Apodization Method Research Articles

Variable apodization method to reduce the effect of edge ringing of aberrated coherent optical systems

The coherent edge imaging of optical systems apodised with amplitude filters has been studied. Edge ringing can be appreciably mitigated using the chosen amplitude filters. The analytical studies were made for circular aperture. It is found that this type of apodization is more useful in reducing the ringing effect and also there is a perceptible increase in the edge gradient. Hence these amplitude filters are found to be effective in enhancing the resolving power aspects of edge imaging characteristics of optical systems

Theoretical investigation of the impact of apodized fiber Bragg grating and machine learning approaches in quasi-distributed sensing

An apodized fiber Bragg grating (FBG) is designed to investigate the impacts of side lobe elimination in quasi-distributed sensing for the estimation of measurands (like temperature and strain) to assess the condition of civil structures, such as bridges. The adjacent FBG spectrums may overlap with each other because of the impacts of temperature and strain due to the presence of a high range of side lobes in a quasi-distributed sensing network. Therefore, elimination of side lobes is necessary, by introducing a method of apodization. The sensitivity of the designed apodized FBG is estimated by analyzing the variations in the Bragg wavelength due to the impacts of temperature and strain. The changes in Bragg wavelength due to the measurands can affect the grating period and the grating index of the FBG. The period of the grating and the grating index of the FBG are simultaneously varied by temperature and strain. To measure the physical parameters effectively, it is essential to distinguish whether the changes in the Bragg wavelength are owing to the impacts of temperature or to the impacts of strain. The effect of cross-sensitivity between the temperature and the strain is a key problem in any FBG-based sensing application as both the measurands can affect the Bragg wavelength. In this work, machine learning methods (the support vector machine, K-nearest neighbors, logistic regression, naïve Bayes, decision tree, and ensemble models) are introduced to differentiate between the effects of temperature and strain on a single Bragg wavelength shift measurement. An artificial neural network is used for the predictive analysis of physical parameters, to identify any measurements of potential concern. It has been noted that the performance of the proposed ensemble model is higher compared to other models for the classification of temperature and strain.

Interferometric apodization by homothety – I. Optimization of the device parameters

ABSTRACT This study is focused on the very high dynamic imaging field, specifically the direct observation of exoplanetary systems. The coronagraph is an essential technique for suppressing the star’s light, making it possible to detect an exoplanet with a very weak luminosity compared to its host star. Apodization improves the rejection of the coronagraph, thereby increasing its sensitivity. This work presents the apodization method by interferometry using homothety, with either a rectangular or circular aperture. We discuss the principle method, the proposed experimental set-up, and present the obtained results by optimizing the free parameters of the system while concentrating the maximum of the light energy in the central diffraction lobe, with a concentration rate of 93.6 per cent for the circular aperture and 91.5 per cent for the rectangular geometry. The obtained results enabled scaling the various elements of the experiment in accordance with practical constraints. Simulation results are presented for both circular and rectangular apertures. We performed simulations on a hexagonal aperture, both with and without a central obstruction, as well as a segmented aperture similar to the one used in the Thirty Meter Telescope (TMT). This approach enables the attainment of a contrast of approximately 10−4 at small angular separations, specifically around 1.8λ/D. When integrated with a coronagraph, this technique exhibits great promise. These findings confirm that our proposed technique can effectively enhance the performance of a coronagraph.

Depth-dependent apodization window based on Chebyshev polynomial for ultrasound imaging.

To improve the image resolution of a portable real-time ultrasound imaging device, this paper proposes a beamformer with composite apodization windows based on Chebyshev polynomial. By introducing the Chebyshev window, the level of sidelobe can be flexibly controlled. The value of weighting changes according to the detection depth and ultrasound attenuation such that it can attain better image resolution than traditional beamformers. The simulations and experiments indicate that the proposed method can flexibly narrow the mainlobe width while keeping the performance of the suppressing artifacts. The full width at half-maximum of this method is 14.1%-27.8% and 4.2%-25.0% narrower than those of traditional apodization methods in the field II simulations and Geabr_0 experiment, respectively.

