Motion-induced phase-corrected homodyne reconstruction for partial Fourier single-shot diffusion-weighted echo planar imaging of the liver.

Partial Fourier encoding is popular in single-shot (ss) diffusion-weighted (DW) echo planar imaging (EPI) because it enables a shorter echo time (TE) and, hence, improves the signal-to-noise-ratio. Motion during diffusion encoding causes k-space shifting and dispersion, which compromises the quality of the homodyne reconstruction. This work provides a comprehensive understanding of the artifacts in homodyne reconstruction of partial Fourier ss-DW-EPI data in the presence of motion-induced phase and proposes the motion-induced phase-corrected homodyne (mpc-hdyne) reconstruction method to ameliorate these artifacts. Simulations with different types of motion-induced phase were performed to provide an understanding of the potential artifacts that occur in the homodyne reconstruction of partial Fourier ss-DW-EPI data. To correct for the artifacts, the mpc-hdyne reconstruction is proposed. The algorithm recenters k-space, updates the partial Fourier factor according to detected global k-space shifts, and removes low-resolution nonlinear phase before the conventional homodyne reconstruction. The mpc-hdyne reconstruction is tested on both simulation and in vivo data. Motion-induced phase can cause signal overestimation, worm artifacts, and signal loss in partial Fourier ss-DW-EPI data with the conventional homodyne reconstruction. Simulation and in vivo data showed that the proposed mpc-hdyne reconstruction ameliorated artifacts, yielding higher quality DW images compared with conventional homodyne reconstruction. Based on the understanding of the artifacts in homodyne reconstruction of partial Fourier ss-DW-EPI data, the mpc-hdyne reconstruction was proposed and showed superior performance compared with the conventional homodyne reconstruction on both simulation and in vivo data.

Low-Coherence Homodyne Interferometer for Sub-Megahertz Fiber Optic Sensor Readout.

This study proposes a method for interferometric fiber optic sensor readouts. The method utilizes the advantages of the active homodyne demodulation technique and low-coherence interferometry. The usage of the tandem low-coherence interferometer enables modulating the reference interferometer without any changes to the sensor. This achieves high sensitivity, high stability, and a wide frequency band. A sensitivity of up to 0.1 nm (RMS) in the frequency range of 5 kHz is demonstrated by detecting acoustic signals with a fiber Michelson interferometer as a sensor.

Enhancing Performance of Continuous-Variable Quantum Key Distribution (CV-QKD) and Gaussian Modulation of Coherent States (GMCS) in Free-Space Channels under Individual Attacks with Phase-Sensitive Amplifier (PSA) and Homodyne Detection (HD).

In recent research, there has been a significant focus on establishing robust quantum cryptography using the continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian modulation of coherent states (GMCS). Unlike more stable fiber channels, one challenge faced in free-space quantum channels is the complex transmittance characterized by varying atmospheric turbulence. This complexity poses difficulties in achieving high transmission rates and long-distance communication. In this article, we thoroughly evaluate the performance of the CV-QKD/GMCS system under the effect of individual attacks, considering homodyne detection with both direct and reverse reconciliation techniques. To address the issue of limited detector efficiency, we incorporate the phase-sensitive amplifier (PSA) as a compensating measure. The results show that the CV-QKD/GMCS system with PSA achieves a longer secure distance and a higher key rate compared to the system without PSA, considering both direct and reverse reconciliation algorithms. With an amplifier gain of 10, the reverse reconciliation algorithm achieves a secure distance of 5 km with a secret key rate of 10-1 bits/pulse. On the other hand, direct reconciliation reaches a secure distance of 2.82 km.

A Compensation Method for Nonlinearity Errors in Optical Interferometry.

