Spatial Frequency Bandwidth Research Articles

Direct amplitude-only hologram realized by broken symmetry.

Holographic displays have been a long-standing ambition for decades to realize true-to-life reconstruction. However, their practical adoption is hindered by their subpar image quality compared to two-dimensional displays, which is fundamentally limited by restricted spatial frequency bandwidth and artifacts. We address the limitation by using a symmetry-broken amplitude-only spatial light modulator, demonstrating image quality comparable to that of two-dimensional displays. The broken conjugate symmetry induced by phase noise of modulators eliminates conjugate image that causes issues in amplitude-only holograms and allows direct reconstruction without additional optical elements. The proposed method provides enhanced robustness against artifacts caused by sub-pixel structures of modulators, enabling experimental reconstruction of high-quality holograms. The full bandwidth and the robustness result in a 5-decibel improvement in peak signal-to-noise ratio compared to state-of-the-art holograms. Furthermore, the hologram has 24 times higher optical efficiency and a smaller volume than the traditional amplitude-only holograms while real-time synthesis is enabled by using a neural network.

Multifunctional Intelligent Metamaterial Computing System: Independent Parallel Analog Signal Processing

Analog computing based on miniaturized surfaces has gained attention for its high‐speed and low‐power mathematical operations. Building on recent advances, an anisotropic space‐time digital metasurface for parallel and programmable wave‐based mathematical operations is proposed. Using frequency conversions, our metasurface performs 1st‐order and 2nd‐order spatial differentiations, integrodifferential equations, and sharp edge detection in spatially encoded images. The anisotropic nature of the meta‐particle enables independent and simultaneous operations for two orthogonal polarizations. Reconfigurability is achieved through tunable gate biasing of an indium tin oxide layer. Illustrative examples demonstrate that the metasurface's output signals and transfer functions closely match ideal transfer functions, confirming its versatility and effectiveness. Unlike other wave‐based signal processors, the design handles wide spatial frequency bandwidths, even with high spatial frequency inputs.

Enhanced-spatial-resolution optical surface profiler based on focusing deflectometry.

Deflectometric slope profiler is an essential technique for accessing the surface metrology of mirrors used in synchrotron radiation beamlines. To increase the upper spatial frequency bandwidth limits of deflectometric slope profiler, reducing the beam spot size on the mirrors is necessary. In this paper, we introduce a profiler system: the focusing long trace profiler (FLTP). It contains a newly developed optical head capable of raising upper spatial frequency bandwidth limits by using a focused beam instead of a collimated beam to scan the sample. This feature has been proven in a numerical simulation experiment, where a spatial resolution of up to around 0.05 mm was reached when the sample is set at focus plane. The system is implemented and characterized in several experiments; calibration of the focusing optical head shows that it can achieve a high angular accuracy of sub-50 nrad root-mean-square (rms) and defocusing of sample under test (SUT) has no effect on the measurement results; the measurement tests also demonstrate the system's advantage in highly curved mirror profile metrology.

Coherence-encoded synthetic aperture for super-resolution quantitative phase imaging

Quantitative phase imaging (QPI) has quickly established its role in identifying rare events and screening in biomedicine or automated image data analysis using artificial intelligence. These and many other applications share the requirement for extensive high-quality datasets, which is challenging to meet because the invariance of the space–bandwidth product (SBP) fundamentally limits the microscope system throughput. Here, we present a method to overcome the SBP limit by achieving QPI super-resolution using a synthetic aperture approach in a holographic microscope with a partially coherent broad source illumination. We exploit intrinsic coherence-gating properties of the partially coherent light combined with the oblique illumination provided by the diffraction on a simple phase grating placed in proximity of the specimen. We sequentially coherence gate the light scattered into each grating’s diffraction order, and we use the acquired images to synthesize QPI with significantly increased spatial frequency bandwidth. The resolution of QPI is increased substantially beyond Abbe’s diffraction limit while a large field of view of low numerical aperture objectives is kept. This paper presents a thorough theoretical treatment of the coherence-gated imaging process supplemented by a detailed measurement methodology. The capability of the proposed method is demonstrated by imaging a phase resolution target and biological specimens. We envision our work providing an easily implementable super-resolution QPI method particularly suitable for high-throughput biomedical applications.

Spatial frequency bands used by patients with glaucoma to recognize facial expressions

ABSTRACT The authors investigated the influence of spatial frequencies in foveal vision in glaucomatous patients in a recognition task of facial expressions. Nineteen patients, 16 age-matched and 14 young controls saw centrally presented photographs of faces. Participants categorized the facial expressions as happy, angry or neutral. Two versions were tested: filtered faces of either low (LSF) or high (HSF) spatial frequency content and hybrid faces constructed from a face with LSF content superimposed on a face with HSF content with differing facial expressions. Compared to age-matched controls a significant deficit was observed both on HSF and on LSF filtered faces for patients. Controls, but not patients, were biased towards the HSF component of the hybrid faces. Different spatial frequencies are normally used to recognize different facial expressions. Impaired processing of a spatial frequency bandwidth due to an ocular pathology can therefore lead to misinterpretation of emotions, and impact on social interactions.

