Fringe Counting Technique Research Articles

Dynamic Low-Pressure Measurement Using a Fiber Optic-based Fabry-Perot Interferometer

A dynamic low-pressure measurement using a fiber optic-based Fabry-Perot Interferometer (FFPI) has been demonstrated in this work. The developed system has been divided into 2 main parts: pressure source and sensing system. The former is a chamber comprised of an elastic diaphragm, which proportionally deflects according to input pressure from an air pump. The FFPI, consequently, detects the material deflection and demodulates the parameter into useful pressure value via the fringe counting technique and Kirchhoff-Love’s plate theory. To validate the performance of the developed system, a reference pressure instrument is utilized while the air pump feeds pressure of 0.34–6.57 mbar with 10 times repeatability into the system. The experimental results indicated that the FFPI can measure the pressure of 0.343–6.568 mbar, while the reference instrument showed the output values from 0.343–6.471 mbar, respectively. Moreover, the average and maximum percentage error in measurement is 1.27% and 2.67%, respectively. The resolution of the FFPI sensor is also analyzed to be approximately 0.05% or 0.0382 mbar/μm over all measurement ranges. Therefore, we conclude that the FFPI has high accuracy, resolution, linearity, and reliability in dynamic low-pressure measurements.

Validation of Fiber Optic-Based Fabry–Perot Interferometer for Simultaneous Heart Rate and Pulse Pressure Measurements

In this work, a fiber optic-based Fabry-Perot interferometer (FFPI) developed for simultaneous heart rate (HR) and pulse pressure (PP) measurement was investigated. Particularly, the FFPI was designed with simplicity in configuration for highly precise and non-invasive arterial distension measurement whose output was then demodulated via fringe counting to simultaneously obtain both HR and PP information through fringe pattern analysis and Kirchhoff-Love’s plate theory, respectively. The sensitivity was then characterized by linear fitting of measured PP inducing a number of interference fringes, whose slope represented the FFPI sensitivity. Experiments were conducted both on a simulating device and healthy subjects, each measurement carried out at least 10 times. Obtained results demonstrated the FFPI sensitivity for PP measurement in both experiments to be ~1.916 mmHg/fringe. For HR measurements, an average difference of 1.24% was found when compared to a digital sphygmomanometer employed as reference. Analysis of the FFPI resolution revealed the impact of the fringe counting technique, interrogating wavelength, and sensing material properties on measurement accuracy. Consequently, the thickness of the transducing thin film was found to have the most impact on PP demodulation. Therefore, optimization of the aforementioned parameters could lead to the development of a more accurate FFPI for PP measurement.

Dynamic bending and rotation sensing based on high coherence interferometry in multicore fiber

Bending and rotation sensing based on high coherence interferometry in seven-core fiber (SCF) is proposed here for the first time. In the suggested scheme, distinct optical paths are formed from the selected cores, thus creating a very compact in-fiber Michelson interferometer. The interferometer consists of an in-line taper structure fabricated on the SCF for a light splitting/coupling element, and a Faraday rotating mirror used as a reflective element. Different strains are exerted on the reference and sensing cores because of the dissimilar distance from the neutral axis. The phase difference between these two interferometer arms resulting from the variations in strain is resolved using a fringe counting technique. The proposed sensor is revealed to be extremely sensitive for curvature and rotation measurement, with sensitivities of 629fringe/m−1 and 6.2fringe/°, respectively. The sensor is capable of detecting the smallest curvature of 0.0032 m−1 or radius of 312 m. The sensor also responds linearly to rotation, with a sensitivity of 6.2fringe/°. This response is highly repeatable; linear; insensitive to slow-varying parameters, such as temperature; and promising for the detection of direction. The proposed sensor is particularly attractive for robotics, wearable medical devices, and structural health-monitoring applications.