An apodization method for guided-mode resonance grating with waveguide cavity

A cavity-resonator-integrated guided-mode resonance mirror (CRIGM) consisting of a small-aperture grating coupler integrated in a waveguide cavity on a high-reflection substrate reflects an incident free-space wave with reflection-phase variation of 2π in a resonance condition. CRIGM has been investigated as a key component in surface mount packaging of VCSEL for future optical interconnects but the reflectance of a fabricated CRIGM was not sufficient. Matching of electric field distribution between an incident Gaussian beam and the reflected beam from the CRIGM is discussed for improving the reflectance. A new apodization method of grating-tooth shift is proposed for the field-distribution matching. CRIGMs with the new and a well-known fill-factor apodization methods are characterized by numerical simulation. It is predicted that the previously measured reflectance will be improved by more than 1.2 dB by introducing either of the apodization methods.

Sidelobe Control for Bistatic SAR Imaging

This letter presents coherent and incoherent nonlinear apodization methods for bistatic synthetic aperture radar (SAR) imaging. The methods are developed on the principle of nonlinear apodization for monostatic SAR imaging and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\omega \,\,-\,\,k$ </tex-math></inline-formula> relationship representing the bistatic region of support. This relationship plays an important role in designing 2-D windows for the apodization methods. The simulation results show that the presented apodization methods work efficiently with bistatic SAR imaging. In the experiment with a coherent dual apodization (CDA) method presented in this letter, the sidelobe attenuates very fast, and the peak sidelobe is reduced about 16 dB, while the resolutions in azimuth and range are maintained.

Femtosecond laser line-by-line inscription of apodized fiber Bragg gratings.

The reflection spectra of conventional fiber Bragg gratings (FBGs) with uniform index modulation profiles typically have strong sidelobes, which hamper the performance of FBG-based optical filters, fiber lasers, and sensors. Here, we propose and demonstrate a femtosecond laser line-by-line (LbL) scanning technique for fabricating apodized FBGs with suppressed sidelobes. This approach can flexibly achieve various apodized modulation profiles via precise control over the length and/or transverse position of each laser-inscribed index modification track. We theoretically and experimentally studied the influences of the apodization function on the side-mode suppression ratio (SMSR) in the fabricated apodized FBG, and the results show that a maximum SMSR of 20.6 dB was achieved in a Gaussian-apodized FBG. Subsequently, we used this method to fabricate various apodized FBGs, and the SMSRs in these FBGs were reduced effectively. Specifically, a dense-wavelength-division-multiplexed Gaussian-apodized FBG array with a wavelength interval of 1.50 nm was successfully fabricated, and the SMSR in such an array is 14 dB. Moreover, a Gaussian-apodized phase-shifted FBG and chirped FBG were also demonstrated with a high SMSR of 14 and 16 dB, respectively. Therefore, such an apodization method based on a modified femtosecond laser LbL scanning technique is an effective and flexible way to fabricate various FBGs with high SMSRs, which is promising to improve the performance of optical filters, fiber lasers, and sensors.

Azimuth apodization for autoregressive synthetic‐aperture radar imaging

Autoregressive backprojection (ARBP) approximates the procedure of forming synthetic-aperture radar (SAR) sequential images as an autoregressive (AR) process, avoiding redundant computation between adjacent images. Azimuth apodization for ARBP entails designing the aforementioned AR process, including AR order selection and AR model parameter estimation. However, the conventional azimuth apodization method for ARBP provides only empirical means to conduct such a procedure. Moreover, it cannot address the ringing effect from the infinite impulse response of the AR model, and consequently, other unwanted azimuth pulses will degrade the SAR images. This study discusses azimuth apodization for ARBP and proposes a scheme that includes methods for AR model order selection and parameter estimation. Firstly, matrix rank-k approximation is adopted for AR model order selection. Then, a revised azimuth apodization procedure for parameter estimation is discussed. It introduces a penalty factor to render the ringing effect and model estimation error controllable. Moreover, experiments based on an open data set validate the proposed ARBP azimuth apodization scheme. In this way, the proposed azimuth apodization obtains a balance between computational complexity and imaging quality for ARBP.

