Optical elements with saddle shaped structures for diffusing or shaping light
Optical elements for efficiently diffusing or shaping light have substrates with saddle shaped structures on their surfaces which provide substantially uniform light along a predefined angular range. Each saddle shaped structure defines an aperture of a lens, where the outer boundary of such aperture, when viewed normal to surface, may be of one of more different shapes, such as square or rectangular, circular, hexagonal, oval, or other geometric or arbitrary shape which may represent a full saddle shape or a subset region thereof. A plurality of saddle shaped structures may be arranged periodically or randomly along the surface. An optical element with a saddle shaped structure is referred to as a saddle lens, and optical elements with different shaped saddle shaped structures provide different types of saddle lenses.
1. An optical element for efficiently diffusing or shaping light comprising:
a substrate having a surface with at least one saddle shaped structure, wherein said saddle shaped structure represents a subset region of a saddle shape.
2. The optical element according to claim 1 wherein said subset region is of a geometric shape.
3. The optical element according to claim 1 wherein said subset region is of an arbitrary shape.
4. The optical element according to claim 1 wherein said subset region is centered in said aperture of said lens.
5. The optical element according to claim 1 wherein said subset region is off centered said aperture of said lens.
6. An optical element for efficiently diffusing or shaping light comprising:
a substrate having a surface with at least one saddle shaped structure, wherein a plurality of ones of said saddle shaped structure are arranged randomly along said substrate.
7. The optical element according to claim 6 wherein said plurality of ones of said saddle shaped structure differ in curvature from each other.
8. The optical element according to claim 6 wherein said plurality of ones of said saddle shaped structure are arranged randomly by spatial location in which one or more overlap each other.
9. The optical element according to claim 6 wherein said plurality of ones of said saddle shaped structure are non-circular and are arranged randomly by spatial location and rotation.
10. An optical element for efficiently diffusing or shaping light comprising:
a substrate having a surface with at least one saddle shaped structure, wherein said saddle shaped structure curvature is defined by sag ζ by an equation:
ϛ
p
(
x
,
y
)
=
α
R
x
-
R
x
p
-
(
κ
x
+
1
)
x
p
p
p
R
y
-
R
y
p
-
(
κ
y
+
1
)
y
p
p
p
sign
(
x
)
sign
(
y
)
,
where x and y are two orthogonal dimensional along the substrate, α is a real constant, R x and R y are radii of curvature in x and y dimensions, respectively, and κ x , and κ y are conic constants in x and y dimensions, respectively, and p is a real number.
11. The optical element according to claim 10
wherein said saddle shaped structure provides substantially uniform scatter pattern or distribution of light along an angular range when light is received by the optical element incident another surface of the substrate.
12. The optical element according to claim 10 wherein said another surface is substantially smooth.
13. The optical element according to claim 10 wherein the substantial uniformity of said scatter pattern or distribution increases with diameter of said saddle shaped structure.
14. The optical element according to claim 10 wherein said optical element is efficient in accordance with sharpness along a transitional region of fall off in intensity of the diffused light along a periphery of said angular range, and substantial absence of diffused light along angles beyond said transitional region.
15. The optical element according to claim 10 wherein said structure operates over one or more wavelengths or ranges of light.
16. The optical element according to claim 10 wherein said saddle shaped structure represent an aperture of a lens defining an outer boundary of the structure when viewed normal to said surface.
17. The optical element according to claim 10 wherein said outer boundary is of a geometric shape other than square or rectangular.
18. The optical element according to claim 10 wherein a plurality of ones of said saddle shaped structure are arranged periodically along said substrate.
19. The optical element according to claim 16 wherein said outer boundary is a square or rectangular.
20. An optical element for efficiently diffusing or shaping light comprising:
a substrate having a surface with at least one saddle shaped structure, wherein said saddle shaped structure provides substantially uniform scatter pattern or distribution of light along an angular range when light is received by the optical element incident another surface of the substrate, wherein said outer boundary is of an arbitrary shape.
21. The optical element according to claim 14 wherein said sharpness of fall off provided by said shaped structure is greater than diffusing optical elements utilizing a non-diffractive non-saddle shaped structure.
22. An optical device comprising:
a body of optical material having a surface; and
a plurality of saddle shaped structures or subsets thereof along said surface capable of diffusing or shaping light incident said body, wherein said plurality of saddle shaped structures or subsets thereof provides substantially uniform distribution of light along an angular range in response to light incident said body, wherein said saddle shaped structure curvature is defined by sag ζ by an equation:
ς
p
(
x
,
y
)
=
α
R
x
-
R
x
p
-
(
κ
x
+
1
)
x
p
p
p
R
y
-
R
y
p
-
(
κ
y
+
1
)
y
p
p
p
sign
(
x
)
sign
(
y
)
,
where x and y are two orthogonal dimensional along the substrate, α is a real constant, R x and R y are radii of curvature in x and y dimensions, respectively, and κ x , and κ y are conic constants in x and y dimensions, respectively, and p is a real number.
23. The optical device according to claim 22 wherein said saddle shaped structures or subsets thereof are in a periodic arrangement along said surface.
24. An optical device comprising:
a body of optical material having a surface; and
a plurality of saddle shaped structures or subsets thereof along said surface capable of diffusing or shaping light incident said body, wherein said saddle shaped structures or subsets thereof are at random spatial locations along said surface.
25. The optical device according to claim 22 wherein said saddle shaped structures or subsets thereof are non-circular and are arranged at one of periodic or random rotation from one another along said surface.
26. An optical device comprising:
a body of optical material having a surface; and
a plurality of saddle shaped structures or subsets thereof along said surface capable of diffusing or shaping light incident said body, wherein one or more of said saddle shaped structures or subsets thereof are different in curvature from each other and overlap along said surface.
27. The optical device according to claim 22 wherein said body is a sheet.
28. The optical device according to claim 22 wherein said surface represents a first surface and said body comprises a second surface opposite said first surface through which said incident light is received.