A High Sensitivity of Vital Signs Detector using Fiber Optic-based Fabry-Perot Interferometer

In this paper, a development of high sensitivity for vital sign detector based on the fiber optic-based Fabry-Perot interferometer (FFPI) has been proposed. Two interested parameters; heart rate (HR), and also blood pressure (BP) are measured as the vital sign parameters for investigating the performance of the FFPI. Particularly, the proposed sensor is exploited to detect human arterial pulse for indicating the number of interference signals (fringes). A fringe counting technique is, consequently, applied in associate with the deflection of material technique to demodulate the observed number of fringes into HR and BP. Additionally, the reflective thin film with reflectance of approximately 55% is utilized for attaching to the human wrist during the measurement. Furthermore, a digital sphygmomanometer model OMRON HEM-7130 is employed as a reference sensor. After 20 times of repeatability on the same human subject, the FFPI could indicate the systolic and diastolic BP, as well as HR, with average error of 0.94%, 1.64%, and 1.01%, respectively. Moreover, the FFPI could determine the mentioned parameters in decimal numbers, as opposed to the reference sensor. This could, thus, verified that the FFPI is a very sensitive and more precise instrument for applying to the vital sign measurement.

Development of an optical fiber-based interferometer for strain measurements in non-destructive application

In this paper, an extrinsic Fabry–Perot interferometer (EFPI) has been demonstrated for strain measurements. A monochromatic light source with a wavelength of 1310 nm is propagated into a single-mode fiber and then passed through the sensing arm. Approximately, 4 % of the beam is reflected off at the fiber end generating the “reference signal”, while the rest is next transmitted to the target and reflected back to the sensing arm as the “sensing beam”. The interference signal is, however, generated from the superposition between two beams (reference and sensing signals) in the fiber arm. The number of interference signal also called “fringe” is, normally, directly proportional to the displacement of the target movement. Fringe counting technique is also proposed for demodulating the fringe number to the displacement information. Consequently, the displacement is then converted to the strain value by referring to a basic of strain theory. A cantilever beam fastened to a mechanical wave driver has been utilized as a vibrator for the experimental studies. Two experiments have been investigated for the sensor performance’s study. By varying the frequency excitation from 60 to 180 Hz, and also the amplitude excitation from 0.25 to 5 V, the output strain range of 0.082–1.556 and 0.246–2.702 \(\upmu \varepsilon \) has been apparent, respectively. In addition, a commercial strain sensor has also been used as a reference, leading to an average percentage error of 1.563 %.

A numerical algorithm to determine straightness error, surface roughness, and waviness measured using a fiber optic interferometer

Fiber optic interferometry has been used to detect small displacements in diverse applications. Counting the number of fringes in fiber-optic interferometry is challenging due to the external effects induced in dynamic systems. In this paper, a novel interference fringe counting technique is developed to convert the intensity of interference data into displacements in the range of micrometers to millimeters while simultaneously resolving external dynamic effects. This technique consists of filtering the rough experimental data, converting filtered optical interference data into displacements, and resolving dynamic effects of the experimental system. Filtering the rough data is performed in time by using the moving average method with a window size of 400 data points. Filtered optical data is further converted into displacement by calculating relative phase differences of each data point compared to local maximum and local minimum points. Next, a linear curve-fit is subtracted from the calculated displacement curve to reveal dynamic effects. Straightness error of the lead screw driven stage, dynamics of the stepper motor, and profile of the reflective surfaces are investigated as the external dynamic effects. Straightness error is characterized by a 9th order polynomial function, and the effect of the dynamics of the stepper motor is fitted using a sinusoidal function. The remaining part of the measurement is the effect of roughness and waviness of the reflective surfaces. As explained in the experimental setup part, two fiber-optic probes detect the vertical relative displacements in the range of 1-50µm, and the encoder probe detects 13.5mm horizontal displacement. Thus, this technique can detect three order of magnitude different dynamic displacements with sub-micrometer resolution. The current methodology can be utilized in different applications which require measuring straightness error of lead-screw driven stages, large area surface profile of specimens, and vibration of actuators such as stepper motors.

Nine-point phase demodulation for interferometric measurement

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.

Generation of phase difference between self-mixing signals in a-cut Nd:YVO₄ laser with a waveplate in the external cavity.

We present a novel method using Nd:YVO4 laser with a waveplate in the external cavity to generate two orthogonally polarized signals with stable and adjustable phase difference. The phase difference is observed in the presence of external interference, and it is determined by the phase retardation of the waveplate. A model based on birefringent external-interference effect is proposed to theoretically explain the phase difference phenomenon, and the arithmetic solution of the relation between the phase difference and the phase retardation of waveplate is given. The simulated results accord with the experimental phenomena. This Letter provides the possibility for the measurement of phase retardation and also offers guidance to the design of interferometers based on fringe counting technique.

