A method and apparatus for providing hardware aware logical volume mirrors are provided. The fixed mirror is formed by laminating a one-layer TiO2 film and a one-layer Ag alloy film. When the system discovers that a new batch of resist is loaded to a tool, historical data is used to calculate a reference dose for each tool. A model for a three-dimensional grating may be constructed by slicing a representative structure into a stack of slabs and creating an array of rectangular blocks to approximate each slab. By arbitrarily constructing an area where these fibrous projections are formed in a predetermined area, it is possible to render the area to have at least either hydrophilicity or water retentivity, so as to provide a silicon structure useful for a variety of devices.