Patent ID: 7848031

Claim:
An optical element comprising at least one optical surface fulfilling the following relationships: σ RMS < 1.0 ⁢ ⁢ nm and max ⁡ ( β ⁡ ( ϕ , x , y ) ) min ⁢ ⁢ ( β ⁡ ( ϕ , x , y ) ) > 1.2 with β ⁡ ( ϕ , x , y ) = 1 / c ⁡ ( ϕ , x , y ) * cos 3 ⁡ ( α ⁡ ( x , y ) ) ( z ⁡ ( x , y ) - d + 1 / c ⁡ ( ϕ , x , y ) * cos ⁡ ( α ⁡ ( x , y ) ) ) wherein: σ RMS is a root-mean-square value of a surface roughness of the optical surface, determined for a spatial length scale in a range from 0.3 mm to 10.0 mm; max(β(φ,x,y)) is a maximum value of β for all locations (x,y) on the optical surface and all orientations (φ); min(β(φ,x,y)) is a minimum value of β for all locations (x,y) on the optical surface and all orientations φ; α(x,y) is an angle between a surface normal of the optical surface at location (x,y) and an average over the surface normals at all locations of the optical surface; c(φ,x,y) is a curvature of the optical surface at location (x,y) and determined at orientation φ, z(x,y) is a surface elevation of the optical surface at location (x,y), wherein for at least one location (x0,y0) z(x0,y0)=0 is fulfilled; and d is a constant with: d =max( z ( x,y ))+50 mm, wherein max(z(x,y)) is a maximum value of z for all locations (x,y) on the optical surface.