The design and analysis of a hybrid diffractive/refractive achromat for optical data storage is presented, beginning with a discussion of the construction and diffraction efficiency of surface relief diffractive lenses. The phase function, which defines a diffractive lens in much the same manner as a surface sag equation defines a refractive lens, is examined. The thin lens, or Sweatt, model of a diffractive lens is discussed, and equations are provided that allow conversion to and from the phase model. The thin lens model provides a good method to design diffractive lenses using conventional lens design software. This model also provides a convenient means of deriving the third-order aberrations of a diffractive lens. A wave propagation approach is used to discuss how decentering or tilting one of the elements with respect to the other will affect the PSF and MTF of a doublet. Two examples of achromat design are presented. First, a conventional refractive achromat with no spherical aberration or coma is designed, and the method is then extended to design a hybrid diffractive/refractive achromat. Finally, design constraints and performance goals for a hybrid diffractive/refractive achromat for use in an optical data storage system is presented. Two figures of merit used to evaluate the performance of the achromat are the Strehl ratio, which should remain greater than 0.96 over a 1 deg half field of view, and the ratio of focal length change per wavelength change, which should remain less than 0.1 micrometers/nm over the wavelength band. An optimized hybrid achromat is presented, and design tolerances with respect to fabrication errors-element misalignment, thickness errors, diffractive surface zone radii errors, blaze height errors, and mask misalignment error--are discussed.