Optical coherent detection is widely used for highly sensitive sensing applications, but nonlinearity issues pose challenges in accurately interpreting the system outputs. Most existing compensation methods require access to raw measurement data, making them not useful when only demodulated data are available. In this study, we propose a compensation method designed for direct application to demodulated data, effectively addressing the 1st and 2nd-order nonlinearities in both homodyne and heterodyne systems. The approach involves segmenting the distorted signal, fitting and removing baselines in each section, and averaging the resulting distortions to obtain precise distortion shapes. These shapes are then used to retrieve compensation parameters. Simulation shows that the proposed method can effectively reduce the deviation caused by the nonlinearities without using the raw data. Experimental results from a silicon-photonics-based homodyne laser Doppler vibrometry prove that this method has a similar performance as the conventional Heydemann correction method.

HFP-QSMGAN: QSM from homodyne-filtered phase images.

PURPOSE: Homodyne filtering is a standard preprocessing step in the estimation of SWI. Unfortunately, SWI is not quantitative, and QSM cannot be accurately estimated from filtered phase images. Compared with gradient-echo sequences suitable for computing QSM, SWI is more readily available and is often the only susceptibility-sensitive sequence acquired in the clinical setting. In this project, we aimed to quantify susceptibility from the homodyne-filtered phase (HFP), acquired for computing susceptibility-weighted images, using convolutional neural networks to solve the compounded problem of (1) computing the solution to the inverse dipole problem, and (2) compensating for the effects of the homodyne filtering. METHODS: Two convolutional neural networks, the U-Net and a modified QSMGAN architecture (HFP-QSMGAN), were trained to predict QSM maps at different TEs from HFP images. The QSM maps were quantified from a gradient-echo sequence acquired in the same individuals using total generalized variation (TGV)-QSM. The QSM maps estimated directly from the HFP were also included for comparison. Voxel-wise predictions and, importantly, regional predictions of susceptibility with adjustment to a reference region, were compared. RESULTS: Our results indicate that the U-Net model provides more accurate voxel-wise predictions of susceptibility compared with HFP-QSMGAN and HFP-QSM. However, regional estimates of susceptibility predicted by HFP-QSMGAN are more strongly correlated with the values from TGV-QSM compared with those of U-Net and HFP-QSM. CONCLUSION: Accurate prediction of susceptibility can be achieved from filtered SWI phase using convolutional neural networks.

Recovering SWI-filtered phase data using deep learning.

PURPOSE: To develop a deep neural network to recover filtered phase from clinical MR phase images to enable the computation of QSMs. METHODS: Eighteen deep learning networks were trained to recover combinations of 13 SWI phase-filtering pipelines. SWI-filtered data were computed offline from five multiorientation, multiecho MRI scans yielding 132 3D volumes (118/7/7 training/validation/testing). Two experiments were conducted to show the efficacy of the networks. First, using QSM processing, local fields were computed from the raw phase and subsequently filtered using the SWI-filtering pipelines. The networks were then trained to invert the filtering operation. Second, the trained networks were fine-tuned to recover unfiltered local fields from filtered local fields computed by applying QSM processing to the SWI-filtered phase. Susceptibility maps were computed from the recovered fields and compared with gold standard multiple orientation sampling reconstructions. RESULTS: Susceptibility maps computed from the raw phase using standard QSM processing have a normalized root mean square error (NRMSE) of 0.732 ± 0.095. Susceptibility maps computed from the recovered phase obtained NRMSEs of 0.725 ± 0.095. The network trained using all 13 processing methods generalized well, obtaining NRMSEs of 0.725 ± 0.89 on filters it has not seen, while matching the reconstruction accuracy of networks trained to recover a single filter. CONCLUSION: It is feasible to recover SWI-filtered phase using deep learning. QSM can be computed from the recovered phase from SWI acquisition with comparable accuracy to standard QSM processing.

Estimating Non-Gaussianity of a Quantum State by Measuring Orthogonal Quadratures.

We derive the lower bounds for a non-Gaussianity measure based on quantum relative entropy (QRE). Our approach draws on the observation that the QRE-based non-Gaussianity measure of a single-mode quantum state is lower bounded by a function of the negentropies for quadrature distributions with maximum and minimum variances. We demonstrate that the lower bound can outperform the previously proposed bound by the negentropy of a quadrature distribution. Furthermore, we extend our method to establish lower bounds for the QRE-based non-Gaussianity measure of a multimode quantum state that can be measured by homodyne detection, with or without leveraging a Gaussian unitary operation. Finally, we explore how our lower bound finds application in non-Gaussian entanglement detection.

