For (i), sufficiently small aberrations or (ii), arbitrary aberrations but a sufficiently small spatial frequency, the modulation and phase transfer functions of a lens system may be expressed as polynomials of the second degree in frequency. In this paper the coefficients of these polynomials are related to the aberrations of a lens system which in general does not have an axis of symmetry. Hence, under assumption (ii) the derived expressions for the modulation and phase transfer functions are applicable to any fabricated lens system, over a limited range of spatial frequencies. In addition, the coefficient of the linear term in the phase function expansion is shown to be the first moment of the spread function, and to be linear in its dependence on aberrations. Advantage may be taken of this relation between a physical observable (the first moment) and the aberrations by using it to generate a set of linear equations having only aberrations as unknowns. By its solution some aberrations of (a), axial symmetry (including coma and distortion of third order) and (b), axial asymmetry, may be physically determined, along with certain linear combinations among aberrations of both symmetry types. In this calculation the aberrations may be of any size.