Three-dimensional simultaneous multiple-surface method and free-form ...

1. A method of defining and manufacturing a free-form optical system, comprising:

simultaneously generating a first set and a second set of span points, where each point has an associated normal vector, such that the first and second sets of span points form interdependent first and second chains of corresponding points, respectively;

curve-fitting through the first set of span points defining an initial first spine;

curve-fitting through the second set of span points defining an initial second spine;

generating first and second sets of ribs extending from said first and second spines, respectively, such that tangent vectors of said ribs are perpendicular to said normal vectors of said spines;

defining patches of a first surface that is bounded by said first set of ribs of said first spine, and defining patches of a second surfaces that is bounded by said second set of ribs of said second spine, where said first and second spines are bounded by respective ones of the patches such that a portion of the spine is not coincident with boundaries of the respective patches; and

manufacturing a free-form optical system having at least two active free-form optical surfaces comprising a body further comprising surfaces corresponding to the first and second surfaces where the optical system receives an input light and emits an output light according to a light prescription.

2. The method of claim 1, wherein said defining the initial first spine comprises defining the first initial spine with first tangent vectors perpendicular to said normal vectors;

said defining the initial second spine comprises defining the second initial spine with second tangent vectors perpendicular to said normal vectors; and

said generating the sets of ribs comprises generating the first and second sets of ribs such that the tangent vectors of said ribs are perpendicular to both said normal vectors and to said first and second tangent vectors, with said first and second sets of ribs of said first and second spines being in the same interdependence as said first and second sets of span points.

3. The method of claim 1, further comprising:

evaluating discontinuities between said patches of said first surface;

adjusting the curve fitting defining an adjusted first spine and re-generating said first set of ribs according to adjusted first spine.

4. The method of claim 1, further comprising:

defining lofted surfaces that unite said patches of said first surface and patches of said second surface.

5. The method of claim 1, further comprising:

defining a first span point of said first surface and said associated surface-normal vector;

defining a first input wavefront and a first ray of said first input wavefront at said first span point;

defining a first output wavefront corresponding to said first input wavefront;

defining a first optical path-length between said first input wavefront and said first output wavefront;

wherein said simultaneous generation of said first set and said second set of span points comprises defining a first span point of said second surface as a point where said first ray of said first input wavefront traverses said first optical path-length; and

defining said associated surface-normal vector at said first span point of said second surface as a vector that deflects said first ray into said first output wavefront.

6. The method of claim 5, further comprising:

defining a second input wavefront;

defining a corresponding second output wavefront;

defining an optical path-length between said second input and output wavefronts;

defining a first ray of said second output wavefront at said first point of said second surface;

defining a second span point of said first surface as a point where said first ray of said second output wavefront is traced backwards to intercept said second input wavefront; and

defining the associated normal vector at said second span point of said first surface as that which deflects said second input wavefront into said backwards traced ray of said second output wavefront.

7. The method of claim 6, further comprising:

propagating from said second span point of said first surface a deflected ray of said first input wavefront until said deflected ray intercepts said first output wavefront, thereby determining a second span point of said second surface, and the associated normal vector of said second span point;

determining from said second span point of said second surface a third span point of said first surface.

8. The method of claim 7, further comprising:

propagating further the first and second sets of span points to form the interdependent first and second chains extending plus-wise from said first span points of said first and second surfaces.

9. The method of claim 7, further comprising:

propagating from said first span point of said first surface a ray of said second input wavefront until it intercepts said second output wavefront, thereby establishing a minus-first span point of said second surface and its associated surface-normal vector;

propagating backwards from said minus-first span point of said second surface a ray of said first output wavefront until it intercepts said first input wavefront, thereby establishing a minus-first span point of said first surface; and

propagating further span points to form two interdependent chains extending minus-wise from said minus-first span points of said surfaces.

10. The method of claim 5, wherein said defining of said first and second output wavefronts comprises defining said first and second output wavefronts as normal congruences according to an output illumination prescription.

11. The method of claim 10, wherein said defining of said first and second input wavefronts comprises defining said first and second input wavefronts according to edge rays of a light source.

12. The method of claim 1, wherein said simultaneous generation of said first and second sets of span points comprises alternatively determining points of said first and second sets of points according to the positions and associated normal vectors of previously determined points of said second and first sets of span points.

13. The method of claim 1, wherein said first and second surfaces define a transparent body between said first and second surfaces.

14. The method of claim 13, wherein said first surface is reflective and said second surface is refractive.

15. The method of claim 14, wherein a third surface is prescribed prior to defining input wavefronts before the input wavefronts encounter said first surface.

