Measured Noise Floor Research Articles

Investigating the repeatability error in thrust measurement on a pendulum-based stand

To accurately measure the thrust of satellite thrusters on the ground, a precise pendulum-based stand was developed. An easy-to-operate conversion scheme is proposed between large and small range configurations. Tests show that the configurations achieve resolutions of 20 nN and 5 μN respectively, with measurement ranges of 1800 μN and 450 mN. The measurement noise floor reaches 20 nN/Hz1/2@10 mHz-1 Hz and 2 μN/Hz1/2@10 mHz-10 Hz. Based on this stand, a study on the repeatability error and its causes was conducted, showing that the regular drift caused by the elastic pivot is the dominated error source, with the drift rate measured to be in the range of η’ ∼ (0.12–0.44)%. Within a measurement time of 1 min, the absolute measurement errors of typical thrusts for the two configurations are evaluated to be 400.00 ± 0.63 μN and 100.00 ± 0.19 mN respectively. This study is also of significant importance for understanding the behavior of other stands which are constructed with elastic components.

Imaging focused laser differential interferometry.

Focused laser differential interferometry (FLDI) is an important diagnostic for measuring density fluctuations in high-speed flows. Currently, however, high dynamic range FLDI is limited to photodiode measurements. In order to spatially resolve multiple locations within complex flows, we present a novel, to the best of our knowledge, refractive-optic imaging FLDI concept that not only produces two-dimensional images without scanning but also reduces the measurement noise floor of those images. To demonstrate this concept, a 33 × 33 grid of FLDI points is first generated using a microlens array. Then, the beams are split and recombined using two polarized Mach-Zehnder interferometers to maximize flexibility in beam separation and optimize signal sensitivity. Next, the FLDI points are collected slightly out of focus on a high-speed camera in order to increase the number of pixels n per FLDI point, thereby reducing noise floor by n. Finally, an under-expanded jet with a characteristic screech at 14.1 kHz is tested with the imaging FLDI setup, showing clear barrel and reflected shock features as well as spatially varying turbulence densities. Overall, this unique concept enables the creation of reduced-noise-floor, two-dimensional FLDI datasets for the study of supersonic and hypersonic flows.

Error analysis of calibration for horizontal tensor rotating accelerometer gravity gradiometer

The rotating accelerometer gravity gradiometer (RAGG) is regarded as a significant tool in geophysics applications such as resource exploration and gravity-assisted navigation research. Here we develop a prototype of the horizontal tensor RAGG and build a dedicated calibration platform for evaluating its performance. The error of calibration is theoretically computed and experimentally verified. The errors considered include higher-order terms of the gravity gradient error, positioning error, demodulation phase error, as well as the dimensions and density error of the gravitational mass. It has witnessed a high-accuracy gravity gradient calibration platform based on a motorized translation stage, with error values of 0.49 E (1 E = 10−9 s2) in channel Γsin and 0.24 E in channel Γcos . At an averaging time of 32 s, the RAGG demonstrates optimal stability, featuring a minimum Allan deviation value of 6.6 E in channel Γsin and 5.5 E in channel Γcos . And the RAGG has achieved a measurement noise floor of about 40 E/√Hz @ 0.001–0.1 Hz in both channels. For simulating engineering applications, the experimental results demonstrate a standard deviation error of only 3.2 E by employing a gravity gradient excitation step signal of 10 E. It shows that this RAGG has the potential for a wide range of applications.

Relative timing jitter in a counterpropagating all-normal dispersion dual-comb fiber laser