Enhanced POCS reconstruction for partial Fourier imaging in multi-echo and time-series acquisitions.

PURPOSE: To improve partial Fourier (PF) imaging reconstruction in time-series or multi-echo acquisitions. METHODS: Many PF methods use a phase estimate to restore Hermitian symmetry before filling missing k-space entries with measured data from the opposite half. This estimate is obtained from the symmetrically sampled, central part of k-space and its low-resolution results in artifacts near high-frequency phase effects (eg, tissue boundaries, vessels), limiting PF undersampling. Enhanced projection onto convex sets (POCS) uses full-resolution phase estimates and relies on alternating the half of k-space that is acquired in time series or multi-echo acquisitions. This enables full-resolution phase estimates to be calculated for each volume/echo, which are fed into the POCS framework. We apply enhanced POCS to high-resolution multi-echo FLASH and 3D-EPI functional MRI time-series data. RESULTS: Reconstruction errors and their bias dramatically reduce compared with existing methods, without leading to temporal blurring in time-series acquisitions. This allows for higher PF acceleration factors at virtually no cost. CONCLUSION: Enhanced POCS results in superior PF reconstructions. Furthermore, as the resolution of the phase estimate used for symmetry correction no longer depends on the PF factor, enhanced POCS is more robust against larger PF omission.

Passive Homodyne Phase Demodulation Technique Based on LF-TIT-DCM Algorithm for Interferometric Sensors.

A passive homodyne phase demodulation technique based on a linear-fitting trigonometric-identity-transformation differential cross-multiplication (LF-TIT-DCM) algorithm is proposed. This technique relies on two interferometric signals whose interferometric phase difference is odd times of π. It is able to demodulate phase signals with a large dynamic range and wide frequency band. An anti-phase dual wavelength demodulation system is built to prove the LF-TIT-DCM algorithm. Comparing the traditional quadrature dual wavelength demodulation system with an ellipse fitting DCM (EF-DCM) algorithm, the phase difference of two interferometric signals of the anti-phase dual wavelength demodulation system is set to be π instead of π/2. This technique overcomes the drawback of EF-DCM-that it is not able to demodulate small signals since the ellipse degenerates into a straight line and the ellipse fitting algorithm is invalidated. Experimental results show that the dynamic range of the proposed anti-phase dual wavelength demodulation system is much larger than that of the traditional quadrature dual wavelength demodulation system. Moreover, the proposed anti-phase dual wavelength demodulation system is hardly influenced by optical power, and the laser wavelength should be strictly limited to lower the reference error.

External Modulation Laser Module Assembly for Improving Measurement Performance of Homodyne Interferometry.

An external modulation laser module assembly (EMLMA) is proposed to suppress nonlinear errors in an interferometry system and improve its measurement performance. The EMLMA employs both phase modulation with radio frequency signal and a specific modulation amplitude switching mode, enabling the suppression of noise introduced by spurious reflections. The amplitude modulation reduces the influence of stray and background light by transforming the signal of interest to a high-frequency bandwidth. Experimental results show that the measurement error and stability of the interferometry system are significantly improved using the proposed light source module. After modulation, the spurious reflection-induced offset is decreased, and the measurement resolution improves from 7 to 2 nm. The EMLMA can replace the light source of any interferometric measurement system without altering the optical measurement structure. The proposed method reduces the influence of nonlinear errors in homodyne interferometry and provides a basis for further improvement of the interferometry performance.

Development of a High-Resolution All-Fiber Homodyne Laser Doppler Vibrometer.