16. The method of claim 13, wherein said first and second surfaces are both refractive.

17. A method designing a free-form optical system to be used in manufacturing the free-form optical system, comprising:

defining first input and output wavefronts and a first optical path length between said first input and output wavefronts;

defining second input and output wavefronts and a second optical path length between said second input and output wavefronts;

defining a deflection type of a first free-form surface and a deflection type of a second free-form surface;

defining a first spine of the first surface and defining a second spine of the second surface;

calculating a first and second seed rib of each of the first and second surfaces, respectively, comprising simultaneously calculating dependent first and second sets of span points, respectively, defining, in part, the first and second surfaces;

defining a first patch of the first surface that is defined by said first seed rib, where said first spine is bounded by said first patch of the first surface such that a portion of the first spine is not coincident with boundaries of the first patch;

defining a second patch of the second surface that is defined by said second seed rib, where said second spine is bounded by said second patch of the second surface such that a portion of the second spine is not coincident with boundaries of the second patch; and

defining the first surface comprising the first patch in accordance with the first seed rib;

defining the second surface comprising the second patch in accordance with the second seed rib; and

storing the defined first and second surfaces and the deflection type of the first and second surfaces to be accessed by a computer, where the defined first and second surfaces and the deflection type of the first and second surfaces are used to manufacture a free-form optical system comprising free-form surfaces as defined by the defined first and second surfaces.

18. The method of claim 17, further comprising:

defining refractive indices of dielectric media on each side of said first surface; and

defining refractive indices of dielectric media on each side of said second surface.

19. The method of claim 17, wherein said first and second surfaces are reflective.

20. The method of claim 17, further comprising:

determining deflective congruences of said first and second input wavefronts by said first surface, providing first and second deflective congruences;

utilizing said deflective congruences as input wavefronts for said second surface; and

defining a third surface relative to said second surface utilizing said output wavefronts.

21. The method of claim 20, further comprising:

determining when a difference between the first surface and the third surface exceeds a tolerance;

equating the first surface to the third surface providing a revised first surface when the difference between the first and third surfaces exceeds the tolerance;

repeating the determining the refraction congruence of the first and second input wavefronts through the revised first surface, providing revised first and second refracted congruence; and

repeating the defining the second surface and the third surfaces relative to the revised first and second refracted congruence.

22. The method of claim 20, wherein the defining the second and third surfaces comprise:

simultaneously generating a first set and a second set of span points defining the second surface and the third surface, respectively, according to the first and second refracted congruence and the first and second output wavefronts, such that the first and second set of span points are interdependent.

23. The method of claim 22, wherein the defining the second and third surfaces further comprise:

curve fitting through the first set of span points defining an initial first spine;

curve fitting through the second set of span points defining an initial second spine; and

defining patches of the first and second surfaces relative to the first and second spines.

24. The method of claim 17, further comprising:

defining the first and second output wavefronts as normal congruence relative to an illumination prescription through a source projection linear approximate.

25. The method of claim 17, wherein the defining the first and second input wavefronts comprise defining the first and second input wavefronts from edge rays of a light source.

26. The method of claim 17, further comprising:

defining a third output wavefront;

defining a third input wavefront, wherein the defining the first, second and third input wavefronts comprise defining the first, second and third wavefronts relative to the first, second and third output wavefronts, respectively, according to a linear approximation; and

determining a direction of each of the three output wavefronts according to planar vectors.

27. The method of claim 26, further comprising:

defining first, second and third optical path lengths for the respective transition of the first, second and third input wavefronts to the first, second and third output wavefronts.

28. The method of claim 17, wherein the first and second output waveforms define in part an intensity gradient such that a portion of the intensity gradient emits with a constant source-image size with the remaining the remaining intensity gradient having source-image size that gradually increases.

29. The method of claim 28, wherein the portion of the intensity gradient comprising constant source-image size defines a cut-off gradient.

30. A free-form optical system, comprising:

a body comprising:

a transparent medium;

a first free-form surface receiving at least a first optical input wavefront and a second optical input wavefront; and

a second free-form surface separated from the first surface and emitting at least a first optical output wavefront and a second optical output wavefront;

the first and second surfaces are respectively defined at least in part according to interdependent first and second sets of span points, and the first and second surfaces are further defined according to patches dictated by the first and second sets of span points, respectively;

the first and second surfaces are further defined by first and second set of spines that are dependent on the first and second sets of span points, respectively, and ribs extending from the first and second sets of span points associated with said first and second sets of spines, respectively, where the ribs are simultaneously generated and at least in part bound the patches and said first and second spines are bounded by first and second patches, respectively, such that a portion of the first spine is not coincident with boundaries of the first patch and a portion of the second spine is not coincident with boundaries of the second patch.

31. The system of claim 30, wherein the ribs are defined along a vector product of a normal and tangent vectors.

32. The system of claim 30, wherein the first surface comprises a first and second point of the first set of span points and the second surface comprises a first point of the second set of span points, where the first point of the first surface is an intercept point of a first ray of the first input wavefront such that the first ray is refracted at the first point of the first surface to produce a first transformed ray that intercepts the second surface and the first point of the second surface, and a first ray of the first output wavefront is emitted from the first point of the second surface according to a refraction of a second transformed ray entering the first surface at the second point where a first ray of the second input intercepts the second point of the first surface.

33. The system of claim 30, wherein the second surface emits the first and second output wavefronts as normal congruence relative to an illumination prescription according to a source projection linear approximate relative to the first and second input wavefronts.

34. The system of claim 30, wherein the first and second surfaces enclose a transparent dielectric and are refractive.