[en] A new fringe subdivision method that employs a large synthetic wavelength to subdivide fringes formed by a small single wavelength is proposed. Based on this subdivision method, we demonstrate a novel dual-wavelength interferometric technique with subnanometric resolution, whose potential fringe subdivision factor derived from an evaluation of the interferometer can reach up to 1/440,000. Theoretical analysis and experimental results with a resolution of 0.05 nm are presented to show the feasibility of the interferometric technique

[en] A novel differential Michelson laser interferometer is proposed to eliminate the influence of environmental fluctuations for nanometer displacement measurement. This differential interferometer consists of two homodyne interferometers in which two orthogonal single frequency beams share common reference arm and partial measurement arm. By modulating the displacement of the common reference arm with a piezoelectric transducer, the common-mode displacement drift resulting from the environmental disturbances can be well suppressed and the measured displacement as differential-mode displacement signal is achieved. In addition, a phase difference compensation method is proposed for accurately determining the phase difference between interference signals by correcting the time interval according to the average speed in one cycle of interference signal. The nanometer displacement measurement experiments were performed to demonstrate the effectiveness and feasibility of the proposed interferometer and show that precision displacement measurement with standard deviation less than 1 nm has been achieved. (paper)

[en] A novel method for measuring air refractive index fluctuation based on a laser synthetic wavelength interferometer is proposed. The change of air refractive index is regarded as an equivalent measured displacement in the measurement arm, which can be realized by tracking a large compensative displacement of the reference mirror in the reference arm of the laser synthetic wavelength interferometer. The merit of the proposed method is that the slight air refractive index fluctuation is magnified to a large displacement on the order of millimeters or micrometers. To verify the feasibility of the proposed method, the correlation experiment between the displacement of the reference mirror and the air refractive index fluctuation and the comparison experiments with Edlén equations both in short time and long time were performed. Experimental results show that the measurement accuracy of the air refractive index fluctuation is better than 3.7 × 10"–"8. (paper)

[en] In order to analyze and characterize the periodic nonlinear error resulting from the misalignment of a polarizing beam splitter (PBS) in a laser heterodyne interferometer more accurately, in this paper, starting from the light separating principle of thin-film PBS, we have found that the root cause of the periodic nonlinear error is the frequency mixing induced by the deviation from the Brewster angle of the incident angle or by the rotation of the incident plane when the PBS is misaligned. Moreover, we have established the direct function relationships between the periodic nonlinear error and different PBSs’ misalignment errors for the first time. The theoretical analysis shows that the periodic nonlinear error arising from the PBS’s yaw error is the largest and the maximal nonlinear errors are unequal even if the positive yaw angle is equal to the negative yaw angle. The nonlinear errors are much smaller under the PBS’s roll and pitch errors. The experiments of polarizing leakage and nonlinear error measurement under the PBS’s yaw error demonstrate that the experimental results are in agreement with the theoretical analysis. (paper)

[en] Correct return of the measuring beam is essential for laser interferometers to carry out measurement. In the actual situation, because the measured object inevitably rotates or laterally moves, not only the measurement accuracy will decrease, or even the measurement will be impossibly performed. To solve this problem, a novel orthogonal return method for linearly polarized beam based on the Faraday effect is presented. The orthogonal return of incident linearly polarized beam is realized by using a Faraday rotator with the rotational angle of 45°. The optical configuration of the method is designed and analyzed in detail. To verify its practicability in polarization interferometry, a laser heterodyne interferometer based on this method was constructed and precision displacement measurement experiments were performed. These results show that the advantage of the method is that the correct return of the incident measuring beam is ensured when large lateral displacement or angular rotation of the measured object occurs and then the implementation of interferometric measurement can be ensured

[en] A novel dual-homodyne interferometer, in which one interferometer acts as the reference interferometer and the other as the measurement one, is proposed to eliminate periodic nonlinearity for nanometer displacement measurement. By using one electro-optic phase modulator to modulate the common reference arm of the two interferometers, the DC interference signals of homodyne interferometers are modulated to AC signals. The measured displacement is carried on the phase difference change of the two AC interference signals. To address the influence of unequal fluctuations of the DC offsets of interference signals on the zero-crossing phase detection, a new phase difference detection method is proposed by counting the sample numbers in positive and negative half periods of interference signals. The merits of this interferometer are not only eliminating the nonlinear errors inherent to heterodyne and homodyne interferometers but also having the abilities of strong anti-interference, insensitivity to laser power drift and the unequal gain of detectors, as well as not demanding quadrature signals. An experiment of nanometer displacement measurement was performed to verify the feasibility of the interferometer, and the results show that sub-nanometer accuracy can be realized without periodic nonlinearity. The large displacement experiment shows that the results obtained with the proposed interferometer are in good accordance with those obtained from a comparison interferometer. These results show that the proposed interferometer can realize large displacement measurement with nanometer accuracy. (paper)

[en] Simultaneous measurement of the straightness error and its position using a modified Wollaston-prism-sensing homodyne interferometer is proposed. In this modified interferometer, we designed a special moving sensor combining a Wollaston prism and a semi-reflective mirror being able to not only avoid the straightness measurement deviation caused by the measured object’s rotation but also simultaneously obtain the straightness error’s position without adding any measuring beam. Further, phase-modulating homodyne interferometry with phase generation carrier (PGC) demodulation is adopted to reduce the nonlinear error of phase measurement. Benefiting from the modified interferometer, the straightness error and its position can be measured simultaneously, and the measurement accuracy and stability can be improved. The optical configuration and the measurement principle of this method are presented. The influence of rotation angles on the straightness measurement result is also discussed. Finally, three experiments were performed to demonstrate the feasibility and applicability of the proposed method. (paper)

[en] On the basis of analyzing sinusoidal phase-modulating Fabry-Perot interferometry, a method, believed to be novel, is proposed for achieving nanometer measurement accuracy by measuring the time interval between equal amplitudes of the two elementary frequency signals of the transmitted intensities of a dual Fabry-Perot interferometer. A nanometer measurement system based on the method was designed and tested. The experimental results show that the displacement resolution of the system is 0.32 nm at a 1-kHz modulating signal

[en] Not only the magnitude but also the position of straightness errors are of concern to users. However, current laser interferometers used for measuring straightness seldom give the relative position of the straightness error. To solve this problem, a laser interferometer for measuring straightness and its position based on heterodyne interferometry is proposed. The optical configuration of the interferometer is designed and the measurement principle is analyzed theoretically. Two experiments were carried out. The first experiment verifies the validity and repeatability of the interferometer by measuring a linear stage. Also, the second one for measuring a flexure-hinge stage demonstrates that the interferometer is capable of nanometer measurement accuracy. These results show that this interferometer has advantages of simultaneously measuring straightness error and the relative position with high precision, and a compact structure.

[en] This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange–Maxwell equations, the discrete analogue of Noether theorems for Lagrange–Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results. (general)