Conventional Interferometry Research Articles

Determination of effective parameters of fishnet metamaterials with vortex based interferometry.

Metamaterials are artificially engineered structures that have unique properties not usually found in natural materials, such as negative refractive index. Conventional interferometry or ellipsometry is generally used for characterizing the optical properties of metamaterials. Here, we report an alternative optical vortex based interferometric approach for the characterization of the effective parameters of optical metamaterials by directly measuring the transmission and reflection phase shifts from metamaterials according to the rotation of vortex spiral interference pattern. The fishnet metamaterials possessing positive, zero and negative refractive indices are characterized with the vortex based interferometry to precisely determine the complex values of effective permittivity, permeability, and refractive index. Our results will pave the way for the advancement of new spectroscopic and interferometric techniques to characterize optical metamaterials, metasurfaces, and nanostructured thin films in general.

Non-Common Band SAR Interferometry Via Compressive Sensing

To avoid decorrelation, conventional synthetic aperture radar interferometry (InSAR) requires that interferometric images should have a common spectral band and the same resolution after proper preprocessing. For a high-resolution (HR) image and a low-resolution (LR) one, the interferogram quality is limited by the LR one since the non-common band (NCB) between two images is usually discarded. In this article, we try to establish an InSAR method to improve interferogram quality by means of exploiting the NCB. To this end, we first define a new interferogram, which has the same resolution as the HR image. Then we formulate the interferometric relationship between the two images into a compressive sensing (CS) model, which contains the proposed HR interferogram. With the sparsity of interferogram in appropriate domains, we model the interferogram formation as a typical sparse recovery problem. Due to the speckle effect in coherent radar imaging, the sensing matrix of our CS model is inherently random. We theoretically prove that the sensing matrix satisfies restricted isometry property, and thus the interferogram recovery performance is guaranteed. Furthermore, we provide a fast interferogram formation algorithm by exploiting computationally efficient structures of the sensing matrix. Numerical experiments show that the proposed method provides better interferogram quality in the sense of reduced phase noise and obtain extrapolated interferogram spectra with respect to CB processing.

Improved reconstruction method for phase stepping data with stepping errors and dose fluctuations.

In conventional grating-based X-ray interferometry, it is necessary to repeatedly translate one of the gratings with high accuracy in regular submicron steps and to ensure a constant dose delivery during each step. However, stepping errors and dose fluctuations inevitably occur due to mechanical inaccuracies and/or thermal drift of the interferometer during the stepping process. As a result of these stepping errors and dose fluctuations, the standard reconstruction procedure without considering them causes artifacts in the images as stripes of specific frequencies. In this report, we propose an improved reconstruction method to process phase stepping data with stepping errors and dose fluctuations. The approach can be used to estimate the stepping errors and dose fluctuations, and reconstruct virtually artifact-free images. Based on numerical simulations and experimental data including stepping errors and dose fluctuations, we demonstrate that the proposed method is more effective to other previously reported approaches.

Simultaneous Measurement of dc and ac Magnetic Fields at the Heisenberg Limit

High-precision magnetic field measurement is an ubiquitous issue in physics and a critical task in metrology. Generally, magnetic field has DC and AC components and it is hard to extract both DC and AC components simultaneously. The conventional Ramsey interferometry can easily measure DC magnetic fields, while it becomes invalid for AC magnetic fields since the accumulated phases may average to zero. Here, we propose a scheme for simultaneous measurement of DC and AC magnetic fields by combining Ramsey interferometry and rapid periodic pulses. In our scheme, the interrogation stage is divided into two signal accumulation processes linked by a unitary operation. In the first process, only DC component contributes to the accumulated phase. In the second process, by applying multiple rapid periodic $\pi$ pulses, only the AC component gives rise to the accumulated phase. By selecting suitable input state and the unitary operations in interrogation and readout stages, and the DC and AC components can be extracted by population measurements. In particular, if the input state is a GHZ state and two interaction-based operations are applied during the interferometry, the measurement precisions of DC and AC magnetic fields can approach the Heisenberg limit simultaneously. Our scheme provides a feasible way to achieve Heisenberg-limited simultaneous measurement of DC and AC fields.

Crosstalk reduction for multi-channel optical phase metrology.

