Spatial Frequency Modulation Research Articles

Topological pumping in acoustic waveguide arrays with hopping modulation

Thouless pumping is the adiabatic transportation of quantized charge, which is regarded as the dynamic version of the quantum Hall effect. Here we propose the design of an acoustic system to demonstrate the topological pumping characterized by transporting acoustic energy from one side to the opposite. The system is composed of coupled acoustic waveguide arrays with modulated coupling along both cross-sections and the propagating direction. We explore multiple topological phases by introducing rich spatial frequency or enlarged range of the hopping modulation. Such distinct topological phases are evidenced by adiabatic evolution of the edge states, where the acoustic system varies continuously and slowly along the state propagating direction. The robustness behavior of the edge states transport is also verified with numerical simulations to imply their topology origin. Our work provides a route to realize topological phases and utilize the corresponding edge states in waveguide arrays that can lead to versatile acoustic wave manipulation applications.

Elimination of spatial Rabi frequency modulation by sideband suppression with a calcite crystal

Elimination of spatial Rabi frequency modulation by sideband suppression with a calcite crystal

Design and analysis of spatial modulation based orthogonal time frequency space system

In this paper, we design a spatial modulation based orthogonal time frequency space (SMOTFS) system to achieve improved transmission reliability and meet the high transmission rate and high-speed demands of future mobile communications, which fully utilizes the characteristics of spatial modulation (SM) and orthogonal time frequency space (OTFS) transmission. The detailed system design and signal processing of the SM-OTFS system have been presented. The closed-form expressions of the average symbol error rate (ASER) and average bit error rate (ABER) of the SM-OTFS system have been derived over the delay-Doppler channel with the help of the union bounding technique and moment-generating function (MGF). Meanwhile, the system complexity has been evaluated. Numerical results verify the correctness of the theoretical ASER and ABER analysis of the SM-OTFS system in the high signal-to-noise ratio (SNR) regions and also show that the SM-OTFS system outperforms the traditional SM based orthogonal frequency division multiplexing (SM-OFDM) system with limited complexity increase under mobile conditions, especially in high mobility scenarios.

Correction and quantification of MTF in scanning laser microscopy.

Observations using conventional microscopy often lack information related to the fine structures of an object, such as intensity and phase, because of limitations in the lens aperture. In this study, the intensity and phase information are appropriately converted into an electrical signal using laser scanning and photodetectors. Intensity and phase are completely separated, and the missing information is restored based on the frequency of the electrical signal. Using this method, the original intensity and phase information of the object to be observed can be correctly restored. Therefore, we propose a novel method to calculate the degree of intensity and phase modulation by calculating the direct and alternating current components obtained from the output of the sum and difference of the two photodetectors. The degree of spatial frequency modulation is corrected according to the electrical signal frequency to detect transparent or unstained cells. We first performed laser scanning of an object. Then, signals were detected using two photodetectors placed in the far-field, separated by the optical axis as the boundary. The output signals of the photodetectors were processed and the intensity and phase were unambiguously separated, thus allowing the visualization of the phase information of the transparent bodies and unstained cells. Spatial frequency correction was performed to correct the modulation. Our method successfully separated the information related to the intensity and optical path difference (OPD). In future work, by accurately correcting the intensity and OPD, it will be possible to separate the absorption rate from the ratio of the irradiation light intensity to the observed intensity and to separate the OPD into the refractive index and the thickness information. This method allows the accurate determination of these parameters in a noninvasive manner.

Active line scan with spatial gating for sub-diffuse reflectance imaging of scatter microtexture.

We examine the value of an active line scan with spatial gating for imaging sub-diffuse, wide-field reflectance microtexture. Line scanning combined with spatial gating and linear translation can be used for localized detection of features in the surface layer of a turbid target. The line scan provides broadband spatial frequency modulation, and the spatial gating effectively high-pass filters the reflectance. The major benefit of this approach is that of high dynamic range (70%-90%) signal preservation and high contrast to noise when imaging at high spatial frequencies. Alternative approaches, such as spatial frequency domain imaging, are degraded by low dynamic range in demodulated images, making it nearly impossible to image over a wide field of view at frequencies over 1.5mm-1 using commercial technology. As such, active line scanning with spatial gating presents as an inherently high sensitivity and high dynamic range method of imaging microscopic scattering features in only the surface layer of a turbid medium.

