Beam Interferometer Research Articles

Bayesian modelling of multiple plasma diagnostics at Wendelstein 7-X

Abstract Inference of electron density and temperature has been performed using multiple, diverse sets of plasma diagnostic data at Wendelstein 7-X. Predictive models for the interferometer, Thomson scattering and helium beam emission spectroscopy (He-BES) systems have been developed within the Minerva framework and integrated into a unified model. Electron density and temperature profiles are modelled using Gaussian processes. Calibration factors for the Thomson scattering system and predictive uncertainties are considered as additional unknown parameters. The joint posterior probability distribution for the electron density and temperature profiles as well as Gaussian process hyperparameters and model parameters is explored through a Markov chain Monte Carlo algorithm. Samples from this distribution are numerically marginalised over the hyperparameters and model parameters to yield marginal posterior distributions for the electron density and temperature profiles. The profile inferences incorporate various data combinations from the interferometer and Thomson scattering as well as constraints at the limiter/divertor positions through virtual observations or edge data from He-BES. Additionally, the integration of x-ray imaging crystal spectrometer data into the model for ion temperature profiles is presented. All profiles presented in this study are inferred with optimally selected hyperparameters and model parameters by exploring the joint posterior distribution, inherently applying Bayesian Occam’s razor.

Micro-displacement measurement of optical interference with two-ring conjugated vortices

In this paper, we propose a two-ring conjugated vortex beam interferometer. The inner ring and outer ring of the vortex beams has different signs and topological charges. When combined, they produce an intricate pattern of interference fringes that resemble a flower petal, featuring both concentric inner and outer rings which rotates with different directions. We use the scale-invariant feature transformation algorithm to find the feature points. Then we use these points to measure the rotation angle of the outer ring relative to the inner ring and calculate the displacement based on it. We realize the measurement of sub-nanometer displacement. The displacement resolution is 0.38° nm−1. It is improved by about 12.55% compared with only the inner ring. The displacement corresponding to the minimum detectable angle of CCD is reduced from 0.080 nm to 0.060 nm. It will be a promising method in precision machining micro-vibration sensing, surface unevenness sensing, and microbial movement sensing and high-precision measurement of micro-displacement.

Matter-wave collimation to picokelvin energies with scattering length and potential shape control

The sensitivity of atom interferometers depends on their ability to realize long pulse separation times and prevent loss of contrast by limiting the expansion of the atomic ensemble within the interferometer beam through matter-wave collimation. Here we investigate the impact of atomic interactions on collimation by applying a lensing protocol to a 39K Bose-Einstein condensate at different scattering lengths. Tailoring interactions, we measure energies corresponding to (340 ± 12) pK in one direction. Our results are supported by an accurate simulation, which allows us to extrapolate a 2D ballistic expansion energy of (438 ± 77) pK. Based on our findings we propose an advanced scenario, which enables 3D expansion energies below 16 pK by implementing an additional pulsed delta-kick. Our results pave the way to realize ensembles with more than 1 × 105 atoms and 3D energies in the two-digit pK range in typical dipole trap setups without the need for micro-gravity or long baseline environments.

Design of optical telescopes for laser field wavefront reconstruction in gravitational-wave detectors

Pick-off beams in Interferometric Gravitational Wave Detectors are often used to derive information on the field circulating in the interferometer. In order to retrieve the wavefront of the field at some chosen location, an optical system has to be deployed so to image the desired field characteristics to an optical bench and ultimately to suitable sensors. In this paper, we detail the requirements in terms of Gouy Phase and ABCD matrix for such an optical system to provide the correct information. We show also that by designing the optical system with adequate Gouy Phase evolution, the same kind of transformation holds true not only for the fundamental Gaussian mode, but also for both even and odd Higher Order Modes (HOMs) of the main interferometer beam. This is important because these HOMs are excited by the aberrations of the optical elements in the interferometer, and carry the information one is interested to. Simulations with two tools (Finesse and Zemax OpticsStudio®) are provided to confirm the analytical results obtained using Gaussian modes expansion of a generic field.

A self-referenced interferometer for in situ cryogenic wafer curvature measurements.

