Screen Ruling Print Resolution AM FM and Hybrid

Screen Ruling, Print Resolution AM, FM and Hybrid Halftoning Sasan Gooran Linköping University Li. U-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 bits/pixel • Grayscale • RGB 8 3*8=24 256 tones 256^3=16. 7 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 Con-tone Image Halftoned Halftoning Image Print

DIGITAL HALFTONING Example Periodic and clustered dots

DIGITAL HALFTONING Example Non-periodic and dispersed dots

$HALFTONE CELL Pixel (/a number of pixels) Halftone cell The fractional area covered by$

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 Halftone cell Original image Halftoned image

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 Ex. A 10 x 15 cm 2 photo that is supposed to be 20 x 30 cm 2 when printed at 150 lpi has to be scanned with a ppi about 2*2*150 = 600.

Micro dot HALFTONE CELL dpi: Number of micro dots per inch This halftone cell represents at most 82 + 1= 65 gray tones

HALFTONE CELL Screen ruling: number of halftone cells per inch (lpi) Micro dot Halftone cell In this case: 17 gray tones Resolution: number of micro dots per inch (dpi)

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

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) 1 st generation – The size of the dots is constant, their frequency varies • FM (Frequency Modulated) 2 nd generation – The size of the dots and their frequency vary

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

AM & FM Halftone AM FM

FM Halftone, 1 st and 2 nd generation First Second

Hybrid Halftoning FM_2 FM_1 AM

THRESHOLDING g and b are the original and the halftoned image, respectively. t is the threshold matrix.

THRESHOLDING 0. 6 1 0. 3 0. 2 Original Image 0 Threshold matrix Halftoned image This threshold matrix represents 10 gray tones

THRESHOLD MATRIX Example: Line 1 2 5 6 9 10 13 14 3 7 11 15 4 8 12 16

THRESHOLD MATRIX Example: Spiral 1 12 11 10 2 13 16 9 3 14 15 8 4 5 6 7

THRESHOLD MATRIX Clustered & Dispersed, 45 degrees 14 5 6 9 19 28 27 24 12 13 4 3 1 2 7 8 21 20 29 30 32 31 26 25 16 10 11 15 17 23 22 18 19 28 27 24 14 5 6 9 21 20 29 30 32 31 26 25 12 13 4 3 1 2 7 8 Clustered 17 23 22 18 16 10 11 15 1 30 8 28 17 9 24 16 5 25 3 32 21 13 19 11 2 29 7 27 18 10 23 15 6 26 4 31 22 14 20 12 1 30 8 28 17 9 24 16 5 25 3 32 21 13 19 11 Dispersed