Far‐Field Superresolution Imaging via Spatial Frequency Modulation

AbstractThe diffraction limit substantially impedes the resolution of the conventional optical microscope. Under traditional illumination, the high‐spatial‐frequency light corresponding to the subwavelength information of objects is located in the near‐field in the form of evanescent waves, and thus not detectable by conventional far‐field objectives. Recent advances in nanomaterials and metamaterials provide new approaches to break this limitation by utilizing large‐wavevector evanescent waves. Here, a comprehensive review of this emerging and fast‐growing field is presented. The current superresolution imaging techniques based on evanescent‐wave‐assisted spatial frequency modulation, including hyperlens, microsphere lens, and evanescent field‐illuminated spatial frequency shift microscopy, are illustrated. They are promising in investigating unobserved details and processes in fields such as medicine, biology, and material research. Some current challenges and future possibilities of these superresolution methods are also discussed.

Exceptional Points of Degeneracy Directly Induced by Space–Time Modulation of a Single Transmission Line

We demonstrate how exceptional points of degeneracy (EPDs) are induced in a single transmission line (TL) directly by applying periodic space-time modulation to the per-unit-length distributed capacitance. In such space-time modulated (STM)-TL, two eigenmodes coalesce into a single degenerate one, in their eigenvalues (wavenumbers) and eigenvectors (voltage-current states) when the system approaches the EPD condition. The EPD condition is achieved by tuning a parameter in the space-time modulation, such as spatial or temporal modulation frequency, or the modulation depth. We unequivocally demonstrate the occurrence of the EPD by showing that the bifurcation of the wavenumber around the EPD is described by the Puiseux fractional power series expansion. We show that the first order expansion is sufficient to approximate well the dispersion diagram, and how this "exceptional" sensitivity of an STM-TL to tiny changes of any TL or modulation parameter enables a possible application as a highly sensitive TL sensor when operating at an EPD.

Dynamically Modulating Plasmonic Field by Tuning the Spatial Frequency of Excitation Light.

Based on the Fourier transform (FT) of surface plasmon polaritons (SPPs), the relation between the displacement of the plasmonic field and the spatial frequency of the excitation light is theoretically established. The SPPs’ field shifts transversally or longitudinally when the spatial frequency components or are correspondingly changed. The SPPs’ focus and vortex field can be precisely located at the desired position by choosing the appropriate spatial frequency. Simulation results are in good agreement with the theoretical analyses. Dynamically tailoring the plasmonic field based on the spatial frequency modulation can find potential applications in microparticle manipulation and angular multiplexed SPP focusing and propagation.

Application of LFM-CPM signal into a DFRC system based on circulating code array

A dual-function radar-communications (DFRC) system based on circulating code array is designed in this paper. The communication symbols are firstly embedded into the continuous phase modulation (CPM) term and then attached to the transmitted basic waveform. The particular configuration of the circulating code array provides a possibility to recover the spectrum of the transmitted basic waveform. According to the relationship between the spectrum of the synthesized signal and the spectrum of the basic waveform, a modified spatial-frequency modulation coefficient (SFMC) is proposed in the demodulation procedure. The proposed technique requires only one waveform to implement a DFRC system with an omnidirectional transmitted beam pattern. The communication function can be realized no matter that the communication direction is within the mainlobe or sidelobe of radar. It is verified that the designed DFRC system can make a balance between radar coherent processing performance and communication bit error rate (BER) performance. The communication information is secure from directions other than the intended ones. Simulation results are presented to validate the performance of the designed DFRC system.

Spatial resonance in an anisotropic medium with modulated gyrotropy

The problem of the propagation of linearly polarized light in an optically anisotropic medium with spatially modulated gyrotropy is considered. The analysis has been carried out using optical Bloch equations in the approximation of a rotating wave. For clarity, the results are interpreted on the Poincaré sphere. It is demonstrated that under the resonance conditions, i.e., when the spatial frequency of modulation of gyrotropy coincides with the spatial frequency of polarization beats, a resonant increase in the amplitude of these beats is observed.

