Method and apparatus for fabricating a light management substrates

• US 20040120136A1
• Filed: 12/18/2002
• Published: 06/24/2004
• Est. Priority Date: 12/18/2002
• Status: Active Grant

• Current Assignee: Sabic Innovative Plastics IP BV (Government of Saudi Arabia)
• Original Assignee: General Electric Company
• Inventors: Olczak, Eugene, Liang, Erwin W.
• Granted Patent: US 6,952,627 B2
• Time in Patent Office: Days
• US Class Current: 362/31
• CPC Class Codes: G05B 19/182 characterised by the machine tool function, e.g. thread cutting, cam making, tool direction control G05B19/21 - G05B19/40 take precedence
• CPC Class Codes: G05B 2219/35261 Use of mathematical expression, functional equation

Abstract

A method of machining a surface of a workpiece is accomplished by bringing a cutting tool into contact with the surface of the workpiece and for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the workpiece along a path in the surface of the workpiece. The path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random or pseudorandom parameters selected from the group consisting of amplitude, phase and period or frequency. Relative movement between the cutting tool and the surface of the workpiece may be accomplished by bandpass filtering a noise signal; providing the bandpass filtered signal to a function generator; generating a randomly modulated mathematical function from the function generator; and in response to the randomly modulated function, directing the relative movement between the cutting tool and the surface of the workpiece along the path in the surface of the workpiece.

Claims

1. A method of machining a surface of a workpiece, the method comprising:

bringing a cutting tool into contact with the surface of the workpiece; and

for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the workpiece along a path in the surface of the workpiece;

wherein the path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random or pseudorandom parameters selected from the group consisting of amplitude, phase and frequency.

2. The method as set forth in claim 1 wherein the mathematical function is defined by the equation

y_i=A_isin{Ψ

_i}=S_i

wherein i is an integer indicative of the number of the cutting path, yi is the instantaneous displacement of the cutting tool relative to C on the ith cutting pass, Ai is the maximum displacement of the cutting tool relative to C,

Ψ

_i|

is the phase of yi and Si is a shift in the starting position of yi.

3. The method as set forth in claim 2 wherein

4. The method as set forth in claim 2 further comprising, for a kth cutting pass, subsequent to the ith cutting pass, shifting the starting point of the mathematical function a distance Si from the starting point of the mathematical function on the ith cutting pass.

5. The method as set forth in claim 2 further comprising nonrandomly, randomly or pseudo randomly assigning a value to Ai.

6. The method as set forth in claim 1 wherein the mathematical function is selected from the group of mathematical functions consisting of triangular function, sawtooth function and square wave function.

7. The method as set forth in claim 2 wherein

8. The method as set forth in claim 7 further comprising, for a kth cutting pass, subsequent to the ith cutting pass, shifting the starting point of the mathematical function a distance Si from the starting point of the mathematical function on the ith cutting pass.

9. The method as set forth in claim 6 further comprising nonrandomly, randomly or pseudo randomly assigning a value to Ai.

10. The method as set forth in claim 1 wherein causing relative movement between the cutting tool and the surface of the workpiece includes:

bandpass filtering a noise signal;

providing the bandpass filtered noise signal to a function generator;

generating a randomly modulated mathematical function from the function generator;

in response to the randomly modulated function, directing the relative movement between the cutting tool and the surface of the workpiece along the path in the surface of the workpiece.

14. A master having a surface machined by the method as set forth in claim 1.

15. The method as set forth in claim 4 wherein for a kth cutting pass, subsequent to the ith cutting pass, a width wk of the kth cutting pass is different than for the ith cutting pass.

16. The method as set forth in claim 15 wherein for a kth cutting pass, subsequent to the ith cutting pass, the difference in the width wk of the kth cutting pass with respect to the ith cutting pass is a gradient over all cutting passes.

17. The method as set forth in claim 15 wherein for a kth cutting pass, subsequent to the ith cutting pass, the difference in the width wk of the kth cutting pass with respect to the ith cutting pass is random or pseudo random.

11. A method of fabricating an optical substrate from a machined surface of a workpiece, the method comprising:

forming a positive or negative electroform over the surface of the surface of the workpiece;

forming a replica of the electroform; and

transferring the replica of the electroform to an optical substrate.

12. An optical substrate comprising:

a surface formed from a master surface machined by bringing a cutting tool into contact with a surface of a workpiece;

for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the workpiece along a path in the surface of the workpiece;

wherein the path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random or pseudorandom parameters selected from the group consisting of amplitude, phase and frequency;

forming a positive or negative electroform over the surface of the surface of the workpiece;

forming a replica of the electroform; and

transferring the replica of the electroform to an optical substrate.

13. A backlight display device comprising:

an optical source for generating light;

a light guide for guiding the light therealong;

a reflective device positioned along the light guide for reflecting the light out of the light guide;

an optical substrate receptive of the light from the light guide, the optical substrate comprising;

a surface formed from a master surface machined by bringing a cutting tool into contact with a surface of a workpiece;

for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the workpiece along a path in the surface of the workpiece;

wherein the path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random or pseudorandom parameters selected from the group consisting of amplitude, phase and frequency;

forming a positive or negative electroform over the surface of the surface of the workpiece;

forming a replica of the electroform; and

transferring the replica of the electroform to an optical substrate.

18. A backlight display device comprising:

an optical source for generating light;

a light guide for guiding the light therealong; and

a reflective device positioned along the light guide for reflecting the light out of the light guide;

wherein the light guide includes a surface formed from a master surface machined by bringing a cutting tool into contact with a surface of a workpiece;

for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the workpiece along a path in the surface of the workpiece;

wherein the path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random or pseudorandom parameters selected from the group consisting of amplitude, phase and frequency;

forming a positive or negative electroform over the surface of the surface of the workpiece;

forming a replica of the electroform; and

transferring the replica of the electroform to an optical substrate.

19. The display device as set forth in claim 18 wherein for a kth cutting pass, subsequent to the ith cutting pass, a width wk of the kth cutting pass is different than the ith cutting pass.

20. The display as set forth in claim 19 wherein for a kth cutting pass, subsequent to the ith cutting pass, the difference in the width wk of the kth cutting pass with respect to the ith cutting pass is a gradient over all cutting passes.

21. The display as set forth in claim 19 wherein for a kth cutting pass, subsequent to the ith cutting pass, the difference in the width wk of the kth cutting pass with respect to the ith cutting pass is random or pseudo random.

22. A method of machining a surface of a cylinder, the method comprising:

bringing a cutting tool into contact with the surface of the cylinder; and

for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the cylinder along a path in a plane tangential to the surface of the cylinder;

wherein the path is in the nature of a mathematical function defined over a segment, C, of the cylinder and characterized by a set of nonrandom, random or pseudorandom selected from the group consisting of amplitude, phase and frequency.