Self-mixing Interferometer Research Articles

Semiconductor laser self-mixing micro-vibration measuring technology based on Hilbert transform

A signal-processing synthesizing Wavelet transform and Hilbert transform is employed to measurement of uniform or non-uniform vibrations in self-mixing interferometer on semiconductor laser diode with quantum well. Background noise and fringe inclination are solved by decomposing effect, fringe counting is adopted to automatic determine decomposing level, a couple of exact quadrature signals are produced by Hilbert transform to extract vibration. The tempting potential of real-time measuring micro vibration with high accuracy and wide dynamic response bandwidth using proposed method is proven by both simulation and experiment. Advantages and error sources are presented as well. Main features of proposed semiconductor laser self-mixing interferometer are constant current supply, high resolution, simplest optical path and much higher tolerance to feedback level than existing self-mixing interferometers, which is competitive for non-contact vibration measurement.

Direct phase extraction of self-mixing displacement measurement using Hilbert transform

Signals of a self-mixing interferometer established on a semiconductor laser diode are analyzed. Phase is extracted out for decoding measurement which contained in self-mixing fringes. The semiconductor laser diode works as light source and receiver without modulation. By combining Hilbert transform with phase condition of self-mixing interference, micron- displacement is reconstructed by phase information at week or even moderate feedback level. Theoretical analysis and simulation results are presented before verification of experimental measurement. Practical feedback level is estimated by a data fitting technique with a programmable high-resolution PZT. Consistence of the results promises that direct phase extraction on self-mixing interferometer is available for micron-displacement measurement with a nanometer accuracy.

Simultaneous measurement of vibration amplitude and rotation angle based on a single-channel laser self-mixing interferometer

Based on a single-channel laser self-mixing interferometer, we present a new simultaneous measurement of the vibration amplitude and the rotation angle of objects that both affect the power spectrum containing two peaks of the interferometer signals. The fitted results indicate that the curve of the peak frequency versus the vibration amplitude follows a linear distribution, and the curve of the difference of the two-peak power values versus the angle follows a Gaussian distribution. A vibration amplitude with an error less than 3.0% and a rotation angle with an error less than 11.7% are calculated from the fitted results.

Single Channel Self-Mixing Interferometer Measures Simultaneously Displacement and Tilt and Yaw Angles of a Reflective Target

We show that a self-mixing interferometer can supply not only to the usual optical-phase signal cos 2ks( $t$ ) of the external reflector displacement $s(t)$ , but also the attitude signal $P(a$ ) because of the dependence of power from the angle a between wavevector k and normal n to the target reflective surface. By proper interrogation of $P(a$ ) along two orthogonal components of tilt and yaw, the two angles can be measured simultaneously, together with the displacement, in a single self-mixing interferometer channel implemented by a single-laser diode and monitor photodiode combination.

Development of a design tool for closed-loop digital vibrometer.

The closed-loop technique has been demonstrated as a possible configuration to design a vibrometer based upon self-mixing interferometry. The electronic feedback loop allows a better linearity while extending the linearity range of a self-mixing interferometer. A deep analysis of the feedback loop is carried out in order to improve stability and performance through a digital approach. This work describes first the simulation of the closed-loop vibrometer, and then the performance obtained through its implementation on an FPGA based prototype.

Sinusoidal phase-modulating self-mixing interferometer with nanometer resolution and improved measurement velocity range.

A new signal-processing method based on an electronic frequency down-conversion technique has been introduced into a sinusoidal phase-modulating, self-mixing interferometer. The developed interferometer employs an electro-optical crystal placed in the external cavity of a He-Ne laser to generate the sinusoidal phase modulation with high modulation rate and ultralow insertion loss. Phase quadrature signals which have been amplitude-modulated by the sine and cosine functions, respectively, of the measured displacement can be extracted from the high-density optical fringes through the use of dual-channel multiplier/filter circuits. Therefore, the displacement of the external target can be retrieved from the phase quadrature signals with nanometer resolution and high computational efficiency. Moreover, a much-improved measurement speed from 2.5 to 22 mm/s has been realized owing to the simplified signal-processing method. The performance of the proposed interferometer has been experimentally verified by comparison to an Agilent 5529A dual-frequency laser interferometer. The measurement results from the two instruments agree well, and we therefore expect that our new technique offers a powerful instrument for high-speed metrology sciences.

