REFLECTIVE SURFACE

• US 20120092784A1
• Filed: 06/11/2010
• Published: 04/19/2012
• Est. Priority Date: 06/11/2009
• Status: Active Grant

• Current Assignee: Drexel University
• Original Assignee: Drexel University
• Inventors: Hicks, Robert Andrew
• Granted Patent: US 8,979,287 B2
• Time in Patent Office: Days
• US Class Current: 359/868
• CPC Class Codes: G02B 27/0012 Optical design, e.g. procedures, algorithms, optimisation routines
• CPC Class Codes: G02B 27/0025 for optical correction, e.g. distorsion, aberration
• CPC Class Codes: G02B 5/10 with curved faces
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544

Abstract

The invention relates to a reflective surface substantially perpendicular to a vector field described by the equation: W(x,y,z)=T (proj(x,v,z))−(x,v,z)+proj(x,v,z)−(x,v,z)∥T(proj(x,y,z))−(x,y,z)∥ ∥proj(x,y,z)−(x,y,z)∥ and a method for forming the reflective surface. The reflective surface is capable of providing a non-reversed, substantially undistorted direct reflection.

Claims

1. A reflective surface substantially perpendicular to a vector field W of the following equation:

2. The reflective surface of claim 1, wherein the reflective surface has an image error quantity, I_e, of less than about 15% when an observer is positioned within the field of view of the reflective surface, and I_e is calculated according to the following equation:

3. The reflective surface of claim 2, wherein the reflective surface has an image error quantity of less than about 10%.

4. The reflective surface of claim 2, wherein the reflective surface has an image error quantity of less than about 5%.

5. The reflective surface of claim 2, wherein the reflective surface has an image error quantity of less than about 3%.

6. The reflective surface of claim 2, wherein said reflective surface is capable of reflecting at least a 30°

field of view when viewed from the perspective of an observer.

7. The reflective surface of claim 2, wherein said reflective surface is capable of reflecting at least a 40°

field of view when viewed from a perspective of an observer.

8. The reflective surface of claim 2, wherein said reflective surface is capable of reflecting at least a 45°

field of view when viewed from a perspective of an observer.

9. The reflective surface of claim 2, wherein said reflective surface is saddle shaped.

10. The reflective surface of claim 2, wherein said reflective surface has a magnification of about unit magnification or less.

11. A method for generating a reflective surface comprising the steps of:

a) inputting data comprising an image surface, a domain of an image surface, an object surface, a non-reversing correspondence T and the coordinates of an eye of an observer;

b) computing a vector field W(x,y,z) as an algebraic expression from the following three equations;

proj(x,y,z)=(1,y/x,z/x)

T(proj(x,y,z)=(x₀−

α

y/x,β

z/x)

wherein k is the distance between the reflective surface and observer, s is the distance from the reflective surface to the object plane, x=x₀=−

(s−

k), and α and

β

are magnification factors,

12. The method of claim 11, wherein a basis of polynomial functions are used to represent the function ƒ

.

13. The method of claim 12, wherein the reflective surface reflects a field of view of at least 30°

when viewed from a perspective of an observer.

14. The method of claim 12, wherein the reflective surface reflects a field of view of at least 40°

when viewed from a perspective of an observer.

15. The method of claim 12, wherein the reflective surface reflects a field of view of at least 45°

when viewed from a perspective of an observer.

16. The method of claim 12, wherein the reflective surface is saddle shaped.

17. The method of claim 12, wherein the reflective surface has an image error quantity, I_e, of less than about 15%, wherein I_e is calculated according to the following equation:

18. The reflective surface of claim 12, wherein the reflective surface has an image error quantity of less than about 10%.

19. The reflective surface of claim 12, wherein the reflective surface has an image error quantity of less than about 5%.

20. The method of claim 11, wherein said magnification factors α

and β

are about k+s or less.