A stable single-carrier optical spring, comprising a pair of dielectric mirrors, each having a dielectric coating, and positioned to form a standing wave from an incident optic field. The dielectric coating has a plurality of layers, where at least the first layer is sized to be an odd multiple of half a wavelength of the laser beam, to feature an opposite-sign photo-thermal effect due to the detailed interaction of the optical field with the coating. This results in an opposite-sign photo-thermal effect at the optical spring frequency. The dampening effect is large enough to stabilize the radiation pressure based optical spring, resulting in a statically and dynamically stable optical spring. As a result this coating allows stable locking of a cavity with a single laser frequency using radiation pressure feedback.

A system method and computer-readable medium for correcting measurements obtained by a down hole tool for residual measurement errors is disclosed. A down hole tool having at least two directional field sensors is disposed in a borehole. The at least two directional sensors are substantially orthogonal to each other and to a longitudinal axis of the down hole tool. Measurements are obtained from the at least two directional sensors during rotation of the tool by at least 360 degrees around the longitudinal axis of the tool. Residual measurement errors are determined for the obtained measurements, and a quality level of the determined residual measurement errors selected. The determined residual measurement errors are applied to the obtained measurements when the determined residual measurement errors are consistent with the selected quality level. In various embodiments, the residual measurement errors are reduced from a first value that does not match the selected quality level to a second value that are consistent with the selected quality level.

An acceleration measuring device is disclosed, for use as a gravimeter or gradiometer for example. The device has a support and a proof mass, connected to each other by at flexures allowing displacement of the proof mass relative to the support. The support defines a space for displacement of the proof mass. The device is configured so that the modulus of the gradient of the force-displacement curve of the proof mass decreases with increasing displacement, for at least part of the force-displacement curve. This is the so-called anti-spring effect. The resonant frequency of oscillation of the proof mass is determined at least in part by the orientation of the device relative to the direction of the force due to gravity. The proof mass is capable of oscillating with a resonant frequency of 10 Hz or less. The proof mass has a mass of less than 1 gram.

An airborne gravity-based transducer is disclosed as two embodiments with similar physical structures but different operating principles. The first design includes a particle acting as an active interface characterized by internal vibrations relating to its de Broglie wave, a resonant cavity for trapping the particle, and a phonon-wave source wherein the de Broglie and phonon waves interact over a junction area. In the second design, mechanical displacements between the transducer elements can be monitored through electromechanical transduction. Both designs include a power source and a biasing circuit for producing an electrical current across the junction, and a sensing system for measuring voltage. Both designs are capable of cancelling slowly-varying gravitational acceleration due to dynamic interaction in motion with the gravitational field and responding to small-scale gravity anomalies. The transducer can be utilized in hydrocarbon exploration to provide information on areas conducive to fluid entrapment in the sedimentary column.

A gravimeter or inertial sensor system and method of operating such a system is provided. The system comprises a variable frequency signal source (100, 101, 102) configured to provide first and second signals, a resonant sensor (103) connected to receive the first signal, a phase comparator (111) connected to the output of the resonant sensor and to receive the second signal, and a controller (114) connected to the phase comparator. In a first mode, the controller controls the desired frequency of the signals from the variable frequency signal source based on a value of the phase comparator output signal to lock the frequency of the input signals to a resonant frequency of the resonant sensor. In a second mode, the controller disconnects from the variable frequency signal source and records an open loop output signal indicative of the physical parameter to be measured based on the response of the resonant sensor.

The application discloses an atom interferometer comprising an optical cavity and method of operation thereof. The atom interferometer includes a vacuum chamber, an optical cavity, a source for providing a cloud of atoms in the optical cavity in use, and one or more light sources. The one or more light sources are for generating, in the cavity, in use a first light beam having a first polarisation and at a first frequency for a two-photon interaction in the atoms; and a counterpropagating second light beam having a second polarisation orthogonal to the first polarisation and at a second frequency for the two-photon interaction in the atoms. The atom interferometer also includes an electro-optic element arranged in the cavity to be operable to simultaneously change: the resonant frequency of the cavity for light in the first polarisation to track changes in the frequency of the first light beam to compensate for the doppler shift of the falling atoms in use; and the resonant frequency of the cavity for light in the second polarisation to track changes in frequency of the counterpropagating second light beam to compensate for the doppler shift of the falling atoms in use.

A method and apparatus for for sensing a change in an acceleration gradient δa(t) between two gravity fields a.sub.1(t) and a.sub.2(t) respectively sensed by the first and second proof masses, the first and second proof masses either being coupled only to a first resonator or being individually coupled to first and second resonators, the first resonator generating, in use, a signal at a frequency f.sub.D which is applied said second resonator, the second resonator being driven, in use, into a non-linear state corresponding to a modal resonant frequency f.sub.Θ wherein it generates a comb of frequencies each tooth of which is separated from each other by a frequency Δ which is frequency-wise proportional a frequency difference between f.sub.D and f.sub.Θ and also proportional to the change in said acceleration gradient δa(t), circuitry for selecting an n.sup.th tooth in said comb of frequencies where the frequency of the n.sup.th tooth is equal to f.sub.D+nΔ, circuitry for detecting a change in the frequency of the n.sup.th tooth and for generating a signal that is proportional to n times the change in an acceleration gradient δa(t).

A sensing element (10) for an intrinsic gravity gradiometer (IGG) for use in sensing variation in a gravity field at a location. The sensing element (10) is flexible, elongate and has unfixed opposed ends (12, 14) when part of the gravity gradiometer. The sensing element can be a metallic ribbon, and can be mounted by a number e.g. 3 or 5, pivot points or axes 30-40 at each of the opposed sides along the sensing element, with the opposed ends of the sensing element free to move. The pivot points or axes can include pins, preferably cylindrical pins (48) or the sensing element may be etched within the side wall and remain joined to the remainder of the side wall by connections. The sensing element (10) can form part of one or more resonant cavities or wave guide (44, 52-66), such as a side or dividing wall (46) or part thereof. A dual phase bridge (61,612) arrangement can be provided. Electrical current (I) can be injected into the sensing element. Feed forward motion compensation (MC or FFMC) can be applied as part of the determination of the current. Applying electrical current into the opposed longitudinal sides (20, 22), such as right and left sides, of the sensing element, such as a ribbon, can be used for several types of compensation. Displacement of the sensing element can be detected by a resonant cavity, electromagnetic sensor or optical sensor.

An acceleration measuring device is disclosed, for use as a gravimeter or gradiometer for example. The device has a support and a proof mass, connected to each other by at flexures allowing displacement of the proof mass relative to the support. The support defines a space for displacement of the proof mass. The device is configured so that the modulus of the gradient of the force-displacement curve of the proof mass decreases with increasing displacement, for at least part of the force-displacement curve. This is the so-called anti-spring effect. The resonant frequency of oscillation of the proof mass is determined at least in part by the orientation of the device relative to the direction of the force due to gravity. The proof mass is capable of oscillating with a resonant frequency of 10 Hz or less. The proof mass has a mass of less than 1 gram.

Example gravity gradiometers are described that utilize high precision resonant optical cavities to measure changes in gravitational forces at high sensitivities. In one example, a sensing system includes a gravity gradiometer and a controller. The gravity gradiometer includes a first mirror and a second mirror arranged to form an optical cavity having an optical axis. The controller is configured to detect, responsive to displacement of at least one of the first mirror and the second mirror along the optical axis, a change in gravity gradient.