IPC분류정보
국가/구분 |
United States(US) Patent
등록
|
국제특허분류(IPC7판) |
|
출원번호 |
US-0377379
(2010-06-11)
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등록번호 |
US-8979287
(2015-03-17)
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국제출원번호 |
PCT/US2010/038334
(2010-06-11)
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§371/§102 date |
20111209
(20111209)
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국제공개번호 |
WO2010/144816
(2010-12-16)
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발명자
/ 주소 |
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출원인 / 주소 |
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대리인 / 주소 |
Medelsohn, Drucker & Dunleavy, P.C.
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인용정보 |
피인용 횟수 :
0 인용 특허 :
4 |
초록
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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
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.
대표청구항
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1. A non-reversing mirror comprising: a reflective surface M perpendicular to a vector field W of the following equations: proj(x,y,z)=(1,y/x,z/x)T(proj(x,y,z))=(x0,−αy/x,βz/x)wherein k is the distance between the reflective surface and observer, s′ is the distance from the reflective surface M to t
1. A non-reversing mirror comprising: a reflective surface M perpendicular to a vector field W of the following equations: proj(x,y,z)=(1,y/x,z/x)T(proj(x,y,z))=(x0,−αy/x,βz/x)wherein k is the distance between the reflective surface and observer, s′ is the distance from the reflective surface M to the object plane, x0=−(s′−k), and α and β are magnification factors, W(x,y,z)=T(proj(x,y,z))-(x,y,z)T(proj(x,y,z))-(x,y,z)+proj(x,y,z)-(x,y,z)proj(x,y,z)-(x,y,z)wherein T is a transformation from an image plane to an object plane of a non-reversed, undistorted direct reflection of an object or object plane, wherein the reflective surface M is represented by a minimizer ƒ* represented by the polynomial function ƒ(x,y,z): f(x,y,z)=∑i+j+k≤Na(i,j,k)xiyjzkwhere N is a fixed positive integer, there are at least three variable coefficients α(i,j,k) and a(1,0,0)=1; wherein the reflective surface M produces a non-reversed perspective view reflection at the image plane when viewed from a perspective of an observer positioned within the field of view of said reflective surface M;wherein the reflective surface M has an image error quantity, Ie, of less than about 15% when viewed from the perspective of the observer is positioned within the field of view of the reflective surface M, and Ie is calculated according to the following equation: Ie=1diameter(T(A))(∫AT(1,y,z)-TM(1,y,z)2ⅆyⅆz)12wherein A is the image of a domain in the image plane over which the reflective surface M is a graph T is a transformation from the image plane to the object plane of a non-reversed, undistorted direct reflection of an object or object plan and TM is a non-reversing image transformation induced from the image plane to the object surface by reflecting at least one ray off reflective surface M; and wherein the reflective surface M is convex or saddle-shaped. 2. The non-reversing mirror of claim 1, wherein the reflective surface M has an image error quantity Ie of less than about 10%. 3. The non-reversing mirror of claim 1, wherein the reflective surface M has an image error quantity Ie of less than about 5%. 4. The non-reversing mirror of claim 1, wherein the reflective surface M has an image error quantity Ie of less than about 3%. 5. The non-reversing mirror of claim 1, wherein said reflective surface M is capable of reflecting at least a 30° field of view when viewed from the perspective of an observer. 6. The non-reversing mirror of claim 1, wherein said reflective surface M is capable of reflecting at least a 40° field of view when viewed from a perspective of an observer. 7. The non-reversing mirror of claim 1, wherein said reflective surface M is capable of reflecting at least a 45° field of view when viewed from a perspective of an observer. 8. The non-reversing mirror of claim 1, wherein said reflective surface M is saddle shaped. 9. The non-reversing mirror of claim 1, wherein said reflective surface M has a magnification of about unit magnification or less. 10. A method for producing a non-reversing mirror comprising generating a non-reversed perspective view reflective surface M comprising the steps of: a) inputting data comprising an image surface, a domain of an image surface, an object surface, a non-reversing undistorted direct correspondence T and 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,−αy/x,βz/x)wherein k is the distance between the reflective surface and observer, s′ is the distance from the reflective surface M to the object plane, x0=−(s′−k), and α and β are magnification factors, W(x,y,z)=T(proj(x,y,z))-(x,y,z)T(proj(x,y,z))-(x,y,z)+proj(x,y,z)-(x,y,z)proj(x,y,z)-(x,y,z);d) representing ƒ as a combination of basis functions of said reflective surface M with unknown coefficients;e) solving for said unknown coefficients by minimizing an integral of the following equation, over the volume V of the cross-product of vector field W(x,y,z) and a gradient vector field ∇ƒ: Cost(f)=∫∫∫V∇f×(W/W)2ⅆxⅆyⅆz=f*(x,y,z),wherein ∇ƒ is the gradient of the function represented by select basis functions; andf) calculating a resulting minimizer ƒ* that represents the reflective surface M as a solutions to an equation ƒ*(x,y,z)=C, where C=ƒ*(a,b,c) for a chosen point (a,b,c) in V wherein minimizer ƒ* is represented by the polynomial function ƒ(x,y,z): f(x,y,z)=∑i+j+k≤Na(i,j,k)xiyjzkwhere N is a fixed positive integer, there are at least three variable coefficients α(i,j,k) and α1,0,0=1; andg) producing a non-reversing mirror using the calculated minimizer ƒ*. 11. The method of claim 10, wherein the reflective surface M reflects a field of view of at least 30° when viewed from a perspective of an observer. 12. The method of claim 10, wherein the reflective surface M reflects a field of view of at least 40° when viewed from a perspective of an observer. 13. The method of claim 10, wherein the reflective surface M reflects a field of view of at least 45° when viewed from a perspective of an observer. 14. The method of claim 10, wherein the reflective surface M is saddle shaped. 15. The method of claim 10, wherein the reflective surface M has an image error quantity, Ie, of less than about 15%, wherein Ie is calculated according to the following equation: Ie=1diameter(T(A))(∫AT(1,y,z)-TM(1,y,z)2ⅆyⅆz)12wherein A is the image of a domain in the image plane over which the reflective surface M is a graph and TM is the non-reversing reflection transformation induced from the image plane to the object surface by reflective surface M. 16. The method of claim 10, wherein the reflective surface M has an image error quantity Ie of less than about 10%, and Ie is calculated according to the following equation: Ie=1diameter(T(A))(∫AT(1,y,z)-TM(1,y,z)2ⅆyⅆz)1/2wherein A is the image of a domain in the image plane over which the reflective surface M is a graph T is a transformation from the image plane to the object plane of a non-reversed, undistorted direct reflection of an object or object plane and TM is a non-reversing image transformation induced from the image plane to the object surface by reflecting at least one ray off reflective surface M. 17. The method of claim 16, wherein the reflective surface M has an image error quantity Ie of less than about 5%. 18. The method of claim 10, wherein said magnification factors α and β are about k+s′ or less.
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