In this thesis, the Circular Bessel Functions are presented for the rst time, as an alternative to the classic Zernike Polynomials, to represent ophthalmic surfaces. It is shown that the Circular Bessel Functions overcome representation drawbacks that the Zernike Circle Polynomials, standard basis in Ophthalmic Optics, exhibit in certain cases of clinical importance. We explain the general mathematical context of modal theory in two dimensional domains and present applications to the field of vision, astronomy and optical traps.