Minimum Detectable Phase Shift Research Articles

A Novel Demodulation Scheme of Fiber-Optic Interferometric Sensor Based on FM SSB Signal

A novel vibration signal demodulation scheme of fiber-optic interferometric sensor is proposed and demonstrated. A frequency-modulated (FM) single sideband (SSB) light-wave signal is generated by applying an FM microwave signal to a Mach–Zehnder modulator (MZM) for the demodulation of fiber-optic vibration interferometric sensor. A method of 12-sample orthogonal demodulation algorithm (ODA) based on setting the system sampling rate to 12 times of the FM frequency is adopted for the generation of two orthogonal signals for arctangent transformation. The experimental results show that the harmonic distortion is well suppressed compared with the traditional phase generation carrier (PGC) arctangent (PGC-Arctan) algorithm, and a minimum detectable phase shift is achieved about $6.3\times 10^{-5}$ rad/ $\surd $ Hz at 5 kHz.

Highly sensitive demodulation of a vibration-induced phase shift based on a low-noise OEO.

A highly sensitive demodulation approach of a vibration-induced phase shift based on a low-noise optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. The vibration-induced optical phase variation is directly converted to the electrical oscillating signal of the OEO with carrier phase-shifted double-sideband (CPS-DSB) modulation, which is realized by cascading a dual-output Mach-Zehnder modulator (DOMZM) and a fiber interferometer. Theoretically, within a CPS-DSB modulated OEO, the minimum detectable optical phase shift is determined by the phase noise achievable, and the sensitivity of the optical phase shift demodulation no longer depends on its frequency. A proof-of-concept OEO oscillating at 100MHz with ultralow phase noise is built for demonstration. The achieved minimum detectable optical phase shift is 0.58 μrad/√Hz at 1kHz and 0.21 μrad/√Hz at 10kHz, which are the best results ever reported, to the best of our knowledge.

States of maximum polarization for a quantum light field and states of a maximum sensitivity in quantum interferometry

The SU(2) group is used in two different fields of quantum optics, the quantum polarization and quantum interferometry. Quantum degrees of polarization may be based on distances of a polarization state from the set of unpolarized states. The maximum polarization is achieved in the case where the state is pure and then the distribution of the photon-number sums is optimized. In quantum interferometry, the SU(2) intelligent states have also the property that the Fisher measure of information is equal to the inverse minimum detectable phase shift on the usual simplifying condition. Previously, the optimization of the Fisher information under a constraint was studied. Now, in the framework of constraint optimization, states similar to the SU(2) intelligent states are treated.

Long-range surface plasmon triple-output Mach-Zehnder interferometers

A triple-output Mach-Zehnder interferometer (MZI) operating with long-range surface plasmon-polariton waves, consisting of a MZI in cascade with a triple coupler, is demonstrated at a wavelength of ~1370 nm, using the thermo-optic effect to produce phase shifting. A theoretical model for three-waveguide coupling is also proposed and was applied to compute the transfer characteristic of various designs. Dimensions for the device were selected to optimize performance, experiments were performed, and the results were compared to theory. The outputs were sinusoidally related to the thermally-induced phase shift and separated by ~2π/3 rad, as expected theoretically. Four detection schemes that take advantage of the 3 times larger dynamic range and suppress time-varying common perturbations are proposed and analyzed in order to improve the detection limit of the device. A minimum detectable phase shift ~2/3 that of a single output was obtained from a power difference scheme and a normalization scheme. The smallest minimum detectable phase shift was 7.3 mrad. The device is promising for sensing applications, including (bio)chemical sensing.

