Minimum Detectable Displacement Research Articles

Monitoring Horizontal Displacements with Low-Cost GNSS Systems Using Relative Positioning: Performance Analysis

Monitoring horizontal displacements, such as landslides and tectonic movements, holds great importance and high-cost geodetic GNSS equipment stands as a crucial tool for the precise determination of these displacements. As the utilization of low-cost GNSS systems continues to rise, there is a burgeoning interest in evaluating their efficacy in measuring such displacements. This evaluation is particularly vital as it explores the potential of these systems as alternatives to high-cost geodetic GNSS systems in similar applications, thereby contributing to their widespread adoption. In this study, we delve into the assessment of the potential of the dual-frequency U-Blox Zed-F9P GNSS system in conjunction with a calibrated survey antenna (AS-ANT2BCAL) for determining horizontal displacements. To simulate real-world scenarios, the Zeiss BRT 006 basis-reduktionstachymeter was employed as a simulation device, enabling the creation of horizontal displacements across nine different magnitudes, ranging from 2 mm to 50 mm in increments of 2, 4, 6, 8, 10, 20, 30, 40, and 50 mm. The accuracies of these simulated displacements were tested through low-cost GNSS observations conducted over a 24 h period in open-sky conditions. Additionally, variations in observation intervals, including 3, 6, 8, and 12 h intervals, were investigated, alongside the utilization of the relative positioning method. Throughout the testing phase, GNSS data were processed using the GAMIT/GLOBK GNSS (v10.7) software, renowned for its accuracy and reliability in geodetic applications. The insightful findings gleaned from these extensive tests shed light on the system’s capabilities, revealing crucial information regarding its minimum detectable displacements. Specifically, the results indicate that the minimum detectable displacements with the 3-sigma rule stand at 22.8 mm, 11.7 mm, 8.7 mm, and 4.8 mm for 3 h, 6 h, 8 h, and 12 h GNSS observations, respectively. Such findings are instrumental in comprehending the system’s performance under varying conditions, thereby informing decision-making processes and facilitating the adoption of suitable GNSS solutions for horizontal displacement monitoring tasks.

Influence of network configuration and stochastic model on the determination of the minimum detectable displacements (MDD) through sensitivity analysis and significance test

Influence of network configuration and stochastic model on the determination of the minimum detectable displacements (MDD) through sensitivity analysis and significance test

Phase-Resolved Optical Coherence Elastography: An Insight into Tissue Displacement Estimation.

Robust methods to compute tissue displacements in optical coherence elastography (OCE) data are paramount, as they play a significant role in the accuracy of tissue elastic properties estimation. In this study, the accuracy of different phase estimators was evaluated on simulated OCE data, where the displacements can be accurately set, and on real data. Displacement (∆d) estimates were computed from (i) the original interferogram data (Δφori) and two phase-invariant mathematical manipulations of the interferogram: (ii) its first-order derivative (Δφd) and (iii) its integral (Δφint). We observed a dependence of the phase difference estimation accuracy on the initial depth location of the scatterer and the magnitude of the tissue displacement. However, by combining the three phase-difference estimates (Δdav), the error in phase difference estimation could be minimized. By using Δdav, the median root-mean-square error associated with displacement prediction in simulated OCE data was reduced by 85% and 70% in data with and without noise, respectively, in relation to the traditional estimate. Furthermore, a modest improvement in the minimum detectable displacement in real OCE data was also observed, particularly in data with low signal-to-noise ratios. The feasibility of using Δdav to estimate agarose phantoms' Young's modulus is illustrated.

10 μm thick ultrathin glass sheet to realize a highly sensitive cantilever for precise cell stiffness measurement.

The micro-cantilever-based sensor platform has become a promising technique in the sensing area for physical, chemical and biological detection due to its portability, small size, label-free characteristics and good compatibility with "lab-on-a-chip" devices. However, traditional micro-cantilever methods are limited by their complicated fabrication, manipulation and detection, and low sensitivity. In this research, we proposed a 10 μm thick ultrathin, highly sensitive, and flexible glass cantilever integrated with a strain gauge sensor and presented its application for the measurement of single-cell mechanical properties. Compared to conventional methods, the proposed ultrathin glass sheet (UTGS)-based cantilever is easier to fabricate, has better physical and chemical properties, and shows a high linear relationship between resistance change and applied small force or displacement. The sensitivity of the cantilever is 15 μN μm-1 and the minimum detectable displacement at the current development stage is 500 nm, which is sufficient for cell stiffness measurement. The cantilever also possesses excellent optical transparency that supports real-time observation during measurement. We first calibrated the cantilever by measuring the Young's modulus of PDMS with known specific stiffness, and then we demonstrated the measurement of Xenopus oocytes and fertilized eggs in different statuses. By further optimizing the UTGS-based cantilever, we can extend its applicability to various measurements of different cells.

