Apodization Function Research Articles

A New qNMR Compliant Savitzky-Golay Apodization Function for Resolution Enhancement.

In this work, we introduce a novel NMR apodization function designed to enhance spectral resolution while maintaining compatibility with qNMR standards. This function is based on a modified Savitzky-Golay filter, adapted for time-domain application. It effectively suppresses the negative components typically associated with derivative spectra, while also ensuring the preservation of quantitative integrity in NMR analyses.

Super-resolution NMR spectroscopy

Spectral resolution is one of the limiting factors in nuclear magnetic resonance (NMR) spectroscopy of biological systems where signal overlap often interferes with chemical shift assignment as well as dynamics and structure analysis. This problem can be addressed in part by using higher magnetic field NMR spectrometers operating at up to 1.2 GHz 1H frequency to enhance the resolution proportionally with the field strength, and by deuteration in combination with transverse relaxation-optimized spectroscopy that reduces the transverse relaxation rate and proportionally the resonance linewidth of the peaks yielding higher spectral resolution. As a complement or alternative to these expensive and often insufficient approaches, we present here a generally applicable method to reduce the linewidth of peaks in indirect dimensions of multi-dimensional NMR spectra by increasing the number of scans per time increment exponentially as a function of time in order to compensate, in part, the decay of the signal caused by transverse relaxation. This enables to achieve a user-defined linewidth of the peaks without undue increase of the noise. Optimization by including in the number of scans also a cosine apodization function as well as processing spectra with an exponential-cosine window function in the direct dimension results typically in a resolution enhancement (linewidth reduction) by a factor of 1.5–2 in comparison to a standard measurement with a constant number of scans per time increment. This is comparable to the 2-fold resolution enhancement that can be obtained by going from a 600 MHz 1H frequency NMR spectrometer to a 1.2 GHz instrument, or from 1.2 GHz to a spectrum measured hypothetically at 2.4 GHz 1H frequency. A factor of two resolution enhancement causes thereby a signal to noise loss of a factor of three. The sensitivity gain by dynamic number of scan sampling is thereby ∼20 % over the use of a digital apodization function.

Optimization and analysis of apodized fiber Bragg grating properties for quasi-distributed sensing

An apodized fiber Bragg grating (FBG) is introduced with a proposed apodization function for the effective quasi-distributed sensing estimation of the temperature and the strain. FBG features such as reflectivity, side lobes, and bandwidth have been optimized for the designed apodized grating to upgrade the effectiveness of FBG for properly measuring the variations in the Bragg wavelength. Based upon the simulation, a comparative analytical study on FBG properties with different apodization function profiles has been demonstrated to achieve the optimum profile with high reflectivity, narrow bandwidth and minimal range of side lobes for quasi-distributed sensing estimation of parameters. A strong linearity has been noted for the sensitivity of designed FBG with different apodization profiles for the temperature and the strain estimation subsequently. It has been reported that the obtained sensitivity of measurands for the FBG with proposed apodization profile are higher as compared with the other profiles. The wavelength division multiplexing (WDM) based quasi-distributed network of four optimized FBGs have been implemented for different apodization profiles to illustrate the impact of apodization to prevent overlapping between neighbouring FBG spectrums in the sensing network with spatial resolution of 2 nm. The maximal detectable temperature/strain sensitivity estimation of 153 °C/1439 μϵ have been obtained for the proposed apodized FBG along with minimal detectable temperature/strain ranges of −102 °C/−1345 μϵ in the quasi-distributed network. The achieved ranges with optimum resolution can be implemented effectively in quasi-distributed based sensing application for condition observation of civil infrastructures in any complex circumstances.

Optical fiber fronthaul segment in open radio access 5G networks: enhanced performance utilizing AFBG

In open Radio access network (oRAN) 5G networks, a fronthaul segment between virtual Distribution unit (vDU) edge cloud and other external Remote radio units (RRUs) sites is very important to transmit high data rate to achieve 5G requirements. Performance parameters such as Quality factor (Q-factor) and Bit error rate (BER) of an optical fiber fronthaul segment are the main important parameters to enhance latency and bit rate. An Apodized fiber bragg grating (AFBG) is utilized with different apodization profiles to optimize linewidth of an optical signal leading to enhance performance. The designed AFBG is used with a data rate of 25 Gb/s optical Ethernet module at the vDU edge cloud to optimize the linewidth of the optical signal between the vDU and the RRU in the fronthaul optical fiber segment. The AFBG is investigated at different connections pre, post, and symmetrical connections, where different apodization functions are used in the AFBG design. It is found that the best results for the maximum Q-factor and minimum BER are 9.2 and 2.72e− 21, respectively, obtained from uniform function in the symmetrical connection. Finally, the proposed model linewidth is 0.408 nm, which is better than 1.56 nm that is evaluated by related work.

