We formulate the dynamics of electron-wave propagation in photoionization microscopy for nonhydrogenic atoms, based on a frame transformation between the spherical and parabolic coordinates used in Harmin's Stark-effect theory. An expression for the wave function for photoelectrons ejected from the nonhydrogenic atomic source has been derived. The spatial distributions of electron current densities or differential cross sections for Na are computed and compared to those from a recently developed coupled-channel theory. The difference between these two approaches is analyzed and attributed to the frame transformation for irregular wave functions. Since more detailed physical information can be extracted by comparing differential cross sections, rather than total cross sections, photoionization microscopy is proposed to test the Stark-effect theory.