Laser Index

Avery 5388 Laser  Inkjet 3 x 5 Index Cards 150 pk
Avery 5388 Laser Inkjet 3 x 5 Index Cards 150 pk
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Avery Laser Inkjet Index Card
Avery Laser Inkjet Index Card
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Avery 5388 Laser  Inkjet 3 x 5 Index Cards 150 pk
Avery 5388 Laser Inkjet 3 x 5 Index Cards 150 pk
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Avery 25 Index Tabs w Printable Inserts Laser Ink Jet
Avery 25 Index Tabs w Printable Inserts Laser Ink Jet
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Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
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Redi tag 39017 Laser Printable Index Tabs Stick On Tabs RTG39017
Redi tag 39017 Laser Printable Index Tabs Stick On Tabs RTG39017
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Avery ExtraWide Ready Index Dividers with Multicolor Tabs Laser Ink Jet Tabs
Avery ExtraWide Ready Index Dividers with Multicolor Tabs Laser Ink Jet Tabs
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Redi Tag Laser Index Tabs  33117
Redi Tag Laser Index Tabs 33117
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Foldover score cards 90 Index 2 up Laser Inkjet Paper
Foldover score cards 90 Index 2 up Laser Inkjet Paper
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NEW Printable Laser Index Tabs Self Stick Plastic
NEW Printable Laser Index Tabs Self Stick Plastic
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Avery Consumer Products Products Index Maker Laser Punched 8 Tab 8 ST Whi
Avery Consumer Products Products Index Maker Laser Punched 8 Tab 8 ST Whi
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1 set of Wilson Jones 8 tabs MultiDex Basic index System Dividers 50818 LASER
1 set of Wilson Jones 8 tabs MultiDex Basic index System Dividers 50818 LASER
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Redi Tag 33001 Laser Index Tabs Tab Indexe
Redi Tag 33001 Laser Index Tabs Tab Indexe
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Redi Tag 33117 Laser Index Tab Tab Indexe
Redi Tag 33117 Laser Index Tab Tab Indexe
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Redi Tag 33120 Laser Index Tab Tab Indexe
Redi Tag 33120 Laser Index Tab Tab Indexe
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5 sets of Avery 5 tabs Index Maker Clear Label Dividers 11416 LASER
5 sets of Avery 5 tabs Index Maker Clear Label Dividers 11416 LASER
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Post cards 90 Index 2 up 25 sheets Laser Inkjet Paper
Post cards 90 Index 2 up 25 sheets Laser Inkjet Paper
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NEW Redi Tag Laser Printable Index Tabs 1 1 8 Inch W
NEW Redi Tag Laser Printable Index Tabs 1 1 8 Inch W
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NEW Index Makerreg White Dividers Clear Laser Ink
NEW Index Makerreg White Dividers Clear Laser Ink
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NEW Printable Laser Index Tabs Self Stick Plastic
NEW Printable Laser Index Tabs Self Stick Plastic
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Redi Tag Laser Index Tab100xTab Blank 100 PK White
Redi Tag Laser Index Tab100xTab Blank 100 PK White
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3 sets of Avery 5 tabs Index Maker Clear Label Dividers 11416 LASER
3 sets of Avery 5 tabs Index Maker Clear Label Dividers 11416 LASER
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Redi Tag 39000 Laser Index Tabs Tab Indexe
Redi Tag 39000 Laser Index Tabs Tab Indexe
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Sparco Spr 21919 Laser Printer Indexing System Dividers 8 X Tab Blank 8
Sparco Spr 21919 Laser Printer Indexing System Dividers 8 X Tab Blank 8
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NEW CARDLASER INDEXWHT ML8576
NEW CARDLASER INDEXWHT ML8576
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Printable Laser Index Tabs 7 16in White 180 pack
Printable Laser Index Tabs 7 16in White 180 pack
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Sparco Products 05850 Laser Printer Index Tab Indexe
Sparco Products 05850 Laser Printer Index Tab Indexe
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100+ Sheets Wausau Papers Exact Index Ivory 49181 Basis 90 Laser Compatible