Digitally enhanced heterodyne interferometry (DEHI) combines the sub-wavelength displacement measurements of conventional laser interferometry with the multiplexing capabilities of spread-spectrum modulation techniques to discriminate between multiple electric fields at a single photodetector. Technologies that benefit from DEHI include optical phased arrays, which require the simultaneous phase measurement of a large number of electric fields. A consequence of measuring the phase of multiple electric fields is the introduction of crosstalk, which can degrade measurement precision. This work analytically and experimentally investigates the crosstalk when using DEHI to measure the phase of an arbitrarily large number of electric fields at a single photodetector. Also considered is the practical limit the dynamic range of the photodetector and shot noise imposes on the number of electric fields that can be discriminated. We describe how to minimize crosstalk by design. Experimental results demonstrate up to 55 dB suppression of crosstalk between two electric fields with a phase measurement bandwidth of 20 kHz and 1-10 pm/Hz displacement sensitivity for audio frequencies. Additionally, we demonstrate scaling of crosstalk proportional to the square-root of the number of electric fields when using an M-sequence modulation. Based on this analysis, we estimate that digitally enhanced heterodyne interferometry should be capable of measuring the phase of several hundreds of electric fields at a single photodetector while maintaining the same measurement bandwidth.

Integration of DInSAR and SBAS Techniques to Determine Mining-Related Deformations Using Sentinel-1 Data: The Case Study of Rydułtowy Mine in Poland

Underground coal exploitation often results in land-surface subsidence, the rate of which depends on geological characteristics, the mechanical properties of the rocks, and the applied extraction technology. Since mining-related subsidence is characterized by “fast” displacement and high nonlinearity, monitoring this process by using Interferometric Synthetic Aperture Radar (InSAR) is very challenging. The Small BAseline Subset (SBAS) approach needs to predefine an a priori deformation model to properly estimate an interferometric component related to displacements. As a consequence, there is a lack of distributed scatterers (DS) when the selected a priori deformation model deviates from the real deformation. The conventional differential SAR interferometry (DInSAR) approach does not have this limitation, since it does not need any deformation model. However, the accuracy of this technique is limited by factors related to spatial and temporal decorrelation, signal delays due to the atmospheric artifacts, and orbital or topographic errors. Therefore, this study presents the integration of DInSAR and SBAS techniques in order to leverage the advantages and overcome the disadvantages of both methods and to retrieve the complete deformation pattern over the investigated study area. The obtained results were evaluated internally and externally with leveling data. Results indicated that the Kriging-based integration method of DInSAR and SBAS can be effectively applied to monitor mining-related subsidence. The root-mean-square Error (RMSE) between modeled and measured deformation by InSAR was found to be 11 and 13 mm for vertical and horizontal displacements, respectively. Moreover, DInSAR technique as a cost-effective and complementary method to conventional geodetic techniques can be applied for effective monitoring fast mining subsidence. The minimum and maximum RMSE between DInSAR displacement and specific leveling profiles were found to be 0.9 and 3.2 cm, respectively. Since the SBAS processing failed in subsidence estimation in the area of maximum deformation rate, the deformation estimates outside the maximum rate could only be compared. In these areas, the good agreement between SBAS and DInSAR indicates that the SBAS technique could be reliable for monitoring the residual subsidence that surrounds the subsidence trough. Using the proposed approach, we detected subsidence of up to −1 m and planar displacements (east–west) of up to 0.24 m.

Double speckle pattern interferometric measurements for micro-angular displacement and the center of rotation

Double speckle pattern interferometry is presented for the measurement of in-plane rotation angle, sign, and center of rotation. The technique employs two conventional in-plane sensitive electronic speckle pattern interferometry systems combined with two-wavelength laser illumination and a phase-shifting method. Angular displacement of micro-rotation including the sign is determined from the wrapped phase difference, and the center of rotation is located by using wrapped phase difference maps related to two-directional displacement. The test setup is described and experimental results indicate that the system can provide angular displacement measurement with accuracy of 1.8 arcsec.

Double-slit interferometry as a lossy beam splitter

We cast diffraction-based interferometry in the framework of post-selected unitary description towards enabling it as a platform for quantum information processing (QIP). We express slit-diffraction as an infinite-dimensional transformation and truncate it to a finite-dimensional transfer matrix by post-selecting modes. Using such a framework with classical fields we show that a customized double-slit setup is effectively a lossy beam splitter in a post-selected sense. Diffraction optics provides a robust alternative to conventional multi-beam interferometry with scope for miniaturization, and also has applications in matter wave interferometry. In this work, the classical treatment of slit-diffraction sets the stage for quantization of fields and implementing higher-dimensional QIP like that done with other platforms such as orbital angular momentum.

