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In this study, a nano-displacement measurement system is proposed and demonstrated both theoretically and experimentally, which was based on a modified Mach-Zehnder (M-Z) interferometer using two conjugated orbital angular momentum (OAM) beams. In contrast to the previous M-Z-based OAM interferometer, a reflection module is inserted into the reference arm instead of a simple mirror. As a result, the effect of the transverse position-dependence phase-shift caused by the dove prism can be clearly eliminated and a stable and robust (off-axis insensitive) petal-like interference pattern can be obtained successfully. More importantly, a significant rotation angle of the petal-like pattern vs. the tiny displacement of the tested object can be clearly observed. In accordance with the modified measurement setup, a novel phase-demodulation method enabling to quickly and accurately characterize the rotation angle of the petal-like interference-patterns is proposed and demonstrated also. A tiny displacement ranging from 50 to 800 nm with resolution of $\sim 50$ pm has been measured successfully. The proposed approach may find applications in not only the ultra-high precision displacement sensor, but also the temperature, strain, and refractive index sensors. [ABSTRACT FROM AUTHOR]

In this paper, a novel self-mixing grating interferometer (SMGI) with dual laser diodes (LDs) is proposed for 2-D dynamic displacement measurement. The light beams emitted from the LDs are incident onto a reflection grating with ±1st order auto-collimation diffraction angles and then diffracted back into the lasers, respectively, which can cause self-mixing interference effect in each LD. Theoretical analysis on the SMGI signals corresponding to 2-D displacement is presented and verified with the experimental observations. Measurement results of 2-D dynamic displacement demonstrate that the proposed system can achieve the measurement resolution better than 10 nm. The proposed SMGI sensing system has the advantages of high stability, compact mechanical structure, and relatively straightforward operation. [ABSTRACT FROM AUTHOR]

In this paper, we present an orthogonally polarized self-mixing grating interferometer (SMGI) for simultaneous measurement of in-plane and out-of-plane displacements. The measurement ranges in both directions are limited only by the length of grating. The orthogonally polarized lights emitted from a birefringent He–Ne laser are separated and enter the grating at ±1st-order Littrow angles. The diffraction beams re-enter the laser cavity and cause self-mixing interference. To differentiate the orthogonally polarized lights and obtain high resolution, phase modulation technique is introduced to extract phases from the orthogonally polarized SMGI signals. The measurement results show that the proposed system can reach a submicron accuracy in the experiment. This work provides a good way to achieve high precision two-dimensional displacement measurement with a robust system configuration. [ABSTRACT FROM AUTHOR]

Pure high frequency periodic triangle phase shift is introduced into optical interference, calculates nine data points in each period and obtains discrete phase values. This paper proposes a novel phase demodulation technology analyzing phase information with a symmetric linear method for depressing sampling error. Traditional low finesse Fabry–Perot interferometer produces typical cosine interference signal, performance of which is greatly improved by proposed technology. In experimental configuration we situate an electro-optics crystal to induce phase shift. The variation of Fabry-Perot cavity length is measured with a resolution much higher than the fringe counting or frequency modulation techniques. Simulation and experimentation both demonstrate feasibility and robustness of proposed algorithm. Reconstructed deviation and noise sources are discussed in detail. Various vibration formats are measured as deeper verification. [ABSTRACT FROM AUTHOR]

In this paper, a simplified phase demodulation scheme is applied to recover vibration trail on a laser self-mixing interferometer for noncontact vibration measurement. The emission of semiconductor laser diode is modulated by injecting sinusoidal wave, and corresponding interference signal is a quasi-sinusoid wave. The vibration mathematical model for semiconductor laser diode is theoretically educed from basic self-mixing theory, the variation of target is converted into phase information. The simulation of demodulation algorithm and standard deviation are presented and the reconstructed waveform displays a desirable consistence with various moving trails. Following the principle, a minimum experimental system is established and position variation of the target mirror driven by voltage signal is translated into phase shifts, feedback is controlled at weak level during experiment, Fourier transform is implemented to analyze phase information. The comparisons of both amplitude and velocity with a Germany Doppler vibrometer are performed to testify vibration model, the error of proposed demodulation method is less than 30 nm and achieve a high accuracy in vibration frequency. The experimental results indicate the traditional phase technology can be applied on complex optical power signal after adaption providing a feasible application prospects in industrial and scientific situation with an inexpensive semiconductor laser. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, self-mixing interference measurement based on phase modulation is demonstrated using a fiber laser system. The measurement setup is built by an erbium-doped fiber laser and an integrated-optic phase modulator. Optical feedback and phase modulated interference is theoretically analyzed, and the phase demodulation algorithm of the interference signal is implemented by Fourier analysis. Error sources induced by the distortion of the interference signal in the presence of optical feedback and the imperfect alignment between the polarization of the light and the electro-optically active axis are evaluated in detail. The system is experimentally applied to reconstruct the motion of a high-precision commercial PZT and a displacement measurement accuracy of λ/20 is obtained, providing a practically feasible solution for displacement measurement based on all optical-fiber sensing applications with high precision. [Copyright &y& Elsevier]