Native signal self-mix interferometer has less than 1 nm noise equivalent displacement.

We demonstrate that the native configuration of a self-mixing interferometer attains a minimum detectable displacement of 0.72 nm or λ/1870 at the laser wavelength of 1310 nm, obtained by the bare laser diode package including a monitor photodiode, observed in the electrical domain by means of an oscilloscope and without any electronic processing of the signal.

NOEMS Based Slotted Photonic Crystal Cavity for the Sensing of Force

In the paper, a two dimensional slotted photonic crystal cavity (2D-SPCC) has been designed and optimized for the application of sensing. The optimized 2D-SPCC has been incorporated in a silicon cantilever to form a nano-opto-electro-mechanical system (NOEMS) for sensing the physical parameters like - force, displacement and strain. An applied force at the cantilever-tip generates strain which results in deformation of the SPCC parameters like slot-width. This structural change in the 2D-SPCC changes the optical behavior of the device, which can be sensed, and thus operate as a physical sensor. Resonant wavelengths of the SPCC are determined for different length and breadth of the cantilever. The results show a linear dependence of the resonant wavelength with the change in the physical parameters. The 2D-SPCC has a high quality factor and sensitivity of $\sim\!9 \, \times\, 10^6$ and 4.2 nm $\mu$ N respectively, due to which the minimum detectable force, displacement and strain for the proposed design are found as 0.0202 $\mu$ N, 0.090 707  $\mu$ m and 0.019 979 respectively for a cantilever of length 40  $\mu$ m and breadth 20  $\mu$ m. Hence, the proposed NOEMS sensor is expected to be highly relevant for different industrial applications.

Flexible PDMS Foams Decorated with Multi–Walled CNTs for Unprecedented Detection of Ultralow Strain and Pressure Coupled with Large Working Range

Over the last years a huge effort has been paid to the development of flexible and wearable strain and pressure sensors for, though not limited to, health care applications. In spite of the tremendous effort paid over the last years, the analysis of the literature on this field points out that it was still unmet the challenge to achieve high performance piezoresistive sensors with simultaneous ultralow limit of detection and large working range both for pressure and strain, able to address both subtle (1Pa-1 kPa) to medium (up to 100 kPa) pressures and ultrasmall (≤0.1%) to large (>50%) strains. In this work, we demonstrate unprecedented simultaneous detection of ultrasmall strain (0.1%) and subtle pressure (20 Pa) coupled with a large working range (up to 60% for strain and 50 kPa for pressure)using piezoelectric, flexible three-dimensional (3D) macroporous PDMS (pPDMS) foams with pores of 500µm decorated with a thin network of pristine multi-walled CNTs. Limit of detection of our sensors are 0.03% for strain (i.e) and 6 Pa for pressure, which corresponds to a minimum detectable displacement of 3 µmover a length of 10 mm and to a minimum detectable force of 0.6 mN over an area of 1 cm2, given that the pPDMS/CNTs foams of this work are cubes of 1 cm in size. Adding to these excellent features, the foams can reliably support deformation up to 6 mm (60% strain) and measure a maximum pressure of about 50 kPa (i.e. a force of 5 N over an area of 1 cm2). In a few words, our foams are able to detect both displacement and pressure produced by a fly (about 70 mg of weight), at the same time being able to measure displacement and pressure produced by an Apple iPad (about 500 g). Remarkably, preparation of our 3D pPDMS/CNTs foams is low-cost and up-scalable. In fact, it is based on simple replica molding of sacrificial sugar templates and subsequent drop-casting of CNT ink drops. We show in the manuscript that the preparation is highly robust in terms of both static and dynamic piezoelectric performance, also for long cycling. Further, by simply changing geometry and size of the sacrificial sugar templates, the foams can be arbitrarily shaped with different areas, ranging from <1 cm2 up to 10 cm x 10 cm, and thicknesses, ranging from 1 mm to 10 mm, and geometry tunable from simple element to complex meshes. We envisage the use our flexible, piezoresistive strain/pressure sensors for high-precision personalized healthcare and, more broadly, for wearable applications, though applications to other fields where displacement and pressure need to be monitored with extremely high resolution can be also envisaged. [1] Flexible Polydimethylsiloxane Foams Decorated with Multiwalled Carbon Nanotubes Enable Unprecedented Detection of Ultralow Strain and Pressure Coupled with a Large Working Range, R Iglio, S Mariani, V Robbiano, L Strambini, G Barillaro, ACS Applied Materials & Interfaces 10 (16), 13877-13885 (2018).

