METHOD AND APPARATUS FOR FABRICATING OPTICAL SUBSTRATES

• US 20090067155A1
• Filed: 11/06/2008
• Published: 03/12/2009
• Est. Priority Date: 12/18/2002
• Status: Abandoned Application

• Current Assignee: Sabic Innovative Plastics IP BV (Government of Saudi Arabia)
• Original Assignee: Sabic Innovative Plastics IP BV (Government of Saudi Arabia)
• Inventors: Liang, Erwin W., Olczak, Eugene
• Application Number:
  US12/266,119
• Publication Number:
  US 20090067155A1
• Time in Patent Office: Days
• US Class Current: 362/97.100
• 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

In one embodiment, an optical substrate that includes a prism structure modulated along a path in a lateral direction. 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.

Claims

1. An optical substrate comprising a prism structure that was modulated along a path in a lateral direction, 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 optical substrate as set forth in claim 1, wherein the mathematical function is defined by the equation

y_i=A_i sin {Ψ

_i}+S_i

wherein i is an integer indicative of the number of the path, y_i is the instantaneous displacement relative to C on the i^th path, A_i is the maximum displacement relative to C, Ψ

_i is the phase of y_i and S_i is a shift in the starting position of y_i.

3. The optical substrate as set forth in claim 2, wherein

${\Psi }_{}$

i = φ



( λ

i - q i + k 2 ) - Φ

i

where φ

is a number between zero and 2π

inclusive,

${\mathrm{\lambda <br><br>}}_i=\frac{2\times <br><br>C}{N}$

where N is a nonrandom, random, or pseudo random positive or negative integer,

$\frac{q_{i+k}}{2}$

is an additive factor modifying λ

_i on a k^th subsequent path and Φ

_i is a nonrandom, random, or pseudo random number between zero and 2π

inclusive.

4. The optical substrate as set forth in claim 2, wherein, for a k^th path subsequent to the i^th path, a starting point of the mathematical function is shifted a distance S_i from the starting point of the mathematical function on the i^th path.

5. The optical substrate as set forth in claim 4, wherein a width w_k of the k^th path is different than for the i^th path.

6. The method as set forth in claim 5, wherein the difference in the width w_k of the k^th path with respect to the i^th path is a gradient over all path.

7. The method as set forth in claim 5, wherein the difference in the width Wk of the k^th path with respect to the i^th path is random or pseudo random.

8. The optical substrate as set forth in claim 2, wherein the value of A_i is nonrandom, random, or pseudo random.

9. The optical substrate as set forth in claim 2, wherein

${\Psi }_{}$

i = φ



( λ

i - q i + k 2 ) - Φ

i - a i 

sin 

{ φ



( λ

i b i - Ω

i ) }

where φ

is a number between zero and 2π

inclusive,

${\mathrm{\lambda <br><br>}}_i=\frac{2\times <br><br>C}{N}$

where N is a nonrandom, random, or pseudo random positive or negative integer,

$\frac{q_{i+k}}{2}$

is an additive factor modifying λ

_i on a k^th subsequent path and Φ

_i is a random or pseudo random number between zero and 2π

inclusive, a_i and b are scalar quantities and Ω

_i is a nonrandom, random, or pseudo random number between zero and 2π

inclusive.

10. The optical substrate as set forth in claim 9, wherein, for a k^th path subsequent to the i^th path, a starting point of the mathematical function is shifted a distance S_i from the starting point of the mathematical function on the i^th path

11. The optical substrate as set forth in claim 9, wherein the value of A_i is nonrandom, random, or pseudo random.

12. The optical substrate 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.

13. A backlight display device comprising:

an optical source capable of generating light;

a light guide capable of guiding the light therealong;

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

an optical substrate capable of receiving the light from the light guide, the optical substrate comprising a prism structure that was modulated along an i^th path in a lateral direction, 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.

14. A backlight display device comprising:

an optical source capable of generating light;

a light guide capable of guiding the light therealong; and

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

wherein the light guide includes a surface that includes a prism structure that was modulated along an i^th path in a lateral direction;

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 pseudo random parameters selected from the group consisting of amplitude, phase, and frequency.

15. The display device as set forth in claim 14, wherein for a k^th path, subsequent to the i^th path, a width Wk of the k^th path is different than the i^th path.

16. The display as set forth in claim 15, wherein the difference in the width Wk of the k^th path with respect to the i^th path is a gradient over all paths.

17. The display as set forth in claim 15, wherein the difference in the width Wk of the k^th path with respect to the i^th path is random or pseudo random.

18. A method of machining a surface of a workpiece, wherein the workpiece comprises a rotating drum, 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 in a direction parallel to an axis of the drum;

wherein causing relative movement between the cutting tool and the surface of the workpiece comprises

bandpass filtering a noise signal;

providing the bandpass filtered noise signal to a function generator;

generating a randomly or pseudorandomly modulated mathematical function from the function generator; and

directing the relative movement between the cutting tool and the surface of the workpiece in response to the randomly or pseudorandomly modulated function.

19. A method of machining a surface of a workpiece, wherein the workpiece comprises a flat plate moving at a velocity v, 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 in a direction across the plate;

wherein causing relative movement between the cutting tool and the surface of the workpiece comprises

bandpass filtering a noise signal;

providing the bandpass filtered noise signal to a function generator;

generating a randomly or pseudorandomly modulated mathematical function from the function generator; and

directing the relative movement between the cutting tool and the surface of the workpiece in response to the randomly or pseudorandomly modulated function.