Limits of applicability of the direct ray approximation in modeling optical properties of liquid-crystal diffraction gratings

Using computer modeling, we estimate limits of applicability of the direct ray approximation in modeling the optical properties of liquid-crystal diffraction gratings with continuous spatial modulation of the local optic axis orientation in a liquid crystal layer. The data presented concerning the influence of the spatial frequency and character of modulation of the local optic axis, as well as the magnitude of birefringence of the medium, on the accuracy of the results obtained in this approximation are also useful in considering birefringent layers with an aperiodic variation of the local optic axis.

Circulating Code Array for a Dual-Function Radar-Communications System

It is possible to demodulate the embedded communication symbols from the transmitted base waveform by using the relationship between the transmitted base signal and the synthesized signal in the spatial domain of a circulating code array. The spatial-frequency modulation coefficient (SFMC) is firstly analyzed to determine the frequency band used for the communication user in a certain direction. Perturbation phase modulation (PM) term is attached to the certain time duration of a linear frequency modulation (LFM) signal to embed communication symbols. The perturbation PM term is designed to be a weighted sum of multiple orthogonal sub-PM terms and the communication symbols are carried out by the coefficients of different sub-PM terms. An adjustable weighted coefficient is applied to control the degree of the perturbation PM term to make a balance between radar performance and communication bit error rate (BER) performance. The designed dual-function radar-communications (DFRC) system has the following properties: 1) Multidimensional waveform design issue for a DFRC system based on multiple input multiple output (MIMO) is converted into a transmitted base waveform design issue; 2) the communication receiver can be located in any direction; 3) the effect of embedded communication symbols on radar performance can be effectively controlled while with a satisfactory BER performance.

Geometrical Optics of an Anisotropic Media with Space Modulated Gyrotropy

The problem of the polarized light propagation in an optically homogeneous anisotropic medium with spatially modulated gyrotropy is considered. The analysis was carried out using a numerical solution of a system of coupled equations obtained in the approximation of geometric optics. For illustrative purposes, the results of numerical analysis are also presented on the Poincare sphere. The resonance character of the dependence of the amplitude of polarization beats as a function of the spatial frequency of gyrotropy modulation is shown.

Single-Point Detection Architecture via Liquid Crystal Modulation for Hyperspectral Imaging Systems

Hyperspectral imaging (HSI) architectures can acquire one-dimension of spatial information and one-dimension of spectral information on a two-dimensional image sensor for an image, such as in the traditional line-scan HSI architecture. However, development of HSI architectures for multiple spatial dimensions is challenging as there is not a third dimension on a two-dimensional image sensor on which to store spectral information. The presented work introduces a snapshot HSI architecture to alleviate this issue. The snapshot HSI architecture incorporates single-point detection via liquid crystal modulation and a single photodiode. Mixing of hyperspectral data is expressed as intermodulation frequency products within the Fourier-domain. Spatial information can be recorded through spatial frequencies and spectral information can be recorded through spectral frequencies. Such modulation is achieved through liquid crystal spatial and spectral arrays of an image beam. The spatial and spectral modulation frequencies form intermodulation frequency products that are recorded on the single photodiode and can be uncovered through Fourier-domain filtering.

Spatial frequency controlled by a phase carrier in spatial periodic modulation

An approach to controlling the spatial frequency of spatial periodic modulation (SPM) on focal plane has been presented. This approach is based on the application of phase carrier in the near-field beam. The phase amplitude of phase carrier is able to modulate the intensity of the spatial frequency of SPM from the maximum to 0. In addition, the period T of phase carrier determines the position of the strongest spatial frequency of amplitude SPM. When the period is increased, the position of the strongest spatial frequency is closer to the center. In order to avoid introducing new modulation to the output near-field beam, it is necessary to choose appropriate value of T to ensure that the strongest spatial frequency is beyond the cutoff frequency of pinhole. The feasibility of this method is verified by theoretical analysis and experimental results. This method provides a different perspective to solve the problems that spatial filter encounter, such as the pinhole closure and the damage to the material of pinhole filter periphery, in high power laser systems, as well as improving the quality of output near-field beam.

