Self-mixing interference in a diode laser: experimental observations and theoretical analysis

Free spectral range measurement based on a multi-longitudinal mode laser self-mixing ellipse fitting degree detection technique

A method by detecting the ellipse fitting degree of the trajectory equation formed by two self-mixing (SM) signals in the multi-longitudinal mode laser SM system with a Wollaston prism is presented to test the free spectral range (FSR) of the laser. By utilizing the orthogonal vector and phase-shift characteristics between adjacent longitudinal modes, the fluctuations in multi-mode SM effects caused by changes in the external cavity length are transformed into alterations in the trajectory composed of two orthogonal SM signals. The FSR is calculated by detecting the difference in external cavity lengths between the two positions, where the trajectory of the two SM signals best fits an ellipse. To achieve an automatic FSR measurement, the ellipse fitting degree is proposed as the criterion for positioning the external cavity mode. Experimental results indicate that the FSR of the laser diode is measured to be 85.23 GHz with a resolution of 0.48 GHz, while the corresponding external cavity resolution is 10 µm, and the resolution of the ellipse fitting degree is less than 1. The compact and straightforward design, coupled with high sensitivity, automated measurements, and immunity to optical feedback, holds significant promise as a robust tool for measuring FSR and assessing laser performance.

Miniaturization of Laser Doppler Vibrometers—A Review

Laser Doppler vibrometry (LDV) is a non-contact vibration measurement technique based on the Doppler effect of the reflected laser beam. Thanks to its feature of high resolution and flexibility, LDV has been used in many different fields today. The miniaturization of the LDV systems is one important development direction for the current LDV systems that can enable many new applications. In this paper, we will review the state-of-the-art method on LDV miniaturization. Systems based on three miniaturization techniques will be discussed: photonic integrated circuit (PIC), self-mixing, and micro-electrochemical systems (MEMS). We will explain the basics of these techniques and summarize the reported miniaturized LDV systems. The advantages and disadvantages of these techniques will also be compared and discussed.

Signal enhancement method based on a Fabry-Perot etalon for a self-mixing laser diode

An enhanced self-mixing interference (SMI) method in a laser diode (LD) based on a Fabry-Perot etalon (FPE) is presented. This method uses uncoated fused silica to form a FPE as a narrowband filter in the LD outer cavity, which can tune the laser wavelength to the edge of the FPE transmission spectrum profile to perform intensity demodulation. We compare the SMI signal based on the FPE filter with the conventional SMI signal. The experimental results show that the amplitude of the SMI signal based on the FPE filter is enhanced about 5 times in the range of 1 µm-5 µm; the displacement reconstruction errors are reduced by 30 nm; and the signal quality is significantly improved.

Secondary envelope extraction based on multiple Hilbert transforms for laser self-mixing micro-vibration measurement

This paper presents a method that can be applied to weak feedback and full-range moderate feedback in the field of self-mixing interference measurement, and the target motion displacement can be obtained by multiple Hilbert transforms of the signal after the secondary envelope extraction. Simulations and experiments of multiple micro-vibration measurements were performed with different optical feedback factors, and the results were consistent with theoretical analysis. This method effectively eliminates the impact of the self-mixing interference signal with fringe shift on micro-vibration reconstruction.

Evaluation of resonance phenomena of mechanical oscillator by self-mixing solid-state laser Doppler vibrometry

We performed self-mixing laser Doppler vibrometry on a vibrating oscillator consisting of a rigid-body laser-light-scattering object attached to a piezoelectric element driven by low-frequency AC voltage to evaluate its motion. The sideband spectrum reflecting the motion of the oscillator is observed in the power spectrum of the modulated wave. The time dependence of the intensity of the sideband spectrum is explained by Newton's second law assuming that the oscillator has a mechanical resonance frequency and undergoes simple vibration under the driving force, which depends on the deformation velocity of the piezoelectric element. Our results indicate that the motion of a slowly moving target with sub-nanometer displacement, which is difficult to measure by general laser Doppler vibrometry, can be evaluated with high spatial and frequency resolutions by detecting the sideband signal, which changes periodically at the driving frequency of the piezoelectric element.

