The Stieltjes imaging method makes possible the computation of photoionization or photodetachment cross sections without use of electronic continuum wave functions. Several practical difficulties are encountered in applying this method to complex atoms. Modifications of the computational procedure are introduced here, allowing the efficient computation of high-order principal representations of oscillator-strength distributions of complex atoms without numerical instabilities inherent in previous methods. Illustrative calculations are reported for the ground states of He and B. Principal representations obtained by variational calculations for these two atoms are used to compute spectroscopic moments and Van der Waals constants, and to reconstruct the oscillator strengths of line spectra at observed excitation wavelengths. Good agreement is found with all available quantitative data. Difficulties in constructing the photoionization cross section from the computed principal representations are shown, analyzed, and tentatively resolved by separating the oscillator-strength distributions into physically distinct excitation series. © 1976 The American Physical Society.