Analysis of Frequency Leakage in Different Optical Paths of Nano-Metrology Systems Based on Frequency-Path Models

The drawing of frequency-path (F-P) models of optical beams is an approach for nonlinearity analysis in nano-metrology systems and sensors based on the laser interferometers. In this paper, the frequency-path models of four nano-metrology laser interferometry systems are designed, analyzed and simulated, including conventional and modified two- and three-longitudinal-mode laser interferometers. The frequency-path model can be used for nonlinearity error analysis resulting from imperfect alignment of optical head and non-ideal laser polarization states. The number of active F-P element in these systems is calculated by multiplying the number of frequency and paths. The number of active F-P elements for conventional and modified two-mode laser interferometer is 4, and this is 6 for conventional and modified three-mode laser interferometer. The output interference terms can be calculated from the active F-P elements which is 10 for conventional and modified two-mode interferometer and is 21 for conventional and modified three-mode one. The interference terms include optical power, ac interference, dc interference, and ac reference. These terms are also investigated in zero (fixed target), low (2mm/s), and high (20mm/s) target velocities using frequency spectrum of photocurrents.