Frequency-Shifted Optical Feedback Measurement Technologies Using a Solid-State Microchip Laser

Since its first application toward displacement measurements in the early-1960s, laser feedback interferometry has become a fast-developing precision measurement modality with many kinds of lasers. By employing the frequency-shifted optical feedback, microchip laser feedback interferometry has been widely researched due to its advantages of high sensitivity, simple structure, and easy alignment. More recently, the laser confocal feedback tomography has been proposed, which combines the high sensitivity of laser frequency-shifted feedback effect and the axial positioning ability of confocal microscopy. In this paper, the principles of a laser frequency-shifted optical feedback interferometer and laser confocal feedback tomography are briefly introduced. Then we describe their applications in various kinds of metrology regarding displacement measurement, vibration measurement, physical quantities measurement, imaging, profilometry, microstructure measurement, and so on. Finally, the existing challenges and promising future directions are discussed.

Fourier spectrometer built by a permanent magnet cylinder falling uniformly in a conductive tube

The possibility of constructing a Fourier transform spectrometer by uniform motion of a permanent magnet cylinder falling in an upright conductive tube was researched. Two identical permanent magnet cylinders were reversely connected to two ends of a non-magnetic rod, making a compound permanent magnet cylinder, to reduce the lateral swing of a single permanent magnet cylinder as it falls. Falling velocity fluctuation of the compound permanent magnet cylinder was measured by laser diode self-mixing interferometry. Spectral lines with a frequency interval of about 9 GHz could be clearly distinguished on a cosine transform spectrum of the self-mixing interference signal under a weak feedback situation.

Full-circle range and microradian resolution angle measurement using the orthogonal mirror self-mixing interferometry

The self-mixing technique based on the traditional reflecting mirror has been demonstrated with great merit for angle sensing applications. In order to solve the problems of the narrow measurement angle range and low resolution in traditional angle measurement method, we proposed an angle measurement system using orthogonal mirror self-mixing interferometry combine an orthogonal mirror with designed mechanical linkage. It overcomes the shortcomings of traditional angle measurement methods and realized the angle measurement with microradian resolution in a full-circle range of 0 rad to 2π rad. In the experiment, the measurement resolution can reach to 5.27 µrad and the absolute error can lower to ± 0.011µrad, which satisfies the requirements of most high accuracy angle measurement.

Optical feedback interferometry for microscale-flow sensing study: numerical simulation and experimental validation

Optical feedback interferometry (OFI) performance for microscale-flow sensing is studied theoretically and experimentally. A new numerical modeling approach for OFI flow meter spectrum reproduction is presented in this work to study the optical effect on the signal due to the micro-scale channel geometry. Two well-defined frequency peaks are found in the OFI spectrum, this phenomenon can be attributed to the reflection of the forward scattered light on the channel rear interface. The flow rate measurement shows good accuracy over a range of fluid velocities from 16.8 mm/s to 168 mm/s, thus providing a promising tool to study and to optimize the OFI microfluidic sensor system.

Equivalent wavelength self-mixing interferometry for displacement measurement

In order to improve fringe precision of a self-mixing signal, a simple and effective method based on an equivalent wavelength self-mixing interferometer is presented. And a linearization fringe counting method is proposed for equivalent wavelength self-mixing interferometry to quickly reconstruct target displacement. The validity of the proposed method was demonstrated by means of simulated signals and confirmed by several experimental measurements for both harmonic and aleatory target displacement with a fringe resolution of ∼125  nm.

Observation of motion of colloidal particles undergoing flowing Brownian motion using self-mixing laser velocimetry with a thin-slice solid-state laser

We achieved a highly sensitive method for observing the motion of colloidal particles in a flowing suspension using a self-mixing laser Doppler velocimeter (LDV) comprising a laser-diode-pumped thin-slice solid-state laser and a simple photodiode. We describe the measurement method and the optical system of the self-mixing LDV for real-time measurements of the motion of colloidal particles. For a condensed solution, when the light scattered from the particles is reinjected into the solid-state laser, the laser output is modulated in intensity by the reinjected laser light. Thus, we can capture the motion of colloidal particles from the spectrum of the modulated laser output. For a diluted solution, when the relaxation oscillation frequency coincides with the Doppler shift frequency, f_d, which is related to the average velocity of the particles, the spectrum reflecting the motion of the colloidal particles is enhanced by the resonant excitation of relaxation oscillations. Then, the spectral peak reflecting the motion of colloidal particles appears at 2×f_d. The spectrum reflecting the motion of colloidal particles in a flowing diluted solution can be measured with high sensitivity, owing to the enhancement of the spectrum by the thin-slice solid-state laser.

