Interferometric Precision Research Articles

Atom interferometry at arbitrary orientations and rotation rates

The exquisite precision of atom interferometers has sparked the interest of a large community for uses ranging from fundamental physics to geodesy and inertial navigation. However, their implementation for onboard applications is still limited, not least because rotation and acceleration are intertwined in a single phase shift, which makes the extraction of a useful signal more challenging. Moreover, the spatial separation of the wave packets due to rotations leads to a loss of signal. We present an atom interferometer operating over a large range of random angles, rotation rates and accelerations. A model of the expected phase shift allows us to untangle the rotation and acceleration signals. We also implement a real-time compensation system using fiber-optic gyroscopes and a rotating reference mirror to maintain the full contrast of the interferometer. We demonstrate a single-shot sensitivity to acceleration of 24 μg for rotation rates reaching 14° s−1.

Nonlinear polarization holography of nanoscale iridium films

Attosecond nonlinear polarization spectroscopy designates the subcycle-precise retrieval of the electric field of a femtosecond laser pulse together with the nonlinear polarization response that the laser pulse triggers in a sample. Here, we introduce a method that is all-optical and applicable to metal films. The method is called nonlinear polarization holography because it is based on the comparison of two time-domain holograms with and without a metal film on a substrate. The working principle can be understood as the time-domain analog of holographic interferometry, in which the comparison of two spatial holograms reveals changes in an object’s size and position with interferometric precision (i.e. to fractions of the wavelength). Analogously, nonlinear polarization holography provides subcycle precision (i.e. to fractions of the optical period). Nonlinear polarization holography is used here to retrieve the time-domain nonlinear response of a nanoscale iridium film. Using density matrix calculations it is shown that the knowledge of the nonlinear response with subcycle precision allows distinguishing excitation and relaxation mechanisms of low-energetic electrons.

Phase Measurement Method Based on Digital Dual Frequency Comb for High-Precision High-Speed Heterodyne Interferometry

The heterodyne interferometer is widely used as a precise displacement sensor in ultraprecision processing. However, there is a trade-off between measurement speed and measurement precision in the existing interference signal processing methods. In this work, a novel phase measurement method based on digital dual frequency comb is proposed. The proposed method uses the intrinsic frequency comb signal and a narrowband low-pass filter to form a band-pass filter bank, which divides the broadband brought by high-speed movement into multiple narrow bands. The signal-to-noise ratio (SNR) is improved for phase calculation. In addition, two groups of intrinsic frequency comb signals are used simultaneously for phase measurement and the rotation of the output, preventing the inaccurate phase measurement of the input signal whose frequency is the average of two frequencies in the frequency comb signal. The heterodyne laser interferometer can maintain high precision at high measurement speed. The simulation results show that the precision of the proposed method is more than 50% higher than that of the phase-locked loop method. The experiment with a circuit board combined with 100 Msps sampling 16-bit A/D converter shows that the phase measurement precision of the input signal frequency in the bandwidth range of 2.5–37.5 MHz can reach 0.77 mrad, equivalent to the displacement measurement precision of the double-pass interferometer (19 pm) at a measurement speed of less than 2.77 m/s.

Digital speckle photography in the presence of displacement gradients

Digital speckle photography is a displacement field measurement method that employs laser speckles as surface markers. Since the approach requires only one reference image without a preparation of the sample and provides a fast, single-shot measurement with interferometric precision, the method is applied for in-process measurements in manufacturing engineering. Due to highly localized loads, higher-order displacement gradients occur in manufacturing processes and it is an open research question how these gradients affect the measurement errors of digital speckle photography. We simulate isotropic Gaussian surface topographies, apply a displacement field and then generate laser speckle patterns, which are evaluated with digital image correlation and subsequently the resulting random and systematic errors of the displacement field are analyzed. We found that the random error is proportional to the first-order displacement gradient and results from decorrelation of the laser speckles. The systematic error is mainly caused by the evaluation algorithm and is linearly dependent on the second-order gradient and the subset size. We evaluated in-process displacement measurements of laser hardening, grinding and single-tooth milling where we determined the relative error caused by displacement gradients to be below 2.5% based on the findings from the simulative study.

