Purpose: We propose the Bessel Circular Functions as alternatives of the Zernike Circle Polynomials to represent relevant circular ophthalmic surfaces. Methods: We assess the fitting capabilities of the orthogonal Bessel Circular Functions by comparing them to Zernike Circle Polynomials for approximating a variety of computationally generated surfaces which can represent ophthalmic surfaces. Results: The Bessel Circular Functions showed better modelling capabilities for surfaces with abrupt variations such as the anterior eye surface at the limbus region, and influence functions. From our studies we find that the Bessel Circular Functions can be more suitable for studying particular features of post surgical corneal surfaces. Conclusions: We show that given their boundary conditions and free oscillating properties, the Bessel Circular Functions are an alternative for representing specific wavefronts and can be better than the Zernike Circle Polynomials for some important cases of corneal surfaces, influence functions and the complete anterior corneal surface.