The imaging characteristics for X-ray wavelengths in the "water window" under incoherent imaging conditions (large detector aperture) are examined for the King's College London scanning transmission X-ray microscope with zone-plate objective installed at the Daresbury (UK) synchrotron. The principal consideration was to express image theory, incorporating wave aberrations and apodised zone plates, and to apply the theory to experimental data. Comparisons are made, showing reasonable agreement, for a range of defocus values and two wavelengths. Due to problems in fabrication it was necessary to determine the effective, or operational, zone-plate parameters (radius of outermost active zone r(N), width of outermost active zone dr(N)); this was accomplished by through-focus series. Calculated point spread functions were used to deblurr images? in through-focus series of two-dimensional scanned X-ray images of specimen bores and test grating patterns. Significant contrast enhancement is achieved after deconvolution with a best point-to-point resolution of about 35 nm. (C) 2000 Elsevier Science B.V. All rights reserved.