100+ Sheets Wausau Papers Exact Index Ivory 49181 Basis 90 Laser Compatible
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100+ Sheets Wausau Papers Exact Index Yellow 110 Laser Compatible
100+ Sheets Wausau Papers Exact Index Yellow 110 Laser Compatible
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NEW Redi Tag Laser Printable Index Tabs 7 16 x 1 Whi
NEW Redi Tag Laser Printable Index Tabs 7 16 x 1 Whi
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NEW Printable Laser Index Tabs Self Stick Plastic
NEW Printable Laser Index Tabs Self Stick Plastic
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Redi Tag B Thomas Enterprises Printable Laser Index Tabs 2w x 7 8h White
Redi Tag B Thomas Enterprises Printable Laser Index Tabs 2w x 7 8h White
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Redi Tag 39020 Laser Index Tab Tab Indexe
Redi Tag 39020 Laser Index Tab Tab Indexe
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Redi Tag 39017 Laser Index Tab Tab Indexe
Redi Tag 39017 Laser Index Tab Tab Indexe
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Avery Ready Index Laser Ink Jet Easy Edit Table of Contents Dividers 1 5 6
Avery Ready Index Laser Ink Jet Easy Edit Table of Contents Dividers 1 5 6
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Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
$13.34
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Kleer Fax Index DividersLaser InkjetUnpunched5 Tab25 Sets PKWhite KLF23256
Kleer Fax Index DividersLaser InkjetUnpunched5 Tab25 Sets PKWhite KLF23256
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Sparco Products 05851 Laser Printer Index Tab Indexe
Sparco Products 05851 Laser Printer Index Tab Indexe
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Avery Laser Inkjet Unruled Index Cards AVE5388
Avery Laser Inkjet Unruled Index Cards AVE5388
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Avery ExtraWide Ready Index Dividers with Multicolor Tabs Laser Ink Jet Tabs
Avery ExtraWide Ready Index Dividers with Multicolor Tabs Laser Ink Jet Tabs
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Sparco Spr 01824 Laser Printer Indexing System Divider 3 X Tab Blank 85 X
Sparco Spr 01824 Laser Printer Indexing System Divider 3 X Tab Blank 85 X
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Sparco Spr 21915 Laser Printer Indexing System Dividers 5 X Tab Blank 5
Sparco Spr 21915 Laser Printer Indexing System Dividers 5 X Tab Blank 5
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AVERY CLEAR LABEL INDEX MAKER DIVIDERS 5 TABS 1 SET  11994 LASER INK JET
AVERY CLEAR LABEL INDEX MAKER DIVIDERS 5 TABS 1 SET 11994 LASER INK JET
$3.25
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NEW Laser Printable Index Tabs 2w x 7 8h White 80
NEW Laser Printable Index Tabs 2w x 7 8h White 80
$10.99
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50 Sets SPARCO Laser Printer Indexing System White 5 Tab Dividers 21916 NEW
50 Sets SPARCO Laser Printer Indexing System White 5 Tab Dividers 21916 NEW
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NEW Redi Tag Laser Printable Index Tabs 1 1 8 x 1 1 4
NEW Redi Tag Laser Printable Index Tabs 1 1 8 x 1 1 4
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50 Sets SPARCO Laser Printer Indexing System 8 Tab Dividers Binder 21919 NEW
50 Sets SPARCO Laser Printer Indexing System 8 Tab Dividers Binder 21919 NEW
$49.87
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25 Sets Custom Index Label System 5 Tab Laser InkJet
25 Sets Custom Index Label System 5 Tab Laser InkJet
$19.95
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AVERY 11415 Index Maker Laser Inkjet 8 Tab 5 Sets
AVERY 11415 Index Maker Laser Inkjet 8 Tab 5 Sets
$24.89
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Avery Index Maker White Dividers 3 Tab Clear Laser Ink Jet Labels 5
Avery Index Maker White Dividers 3 Tab Clear Laser Ink Jet Labels 5
$19.92
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Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
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Avery 5388 Index Cards Inkjet LaserWhite 150 Cards
Avery 5388 Index Cards Inkjet LaserWhite 150 Cards
$19.99