Thermomechanical Noise Characterization in Fully Monolithic CMOS-MEMS Resonators.

We analyzed experimentally the noise characteristics of fully integrated CMOS-MEMS resonators to determine the overall thermomechanical noise and its impact on the limit of detection at the system level. Measurements from four MEMS resonator geometries designed for ultrasensitive detection operating between 2-MHz and 8-MHz monolithically integrated with a low-noise CMOS capacitive readout circuit were analyzed and used to determine the resolution achieved in terms of displacement and capacitance variation. The CMOS-MEMS system provides unprecedented detection resolution of 11 yF·Hz−1/2 equivalent to a minimum detectable displacement (MDD) of 13 fm·Hz−1/2, enabling noise characterization that is experimentally demonstrated by thermomechanical noise detection and compared to theoretical model values.

Nanometric displacement measurement based on interference fringes deflection

A hybrid method to obtain nanometric displacements based on interference fringes movement by optical beam deflection is proposed. A proof-of-principle experiment is described as a new method for real-time detection and measurement of small vibrations, experimental results shows an increase in the resolution compared with a simply optical beam deflection read out. Also, there is minimum detectable displacement in an assumed noise environment.

Optically read displacement detection using phase-modulated diffraction gratings with reduced zeroth-order reflections

Displacement detection using optical interferometric techniques allows for low minimum detectable displacements which are unmatched by other displacement measurement methods as device sizes are scaled down. The use of diffractive optical elements as beam splitters has proven an effective way to realize miniature and robust optical interferometers. Diffraction gratings commonly used in such applications, however, can generate a zeroth-order reflected beam, which results in reduced sensor performance, packaging limitations, and laser instability. A diffraction grating concept has been designed, fabricated, and tested, which has the effect of reducing the zeroth-order component by imparting a half-wavelength phase shift to a portion of the reflected light. The design criteria for zeroth-order beam elimination are illustrated using a simple model based on phasor arithmetic. The microfabrication process used to prototype gratings is presented, and experimental measurements collected from the prototype are reported. The minimum detectable displacement achievable in sensor applications is found to be 3.6 fm/√Hz, which is comparable to sensors built using more conventional gratings. Finally, comparisons are made between the test results and the simple model predictions.

Optical displacement detection using multi-level diffraction gratings having no zeroth-order reflection

Displacement detection using optical interferometric techniques allows for low minimum detectable displacements which are unmatched by other displacement measurement methods. However, diffraction gratings commonly used in such applications can generate zeroth-order reflected beams which result in reduced sensor performance, packaging limitations, and laser instability. A new grating concept has been fabricated and tested which has the effect of eliminating the zeroth-order component by imparting a half-wavelength phase shift to a portion of the reflected light. The design criteria for zeroth-order beam elimination is illustrated using a simple model based on phasor arithmetic. Fabrication methods for producing these optical gratings, as well as comparisons between experimental test results and models, will be reported.

Dynamic near-field optical interaction between oscillating nanomechanical structures.

Near-field optical techniques exploit light-matter interactions at small length scales for mechanical sensing and actuation of nanomechanical structures. Here, we study the optical interaction between two mechanical oscillators—a plasmonic nanofocusing probe-tip supported by a low frequency cantilever, and a high frequency nanomechanical resonator—and leverage their interaction for local detection of mechanical vibrations. The plasmonic nanofocusing probe provides a confined optical source to enhance the interaction between the two oscillators. Dynamic perturbation of the optical cavity between the probe-tip and the resonator leads to nonlinear modulation of the scattered light intensity at the sum and difference of their frequencies. This double-frequency demodulation scheme is explored to suppress unwanted background and to detect mechanical vibrations with a minimum detectable displacement sensitivity of 0.45 pm/Hz1/2, which is limited by shot noise and electrical noise. We explore the demodulation scheme for imaging the bending vibration mode shape of the resonator with a lateral spatial resolution of 20 nm. We also demonstrate the time-resolved aspect of the local optical interaction by recording the ring-down vibrations of the resonator at frequencies of up to 129 MHz. The near-field optical technique is promising for studying dynamic mechanical processes in individual nanostructures.

