Spatial Frequency Response Research Articles

In-silico CT lung phantom generated from finite-element mesh.

Several lung diseases lead to alterations in regional lung mechanics, including ventilator- and radiation-induced lung injuries. Such alterations can lead to localized underventilation of the affected areas, resulting in the overdistension of the surrounding healthy regions. Thus, there has been growing interest in quantifying the dynamics of the lung parenchyma using regional biomechanical markers. Image registration through dynamic imaging has emerged as a powerful tool to assess lung parenchyma's kinematic and deformation behaviors during respiration. However, the difficulty in validating the image registration estimation of lung deformation, primarily due to the lack of ground-truth deformation data, has limited its use in clinical settings. To address this barrier, we developed a method to convert a finite-element (FE) mesh of the lung into a phantom computed tomography (CT) image, advantageously possessing ground-truth information included in the FE model. The phantom CT images generated from the FE mesh replicated the geometry of the lung and large airways that were included in the FE model. Using spatial frequency response, we investigated the effect of " imaging parameters" such as voxel size (resolution) and proximity threshold values on image quality. A series of high-quality phantom images generated from the FE model simulating the respiratory cycle will allow for the validation and evaluation of image registration-based estimations of lung deformation. In addition, the present method could be used to generate synthetic data needed to train machine-learning models to estimate kinematic biomarkers from medical images that could serve as important diagnostic tools to assess heterogeneous lung injuries.

An aerodynamic optimization method based on virtual Nash equilibrium for global and local parameter decoupling

The parameterization of aerodynamic shape in the aircraft design optimization usually includes both global and local configuration features. The global parameters determine the wing span, aspect ratio, angle of attack, twist angle, and sweep angle. Meanwhile, the local parameters define the geometric shape of the wing section, including thickness and camber, etc. The changes in different types of parameters during the optimization process will lead to perturbations in the corresponding wavelength of the geometric shape, which in turn will cause different spatial frequency responses in the flow field. Generally, local parameter changes will generate high-frequency perturbations in the flow field and propagate only near the disturbance source; While global parameter changes will cause low-frequency perturbations in the flow field and propagate throughout the entire flow field. If these two different types of parameters are optimized at all once, it will lead to significant mutual interference, thereby reducing optimization efficiency. Therefore, this paper proposes an efficient optimization algorithm NashGL based on the concept of virtual Nash equilibrium. It decouples global and local variables and optimizes them simultaneously on different populations, effectively isolating interference between these two types of design variables. On the other hand, due to the small number of global variables, their rapid convergence can guide local variables towards the optimal solution. Through two aerodynamic optimization cases of NACA0012 airfoil and wing body aircraft, it is shown that compared with the method of simultaneously optimizing global and local parameters, the NashGL algorithm in this paper has the highest optimization efficiency, with an improvement of about 30% and 60%, respectively.

Poster Session II: SSVEP measurements of color and spatial frequency response in V1.

Recent work from our group (Segala et al, eLife, 2023) shows that the rules for binocular luminance signal combination depend on spatial frequency (SF). Structured patterns show strong interocular suppression while unstructured inputs (mean field disks) do not. Here, we used SSVEPs to ask if SF dependence is also found in chromatic pathways. SSVEPs were recorded from 12 subjects using a canonical V1 template (Poncet & Ales, 2023). Eyes were targeted using shutter goggles and stimuli were contrast-reversing gratings or disks at 5Hz (left eye) and 7Hz (right eye). Experimental factors were stimulus SF (disk, grating 1cpd), chromaticity (LMS, L-M or S-cone isolating) and ocularity (left, right or both). Monocular conditions generated large responses at 2F. In binocular conditions, all 2F responses showed suppression, and significant intermodulation (IM) terms (sums and differences of the inputs - e.g., 2Hz) were present. The magnitude of both suppression and IM in the binocular condition depended on SF and chromaticity; IM amplitudes were higher for gratings compared to disks in the luminance condition, but higher for disks compared to gratings in the chromatic conditions. Overall we found significant differences in the spectral response signatures across all stimulus combinations. All inputs undergo binocular combination in V1 but the rules governing the combination appear to depend on both chromaticity and SF.

