Laser diode feedback interferometer for stabilization and displacement measurements

Feedback Regimes of LFI Sensors: Experimental Investigations

In this article, we revisit the concept of optical feedback regimes in diode lasers and explore each regime experimentally from a somewhat unconventional point of view by relating the feedback regimes to the laser bias current and its optical feedback level. The results enable setting the operating conditions of the diode laser in different applications requiring operation in different feedback regimes. We experimentally explored and theoretically supported this relationship from the standard Lang and Kobayashi rate equation model for a laser diode under optical feedback. All five regimes were explored for two major types of laser diodes: inplane lasers and vertical-cavity surface emitting lasers. For both lasers, we mapped the self-mixing strength vs. drive current and feedback level, observed the differences in the shape of the self-mixing fringes between the two laser architectures and a general simulation, and monitored other parameters of the lasers with changing optical feedback.

Nanometric sensing with laser feedback interferometry

We demonstrate a nanometric sensor based on feedback interferometry in a distributed feedback (DFB) laser by using a measurement of either the optical frequency or laser voltage. We find that in an optimal range of optical feedback, the sensor operates reliably down to an extrapolated 12 nm; for the sensor demonstrated here at ∼1550  nm, this provides a minimum detectible displacement of λ/130.

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.

Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser

We have demonstrated and characterized the generation of ultra broadband microwave frequency combs with an optical pulse-injected semiconductor laser. Through optical pulse injection, the microwave frequency combs generated in the slave laser (SL) have bandwidths greater than 20 GHz within a +/-5 dB amplitude variation, which is almost 3-fold of the 7 GHz relaxation oscillation frequency of the laser used. The line spacing of the comb is tunable from 990 MHz to 2.6 GHz, determined by the repetition frequency of the injection optical pulses produced by the master laser (ML) with optoelectronic feedback. At an offset frequency of 200 kHz, a single sideband (SSB) phase noise of -60 dBc/kHz (-90 dBc/Hz estimated) in the 1(st) harmonic is measured while a noise suppression relative to the injected regular pulsing state of the ML of more than 25 dB in the 17(th) harmonic is achieved. A pulsewidth of 29 ps and a ms timing jitter of 18.7 ps are obtained in the time domain for the microwave frequency comb generated. Further stabilization is realized by modulating the ML at the fundamental frequency of the injected regular pulsing state. The feasibility of utilizing the generated microwave frequency comb in frequency conversion and signal broadcasting is also explored. The conversion gain of each channel increases linearly as the signal power increases with a ratio of about 0.81 dB/dBm.

Active control of grating interferometers for extended-range low-noise operation

An active control method is proposed and demonstrated to improve grating-based laser interferometry to achieve low-noise (subpicometer resolution) and multiwavelength unambiguous range of operation simultaneously. The method modifies a recurrent calibration-based path stabilization algorithm to extract high-resolution and low-resolution data in parallel. This extended range recurrent calibration method is experimentally verified by implementing it on the micromachined scanning grating interferometer (microSGI).

Measurement of air turbulence for on-machine interferometry

There is increasing demand for in situ shape measurements performed on ultraprecision processing machines. One major source of error during interferometric measurements performed on machines is fringe displacement due to external disturbances. We have developed an interferometer equipped with an electro-optic phase modulator that measures the phase of interference fringes before they are displaced by air turbulence. The frequency characteristics of air turbulence induced by a heat source are derived from successive measurements of a test surface. Experimental results show that the phase of the interference fringes can be accurately measured in the presence of air turbulence when the intensity of the fringes is sampled at a speed of several hundred hertz.

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.

Stabilization improvements of laser-diode closed-loop heterodyne phase-shifting interferometer for surface profile measurement

To stabilize the phase-shifting Fizeau-type interferometer against environmental disturbances (namely, vibration and temperature variations), the feedback scheme that uses the current-induced frequency modulation of a laser diode (lambda = 633 nm) and the two-frequency optical heterodyne method has been investigated, with particular attention to improvement of the achievable stabilization. It is demonstrated that introduction of the proportional-integral control into the feedback system improves stabilization against the proportional control case; e.g., stabilization is improved 5 times for 100-nm(p-p) vibration at the frequency range at 30 Hz. The surface profile measurement for a sample mirror was conducted with a reproducibility of 6.8 nm in the root mean square under the subwavelength-amplitude vibration at 100 Hz.

Phase-shift-locked interferometer with a wavelength-modulated laser diode

A phase-shift-locked interferometer has been constructed for distance measurement. A phase shift produced by sawtooth-current modulation of a laser diode is locked to a phase difference preset by polarization optics that consists of a quarter-wave plate and polarizers through an electrical feedback technique. An optical path difference can be measured from the locked sawtooth-wave current amplitude in real time. The sensitivity of the interferometer is discussed.