Validating Dual Fluoroscopy System Capabilities for Determining In‐Vivo Knee Joint Soft Tissue Deformation: A Strategy for Registration Error Management

Knee osteoarthritis (OA) causes structural and mechanical changes within tibiofemoral (TF) cartilage affecting tissue load deformation behavior. Quantifying in-vivo TF soft tissue deformations in healthy and early OA may provide a novel biomechanical marker, sensitive to alterations occurring prior to radiographic change. Dual Fluoroscopy (DF) allows accurate in-vivo TF soft tissue deformation assessment but requires validation. In-vivo healthy and early OA TF cartilage deforms 0.3–1.2mm during static standing full body-weight loading. Our aim was to establish minimum detectable displacement (MDD) for femoral translation in a DF system using a marker-based and markerless approach with variable image intensifier magnifications. An instrumented frame allowed controlled femur specimen translations. Bone positions were reconstructed from DF data using centroids of affixed steel beads (marker-based) and 2D–3D bone feature registration (markerless). Statistical analyses included independent samples t-tests and reliability analysis. Markerless measurements by three trained operators had large variations making it prudent to have an appropriate error management strategy when performing 2D–3D registration. Marker-based MDD improved with image resolution and was 0.05mm at 3.2LP/mm (LP: line pairs). Markerless MDD at 3.2LP/mm was 0.08mm. Average femur and tibia 2D–3D registrations yielded excellent reliability (84.4%). Therefore, DF images acquired at resolution greater than 3.2LP/mm would be capable for determining accurate and reliable in-vivo healthy and early OA TF soft tissue deformation. This study provides a registration error management strategy for in-vivo TF soft tissue deformation assessment that could be applied for future clinical applications to establish non-invasive biomechanical markers for early OA diagnosis.

Inter-rater accuracy and precision of markerless quantification of 3d tibiofemoral displacement using dual fluoroscopy

Purpose: Early changes in osteoarthritic (OA) knee cartilage include tissue swelling and softening, which may predispose cartilage to mechanical damage during activities of daily living. Current clinical OA diagnosis relies on radiographic bone morphology change and pain, which can be insensitive to early change. Developing a marker that specifically targets early mechanical tissue changes may advance the current state of OA assessment. Potential candidates for such markers are in-vivo magnitude and rate of tibiofemoral (TF) soft tissue deformation during weight bearing (compression) and unloading (recovery). Respective joint “signatures” for healthy and OA groups may then allow for early OA identification. Dual Fluoroscopy (DF) is an emerging tool with the potential to provide the temporal and spatial resolutions necessary for such assessment. Tissue deformation mechanics may be derived using translation and rotation changes of the femur with respect to the tibia over time. Using a bead tracking technique, similar to radiostereometric analysis (RSA), translation changes of 0.05 mm (1/ 10th expected maximal cartilage deformation) have previously been accurately detected. It is however unknown if a non-invasive markerless DF approach is sufficiently accurate and precise for quantifying the small changes during weight bearing. The purpose of this study was to establish the Minimum Detectable Displacement (MDD) of 3D femoral translations with respect to the tibia in a custom built DF system using a markerless shape matching image registration approach. Methods: The DF system consisted of two X-ray tubes (Varian, USA) and generators (EMD, Canada), quad mode image intensifiers (Toshiba, Japan) and high speed digital video cameras (PCO, Germany). DF images were acquired with an entrance field diameter of 228 mm and 0.155 x 0.155 mm2 pixel resolution. Dry tibia and femur bones were fixed to a plexiglass frame, where the tibia remained stationary and the femur was translated using a digital micrometer (Mitutoyo, Japan). The frame was placed within the DF field-of-view and did not move during data capture. Ten displacement intervals (0.01-0.1 mm)were imagedwith 10 repetitions of each interval. DF calibration was performed using a calibration cube and modified direct linear transform. Images were distortion corrected using a perforated steel grid and XrayProject (Brown University, USA). 3D femur and tibia bone models were generated using segmentation (Amira, USA) of Computed Tomography image sequences (0.21 x 0.21 x 0.31 mm). 3D bone orientations were obtained by three raters using AutoScoper (Brown University, USA) and a markerless shape matching approach. Bone-specific models were positioned to align their visible features to those of the underlying 2D X-ray images. Relative femur and tibia displacements were obtained using the Euclidean distance between bone models. Independent samples t-tests were used to detect MDDs of the moving femur relative to the stationary tibia at each displacement interval. Accuracy and precision were computed as means and standard deviations of the absolute differences of the femur translations compared to the micrometer displacements. Inter-rater reliability values of the femur were computed using intra-class correlation coefficient (ICC). All statistical analyses were performed in SPSS (IBM, USA) and p 0.05. Results: Femur displacement measurements were significantly different from tibia (p<0.045) and had greater than 95% confidence in accuracy at micrometer displacements 0.:08mm (accuracy precision: 0.022 0.019) (Figure 1). Between raters femur displacement measurements were not significant for micrometer displacements 0.:05mm and inter-rater reliability across all displacements was 92%. Conclusions: These findings indicate that 3D bone translations within relevant in-vivo ranges can be observed accurately and precisely using a markerless DF shape matching approach. Femur displacements of 0.:08mm were accurately and reliably detected with respect to set micrometer displacements. The data further indicated good between rater agreement when quantifying femur displacements. Given the above system specifications, the markerless DF approach provides a means for non-invasive in-vivo quantification of TF tissue response to loading and unloading stimuli. Using this approach, further workwill be performed to establish the mechanical behaviour of TF soft tissues of healthy and ligament deficient and OA knees. While significant user input is required, compared to RSA type techniques, this non-invasive approach may be more readily applied in a future clinical setting.