A self-referenced interferometer to measure time-varying curvature in mechanically unstable environments is needed in many applications. One application that demands this measurement technique with fast data acquisition, 2D sensitivity, and insensitivity to vibration is the measurement of thermal strain in thin films in operational environments. The diverging beam interferometer described here demonstrates an angular sensitivity to the local curvature using interferograms captured by a CMOS camera. Two-dimensional Fourier analysis is used to extract curvature changes. The interferometer demonstrates an experimental sensitivity to curvature changes on the order of 10-4 m-1 and is used to measure thermal stresses in a cryogenic environment of a polycrystalline titanium nitride thin film on a silicon wafer that exhibits anisotropic curvature.

Collimating three-axicon zoom system for interferometric Bessel beam side lobe cancellation

Optical Bessel beams are used in numerous applications like fluorescence microscopy, material processing and optical trapping. These applications require Bessel beams having a central core with defined full width at half maximum and a defined axial length. Often, the side lobes of Bessel beams, which are associated with their non-diffracting properties, can interfere with the experimental process. We theoretically describe and practically verify the performance of a new refractive optical system to generate zoomable annular ring intensities. The ability to zoom the output ring diameter allows for flexibly choosing the Bessel beam parameters. Secondly, we introduce the use of a Michelson interferometer for destructively interfering Bessel beam side lobes in one direction. If two Bessel beams of zeroth order and first kind are coherently superposed with a small shift with respect to each other, their side lobes are enhanced in one direction and cancelled in the other direction. We suggest that applications like light-sheet microscopy can exploit the axis of destructive interference to improve their contrast.

Cepstrum-based interferometric microscopy (CIM) for quantitative phase imaging

A universal methodology for coding-decoding the complex amplitude field of an imaged sample in coherent microscopy is presented, where no restrictions on any of the two interferometric beams are required. Thus, the imaging beam can be overlapped with, in general, any other complex amplitude distribution and, in particular, with a coherent and shifted version of itself considering two orthogonal directions. The complex field values are retrieved by a novel Cepstrum-based algorithm, named as Spatial-Shifting Cepstrum (SSC), based on a weighted subtraction of the Cepstrum transform in the cross-correlation term of the object field spectrum in addition with the generation of a complex pupil from the combination of the information retrieved from different holographic recordings (one in horizontal and one in vertical direction) where one of the interferometric beams is shifted 1 pixel. As a result, the field of view is tripled since the complex amplitudes of the three interferometric fields involved in the process are retrieved. Proof-of-concept validation of this methodology, named as Cepstrum-based Interferometric Microscopy (CIM), is provided considering an off-axis holographic configuration for retrieving the cross-correlation of the two interferometric complex amplitude fields in a compact quasi-common path Michelson interferometric configuration. Experimental results for different types of phase samples (resolution test targets for step-by-step calibration and demonstration as well as fixed biosamples) are included.

Coriolis force compensation and laser beam delivery for 100-m baseline atom interferometry

The Coriolis force is a significant source of systematic phase errors and dephasing in atom interferometry and is often compensated by counter-rotating the interferometry laser beam against Earth's rotation. We present a novel method for performing Coriolis force compensation for long-baseline atom interferometry, which mitigates atom-beam misalignment due to beam rotation, an effect which is magnified by the long lever arm of the baseline length. The method involves adjustment of the angle of the interferometer beam prior to a magnifying telescope, enabling the beam to pivot around a tunable position along the interferometer baseline. By tuning the initial atom kinematics and adjusting the angle with which the interferometer beam pivots about this point, we can ensure that the atoms align with the center of the beam during the atom optics laser pulses. This approach will be used in the MAGIS-100 atom interferometer and could also be applied to other long-baseline atom interferometers. An additional challenge associated with long baseline interferometry is that since long-baseline atom interferometers are often located outside of typical laboratory environments, facilities constraints may require lasers to be housed in a climate-controlled room a significant distance away from the main experiment. Nonlinear effects in optical fibers restrict the use of fiber-based transport of the high-power interferometry beam from the laser room to the experiment. We present the design of and prototype data from a laser transport system for MAGIS-100 that maintains robustness against alignment drifts despite the absence of a long fiber.