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Sparco Spr 21918 Laser Printer Indexing System Dividers 8 X Tab Blank 8
Sparco Spr 21918 Laser Printer Indexing System Dividers 8 X Tab Blank 8
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Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
$22.55
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Avery Ready Index Laser Ink Jet Easy Edit Table of Contents Dividers 1 8 6
Avery Ready Index Laser Ink Jet Easy Edit Table of Contents Dividers 1 8 6
$19.06
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CARDLASER INDEXWHT
CARDLASER INDEXWHT
$15.99
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Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
Redi Tag B Thomas Enterprises Printable Laser Index Tabs Self Stick Plastic
$15.22
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RTG 39000 2 Redi tag Laser Printable Index Tabs 7 16 x 1
RTG 39000 2 Redi tag Laser Printable Index Tabs 7 16 x 1
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Avery Laser Inkjet Index Card Perforated 3 x 5 150 BX White
Avery Laser Inkjet Index Card Perforated 3 x 5 150 BX White
$21.76
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NEW Ready Indexreg Laser Ink Jet Easy Edit Table of
NEW Ready Indexreg Laser Ink Jet Easy Edit Table of
$15.99
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NEW Index Maker White Dividers 3 Tab Clear Laser In
NEW Index Maker White Dividers 3 Tab Clear Laser In
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Redi tag Laser Printable Index Tabs RTG39000
Redi tag Laser Printable Index Tabs RTG39000
$21.36
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REDI TAG 33001 LASER PRINTABLE INDEX TABS 7 16 WHI
REDI TAG 33001 LASER PRINTABLE INDEX TABS 7 16 WHI
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RTG 33171 6 Redi tag Laser Printable Index Tabs 2 x 7 8
RTG 33171 6 Redi tag Laser Printable Index Tabs 2 x 7 8
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Avery Ready Index Laser Ink Jet Easy Edit Table of Contents Dividers 1 10 6
Avery Ready Index Laser Ink Jet Easy Edit Table of Contents Dividers 1 10 6
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Sparco Indexing Divider System F Laser Printers Punched5 Tab WE
Sparco Indexing Divider System F Laser Printers Punched5 Tab WE
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Redi tag 39020 Laser Printable Index Tabs Stick On Tabs RTG39020
Redi tag 39020 Laser Printable Index Tabs Stick On Tabs RTG39020
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Printable Laser Index Tabs 1 1 8in White 100 pack
Printable Laser Index Tabs 1 1 8in White 100 pack
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NEW Laser Printable Index Tabs 2w x 7 8h White 30
NEW Laser Printable Index Tabs 2w x 7 8h White 30
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RTG 33117 6 Redi tag Laser Printable Index Tabs 1 1 8 Inch
RTG 33117 6 Redi tag Laser Printable Index Tabs 1 1 8 Inch
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RTG 33120 6 Redi tag Laser Printable Index Tabs 1 1 8 Inch Five Colors
RTG 33120 6 Redi tag Laser Printable Index Tabs 1 1 8 Inch Five Colors
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RTG 33001 6 Redi tag Laser Printable Index Tabs 7 16 Inch
RTG 33001 6 Redi tag Laser Printable Index Tabs 7 16 Inch
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RTG 39017 6 Redi tag Laser Printable Index Tabs 1 1 8 x 125
RTG 39017 6 Redi tag Laser Printable Index Tabs 1 1 8 x 125
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RTG 39020 6 Redi tag Laser Printable Index Tabs 1 1 8 x 125
RTG 39020 6 Redi tag Laser Printable Index Tabs 1 1 8 x 125
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RTG 39170 2 Redi tag Laser Printable Index Tabs 2 x 7 8
RTG 39170 2 Redi tag Laser Printable Index Tabs 2 x 7 8
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Redi tag 33117 Laser Printable Index Tabs 3 Item Bundle Stick On Tabs
Redi tag 33117 Laser Printable Index Tabs 3 Item Bundle Stick On Tabs
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Avery 5388 Laser Inkjet Unruled Index Cards 3x5 150 Box 5
Avery 5388 Laser Inkjet Unruled Index Cards 3x5 150 Box 5
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Avery Index Maker White Dividers 5 Tab Clear Laser Ink Jet Labels 5
