This paper gives a comprehensive survey of the chromatic correction, imaging quality, and spherochromatic aberrations of imaging systems consisting of two or three holographic optical elements (HOEs). HOEs generally represent holographic lenses and holographic gratings. By a suitable combination of two or more HOEs the transversal and longitudinal chromatic aberrations of imaging systems consisting of HOEs can be corrected. The quality of such imaging systems is measured in terms of optical transfer functions (OTFs), and may be demonstrated by transversal ray aberrations. In experiments, OTFs for polychromatic and nearly monochromatic, spatially incoherent radiation are measured and compared with theoretical results. With a system consisting of one holographic grating and one holographic lens only, the transversal chromatic aberration can be corrected. In a system of two or more holographic lenses, however, the longitudinal chromatic aberrations can also be corrected. A system of two holographic lenses behaves like an achromat and a system of three holographic lenses behaves like an apochromat. The measured and calculated OTFs give the quality of such systems in terms of aperture, wavelength range, wavefront aberrations and image field, where the residual aberrations after chromatic correction are the spherochromatic aberrations of different order and the geometrical aberrations introduced by imperfect optical components during the recording of HOEs. With the OTF as a merit function, closed solutions on the basis of the Kirchhoff-Fresnel diffraction integral and computer optimization programs based on ray-tracing show the behaviour and the best geometrical parameters for each system of HOEs. After computer optimization, the best image plane frequently differs considerably from the image plane given by the expression for achromatic behaviour (achromization condition) in the case of large wavelength ranges.