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%.

Quality of radiation conversion under four-wave mixing on thermal nonlinearity with feedback

Quality of radiation conversion under four-wave mixing on thermal nonlinearity with feedback for both signal and object waves has been investigated at high reflection coefficients. It has been shown that the optimal operating mode of a four-wave converter on thermal nonlinearity is the mode in which the pumping waves have equal intensities and there is a compensation for a phase shift arising from the pumping wave self-action. In this operating mode of the four-wave radiation converter, as compared with the case of the absence of feedback for both signal and object waves, a significant increase in the amplitude reflection coefficient is observed with an increase in the pumping waves intensities. In this case, despite the decrease in the bandwidth of spatial frequencies of the object wave with an increase in the pumping wave intensities, the quality of radiation conver-sion with feedback for both signal and object waves is better than in the absence of feedback.

Organic Hyperbolic Material Assisted Illumination Nanoscopy.

Resolution capability of the linear structured illumination microscopy (SIM) plays a key role in its applications in physics, medicine, biology, and life science. Many advanced methodologies have been developed to extend the resolution of structured illumination by using subdiffraction‐limited optical excitation patterns. However, obtaining SIM images with a resolution beyond 40 nm at visible frequency remains as an insurmountable obstacle due to the intrinsic limitation of spatial frequency bandwidth of the involved materials and the complexity of the illumination system. Here, a low‐loss natural organic hyperbolic material (OHM) that can support record high spatial‐frequency modes beyond 50k 0, i.e., effective refractive index larger than 50, at visible frequencies is reported. OHM‐based speckle structured illumination microscopy demonstrates imaging resolution at 30 nm scales with enhanced fluorophore photostability, biocompatibility, easy to use and low cost. This study will open up a new route in super‐resolution microscopy by utilizing OHM films for various applications including bioimaging and sensing.

Analog signal processing through space-time digital metasurfaces

Abstract In the quest to realize analog signal processing using subwavelength metasurfaces, in this paper, we present the first demonstration of programmable time-modulated metasurface processors based on the key properties of spatial Fourier transformation. Exploiting space-time coding strategy enables local, independent, and real-time engineering of not only amplitude but also phase profile of the contributing reflective digital meta-atoms at both central and harmonic frequencies. Several illustrative examples are demonstrated to show that the proposed multifunctional calculus metasurface is capable of implementing a large class of useful mathematical operators, including 1st- and 2nd-order spatial differentiation, 1st-order spatial integration, and integro-differential equation solving accompanied by frequency conversions. Unlike the recent proposals based on the Green’s function (GF) method, the designed time-modulated signal processor effectively operates for input signals containing wide spatial frequency bandwidths with an acceptable gain level. Proof-of-principle simulations are also reported to demonstrate the successful realization of image processing functions like edge detection. This time-varying wave-based computing system can set the direction for future developments of programmable metasurfaces with highly promising applications in ultrafast equation solving, real-time and continuous signal processing, and imaging.

Gauging diffraction patterns: field of view and bandwidth estimation in lensless holography.

The purpose of this work is to provide a theoretically grounded assessment on the field of view and bandwidth of a lensless holographic setup. Indeed, while previous works have presented results with super-resolution and field-of-view extrapolation, there are no well-established rules to determine them. We show that the theoretical field of view can be large with a spatial-frequency bandwidth only limited by the wavelength, leading to an unthinkable number of degrees of freedom. To keep a realistic field of view and bandwidth, we propose several practical bounds based on a few setup properties, namely, the noise level and spatiotemporal coherence of the source.

Synergy of spatial frequency and orientation bandwidth in texture segregation.

Defining target textures by increased bandwidths in spatial frequency and orientation, we observed strong cue combination effects in a combined texture figure detection and discrimination task. Performance for double-cue targets was better than predicted by independent processing of either cue and even better than predicted from linear cue integration. Application of a texture-processing model revealed that the oversummative cue combination effect is captured by calculating a low-level summary statistic (), which describes the differential contrast energy to target and reference textures, from multiple scales and orientations, and integrating this statistic across channels with a winner-take-all rule. Modeling detection performance using a signal detection theory framework showed that the observers’ sensitivity to single-cue and double-cue texture targets, measured in units, could be reproduced with plausible settings for filter and noise parameters. These results challenge models assuming separate channeling of elementary features and their later integration, since oversummative cue combination effects appear as an inherent property of local energy mechanisms, at least for spatial frequency and orientation bandwidth-modulated textures.