Based on the homodyne detection, a compact and cost-effective all-fiber laser Doppler vibrometer (LDV) with high resolution is presented. For the signal processing, the discrimination algorithm combined with the nonorthogonal correction is applied. The algorithm corrects the quadrature imbalance and other nonlinearity. In the calibration experiment, with the glass pasted on a piezoceramic transducer (PZT), the velocity resolution of 62 nm/s at 4 kHz and displacement resolution of 2.468 pm are achieved. For the LDV-based acousto-optic communication, the minimum detectable sound pressure level (SPL) reached 0.12 Pa under the hydrostatic air-water surface. The results demonstrate that the designed homodyne LDV has a low system background noise and can offer high precision in the vibration measurement.

Real-Time Correction and Stabilization of Laser Diode Wavelength in Miniature Homodyne Interferometer for Long-Stroke Micro/Nano Positioning Stage Metrology.

A low-cost miniature homodyne interferometer (MHI) with self-wavelength correction and self-wavelength stabilization is proposed for long-stroke micro/nano positioning stage metrology. In this interferometer, the displacement measurement is based on the analysis of homodyne interferometer fringe pattern. In order to miniaturize the interferometer size, a low-cost and small-sized laser diode is adopted as the laser source. The accuracy of the laser diode wavelength is real-time corrected by the proposed wavelength corrector using a modified wavelength calculation equation. The variation of the laser diode wavelength is suppressed by a real-time wavelength stabilizer, which is based on the principle of laser beam drift compensation and the principle of automatic temperature control. The optical configuration of the proposed MHI is proposed. The methods of displacement measurement, wavelength correction, and wavelength stabilization are depicted in detail. A laboratory-built prototype of the MHI is constructed, and experiments are carried out to demonstrate the feasibility of the proposed wavelength correction and stabilization methods.

High-Throughput Optical Imaging and Spectroscopy of One-Dimensional Materials.

Direct visualization of one-dimensional (1D) materials under an optical microscope in ambient conditions is of great significance for their characterizations and applications. However, it is full of challenges to achieve such goal due to their relative small size (ca. 1 nm in diameter) in the optical-diffraction-limited laser spot (ca. 1 µm in diameter). In this Concept article, we introduce a polarization-based optical homodyne detection method that can be used as a general strategy to obtain high-throughput, real-time, optical imaging and in situ spectroscopy of polarization-inhomogeneous 1D materials. We will use carbon nanotubes (CNTs) as an example to demonstrate the applications of such characterization with respect to the absorption signal of individual nanotubes, real-time imaging of individual nanotubes in devices, and statistical structure information of nanotube arrays.

Multidie LED combined with homogenizing optics to improve frequency response and intensity for FLIM applications.

Application of light-emitting diodes (LEDs) in frequency-domain fluorescence lifetime imaging microscopy (FLIM) has been limited by the trade-off between modulation frequency and illumination intensity of LEDs, which affects the signal-to-noise ratio in fluorescence lifetime measurements. To increase modulation frequency without sacrificing output power of LEDs, we propose to use LEDs with multiple dice connected in series. The LED capacitance was reduced with series connection; therefore, the frequency response of multidie LED was significantly increased. LEDs in visible light, including blue, green, amber and red, were all applicable in FLIM. We also present a homogenizing optics design, so that multidie LEDs produced uniform illumination on the same focal spot. When the homogenizing optics was combined with multicolour emitters, it provides multiple colour selection in a compact and convenient design.

Systematic determination of absolute absorption cross-section of individual carbon nanotubes.