Solving self-mixing equations for arbitrary feedback levels: a concise algorithm

Self-mixing laser sensors show promise for a wide range of sensing applications, including displacement, velocimetry, and fluid flow measurements. Several techniques have been developed to simulate self-mixing signals; however, a complete and succinct process for synthesizing self-mixing signals has so far been absent in the open literature. This article provides a systematic numerical approach for the analysis of self-mixing sensors using the steady-state solution to the Lang and Kobayashi model. Examples are given to show how this method can be used to synthesize self-mixing signals for arbitrary feedback levels and for displacement, distance, and velocity measurement. We examine these applications with a deterministic stimulus and discuss the velocity measurement of a rough surface, which necessitates the inclusion of a random stimulus.

High-accuracy fiber optical microphone in a DBR fiber laser based on a nanothick silver diaphragm by self-mixing technique

A high-accuracy fiber optical microphone (FOM) is first applied by self-mixing technique in a DBR fiber laser based on a nanothick silver diaphragm. The nanothick silver diaphragm fabricated by the convenient and low cost electroless plating method is functioned as sensing diaphragm due to critically susceptible to the air vibration. Simultaneously, micro-vibration theory model of self-mixing interference fiber optical microphone is deduced based on quasi-analytical method. The dynamic property to frequencies and amplitudes are experimentally carried out to characterize the fabricated FOM and also the reproduced sound of news and music can clearly meet the ear of the people which shows the technique proposed in this paper guarantee steady, high signal-noise ratio operation and outstanding accuracy in the DBR fiber laser which is potential to medical and security applications such as real-time voice reproduction for throat and voiceprint verification.

Self-mixing interference measurement system of a fiber ring laser with ultra-narrow linewidth

A novel device for self-mixing interference measurement based on the fiber ring laser with ultra-narrow linewidth was investigated for the first time. In order to achieve requirement of our measurement system, a saturable-absorber which consists of a segment un-pumped erbium-doped fiber and a fiber Bragg grating is employed to provide a fine mode selection and guarantee the ultra-narrow linewidth operation. Results demonstrate that the signal-to-noise ratio of the self-mixing interference signal could be enhanced from 18.01 dB to 38.35 dB by inserting a saturable-absorber in the laser cavity. It is in good agreement with the theoretical analysis and proved potential using in self-mixing interference measurement system for high sensitivity and remote measurement.

High density fringes and phase behavior in birefringence dual frequency laser with multiple feedback

The high density intensity fringes and phase behavior in birefringent dual frequency laser with multiple feedback are studied for the first time. It was discovered that the fringes of output intensity are made of bipolar pulses with symmetric external cavity feedback and the fringe density is as high as compared to the conventional feedback. The high density cosine-like fringes are obtained with asymmetric external cavity feedback by adjusting the tilt angle of the feedback mirror and the fringe density is about 22 times higher compared to the conventional feedback. Moreover, there is a phase difference between the two cosine-like fringes and the phase difference is varied with the change of the external cavity length. The experimental results and a theoretical analysis are presented in this work. These results offer a large increase in the resolution for the optical feedback interferometer with the birefringence dual frequency laser.

Fringe abnormality induced by the external interference effect in laser feedback

This paper presents the abnormal phenomena of the feedback fringes detected in the primary output direction compared to those detected in the rear of the laser. These abnormalities appear as the waveform deformation or abnormal phase. Experiments and calculations are carried out to investigate the mechanisms of such phenomena. It is found that they are mainly caused by the interference effects or signal superposition, both of which are introduced by the optical elements in the external cavity. Some approaches are taken to avoid those effects. And then the normal feedback fringes are attained in different detection positions, with similar waveform and phase.