High-dimensional inference of radio interferometer beam patterns I: parametric model of the HERA beams

ABSTRACT Accurate modelling of the primary beam is an important but difficult task in radio astronomy. For high dynamic range problems such as 21 cm intensity mapping, small modelling errors in the sidelobes, and spectral structure of the beams can translate into significant systematic errors. Realistic beams exhibit complex spatial and spectral structure, presenting a major challenge for beam measurement and calibration methods. In this paper series, we present a Bayesian framework to infer per-element beam patterns from the interferometric visibilities for large arrays with complex beam structure, assuming a particular (but potentially uncertain) sky model and calibration solution. In this first paper, we develop a compact basis for the beam so that the Bayesian computation is tractable with high-dimensional sampling methods. We use the Hydrogen Epoch of Reionization Array (HERA) as an example, verifying that the basis is capable of describing its single-element E-field beam (i.e. without considering array effects like mutual coupling) with a relatively small number of coefficients. We find that 32 coefficients per feed, incident polarization, and frequency, are sufficient to give percent-level and $\sim$10 per cent errors in the mainlobe and sidelobes, respectively, for the current HERA Vivaldi feeds, improving to $\sim 0.1{{\ \rm per\ cent}}$ and $\sim 1{{\ \rm per\ cent}}$ for 128 coefficients.

Hollow-conical atomic beam from a low-velocity intense source.

We demonstrate, for the first time, a hollow-conical atomic beam from a standard low-velocity intense source. Experimental results and numerical simulations indicate that the hollow-conical feature is caused by the converging-diverging extraction process. The degree of hollowness can be reduced by using a weaker push beam and extending the length of transverse cooling. Analytical models are proposed to quantitatively describe the hollowness of the atomic beam. This study can find applications where a compact and solid atomic beam is needed, such as coupling cold atoms into matter waveguides or continuous cold atomic beam interferometers.

High Stability Dual Beam Interferometer Sensor for Non-contact Photoacoustic Imaging

As a non-contact photoacoustic sensor, the reflector of one arm of dual beam interferometer sensor is usually composed of the upper surface of the ultrasonic coupling liquid coated on the surface of the sample. The vibration of the outside and the scanning motor cause the liquid level to shake, causing the reflected probe light path to deviate from the incident light path, which then reduces the detection stability of the sensor. In view of the above problems, a novel high stability dual beam interferometer sensor is introduced in this paper, in which the reflected probe light is derived from the original optical path by using the combination of PBS and quarter wave plate, and the reflected probe light is coupled into 50/50 beam splitting fibre by using aspheric mirror group. The influence of the radius and focal length of each aspheric mirror and the numerical aperture of the optical fibre on the detection stability of the sensor is theoretically analyzed. The results show that the structural design greatly reduces the effect of the vibration of the outside and the scanning motor on the detection stability of the sensor, and provides a theoretical basis for the development and performance optimization of the sensor.

Shock state distributions in porous tantalum and characterization with multipoint velocimetry

Heterogenous materials under shock compression can be expected to reach different shock states throughout the material according to local differences in microstructure and the history of wave propagation. Here, a compact, multiple-beam focusing optic assembly is used with high-speed velocimetry to interrogate the shock response of porous tantalum films prepared through thermal-spray deposition. The distribution of particle velocities across a shocked interface is compared to results obtained using a set of defocused interferometric beams that sampled the shock response over larger areas. The two methods produced velocity distributions along the shock plateau with the same mean, while a larger variance was measured with narrower beams. The finding was replicated using three-dimensional, mesoscopically resolved hydrodynamics simulations of solid tantalum with a pore structure mimicking statistical attributes of the material and accounting for radial divergence of the beams, with agreement across several impact velocities. Accounting for pore morphology in the simulations was found to be necessary for replicating the rise time of the shock plateau. The validated simulations were then used to show that while the average velocity along the shock plateau could be determined accurately with only a few interferometric beams, accurately determining the width of the velocity distribution, which here was approximately Gaussian, required a beam dimension much smaller than the spatial correlation lengthscale of the velocity field, here by a factor of ∼30×, with implications for the study of other porous materials.