Optical absorption is the most fundamental optical property characterizing light-matter interactions in materials and can be most readily compared with theoretical predictions. However, determination of optical absorption cross-section of individual nanostructures is experimentally challenging due to the small extinction signal using conventional transmission measurements. Recently, dramatic increase of optical contrast from individual carbon nanotubes has been successfully achieved with a polarization-based homodyne microscope, where the scattered light wave from the nanostructure interferes with the optimized reference signal (the reflected/transmitted light). Here we demonstrate high-sensitivity absorption spectroscopy for individual single-walled carbon nanotubes by combining the polarization-based homodyne technique with broadband supercontinuum excitation in transmission configuration. To our knowledge, this is the first time that high-throughput and quantitative determination of nanotube absorption cross-section over broad spectral range at the single-tube level was performed for more than 50 individual chirality-defined single-walled nanotubes. Our data reveal chirality-dependent behaviors of exciton resonances in carbon nanotubes, where the exciton oscillator strength exhibits a universal scaling law with the nanotube diameter and the transition order. The exciton linewidth (characterizing the exciton lifetime) varies strongly in different nanotubes, and on average it increases linearly with the transition energy. In addition, we establish an empirical formula by extrapolating our data to predict the absorption cross-section spectrum for any given nanotube. The quantitative information of absorption cross-section in a broad spectral range and all nanotube species not only provides new insight into the unique photophysics in one-dimensional carbon nanotubes, but also enables absolute determination of optical quantum efficiencies in important photoluminescence and photovoltaic processes.

Infrared Vibrational Nanospectroscopy by Self-Referenced Interferometry.

Infrared vibrational scattering scanning near-field optical microscopy (s-SNOM) has emerged as a new frontier in imaging science due to its potential to provide nanoscale spatially resolved chemical spectroscopy for the investigation of molecular, soft-matter, and biological materials. As a phase-sensitive technique able to yield the full complex dielectric function of materials, different interferometric schemes have been developed involving asymmetric interferometry between sample and reference arms. In this work, we take advantage of a greatly simplified symmetric geometry that uses the spatially coherent background scattered light from within the confocal sample volume as a reference field for signal amplification in both self-homodyne and self-heterodyne interferometry. On the basis of a simple model for tip-sample scattering and interferometric detection, we demonstrate the measurement of the vibrational response of molecular materials in good agreement with established values. In addition to a compact design, enhanced signal levels, and a reduced sensitivity to fluctuations and drift, including those from the light source, self-referenced interferometry brings benefits for routine s-SNOM chemical spectroscopy, remaining robust even under a wide range of challenging experimental environments.

Partial fourier and parallel MR image reconstruction with integrated gradient nonlinearity correction.

PURPOSE: To describe how integrated gradient nonlinearity (GNL) correction can be used within noniterative partial Fourier (homodyne) and parallel (SENSE and GRAPPA) MR image reconstruction strategies, and demonstrate that performing GNL correction during, rather than after, these routines mitigates the image blurring and resolution loss caused by postreconstruction image domain based GNL correction. METHODS: Starting from partial Fourier and parallel magnetic resonance imaging signal models that explicitly account for GNL, noniterative image reconstruction strategies for each accelerated acquisition technique are derived under the same core mathematical assumptions as their standard counterparts. A series of phantom and in vivo experiments on retrospectively undersampled data were performed to investigate the spatial resolution benefit of integrated GNL correction over conventional postreconstruction correction. RESULTS: Phantom and in vivo results demonstrate that the integrated GNL correction reduces the image blurring introduced by the conventional GNL correction, while still correcting GNL-induced coarse-scale geometrical distortion. Images generated from undersampled data using the proposed integrated GNL strategies offer superior depiction of fine image detail, for example, phantom resolution inserts and anatomical tissue boundaries. CONCLUSION: Noniterative partial Fourier and parallel imaging reconstruction methods with integrated GNL correction reduce the resolution loss that occurs during conventional postreconstruction GNL correction while preserving the computational efficiency of standard reconstruction techniques. Magn Reson Med 75:2534-2544, 2016. © 2015 Wiley Periodicals, Inc.

Artifactual microhemorrhage generated by susceptibility weighted image processing.