A Phase-Sensitive Optical Time Domain Reflectometry with Non-Uniform Frequency Multiplexed NLFM Pulse.

In the domain of optical fiber distributed acoustic sensing, the persistent challenge of extending sensing distances while concurrently improving spatial resolution and frequency response range has been a complex endeavor. The amalgamation of pulse compression and frequency division multiplexing methodologies has provided certain advantages. Nevertheless, this approach is accompanied by the drawback of significant bandwidth utilization and amplified hardware investments. This study introduces an innovative distributed optical fiber acoustic sensing system aimed at optimizing the efficient utilization of spectral resources by combining compressed pulses and frequency division multiplexing. The system continuously injects non-linear frequency modulation detection pulses spanning various frequency ranges. The incorporation of non-uniform frequency division multiplexing augments the vibration frequency response spectrum. Additionally, nonlinear frequency modulation adeptly reduces crosstalk and enhances sidelobe suppression, all while maintaining a favorable signal-to-noise ratio. Consequently, this methodology substantially advances the spatial resolution of the sensing system. Experimental validation encompassed the multiplexing of eight frequencies within a 120 MHz bandwidth. The results illustrate a spatial resolution of approximately 5 m and an expanded frequency response range extending from 1 to 20 kHz across a 16.3 km optical fiber. This achievement not only enhances spectral resource utilization but also reduces hardware costs, making the system even more suitable for practical engineering applications.

Contributed Session III: In vivo calcium imaging of macaque foveolar retinal ganglion cells reveals spatiochromatic receptive field properties.

Here, we optically record responses to spatial and chromatic stimuli using a calcium indicator in the living macaque eye to characterize the receptive field (RF) properties of retinal ganglion cells (RGCs) serving the foveal center. GCaMP6s was expressed in three female macaques. Adaptive optics ophthalmoscopy was used to image fluorescence (488nm ex, 520/35nm em) from RGCs whose RF centers were driven by cones in the central 36 arcmin of the fovea and additional RGCs driven by cones in the central 6 arcmin of the foveola. Using cone isolating and luminance flicker (1.3deg, 0.15Hz, LED 420nm, 530nm, 660nm), we derived cone weights in over 250 RGCs. Using drifting gratings (1.9deg, 6Hz, 4-50c/deg, 561nm), we derived the spatial frequency responses of 15 L vs. M cone opponent RGCs at the foveolar center. Employing computational modeling (ISETbio), we inferred the full spatial difference of gaussians center and surround structure for those 15 cells. Of the 34 foveolar RGCs, 44% exhibited L vs. M cone opponency, 15% were L+M ON, 6% were -L-M OFF, and 35% showed only L or only M responses. The spatial frequency response functions of 12/15 L vs. M opponent cells peaked at high spatial frequencies (25-40c/deg) and had a strong bandpass characteristic. Our model indicates that the responses of all 15 L vs. M opponent cells are consistent with single cone input to their RF centers and that our data are consistent with extrafoveal data when the blurring of the optics is accounted for.

Accurate Spatial-Frequency Response Controllable Frequency Invariant Beampattern Synthesis With Minimum Beamwidth

This communication proposes a new relaxation variable based cost function for the problem of frequency invariant (FI) beampattern synthesis. Two constraints in the spatial and frequency domains are imposed on the optimization problem. The objective of sparsifying the relaxation variable is exploited in constructing the constraint in the spatial domain, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -spatial response variation (SRV) is introduced in the frequency domain constraint to reduce frequency variance. These constraints enable a desirable trade-off between beamwidth and FI properties while achieving accurate spatial-frequency response control. Since the resulting optimization problem is sparse and non-convex, it is then proposed to be solved by exploiting the reweighted- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm in this paper. The remarked feature of the new approach is the improved target detection and anti-interference performance in radar and communication systems without waveform distortion. Simulation results validate the effectiveness of the proposed method.