The counterpropagating all-normal dispersion (CANDi) fiber laser is an emerging high-energy single-cavity dual-comb laser source. Its relative timing jitter (RTJ), a critical parameter for dual-comb timing precision and spectral resolution, has not been comprehensively investigated. In this paper, we enhance the state-of-the-art CANDi fiber laser pulse energy from 1 nJ to 8 nJ. We then introduce a reference-free RTJ characterization technique that provides shot-to-shot measurement capability at femtosecond precision. The measurement noise floor reaches 1.6 × 10 − 7 f s 2 / H z , and the corresponding integrated measurement precision is only 1.8 fs (1 kHz, 20 MHz). With this characterization tool, we are able to study the physical origin of the CANDi laser’s RTJ in detail. We first verify that the cavity length fluctuation does not contribute to the RTJ. Then we measure the integrated RTJ to be 39 fs (1 kHz, 20 MHz) and identify the pump relative intensity noise (RIN) to be the dominant factor responsible for it. In particular, pump RIN is coupled to the RTJ through the Gordon–Haus effect. Finally, solutions to reduce the free-running CANDi laser’s RTJ are discussed. This work provides a general guideline to improve the performance of compact single-cavity dual-comb systems such as the CANDi laser, benefitting various dual-comb applications.

Analysis of an inverse weak-value tiltmeter in the kilohertz regime.

We present a follow-on experiment to the recent study from The University of Rochester [Opt. Lett.42, 2479 (2017)OPLEDP0146-959210.1364/OL.42.002479], which reported a new architecture for an inverse weak-value tiltmeter. We recreate the Rochester tiltmeter and specifically investigate mirror oscillations in the low-kilohertz frequency regime, which is relevant to certain potential applications, such as Coriolis vibratory gyroscopes. We find that the inverse weak-value amplification effect persists in this regime, although our measured noise floors are higher than those obtained in the Rochester experiment-approximately 2prad/Hz for mirror oscillation frequencies between 1 and 25 kHz.

Noise Efficient Integrated Amplifier Designs for Biomedical Applications

The recording of neural signals with small monolithically integrated amplifiers is of high interest in research as well as in commercial applications, where it is common to acquire 100 or more channels in parallel. This paper reviews the recent developments in low-noise biomedical amplifier design based on CMOS technology, including lateral bipolar devices. Seven major circuit topology categories are identified and analyzed on a per-channel basis in terms of their noise-efficiency factor (NEF), input-referred absolute noise, current consumption, and area. A historical trend towards lower NEF is observed whilst absolute noise power and current consumption exhibit a widespread over more than five orders of magnitude. The performance of lateral bipolar transistors as amplifier input devices is examined by transistor-level simulations and measurements from five different prototype designs fabricated in 180 nm and 350 nm CMOS technology. The lowest measured noise floor is 9.9 nV/√Hz with a 10 µA bias current, which results in a NEF of 1.2.

Chip-Scale Ultra-Low Field Atomic Magnetometer Based on Coherent Population Trapping.

We report a chip-scale atomic magnetometer based on coherent population trapping, which can operate near zero magnetic field. By exploiting the asymmetric population among magnetic sublevels in the hyperfine ground state of cesium, we observe that the resonance signal acquires sensitivity to magnetic field in spite of degeneracy. A dispersive signal for magnetic field discrimination is obtained near-zero-field as well as for finite fields (tens of micro-tesla) in a chip-scale device of 0.94 cm3 volume. This shows that it can be readily used in low magnetic field environments, which have been inaccessible so far in miniaturized atomic magnetometers based on coherent population trapping. The measured noise floor of 300 pT/Hz1/2 at the zero-field condition is comparable to that of the conventional finite-field measurement obtained under the same conditions. This work suggests a way to implement integrated atomic magnetometers with a wide operating range.

Fast Estimation of Sparse Quantum Noise

As quantum computers approach the fault tolerance threshold, diagnosing and characterizing the noise on large scale quantum devices is increasingly important. One of the most important classes of noise channels is the class of Pauli channels, for reasons of both theoretical tractability and experimental relevance. Here we present a practical algorithm for estimating the $s$ nonzero Pauli error rates in an $s$-sparse, $n$-qubit Pauli noise channel, or more generally the $s$ largest Pauli error rates. The algorithm comes with rigorous recovery guarantees and uses only $O(n^2)$ measurements, $O(s n^2)$ classical processing time, and Clifford quantum circuits. We experimentally validate a heuristic version of the algorithm that uses simplified Clifford circuits on data from an IBM 14-qubit superconducting device and our open source implementation. These data show that accurate and precise estimation of the probability of arbitrary-weight Pauli errors is possible even when the signal is two orders of magnitude below the measurement noise floor.