Sensitive Vibration Detection Using Ground-Penetrating Radar

A high-dynamic-range vibration detection system is presented based on analog cancellation. The prototype system operates at 900 MHz and is shown to detect vibrational displacement as low as 11 nm for a rectangular aluminum plate at a standoff distance of 2 m. By operating at a lower frequency than previous radar vibrometers, the system gains ground-penetrating capability and is shown to detect vibrations through 13 cm of sand. A fundamental relationship is introduced relating the minimum detectable vibration displacement to the standoff distance and system dynamic range.

Preliminary assessment of one-dimensional MR elastography for use in monitoring focused ultrasound therapy

The purpose of this work is to assess a fast technique that measures tissue stiffness and temperature during focused ultrasound thermal therapy (FUS). A one-dimensional (1D) MR elastography (MRE) pulse sequence was evaluated for the purpose of obtaining rapid measurements of thermally induced changes in tissue stiffness and temperature for monitoring FUS treatments. The accuracy of the 1D measurement was studied by comparing tissue displacements measured by 1D MRE with those measured by the well-established 2D MRE pulse sequence. The reproducibility of the 1D MRE measurement was assessed, in gel phantoms and ex vivo porcine tissue, for varied FUS intensity levels (31.5–199.9 W cm−2) and over a range of displacements at the focus (0.1–1 µm). Temperature elevations in agarose gel phantoms were measured using 1D MRE and calibrated using fiberoptic-thermometer-based measurements. The 1D MRE displacement measurements are highly correlated with those obtained with the 2D technique (R2 = 0.88–0.93), indicating that 1D MRE can successfully measure tissue displacement. Ten repeated trials at each FUS power level yielded a minimum detectable displacement change of 0.2 µm in phantoms and 0.4 µm in tissue (at 95% confidence level). The 1D MRE temperature measurements correlated well with temperature changes measured simultaneously with fiberoptic thermometers (R2 = 0.97). The 1D MRE technique is capable of detecting tissue displacements as low as 0.4 µm, which is an order of magnitude smaller than 5 µm displacements expected during FUS therapy (Le et al 2005 AIP Conf. Proc.: Ther. Ultrasound 829 186–90). Additionally, 1D MRE was shown to provide adequate measurements of temperature elevations in tissue. These findings indicate that 1D MRE may be an effective tool for monitoring FUS treatments.