Modified CFBG-based approach for chromatic dispersion compensation in high speed DWDM links.

Chromatic dispersion (CD) is a major concern in high speed fiber optics communication systems. This work presents an efficient optical compensation technique with reduced complexity to mitigate CD effects in single mode fiber (SMF) at high data rates. The proposed method includes a post-dispersion mitigation system using a single linear chirped fiber Bragg grating (CFBG) with tanh apodization. Here, various parameters of CFBG, such as grating length, effective refractive index, and apodization function, are optimized to achieve effective CD compensation. Then, the system is extended to a 16-channel WDM link with each channel carrying data at 25Gbps over 100km. The simulation results show that the proposed model enhances the system performance while minimizing overall system complexity. The proposed system is also compatible with the prevailing fiber optics networks. The results are consistent with the findings published in recent studies.

Su8-waveguide based phase corrected fourier transform spectrometer chip with low side ripples

Integrated Fourier transform spectrometer (FTS) chip is of great interest recently due to its small size, low cost, and inherent high throughput. Phase and intensity errors caused by fabrication imperfections can give rise to severe side ripples in the retrieving spectrum of an FTS chip. To suppress the side ripples poses a great challenge, especially for the spatial heterodyne spectrometer (SHS) chip constituted by numerous Mach-Zehnder interferemoters (MZI) and having a relatively large size. Pseudoinverse algorithm combined with apodization function is considered to be able to compensate the phase and intensity errors efficiently. However, recent researches show that it still has its limitations, some results illustrate the side ripples of the retrieving spectra can be as large as −6 dB. In this article, we design, fabricate and characterize an Su8-waveguide based SHS chip with 51 MZIs, each MZI is accompanied with a pair of heating electrodes to correct the phase error. Different factors that contribute to the side ripples of the retrieved spectrum are analyzed and simulated. Our experimental result shows that by means of physically heat-tuning the metal electrodes and mathematically compensating the transmissivity fluctuations, the side ripples can be suppressed to be in the range from −19 dB to −15 dB for monochromatic and doublet light in our Su8-waveguide based SHS chip.

Norton-Beer apodization and its Fourier transform.

In Fourier transform spectroscopy, apodization is used to alter the instrument line shape, reducing the prominence of its side lobes. The Fourier transform of the apodization window is of great interest as it allows us to compute or optimize the line shape. In the last decades, many apodization windows have been proposed, from which the group of Norton-Beer apodization functions gained large popularity in Fourier transform spectroscopy. While for a small set of specific Norton-Beer apodization functions analytical solutions of the Fourier transform have been presented in the past, we present here a general method, which allows us to calculate the analytical solution of the Fourier transform for any Norton-Beer apodization function. This paper also documents the free Python library called norton_beer. It contains functions to generate apodization windows and their Fourier transform following the presented analytical solution. Furthermore, new Norton-Beer apodization functions can be generated for any desired spectral resolution.

Calculation of the intensity at the sharp focus of a cylindrical vector beam by three methods

We conduct a comparative analysis of diffraction fields upon sharply focusing vortex and non-vortex incident beams, calculated using three non-paraxial methods. The methods employed are a finite difference time domain (FDTD) method, a Rayleigh–Sommerfeld integral, and a Richards–Wolf transformation. The Richards–Wolf transformation is used with two apodization functions of the exit pupil, for a spherical lens and a thin diffractive lens. The numerical simulation shows that the Rayleigh–Sommerfeld integral and the Richards–Wolf transformation can produce almost the same result and save time significantly. Meanwhile, the root-mean-square deviation of the results of both methods from the FDTD method can be as low as 2%. If an ultra-short focal length is used, the Richards–Wolf transformation is found to be more accurate, whereas with increasing distance from the initial plane and outside the focal plane, the Rayleigh-Sommerfeld integral is more accurate.

Optimal transmit apodization for the maximization of lag-one coherence with applications to aberration delay estimation

Phase aberration is one of the major sources of image degradation in medical ultrasound imaging. One of the earliest and simplest techniques to correct for phase aberration involves nearest-neighbor cross correlation to estimate delays between neighboring receive channels and the compensation of aberration delays in a delay-and-sum beamformer. The main challenge is that neighboring receive channels may not have sufficient signal correlation to accurately estimate the aberration delays. Although algorithms such as the translating transmit aperture or the common midpoint gather are designed to perfectly maximize signal correlations between received signals, these algorithms require the use of different transmit apertures for each received signal. Instead, this work proposes the use of a single globally-applicable transmit apodization function that optimizes the lag-one coherence based on the van Cittert–Zernike theorem. For the application to phase aberration correction, it is shown across 20 different zero-mean Gaussian-random aberrators that the proposed optimal apodization function reduces the estimation error in the aberration delay profile from 22.85% to 15.72%.