Computational Optics for Mobile Terminals in Mass Production.

Correcting the optical aberrations and the manufacturing deviations of cameras is a challenging task. Due to the limitation on volume and the demand for mass production, existing mobile terminals cannot rectify optical degradation. In this work, we systematically construct the perturbed lens system model to illustrate the relationship between the deviated system parameters and the spatial frequency response (SFR) measured from photographs. To further address this issue, an optimization framework is proposed based on this model to build proxy cameras from the machining samples' SFRs. Engaging with the proxy cameras, we synthetic data pairs, which encode the optical aberrations and the random manufacturing biases, for training the learning-based algorithms. In correcting aberration, although promising results have been shown recently with convolutional neural networks, they are hard to generalize to stochastic machining biases. Therefore, we propose a dilated Omni-dimensional dynamic convolution (DOConv) and implement it in post-processing to account for the manufacturing degradation. Extensive experiments which evaluate multiple samples of two representative devices demonstrate that the proposed optimization framework accurately constructs the proxy camera. And the dynamic processing model is well-adapted to manufacturing deviations of different cameras, realizing perfect computational photography. The evaluation shows that the proposed method bridges the gap between optical design, system machining, and post-processing pipeline, shedding light on the joint of image signal reception (lens and sensor) and image signal processing (ISP).

Managing deviant data in spatial frequency response (SFR) measurement by outlier rejection

The edge-based Spatial Frequency Response (e-SFR) method was first developed for evaluating camera image resolution and image sharpness. The method was described in the first version of the ISO 12233 standard. Since then, the method has been applied in a wide range of applications, including medical, security, archiving, and document processing. However, with this broad application, several of the assumptions of the method are no longer closely followed. This has led to several improvements aimed at broadening its application, for example for lenses with spatial distortion. We can think of the evaluation of image quality parameters as an estimation problem, based on the gathered data, often from digital images. In this paper, we address the mitigation of measurement error that is introduced when the analysis is applied to low-exposure (and therefore, noisy) applications and those with small analysis regions. We consider the origins of both bias and variation in the resulting SFR measurement and present practical ways to reduce them. We describe the screening of outlier edge-location values as a method for improved edge detection. This, in turn, is related to a reduction in negative bias in the resulting SFR.

A tool for deriving camera spatial frequency response from natural scenes (NS-SFR)

Recent research on digital camera performance evaluation introduced the Natural Scene Spatial Frequency Response (NS-SFR) framework, shown to provide a comparable measure to the ISO12233 edge SFR (e-SFR) but derived outside laboratory conditions. The framework extracts step-edges captured from pictorial natural scenes to evaluate the camera SFR. It is in 2-parts. The first utilizes the ISO12233 slanted-edge algorithm to produce an &#x2018;envelope&#x2019; of NS-SFRs. The second estimates the system e-SFR from this NS-SFR data. One drawback of this proposed methodology has been the computation time. The process was not optimized, as it first derived NS-SFRs from all suitable step-edges and then further validated and statistically treated the results to estimate the e-SFR. This paper presents changes to the framework processes, aiming to optimize the computation time so that it is practical for real-world implementation. The developments include an improved framework structure, a pixel-stretching filter alternative, and the capability to utilize Graphics Processing Unit (GPU) acceleration. In addition, the methodology was updated to utilize the latest e-SFR algorithm implementation. The resulting code has been incorporated into a self-executable user interface prototype, available in GitHub. Future goals include making it an open-access, cloud-based solution to be used by scientists, camera evaluation labs and the general public.

Does the slanted-edge method provide the true value of spatial frequency response?