Measured element phase-shifting interferometry with a single piezoelectric transducer and low-friction workbench

Moving a large-aperture reference mirror (RM) with a significant weight through piezoelectric transducers (PZTs) for phase-shifting introduces considerable challenges and potential problems in conventional reference mirror phase-shifting interferometry (RMPSI). In this report, we present measured element phase-shifting interferometry (MEPSI), which provides an alternative approach for RMPSI without the restrictions of both the aperture and weight of the RM. The proposed MEPSI actuates a low-friction workbench with an ME on board by single PZT to realize high-accuracy phase-shifting, which is not affected by the aperture or the RM weight of. On this basis, a tilt-shift immune phase-shifting algorithm is further applied to restrain the influence of residual tilt-shift errors and other possible error sources on the measuring accuracy. Theoretical analysis and preliminary experiments indicate that the proposed MEPSI can achieve the same level of accuracy as RMPSI and a ZYGO interferometer, and the repeatability of MEPSI, which is not affected by the weight of the ME, is superior to 0.002 λ (PV). MEPSI solves the problems of phase-shifting with large-aperture and heavy-weight RM, thereby providing a simple and feasible alternative approach for conventional RMPSI with the same level of accuracy and with no phase-shift calibration.

8-port homodyne detection of optical fields using IQ demodulation

A phase-sensitive detection scheme for optical fields is described, which allows for the simultaneous measurement of orthogonal field quadratures. The recent achievement of -radian cross-phase shifts between a single photon and a second light field has opened the door to quantum computing protocols which utilize photonic quantum bits. Optical phase measurements play an integral role in these schemes. The detection scheme presented here was designed to measure such transient phase shifts of a laser field as it interacts with another light field through a cloud of laser-cooled Rb atoms. In place of conventional spatial interferometry, which is very sensitive to mechanical instabilities, the scheme utilizes beat-note interferometry to improve on the robustness of the measurement. Beat-note interferometry serves to map a signal from a THz-frequency carrier onto a radio-frequency carrier. A variant of 8-port optical homodyne detection, the scheme then uses IQ demodulation, a well-established technique in communications engineering, to extract amplitude information for both the in-phase (I) and quadrature-phase (Q) components of the radio-frequency signal. This IQ data can then be used to extract any amplitude variation and/or phase shifts of the original THz-frequency optical field. The technique is illustrated here by simultaneously measuring the absorption and dispersion experienced by an optical beam as it passes through a cloud of laser-cooled atoms, which have been prepared in a state of electromagnetically-induced transparency. A thorough characterization of the measurement is presented, which identifies the dominant noise sources and illustrates the utility of IQ demodulation in eliminating noise. This scheme has been used to measure rad phase shifts on nanosecond time scales.

A New Single-Pass SAR Interferometry Technique with a Single-Antenna for Terrain Height Measurements

One of the prospective research topics in radar remote sensing technology is the methodology for designing an optimal radar system for high-precision two-dimensional and three-dimensional image acquisition of the Earth’s surface with minimal hardware requirements. In this study, we propose a single-pass interferometric synthetic aperture radar (SAR) imaging technique with only a single antenna for the estimation of the terrain height. This technique enabled us to obtain terrain height information in one flight of the carrier, on which only one receiving antenna was mounted. This single-antenna single-pass interferometry required a squint angle look geometry and additional image synthesis processing. The limiting accuracy of the terrain height measurement was approximately 1.5 times lower than that of the conventional two-pass mode and required a longer baseline than two-pass interferometry to have an equivalent accuracy performance. This imaging method could overcome the temporal decorrelation problem of two-pass interferometry due to a short time gap in the radar echo acquisitions during two sub-aperture intervals. We compared the accuracy performance of the terrain height measurements of our method with the conventional two-pass interferometry. This comparison was carried out at various spectral bandwidths, degrees of surface roughness, and baseline lengths. We validated our idea with numerical simulations of a digital elevation map, and showed real extracted data of the terrain heights in the Astrakhan and Volga regions of the Russian Federation, obtained from airborne SAR with our single-antenna single-pass interferometry technique.

Low-Coherence Interferometry Using Microwave Photonics for Multilayered Samples

A photonic structure is proposed by exploiting the advantages of the Microwave Photonics technology over conventional low coherence interferometry. The proposed scheme is based in the analysis of the interference pattern of an incoherent optical signal which is amplitude modulated and transmitted through a dispersive element. The strategic allocation of an interferometric structure combined with balanced photodetection are used to improve the system performance compared to the previous proposals. To the best of our knowledge, an exhaustive theoretical analysis and an experimental demonstration of the structure for multilayered samples are provided in this paper.