Novel Apodized Fiber Bragg Grating Applied for Medical Sensors: Performance Investigation

Sensors play an important role in shaping and monitoring human health. Exploration of methods to use Fiber Bragg Grating (FBG) with enhanced sensitivity has attracted great interest in the field of medical research. In this paper, a novel apodization function is proposed and performance evaluation and optimization of the same have been made. A comparison was conducted between various existing apodization functions and the proposed one based on optical characteristics and sensor parameters. The results evince the implementation of the proposed apodization function for vital sign measurement. The optical characteristics considered for evaluation are Peak Resonance Reflectivity level, Side Lobes Reflectivity level and Full Width Half Maximum (FWHM). The proposed novel apodization novel function has better FWHM, which is narrower than the FWHM of uniform FBG. Sensor characteristics like a quality parameter, detection accuracy and sensitivity also show improvement. The proposed novel apodization function is demonstrated to have a better shift in wavelength in terms of temperature and pulse measurement than the existing functions. The sensitivity of the proposed apodized function is enhanced with a Poly-dimethylsiloxane coating of varying thickness, which is 6 times and 5.14 times greater than uniform Fiber Bragg grating and FBG with the proposed novel apodization function, respectively, enhancing its utilization in the field of medicine.

Sensitivity analysis of designed apodized fiber Bragg grating sensor using artificial neural network and tree-based models

An apodized FBG is designed to eliminate the side lobes from the reflectivity spectrum for the sensitivity measurement of physical parameters including temperature, strain, and pressure. The impact of the proposed apodization function is discussed with several other apodization profiles for the elimination of side lobes from the FBG spectrum. The sensitivity of the measurand is measured by analyzing the changes that occur in the Bragg wavelength, which is sensitive to the physical parameters. A strong linear response has been observed for the sensitivity of temperature, strain, and pressure for the designed apodized FBG. Machine Learning (ML) methods such as Artificial Neural Network (ANN) and Tree-based models are implemented for the predictive analysis of physical parameters and their respective Bragg wavelength shifts for the reliability of the designed apodized FBG sensor to achieve improved sensing outcomes, particularly to work in a hazardous environment for understanding any adverse scenario of a measurand. Decision Tree (DT) and Random Forest (RF) are used as Tree-based models in this work. Different statistical measures are introduced to evaluate the predictive analysis performance of the ML models. It has been observed that the predictive analysis performance of the ANN is better compared to the Tree-based models.

Enhanced dispersion reduction using apodized uniform fiber Bragg grating for optical MTDM transmission systems

The aim of this work is to propose a model for enhancing chromatic dispersion compensation in standard single mode optical fibers (SSMFs). The proposed model consists of a single stage Apodized Uniform Fiber Bragg Gratings (AUFBG) in a post-compensation scheme. It is based on the Maximum Time Division Multiplexing (MTDM) technique. The performance of the proposed model is evaluated through the quality factor (Q-factor) and Bit Error Rate (BER) in four cases, in a comparative study. In case one, the system performance is evaluated without using UFBG. The other cases study the effect of the proposed model with using different connections schemes and the most common apodization functions. For simulation, the proposed model is connected in a 10 Gbps WDM 70 km link under ordinary operating parameters. The simulation and evaluation process is conducted by Optisystem 7.0. In the pre-compensation scheme, the best results are obtained as a maximum Q-factor of 9.2 and a minimum BER of 3.25 × 10–20, using a tanh apodization function. The proposed model realizes an improvement over the related work by at least ~ 68%.

