127 32 31 22 6 1 2 1124 26 25 18 9 7 8 15 24 26 25 18 9 7 8 15

1 30 8 28 2 29 7 271 30 8 28 2 29 7 2717 9 24 16 18 10 23 1517 9 24 16 18 10 23 15 5 25 3 32 6 26 4 31 5 25 3 32 6 26 4 3121 13 19 11 22 14 20 1221 13 19 11 22 14 20 12 2 29 7 27 1 30 8 28 2 29 7 27 1 30 8 28 18 10 23 15 17 9 24 16 18 10 23 15 17 9 24 16 6 26 4 31 5 25 3 32 6 26 4 31 5 25 3 32 22 14 20 12 21 13 19 11 22 14 20 12 21 13 19 11

Clustered Dispersed

TABLE HALFTONING

0.6

0.2 0

Original Image Halftoned image

MeanMean

TABLE HALFTONING

Clustered Dispersed

FM HALFTONING Error Diffusion

0.7

Threshold0.5

Original image Halftoned Image

0.3

error-Filter

7

3 5 1(*1/16)

COLOR PRINT

Additive color mixing, TV, Computer screen

COLOR PRINT

Subtractive color mixing, Printers

COLOR PRINT

• Three primary colors

• CYAN (C)• MAGENTA (M)• YELLOW (Y)

COLOR PRINT

• Three secondary colors

• And Black

• RED (R, MY)• GREEN (G, CY)• BLUE (B, CM)

• BLACK (K, CMY)

COLOR PRINT

Original

COLOR PRINT

AM

COLOR PRINT

FM

AM HALFTONE same angle for C, M, Y & K

Conventional Color HalftoningSame raster angle

Error in position can cause color shift

Conventional Color HalftoningSame raster angle

Error in raster angle can cause Moiré

Conventional Color Halftoning Different raster angle, 0, 15, 75 and 45 degrees

AM different anglesRosette patterns

FM

AM HALFTONE different angles for C, M, Y and K

15, 75, 0 and 45 degrees

ROSETTE PATTERN

ROSETTE PATTERN