Resonant fiber-optic strain and temperature sensor achieving thermal-noise-limit resolution.

In the area of fiber-optic sensors (FOSs), the past decade witnessed great efforts to challenge the thermal-noise-level sensing resolution for passive FOS. Several attempts were reported claiming the arrival of thermal-noise-level resolution, while the realization of thermal-noise-level resolution for passive FOSs is still controversial and challenging. In this paper, an ultrahigh-resolution FOS system is presented with a sensing resolution better than existing high-resolution passive FOSs. A fiber Fabry-Perot interferometer as the sensing element is interrogated with an ultra-stable probe laser by using the Pound-Drever-Hall technique. Both strain and temperature measurements are carried out to validate the performance of the sensor. The measured noise floor agrees with the theoretical thermal noise level very well.

A Theoretical and Experimental Evaluation on the Performance of LoRa Technology

A theoretical study and an experimental evaluation on the performance of the long-range (LoRa) technology are presented in this paper. After an instructive mathematical review of important concepts, we assess the LoRa performance in additive white Gaussian noise (AWGN) channels through a numerical model, to elucidate its communication capabilities in negative signal-to-noise ratio (SNR) conditions and, as consequence, in the long distances promised by such low power and narrowband technology. Because of the significance of forward error correction codes in the performance of modern systems, we propose an analytical bit-error-rate (BER) expression that considers the influence of LoRa code rate ( $\textit {CR}$ ) parameter. The agreement between the theoretical and the numerical results of a Hamming coded system validated the closed-form BER, evaluated in terms of SNR in AWGN channels. Moreover, an experimental setup with off-the-shelf LoRa wide area network (LoRaWAN) equipment was prepared to demonstrate the feasibility of this promising technology, as well the impact of the $\textit {CR}$ parameter on the packet error rate (PER), in a link with a single end-device. As expected, communication in urban and open areas with distances up to ≈ 3 and ≈ 10 km, respectively, were achieved, according to measurements of the average received signal indicators around −100 dBm for an average SNR ≈ 5 dB. The usefulness of the practical analysis was confirmed by the agreement between the theoretical and the measured noise floors, and by the verification of the substantial impact of the parameter $\textit {CR}$ on the system PER.

Correlation Between Measured Man-Made Noise Levels and the Density of Habitation

The results of the man-made noise measurement campaign, organized by the Dutch society of radio amateurs, VERON, are compared with geographical data like the number of residential livings inside a circular area around the measurement location limited by a chosen distance. For each frequency band, correlation factors are derived as a function of the distance. It is shown that a strong correlation exists between the measured man-made noise floor and the density of habitation. This result proves that in this campaign, measured noise floor levels are mainly the result of accumulation of noise power from a large number of small sources spread in the houses, instead of being caused by a single, or a few, strong sources. The correlation is maximal at distances up to 200–300 m from the measurement location. Beyond that range, the correlation decreases, indicating that mainly sources in a range up to 300 m are relevant in determining the noise floor. This conclusion is supported by the observation that the slope of regression lines increasingly deviates from a theoretically derived slope at ranges over 300 m.

An All-Polarization-Maintaining Multi-Branch Optical Frequency Comb for Highly Sensitive Cavity Ring-Down Spectroscopy**Supported by the National Natural Science Foundation of China (Grant Nos. 61825505 and 91536217).

We demonstrate a multi-branch all polarization-maintaining Er:fiber frequency comb with five application ports for precise measurement of atomic/molecular transition frequencies in the near-infrared region. A fully stabilized Er:fiber frequency comb with a nonlinear amplifying loop mirror is achieved. The in-loop relative instability of stabilized carrier-envelope-offset frequency is 5.6 × 10−18 at 1 s integration time, while that of the repetition rate is well below 1.8 × 10−12 limited by the measurement noise floor of the commercial frequency counter. Five application ports are individually optimized for applications with different wavelengths (1064 nm, 1083 nm, 1380 nm, 1637 nm and 1750 nm). The beat note between the optical frequency comb and continuous laser exhibits the signal-to-noise ratio of at least 30 dB at a resolution bandwidth of 100 kHz. The in-loop frequency instability of the comb is evaluated to be good enough for measurement of rotation-resolved transitions of molecules below 1 kHz resolution.