Evaluation of MLC leaf positioning using a scanning liquid ionization chamber EPID

A method was developed to determine the accuracy of multileaf collimator (MLC) positioning using transmitted dose maps measured by a scanning liquid ionization chamber electronic portal imaging device (SLIC-EPID). Several MLC fields were designed, using the Varian C-series standard MLC-80, as reference fields for open fields. The MLC leaves were then shifted from the reference positions along the direction of MLC leaf movement towards the central axis from 0.1 to 1.6 mm. The electronic portal images (EPIs), acquired for each case, were converted to two-dimensional dose maps using an appropriate calibration method and the relative dose difference maps were then calculated. The experiment was then performed at non-zero gantry angles in the presence of an anthropomorphic phantom for typical prostate and head and neck fields. Several standard edge detection algorithms were also used in order to find the shifted MLC leaf position. In addition, the short-term reproducibility of MLC leaf positioning was evaluated using the above-mentioned methods. It was found that the relationship between the relative dose difference and MLC leaf spatial displacement is linear. A variation of 0.2 mm in leaf position leads to approximately 4% change in the relative dose values for open fields. The variation of the relative dose difference for phantom studies depends on the phantom positioning and the EPI normalization. From the standard edge detection algorithms, used in the current study, the ‘Canny’ algorithm was found to be the optimum method to identify the minimum detectable MLC leaf displacements with a precision of approximately 0.1 mm for all cases. However, the result of edge detection algorithms generally is binary and there is no additional information compared to the relative dose maps. The reproducibility of MLC positions was found to be within 0.3 mm. In conclusion, a SLIC-EPID can be used for regular quality assurance (QA) of MLC leaf positioning. Despite significant difference in the pixel size of the acquired SLIC-EPIs, it can be concluded that the SLIC-EPID can be used for MLC quality assurance protocols with similar accuracy compared to amorphous silicon (a-Si) EPID results.

A micro Fabry–Perot sensor for nano-lateral displacement sensing with enhanced sensitivity and pressure resistance

This paper proposes a novel sensitivity/signal enhancement method for a nano-displacement sensor fabricated by polymer MEMS technology and operated by Fabry–Perot interferometry. The surface roughness of the floating element fabricated by UV lithography on SU-8 photoresist is better than 5 nm (Ra value) on 35 μm×35 μm area and can be served as reflection mirror. Silicon oil with refractive index 1.406 is filled into the sensor cavity as an index matching medium for signal and sensitivity enhancement as well as a buffer material for pressure resistance and vibration reduction. With silicon oil filling, the sensor sensitivity can be improved by 1.85 times and signal intensity is increased by 16.4 dB, respectively. The minimum detectable displacement and shear stress have been demonstrated to be 10 nm and 0.33 Pa, respectively. The sensitivity of displacement and shear stress sensing are of 0.1249 nm/nm (wavelength shift/floating element displacement) and 6.825 nm/Pa (wavelength shift/shear stress), respectively. Besides, the signal spectrum shifts have been tested within 1 nm under static pressure from 1 to 6 atm or acoustic vibration from 1 Hz to 5 kHz, because of the incompressibility and damping effect of the silicon oil. However, the temperature dependency and hysteresis of the sensor due to the thermal effect need to be improved or compensated for practical applications in the future.

Fundamental limits of optical microrheology

We estimate the fundamental limits of different microrheological techniques based on optical detection. It is suggested that particle tracking systems using nondifferential detection have a minimum detectable displacement given by 0.2(λ0/NA)(1/SNR), where λ0 is the wavelength, NA is the numerical aperture of the focusing objective, and SNR is the signal-to-noise ratio of the system. This limit has important consequences in microrheology, since the noise contributes with an apparent diffusion constant of Dl≈0.02(λ0/NA)2(B/SNR), where B is the bandwidth of the detection unit. As the SNR of ordinary microscopes is limited, one should be extra careful when probing soft materials with low diffusion constants. On the other hand, in differential systems based on laser detection, the SNR is considerably increased due to reduced laser noise, and the minimum detectable displacement is given by 0.4(λ0/NA)(1/SNR). One may therefore expect to measure the diffusion constant with higher accuracy if the SNR is large. Finally, we find that total internal reflection microscopy (TIRM) has a minimum detectable displacement given by 0.1λ0/SNR.

Cavity ringdown strain gauge.

Biconical tapered single-mode fiber, which is common in many telecommunications components, offers an alternative sensor to typical optical fiber strain gauges that are susceptible to temperature and pressure effects and require expensive and sophisticated signal acquisition systems. Cavity ringdown spectroscopy, a technique commonly applied to high-sensitivity chemical analysis, offers detection sensitivity advantages that can be used to improve strain measurement with biconical tapers. Combining these two technologies in a spatially extended resonator, we demonstrate a minimum detectable change in ringdown time of 0.08%, corresponding to a minimum detectable displacement of 4.8 nm, and a sensitivity to strain as small as 79 n epsilon/square root(Hz) over a 5-mm taper length.