An extrinsic fiber Fabry-Perot interferometer for dynamic displacement measurement

A versatile fiber interferometer was proposed for high precision measurement. The sensor exploited a double-cavity within the unique sensing arm of an extrinsic-type fiber Fabry-Perot interferometer to produce the quadrature phase-shifted interference fringes. Interference signal processing was carried out using a modified zero-crossing (fringe) counting technique to demodulate two sets of fringes. The fiber interferometer has been successfully employed for dynamic displacement measurement under different displacement profiles over a range of 0.7 μm to 140 μm. A dedicated computer incorporating the demodulation algorithm was next used to interpret these detected data as well as plot the displacement information with a resolution of λ/64. A commercial displacement sensor was employed for comparison purposes with the experimental data obtained from the fiber interferometer as well as to gauge its performance, resulting in the maximum error of 2.8% over the entire displacement range studied.

Birefringent prism based Fourier transform spectrometer

This paper presents the design of a rugged and compact Fourier transform spectrometer (FTS) utilizing a birefringent prism, a pair of polarizers and a linear CCD array. This design improves on existing FTS by eliminating moving parts and spreading the optical path difference (OPD) spatially (rather than temporal scanning), making the system smaller, more reliable, and dramatically reducing measurement times. Both the theoretical models for the design and experimental results of the prototype are presented. The optical performance is tested using LEDs of known wavelengths, with the fringe counting technique employed during interferogram acquisition to ensure accurate sampling of the interferogram at constant OPD intervals. Reconstructing the spectra showed that the detected wavelengths deviated from the actual wavelengths by less than 1 nm.

A Miniaturized Lamellar Grating Based Fourier Transform Spectrometer With Electrostatic Actuation

We report a miniaturized oscillating Fourier transform spectrometer (FTS), of which the novel features are specially designed suspension springs with reduced thickness and a square honey-combed platform which supports the movable grating facets. The proposed design is electrostatically driven by parallel plate actuators at its resonant frequency of 230 Hz. It uses lamellar grating to modulate the incident radiation and the movable part of the grating is capable of bidirectional out-of-plane motion. A maximum displacement of about 100 is achieved with an 80 V peak-to-peak driving voltage superimposed on a DC bias of 110 V in ambient pressure. The optical performance of the model is tested using a tunable infrared (IR) laser source. Fringe counting technique is employed in the IR interferogram acquisition process to ensure accurate sampling of the interferogram at constant optical path difference (OPD) intervals. The reconstructed spectra yielded detected wavelengths which deviated by less than 1 nm from the actual wavelengths, indicating excellent wavelength accuracy and an impressive resolving power.

A new method of non-contact gauge block calibration using a fringe-counting technique: I. Theoretical basis

A new non-contact interference method for gauge block or length bar calibration is presented. A central interference fringe of polychromatic light is used for the determination of the end surface position of the measured artefact. Distances referring to these positions are measured using a fringe-counting technique, with a wavelength-stabilized laser interferometer. Absolute and comparative measurement methods are proposed. A new technique for central interference fringe detection and identification is discussed.

Modified fringe-counting technique applied to a dual-cavity fiber Fabry-Pérot vibrometer

We report a relatively innovative method for automated fringe counting of a dual-cavity extrinsic fiber Fabry-Perot interferometer for vibration measurements based on the adaptation of the conventional zero-crossing technique to take into consideration two interdependent series of interference fringes. Two sets of interference signals generated by the fiber interferometric vibrometer are quadrature phase-shifted us- ing phase retarding optics and exploited in the fringe counting process to generate the desired crossing-over signals. Each time period of the in- dividual set of interference signal is subdivided into 16 crossing points via the modified fringe-counting method. A program written in MATLAB ®i s next developed for calculating the number of crossing points and plotting the displacement curve. This method has been found to be capable of automatically processing the two sets of interference fringes reliably. In addition, the program also calculates the displacement amplitudes of a vibrating target measured by the sensor to a resolution of /64. A refer- ence displacement sensor has been used for comparison with output data from the interferometer, resulting in a percentage error of approxi- mately 0.41% in the measured displacement. © 2007 Society of Photo-Optical

Hybrid numerical—experimental approach for investigation of dynamics of microcantilever relay system

The time average holography measurements of the vibrating microelectromechanical switch (MEMS) were performed in this study. Experimental measurement results exhibit good agreement with computer generated holographic interferogram analysis. The validation of experimental investigations versus numerical analysis provides the necessary background to analyze the dynamical characteristics of micromechanical systems in virtual numerical environments. Direct application of fringe counting techniques for reconstruction of motion from time average holograms cannot be straightforward if the analyzed micromechanical systems contain motion limiters. Modifications of a classical time average holographic technique enable qualitative analysis of MEMS and can be applied for investigation of dynamical properties of much broader classes of MEMS systems.