Differential interferometry of the rapid rotator Regulus

We analyse interferometric data obtained for Regulus with AMBER (Astronomical Multi- BEam combineR) at high spectral resolution ($\lambda/\delta\lambda \approx 12000$) across the Br$\gamma$ spectral line. The study of the photocentre displacement allows us to constrain a large number of stellar parameters -- equatorial radius $R_{\rm eq}$, equatorial velocity $V_{\rm eq}$, inclination $i$, rotation-axis position angle $PA_{\rm rot}$, and flattening -- with an estimation of gravity-darkening coefficient $\beta$ using previously published theoretical results. We use the Simulation Code of Interferometric-observations for ROtators and CirCumstellar Objects (SCIROCCO), a semi-analytical algorithm dedicated to fast rotators. We chose Regulus because it is a very well-known edge-on star, for which an alternative approach is needed to check the previously published results. Our analysis showed that a significant degeneracy of solution is present. By confronting the results obtained by differential interferometry with those obtained by conventional long-base interferometry, we obtain similar results (within the uncertainties), thereby validating our approach, where $V_{eq}$ and $i$ are found separately. From the photocentre displacement, we can independently deduce $PA_{rot}$. We use two minimization methods to restrict observed stellar parameters via a fast rotator model: a non-stochastic method ($\chi^2$ fit) and a stochastic one (Markov Chain Monte Carlo method), in order to check whether the correct global minimum is achieved particularly with respect to the degeneracies of the gravity darkening parameter $\beta$, where we demonstrate, using a quantitative analysis of parameters, that the estimate of $\beta$ is easier for stars with an inclination angle of around $45^\circ$.

Doppler synthetic aperture radar interferometry: a novel SAR interferometry for height mapping using ultra-narrowband waveforms

This paper introduces a new and novel radar interferometry based on Doppler synthetic aperture radar (Doppler-SAR) paradigm. Conventional SAR interferometry relies on wideband transmitted waveforms to obtain high range resolution. Topography of a surface is directly related to the range difference between two antennas configured at different positions. Doppler-SAR is a novel imaging modality that uses ultra-narrowband continuous waves (UNCW). It takes advantage of high resolution Doppler information provided by UNCWs to form high resolution SAR images.We introduce the theory of Doppler-SAR interferometry. We derive an interferometric phase model and develop the equations of height mapping. Unlike conventional SAR interferometry, we show that the topography of a scene is related to the difference in Doppler frequency between two antennas configured at different velocities. While the conventional SAR interferometry uses range, Doppler and Doppler due to interferometric phase in height mapping; Doppler-SAR interferometry uses Doppler, Doppler-rate and Doppler-rate due to interferometric phase in height mapping. We demonstrate our theory in numerical simulations.Doppler-SAR interferometry offers the advantages of long-range, robust, environmentally friendly operations; low-power, low-cost, lightweight systems suitable for low-payload platforms, such as micro-satellites; and passive applications using sources of opportunity transmitting UNCW.

Phase imaging by spatial wavefront sampling

Phase imaging techniques extract the optical path-length information of a scene, whereas wavefront sensors provide the shape of an optical wavefront. Since these two applications have different technical requirements, they have developed their own specific technology. Here we show how to perform phase imaging combining wavefront sampling using a reconfigurable spatial light modulator with a beam position detector. The result is a time-multiplexed detection scheme, capable of being shortened considerably by compressive sensing. This robust reference-less method does not require the phase unwrapping algorithms demanded by conventional interferometry, and its lenslet-free nature removes tradeoffs usually found in Shack-Hartmann sensors.

A novel plasmonic interferometry and the potential applications

Abstract In this article, we have proposed the plasmonic interferometry concept and analytical details given. By using the conventional optical interferometry, which can be simply calculated by using the relationship between the electric field and electron mobility, the interference mobility visibility (fringe visibility) can be observed. The surface plasmons in the sensing arm of the Michelson interferometer is constructed by the stacked layers of the silicon-graphene-gold, allows to characterize the spatial resolution of light beams in terms of the electron mobility down to 100-nm scales, with measured coherence lengths as low as ∼100 nm for an incident wavelength of 1550 nm. We have demonstrated a compact plasmonic interferometer that can apply to the electron mean free paths measurement, from which the precise determination can be used for the high-resolution mean free path measurement and sensing applications. This system provides the practical simulation device parameters that can be fabricated and tested by the experimental platform.

Interferometric enhancement for forward-looking synthetic aperture radar target imaging

We present a technique for interferometric processing of extreme high-squint synthetic aperture radar (SAR) target images. The technique is an improvement over conventional SAR interferometry, as it takes into account the change in relative phase between channels that occur as the radar moves through the synthetic aperture, which can be significant for forward-looking data acquisition geometry. We apply the technique to simulate data from a variety of imaging cases and show that, unlike the conventional interferometric technique, the proposed technique is robust to synthetic aperture length, scatterer elevation, and scatterer dimension in forward-looking scenarios. The technique may be used for various applications related to situational awareness, such as remote sensing for collision avoidance or forward-looking reconnaissance.

