Free-form lenses for rectangular illumination zones
A light source emits light into a solid angle exceeding pi steradians with a known intensity distribution. An illumination lens has a first surface that receives at least 90% of the light of the known intensity distribution and has a shape that transforms the known intensity distribution into an intermediate intensity distribution within the transparent material of the lens. A second surface receives the intermediate intensity distribution and is shaped to transform the intermediate intensity distribution into a final intensity distribution that produces a prescribed illumination distribution upon a rectangular target zone. At least one of the shapes of the first and second surfaces is non-rotationally symmetric and is approximated by a super-ellipsoid.
1. An illumination system comprising a light source, an illumination lens, and at least one rectangular target zones, the light source emitting light into a solid angle exceeding pi steradians with a known intensity distribution, the illumination lens comprising a first surface that receives at least 90% of the light of the known intensity distribution, the first surface shaped to transform the known intensity distribution into an intermediate intensity distribution within the transparent material of the lens, the lens further comprising a second surface that receives the intermediate intensity distribution, the second surface shaped to transform the intermediate intensity distribution into a final intensity distribution that produces a prescribed illumination distribution upon the at least one rectangular target zone, at least one of the shapes of the first and second surfaces being non-rotationally symmetric and being mathematically generated by:
identifying a rectangular grid on the target; and;
in correspondence with the rectangular grid on the target, establishing a sphere-covering pseudo-rectangular grid on the solid angle of the source emission, wherein:
the pseudo-rectangular grid has the same proportions and the same number of cells as the rectangular grid on the target;
the cells of the rectangular grid on the target and the cells of the pseudo-rectangular grid have the same relative assignment of light flux; and
each cell has a representative central ray.
2. The illumination lens as defined in claim 1 , wherein the lower surface is rotationally symmetric.
3. The illumination lens as defined claim 1 , comprising an upper surface that is a super-ellipsoid described by an equation:
(
x
a
)
P
+
(
y
b
)
Q
+
(
z
-
z
0
c
)
R
=
1
wherein a, b, and c are adjustable semi-axes, z 0 is an adjustable vertical position, and P, Q, and R are adjustable exponents, with at least one of the exponents not equal to 2.
4. The illumination lens as defined in claim 3 , wherein the equation has exponent P 4, the exponent Q=4 and the exponent R=1.4.
5. The illumination lens as defined in claim 2 also comprising a lower surface that is bell-shaped.
6. The illumination lens as defined in claim 5 wherein the bell-shaped lower surface comprises a central paraboloid and a lower toroidal section surrounding it, the toroidal section adjoining thereto with the same tangent as the paraboloid, the central paraboloid adjustable both in vertex radius of curvature and in the amount of higher-order modification, the toroidal section adjustable both in radius of curvature and the variability thereof.
7. The illumination lens as defined in claim 6 also comprising mounting pegs protruding downward from the transition surface.
8. The illumination lens as defined in claim 2 also comprising a conical transition surface connecting the lower surface and the upper surface.
9. The illumination lens as defined in claim 2 , also comprising a mounting flange protruding laterally from the transition surface.
10. The illumination lens as defined in claim 1 , also comprising a vertically oriented planar mirror positioned adjacent to the light source so as to reflect light back across the center of the lens.
11. The illumination system as defined in claim 1 comprising a multiplicity of the lenses and light sources positioned to form a linear array, also comprising a transparent diffusing cover with its diffusion predominantly in the direction of the array.
12. An illumination system comprising a light source, an illumination lens, and at least one rectangular target zones, the light source emitting light into a solid angle exceeding pi steradians with a known intensity distribution, the illumination lens comprising a first surface that receives at least 90% of the light of the known intensity distribution, the first surface shaped to transform the known intensity distribution into an intermediate intensity distribution within the transparent material of the lens, the lens further comprising a second surface that receives the intermediate intensity distribution, the second surface shaped to transform the intermediate intensity distribution into a final intensity distribution that produces a prescribed illumination distribution upon the at least one rectangular target zone, at least one of the shapes of the first and second surfaces being non-rotationally symmetric.