Optical linear displacement encoders are frequently used to measure and control the motion of high-precision machine tools and measurement systems. The encoder scales are typically fabricated as diffraction gratings, where the period of the grating is determined by the required resolution and other system design requirements. Coarse gratings - with a period of ~10 um - rely on incoherent sources and Talbot imaging to relay the moving scale pattern to a detector array without using lenses. Higher resolution encoders use finer encoder pitch (<1 um) and laser sources to form grating interferometers which can detect scale displacement to a resolution of better than 10 nm. In all cases, scale motion is detected by measuring interference between wavefronts diffracted by the scale.
Although the first-order design of such systems is well understood, the need for high resolution and accuracy demands a detailed understanding of higher order effects resulting from misalignment, aberrations, coherence, and other physical optics effects. In this paper, we show how simulation methods based on wavefront models derived from ray-trace data can provide a detailed and accurate prediction of how system performance depends on a wide variety of design and construction parameters. The resulting simulation is a useful tool for optimizing encoder designs and establishing fabrication and alignment tolerance budgets.