Interferometric Quantification of the Impact of Relative Humidity Variations on Cultural Heritage

It has been shown that Relative Humidity (RH) provokes dimensional displacement detectable directly from surfaces using holographic interferometry. RH variations constitute a physical environmental load that drives organic materials to a constant equilibrium cycle. This paper is a small synopsis of the interferometric research direction and a data acquisition on the detection of the dimensional impact of relative humidity on cultural heritage objects. Since RH cycling is unavoidable, the interferometric data change depends on the object structure and RH cycle characteristics. Based on the fact that each artwork is by construction unique, and on the observation that the effects of an RH cycle on the structural condition of any artwork are also unique but the preventive conservation strategies require generalised approaches and not on a case-by-case study, being introduced is a novel, universal, preventive deterioration methodology: “deformation threshold value” (DTV). DTV is assignable to each distinct object in order to control routinely its structural condition and prevent damage. DTV is not assigned hypothetically based on any assumed/expected reactions but from a monitored calibration of the artwork in its environment. Each artwork in its hosted environment has its unique reaction. The reaction, though, is not steady but changes as the artwork changes. DTV can be acquired routinely and valued accordingly to seasonal RH change. Monitoring the seasonal RH and seasonal dimensional reaction has been shown to correspond to a standard DTV pattern whose deviations violate the expected seasonal reaction. Through the interferometric monitoring of surface, the distinct DTV acts as a safeguard for the artwork. In this synopsis, some results of the generation of DTVs are shown. Our future plan is for the DTV numbers to serve as data inputs for preventive models to formulate a distinct risk index representative of each artwork condition and to be used as remote risk warning to prevent its deterioration. Based on the DTV concept, methods and instruments for sequential data acquisition aim to present experimental data outputs as DTVs that identify transient shape changes prior to visible damage have been developed. In this research, the starting point was the interferometric quantification of the displacement of well-characterized fresh samples. The fresh samples are known in terms of density, cut, thickness, moisture content, structural condition and are submitted to RH simulation cycles. Shown here are three exemplary cases: usual, abrupt and smooth. The interferometric monitoring following the cycles of RH is a long-term duration of several weeks; measurements are performed directly from the surface, and relative displacement (RD) from temporal measurements of interference fringes provide the required output data to calculate the rate of displacement (RoD) of the surface. Measuring the impact of RH directly from the artwork surface allows the detection of the temporal diversity of structural reactions to the same RH cycle for distinct artworks. The monitoring system uses interferometric precision provided by digital holographic speckle-pattern interferometry (DHSPI) placed on a specially designed climate chamber DHSPI monitoring workstation.

Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study

In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.

Two-Colour Spectrally Multimode Integrated SU(1,1) Interferometer

Multimode integrated interferometers have great potential for both spectral engineering and metrological applications. However, the material dispersion of integrated platforms constitutes an obstacle that limits the performance and precision of such interferometers. At the same time, two-colour nonlinear interferometers present an important tool for metrological applications, when measurements in a certain frequency range are difficult. In this manuscript, we theoretically developed and investigated an integrated multimode two-colour SU(1,1) interferometer operating in a supersensitive mode. By ensuring the proper design of the integrated platform, we suppressed the dispersion, thereby significantly increasing the visibility of the interference pattern. The use of a continuous wave pump laser provided the symmetry between the spectral shapes of the signal and idler photons concerning half the pump frequency, despite different photon colours. We demonstrate that such an interferometer overcomes the classical phase sensitivity limit for wide parametric gain ranges, when up to 3×104 photons are generated.