The slanted-edge method is commonly used for measuring the spatial frequency response (SFR) of digital imaging systems. To investigate the intrinsic capability of the slanted-edge method, this study formulated a procedure for calculating the SFR and proposed a numerical method for evaluating the accuracy of the estimated SFR relative to the theoretical value. It is shown that the slanted-edge method yields an accurate value of the SFR under ideal conditions and is a rational and consistent tool for determining the true resolution characteristics. However, under practical conditions, this includes some estimation errors. Based on this analysis, it is possible to identify the parameter that influences the estimation accuracy in the SFR computation.

Angular dependence of spatial frequency modulation in diffusion media

An optical field will undergo coherent diffusion when it is mapped into thermal-motioned atoms, e.g., in a slow or storage light process. As was demonstrated before, such diffusion effect is equivalent to a spatial low-pass filter attenuating the high spatial frequency (SF) components of the optical field. Here, employing electromagnetically induced transparency (EIT) based light storage in hot atomic vapor, we demonstrate that the angular deviation between the control and probe beams could be utilized as a degree of freedom to modulate the SF of the probe beam. The principle is to change the diffusion-induced low-pass filter into a band-pass filter, whose SF response can be tuned by varying the direction and magnitude of the angular deviation. Transverse multimode light fields, such as optical images and Laguerre-Gaussian modes are utilized to study such SF modulation. Our findings could be broadly applied to the fields of quantum information processing, all-optical image manipulation and imaging through diffusive media.

Estimating uncertainty for the instrument transfer function measurement of 3D scanners.

Spatial resolution is an important aspect of many optical instruments. It is defined as the ability of surface-topography measuring instruments to distinguish closely spaced surface features. Following convention, spatial resolution can be defined as the spatial frequency response of the instrument, known as the instrument transfer function (ITF). In this paper, we describe the step-artifact approach for estimating the ITF for 3D scanners, discuss step artifact characterization and validation approaches, and present a method to estimate the combined uncertainty of the ITF measurement. The approach is demonstrated using the EinScan-Pro 3D scanner. A step artifact is used for the measurement that takes advantage of the cleaving properties of a single-side polished silicon wafer. The uncertainty analysis includes simulations to estimate the contribution due to influencing factors such as the alignment of the step artifact to the measurement axis, the diffuse versus specular scattering properties of the step edge, and various processing parameter choices.

Novel Measurement-Based Efficient Computational Approach to Modeling Optical Power Transmission in Step-Index Polymer Optical Fiber

Polymer optical fibers (POFs) are playing an important role in industrial applications nowadays due to their ease of handling and resilience to bending and environmental effects. A POF can tolerate a bending radius of less than 20 mm, it can work in environments with temperatures ranging from −55 °C to +105 °C, and its lifetime is around 20 years. In this paper, we propose a novel, rigorous, and efficient computational model to estimate the most important parameters that determine the characteristics of light propagation through a step-index polymer optical fiber (SI-POF). The model uses attenuation, diffusion, and mode group delay as functions of the propagation angle to characterize the optical power transmission in the SI-POF. Taking into consideration the mode group delay allows us to generalize the computational model to be applicable to POFs with different index profiles. In particular, we use experimental measurements of spatial distributions and frequency responses to derive accurate parameters for our SI-POF simulation model. The experimental data were measured at different fiber lengths according to the cut-back method. This method consists of taking several measurements such as frequency responses, angular intensity distributions, and optical power measurements over a long length of fiber (&gt;100 m), then cutting back the fiber while maintaining the same launching conditions and repeating the measurements on the shorter lengths of fiber. The model derivation uses an objective function to minimize the differences between the experimental measurements and the simulated results. The use of the matrix exponential method (MEM) to implement the SI-POF model results in a computationally efficient model that is suitable for POF-based system-level studies. The efficiency gain is due to the independence of the calculation time with respect to the fiber length, in contrast to the classic analytical solutions of the time-dependent power flow equation. The robustness of the proposed model is validated by calculating the goodness-of-fit of the model predictions relative to experimental data.