Uniform spatial pooling explains topographic organization and deviation from receptive-field scale invariance in primate V1

Receptive field (RF) size and preferred spatial frequency (SF) vary greatly across the primary visual cortex (V1), increasing in a scale invariant fashion with eccentricity. Recent studies reveal that preferred SF also forms a fine-scale periodic map. A fundamental open question is how local variability in preferred SF is tied to the overall spatial RF. Here, we use two-photon imaging to simultaneously measure maps of RF size, phase selectivity, SF bandwidth, and orientation bandwidth—all of which were found to be topographically organized and correlate with preferred SF. Each of these newly characterized inter-map relationships strongly deviate from scale invariance, yet reveal a common motif—they are all accounted for by a model with uniform spatial pooling from scale invariant inputs. Our results and model provide novel and quantitative understanding of the output from V1 to downstream circuits.

Differential Effects of Orientation and Spatial-Frequency Spectra on Visual Unpleasantness.

Increasing psychophysical evidence suggests that specific image features – or statistics – can appear unpleasant or induce visual discomfort in humans. Such unpleasantness tends to be particularly profound if the image’s amplitude spectrum deviates from the regular 1/f spatial-frequency falloff expected in natural scenes. Here, we show that profound unpleasant impressions also result if the orientation spectrum of the image becomes flatter. Using bandpass noise with variable orientation and spatial-frequency bandwidths, we found that unpleasantness ratings decreased with spatial- frequency bandwidth but increased with orientation bandwidth. Similarly, a subsequent experiment revealed that sinusoidal modulations in the amplitude spectrum of 1/f noise along the spatial frequency increased unpleasantness, but modulations along the orientation decreased it. Given that natural scenes tend to have a linear slope along the spatial frequency but an uneven spectrum along the orientation dimension, our opposing results in the spatial-frequency and orientation domains commonly support the idea that images deviating from the spectral regularity of natural scenes can give rise to unpleasant impressions.

Anatomy and Physiology of Macaque Visual Cortical Areas V1, V2, and V5/MT: Bases for Biologically Realistic Models.

The cerebral cortex of primates encompasses multiple anatomically and physiologically distinct areas processing visual information. Areas V1, V2, and V5/MT are conserved across mammals and are central for visual behavior. To facilitate the generation of biologically accurate computational models of primate early visual processing, here we provide an overview of over 350 published studies of these three areas in the genus Macaca, whose visual system provides the closest model for human vision. The literature reports 14 anatomical connection types from the lateral geniculate nucleus of the thalamus to V1 having distinct layers of origin or termination, and 194 connection types between V1, V2, and V5, forming multiple parallel and interacting visual processing streams. Moreover, within V1, there are reports of 286 and 120 types of intrinsic excitatory and inhibitory connections, respectively. Physiologically, tuning of neuronal responses to 11 types of visual stimulus parameters has been consistently reported. Overall, the optimal spatial frequency (SF) of constituent neurons decreases with cortical hierarchy. Moreover, V5 neurons are distinct from neurons in other areas for their higher direction selectivity, higher contrast sensitivity, higher temporal frequency tuning, and wider SF bandwidth. We also discuss currently unavailable data that could be useful for biologically accurate models.

Spatial frequency selectivity of the human visual cortex estimated with pseudo-random visual evoked cortical potential (VECP)

Single-cell recordings in the primary visual cortex (V1) show neurons with spatial frequency (SF) tuning, which had different responses to chromatic and luminance stimuli. Visually evoked cortical potential (VECP) investigations have reported different spatial profiles. The current study aimed to investigate the spatial selectivity of V1 to simultaneous stimulus of chromatic and luminance contrasts. Compound stimuli temporally driven by m-sequences at 8 SFs were utilized to generate VECP records from thirty subjects (14 trichromats and 16 colorblind subjects). We extracted the second-order kernel, first and second slices (K2.1 and K2.2, respectively). Optimal SF, SF bandwidth, and high SF cut-off were estimated from the best-fitted functions to the VECP amplitude vs SF. For trichromats, K2.1 waveforms had a negative component (N1 K2.1) at 100 ms followed by a positive component (P1 K2.1). K2.2 waveforms also had a negative component (N1 K2.2) at 100 ms followed by a positive deflection (P1 K2.2). SF tuning of N1 K2.1 and N1 K2.2 had a band-pass profile, while the P1 K2.1 was low-pass tuned. P1 K2.1 optimal SF differed significantly from both other negative responses and from P1 K2.2. We found differences in the optimal SF, SF tuning and high SF cut-off among the VECP components. Dichromats had little or no response for all stimulus conditions. The absence of the responses in dichromats, the similarity between the high SF cut-off of the pseudorandom VECPs and psychophysical chromatic visual acuity, and presence of multiple SF tunings suggested that pseudorandom VECPs represented the activity of cells that responded preferentially to the chromatic component of the compound stimuli.

