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.