Dispersion compensation using cascaded apodized CFBGs under MTDM transmission technique: Enhanced system performance

This study focuses on compensating chromatic dispersion affecting the propagated signal in a standard single mode optical fibers (SSMFs). We propose a model that consists of an identical four stages cascaded linear chirped apodized fiber Bragg gratings (CFBGs) in a post-compensation scheme under Maximum Time Division Multiplexing (MTDM) technique. MTDM is free of the limitations resulting from the fiber nonlinear effects. It, thus, effectively utilizes optical wavelength and operating in various network of different distances and capacities. Therefore, MTDM is designed to be used in the high-capacity and high-speed transmission systems. The evaluation of the proposed model performance is performed through a comparative study using different connections and the most common apodization functions. This comparative study includes three cases based on the used connection scheme. A 10 Gbps Wavelength Division Multiplexing (WDM) 70 km link is simulated under ordinary operating parameters. Optisystem 7.0 is used for the simulation and evaluation process, in terms of two metrics which are quality factor (Q-factor) and bit error rate (BER). In the pre-compensation scheme, the highest results are: Q-factor = 7.664 and BER = 8.99 × 10–15, using the raised cosine apodization function. Using the raised sine apodization in the post-compensation connection realizes the best performance: Q-factor = 8.58 and BER = 4.77 × 10–18. In the symmetrical-compensation scheme and using the raised sine apodization, the proposed model attains the highest Results: Q-factor = 7.49 and BER = 3.53 × 10–14. The proposed model achieves at least 92.6% improvement in BER and 3.75% in Q-factor over the related works. The study is a simulation work and is performed through Optisystem ver. 7.

Light localization in defective periodic photonic moiré-like lattices.

Photonic moiré-like lattices, a readily accessible platform for realizing the spatial localization of light, attract intensive attention due to their unique flatband characteristics. In this paper, a periodic moiré-like lattice with embedded defects is proposed theoretically, and the linear propagation of the probe beam in such a system is investigated intensively. The results show that the positions of defects in periodic moiré-like lattices depend on the sublattice rotation angle. Further studies show that the localization of light could be improved by adjusting the apodization function of defects. In addition, the experimental observation of the moiré-like lattice with apodized defects also confirms the theoretical analysis. Our study enriches the physical connotation of photonic moiré lattices and guides the design of novel photonic crystal fibers.

Research on Spectral Restoration and Gas Concentration Inversion Accuracy Based on Quasi-Trapezoidal Window

The Fourier transform is a popular method for analyzing and processing interference data in which spectrum leakage occurs. Generally, window function (also called apodization function) weighting is employed to limit spectrum leakage. A rectangular window with optimal main-lobe performance and the Rife-Vincent (R-V) window were introduced to improve the window function performance, resulting in the establishment of a quasi-trapezoidal window function. Based on the experimental interference data, the quasi-trapezoidal window function was used in the spectral restoration process. The experimental results show that when the apodization degree of the quasi-trapezoidal window was 1.06, the spectral resolution was improved by 17.46% compared with that of the Hanning window; when the apodization degree was 2.71, the spectral signal-to-noise ratio (SNR) was improved by 130.09% compared with that of the Blackman-Harris window function. In the propane (C3H8) and ethylene (C2H4) gas concentration inversion experiment, when the apodization degree was increased from 1.06 to 2.58, the inversion precision was increased by 6.94% for C3H8 gas and 23.93% for C2H4 gas. Through the parameter adjustment, the quasi-trapezoidal window may achieve a high SNR or high-resolution spectral restoration, which can improve the accuracy of gas concentration inversion to some extent.

Structural health monitoring: modeling of simultaneous effects of strain, temperature, and vibration on the structure using a single apodized π-Phase shifted FBG sensor

There are vast fields of application for optical fiber sensors. Fiber Bragg Gratings (FBGs) are commonly used for Structural Health Monitoring (SHM) as an optical sensor to detect various physical phenomena affecting the system to assess its structure in a reliable and accurate manner. Due to the cross-sensitivity of the FBG detection, identifying the effects of each individual parameter on the FBG is a nontrivial task. This paper describes theoretical analysis of a single π-Phase Shifted Fiber Bragg Grating(π-PSFBG) behavior under axial distributions of three simultaneous parameters. Moreover, numerical simulations of an Apodized π-PSFBG are conducted to evaluate the performance of this non-uniform FBG under various strain, temperature, and vibration loads. The optimum apodization function is applied to the spectral signal to improve the properties of the sensor spectrum. Finally, the affecting parameters should be separated to determine the real cause of stress. Towards this end, the reference method is used to compensate for the strain measurements. In order to isolate the effects of stress on the structure, the performance of an apodized π-PSFBG to measure the effects of the above individual parameters on FBG is investigated and characterized with high accuracy.

