Spatial Frequency Bandwidth Research Articles

An Investigation of Using the Spectral Characteristics From Ground Penetrating Radar for Landmine/Clutter Discrimination

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Ground penetrating radar (GPR)-based discrimination of landmines from clutter is known to be challenging due to the wide variability of possible clutter (e.g., rocks, roots, and general soil heterogeneity). This paper discusses the use of GPR frequency-domain spectral features to improve the detection of weak-scattering plastic mines and to reduce the number of false alarms resulting from clutter. The motivation for this approach comes from the fact that landmine targets and clutter objects often have different shapes and/or composition, yielding different energy density spectrum (EDS) that may be exploited for their discrimination (this information is also present in time-domain data, but in the frequency domain we can remove a phase if desired and can reveal better spatial characteristics and therefore often achieve greater robustness). This paper first applies the finite-difference time-domain (FDTD) modeling technique to establish the theoretical foundation. The method to generate EDS from GPR measurements is then described. The consistency of the frequency-domain features is examined through two different GPRs that have different spatial sampling rates and frequency bandwidths. Experimental results from several test sites, based on GPR data collected over buried mines and emplaced buried clutter objects, corroborate the theoretical development and the effectiveness of the proposed spectral feature to increase the accuracy of landmine detection and discrimination. </para>

Spatial information transmission beyond a system’s diffraction limit using optical spectral encoding of the spatial frequency

We propose optical spectral encoding of an object's spatial frequencies as a means of transmitting, through a low-numerical-aperture optical system, spatial information with an instantaneous spatial frequency bandwidth wider than the optical system's diffraction-limited bandwidth. We validate this new superresolution approach experimentally and demonstrate one of its possible practical implementations - wide-field spectrally encoded imaging that is sensitive to nanometre-scale local variations in the microstructure of centimetre-scale samples.

Binocular contrast interactions: Dichoptic masking is not a single process

To decouple interocular suppression and binocular summation we varied the relative phase of mask and target in a 2IFC contrast-masking paradigm. In Experiment I, dichoptic mask gratings had the same orientation and spatial frequency as the target. For in-phase masking, suppression was strong (a log–log slope of ∼1) and there was weak facilitation at low mask contrasts. Anti-phase masking was weaker (a log–log slope of ∼0.7) and there was no facilitation. A two-stage model of contrast gain control [Meese, T.S., Georgeson, M.A. and Baker, D.H. (2006). Binocular contrast vision at and above threshold. Journal of Vision, 6: 1224–1243] provided a good fit to the in-phase results and fixed its free parameters. It made successful predictions (with no free parameters) for the anti-phase results when (A) interocular suppression was phase-indifferent but (B) binocular summation was phase sensitive. Experiments II and III showed that interocular suppression comprised two components: (i) a tuned effect with an orientation bandwidth of ∼±33° and a spatial frequency bandwidth of >3 octaves, and (ii) an untuned effect that elevated threshold by a factor of between 2 and 4. Operationally, binocular summation was more tightly tuned, having an orientation bandwidth of ∼±8°, and a spatial frequency bandwidth of ∼0.5 octaves. Our results replicate the unusual shapes of the in-phase dichoptic tuning functions reported by Legge [Legge, G.E. (1979). Spatial frequency masking in human vision: Binocular interactions. Journal of the Optical Society of America, 69: 838–847]. These can now be seen as the envelope of the direct effects from interocular suppression and the indirect effect from binocular summation, which contaminates the signal channel with a mask that has been suppressed by the target.

Spectral receptive field properties of neurons in the feline superior colliculus

The spatio-temporal frequency response profiles of 73 neurons located in the superficial, retino-recipient layers of the feline superior colliculus (SC) were investigated. The majority of the SC cells responded optimally to very low spatial frequencies with a mean of 0.1 cycles/degree (c/deg). The spatial resolution was also low with a mean of 0.31 c/deg. The spatial frequency tuning functions were either low-pass or band-pass with a mean spatial frequency bandwidth of 1.84 octaves. The cells responded optimally to a range of temporal frequencies between 0.74 cycles/s (c/s) and 26.41 c/s with a mean of 6.84 c/s. The majority (68%) of the SC cells showed band-pass temporal frequency tuning with a mean temporal frequency bandwidth of 2.4 octaves, while smaller proportions of the SC units displayed high-pass (19%), low-pass (8%) or broad-band (5%) temporal tuning. Most of the SC units exhibited simple spectral tuning with a single maximum in the spatio-temporal frequency domain, while some neurons were tuned for spatial or temporal frequencies or speed tuned. Further, we found cells excited by gratings moving at high temporal and low spatial frequencies and cells whose activity was suppressed by high velocity movement. The spatio-temporal filter properties of the SC neurons show close similarities to those of their retinal Y and W inputs as well as those of their inputs from the cortical visual motion detector areas, suggesting their common role in motion analysis and related behavioral actions.