Noise Cancellation in Long-Range Surface Plasmon Dual-Output Mach-Zehnder Interferometers

The characterisation of dual-output Mach-Zehnder interferometers operating with long-range surface plasmon-polaritons at a free-space wavelength of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\sim$</tex></formula> 1370 nm is reported. The devices were constructed by embedding Au stripes in Cytop claddings, and consist of a symmetric Mach-Zehnder interferometer in cascade with a 50:50 coupler. By injecting electric current via probes to generate heat in the active region in one arm of the interferometer, a phase difference between the arms was thermo-optically induced, modulating the optical power of the two outputs. The outputs were complementary as expected theoretically, thus demonstrating the switching abilities of the structure. The advantages for sensing applications of a dual-output interferometer over a single-output one are a 2X larger dynamic range and the ability to cancel common noise and source fluctuations. The larger dynamic range and noise cancellation produced a minimum detectable phase shift 4X lower than obtained by monitoring a single output. The smallest value of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\Delta\phi_{\min}$</tex> </formula> obtained was <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\sim$</tex> </formula> 3 mrad. The structure is especially promising for (bio)chemical sensing applications.

Impaired predictive timing with spared time interval production in individual with schizophrenia

There is evidence for timing dysfunctions in schizophrenia. However, few studies have evaluated the processing of intervals in the hundreds of milliseconds range, despite their role in the timing of speech, music and movements. This study looked into the prediction and estimation mechanisms for intervals in that time range in individuals with schizophrenia and age-matched neurotypical controls. Specifically, we questioned the capacity of the patients to detect a phase shift that requires the processing of a deviation from ‘what should happen when’ given prior event regularity. The minimum detectable phase shift was estimated from an adaptive staircase procedure with or without the need for sensorimotor synchronization. Results revealed that patients were significantly impaired relative to controls, at each of the tested inter-onset intervals (IOI=300, 600 and 900ms). A control experiment used the method of repeated interval production to show that both groups performed similarly in the production of target intervals (T=500ms and 1000ms). We conclude that schizophrenia is associated with predictive timing deficits, which cannot be attributed directly to a faster or slower running internal clock.

用于探测极低频信号的光纤传感器相位生成载波解调方法

A high resolution ultra low frequency phase generated carrier(PGC) demodulation technique for interferometric fiber sensors is proposed. The differential cross multiplication(DCM) algorithm and the Arctangent algorithm of PGC technique are analyzed theoretically and simulated by computer for ultra low frequency demodulation. And the results show that an unnecessary random direct current(DC) drift is induced in the recovered signal of DCM-PGC, but it doesn't exit in that of Arctangent-PGC. To demonstrate the conclusion, an optical fiber interferometer-based ultra low frequency sensing system is set up, and the comparable experiments of DCM-PGC and Arctangent-PGC are carried out. The experimental results show that only Arctangent-PGC can be used for ultra low frequency demodulation, for it avoids the problem of DC drift as DCM-PGC. At last the ultra low frequency demodulation system is achieved by Arctangent-PGC, and the testing results show that the system has the lowest frequency of0.01 Hz, a minimum detectable phase shift of4×10-4 rad/√Hz, a dynamic range of110 dB@1 Hz and a linearity of99.99%.

An Ameliorated Phase Generated Carrier Demodulation Algorithm With Low Harmonic Distortion and High Stability

A novel ameliorated phase generated carrier (PGC) demodulation algorithm based on arctangent function and differential-self-multiplying (DSM) is proposed in this paper. The harmonic distortion due to nonlinearity and the stability with light intensity disturbance (LID) are investigated both theoretically and experimentally. The nonlinearity of the PGC demodulation algorithm has been analyzed and an analytical expression of the total-harmonic-distortion (THD) has been derived. Experimental results have confirmed the low harmonic distortion of the ameliorated PGC algorithm as expected by the theoretical analysis. Compared with the traditional PGC-arctan and PGC-DCM algorithm, the ameliorated PGC algorithm has a much lower THD as well as a better signal-to-noise-and-distortion (SINAD). A THD of below 0.1% and a SINAD of 60 dB have been achieved with PGC modulation depth (C value) ranges from 1.5 to 3.5 rad. The stability performance with LID has also been studied. The ameliorated PGC algorithm has a much higher stability than the PGC-DCM algorithm. It can keep stable operations with LID depth as large as 26.5 dB and LID frequency as high as 1 kHz. The system employing the ameliorated PGC demodulation algorithm has a minimum detectable phase shift of 5 μrad/√Hz @ 1 kHz, a large dynamic range of 120 dB @ 100 Hz, and a high linearity of better than 99.99%.

