1. An optical imaging system with extended depth of focus for providing an image with a depth of focus, comprising: an optical imaging module, having a specific longitudinal spherical aberration corresponding to a depth of focus, wherein the specific longitudinal spherical aberration is characterized by the wave-front aberration equation; W ( ρ ) = ∑ n = 4 , 6 , 8 , … ( Δ z 4 n ( F # ) 2 ) ( - Δ z f 0 ) n - 4 2 ρ n where, W(ρ) is the wave-front aberration, ρ is normalized pupil radius, f 0 is paraxial focal length, Δz is desired depth of focus, F# is F Number, n is the order of spherical wave-front aberration, n=4 is 3 rd order spherical aberration, n=6 is 5 th order spherical aberration and so on; an array type detector coupled to the optical imaging module for obtaining an image via the specific longitudinal spherical aberration provided by the optical imaging module; and an image restoration module coupled to the array type detector, wherein the array type detector converts the obtained image to a digitalized image and the image restoration module receives the digitalized image and performs an image restoration operation to the digitalized image to form an image with depth of focus.