Avery Index Maker White Dividers 5 Tab Clear Laser Ink Jet Labels 5
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Sparco Indexing Divider System F Laser Printers Unpunched 5 Tab WE
Sparco Indexing Divider System F Laser Printers Unpunched 5 Tab WE
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Business Source 16482 Punched Laser Index Divider Tab Dividers BSN16482
Business Source 16482 Punched Laser Index Divider Tab Dividers BSN16482
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Redi tag 39170 Laser Printable Index Tabs Stick On Tabs RTG39170
Redi tag 39170 Laser Printable Index Tabs Stick On Tabs RTG39170
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Redi tag 33171 Laser Printable Index Tabs 2 Item Bundle Stick On Tabs
Redi tag 33171 Laser Printable Index Tabs 2 Item Bundle Stick On Tabs
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Redi tag 33120 Laser Printable Index Tabs 3 Item Bundle Stick On Tabs
Redi tag 33120 Laser Printable Index Tabs 3 Item Bundle Stick On Tabs
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Redi tag 33001 Laser Printable Index Tabs 3 Item Bundle Stick On Tabs
Redi tag 33001 Laser Printable Index Tabs 3 Item Bundle Stick On Tabs
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Printable Laser Index Tabs 1 1 8w x 1 1 4h White 375 pack
Printable Laser Index Tabs 1 1 8w x 1 1 4h White 375 pack
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Avery Index Maker White Dividers 12 Tab Clear Laser Ink Jet Labels 5
Avery Index Maker White Dividers 12 Tab Clear Laser Ink Jet Labels 5
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Redi Tag B Thomas Enterprises Printable Laser Index Tabs 2w x 7 8h White
Redi Tag B Thomas Enterprises Printable Laser Index Tabs 2w x 7 8h White
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Avery Index Maker White Dividers 3 Tab Clear Laser Ink Jet Labels 25
Avery Index Maker White Dividers 3 Tab Clear Laser Ink Jet Labels 25
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Business Source Punched Laser Index Divider 3 x Tab 25 Box White Tab
Business Source Punched Laser Index Divider 3 x Tab 25 Box White Tab
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Avery Index Maker White Dividers 8 Tab Clear Laser Ink Jet Labels 5
Avery Index Maker White Dividers 8 Tab Clear Laser Ink Jet Labels 5
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Business Source 16488 Laser Printer Index Divider Tab Dividers BSN16488
Business Source 16488 Laser Printer Index Divider Tab Dividers BSN16488
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Printable Laser Index Tabs 2w x 7 8h White 80 pack
Printable Laser Index Tabs 2w x 7 8h White 80 pack
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Sparco Indexing Divider System F Laser Printers Punched3 Tab WE
Sparco Indexing Divider System F Laser Printers Punched3 Tab WE
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Sparco Indexing Divider System F Laser Printers Unpunched 8 Tab WE
Sparco Indexing Divider System F Laser Printers Unpunched 8 Tab WE
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Sparco Indexing Divider System F Laser Printers Punched8 Tab WE
Sparco Indexing Divider System F Laser Printers Punched8 Tab WE
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Avery Index Maker White Dividers 5 Tab Clear Laser Ink Jet Labels 25
Avery Index Maker White Dividers 5 Tab Clear Laser Ink Jet Labels 25
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Kleer Fax Index DividersLaser InkjetUnpunched5 Tab5 Sets PKWhite KLF23056
Kleer Fax Index DividersLaser InkjetUnpunched5 Tab5 Sets PKWhite KLF23056
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Prepunched Index Maker Dividers w Tabs Laser Punched 8 Tabs 50 BX White
Prepunched Index Maker Dividers w Tabs Laser Punched 8 Tabs 50 BX White
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Laser and Inkjet Compatible Index or Postcards 4 x 6 Two Sheet 100 Cards Box
Laser and Inkjet Compatible Index or Postcards 4 x 6 Two Sheet 100 Cards Box
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Avery Index Maker White Dividers Clear 8 Tab Labels Laser 3 Hole 25
Avery Index Maker White Dividers Clear 8 Tab Labels Laser 3 Hole 25
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Laser Index
Laser Index

