Projection-receiving surface

1. A projection-receiving surface comprising:

a refraction surface having an undulating contour, said undulating contour of said first surface comprising a plurality of alternating convex cylindrical surface segments and concave cylindrical surface segments, said convex cylindrical surface segments and concave cylindrical surface segments of said undulating contour of said first surface arranged with cylindrical axes in a first direction; and

a reflection surface having an undulating contour, said undulating contour of said second surface comprising a plurality of alternating convex cylindrical surface segments and concave cylindrical surface segments, said convex cylindrical surface segments and concave cylindrical surface segments of said undulating contour of said second surface arranged with cylindrical axes in a second direction;

wherein said first direction and second direction are skew with each other; and

wherein said undulating contour of said refraction surface approximately follows a curve defined by application of an equation of y=sqrt{[(qn−1)P/tanφ] 2 −(x−1) 2 ]}−{P/2tan(φ)}, where n is an index of refraction, q is a surface interaction coefficient, P is a dimension across a pixel, (φ) is one half of a full field angle, x and y are coordinates defining the curve, 1 is an offset parameter =mP/2, with m=1,3,5, . . . M.

2. The projection-receiving surface of claim 1 wherein said undulating contour of said reflection surface approximately follows a curve defined by application of an equation of y=sqrt[P/2sinθ) 2 −(x−k) 2 ]−[P/2tan(θ)], wherein P is a dimension across a pixel, θ is one quarter of a full field angle, x and y are coordinates defining the curve, k is an offset parameter mP/2, with m=1,3,5, . . . M.

3. The projection-receiving surface of claim 1 wherein said first direction is horizontal and said second direction is vertical.

4. The projection-receiving surface of claim 1 wherein said reflection surface is coated with a reflective film.

5. The projection-receiving surface of claim 1 wherein said refraction surface is covered by a transparent protection film.

6. The projection-receiving surface of claim 1 further comprising an optical sheet made of transparent material, wherein said optical sheet has said refraction surface on one side and said reflection surface on the other side.

7. The projection-receiving surface of claim 1 further comprising a first optical sheet and a second optical sheet, wherein said first optical sheet has said refraction surface and said second optical sheet has said reflection surface.

8. The projection-receiving surface of claim 7 wherein said first optical sheet and said second optical sheet are bonded to each other.

9. The projection-receiving surface of claim 7 wherein said first optical sheet and said second optical sheet are distanced from each other.

10. The projection-receiving surface of claim 1 wherein said reflection surface further has an additional surface feature selected from a group comprising striations, convex/concave cusps, and/or nanoflaked reflector leaves.

11. The projection-receiving surface of claim 10 wherein said additional surface feature is at least partially non-curved.

12. The projection-receiving surface of claim 1 wherein said reflection surface further has striations comprising a plurality of alternating convex segments and concave segments formed in an undulating manner arranged in said first direction.

13. The projection-receiving surface of claim 12 wherein the spatial frequency of said striations is higher than the spatial frequency of said undulating contour of said reflection surface.

14. The projection-receiving surface of claim 12 wherein said striations have about ten times the spatial frequency of said undulating contour of said reflection surface.

15. The projection-receiving surface of claim 12 wherein the undulating amplitude of said striations is smaller than the undulating amplitude of said undulating contour of said reflection surface.

16. The projection-receiving surface of claim 12 wherein said striations have from one-thirtieth to one-twentieth the amplitude of said undulating contour of said reflection surface.

17. The projection-receiving surface of claim 12 wherein said reflection surface further has striations comprising a plurality of alternating convex segments and concave segments formed in an undulating manner arranged in said first direction, and wherein said striations approximately follows a curve defined by application of the same equation with a spatial frequency higher than the spatial frequency of said undulating contour of said reflection surface.

18. The projection-receiving surface of claim 1 wherein said refraction surface further has additional surface feature.

19. The projection-receiving surface of claim 6 wherein said undulating contours of said refraction surface and reflection surface are formed by a process selected from the group comprising machining, milling, pressing, stamping, etching, vacuum forming, electroforming, rolling, molding, injection, casting, deposition, precipitation, photo-processes, broaching, film-suspension, and photo-processes.