BACKGROUND: To report that artifactual microhemorrhages are introduced by the two-dimensional (2D) homodyne filtering method of generating susceptibility weighted images (SWI) when open-ended fringelines (OEF) are present in phase data. METHODS: SWI data from 28 traumatic brain injury (TBI) patients was obtained on a 3 tesla clinical Siemens scanner using both the product 3D gradient echo sequence (GRE) with generalized autocalibrating partially parallel acquisition acceleration and an in-house developed segmented echo planar imaging (sEPI) sequence without GRAPPA acceleration. SWI processing included (i) 2D homodyne method implemented on the scanner console and (ii) a 3D Fourier-based phase unwrapping followed by 3D high pass filtering. Original and enhanced magnitude and phase images were carefully reviewed for sites of type III OEFs and microhemorrhages by a neuroradiologist on a PACS workstation. RESULTS: Nineteen of 28 (68%) phase datasets acquired using GRAPPA-accelerated GRE acquisition demonstrated type III OEFs. In SWI images, artifactual microhemorrhages were found on 17 of 19 (89%) cases generated using 2D homodyne processing. Application of a 3D Fourier-based unwrapping method prior HP filtering minimized the appearance of the phase singularities in the enhanced phase, and did not generate microhemorrhage-like artifacts in magnitude images. CONCLUSION: The 2D homodyne filtering method may introduce artifacts mimicking intracranial microhemorrhages in SWI images when type III OEFs are present in phase images. Such artifacts could lead to overestimation of pathology, e.g., TBI. This work demonstrates that 3D phase unwrapping methods minimize this artifact. However, methods to properly combine phase across coils are needed to eliminate this artifact.

Quantitative assessment of susceptibility-weighted imaging processing methods.

PURPOSE: To evaluate different susceptibility-weighted imaging (SWI) phase processing methods and parameter selection, thereby improving understanding of potential artifacts, as well as facilitating choice of methodology in clinical settings. MATERIALS AND METHODS: Two major phase processing methods, homodyne-filtering and phase unwrapping-high pass (HP) filtering, were investigated with various phase unwrapping approaches, filter sizes, and filter types. Magnitude and phase images were acquired from a healthy subject and brain injury patients on a 3T clinical Siemens MRI system. The results were evaluated based on image contrast-to-noise ratio and presence of processing artifacts. RESULTS: When using a relatively small filter size (32 pixels for the matrix size 512 × 512 pixels), all homodyne-filtering methods were subject to phase errors leading to 2% to 3% masked brain area in lower and middle axial slices. All phase unwrapping-filtering/smoothing approaches demonstrated fewer phase errors and artifacts compared to the homodyne-filtering approaches. For performing phase unwrapping, Fourier-based methods, although less accurate, were 2-4 orders of magnitude faster than the PRELUDE, Goldstein, and Quality-guide methods. CONCLUSION: Although homodyne-filtering approaches are faster and more straightforward, phase unwrapping followed by HP filtering approaches perform more accurately in a wider variety of acquisition scenarios.

Three-Dimensional Homodyne Light Detection (3D-HLD) for High-Throughput Submicron Particle Analysis in (Highly Concentrated) Protein Biopharmaceuticals, Viral Vectors, and LNPs.

During biopharmaceutical development, particle monitoring and characterization are crucial. Notably, particles can be impurities considered as critical quality attribute, or active pharmaceutical ingredient (e.g., viral vectors) or drug delivery system (e.g., lipid nanoparticles) itself. Three-dimensional homodyne light detection (3D-HLD) is a novel technique that can characterize particles in the ∼0.2 µm to 2.0 µm size range. We evaluated 3D-HLD for the analysis of high concentration protein formulations (up to 200 mg/mL), where formulation refractive index and background noise became limiting factors with increasing protein concentration. Sample viscosity however did not impact 3D-HLD results, in contrast to comparative analyses with NTA and MRPS. We also applied 3D-HLD in high-throughput screenings at high protein concentration or of lipid nanoparticle and viral vector formulations, where impurities were analyzed in the presence of a small (<0.2 µm) particulate active pharmaceutical ingredient. 3D-HLD turned out to be in good agreement with or a good complement to other state-of-the-art particle characterization techniques, including BMI, MRPS, and DLS. The main application of 3D-HLD is high-throughput particle analysis at low sample volume. Follow-up investigation of the optimized particle sizing approach and of detection settings could further improve the understanding of the method and potentially increase ease of operation.