Periodic error is a main error source that limits the measurement accuracy in heterodyne laser interferometry.
An external cavity diode laser (ECDL) based Fabry-Perot (F-P) interferometer referenced to an optical frequency
comb (OFC) is proposed to characterize the periodic error in heterodyne interferometers. The Pound-Drever-Hall
locking technique is employed to lock the tracking ECDL frequency to the resonance of a high finesse F-P cavity.
The frequency of a reference ECDL is locked to a selected mode of an OFC to generate a stable single optical
frequency. The frequency change of the tracking ECDL induced by the cavity displacement is measured by
beating with the reference ECDL locked to the OFC. Experiments show that the F-P interferometer system has
a displacement resolution of 1.96 pm. We compared the measurement results of our system with a commercial
plane mirror heterodyne interferometer. The period if the periodic error is about half wavelength, with an error
amplitude of 4.8 nm.
A theoretical model has been developed to analyze the output polarization state of a total internal reflection-based retroreflector as a function of pitch and yaw motions. There are six different beam paths in the retroreflector, and thus output polarization states, for a given pitch or yaw misalignment. This polarization model discusses the electric field changes of the laser beam based on Fresnel equations for phase and polarization change on reflection. Jones matrices are computed based on Snell’s law, Fresnel equations, the solid geometry, and coordinate transformations to obtain a Jones matrix model of the retroreflector for a given misalignment. Modeling results show that there is always a rotation to the input beam’s polarization and there are specific input regions that are not sensitive to pitch motions but are sensitive to yaw motions. Validation of the model is also presented, using both theoretical and experimental results published by Kalibjian in 2004.