Implementation of the reflection phase-shift laser self-mixing interferometer for large-scale displacement measurement

Beginning with introducing π/2 phase-shift on the laser self-mixing front output signal reflected by the metal–dielectric film, the new measurement technique of laser self-mixing interferometer is studied. Through the glass substrate coated by metal film attenuating the laser intensity while introducing π/2 phase-shift on the reflection self-mixing interference front signal in the electronic domain, it is easy to make the laser self-mixing interferometer system work under weak feedback conditions and to produce two orthogonal interference signals which are used to measure the displacement. The simulation result indicates high measurement accuracy. In order to improve the measurement accuracy and resolution of interferometer in 100mm level displacement, the collected self-mixing interference signal is dealt with electronics subdivision in the digital domain, improving the noise performance and measurement reliability. Calibration experiments with high precision guide shows that 0.4μm resolution in 100mm displacement measurement process is achieved. As the self-mixing interference signals are acquired directly, the system measurement speed can be high. But subject to sampling rate of the data collection and processing system, the speed can reach close to 100mm/s in 100mm range displacement measurement theoretically.

High-accuracy self-mixing interferometer based on single high-order orthogonally polarized feedback effects

A simple and high-accuracy self-mixing interferometer based on single high-order orthogonally polarized feedback effects is presented. The single high-order feedback effect is realized when dual-frequency laser reflects numerous times in a Fabry-Perot cavity and then goes back to the laser resonator along the same route. In this case, two orthogonally polarized feedback fringes with nanoscale resolution are obtained. This self-mixing interferometer has the advantages of higher sensitivity to weak signal than that of conventional interferometer. In addition, two orthogonally polarized fringes are useful for discriminating the moving direction of measured object. The experiment of measuring 2.5nm step is conducted, which shows a great potential in nanometrology.

Refractive Index Measurement With High Precision by a Laser Diode Self-Mixing Interferometer

A new method based on the laser diode self-mixing interference effect for refractive index measurement is demonstrated. It employs a simple translation method to measure the optical phase shift as a function of the moving distance of the sample. The refractive index is determined by analyzing a fringe number of self-mixing signals with respect to the moving distance and the incidence angle, with an experimental accuracy of 0.004. Interestingly, the setting error of the proposed system can be effectively decreased by modifying the incidence angle. This method also shows the advantage of a large measurable range of the refractive index.

A Novel Phase Modulation Accelerometer

A novel phase modulation accelerometer based on self-mixing effect is presented. A quartz pendulous reed suspended by dual flexible beam is used as the first step sensing unit, which translates the acceleration signal to the displacement of quartz pendulous reed. The laser self-mixing interferometer reads out the displacement of quartz pendulous reed while the sensor experience acceleration. All-phase spectrum analysis is applied to detect the phase of self-mixing interference signals to reconstruct the acceleration. Finally, performances of the novel phase modulation accelerometer are measured by experiments. Experimental results indicate that the resolution of the acceleration sensor based on laser self-mixing interference can achieve sub micro-g. The phase modulation accelerometer has the potential to achieve high-precision, compact accelerometers.

Self-mixing vibration measurement using emission frequency sinusoidal modulation

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 30nm 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.

Systematic and random errors in self-mixing measurements: effect of the developing speckle statistics.

We consider the errors introduced by speckle pattern statistics of a diffusing target in the measurement of large displacements made with a self-mixing interferometer (SMI), with sub-λ resolution and a range up to meters. As the source on the target side, we assume a diffuser with randomly distributed roughness. Two cases are considered: (i) a developing randomness in z-height profile, with standard deviation σ(z), increasing from ≪λ to ≫λ and uncorrelated spatially (x,y), and (ii) a fully developed z-height randomness (σ(z)≫λ) but spatially correlated with various correlation sizes ρ(x,y). We find that systematic and random errors of all types of diffusers converge to that of a uniformly illuminated diffuser, independent of the actual profile of radiant emittance and phase distribution, when the standard deviation σ(z) is increased or the scale of correlation ρ(x,y) is decreased. This convergence is a sign of speckle statistics development, as all distributions end up with the same errors of the fully developed diffuser. Convergence is earlier for a Gaussian-distributed amplitude than for other spot distributions. As an application of simulation results, we plot systematic and random errors of SMI measurements of displacement versus distance, for different source distributions standard deviations and correlations, both for intra- and inter-speckle displacements.