SAR-revealed slip partitioning on a bending fault plane for the 2014 Northern Nagano earthquake at the northern Itoigawa–Shizuoka tectonic line

By applying conventional cross-track synthetic aperture radar interferometry (InSAR) and multiple aperture InSAR techniques to ALOS-2 data acquired before and after the 2014 Northern Nagano, central Japan, earthquake, a three-dimensional ground displacement field has been successfully mapped. Crustal deformation is concentrated in and around the northern part of the Kamishiro Fault, which is the northernmost section of the Itoigawa-Shizuoka tectonic line. The full picture of the displacement field shows contraction in the northwest–southeast direction, but northeastward movement along the fault strike direction is prevalent in the northeast portion of the fault, which suggests that a strike-slip component is a significant part of the activity of this fault, in addition to a reverse faulting. Clear displacement discontinuities are recognized in the southern part of the source region, which falls just on the previously known Kamishiro Fault trace. We inverted the SAR and GNSS data to construct a slip distribution model; the preferred model of distributed slip on a two-plane fault surface shows a combination of reverse and left-lateral fault motions on a bending east-dipping fault surface with a dip of 30° in the shallow part and 50° in the deeper part. The hypocenter falls just on the estimated deeper fault plane where a left-lateral slip is inferred, whereas in the shallow part, a reverse slip is predominant, which causes surface ruptures on the ground. The slip partitioning may be accounted for by shear stress resulting from a reverse fault slip with left-lateral component at depth, for which a left-lateral slip is suppressed in the shallow part where the reverse slip is inferred. The slip distribution model with a bending fault surface, instead of a single fault plane, produces moment tensor solution with a non-double couple component, which is consistent with the seismically estimated mechanism.

SPR phase sensitivity enhancement in common-path polarization heterodyne interferometer by polarization tuning

In this work, we have theoretically investigated three designs of common-path polarization heterodyne interferometry (CPHI) with the possibility of to enhance the phase sensitivity and sensitivity-tunable ability. The schemes are established by utilizing some quarter wave plates (QWP) to control the ellipticity of polarization of light, and adjusting the azimuthal angle to achieve adequate phase sensitivity. The theoretical analysis has been done by Jones calculus and the results will be compared with conventional polarization heterodyne interferometry. The proposed designs have high phase sensitivity and sensitivity-tunable ability. Additionally it causes to shift the point of the extreme slope to the smaller incidence angle which usually is more convenient for SPR measurement. By the simulation, the phase sensitivity and resolving power of refractive index measurement has been estimated 5.5 × 105 °/RIU and 1.8 × 10−8 RIU, respectively.

Combination of Persistent Scatterer Interferometry and Single-Baseline Polarimetric Coherence Optimisation to Estimate Deformation Rates with Application to Tehran Basin

This study reports on the monitoring of land subsidence in a rural area located in the southwest of the Tehran basin, Iran, by combining a persistent scatterer interferometry (PSI) method with a single-baseline polarimetric coherence optimisation. Owing to vegetation coverage in this rural area, coherence level experiences a decline and the performance and coverage of conventional interferometry to estimate deformation rate reduces concomitantly. Since the launch of satellites with polarimetric information, the polarimetric InSAR (PolInSAR) technique, which is vector interferometry with different polarimetric channels, has been introduced to optimise the coherence level. One of the most common criteria to select PS pixels is coherence and maximising the coherence can lead to an increased number of selected PS pixels and enhanced PSI performance. The single-baseline polarimetric coherence optimisation method assumes equal polarisation states at the end of each baseline. In order to apply this technique in our study, two different multi-look windows for coherence calculation and also two TerraSAR-X data sets with different numbers of images are used to assess their effect on the polarimetric PSI. Combination of the single-baseline coherence optimisation method with PSI shows significant improvements (more than 50%) in terms of the number of selected PS pixels in the case study even using a data set with a small number of images. A 15 times 15 multi-look window selects a greater number of PS pixels compared to a 9 times 9 multi-look window, although this entails reducing spatial resolution. The most effective PSI approach in terms of the density of the selected PS turned out to be polarimetric PSI using a data set with a large number of images and a selection of a 15 times 15 multi-look window. Validation of the PSI methods using a large number of images with 9 times 9 and 15 times 15 multi-look windows via levelling measurements confirms the accuracy and reliability of the results obtained.