Perceived regularity of a texture is influenced by the regularity of a surrounding texture

Previous studies have shown that texture regularity is adaptable, and have suggested that texture regularity might be coded by the peakedness of the underlying spatial frequency distribution. Here we demonstrate the related phenomenon of simultaneous regularity contrast (SRC), in which the perceived regularity of a central texture is influenced by the regularity of a surrounding texture. We presented center-surround arrangements of textures and measured the perceived regularity of the centre, using a centre-only comparison stimulus and a 2AFC procedure. From the resulting psychometric functions the SRC was measured as the difference between test and comparison regularity at the PSE (point of subjective equality). Observers generally exhibited asymmetric bidirectional SRC, in that more regular surrounds decreased the perceived regularity of the centre by between 20–40%, while less regular surrounds increased the perceived regularity of the centre by about 10%. Consistent with previous studies, a wavelet spatial frequency (SF) analysis of the stimuli revealed that their SF distributions became sharper with increased regularity, and therefore that distribution statistics such as kurtosis and SF bandwidth might be used to code regularity.

Multicolor Discrete Frequency Infrared Spectroscopic Imaging.

Advancement of discrete frequency infrared (DFIR) spectroscopic microscopes in image quality and data throughput are critical to their use for analytical measurements. Here, we report the development and characterization of a point scanning instrument with minimal aberrations and capable of diffraction-limited performance across all fingerprint region wavelengths over arbitrarily large samples. The performance of this system is compared to commercial state of the art Fourier transform infrared (FT-IR) imaging systems. We show that for large samples or smaller set of discrete frequencies, point scanning far exceeds (∼10-100 fold) comparable data acquired with FT-IR instruments. Further we show improvements in image quality using refractive lenses that show significantly improved contrast across the spatial frequency bandwidth. Finally, we introduce the ability to image two tunable frequencies simultaneously using a single detector by means of demodulation to further speed up data acquisition and reduce the impact of scattering. Together, the advancements provide significantly better spectral quality and spatial fidelity than current state of the art imaging systems while promising to make spectral scanning even faster.

Near-field spatial frequency filtering model for surface plasmon self-interference virtual probe

Abstract The azimuthal angle relation for obliquely excited standing-wave surface plasmon is analytically studied in detail and thereby a near-field spatial frequency filtering model is proposed, in which the azimuthal angle relation and criterion similar to Heisenberg uncertainty principle are combined to describe the spatial resolving power of surface plasmon self-interference virtual probe imaging system. It is revealed that the incidence coupling possesses spatial anisotropy due to polarization modulation, and the mechanism for spatial resolution degradation is the compression of spatial frequency bandwidth in the near-field domain.

Feature selectivity is stable in primary visual cortex across a range of spatial frequencies

Reliable perception of environmental signals is a critical first step to generating appropriate responses and actions in awake behaving animals. The extent to which stimulus features are stably represented at the level of individual neurons is not well understood. To address this issue, we investigated the persistence of stimulus response tuning over the course of 1–2 weeks in the primary visual cortex of awake, adult mice. Using 2-photon calcium imaging, we directly compared tuning stability to two stimulus features (orientation and spatial frequency) within the same neurons, specifically in layer 2/3 excitatory neurons. The majority of neurons that were tracked and tuned on consecutive imaging sessions maintained stable orientation and spatial frequency preferences (83% and 76% of the population, respectively) over a 2-week period. Selectivity, measured as orientation and spatial frequency bandwidth, was also stable. Taking into account all 4 parameters, we found that the proportion of stable neurons was less than two thirds (57%). Thus, a substantial fraction of neurons (43%) were unstable in at least one parameter. Furthermore, we found that instability of orientation preference was not predictive of instability of spatial frequency preference within the same neurons. Population analysis revealed that noise correlation values were stable well beyond the estimated decline in monosynaptic connectivity (~250–300 microns). Our results demonstrate that orientation preference is stable across a range of spatial frequencies and that the tuning of distinct stimulus features can be independently maintained within a single neuron.

Selection of a two-dimensional image edge using polarisation-independent acousto-optic diffraction

A method for filtering two-dimensional distributions of light-wave spatial frequencies, based on the use of polarisation-independent acousto-optic (AO) Bragg diffraction, is proposed. This method provides a maximally possible transmission bandwidth of spatial frequencies and a minimum size of the resolved AO element. A selection of a two-dimensional edge in the zero Bragg order is demonstrated. The main theoretical conclusions are experimentally confirmed using a paratellurite AO filter.