**Presenter: Ethan Edwards, College of Physical and Mathematical Sciences, Physics and Astronomy**

**Authors: Ethan Edwards, R. Steven Turley**

**Faculty Advisor: Steven Turley, College of Physical and Mathematical Sciences, Physics and Astronomy**

**Institution: Brigham Young University**

When the wavelength of light is comparable to the length scale of a surface's roughness, physical and geometrical optics approximations of reflectance fail. Since even the smoothest surfaces have nanometer-scale roughness, finding alternative methods is important in the extreme ultraviolet. To directly calculate reflectance, one can solve the electric field integral equation (EFIE) over a surface. In this project the Nyström method was used with the EFIE to calculate far-field reflection of monochromatic plane-wave light from a one-dimensional blazed grating. Three imperfections were studied: uncorrelated and correlated ruling errors, and surface roughness. Changes in efficiency and resolving power (Rp) were considered. It was found that rms roughness up to 0.25λ decreased Rp by less than 1% and efficiency by 96%, uncorrelated ruling errors up to 0.1λ decreased Rp by 1% and efficiency by 10%, and correlated ruling error up to 0.05λ decreased Rp by 29% and efficiency by 90%. This data reveals that correlated ruling error has a significant effect on both Rp and efficiency, roughness has a significant effect on efficiency, and uncorrelated ruling error has a minor effect on efficiency.