Determining the Three-Dimensional Position of an Atomic Cloud in an Atom Interferometer Using One Laser Beam

Accurately measuring the three-dimensional position of an atomic cloud is essential for improving the precision of atom interferometers. In the work presented here, the three-dimensional position of an atomic cloud in an atom interferometer is measured with only one laser beam, generated by a phase modulator. The vertical position is determined from the change in the additional-sideband effect with the time interval $T$ between adjacent Raman pulses in the atom interferometer. Based on this method, the vertical position of the atomic cloud is measured with an uncertainty of 0.2 mm; therefore, the uncertainty in a gravity measurement contributed by the gravity gradient is not limited by the uncertainty in the measurement of the vertical position at the level of $0.1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{Gal}$. Furthermore, a method of measuring Rabi oscillations at different horizontal positions to determine the horizontal position of the atomic cloud is proposed and is demonstrated experimentally. With this method, the horizontal position can be determined with an uncertainty of less than 0.1 mm, and the horizontal velocity of the atomic cloud can also be deduced. The methods demonstrated in this paper are helpful for evaluating systematic errors in atom interferometers, and also useful in precision measurements based on an atomic fountain.

Dynamic measurements at up to 130-kHz sampling rates using Ti:sapphire dual-comb distance metrology

By using fully-locked Ti:sapphire combs operating with repetition-frequencies of 513 MHz, we demonstrate high-speed dual-comb distance metrology with update rates up to 130 kHz, equivalent to a sampling interval of 7.7 µs. This measurement bandwidth is achieved by limiting detection to a wavelength range much less than the pulse bandwidth, enabling interferometric precision to be reached in a time of 2.6 ms and yielding a precision of 2 nm in 100 ms. The repetition frequency achieves an instantaneous non-ambiguity range of 29.2 cm, while the high sampling rate provides the ability to make dynamic measurements, which is demonstrated by using the system to directly sample audio waveforms by recording the displacement of a mirror mounted on a loudspeaker.

Determination of the refractive index profile and surface topography of optically smooth objects using interference of optical vortices

In this paper, we present the results of the propagational dynamics of vortex beams in the scope of their possible applications for interferometric non-contact robust and precision optical surface profilometry with nanoscale longitudinal resolution. The result of coaxial superposition of the reference plane wave with singly charged vortex beams represents a dynamically changing intensity distribution. The nature of this changes, namely, rotational effects of intensity zeros, allows to determine directly the optical path difference which is introduced by the surfaces and internal structure of test object. We have proposed the experimental setup for examination of reflecting and transmitting objects.

Digital holography in production: an overview

Many challenging measurement tasks in production simultaneously have high requirements for accuracy, measurement field size, lateral sampling, and measurement time. In this paper, we provide an overview of the current state of the art in digital holography for surface topography measurements and present three applications from completely different productions with no alternative to digital holography; we describe the HoloTop sensor family, which has been designed specifically for industrial use, and present the most recent results achieved in real-life industrial applications. All applications address measurement tasks that could not be solved until now, either by optical or tactile means. We start with a description of the first-ever inline integration of a digital holographic measurement system that inspects precision turned parts for the automotive industry. We proceed by presenting measurements performed with a compact sensor that can be placed inside a tooling machine and operated fully wirelessly. In this case, the tool holder was used to position the sensor directly. Integration into a tooling machine places high demands on both robustness and reliability. Finally, the quality control of electronic interconnectors such as microbumps with the highest demand for accuracy and repeatability is demonstrated. All of these applications illustrate the major advantages of digital holographic systems: it is possible to measure a relatively large field of view with interferometric precision and very short acquisition times. Additionally, both reflective and matt surfaces can be measured simultaneously. We end this publication with an assessment of the future potential of this technology and the necessary development steps involved.