Phase triangulation method with spatial modulation frequency optimization

The paper proposes the phase triangulation method with an optimization of spatial modulation frequency. The optimal frequency is calculated based on the analysis of the amplitude-frequency characteristics of the measuring optical path according to the data obtained during the formation of structured images encoding the binary Gray code. The proposed approach makes it possible to use the optimal frequency of optical source spatial modulation in the 3D geometry measurements using phase steps triangulation and binary Gray code approaches. As a result, the method provides the minimum level of measurement error, regardless to parameters of the used optical-electronic elements of the measuring system.

Steering the propagation of finite-energy Airy beam by spatial phase modulation

Abstract The effect of spatial phase modulation on the propagation of finite-energy Airy beam (FEAB) is investigated. A sinusoidal phase is introduced on a FEAB and the propagation behavior is analyzed in Kerr medium by numerical simulation. The basic idea is to impose a sinusoidal phase modulator on the beam before entering the medium. It is found that optical amplitude, spatial modulation frequency, phase shift and truncated factor have important impact on the propagation behavior. Deflection, soliton-like propagation, beam splitting and periodical oscillation can be easily realized by choosing different values of modulation parameters. These results may found novel applications in beam splitter, modulator and other optical steering application for Airy beams.

Adaptive Control of the Spatial Modulation Frequency in the Phase Triangulation Method

The method for determining the optimal frequency of spatial modulation in the measurement of three-dimensional geometry by the method of phase triangulation is proposed. The method is based on the construction of the frequency response of the measuring system. The proposed approach makes it possible to use the optimal frequency of spatial modulation of an optical source in measurements of three-dimensional geometry by the method of phase steps and the Gray binary code. As a result, this method makes it possible to create a universal control algorithm that provides measurement of three-dimensional geometry by the method of phase steps with the smallest error.

Thermometry in gas flows using two-line fluorescence imaging and structured illumination

We present a feasibility demonstration of the instantaneous determination of temperature fields in gaseous flows based on planar laser-induced fluorescence by integrating structured illumination with the two-line thermometry technique using nitric oxide as a tracer. This approach allows the capture of two fluorescence images originating from the simultaneous probe of two rotational states of nitric oxide (X2Π, v” = 0) using one detector and their subsequent deconvolution using spatial frequency analysis. Average experimental temperature measurements in an underexpanded jet demonstrate the viability of this approach, suggesting that the laser spatial modulation frequency and laser orientation with respect to the flow field under study impose the achievable spatial resolution limits.

Contrast and spatial frequency modulation for diagnosis of amblyopia: An electrophysiological approach

PurposeTo evaluate the diagnostic value of visual evoked potentials (VEPs) and to find out which test setting has the most sensitivity and specificity for amblyopia diagnosis. MethodsThirty-three adult anisometropic amblyopes were intended in this study and were tested for visual evoked potentials with different stimulus conditions including three spatial frequencies [1, 2, and 4-cycles-per-degree (cpd)] at four contrast levels (100, 50, 25, and 5%). We also tested psychophysical contrast sensitivity and compared the results with electrophysiological ones. We plotted Receiver Operating Characteristic (ROC) curve for each VEP recording and psychophysical contrast sensitivity to evaluate the area under the curve, sensitivity, specificity, and cut-point value of each test stimulus for detecting amblyopic eyes. ResultsThirty-three amblyopic and 33 non-amblyopic eyes were examined for psychophysical contrast sensitivity and VEPs. Area under the ROC curve (AURC) findings showed that VEP with different stimulus settings can significantly detect amblyopic eyes, as well as psychophysical contrast sensitivity test. We found that P100 amplitudes had the largest AURC in response to stimuli of 2-cpd spatial frequency at 50 (P < 0.001) and 25% (P < 0.001) contrast levels, respectively. Cut-off amplitudes for these stimuli were 8.65 and 4.50 μV, which had a sensitivity of 0.758 and 0.697 and a specificity of 0.788 and 0.848, respectively. The sensitivity and specificity of VEP P100 amplitude in response to the stimuli with 2 cpd spatial frequency and 50 and 25% contrast were greater than the findings obtained from psychophysical contrast sensitivity test. ConclusionAccording to our findings, assessment of VEP amplitudes in response to stimuli of 2-cpd spatial frequency at 50 and 25% contrast levels can best detect amblyopia with highest sensitivity and specificity and thus, are the protocols of choice for detection of amblyopic eyes.