Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

Cranch, Geoffrey A.; Foster, Scott

doi:10.1126/science.1205452

Cited by 20 publications

(10 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, very recently a new model for low-frequency thermally induced length fluctuations in optical fibers was proposed by Duan (12,13), following an approach based on the fluctuation-dissipation theorem (14). A comparison with our data is already shown by Cranch and Foster (6), but a deeper analysis reveals that the expression derived from (12) is much closer to experimental findings than others.…”

supporting

confidence: 80%

Response to Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

Gagliardi

Salza

Avino

et al. 2012

Science

View full text Add to dashboard Cite

Cranch and Foster argue that the strain resolution of our fiber resonator sensor is not limited by thermal noise. However, extension of common theoretical models to high-finesse passive resonators at low frequency needs further attention. Our findings are consistent with noise of thermodynamic nature for which no experimental evidence in the infrasonic range was available until recently.T hermally induced phase fluctuations in optical fibers have long been studied because they set a fundamental limit to strain resolution of sensors as well as frequency stability of fiber lasers (1, 2). In our original paper (3), we reported an unprecedented resolution level in strain sensing using a high-finesse fiber Bragg-grating (FBG) resonator interrogated by an opticalfrequency-comb (OFC) stabilized diode laser. The OFC minimizes noise contribution from the laser, which is usually dominant in similar systems, particularly in the infrasonic frequency range (4, 5). Taking into account the laser-frequency noise when locked to the OFC, we estimated the ultimate limit of our technique to be 120 fe/√Hz at 2 Hz (3). Despite that, the strain resolution was found to be above the expected value.Cranch and Foster (6) compare our strain noise with that predicted by their model with an effective fiber length equal to twice the FBGs distance (analogous to fiber lasers) (7). We remark that the definition of effective length given in (7) is difficult to match with the popular Wanser's model (8). Wanser's theory provides the only analytical expression of thermal phase fluctuations for finite-cladding fibers. Over the past two decades, few experiments have confirmed this model for long-fiber interferometers-and those have been only in the acoustic range-whereas strong deviations were found at low frequency (9, 10). A similar theory was developed for fiber lasers, but a discrepancy with Wanser's expression was pointed out, and the measured low-frequency noise was far from the predicted level as well (7). To explain this behavior, a different theoretical model was proposed for fiber lasers, based on the introduction of source terms in the stochastic heat diffusion equation (11). However, the extrapolation of the predictions of these models at low frequencies is still questionable. To our knowledge, no theory or experiment has been reported to date for high-finesse passive fiber resonators, which leaves open the question of which theoretical approach better describes the observed noise. In the absence of other models, we used Wanser's formula with a finesse-dependent length to account for the power storage inside the cavity due to multiple reflections. Although the use of this scaling factor is arguable, it leads to a factor 8 in the noise calculation compared with the original Wanser's formulation, and it describes well the observed noise. Finally, we note that the OFC noise-limited strain resolution is about a factor 6 below the measured noise floor, thereby indicating that we were approaching the thermal fluctuation level predicted by Wanser...

show abstract

supporting

confidence: 80%

Response to Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

Gagliardi

Salza

Avino

et al. 2012

Science

View full text Add to dashboard Cite

show abstract

“…In fact, a thorough analysis recently reported by Skolianos et al shows that the predicted thermal noise is nearly an order of magnitude below the measured noise in [15], indicating the reported strain sensitivity may still be limited by other noises, such as the laser phase noise. Nevertheless, this debate prompts the question of whether the current technology is ready to attain thermal noise-limited fiber-optic sensing in the infrasonic range [3], [4]. The present work is an attempt by the author to address this question.…”

Section: Introductionmentioning

confidence: 98%

“…In a similar effort, Gagliardi et al demonstrated the highest strain sensitivity below 10 Hz with a fiber Fabry-Perot (FP) cavity and a frequency combstabilized diode laser [2]. However, their claim of reaching the thermal noise limit at infrasonic frequencies (below 20 Hz) has been shown to be inconsistent with theoretical predictions [3], [11], [15]. In fact, a thorough analysis recently reported by Skolianos et al shows that the predicted thermal noise is nearly an order of magnitude below the measured noise in [15], indicating the reported strain sensitivity may still be limited by other noises, such as the laser phase noise.…”

Section: Introductionmentioning

confidence: 99%

Thermal Noise-Limited Fiber-Optic Sensing at Infrasonic Frequencies

Duan

2015

IEEE J. Quantum Electron.

View full text Add to dashboard Cite

The fundamental thermal noise in fiber-optic sensors remains to be an interesting research topic. In particular, its spectral behavior in the infrasonic frequency range has yet to be observed experimentally. In this paper, we assess the feasibility of probing the thermal noise floor at infrasonic frequencies with two sensor configurations: 1) fiber Fabry-Perot strain sensors and 2) Mach-Zehnder-Fabry-Perot hybrid phase sensors. In each case, we compare the theory-predicted thermomechanical noise (the dominant thermal noise in fibers at low frequencies) with other potential system noises such as laser noises and detector noises. Our analysis indicates that the thermal-noise-limited fiber-optic sensing can be very difficult to achieve with the strainsensing scheme, but much more feasible with the hybrid phase sensors.Index Terms-1f noise, Fabry-Perot, low-frequency noise, noise measurement, optical fiber sensors, phase noise, strain measurement, thermal noise.

show abstract

“…For the range of infrasonic frequencies (10 mHz to 30 Hz), Gagliardi et al 4 reported strain measurements with the highest sensitivity obtained by using a fiber Fabry-Perot (FP) cavity. However, the sources of the noise floor are still in doubt 18,24,25 . Recently, in the experiment for ultra-stable fiber-stabilized laser, Dong et al 8 observed that the frequency noise PSD range from 1 Hz to 100Hz exhibits a 1 f characteristic seems consistent with Duan's theory.…”

mentioning

confidence: 99%

Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies

Dong

Huang

et al. 2016

Applied Physics Letters

View full text Add to dashboard Cite

The intrinsic thermal noise in optical fibers represents the ultimate limit for fiber-based systems. However, at infrasonic frequencies, the spectral behavior of the intrinsic thermal noise is still unclear. In this letter, we present measurements of the fundamental thermal noise in optical fibers that are obtained using a balanced fiber Michelson interferometer. When an ultra-stable laser is used as the laser source and other noise sources are carefully controlled, the 1/f spectral density of the thermal noise is observed down to infrasonic frequencies, and the measured magnitude is consistent with the results of theoretical predictions at frequencies over the range from 0.2 Hz to 20 kHz. Moreover, as observed experimentally, the level of the 1/f thermal noise can be reduced by changing the coatings of the optical fibers. This therefore indicates one possible way to reduce thermal noise in optical fibers at low Fourier frequencies. Finally, the inconsistency between the experimental data and the existing theory for thermomechanical noise is discussed.

show abstract

Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

Cited by 20 publications

References 15 publications

Response to Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

Response to Comment on “Probing the Ultimate Limit of Fiber-Optic Strain Sensing”

Thermal Noise-Limited Fiber-Optic Sensing at Infrasonic Frequencies

Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies

Contact Info

Product

Resources

About