Closed-loop phase stepping in a calibrated fiber-optic fringe projector for shape measurement

Active homodyne feedback control can be used to stabilize an interferometer against unwanted phase drifts introduced by, for example, temperature gradients. The technique is commonly used in fiber-optic sensors to maintain the fiber at its most sensitive (quadrature) position. We describe an extension of the technique to introduce stabilized, pi/2-rad phase steps in a full-field interferometer. The technique was implemented in a single-mode, fiber-optic interference fringe projector used for shape measurement and can be easily applied to other fiber- or bulk-optic interferometers, for example, speckle pattern and holographic interferometers. Fresnel reflections from the distal fiber ends undergo a double pass in the fibers and interfere at the fourth port of a directional coupler. The interference intensity (and hence phase) is maintained at quadrature by feedback control to a phase modulator in one of the fiber arms. Stepping between quadrature positions (separated by pi rad for light undergoing a double pass) introduces stabilized phase steps in the projected fringes (separated by pi/2 rad for a single pass). A root-mean-square phase stability of 0.61 mrad in a 50-Hz bandwidth and phase step accuracy of 1.17 mrad were measured.

Disturbance-free high-speed sinusoidal phase-modulating laser diode interferometer

A surface profiler that incorporates a feedback controller to eliminate external disturbances is proposed and demonstrated. Its overall performance is dependent on the frequency response of the feedback loop. The frequency of the modulating signal strongly influences the response of the feedback controller. When we used the integrating-bucket method, the CCD camera had to be operated at a low-frequency video rate. Our technique uses a CCD camera equipped with an electronic shutter. The shutter function enables us to apply high-speed sinusoidal phase modulation to the conventional integrating-bucket method under the standard video rate.

Stabilized phase-shifting fringe analysis by use of current-induced frequency modulation of laser diodes

A closed-loop phase-shifting Fizeau-type interferometer was constructed that uses direct frequency modulation of a laser diode. The interferometer is servo controlled entirely in the phase domain, where optical phases are detected by two-frequency optical heterodyning. A detailed study of stabilization of the interferometer under feedback control was conducted both experimentally and theoretically. The interferometer showed good stability against vibration up to 200 Hz. The stabilization factors obtained experimentally are in good agreement with the theoretical calculations. The phase-shifting experiment was accomplished with high precision as well as with high stability against external disturbances. The profile measurement of a mirror surface was made with a phase-shifting analysis algorithm, and good measurement reproducibility of lambda/60 in the root-mean-square value was obtained for ten measurements within a period of 20 min.

Surface profilometry with laser-diode optical feedback interferometer outside optical benches

A simple and robust interferometer with a laser diode subject to optical feedback from the interferometer is presented for surface testing of a spherical mirror. The fringe phase can be locked by the optical feedback within less than 0.2pi (peak-to-valley value) even when the interferometer is placed on a wooden table. The fringe locking is caused by the change of lasing wavelength that suppresses the net phase change to be much less than 2pi. The locked fringe pattern with spatial carriers can be analyzed by a fringe analyzer at a video rate, and the measurement results of the spherical mirror showed the same result as on an optical bench.

Analysis of fringe locking in a laser diode interferometer under injection-current modulation

A theoretical analysis has been performed that explains a fringe-locking phenomenon observed in a two-beam interferometer in which a laser diode was subjected to optical feedback and modulation of its injection current. The dependence of wavelength change on the injection-current variation is calculated by use of a model of coupled resonators consisting of the laser cavity and the interferometer. The fringe phase change caused by modulation of the injection current is derived from this model and has proved to be suppressed within much less than 2pi in excess of an integer multiple of 2pi if the path difference of the interferometer is longer than 10 mm. The calculated phase fluctuation agrees well with those observed in experiments.

Surface-profile measurement by means of a polarization Sagnac interferometer with parallel optical feedback

We describe a novel feedback interferometer for real-time, unambiguous measurement of surface profiles that consists of a polarization Sagnac interferometer and an optically addressed phase-only spatial light modulator. In this system the output intensity from the Sagnac interferometer is optically fed back to the phase modulator placed in one arm of the interferometer, which produces a sawtooth fringe intensity profile (instead of the conventional cosinusoidal one) that is directly and unambiguously related to the surface profile. Preliminary experimental results demonstrate the feasibility of applying this system to surface-profile measurement.

Dynamic microforce measurement by distortion detection with a coupled-cavity laser displacement sensor stabilized in a mechanical negative-feedback loop

A small displacement sensor for dynamically measuring small forces is presented. Employing a coupled-cavity laser configuration constructed with a moving external mirror, this sensor provides high sensitivity with a minimum detectable displacement of 0.8 nm, independently of the lasing wavelength, while the lasing state is mechanically stabilized by a negative-feedback loop to maintain a constant external-cavity length. The sensor is shown to be of great use for detecting extremely small distortions in a stiff cantilever, reflecting transient variations in small friction forces in mechanical systems.

Closed-loop phase-shifting interferometry with a laser diode

A closed-loop phase-shifting Fizeau-type interferometer at lambda=633 nm was constructed with the direct frequency modulation of laser diodes. The interferometer is servo controlled fully in the phase domain where optical phases are detected by a two-frequency optical heterodyne method. Stepwise phase shifting was accomplished with good stabilization against external disturbances (vibration, air flow, etc.) and laser frequency fluctuations.