Three-channel three-dimensional self-mixing thin-slice solid-state laser-Doppler measurements

We report successful real-time three-channel self-mixing laser-Doppler measurements with extreme optical sensitivity using a laser-diode-pumped thin-slice Nd:GdVO(4) laser in the carrier-frequency-division-multiplexing scheme with three pairs of acoustic optical modulators (i.e., frequency shifters) and a three-channel FM-wave demodulation circuit. We demonstrate (1) simultaneous independent measurement of three different nanometer-vibrating targets, (2) simultaneous measurements of small particles in Brownian motion from three directions, and (3) identification of the velocity vector of small particles moving in water flowing in a small-diameter glass pipe.

A simple readout electronics for automatic power controlled self-mixing laser diode systems

The paper describes a simple electronic circuit to drive a laser diode for self-mixing interferometry. The network integrates a stable commercial automatic power controller and a current mirror based readout of the interferometric signal. The first prototype version of the circuit has been realized and characterized. The system allows easily performing precise interferometric measurements with no thermostatic circuitry to stabilize the laser diode temperature and an automatic control gain network to compensate emitted optical power fluctuations. To achieve this result, in the paper a specific calibration procedure to be performed is described.

Effects of optical feedback in a birefringence-Zeeman dual frequency laser at high optical feedback levels

Optical feedback effects are studied in a birefringence-Zeeman dual frequency laser at high optical feedback levels. The intensity modulation features of the two orthogonally polarized lights are investigated in both isotropic optical feedback (IOF) and polarized optical feedback (POF). In IOF, the intensities of both beams are modulated simultaneously, and four zones, i.e., the e-light zone, the o-light and e-light zone, the o-light zone, and the no-light zone, are formed in a period corresponding to a half laser wavelength displacement of the feedback mirror. In POF, the two orthogonally polarized lights will oscillate alternately. Strong mode competition can be observed, and it affects the phase difference between the two beams greatly. The theoretical analysis is presented, which is in good agreement with the experimental results. The potential use of the experimental results is also discussed.

High-frequency intensity modulation in orthogonal polarized dual frequency lasers with optical feedback

High-frequency modulation of laser output intensity is studied with asymmetric feedback induced by the misalignment of an external feedback reflector in an orthogonal polarized dual frequency laser. The fringe frequency of the optical feedback system is seven times higher than that of a conventional optical feedback system, due to multiple feedback effects. The output characteristics of two orthogonal polarized modes are also investigated. Mode competition is observed between the two modes. When initial intensities of the two modes are unequal, the mode competition will be strong. The difference in initial intensity between the two orthogonally polarized modes plays an important role in the mode competition with optical feedback. Experimental results are presented, as well as a theoretical explanation. The high-frequency modulation of laser intensity can greatly increase the resolution of an optical feedback sensing system.

Analysis of the effects of feedback asymmetry in external cavity He-Ne lasers

A theoretical analysis of the characteristics of an external cavity He-Ne laser with asymmetric feedback induced by the misalignment of an external feedback mirror is proposed. The theoretical model considers both the multiple reflections and the phase variation caused by the asymmetric external cavity. It is found that the phase variation is of importance in determining the effects of asymmetric feedback. The three-order asymmetric feedback effects are experimentally observed and can be interpreted well by this model. The fringe frequency of the asymmetric optical feedback system can also be increased. The experimental results are in good agreement with the theoretical analysis. The theoretical and experimental results offer a potential increase in the resolution of an optical feedback system with asymmetric feedback.

Absolute distance measurement with heterodyne optical feedback on a Yb:Er glass laser

Absolute distance measurement based on optical feedback using a single-frequency Yb:Er glass laser is demonstrated via the combination of heterodyne detection and frequency sweep. The technique allows for the enhancement of the sensitivity of the laser response to self-mixing thanks to resonant excitation close to the relaxation-oscillation frequency peak. The experimental results on noncooperative targets are in good agreement with the theory, and the shape of the resulting signal is analyzed in both the temporal and the frequency domains considering the specific dynamic of the class B solid-state laser. Suggestions are provided for further improvements on the signal processing.