Advantages and Disadvantages of Etching with Beam-Steered Laser

This year, over one-third of all material processing lasers will be installed for product or package marking applications. Since their introduction in the early-1970's, laser markers have evolved as an effective tool for manufacturers who require a combination of speed, permanence, and image flexibility not available from more traditional marking technologies.

Two marking system designs have emerged with notably different strengths and weaknesses. Careful consideration of these laser and imaging optics combinations can provide the optimum tool for a wide range of marking requirements.
Process Fundamentals

Laser marking is a thermal process that employs a high-intensity beam of focused laser light to create a contrasting mark. The laser beam increases the surface temperature to induce either a color change in the material and/or displace material by vaporization to engrave the surface. Both marking system configurations utilize this principle of surface modification but differ in the method used to project the laser beam and create the marking image.

The beam-steered laser marker provides the greatest degree of image manipulation. To create the marking image, two beam-steering mirrors mounted on high-speed, computer-controlled galvanometers direct the laser beam across the target surface. Each galvanometer provides one axis of beam motion in the marking field. The beam projects through a multi-element, flat-field lens assembly after reflecting off the final steering mirror. The lens assembly focuses the laser light to achieve the highest power density possible on the work surface while maintaining the focused spot travel on a flat plane. The laser output is gated between marking strokes. This design offers the user the advantages of a computer generated marking image and utilization of the entire laser output for the highest marking power possible.

The mask or "stencil" marking system sacrifices image quality and versatility for significantly increased marking speed. The marking image is created by enlarging the laser beam, projecting it through a copper stencil of the desired image, and refocusing the beam on the target surface to "burn" the image into the material. A single pulse of the laser creates the entire image. If the alphanumeric characters must be altered part-to-part, (i.e., serialization, etc.), computer-controlled rotary stencil wheels index the characters. This technique is aesthetically limiting in that images exhibit a "stencil" appearance with breaks in the marking lines. Since the mask blocks a high percentage of the laser beam, marking power and resultant surface penetration is limited.

Laser and Imaging Combinations

Beam-steered Nd:YAG
The combination of the Nd:YAG (Neodymium:Yttrium Aluminum Garnet) laser and the beam-steered delivery optics marks the widest range of materials and provides the versatility of computer controlled image generation.

Nd:YAG lasers amplify light in the near-infrared at 1.06 mm. Metallic materials absorb a comparatively high percentage of the light in this region of the spectrum. In the pulsed mode, the Nd:YAG laser produces peak powers considerably higher than the normal continuous-wave output. A 90 watt CW Nd:YAG laser, pulsed at 1 kHz, will emit a train of pulses with peak powers of 110,000 watts. The Nd:YAG lasers ability to emulate an "optical capacitor" provides the power necessary to vaporize metallics and other materials. The high peak power will vaporize material up to 0.005 inches deep in a single pass or greater with multiple passes. The non-metallic materials normally associated with the far-infrared wavelength of the CO2 laser are usually highly reflective to the Nd:YAG. However, the high peak power of the Nd:YAG can often overcome the higher reflectivity. Some overlap does occur among many plastics that absorb both wavelengths equally well.

The beam-steered marker can duplicate virtually any vector graphic image including variable line widths and images as small as 0.010 inch or less. In addition, the computer can instantly change any graphic element or the entire marking program before a new part is positioned for marking.
The Nd:YAG laser offers a greater range of adjustable process variables to achieve a specific material modification but at a correspondingly higher purchase price than the CO2 laser.

Beam-steered CO2
The continuous-wave CO2 laser can also be combined with the beam-steered delivery system.
CO2 lasers emit a narrow bandwidth of light in the far infrared at 10.6 mm. This wavelength is most suitable for organic materials such as paper and other wood products, many plastics, removing thin layers of ink or paint from a substrate, and for marking ceramics. It does not produce high peak powers when pulsed.

Typically utilizing laser powers up to 50 watts, these systems combine the far infrared wavelength with the image control and flexibility of beam-steered image generation. Typical uses include serialization of ceramic and plastic products that require high-quality graphics such as company logos and/or significant amounts of additional alphanumeric text. The lower power CO2 marker does not provide the power to "engrave" substrates but, due to the comparative simplicity of design, can be purchased at a lower cost than the beam-steered Nd:YAG marker.

