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In this study, a multiple-dimensional displacement measurement technology is demonstrated by using self-mixing interferometry (SMI) cooperating with a frequency division multiplexing (FDM) technique. The proposed SMI configuration with a single laser generates three modulated light beams with different carrier frequencies. Each beam is incident on a planar grating with its own auto-collimation diffraction angle. The diffracted beams return to the laser cavity and then self-mixing interference occurs. An algorithm based on FDM is developed for multiple-dimensional displacement reconstruction from a single SMI signal. Experiments are conducted to verify the proposed approach. This paper shows an attractive sensing system for multiple-dimensional displacement featuring compact configuration, high resolution and better immunity to environmental disturbances. [ABSTRACT FROM AUTHOR]

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 letter, we proposed an innovative laser self-mixing interferometer (SMI) with a reflection-type two-dimensional (2D) grating for three-dimensional (3D) dynamic displacement sensing. When the beams emitted by three lasers are incident on a reflective 2D grating with auto-collimation diffraction angles, the diffracted beams will return into the lasers along the original path, thus generating self-mixing interference effect in each laser. In order to obtain higher measurement resolution, phase-modulation technique is applied to the proposed interferometer. The operating principle for the proposed system has been demonstrated in detail. Measurement results show that our method is capable of sensing 3D dynamic displacement with resolution of nanometer level. The SMI presented in this letter has the merits of high resolution, compact system configuration and straightforward operation. [ABSTRACT FROM AUTHOR]

A multichannel laser self-mixing interferometry (SMI) is proposed based on a combination of linear injection current modulation and carrier frequency division multiplexing (FDM) technique. The laser output is split into several beams with each beam directed toward a specific target for measurement. The reflected beams then return to the laser cavity, where self-mixing interference takes place. Since the external cavity length of each measurement channel is different, the SMI signal contains multiple carriers due to the injection current modulation. An algorithm based on FDM is developed for displacement sensing of multiple targets from a single SMI signal. Experimental results show that the relative error of multichannel displacement measurement is <1.4%. This work demonstrates an attractive multichannel SMI for displacement sensing featuring compact configuration and high resolution. [ABSTRACT FROM AUTHOR]

In this work, a novel fringe double scheme with a Fabry–Pérot (F–P) cavity is proposed for self-mixing interferometry based on the narrow transmission spectrum mapping. While the laser beam with self-mixing interference (SMI) propagates through the F–P cavity with the narrow transmission spectrum, the SMI fringe doubles as the optical frequency modulation caused by SMI sweeps the peak of the transmission spectrum of the F–P cavity completely. The doubled SMI signal is very suitable for displacement reconstruction with fringe counting and velocity monitoring with joint time-frequency analysis, since it inherits the merits of the transmission spectrum of the F–P cavity (sharp, neat, and stable). This method has the potential to simplify signal processing and improve the resolution of SMI measurement systems. [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]

Abstract: In order to realize real-time displacement measurement with high resolution, sinusoidal phase modulation and integrating-bucket method are introduced in the self-mixing interference (SMI) system firstly. The phase of the laser beam is modulated by an electro-optic modulator (EOM) in the external cavity. Theoretical analysis, simulation results and error evaluation are presented. Experimentally, the micro-displacement of a high-precision commercial PZT is reconstructed and the reconstruction accuracy is on the order of nanometers for displacements of a few micrometers. [Copyright &y& Elsevier]

Abstract: A novel self-mixing interferometer based on temporal-carrier phase-shifting technique is presented. The phase of the laser beam is modulated with a triangular wave by an electro-optic modulator (EOM) in the external cavity. Phase demodulation of the interference signal is achieved by five-step Schwider–Hariharan algorithm combined with a special sampling technique. Theoretical analysis and simulation results are presented. Some errors of the technique have been discussed. Experimentally, the new interferometer is applied to measure the displacement of a high precision commercial PZT and a displacement measurement accuracy of λ/60 can be obtained. [Copyright &y& Elsevier]