Variable-rate frequency sweeps and their application to the measurement of otoacoustic emissions.

Swept tones allow the efficient measurement of otoacoustic emissions (OAEs) with fine frequency resolution. Although previous studies have explored the influence of different sweep parameters on the measured OAE, none have directly considered their effects on the measurement noise floor. The present study demonstrates that parameters such as sweep type (e.g., linear or logarithmic), sweep rate, and analysis bandwidth affect the measurement noise and can be manipulated to control the noise floor in individual subjects. Although responses to discrete-tone stimuli can be averaged until the uncertainty of the measurement meets a specified criterion at each frequency, linear or logarithmic sweeps offer no such flexibility. However, measurements of the power spectral density of the ambient noise can be used to construct variable-rate sweeps that yield a prescribed (e.g., constant) noise floor across frequency; in effect, they implement a form of frequency-dependent averaging. The use of noise-compensating frequency sweeps is illustrated by the measurement of distortion-product OAEs at low frequencies, where the ear-canal noise is known to vary significantly.

Highly-Sensitive Phase and Frequency Noise Measurement Technique Using Bayesian Filtering

Spectral purity of laser sources is typically investigated using phase or frequency noise measurements, which require extraction of the optical phase. This is a challenging task if the signal-to-noise-ratio (SNR) of the spectral line or the linewidth-to-noise-ratio (LNR) are not sufficiently high. In this letter, we present a statistically optimal method for optical phase noise measurement that relies on coherent detection and Bayesian filtering. The proposed method offers a record sensitivity, as the optical phase is measured at a signal power of -75 dBm (SNR of -11 dB in 1.1 GHz receiver bandwidth). Practically, this means that the phase noise measurements are, up to a high-degree, not limited by the measurement noise floor. This allows measurements down to -200 dB rad 2 /Hz and up to 10 GHz, which is useful when measuring the Schawlow-Townes (quantum noise limited) laser linewidth. Finally, the estimated optical phase is highly accurate allowing for quantum limited signal demodulation. The method thus holds the potential to become a reference measurement tool.

Characterizing Background Signals and Noise in Spaceborne GNSS Reflection Ocean Observations

This letter analyzes the background signals and thermal noise received over ocean scenes in spaceborne global navigation satellite system (GNSS)-reflectometry (GNSS-R) remote sensing using observations from the cyclone GNSS (CYGNSS) constellation. The measured noise floor contains a stable and predictable radiometric thermal noise component and a more variable background signal component from unintended specular reflections within the CYGNSS receive antenna pattern from all GNSS satellite constellations (GPS, Galileo, GLONASS, Beidou, and all SBAS). The presence of SBAS reflections, in particular, is evident in the noise floor measurements, especially the U.S. wide area augmentation system (WAAS) satellites. The results show that the impact is negligible, since background signal contributions by other GNSS transmitters affect both the “signal” and “noise” portions of CYGNSS’s delay Doppler map measurements, and therefore cancel when the measured noise floor is subtracted from the desired signal. The potential increase in measurement uncertainty introduced by any residual background signal to the CYGNSS calibration is analyzed.

Ultrastable Optical Magnetometry

Optical magnetometers are important in a myriad of applications requiring highly sensitive measurements of magnetic fields. However, the presence of technical noise often degrades their performance severely at low Fourier frequencies, thereby preventing their use when high stability over long time scales is needed. This study demonstrates an ultrastable optical magnetometer that exhibits high sensitivity across $e\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}g\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}t$ orders of magnitude in Fourier frequency. The contributions of a multitude of noise sources, both fundamental and technical, are investigated. The measured noise floor is primarily limited by magnetic field fluctuations, not the sensor itself.

