The theory of the far-zone waveguide optical microscopy (WOM) image formation is described. The analysis of linear direct and inverse problems of the WOM is accomplished. The theoretical investigation predicts: the lateral resolution can attain ∼20 nm and the vertical resolution (in RMS height) can attain ∼1 Å. The limiting lateral resolution is a ∼15-times less than Abbe's diffraction limit. Thus the superresolution may be accomplished by the waveguide optical microscopy. The increasing of WOM's resolution depends on a priori information of the object under the test and on a sufficiently high signal-to-noise ratio (SNR). Copyright © 1998 by Astro, Ltd.