Theory of optical edge detection and imaging of thick layers

The optical microscope measurement of small objects, 0.5 to 10 μm in diameter, is complicated by the apparent change in the dimension of the object with a change in the spatial coherence of the illumination. Coherent edge-detection methods have been developed for the measurement of line objects on integrated-circuit photo masks and wafers. A generalization is presented of the coherent threshold equation that permits the extension to any state of partial coherence of the illumination as well as extension to the measurement of nonplanar objects. In the latter case, a waveguide model is developed for imaging of lines patterned in thick layers and is compared with experimental data.