Bio-Inspired Rectangular Shaped Piezoelectric MEMS Directional Microphone

The noise floor of a piezoelectric MEMS directional microphone largely depends on piezoelectric materials and transducer modes. A careful choice of these parameters (piezoelectric materials and transducer modes) can help to significantly improve the difficulties of noise floor. Here, we present a unique diaphragm-based biomimetic MEMS directional microphone having multiple-port sensing schemes. The diaphragm is separated into two wings and supported by two torsional beams, which are hinged to a fixed support as to imitate the unique inter-tympanal feature of the fly Ormia ochracea . In this microphone, the thermal-mechanical noise (Johnson noise) is minimized by adopting aluminium nitride-based piezoelectric sensing. The d33 mode is incorporated with a prime focus on sensitivity enhancement which leads to signal-to-noise ratio improvement. Measured directivity patterns of both wings show a strong agreement with the direction of applied acoustic pressure as expected for an ideal bi-directional microphone. The measured noise floor at 1-kHz frequency and overall A-weighted noise floor across the audio frequency are 31.35 dB SPL and 32.5 dBA, respectively, which are quite less than some notable works on directional microphones. The experimental results verify the uniqueness of this work.

A 250 μm × 57 μm Microscale Opto-electronically Transduced Electrodes (MOTEs) for Neural Recording.

Recording neural activity in live animals in vivo with minimal tissue damage is one of the major barriers to understanding the nervous system. This paper presents the technology for a tetherless opto-electronic neural interface based on 180 nm CMOS circuits, heterogeneously integrated with an AlGaAs diode that functions as both a photovoltaic and light emitting diode. These microscale opto-electrically transduced electrodes (MOTEs) are powered by and communicate through an optical interface, simultaneously enabling high temporal-resolution electrical measurements without a tether or a bulky RF coil. The MOTE presented here is 250 μm × 57 μm, consumes 1 μW of electrical power, and is capable of capturing and encoding neural signals before transmitting the encoded signals. The measured noise floor is as low as 15 μVRMS at a 15 kHz bandwidth.

Ultra-low noise microwave generation with a free-running optical frequency comb transfer oscillator.

We present ultra-low noise microwave synthesis by optical to radio-frequency (RF) division realized with a free-running or RF-locked optical frequency comb (OFC) acting as a transfer oscillator. The method does not require any optical lock of the OFC and circumvents the need for a high-bandwidth actuator. Instead, the OFC phase noise is electrically removed from a beat-note signal with an optical reference, leading to a broadband noise division. The phase noise of the ∼15 GHz RF signal generated in this proof-of-principle demonstration is limited by a shot-noise level below -150 dBc/Hz at high Fourier frequencies and by a measurement noise floor of -60 dBc/Hz at 1Hz offset frequency when performing 1,100 cross-correlations. The method is attractive for high-repetition-rate OFCs that lead to a lower shot-noise, but are generally more difficult to tightly lock. It may also simplify the noise evaluation by enabling the generation of two or more distinct ultra-low noise RF signals from different optical references using a single OFC and their direct comparison to assess their individual noise.

High-detectivity optical heterodyne method for wideband carrier-envelope phase noise analysis of laser oscillators.

Broadband characterization of the carrier-envelope phase (CEP) noise spectral density of free-running mode-locked lasers is essential for advanced low-noise optical frequency comb designs. Here we present a direct method that utilizes an optical heterodyne beat between a pair of repetition-rate-locked mode-locked lasers for CEP noise characterization, without requiring an f-2f interferometer or nonlinear optical conversion steps. A proof-of-principle experiment in a femtosecond Yb-fiber laser achieves CEP noise spectral density characterization with >270 dB dynamic range over a Fourier frequency range from 5mHz to 8MHz. The measurement noise floor is well below 1 μrad/√Hz, enabling dependable detection down to a quantum-limited noise floor. The method can resolve various noise mechanisms that cause specific CEP noise spectral shapes. The underlying mechanisms are further analyzed in terms of spurious temporal correlation to distinguish between technical and stochastic noise signatures. Moreover, a Hadamard deviation analysis reveals a varying degree of frequency stability in the measured CEP time series.