Retrace error calibration for interferometric measurements using an unknown optical system.

In classical interferometric null test measurements, the measurement and reference beam path should be the same. A difference in the beam paths results in the so called retrace error. One very common approach to avoid retrace errors is to adapt the measurement wavefront to the reference wavefront with a computer generated hologram (CGH), which is costly and time consuming. A much more flexible approach is to do non nulltest measurement in combination with mathematical treatment of retrace errors. Most of such methods are based on iterative optimization or calibration of the nominal optical design of the interferometer. While this may be a convenient solution in the context of research, the more common use may be limited due to the need of the optical design of all interferometer components. In many cases, the optical designs of standard off the shelf optical assemblies are not available or disclosed by the manufacturer. This is especially true for transmission spheres of interferometers. We introduce the so called Black Box Model (BBM), used in the well known Tilted Wave Interferometry (TWI), as a mathematical model to account for retrace errors in interferometry. The Black Box Model is based on point characteristic functions which are adapted to the result and behavior of a real interferometer by calibration. With an extended calibration method, the need of a specific optical design of the interferometer is no longer necessary. Thus the method is attractive for a wide field of use in interferometry with standard off the shelf components.

Arbitrary Achromatic Polarization Control with Reconfigurable Metasurface Systems

AbstractDynamic control over the polarization state of light is foundational for many scientific and technological applications, yet it remains a challenge to dynamically tailor responses with arbitrary polarization bases over a broad bandwidth. Broadband metasurface systems that utilize microscale displacements between two metasurfaces to enable reconfigurable polarization responses within a predefined polarization basis are reported. The metasurface pairs form an interferometer, and the lateral displacements produce detour phase shifts within the interferometer beam paths that mediate polarization state tuning. It is shown how the metasurface systems can be designed using freeform topology optimization to enable tailorable elliptical birefringence responses over a large bandwidth and how cascaded metasurface systems can enable the mapping of input and output polarization states between any two points on the Poincare sphere. It is anticipated that these concepts will have utility in imaging, display, communications, and metrology applications in classical and quantum optical domains.

Dynamic non-uniform phase shift measurement via Doppler frequency shift in vortex interferometer.

A vortex beam interferometer based on Doppler frequency shift is proposed to retrieve the dynamic non-uniform phase shift from the petal-like fringes produced by the coaxial superposition of high-order conjugated Laguerre-Gaussian modes. Unlike the uniform phase shift measurement in which the petal-like fringes rotate as a whole, the fringes due to the dynamic non-uniform phase shift rotate at different angles at different radii, resulting in highly twisted and stretched petals; this hinders rotation angle identification and phase retrieval via image morphological operation. To address the problem, a rotating chopper combined with a collecting lens and a point photodetector are placed at the exit of the vortex interferometer to introduce a carrier frequency in the absence of the phase shift. Once the phase starts to shift non-uniformly, the petals at different radii generate different Doppler frequency shifts, owing to their different rotation velocities. Thus, identification of spectral peaks near the carrier frequency immediately indicates the rotation velocities of the petals and the phase shifts at those radii. The results verified a relative error of phase shift measurement to be within 2.2% at the surface deformation velocities of 1, 0.5, and 0.2 µm/s. The method manifests itself to have potential in exploiting mechanical and thermophysical dynamics from the nanometer to micrometer scale.

The Next Generation Heterodyne Laser Interferometer in Joule Balance

In the joule balance, it is important to measure the relative displacement between the exciting magnet and the suspended coil. So we have designed and applied a compact dual-axis heterodyne interferometer, which is vacuum compatible, and have been carefully aligned for dual parallel measurement arms. However, with the wear of the linear translation stage and the coupling of 3-axis relative displacement locking, the periodic nonlinearity error may drift during the displacement measurement of joule balance, and so the performance of the existing laser interferometer system is not so stable. In order to solve this problem, in this paper, we have designed and employed a new heterodyne interferometer based on spatially separated beams (SPB) to restrain the periodic nonlinearity error caused by the double-frequency mixing. As to this SPB heterodyne interferometer, the input and output (I/O) beams can share the same optical space, which will contribute a lot to a compact structure in the joule balance. Meanwhile, the spatial attitude of interferometer is precisely controlled to restrain the error caused by ghost reflections. The experimental result shows the validation of this SPB heterodyne interferometer for the displacement measurement in the joule balance.