Broadband achromatic metasurface filter for apodization imaging in the visible

Apodization has found many important applications in imaging and optical communication. Traditional apodization methods are based on the phase or amplitude modulation, suffering from either narrow working bandwidth, or reduced spatial resolution. Here, a broadband achromatic metasurface filter is proposed to realize apodization imaging without sacrificing the spatial resolution. With this filter, a nearly dispersionless phase modulation in the entire visible waveband can be achieved. The simulated results indicate that the focusing efficiency of the metasurface filter is twice larger than that of the phase filter and the imaging contrast can be improved by three times with the metasurface filter compared to the Gaussian filter. The sidelobes in the point spread function can also be efficiently suppressed to the scale of 10-5 in the whole visible spectrum ranging from 400 nm to 700 nm with our design. Additionally, the resolution of diffraction limit or even sub-diffraction can be achieved with this method.

Femtosecond Laser Fabricated Apodized Fiber Bragg Gratings Based on Energy Regulation

In this paper, an energy regulation method based on the combination of a half-wave plate (HWP) and a polarization beam splitter (PBS) is proposed for the fabrication of apodized fiber gratings, which can effectively improve the side lobe suppression ratio of high-reflectivity fiber Bragg gratings (FBGs) fabricated by femtosecond laser. The apodized FBGs prepared by this method has good repeatability and flexibility. By inputting different types of apodization functions through the program, the rotation speed of the stepping motor can be adjusted synchronously, and then the position of the HWP can be accurately controlled so that the laser energy can be distributed as an apodization function along the axial direction of the fiber. By using the energy apodization method, the gratings with a reflectivity of 75% and a side lobe suppression ratio of 25 and 32 dB are fabricated in the fiber with a core diameter of 9 and 4.4 μm, respectively. The temperature and strain sensitivities of the energy-apodized fiber gratings with a core diameter of 4.4 μm are 10.36 pm/°C and 0.9 pm/με, respectively. The high-reflectivity gratings fabricated by this energy apodization method are expected to be used in high-power narrow-linewidth lasers and wavelength division multiplexing (WDM) systems.

400 MHz ultrafast optical coherence tomography

An ultrafast time-stretched swept source with a sweep rate of 400 MHz is demonstrated based on the buffering of a 100 MHz femtosecond laser pulse train. To the best of our knowledge, this is the highest sweep rate of swept sources for optical coherence tomography (OCT) that has been reported. With a 10 dB sweep range of ∼100nm, an axial resolution of 19 µm is obtained in the OCT. OCT imaging of high-speed rotating disks is demonstrated. A composite complex apodization method is proposed and demonstrated to enhance the signal to noise ratio in the OCT imaging.

Investigation and Analysis of Ultrasound Imaging Based on Linear CMUT Array

In the next generation of ultrasound imaging systems, Capacitive micromachined ultasonic transducer (CMUT) based on microelectromechanical systems (MEMS) is a promising research direction of transducers, which has wide application prospects. In this paper, based on the study of three imaging methods, including classical phased array (CPA) imaging, classical synthetic aperture (CSA) imaging and phased subarray (PSA) imaging, several different imaging schemes are designed for linear CMUT array, after that the performances of these imaging schemes are compared and analyzed. The effects of the three imaging methods are verified and analyzed based on the linear CMUT array. Through analysis, it is found that the image quality of the classical phased array imaging method is the best, the imaging quality of the above three imaging methods can be effectively improved by adopting the amplitude apodization and dynamic focusing method. The research results in this paper will provide theoretical basis and application reference for the design of ultrasonic imaging system based on linear CMUT array in the future.

