Optical design methods for imaging systems and optical systems designed therewith

The present invention provides methods to design centered imaging systems by solving differential equations derived from Fermat's principle. These imaging systems consist of a sequence of (moveable or fixed) spherical or aspherical surfaces, or combinations thereof. The power series solution approach allow calculating of a predefined number of surfaces parameters equal to a number of selected aberration terms to vanish nominally. In addition, the methods provide mapping functions coefficients that allow describing exactly where arbitrary rays intersect each individual surface.