A 3D Passive Laser Tracker for Accuracy Calibration of Robots

Laser trackers are usually used to measure spatial positional error of the moving targets on large-scaled objects, such as the airplane profile. It is a spherical coordinate system with a dual-axis tracking mirror actively controlled by the built-in servo system to direct the laser interferometer beam always toward the reflecting target. It is very expansive when used in testing the spatial positional accuracy of industrial robots, which are rapidly growing for factory automation in recent years. Therefore, simplified from the laser tracker structure, a 3D passive laser tracker (3DPLT) for measuring spatial trajectory of a moving target is proposed. It is composed of a 2D rotary stage and a linear telescopic mechanism with an end-ball, which can be magnetically sucked by the moving target. The rotational angles of the 2D rotary stage are measured by two respective encoders, and the radial displacement of the telescopic mechanism is detected by an equipped laser interferometer. The world coordinate of the target can be obtained by the coordinate transformation from the spherical measuring system of 3DPLT. Multibody system error modeling is used to analyze the measurement error of the instrument, and testing methods of the main error sources are also proposed. After accuracy calibration and error compensation, the measurement error of the 3DPLT is 49.2 μm, which is good enough to calibrate the spatial trajectory error of the robot.

From concept to reality: computing visual vortex beam interferometer for displacement measurement.

In addition to the concept of picometer resolution, we discuss macro displacement measurement with a vortex beam interferometer. Three factors limiting large displacement measurement are resolved. Small topological charge numbers promise both high sensitivity and large displacement measurements. With a computing visual method, a virtual moiré pointer image immune to beam misalignment is proposed to calculate displacements. Interestingly, the absolute benchmark is found for cycle counting in the moiré pointer image of fractional topological charge. The vortex beam interferometer would not stop at the tiny displacement measurement in simulations. We report experimental measurements of nanoscale to hundred millimeter displacement in a vortex beam displacement measurement interferometer (DMI) for the first time, to the best of our knowledge.

Even sampling photonic-integrated interferometric array for synthetic aperture imaging.

To improve the effectiveness of spatial spectrum sampling for the photonic-integrated interferometric imaging, an array forming scheme is proposed with evenly distributed interferometric baselines, which is referred to as the even sampling photonic-integrated interferometric array (ESPIA). The subaperture array of ESPIA is configured as equi-spaced concentric rings. The subaperture beams are coupled and transmitted to the photonic integrated circuit through fiber optic channels and paired into baselines by the interferometric beam combination. The characteristics of ESPIA are analyzed with the discrete modulation transfer function (D-MTF) and multi-resolution mutual information (MR-MI). The simulation results show that it can realize the even sampling coverage of spatial spectrum effectively. With the same scale of synthetic aperture and subaperture array, it can also improve the capabilities of information acquisition for the interferometric array.

High-Accuracy Online Calibration Scheme for Large-Scale Integrated Photonic Interferometric Measurements

High-accuracy interferometric measurement is crucial for integrated photonic interferometric imaging. In this paper, we propose an online calibration approach for large-scale integrated photonic beam combination that can realize high-accuracy measurement. By leveraging a simple four-step switching condition and the optical path differences between interferometric beams, the instrumental characteristics of the beam combiner, including the transmittances, visibilities, and phase relations, could be calibrated accurately. Compared to the conventional approach, the calibration procedure and estimation method are greatly simplified in our proposed scheme. The effectiveness of the proposed approach is validated using a photonic integrated circuit with two interferometric channels. The calibration results show that the differences between the phase relations are less than 1.41% between the proposed and conventional approaches. The proposed scheme shows significant advantages in optical synthetic aperture imaging systems using photonic integrated circuits especially for applications in harsh environments.