Two-channel self-mixing laser Doppler measurement with carrier-frequency-division multiplexing

We demonstrate real-time two-channel self-mixing laser-Doppler measurement with extreme optical sensitivity using a laser-diode-pumped thin-slice LiNdP4O12 laser. Successful carrier-frequency-division-multiplexed two-channel operations are realized by using one laser, two sets of optical frequency shifters, and a two-channel frequency-modulated-wave demodulation circuit. Simultaneous independent measurements of vibrations of speakers and averaged motions of small Brownian particles in different scattering cells are demonstrated. Self-mixing photon correlation spectroscopy of particle size distributions is also discussed.

Effect of external cavity length on self-mixing signals in a multilongitudinal-mode Fabry-Perot laser diode

The effect of external-cavity length on self-mixing signals in a multilongitudinal-mode Fabry-Perot laser diode (FP-LD) was investigated experimentally. It has been shown that the output waveforms of self-mixing signals vary periodically when the length of the external cavity changes. This result agrees well with our theoretical calculations for the self-mixing effect of two adjacent longitudinal modes in a FP-LD. Moreover, the time-averaged output intensities of self-mixing signals has also been measured and compared with theoretical analysis.

Optical feedback laser with a quartz crystal plate in the external cavity

We studied the optical feedback characteristics of a single-mode He-Ne laser with a quartz crystal plate in the external cavity. The fringe frequency of the laser system can be doubled when the quartz crystal plate is positioned at a certain angle between the crystalline axis and the beam in the crystal plate. Theoretical analysis shows that the birefringent effect of the quartz crystal plate and the laser beam's second pass through the external cavity result in this phenomenon. The experimental results are in good agreement with the theoretical analysis. A quartz crystal plate can double the resolution of a self-mixing sensing system.

Self-mixing in a diode laser as a method for cardiovascular diagnostics

Our aim is the development of a simple optical method for pulse wave profile, pulse wave delay time, and blood flow measurement. The method is based on recording the Doppler frequency shift related to a moving target--blood vessel walls or small particles. The Doppler signal is detected using the self-mixing that occurs in the diode laser cavity when radiation scatters back from the moving target into the laser and interferes with the field inside. Two different ways can be simultaneously used for the self-mixing signal extraction: a photodiode accommodated in the rear facet of the diode laser package and a resistor from the laser pump current. An experimental device with a pigtail laser diode is developed that is able to detect the pulsation of major arteries with potentially useful information, including the pulse wave profile and the pulse wave delay time. The pulse wave delay time in different regions of the human body is measured relative to the electrocardiogram (ECG) signal. Also the flow velocity of a liquid suspension containing particles the size of erythrocytes (equivalent to blood flow) is measured. Registered signals are stored after digitalization and preprocessed using LabView for a Windows environment. The described device has the application of the self-mixing method and highlights significant advantages of simplicity, compactness, and robustness as well as the self-aligning and self-detecting abilities of such method, compared with the use of conventional interferometric method.

Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode

We propose a novel self-mixing laser diode speckle velocimeter based on autocorrelation. The self-mixing laser diode launches and receives reflected light from a moving surface that has a random reflection profile. Some portion of the scattered light backcouples into the laser cavity and causes random intensity variations in the form of speckle signals. These speckle signals obtained from a self-mixing laser diode are processed by use of autocorrelation. The linear relation between the velocity and the reciprocal of the correlation time of the speckle intensity fluctuations allows us to determine the velocity easily if proper calibration is performed. The range of the investigated velocity is 20-450 mm/s. For an aluminum target that moves at a velocity of 350 mm/s, the measurement error is less than 2%.

Active optical feedback in a dual-diode laser configuration applied to displacement measurements with a wide dynamic range

The principles, experimental apparatus, and advantages of the use of an optical feedback technique for extended displacement measurements based on the use of a dual-diode laser configuration are described. This device is capable of creating a synthetic wavelength from the two lasers simultaneously through the frequency selectivity of the individual lasers, which respond only to their own wavelength. Theoretical analysis and experimental evidence are presented to show the feasibility of the measurement method and the simplicity of its operation.