Diffractive lenses can be obtained by recording the interference pattern originated by interference of two different spherical waves. The imaging quality of such optical elements usually is described in terms of III-order aberrations. The aberration coefficients depend on the radii of curvature of waves used for the lens recording and location of its input pupil. The imaging quality also depends on such factors as image contrast and background illumination level (due to scattered light). Those factors do not result from aberrations, but are dependent on the type of recording process. Namely, light diffraction occurs on the system of fringes of profile depending on the transmittance-versus-exposure characteristics of the recording material. Several types of lenses including kinoform, linear, nonlinear, and binary amplitude, as well as linear and binary phase diffractive lenses of the same III-order aberrations, are investigated. Point spread function and incoherent transfer function numerically calculated are compared. The other factor influencing the imaging quality is modulation transfer function of the recording material. The different local spatial frequency of the diffractive lens microstructure corresponds to the different local diffraction efficiency. This effect is similar to apodising and also can change the imaging characteristics. Four typical material modulation transfer functions are considered: linear, parabolic, hyperbolic, and band-pass -- typical for photothermoplastics. The resulting point spread functions and incoherent transfer functions are calculated for diffractive lenses with aberrations: one having uncompensated astigmatism, the other with considerable coma.