Characterization of fiber-laser-based sub-Doppler NICE-OHMS for quantitative trace gas detection

The potential of fiber-laser-based sub-Doppler noise-immune cavity-enhanced optical heterodyne molecular spectrometry for trace gas detection is scrutinized. The non-linear dependence of the on-resonance sub-Doppler dispersion signal on the intracavity pressure and power is investigated and the optimum conditions with respect to these are determined. The linearity of the signal strength with concentration is demonstrated and the dynamic range of the technique is discussed. Measurements were performed on C(2)H(2) at 1531 nm up to degrees of saturation of 100. The minimum detectable sub-Doppler optical phase shift was 5 x 10(-11) cm(-1) Hz(-1/2), corresponding to a partial pressure of C(2)H(2) of 1 x 10(-12) atm for an intracavity pressure of 20 mTorr, and a concentration of 10 ppb at 400 mTorr.

Interferometric detection of optical phase shift using twin beams

An interferometric detection scheme to measure optical phase shift with sensitivity beyond the shot noise limit is proposed. The theoretical calculation shows that using the quantum correlated twin beams produced from an optical parametric amplifier as the input fields of a Mach-Zehnder interferometer, the minimum detectable phase shift will exceed the shot noise limit N-1/2 and approach the Heisenberg limit N-1. The parametric dependences of the minimum detectable phase shift on the nonlinear interaction, input photon number, and detection efficiency are shown.

Interferometry as a binary decision problem

Binary decision theory has been applied to the general interferometric problem. An optimal detection scheme - according to the Neyman-Pearson criterion - has been considered for different phase-enhanced states of the radiation field, and the corresponding bounds on the minimum detectable phase shift have been evaluated. A general bound on interferometric precision has been also obtained in terms of photon number fluctuations of the signal mode carrying the phase information.

Nonclassical interferometry with intelligent light.

We study the phase sensitivity of SU(2) and SU(1,1) interferometers fed by two-mode field states which are intelligent states for Hermitian generators of the SU(2) and SU(1,1) groups, respectively. Intelligent states minimize uncertainty relations and this makes possible an essential reduction of the quantum noise in interferometers. Exact closed expressions for the minimum detectable phase shift are obtained in terms of the Jacobi polynomials. These expressions are compared with results for some conventional input states, and some known results for the squeezed input states are reviewed. It is shown that the phase sensitivity for an interferometer that employs squeezing-producing active devices (such as four-wave mixers) should be analyzed in two regimes: (i) fixed input state and variable interferometer, and (ii) fixed interferometer and variable input state. The behavior of the phase sensitivity is essentially different in these two regimes. The use of the SU(2) intelligent states allows us to achieve a phase sensitivity of order $1/\bar{N}$ (where $\bar{N}$ is the total number of photons passing through the phase shifters of the interferometer) without adding four-wave mixers. This avoids the duality in the behavior of the phase sensitivity that occurs for the squeezed input. On the other hand, the SU(1,1) intelligent states have the property of achieving the phase sensitivity of order $1/\bar{N}$ in both regimes.

Interferometric detection of optical phase shifts at the Heisenberg limit.

We show that the uncertainty in the relative quantum phase of two fields propagating in the arms of a Mach-Zehnder interferometer can be reduced to the Heisenberg limit by driving the interferometer with two Fock states containing equal numbers of photons. This leads to a minimum detectable phase shift far below that of any interferometer driven by a coherent light source.

GenericJ1…J4Method of Optical Phase Detection

Abstract Two new expressions for the linear, direct measurement of dynamic phase shift in a no-feedback, no-phase bias optical homodyne interferometer are presented based on the recent, generic J 1…J 4 technique. These new methods, the J 1…J 6(neg) and the J 1…J 6(pos) schemes, consider the voltage amplitude at the fundamental frequency and the next five harmonics in comparison to the four components utilized for the J 1…J 4 method. With this development, the accuracy and the minimum detectable phase shift (MDPS) are greatly improved by the J 1…J 6(neg) method, while the dynamic range of phase shift is enhanced by the J 1…J 6(pos) method. An excellent agreement between the experimental results and the predicted values based on the 1/f noise model is demonstrated for all the three methods. For the experimental noise factor k of 0·0011 for the particular set-up used, the MDPS is 0·05, 0·175 and 0·2 rad respectively for the J 1…J 6(neg), J 1…J 4 and the J 1 …J 6(pos) methods.