RESEARCH OF PARAMETERS OF FIBER-OPTICAL MEASURING SYSTEMS

At present there exist a lot of technical devices, the failure of which can be connected not only with huge financial losses, but with the treat to the environment as well. Therefore, an important problem is the effective devices conditions diagnostics, including electronic components and check of their operation. Timely faults detecting allows introducing the prevention measures and avoiding serious consequences. Fiber-optic sensors have several advantages, more important of which include the immunity to electromagnetic disturbances, little weight and possibility to be included into the structure being measured. The most perspective are the sensors based on the Bragg fiber gratings. Bragg fiber gratings have several advantages, for instance, they allow creating the distributed measuring massifs, which contain several sensors. As well, they are insensitive to the optic power source vibrations. Variety of using the fiber sensors based on the Bragg fiber gratings has led to producing the Bragg fiber gratings with different spectral characteristics. Homogeneous Bragg fiber gratings have the spectra with solid side lobes, which can influence at the temperature sensor processing characteristics. To level the side lobes there is applied the apodization method, which is one of the means to affect the spectral form. The article herein considers the issues of the Bragg fiber gratings mathematical and computer modeling using the transfer matrix method. Transfer matrix method allows defining the optical components spectral characteristics based on the bound modes theory and description of electromagnetic wave, passing through an optic fiber. In the article there have been analyzed the Bragg fiber gratings in compliance with spectral features, such as transmission and reflectance spectra. As well, there has been carried out the experiment with influence of various parameters at the Bragg fiber gratings spectral characteristics. There have been studied the Bragg fiber gratings spectral features and selected the grating optimal parameters for designing the fiber-optic sensors based on the Bragg fiber gratings.

High spatial resolution temperature field measurements by apodized short fiber Bragg grating sensors

To realize the high spatial resolution measurement of the temperature field, a temperature sensor array composed of eight apodized short fiber Bragg gratings with grating length of 1 mm and spatial spacing of 2 mm are fabricated. To suppress the side lobes, apodization methods by single-slit diffraction are designed. The sensor array is proposed to measure the real-time temperature distribution. The experimental results show that the temperature-sensing array can accurately measure the temperature field distribution with high spatial resolution and rapid response.

Intensity‐Enhanced Apodization Effect on an Axially Illuminated Circular‐Column Particle‐Lens

AbstractA particle can function as a refractive lens to focus a plane wave, generating a narrow, high intensive, weak‐diverging beam within a sub‐wavelength volume, known as the ‘photonic nanojet’. It is known that apodization method, in the form of an amplitude pupil‐mask centrally situated on a particle‐lens, can further reduce the waist of a photonic nanojet, however, it usually lowers the intensity at the focus due to blocking the incident light. In this paper, the anomalously intensity‐enhanced apodization effect was discovered for the first time via numerical simulation of focusing of the axially illuminated circular‐column particle‐lenses, and a greater than 100% peak intensity increase was realised for the produced photonic nanojets.

Tailoring axial intensity of laser beams with a heart-shaped hole.

We demonstrated a simple heart-shaped hole to tailor the axial intensity of a collimated laser beam. This hole is transformed from a soft-boundary one, which avoids the difficulty in fabricating the soft-boundary mask designed by the apodization method, as well as the interference problem caused by the pixel structure of the spatial light modulator. When a collimated light passes through this hole, its axial intensity oscillates less than 11% within a certain distance, while the fluctuation after the circular aperture is up to 200%. We compared the propagation of beams after this hole and a circular aperture experimentally and theoretically. The results show that this hole is a useful tool to get the laser beam with uniform axial intensity.

