Periodic nonlinearity of a frequency-modulated homodyne interferometer using least-squares circle fitting and subtraction
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, possi...
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| Published in: | Applied physics. B, Lasers and optics Vol. 129; no. 6 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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| 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. |
|---|---|
| AbstractList | 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. 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. |
| ArticleNumber | 83 |
| Author | Nguyen, Thi Phuong Mai Vu, Toan Thang Vu, Thanh Tung Nguyen, Thanh Dong |
| Author_xml | – sequence: 1 givenname: Thanh Dong orcidid: 0000-0001-7719-6660 surname: Nguyen fullname: Nguyen, Thanh Dong organization: School of Mechanical Engineering, Hanoi University of Science and Technology – sequence: 2 givenname: Thi Phuong Mai surname: Nguyen fullname: Nguyen, Thi Phuong Mai organization: School of Mechanical Engineering, Hanoi University of Science and Technology – sequence: 3 givenname: Thanh Tung surname: Vu fullname: Vu, Thanh Tung email: tung.vuthanh@hust.edu.vn organization: School of Mechanical Engineering, Hanoi University of Science and Technology – sequence: 4 givenname: Toan Thang surname: Vu fullname: Vu, Toan Thang email: thang.vutoan@hust.edu.vn organization: School of Mechanical Engineering, Hanoi University of Science and Technology |
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| Cites_doi | 10.1088/1361-6501/aab706 10.1016/j.sna.2020.111880 10.1088/0957-0233/7/4/009 10.1088/0957-0233/12/10/318 10.1364/OE.17.000828 10.1109/MWP.2004.1396857 10.1088/0957-0233/21/4/045106 10.1063/1.1150715 10.1364/AO.396922 10.1007/s00340-020-7391-9 10.1088/1361-6501/ac929e 10.1016/j.precisioneng.2017.09.009 10.1016/j.precisioneng.2018.04.020 10.1063/1.3097187 10.1364/JOSAA.396298 10.1364/OL.22.000478 10.1364/AO.33.006294 10.1364/AO.400682 10.1088/0957-0233/20/8/084008 10.1016/0734-189X(89)90088-1 10.1364/AO.20.003382 10.1088/0957-0233/27/10/105201 10.1364/OL.9.000451 10.1016/0141-6359(90)90060-C 10.1109/JQE.1982.1071603 |
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| Snippet | The purpose of this paper was to investigate the periodic nonlinearity of a frequency-modulated homodyne interferometer that limits the accuracy of... |
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| SubjectTerms | 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 |
| Title | Periodic nonlinearity of a frequency-modulated homodyne interferometer using least-squares circle fitting and subtraction |
| URI | https://link.springer.com/article/10.1007/s00340-023-08028-5 https://www.proquest.com/docview/2810188050 |
| Volume | 129 |
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