A non-linear error signal extraction technique for length control of a Fabry-Perot cavity

We present a non-linear signal extraction technique which provides a signal proportional to the length of a FP cavity with an rms motion larger than one laser wavelength. This method, based on a mechanical or frequency modulation plus a suitable fringe counting technique, can be used in a closed loop configuration allowing to reduce the length variation within one resonance peak of the cavity. This is a starting point for usual linear servo-loops. The principle of operation is described. The results of a computer simulation are confirmed by an experimental test on a bench top interferometer. A possible application is the guidance into lock of a suspended FP cavity, such as those used for long baseline interferometric antennas like VIRGO or LIGO.

Length measurement by a two-colour interferometer using two close wavelengths to reduce errors caused by air turbulence

An improved two-colour interferometer for length measurements was developed to reduce both the errors caused by air turbulence and the effects of chromatic aberration in the optical system. The method combines a fringe-counting technique and a phase-measurement technique. The phases of interference fringes with respect to laser wavelength 1 and synthetic wavelength s are detected simultaneously by only one detector by using a band-pass filter technique. We verified this new method by measuring lengths of up to 2 m and then comparing the results with those measured by an HP 5528 interferometer. The comparison shows that the relative accuracy of this improved method is 5 × 10-7.

Dynamic pressure sensing with a fiber-optic polarimetric pressure transducer with two-wavelength passive quadrature readout

We describe the combination of a polarimetric pressure sensor with a two-wavelength passive quadrature demodulation system allowing for dynamic pressure sensing in the 10-MPa range with unambiguous fringe counting. Furthermore, continuous phase measurement with the arctan method applied to the quadrature interference signals after automatic offset subtraction is demonstrated for the first time, to our knowledge. A single low-coherent superluminescent diode is used as a light source, and a polarizing beam splitter in combination with two adjustable interference filters of slightly different central wavelengths serves for the creation of the quadrature signals. Results of initial experiments with 60-ms pressure relaxation-time constants with the fringe-counting technique demonstrate the performance that was predicted theoretically. The measured pressure sensitivity exhibits excellent agreement with the previous research of Bock and Urbanczyk [IEEE Trans. Instrum. Meas. 44, 694-697 (1995)] using a polarimetric readout. The fringe-contrast variation and the measurement range obtained experimentally show the fiber dispersion to influence dephasing (deviation from quadrature) and visibility decrease significantly with increasing pressure.

Polychromatic light interferometer for high-accuracy positioning

Superposition of different-wavelength, multimode- and single-mode laser diode beams is investigated to locate the fringe of zero interference order in a Twyman-Green interferometer. The possibility of central fringe detection using three multimode laser diodes or one single-mode together with a pair of multimode laser diodes is shown. If a single-mode laser diode is applied, a simultaneous fringe-counting technique for displacement measurement is available. The influence of the angle between wavefronts entering the interferometer is analyzed. A repeatability of about 5 nm is shown for surface position determination when using three-beam source.

Fringe-counting technique used to lock a suspended interferometer

We implement a digital fringe-counting technique to measure in real time the relative mirror displacement of a suspended Michelson interferometer with modulated optical path length for oscillations much larger than the laser wavelength (λ). This provides the proper error signal for a servo mechanism that reduces the relative displacement within λ/2. The implemented technique does not require extra optics or polarizers and thus can be used for interferometric gravitational wave detectors as a starting procedure to get the system locked.

The physical principles of wavelength-shift interferometric laser rangefinders

The authors review the recent progress in dynamic interferometry applied to optical distance measurement devices. These techniques are based on modulating laser diodes to obtain a continuous wavelength-shift. Measurements can be done by a fringe counting technique or by detecting the beat frequency that is proportional to the time-of-flight. This paper shows too the importance of the spectral analysis of the photodetected signal. A signal processing allows the use of multiple-beam interferometers with multiple reflectors. It's also possible to determine absolute distances with rough targets from the ratio of the amplitudes of two harmonics.