High Precision Displacement-Measuring Interferometer Based on Phase Modulation Technique and Modulation Index Instability Elimination
Main Article Content
Abstract
A high precision displacement-measuring interferometer based on a phase modulation technique was developed. A PZT actuator was utilized to drive a mirror of a Michelson interferometer by applying a sinusoidal voltage to the PZT controller. The path difference between two arms of the interferometer was modulated leading to modulation in the phase of the interference signal with a frequency of 3 kHz. The first and second harmonics of the interference signal were detected at the modulation index of 2.63 rad, a special value when the values of the first and second orders of Bessel function are equal. The displacement was determined by the ratio of the second and third harmonic in which the effects of modulation index instability and intensity fluctuation were neglected. Moreover, the direction of the displacement that was ambiguous of the traditional interferometers was clarified in a real time. A measurement precision of 60 nm was obtained using the phase modulation interferometer.
Keywords
Phase modulation, Bessel function, Modulation index, PZT actuator, Michelson interferometer
Article Details
References
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[2] F. Petrů and O. Číp, Problems regarding linearity of data of a laser interferometer with a single frequency laser, Precision Engineering 23 (1999) 39-50.
[3] C. C. Wu et al., Optical heterodyne laser encoder with sub-nanometer resolution, Measurement Science and Technology 19 (2008) 045305.
[4] F. C. Demarest, High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics, Measurement Science and Technology 9 (1998) 1024-1031.
[5] Thanh-Tung Vu, Masato Higuchi, and Masato Aketagawa, Accurate displacement-measuring interferometer with wide range using an I2 frequency-stabilized laser diode based on sinusoidal frequency modulation, Measurement Science and Technology 27 (2016), 105201.
[6] Thanh-Tung Vu, Yoshitaka Maeda, and Masato Aketagawa, Sinusoidal frequency modulation on laser diode for frequency stabilization and displacement measurement, Measurement, Vol. 94, pp. 927-933, 2016.
[7] J. Lawall and E. Kessler, Michelson interferometry with 10 pm accuracy, Review of Scientific Instruments 71 (2000) 2669-2679.
[8] M. Pisani, Multiple reflection Michelson interferometer with picometer resolution, Optics Express 26 (2008) 21558-21563.
[9] J. Ahn et al., A passive method to compensate nonlinearity in a homodyne interferometer, Optics Express, 17 (2009) 23299-23308.
[10] K. N. Joo et al., High resolution heterodyne interferometer without detectable periodic nonlinearity, Optics Express 18 (2010) 1159-1165.
[11] Riehle, Fritz. Frequency standards: basics and applications. John Wiley & Sons, (2006)