In this article, we have systematically investigated the dependencies of k(1) on illumination conditions such as coherence setting and opening angle in off-axis illumination scheme. As result, conventional Rayleigh's equations are not sufficient to address the effect of the numerical aperature and coherence on the depth of focus. Therefore, a metric called the coherency factor (sigma(c)) is proposed as a complementary metric of the low k(1) lithography. Coherency factor (sigma(c)) is defined as the ratio of areas of captured first order and zero order light. The theory is based on simple geometrical analysis of the diffraction orders in the pupil plane. Areas of different diffraction orders captured by the pupil are evaluated as a function of wavelength, numerical aperture, and pitch. As corresponding to experimental results, a higher sigma(c) value concurs with a larger depth of focus. Extracting from Fraunhofer diffraction equation for a single slit and incorporating coherency factor sigma(c), we have modified and extend the use of Rayleigh's equations for 90 nm processes and below. Results show that the extension of Rayleigh's equations is capable to optimize the depth of focus and map out the forbidden pitch locations for any design rules and illumination conditions. More importantly, it can complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design in order to suppress the forbidden pitch phenomenon. (C) 2004 American Vacuum Society.