Periodic nonlinearity of a frequency-modulated homodyne interferometer using least-squares circle fitting and subtraction

• Published in: Applied physics. B, Lasers and optics Vol. 129; no. 6
• Main Authors: Nguyen, Thanh Dong, Nguyen, Thi Phuong Mai, Vu, Thanh Tung, Vu, Toan Thang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2023; Springer Nature B.V
• Subjects: Amplitude modulation; Applied physics; Current modulation; Displacement measurement; Engineering; Errors; External-cavity lasers; Injection current; Interferometers; Lasers; Least squares; Lock in amplifiers; Nonlinearity; Optical Devices; Optics; Photonics; Physical Chemistry; Physics; Physics and Astronomy; Polynomials; Quantum Optics; Semiconductor lasers
• ISSN: 0946-2171; 1432-0649
• DOI: 10.1007/s00340-023-08028-5

The purpose of this paper was to investigate the periodic nonlinearity of a frequency-modulated homodyne interferometer that limits the accuracy of displacement measurements to the nanometer order. We considered the idea that residual amplitude modulation (RAM) and ghost/parasitic reflections, possibly caused by a pair of semi-transparent mirrors (STMs), could induce periodic errors in our interferometric system. In our experiment, we implemented a micrometer-range linear mechanical displacement measurement using two synchronized lock-in amplifiers (LIAs) whose outputs were the second and third harmonics of the interference signal. The periodic errors of amplitude and phase were found by least-squares circle (LSC) fitting and subtraction via a polynomial fit, respectively. We clarified the existence of the periodic nonlinearity error of
λ
/4 caused by RAM generated by injection current modulation of an external cavity laser diode (ECLD). The experimental results showed that both methods determined a p–p periodic error amplitude of ~± 10 nm for the interferometer. The obtained periodic error components of
λ
/2,
λ
/4, and
λ
/8 were 5 nm rms or less over a linear displacement length of 1.5 μm, corresponding to relative periodic errors of 0.33% or less. Both methods give a good agreement within the calculated estimation, accepting the reliability of our results.