Mask CO2
Applications that require high speed but not high power and do not vary the marking image except for alphanumeric text (i.e., serialization, date code, etc.) utilize the mask CO2 marker. The CO2 laser is pulsed at rates of up to 1,200 pulses per minute. The high repetition rate provides marking of parts "on-the-fly" at high part-transfer speeds. Computer controlled masks can alter up to three lines of text at speeds of up to 720 parts per minute if the alphanumeric code must be changed.

Advantages and Disadvantages

Beam-steered Nd:YAG
The beam-steered Nd:YAG provides more marking power and far superior imaging than any other laser marker configuration. The available high peak power can mark or engrave a wide variety of materials including hardened metallics. Present computer technology produces highly intricate graphics with linewidths and accuracy's of less than 0.001 inch. Because "drawing" with the laser beam creates the image, the marking time is dependent on the amount of text and the complexity of any graphics. The Nd:YAG laser marker is the most costly of the three system configurations.
The beam-steered Nd:YAG marker frequently replaces acid and electro-etch systems, stamping and punching systems, and those other marking systems which permanently mark products by imprinting or engraving. It also replaces ink jet and other color printing systems. Typical applications include marking pistons, bearings, valves, gears, and a multitude of other components in the automotive industry; heart pacemakers, replacement hip joints, and surgical tools in the medical industry; computer chassis, disk drives, and integrated circuits in the electronics industry; tool holders, drill bits, and cutting tools in the tool industry; and writing pens, nameplates, and golf club grips.

Beam-steered CO2
The acquisition and operating costs of the beam-steered CO2 marker are lower than the Nd:YAG marker due to the relative simplicity of the laser. Image generation is equal to that of the other beam-steered system while speed and depth of penetration are considerable lower due to the lower power of the CO2 laser. Although not as popular as the beam-steered Nd:YAG and mask CO2 markers, the beam-steered CO2 system is frequently used for marking general plastics and plastic and ceramic connectors and packages within the electronics industry.

Mask CO2
Although the mask CO2 does not offer the imaging capabilities of the beam-steered design, it is far superior in speed. Because a single pulse of the laser creates the entire image, throughput is typically limited only by the pulse rate of the laser and the transfer speed of the parts handling system. While the part must be stationary while marking with the beam-steered design, parts are marked in motion with mask systems. Depth of penetration is less than the beam-steered CO2 marker since the laser output is spread over a large area with correspondingly low power density.
Masked CO2 markers most frequently compete with ink-jet marking. The mask CO2 laser is often the marker of choice for sequenced coding, batch coding, open or closed date coding, and real-time coding of paper or cardboard, ink or paint coatings, glass, plastics, coated metals, and ceramics.
While the beam-steered design provides superior imaging and material penetration and the mask design provides superior speed, either system provides a better combination of speed, permanence, and imaging flexibility than other marking techniques. Many users also benefit from the non-contact nature of laser marking and the elimination of additive materials such as inks or paints.

The development of a successful marking application requires careful consideration of the laser output characteristics, the design of the optical beam delivery and image generation system, the properties of the target material, and the aesthetic and physical properties of the desired mark. Industrial laser marking systems provide prospective users with several system designs from which to choose to match the optimum marking performance with the users unique requirements.

About the Author

Richard Stevenson is the Sales Director for Control Micro Systems, Inc. a manufacturer of beam-steered laser marking systems. He has published and presented numerous technical papers and articles on laser marking in trade publications. For information on UID Marking, Laser Welding, Engraving, Cutting, Etching or Marking call 407-679-9716 or email sales@cmslaser.com

How long does it take for a short pulse of light to travel from one end of the glass to the other?

A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness and index of refraction . The wavelength of the laser light in vacuum is and its frequency is . In this problem, neither the constant nor its numerical value should appear in any of your answers.

Express your answer in terms of the frequency, . Use the numeric value given for in the introduction.
t=?s

Let d = thickness in m. The index n = C/c; where C = light speed in a vacuum, and c = the wavefront speed in the glass. Then the transit time t = d/c = dn/C = dn/(fL) = ? sec, where f and L are the frequency and wavelength of the laser light.

Sorry but I have no idea what "constant" you are talking about. And the "numeric value" for what? But clearly, if n, d, and f are given and L = C/f, you can find t with this equation. Of course, as C = fL and we know C, it's not clear why we'd bother with f.

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