Amplitude-stabilized frequency-modulated laser diode and its interferometric sensing applications

A direct frequency-modulated (FM) laser diode light source without light power variation is developed. The amplitude variation of the FM laser diode is compensated by means of a feedback system with use of a superluminescent diode as an external light power controller. Output power greater than 1 mW is obtained at the modulation frequency to 5 kHz with a >10 stabilization factor. By use of the amplitude-stabilized FM laser diode, we measured subfringes with high accuracy in FM continuous wave interferometry, increased the dynamic range of the displacement measurement, and improved the stabilization factor in the laser diode feedback interferometer.

Increased spatial frequency in interferential undulations of coupled cavity lasers

Increased spatial frequency is experimentally observed in the interferential light-output undulation of coupled cavity lasers that use a Fabry-Perot laser diode. The frequencies correspond to undulation periods of λ/4, λ/6, λ/8, and λ/10, which are extremely short compared with the normal period of λ/2. This increase is explained theoretically with a multiple-mode model in which one of the longitudinal modes of a coupled cavity laser with the lowest lasing threshold is selected as a lasing mode. This theoretical explanation is confirmed through experiments with a distributed feedback laser that shows a strong single-mode oscillation and yields light-output undulations with a spatial period of λ/2.

Differential type of phase-locked laser diode interferometer free from external disturbance

A phase-locked laser diode interferometer with differential detection to eliminate external disturbance is proposed. In this interferometer, the measurements are implemented at two different points at the same time. The surface profile that contains the disturbance is obtained at the scanned measuring point, and the disturbance is obtained at the fixed measuring point. The exact profile is obtained by subtracting the latter from the former. The limitations and characteristics are examined theoretically. The analytical results agree well with the experimental results. The repeated measurement accuracy is estimated to be ~5 nm in this interferometer.

Bistable fiber-optic Michelson interferometer that uses wavelength control

Feedback of the interference signal of an unbalanced Michelson interferometer to the current supply of the semiconductor-laser source yields bistability under input intensity variation owing to wavelength-induced phase modulation. A linear stability analysis of the system's differential equation gives the ratio of the system time constant tau to the feedback delay time T to determine the critical input intensity for the onset of self-oscillations. Input-output characteristics that exhibit bistability and self-oscillations are obtained experimentally through modulation of the input power by using an integrated-optics intensity modulator.

Precision displacement measurement by active laser heterodyne interferometry

We demonstrate an active laser heterodyne interferometer which can automatically compensate environmental disturbances and is capable of precision displacement measurement. Two Zeeman He-Ne lasers were employed. Laser II was used as the light source to stabilize the interferometer by using a piezomirror in a feedback loop. The hetereodyne signal of the two lasers was used to directly calibrate mirror displacement, with the wavelength of laser I tuned to compensate change in the interference signal due to displacement only. Separation of the contributions to the interference signal from displacement and external disturbances was accomplished by using polarization optics. This interferometer was used to measure the hysteresis of a piezoelectric transducer (PZT) over a dynamic range of 0.5 microm with a resolution of +/-0.8 nm.

Profilometry with a coherence scanning microscope

Coherence scanning microscopy is a new technique in high resolution imaging. It shares many of the features of confocal microscopy but uses coherence effects to enhance the lateral and longitudinal resolution rather than physical apertures. This approach has two significant implications for profilometry: the longitudinal resolution is decoupled from the lateral resolution, and interference effects can be used to further enhance the longitudinal resolution. We detail the features of coherence scanning profilometry and give some examples.

Optical bistability and multistability in an active interferometer

Optoelectronic hybrid bistability and multistability in an active interferometer using a laser diode are demonstrated experimentally. The active laser-diode interferometer is composed of a Twyman-Green interferometer with an electronic feedback circuit. By feeding back the interferometer output together with an external light input through a detector to control thelaser-diode injection current, the optical bistable and multistable states of the output power from the laser diode are observed. Bistable operation does not require cutoff or saturation in the amplifier. The theoretical background of the phenomena is discussed.

Phase locked laser diode interferometry for surface profile measurement

We propose a new type phase locked interferometer which uses tunability of the wavelength of a laser diode. The phase lock is achieved by controlling the injection current of the laser diode. A CCD image sensor is used as a photodetector to scan electrically a measuring point along the surface of the object. Since this interferometer uses no mechanical elements such as a piezoelectric transducer and galvanomirror, the measurement accuracy is not limited by the mechanical properties. The characteristics of the feedback control system for the phase lock are examined through measurements of surface profiles of the diamond-turned aluminum disks.

Laser feedback metrology of optical systems

A simple interferometric metrology instrument based on the effect of weak optical feedback on the power output of laser diodes is described. Laboratory demonstrations of the principle applied to the analysis of wavefront aberrations in optical systems is reported.