Real-Time Self-Mixing Interferometer for Long Distances

This paper describes a novel instrument based on a self-mixing optical interferometer, able to reconstruct the target speed and direction, without heterodyne detection. The real-time elaboration employs the signal nonlinearity to recover the speed sign in the frequency domain. The target speed is measured by the signal frequency, while the speed sign is evaluated by the phase of the harmonics in the frequency domain. The high-sensitivity of the elaboration allows the measurement over diffusive target with distances up to 10 m. The measurements results have been successfully compared with a very-high resolution commercial calibrated instrument.

Speckle Pattern Errors in Self-Mixing Interferometry

We analyze the random errors occurring in interferometric measurements because of the speckle pattern regime, when the remote target is a diffusing surface. First, we review the statistical properties of speckle and discuss amplitude fading that is affecting the self-mixing interferometer (SMI) signal and methods to alleviate it. Second, we derive intra-speckle phase errors using the bivariate conditional probability, and find that the noise-equivalent-displacement for small displacement Δ is proportional to the ratio of Δ to speckle longitudinal size s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub> . Last, we extend the analysis to inter-speckle displacements (Δ > s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ) and, after deriving speckle systematic and random errors, show that operation up to meters on a diffusing surface target is possible with a small (≈ λ) error. Results are mainly focussed on SMI, yet they have general validity for any configuration of interferometry.

Spectral Analysis for Velocity Measurement Through Self-Mixing Interferometry

A novel elaboration technique for a self-mixing interferometer is presented. It enables the measurement of speed and direction for a remote target, without using heterodyne detection. The elaboration employs the signal non-linearity for recovering the speed sign directly in the frequency domain. The target speed is measured by the signal frequency, whereas the speed sign is evaluated by the phases of the signal.

Numerical simulation of phase modulation method used as high sensitive self-mixing vibrometry in vertical-cavity surface-emitting laser

The self-mixing interference technique is a compact sensing technique that has widely used for measuring vibrations. For purpose of increasing the accuracy of the vibration measurement system, a new phase modulation technique based on the self-mixing interferometer is presented. The phase modulation is obtained by varying the length of external cavity periodically. The vibration information of the external target is determined by the Fourier analysis method. Theoretical analysis and numerical simulations of phase modulation method used as high sensitive self-mixing vibrometry based on vertical-cavity surface-emitting laser are given in this paper.

Research on micro-vibration measurement by a laser diode self-mixing interferometer

The self-mixing vibration signals are observed in the laser diode when the optical beam is back-scattered into the laser cavity which causes laser output power modulated. Based on these properties, a laser diode self-mixing vibrometer with wide dynamic range is proposed. This current investigation further reports new work to improve the accuracy and range of the measured vibration signals. Numerical simulations and experimental results are given and discussed. The experimental results show that the frequency measurement range can be achieved up to 22kHz with 0.241% maximum relative error while utilizing the reflecting film. For amplitude measurement utilizing the same reflecting film, the error of measurement result is 4.77nm which has approached nanometer order of magnitude.

Phase modulated self-mixing interferometer of a fiber laser system

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.

Laser self-mixing interferometer for MEMS dynamic measurement

Laser self-mixing interferometer has the advantages of simple architecture, compact size, naturally self-aligned optical characteristics, and low cost. It is promising to replace conventional interferometers for physical measurements, such as displacement, distance, velocity, vibration, and so on. In this paper, this interferometer was tried to be used for micro-electromechanical system (MEMS) dynamic measurement. Firstly, its measurement principle based on a three-mirror cavity model was presented, and then the laser self-mixing interferometer for MEMS dynamic measurement was designed, experiments were finally performed as target moves with different forms. Experimental results suggest that self-mixing interferometer is available for MEMS dynamic measurement, and may have wider applications in the future.

Development of a sinusoidal phase-shifting self-mixing interferometer for real-time displacement measurement with nanometer accuracy

By combining the principles of sinusoidal phase-shifting technique and self-mixing interferometry, a novel instrument has been developed for real-time displacement measurement with nanometer accuracy. The sinusoidal phase shifting is introduced by an electro-optic modulator and the displacement of the object is measured by analyzing the harmonic components in the interference signal during each phase-shifting period. Theoretical analysis and simulation results are presented and some error sources are discussed in detail. The displacement measurement experiments by using a high precision nano-positioning stage and a long-range linear stage are performed to verify the performance of the interferometer. The measurement results of the interferometer are in good agreement with the data from a commercial dual-frequency interferometer, showing that the development of the interferometer is feasible for implementation in a real-time displacement sensor with high accuracy.