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- Title
Periodic nonlinearity of a frequency-modulated homodyne interferometer using least-squares circle fitting and subtraction.
- Authors
Nguyen, Thanh Dong; Nguyen, Thi Phuong Mai; Vu, Thanh Tung; Vu, Toan Thang
- Abstract
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.
- Subjects
DISPLACEMENT (Mechanics); SEMICONDUCTOR lasers; AMPLITUDE modulation; INTERFEROMETERS
- Publication
Applied Physics B: Lasers & Optics, 2023, Vol 129, Issue 6, p1
- ISSN
0946-2171
- Publication type
Article
- DOI
10.1007/s00340-023-08028-5