Characterization and Quantum Efficiency Determination of Monocrystalline Silicon Solar Cells as Sensors for Precise Flux Calibration

As the precision frontier of astrophysics advances toward the one millimagnitude level, flux calibration of photometric instrumentation remains an ongoing challenge. We present the results of a lab-bench assessment of the viability of monocrystalline silicon solar cells to serve as large-aperture (up to 125[Formula: see text]mm diameter), high-precision photodetectors. We measure the electrical properties, spatial response uniformity, quantum efficiency (QE), and frequency response of third-generation C60 solar cells, manufactured by Sunpower. Our new results, combined with our previous study of these cells’ linearity, dark current, and noise characteristics, suggest that these devices hold considerable promise, with QE and linearity that rival those of traditional, small-aperture photodiodes. We argue that any photocalibration project that relies on precise knowledge of the intensity of a large-diameter optical beam should consider using solar cells as calibrating photodetectors.

Mechanism underpinning the sharpening of orientation and spatial frequency selectivities in the tree shrew (Tupaia belangeri) primary visual cortex.

Most neurons in the primary visual cortex (V1) of mammals show sharp orientation selectivity and band-pass spatial frequency tuning. Here, we examine whether sharpening of the broad tuning that exists subcortically, namely in the retina and the lateral geniculate nucleus (LGN), underlie the sharper tuning seen for both the above features in tree shrew V1. Since the transition from poor feature selectivity to sharp tuning occurs entirely within V1 in tree shrews, we examined the orientation selectivity and spatial frequency tuning of neurons within individual electrode penetrations. We found that most layer 4 and layer 2/3 neurons in the same cortical column preferred the same stimulus orientation. However, a subset of layer 3c neurons close to the layer 4 border preferred near orthogonal orientations, suggesting that layer 2/3 neurons may inherit the orientation preferences of their layer 4 input neurons and also receive cross-orientation inhibition from layer 3c neurons. We also found that layer 4 neurons showed sharper orientation selectivity at higher spatial frequencies, suggesting that attenuation of low spatial frequency responses by spatially broad inhibition acting on layer 4 inputs to layer 2/3 neurons can enhance both orientation and spatial frequency selectivities. However, in a proportion of layer 2/3 neurons, the sharper tuning of layer 2/3 neurons appeared to arise also or even mainly from inhibition specific to high spatial frequencies acting on the layer 4 inputs to layer 2/3. Overall, our results are consistent with the suggestion that in tree shrews, sharp feature selectivity in layer 2/3 can be established by intracortical mechanisms that sharpen biases observed in layer 4, which are in turn inherited presumably from thalamic afferents.

Updated Camera Spatial Frequency Response for ISO 12233

The edge-based Spatial Frequency Response (e-SFR) method is well established and has been included in the ISO 12233 standard since the first version in 2000. A new 4th edition of the standard is proceeding, with additions and changes that are intended to broaden its application and improve reliability. We report on results for advanced edge-fitting which, although reported before, was not previously included in the standard. The application of the e-SFR method to a range of edge-feature angles is enhanced by the inclusion of an angle-based correction, and use of a new test chart. We present examples of the testing completed for a wider range of edge test features than previously addressed by ISO 12233, for near-zero- and -45-degree orientations. Various smoothing windows were compared, including the Hamming and Tukey forms. We also describe a correction for image non-uniformity, and the computing of an image sharpness measure (acutance) that will be included in the updated standard.

Creation and evolution of ISO 12233, the international standard for measuring digital camera resolution

Thirty years ago, ISO/TC42 WG18, a newly created ISO working group on digital photography, began developing a standard to measure the spatial resolution of digital cameras. After years of proposals, testing, and analysis, consensus was reached on a test chart with tilted edge features for measuring spatial frequency response (SFR) and hyperbolic wedges for measuring visual and limiting resolution. The group ensured that the test chart and analysis software would be available internationally. First published in 2000, ISO 12233 is now used to measure cameras in a wide range of applications. It was revised in 2014 to define three new charts, a sine-wave modulated target in polar format, a low contrast e-SFR target, and the CIPA chart with software which computes a &#xE2;&#x20AC;&#x153;human equivalent visual resolution&#xE2;&#x20AC;&#x9D; value. ISO 12233 is now being revised to provide improved results in challenging applications. This paper describes early resolution measurement approaches, and work in the 1990s to standardize the SFR method. It also describes enhancement made in later editions, including the 4th edition which is nearing publication.