A hyperspectral microscope based on an ultrastable common-path interferometer

We introduce a wide field hyperspectral microscope using the Fourier-transform approach. The interferometer is based on the translating-wedge-based identical pulses encoding system, a common-path birefringent interferometer which combines compactness, intrinsic interferometric delay precision, long-term stability, and insensitivity to vibrations. We describe two different implementations of our system, which maximize fringe visibility and phase invariance over the field of view, respectively. We also demonstrate that our system can be installed as an add-on in a commercial microscope. We show high-quality hyperspectral fluorescence microscopy from stained cells and powders of inorganic pigments in the spectral range from 400 to 1100 nm, proving that our device is suited to biology and materials science. We also introduce an acquisition method that synthesizes a tunable spectral filter, providing band-passed images with the measurement of only two maps.

Impact of Relative Humidity on Wood Sample: A Climate Chamber Experimental Simulation Monitored by Digital Holographic Speckle Pattern Interferometry.

Relative humidity (RH) changes are a natural environmental effect that forces organic materials to a constant cycle of achieving equilibrium. The present work is part of an ongoing research based on the hypothesis that the inevitable deleterious effects of the RH natural cycle may be prevented or minimized if a deformation threshold is assigned to each monitored endangered object prior to exposure to structural damage. In this paper the characterization of the behavior of a softwood sample (1.0 cm thick) submitted to RH abrupt cycles has been performed, in terms of mass and rate of displacement of the surface. The exemplary study is based on the concept of recording the RH impact directly from the material surface, allowing us to identify diversity in reaction with time, which in turn could determine the onset of structural changes prior to irreversible damage. The RH impact is measured as surface deformation from interference fringes, using a custom-made real time holography system with interferometric precision termed digital holographic speckle-pattern interferometry (DHSPI). The main observations presented here are a hysteresis in the dynamic sorption isotherm and a greater rate of displacement during the drying. A long-term experiment was performed to identify signs of ageing of the sample. The evolution of the mass and the rate of displacement stayed similar, an offset with an interesting behavior was observed and highlights ageing of wood. In order to produce a future preventive model for distinct art objects it is necessary to determine a deformation threshold for each material. In this context the study was planned to continue with organic samples bearing variable density and thickness under longer-term RH cycles and monitoring until the samples show visible signs of irreversible damage.

Improving precision of Mach-Zehnder interferometer with compensation employing weak measurement

Imperfections and environmental disturbances will unavoidably cause undesired deviations and bias in the output of devices deployed in the Mach–Zehnder interferometer. In particular, for a feedback scheme, the inevitable imperfections of the optical phase controller severely limit the final measurement precision. In this letter, we propose an approach making use of the well-known weak measurement technique for control operation in order to conquer the imperfections. In consequence, the practical measurement precision can be effectively improved. Interestingly, the improvement, which can be intense with a proper weak measurement, follows a small weak value instead of the common large one. In addition, a proof-of principle experiment is demonstrated to verify the effects of the proposed approach. We anticipate that our approach can be widely extended to many fields requiring high accuracy control.

Hyperspectral imaging with a TWINS birefringent interferometer.

We introduce a high-performance hyperspectral camera based on the Fourier-transform approach, where the two delayed images are generated by the Translating-Wedge-Based Identical Pulses eNcoding System (TWINS) [Opt. Lett. 37, 3027 (2012)], a common-path birefringent interferometer that combines compactness, intrinsic interferometric delay precision, long-term stability and insensitivity to vibrations. In our imaging system, TWINS is employed as a time-scanning interferometer and generates high-contrast interferograms at the single-pixel level. The camera exhibits high throughput and provides hyperspectral images with spectral background level of -30dB and resolution of 3 THz in the visible spectral range. We show high-quality spectral measurements of absolute reflectance, fluorescence and transmission of artistic objects with various lateral sizes.

Interferometric measurement of micro-g acceleration with levitated atoms

The sensitivity of atom interferometers is usually limited by the observation time of a free falling cloud of atoms in Earth’s gravitational field. Considerable efforts are currently made to increase this observation time, e.g. in fountain experiments, drop towers and in space. In this article, we experimentally study and discuss the use of magnetic levitation for interferometric precision measurements. We employ a Bose–Einstein condensate of cesium atoms with tuneable interaction and a Michelson interferometer scheme for the detection of micro-g acceleration. In addition, we demonstrate observation times of 1s, which are comparable to current drop-tower experiments, we study the curvature of our force field, and we observe the effects of a phase-shifting element in the interferometer paths.