20. The projection-receiving surface of claim 7 wherein said refraction surface of said first optical sheet and said reflection surface of said second optical sheet are formed by a process selected from the group comprising machining, milling, pressing, stamping, etching, vacuum forming, electroforming, rolling, molding, injection, casting, deposition, precipitation, photo-processes, broaching, photo-processes, film-suspension, and extruding.

21. The projection-receiving surface of claim 6 wherein said optical sheet further contains absorption dye.

22. A projection-receiving surface comprising:

a reflection surface having an undulating contour; said undulating contour comprising a plurality of alternating convex cylindrical surface segments and concave cylindrical surface segments, said convex cylindrical surface segments and concave cylindrical surface segments of said undulating contour of said reflection surface arranged with cylindrical axes in a first direction;

wherein said reflection surface further has an additional surface feature selected from a group comprising striations, cusps, and nanoflaked reflector leaves; and

wherein said undulating contour of said reflection surface approximately follows a curve defined by application of an equation of y=sqrt[P/2sinθ) 2 −(x−k) 2 ]−[P/2tan(θ)], where P is a dimension across a pixel, θ is one quarter of a full field angle, x and y are coordinates defining the curve, k is an offset parameter mP/2, with m=1,3,5, . . . M.

23. The projection-receiving surface of claim 22 , wherein said striations comprise a plurality of alternating convex segments and concave segments formed in an undulating manner arranged in a second direction skew with said first direction.

24. A projection-receiving surface comprising:

a refraction surface; and

a reflection surface,

wherein said first surface and second surface form a plurality of pixels;

wherein said plurality of pixels comprise convex-convex pixels, convex-concave pixels, concave-convex pixels, and concave-concave pixels, each of said convex-convex pixels formed by a convex refraction surface and a concave reflection surface, each of said convex-concave pixels formed by a convex refraction surface and a concave reflection surface, each of said concave-convex pixels formed by a concave refraction surface and a convex reflection surface, each of said concave-concave surface formed by a concave refraction surface and a concave reflection surface; and

wherein said undulating contour of said refraction surface approximately follows a curve defined by application of an equation of y=sqrt{[(qn−1)P/tanφ] 2 −(x−1) 2 ]}−{P/2tan(φ))}, where n is an index of refraction, q is a surface interaction coefficient, P is a dimension across a pixel, φ is one half of a full field angle, x and y are coordinates defining the curve, 1 is an offset parameter=mP/2, with m=1,3,5, . . . M.

25. A projection-receiving surface comprising:

a refraction surface having an undulating contour, said undulating contour of said first surface comprising a plurality of alternating convex cylindrical surface segments and concave cylindrical surface segments, said convex cylindrical surface segments and concave cylindrical surface segments of said undulating contour of said first surface arranged with cylindrical axes in a first direction; and

a reflection surface having an undulating contour, said undulating contour of said second surface comprising a plurality of alternating convex cylindrical surface segments and concave cylindrical surface segments, said convex cylindrical surface segments and concave cylindrical surface segments of said undulating contour of said second surface arranged with cylindrical axes in a second direction;

wherein said first direction and second direction are skew with each other; and

wherein said undulating contour of said reflection surface approximately follows a curve defined by application of an equation of y=sqrt[P/2sinθ) 2 −(x−k) 2 ]−[P/2tan(θ)], where P is a dimension across a pixel, θ is one quarter of a full field angle, x and y are coordinates defining the curve, k is an offset parameter mP/2, with m=1,3,5, . . . M.

26. A projection-receiving surface comprising:

a refraction surface having an undulating contour, said undulating contour of said first surface comprising a plurality of alternating convex cylindrical surface segments and concave cylindrical surface segments, said convex cylindrical surface segments and concave cylindrical surface segments of said undulating contour of said first surface arranged with cylindrical axes in a first direction; and

a reflection surface having an undulating contour, said undulating contour of said second surface comprising a plurality of alternating convex cylindrical surface segments and concave cylindrical surface segments, said convex cylindrical surface segments and concave cylindrical surface segments of said undulating contour of said second surface arranged with cylindrical axes in a second direction;

wherein said first direction and second direction are skew with each other;

wherein said reflection surface further has striations comprising a plurality of alternating convex segments and concave segments formed in an undulating manner arranged in said first direction; and

wherein said striations have from one-thirtieth to one-twentieth the amplitude of said undulating contour of said reflection surface.