Imageless Shape Detection Using a Millimeter-Wave Dynamic Antenna Array and Noise Illumination

We present a dynamic millimeter-wave antenna array with rotational dynamics to detect shapes in a scene without image formation. The rotationally dynamic two-element receiving array is able to capture responses in the spatial Fourier (spatial frequency) domain corresponding to sharp edges in the spatial domain. By implementing a dynamic rotation of 180°, a ring-shaped filter is obtained in the spatial frequency domain. Sharp edges in a scene manifest broad spatial–spectral responses that are localized at specific spatial frequency angles and extend radially outward. The ring filter is orthogonal to these strong responses and thus captures them as a function of spatial frequency angle. Shapes with multiple sharp edges produce responses at angles orthogonal to the edge direction, thereby supporting the ability to classify objects based only on the strength and angular location of the spatial frequency responses. Accurate representation of the spatial Fourier domain requires the scattered fields to be spatially and temporally incoherent, and thus, we transmit noise signals from multiple separate noise transmitters, thereby illuminating the scene with incoherent radiation. The dynamic antenna array thus obtains a high signal-to-noise ratio on the received signals, allowing the use of traditional, low-gain millimeter-wave hardware. We evaluate the concept experimentally with a 38-GHz, two-element dynamic antenna array. We demonstrate the detection of spatial frequency signals via rotational dynamics for several reflecting targets of different shapes. The results demonstrate good agreement with simulations and further support the feasibility of detecting shapes in a scene without image formation.

Analysis of Imageless Ground Scene Classification Using a Millimeter-Wave Dynamic Antenna Array

We present an analysis of the capability for imageless ground scene classification using a subset of the Fourier domain information obtained with a rotationally dynamic millimeter-wave antenna array. The concept is based on the detection of signal artifacts generated by artificial objects in a scene, which manifests in the Fourier, or spatial frequency, domain. Man-made, artificial structures, such as buildings and roads, are generally characterized by sharp edges, which generate spatial frequency responses that are confined to a narrow angular range but extend over a broad spatial frequency bandwidth. These artifacts can be detected by generating a ring-shaped filter in the Fourier domain, which can be obtained through the novel design of a linear antenna array with rotational dynamics. We discuss the design of a millimeter-wave linear dynamic array for generating ring-filters and analyze the ability of such an array to classify ground scenes containing artificial structures from those without when mounted on an aerial platform, such as a drone. We compare ring filter designs and explore the use of a heuristic classifier and the K-nearest neighbor (K-NN) classifier on a large dataset of microwave ground scenes obtained from a database. Using a single ring filter that can be implemented with a two-element antenna array, small classification errors of 0.6%–3.2% were observed. Implementing multiple filters in a linear array consisting of four elements reduced the error to 0.3%.

Influence of photodetector-array patterns on spatial-frequency response

This paper presents the spatial-frequency responses of various photodetector-array patterns. It discusses modern photodetector arrays: those having a Bayer pattern, multilayer structures, and composite authoring systems. The last combine spatial color separation with multilayer cells into which IR-sensitive layers are introduced. A comparative analysis of the spatial-frequency responses of color photoarrays showed that composite-system-based patterns have better spatial resolution and higher spatial (contrast) sensitivity than a Bayer pattern. Multilayer systems showed the best result in the comparison. Composite authoring systems also showed that these designs were promising. Calculations are presented as evidence, along with spatial-frequency-response curves of various systems.