Theory of a novel high sensitivity optical fibre gyroscope

A novel optical fibre gyroscope, with a structure making use of the combination of a Sagnac interferometer with an active fibre ring-resonator, is proposed and analysed. It can be regarded as a generalised structure of the conventional Sagnac interferometric fibre optic gyroscope (SIFOG). Counter-propagating optical waves in the gyroscope can circulate many times in the sensing loop into which an optical amplifier is incorporated to compensate partially for optical losses of each circulation. The optical response is effectively the sum of the optical responses of a series of conventional Sagnac interferometric fibre optic gyroscopes having effective loop length equal to the fibre loop length multiplied by the number of circulations. We show that the sensitivity of the proposed gyroscope can be two orders of magnitude higher than that for a conventional SIFOG and that the minimum detectable nonreciprocal phase shift limited by the amplifier noise is nearly one order of magnitude smaller than that of conventional SIFOG limited by quantum noise. These performance enhancements cannot be obtained by incorporating an optical amplifier into the conventional SIFOG structure.

Minimum detectable phase shift in spectrum-analysis techniques of optical interferometric vibration detection

The minimum detectable phase shift indicated in recent experimental reports of new linear spectrumanalysis techniques of optical interferometric vibration detection is established as the direct consequence of the 1/f noise voltage in the system components. The dynamic range and inaccuracy predicted by the simple theoretical model presented is in good agreement with experimental measurements. The conclusions of the analysis are compared with experimental reports of heterodyne shot-noise-limited optical systems. With this effective tool the generic class of spectrum-analysis techniques can be analyzed and relatively weighed to assess the effect of noise. This analysis is applicable to optical interferometry in general, although the experiments specifically involved fiber-optic modulators.

Linear measurement of static phase change in optical homodyne interferometers: an analysis

A new highly accurate linear method of dc phase-shift measurement based on spectrum analysis in a general optical homodyne interferometer is presented. The dc phase is superimposed onto a controllable ac phase modulation. The dc phase error is theoretically analyzed based on the excellently matching predicted and experimental reports of ac phase error. Significantly, for low values of dc phase, a constant correction factor can be utilized that leads to an ultralow minimum detectable dc phase shift.

New spectrum analysis technique for interferometric vibration measurement

A new spectrum analysis technique for linear, direct measurement of dynamic phase shift in an unstabilised, no-phase bias optical homodyne interferometer is described. A minimum detectable phase shift of 0.01 rad is demonstrated for a fiber sensor/ modulator configuration.

Multimode Fibre Axial Strain Sensor Utilizing End Reflection Interference

Abstract A generic class of single-arm multimode optical fibre sensors based on end reflection interference (ERI) is described and demonstrated. The ERI mechanism provides a simple and viable alternative to the well-established approach of single mode fibre interferometric sensing. A high static phase sensitivity of 3·45 × 107 rad/m, a dynamic phase shifting coefficient of 1·1 rad/Vp − m and a minimum detectable phase shift of 2·3 × 10−5 rad/√Hz have been measured for the reported configuration. Based on theoretical considerations and experimental observations of the periodicity and the magnitude of the intensity fluctuations, it has been unambiguously established that under normal ambient conditions the ERI is the dominant contributor to the intensity changes.

Linear readout of dynamic phase change in a fiber-optic homodyne interferometer

A new technique that provides linear measurement of dynamic phase change in a no-feedback, no-phase-bias fiber-optic interferometer is described. The phase measurement is unaffected by random changes in phase, source intensity, and fringe visibility. A minimum detectable phase shift of 0.1 rad has been measured for the configuration reported.