Twisted optical-fiber-based acousto-optic tunable filter controlled by the flexural acoustic polarization

The spectral characteristics of twisted fiber-based acousto-optic filters are theoretically investigated. The influences of three types of flexural acoustic polarization states — linear, circular, and elliptical polarizations — on filter spectra are studied under realistic experimental conditions: a fiber length of 5 – 20 cm and a circumferential fiber twist angle of 80 nm for a twist angle of 12π. We will describe how the transmission of each resonance peak can also be selectively tuned by adjusting the ellipticity of the input acoustic polarization from linear to circular. The results illustrate that our approach exploiting a combination of the fiber twist and acoustic polarization management offers an excellent route to the spectral shaping of all-fiber acousto-optic devices in that the transmission of multiple resonances, as well as their spectral positions, are readily and individually controllable in a single device configuration. In addition, we also propose a novel cosine apodization method to suppress the undesirable sidelobe spectra occurring between the dual resonance peaks. The technique is based on a cosine modulation of the AO coupling strength along the fiber, which is achieved by using a combination of the fiber’s circumferential twist and the linear acoustic polarization. The proposed scheme is useful to minimize the crosstalk occurring between adjacent resonance peaks. We highlight that our approach is directly applicable to matched filtering as robust, adaptable, stable, and versatile optical filters.

Enhanced ISAR imaging method using back‐projection and SVA algorithm

ABSTRACTWe present an inverse synthetic aperture radar image enhancement technique that combines the plane‐wave approximation‐based back‐projection (BP) algorithm and the spatially variant apodization (SVA) method. The SVA technique is applied to reduce the sidelobe levels while retaining the cross‐range resolution. To demonstrate the performance of our algorithm, we compare the conventional fast Fourier transform (FFT)‐based algorithm, the combined FFT and SVA method, the BP algorithm, and the proposed method (combined BP and SVA method). The cross‐range resolution and peak to sidelobe ratio (PSLR) are selected as performance measures. Our algorithm has better resolution than the conventional combined FFT and SVA method, while the combined FFT and SVA method has better PSLR than our method. We validate our algorithm via a numerical simulation and measurements conducted in a compact range. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:993–997, 2015

Apodization Method for Standard Load Modulation Amplitude Measurement on Proximity Integrated Circuit Cards

Standard tests on ISO/IEC 14443 proximity integrated circuit cards/objects include verification that the amplitude of the modulation is within specification, performed by digitizing a test-antenna signal with an ordinary digital storage oscilloscope and calculating the relevant component with a finite Fourier series. Leakage errors may occur due to lack of synchronization between sampling clock and carrier and limited precision of measurement of carrier frequency, leading to inconsistent test results. The problem is eliminated by the application of a Bartlett window in the time domain. In this paper, the theory of the technique is presented formally. Closed-form expressions for the leakage before and after apodization are derived, from which the effects of sampling frequency and carrier frequency, the error in carrier frequency, and the number of samples can be seen immediately.

Reduction of voxel bleeding in highly accelerated parallel 1H MRSI by direct control of the spatial response function

To substantially improve spatial localization in magnetic resonance spectroscopic imaging (MRSI) accelerated by parallel imaging. This is important in order to make MRSI more reliable as a tool for clinical applications. The sensitivity encoding acceleration technique with spatial overdiscretization is applied for the reconstruction of parallel MRSI. In addition, the spatial response function is optimized by minimizing its deviation from a previously chosen target function. This modified minimum-norm sensitivity encoding-MRSI reconstruction approach is applied in this article for in vivo pulse-acquire MRSI of human brain at 7T with simulated acceleration factors of 2, 4, and 9 as well as actual 4-fold accelerated MRSI. The sidelobes of the spatial response function are significantly suppressed, which reduces far-reaching voxel bleeding. At the same time, the major enlargement of the effective voxel size, which would be introduced by conventional k-space apodization methods, is largely avoided. Regularization allows for a practical trade-off between noise minimization, effective voxel size, and unaliasing. Although not aiming at increasing the nominal spatial resolution, a better spatial specificity is achieved. Simultaneous suppression of short- and far-reaching voxel bleeding in MRSI is analyzed and reconstruction of highly accelerated parallel in vivo MRSI is demonstrated.