Patent ID: 8180606

Claim:
A reflective surface substantially perpendicular to a vector field defined by equations 1-2: W ⁡ ( x , y , z ) = target ⁢ ( x , y , z ) - [ x , y , z ]  target ⁢ ( x , y , z ) - [ x , y , z ]  + source ⁢ ( x , y , z ) - [ x , y , z ]  source ⁢ ( x , y , z ) - [ x , y , z ]  Equation ⁢ ⁢ 1 wherein target (x,y,z) is a point on an object plane defining a surface of an object and source (x,y,z) is a corresponding point on an image plane viewed by an observer that is intersected by a ray containing point (x,y,z) on the reflective surface and coordinates corresponding to a location of an eye of the observer, and target( x,y,z )= kλ source 2 ( x,y,z )[−sin(ψ), cos(ψ),0]+kλsource 3 ( x,y,z )[0,0,1 ]+k[ cos(ψ), sin(ψ),0] Equation 2 wherein k is a distance between the reflective surface and the object plane, ψ is an angle of deflection of the reflective surface formed between the observer and object plane and λ is a magnification factor, wherein the reflective surface is capable of functioning as a driver's side mirror and reflecting at least a 30° field of view from a perspective of a seated driver, and wherein the reflective surface has an image error quantity, I e , of less than about 15% as calculated according to equation 3: I e = 1 diameter ⁡ ( T ⁡ ( A ) ) ⁢ ( ∫ A ⁢  T ⁡ ( y , z ) - T m ⁡ ( y , z )  2 ⁢ ⅆ y ⁢ ⅆ z ) 1 / 2 Equation ⁢ ⁢ 3 wherein T(A) is a transform function that maps a domain, A, in the object plane to the image plane over which the reflective surface, M, is graphed, T(y,z) is a transform function that maps points on the image plane to points on the object plane, and T M is a transform function induced from the image plane to the object plane by reflecting at least one ray off M.