Chromatic dispersion compensation by cascaded FBG with duobinary modulation scheme

In this paper, we propose a dispersion compensation model to minimize the chromatic dispersion to enhance system performance. The proposed model is based on applying the duobinary modulation scheme on 4-stages of cascaded identical apodized uniform fiber Bragg grating. Different apodization functions are tested to determine the one that provides the best performance. The proposed model is connected in three different connection schemes: pre, post and symmetrical, to get the best connection. To evaluate the performance of the proposed system, a comparative study is conducted using non-return to zero (NRZ) and modified duobinary (MDB) modulation schemes. For evaluation, a 10 Gbps WDM link is simulated at a distance of 100 km under a set of predefined operating parameters. Optisystem 17.0 is used for simulation and evaluation. Both quality factor (Q-factor) and bit error rate (BER) are used as performance indices. All cases of NRZ modulation scheme do not meet the minimum operational requirements in terms of Q-factor and BER. Only in the case of MDB modulation scheme, the symmetrical compensation with tanh apodization meets the minimum operational requirements with a Q-factor of 6.39 and BER of 8.44 × 10–11. The proposed model achieves better results as compared to the other modulation schemes: a maximum Q-factor values of 8.964 and a BER of 1.3 × 10–19 with tanh apodization in the pre-compensation scheme. As compared to related work, the system performance achieves ~ 99% improvement.

Distributed strain sensing, employing apodized π-phase shifted FBG: Application in power transformer oil breakdown detection

Early detection of power transformer oil breakdown can save the transformer and power grid from any potential damages. In this article, a novel distributed strain sensing system based on apodized π-phase-shifted Fiber Bragg Grating (FBG) is presented in order to detect power transformer oil breakdown. The main objective is to detect high-frequency acoustic waves and ultra-small strains resulting from partial discharge (PD) occurrence. To this end, optical fiber under various time and position dependent strain conditions is simulated by employing transfer matrix method. Strain is incorporated in the equations by employing photo-elastic constants. For a single FBG sensor case employing a laser at a fixed wavelength of 1550 nm, it is shown that incorporation of a π phase shift drastically increases the sensitivity, reaching values as high as 60 %/0.1μstrain in reflected light intensity. However, maximum measurable strain is limited to only 0.25 μstrain. Afterwards, a suitable Gaussian apodization function is applied to the FBG which drastically increased the strain measurement range to almost 0.45 μstrain by a complete suppression of sidelobes in the reflected light spectrum. It is shown that the proposed system is capable of detecting high-frequency PD-induced acoustic waves of up to 500 kHz.

A reduced power budget and enhanced performance in a wdm system: a new fbg apodization function

The apodization profiles improve chirped fiber Bragg grating (CFBG) capability to compensate dispersion which enhances the performance of the wavelength division multiplexing (WDM) systems. In this paper, a new apodization profile is proposed to enhance performance and reduces the power budget for a WDM system. The newly apodization profile is implemented to a CFBG as a post compensator in a WDM system for 100 km. It is found the proposed profile enhances the performance and reduces the transmitted power at BER of 10−9. The evaluation of the proposed profile is compared with a previously published work. It is found the proposed profile enhances the Q-factor by 1.08%, decreases BER by 52.8%, and reduces the power budget by 4% than the related work.

Characterization of the Time-Domain Isotopic Beat Patterns of Monoclonal Antibodies in Fourier Transform Mass Spectrometry.

The time-domain transients in the Fourier transform mass spectrometry (FTMS) analysis of monoclonal antibodies (mAbs) are known to exhibit characteristic isotopic beat patterns. These patterns are defined by the isotopic distributions of all gaseous mAb ions present in the FTMS mass analyzer, originating from single or multiple charge states, and from single or multiple proteoforms. For an isolated charge state of a single proteoform, the mAb isotopic beat pattern resembles narrow splashes of signal amplitude (beats), spaced periodically in the time-domain transient, with broad (often exceeding 1 s) "valleys" between them. Here, we reinforce the importance of isotopic beat patterns for the accurate interpretation and presentation of FTMS data in the analysis of mAbs and other large biopolymers. An updated, mAb-grade version of the transient-mediated FTMS data simulation and visualization tool, FTMS Simulator is introduced and benchmarked. We then apply this tool to evaluate the charge-state dependent characteristics of isotopic beats in mAbs analyses with modern models of Orbitrap and ion cyclotron resonance (ICR) FTMS instruments, including detection of higher-order harmonics. We demonstrate the impact of the isotopic beat patterns on the analytical characteristics of the resulting mass spectra of individual and overlapping mAb proteoforms. The results reported here detail highly nonlinear dependences of resolution and signal-to-noise ratio on the time-domain transient period, absorption or magnitude mode spectra representation, and apodization functions. The provided description and the demonstrated ability to routinely conduct accurate simulations of FTMS data for large biopolymers should aid the end-users of Orbitrap and ICR FTMS instruments in the analysis of mAbs and other biopolymers, including viruses.