Quantum sensing for gravity cartography.

The sensing of gravity has emerged as a tool in geophysics applications such as engineering and climate research1-3, including the monitoring of temporal variations in aquifers4 and geodesy5. However, it is impractical to use gravity cartography to resolve metre-scale underground features because of the long measurement times needed for the removal of vibrational noise6. Here we overcome this limitation by realizing a practical quantum gravity gradient sensor. Our design suppresses the effects of micro-seismic and laser noise, thermal and magnetic field variations, and instrument tilt. The instrument achieves a statistical uncertainty of 20 E (1 E = 10-9 s-2) and is used to perform a 0.5-metre-spatial-resolution survey across an 8.5-metre-long line, detecting a 2-metre tunnel with a signal-to-noise ratio of 8. Using a Bayesian inference method, we determine the centre to ±0.19 metres horizontally and the centre depth as (1.89 -0.59/+2.3) metres. The removal of vibrational noise enables improvements in instrument performance to directly translate into reduced measurement time in mapping. The sensor parameters are compatible with applications in mapping aquifers and evaluating impacts on the water table7, archaeology8-11, determination of soil properties12 and water content13, and reducing the risk of unforeseen ground conditions in the construction of critical energy, transport and utilities infrastructure14, providing a new window into the underground.

Adaptive coded-aperture imaging with subpixel superresolution.

We describe an adaptive coded-aperture imager operating in the midwave IR. This consists of a coded-aperture mask, a set of optics, and a 4k×4k focal plane array (FPA). This system can produce images with a resolution better than the detector pixel limit by combining multiple frames of data recorded with different coding. This superresolution capability has been demonstrated both in the laboratory and with targets placed outside, the highest resolution being one-half of the FPA pixel pitch.

Measurements of laser phase fluctuations induced by atmospheric turbulence over 2 km and 17.5 km distances.

A laser heterodyne system was used to measure the phase fluctuations imposed on a 1.5 µm wavelength laser beam when double-passed over long atmospheric paths. Two distances were used: 2 and 17.5 km. Results are given for intensity scintillation, phase fluctuation time series and spectra, and phase structure function. The results are found to agree well with theory: the spectrum of phase fluctuations follows the 8/3 power law predicted for Kolmogorov turbulence over 3 orders of magnitude in frequency. The methods reported here could be used to investigate large-scale temperature variations in the atmosphere.

Statistical properties of finite-bandwidth radiation scattered by random amplitude screens and random phase screens.

We investigate the effect of finite bandwidth of the incident radiation on scattering by thin layers that introduce random phase or amplitude variations. In particular, we calculate the scintillation index of the propagating radiation for smoothly varying and fractal phase screens and for random telegraph wave and checkerboard amplitude screens. Increasing the bandwidth of the incident radiation reduces the fluctuations of the scattered intensity over the whole propagation path, except in the case of the smoothly varying phase screen, where geometrical optics features in the pattern persist in the focusing region.

Fiber-based 1.5 microm lidar vibrometer in pulsed and continuous modes.

A fiber-based 1.5 mum heterodyne lidar that is easily switched between pulse-pair and cw modes is described. In laboratory experiments using well-controlled vibrating targets, and in computer simulations, the performance of the two modes is compared given the same average laser power. The accuracy of Doppler frequency (target velocity) estimates, and the signal-to-noise ratio in spectrally resolved plots of vibrational features, are evaluated. When the target-induced frequency modulation is wideband, pulse-pair often has clearly higher carrier-to-noise. But its advantage in signal-to-noise is smaller because combining the more numerous cw measurements improves the estimates of vibration frequencies and amplitudes. They are combined here through autocorrelation-based demodulation, one of several methods that can outperform phase-differencing.

Chirp-pulse-compression three-dimensional lidar imager with fiber optics.

A coherent three-dimensional (angle-angle-range) lidar imager using a master-oscillator-power-amplifier concept and operating at a wavelength of 1.5 microm with chirp-pulse compression is described. A fiber-optic delay line in the local oscillator path enables a single continuous-wave semiconductor laser source with a modulated drive waveform to generate both the constant-frequency local oscillator and the frequency chirp. A portion of this chirp is gated out and amplified by a two-stage fiber amplifier. The digitized return signal was compressed by cross correlating it with a sample of the outgoing pulse. In this way a 350-ns, 10-microJ pulse with a 250-MHz frequency sweep is compressed to a width of approximately 8 ns. With a 25-mm output aperture, the lidar has been used to produce three-dimensional images of hard targets out to a range of approximately 2 km with near-diffraction-limited angular resolution and submeter range resolution.

Heterodyne measurements of laser light scattering by a turbulent phase screen.

We report experiments in which a fiber-coupled heterodyne laser system operating at a wavelength of 1.5 microm is used to measure the phase fluctuations induced on a laser beam by passage through a thin layer of turbulent air and subsequent propagation through free space. We investigate the statistical properties and power spectra of the phase and its rate of change, in addition to the intensity statistics. We find that the power spectrum of the rate of change of phase has a simple negative exponential form. We discuss our results in the context of the problem of detection of phase variations over an extended turbulent atmospheric path.

Lidar frequency modulation vibrometry in the presence of speckle.

We report laboratory target vibration measurements that use an easily aligned and adjusted fiber-based 1.5-microm heterodyne lidar. The targets are simple spherically curved retroreflectors with well-controlled vibration frequencies and amplitudes. A rotating ground-glass screen creates Gaussian speckle. We wish to understand the modulated and fast-fading lidar returns seen from real target. We frequency demodulated the recorded laboratory data by phase differencing to provide estimates of dphi/dt, where phi is the phase of the received carrier-plus-noise phasor. Experimental results for signal strength and signal-to-noise ratio, for specific target modulation parameters, agree well with our recently developed dphi/dt correlation-function theory.

Dual-channel heterodyne measurements of atmospheric phase fluctuations.

A dual-channel fiber-coupled laser heterodyne system operating at a 1.55-microm wavelength is used to investigate phase fluctuations induced on a laser beam by propagation through turbulent air. Two receivers are used to characterize spatial and temporal variations produced by a turbulent layer of air in the laboratory. The system is also used for measurements through extended turbulence along an 80-m outdoor atmospheric path. Phase structure functions, power spectral densities, and cross correlations are presented.