Holographic optical elements (HOEs) recorded with arbitrary aspheric wavefronts can now be analyzed with a holographic ray-tracing design program. The recording wavefronts are defined by analytical phase functions, for example, a two-dimensional polynomial expansion. The coefficients of the functional representations of the HOE recording wavefronts are used as parameters to optimize the performance of an optical system containing the HOE. The optimum recording wavefronts are then produced with the help of computer-generated holograms. Several useful arbitrary wavefront phase functions are discussed. Design predictions and experimental results are presented for a holographic Fourier transform lens recorded with the aid of a computer-generated hologram.