Interferometric detection of 3D motion using computational subapertures in optical coherence tomography.

Doppler optical coherence tomography (OCT) quantifies axial motion with high precision, whereas lateral motion cannot be detected by a mere evaluation of phase changes. This problem was solved by the introduction of three-beam Doppler OCT, which, however, entails a high experimental effort. Here, we present the numerical analogue to this experimental approach. Phase-stable complex-valued OCT datasets, recorded with full-field swept-source OCT, are filtered in the Fourier domain to limit imaging to different computational subapertures. These are used to calculate all three components of the motion vector with interferometric precision. As known from conventional Doppler OCT for axial motion only, the achievable accuracy exceeds the actual imaging resolution by orders of magnitude in all three dimensions. The feasibility of this method is first demonstrated by quantifying micro-rotation of a scattering sample. Subsequently, a potential application is explored by recording the 3D motion vector field of tissue during laser photocoagulation in ex-vivo porcine retina.

Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms

Interferometry is a paradigm for most precision measurements. Using N uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), [Formula: see text], due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using M modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of [Formula: see text] dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.

Quantum-enhanced interferometry with cavity QED-generated non-classical light

We propose an enhanced optical interferometer based on tailored non-classical light generated by nonlinear dynamics and projective measurements in a three-level atom cavity QED system. A coherent state in the cavity becomes dynamically entangled with two ground states of the atom and is transformed to a macroscopic superposition state via a projective measurement on the atom. We show that the resulting highly non-classical state can improve interferometric precision measurements well beyond the shot-noise limit once combined with a classical laser pulse at the input of a Mach–Zehnder interferometer. For a practical implementation, we identify an efficient phase shift estimation scheme based on the counting of photons at the interferometer output. Photon losses and photon-counting errors deteriorate the interferometer sensitivity, but we demonstrate that it still can be significantly better than the shot-noise limit under realistic conditions.Graphical abstract

Fourier transform spectrometers for remote sensing of planetary atmospheres and surfaces

In planetary research, Fourier transform infrared spectrometers (FTIR) solve a number of important scientific goals related both to the atmosphere and to the surface sounding. For remote orbital measurements, these goals are the thermal sounding of the atmosphere using, in particular, the 15-µm CO2 band, sensitive detections of minor gaseous species and aerosol characterization. FTIR can address similar atmospheric science goals when observing from a planetary surface allowing for better-resolved boundary layer and achieving greater accuracy (longer integration) for minor species detection. For studies of planetary surfaces, characterization of mineralogical composition in a wide IR range including sensitive measurements of hydration of the soil on airless bodies can be done. We outline a family of FTIR instruments dedicated to studies of Mars and the Moon. TIRVIM is a channel of ACS on ExoMars TGO (in orbit around Mars since October 2016). It is a 2-inch interferometer for nadir and solar occultation measurements of Mars’ atmosphere. It covers a spectral range of 1.7–17 µm with spectral resolution up to 0.13 cm−1. LUMIS is a similar instrument for Luna-Resource Orbiter (Luna-26) Roscosmos mission dedicated to the search for hydration of the lunar regolith in the 6-µm band. The spectral range of LUMIS is broad (1.7–17 µm), but its sensitivity is optimized for the 4–8 µm region. The spectral resolution is 50 cm−1. We also describe recent developments focused on technical solutions for miniaturized FTIR instruments with a very high spectral resolution (0.05 cm−1 and higher). The prototype targets measurements of minor atmospheric species from the surface of Mars using the Sun tracking. One important task is to provide a high precision of interferometer’s mirror movement. Another task is the development of a precise two-coordinate mechanism to seek for and follow the Sun.