Frequency analysis of the wavefront-coding odd-symmetric quadratic phase mask

A mathematical analysis of the frequency response of the wavefront-coding odd-symmetric quadratic phase mask is presented. An exact solution for the optical transfer function of a wavefront-coding imager using this type of mask is derived from first principles, whose result applies over all misfocus values. The misfocus-dependent spatial filtering property of this imager is described. The available spatial frequency bandwidth for a given misfocus condition is quantified. A special imaging condition that yields an increased dynamic range is identified.

A Two-Dimensional Bandwidth Extrapolation Technique for Polarimetric Synthetic Aperture Radar Images

The resolution of a synthetic aperture radar (SAR) image, in range and azimuth, is determined by the transmitted bandwidth and the synthetic aperture length, respectively. Various superresolution techniques for improving resolution have been proposed, and we have proposed an algorithm that we call polarimetric bandwidth extrapolation (PBWE). To apply PBWE to a radar image, one needs to first apply PBWE in the range direction and then in the azimuth direction, or <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vice versa </i> . In this paper, PBWE is further extended to the 2-D case. This extended case (2D-PBWE) utilizes a 2-D polarimetric linear prediction model and expands the spatial frequency bandwidth in range and azimuth directions simultaneously. The performance of the 2D-PBWE is shown through a simulated radar image and a real polarimetric SAR image

Influences of time and spatial frequency on the perceptual bias: Evidence for competition between hemispheres

Perceptual biases for various visual features, such as size, luminance and numerosity, have been implicated with a right-hemisphere dominance in spatial and attentional functions and/or an asymmetrical competition between the two hemispheres. However, the mechanisms underlying these biases are poorly understood. For example, it has been largely ignored that processing of those features is closely interconnected with spatial frequency filters. To probe the influence of spatial frequencies on perceptual biases, here we used a new gratingscales task in neurologically healthy participants. We found that perceptual bias was strongly influenced within a bandwidth of spatial frequencies and that this bias correlated with a bias for luminance depending on presentation time. Furthermore, our participants, divided into two subgroups of perceptually “sensitive” and “insensitive” performers, showed considerably different, presentation time-dependent patterns of perceptual bias. While both groups were biased to the left, insensitive performers more than sensitive performers, these biases varied in a mirror-symmetric manner such that one group showed peaks of bias at times when the other group showed minima and vice versa. Our data suggest that perceptual bias results from an interhemispheric competition within a right-dominant system responsive to spatial frequencies, luminance and perhaps other magnitudes including abstract ones.

Anisotropic local contrast normalization: The role of stimulus orientation and spatial frequency bandwidths in the oblique and horizontal effect perceptual anisotropies

Visual ability for sine waves and other narrowband stimuli shows an oblique effect—worst performance at obliques, best at horizontal and vertical orientations. Recently, we have shown that with broadband stimuli (either 1/ f α visual noise or natural scenes), performance for detecting oriented content is worst at horizontal, best at the obliques, and intermediate at vertical orientations (a “horizontal effect”). This horizontal effect has been explained by a cortical contrast normalization model that is both local (over orientation and spatial frequency) and anisotropic (due to a numerical bias of neurons with different preferred orientations). Here, the bandwidth of content at which an oblique effect or horizontal effect occurs was assessed in two suprathreshold matching experiments conducted with 1/ f α noise stimuli filtered with a triangle increment function of varied bandwidth (16 levels of orientation and spatial frequency bandwidth). The results provided further support for the local anisotropic normalization model in that an oblique effect was observed when a fairly small range of orientations and high spatial frequencies were tested and the horizontal effect was observed for broadband increments ⩾20° orientation bandwidth and ⩾1-octave in frequency. At intermediate spatial frequency and orientation increment bandwidths, a blend of the two anisotropies was observed.

Spectral Receptive Field Properties Explain Shape Selectivity in Area V4

Neurons in cortical area V4 respond selectively to complex visual patterns such as curved contours and non-Cartesian gratings. Most previous experiments in V4 have measured responses to small, idiosyncratic stimulus sets and no single functional model yet accounts for all of the disparate results. We propose that one model, the spectral receptive field (SRF), can explain many observations of selectivity in V4. The SRF describes tuning in terms of the orientation and spatial frequency spectrum and can, in principle, predict the response to any visual stimulus. We estimated SRFs for neurons in V4 of awake primates by linearized reverse correlation of responses to a large set of natural images. We find that V4 neurons have large orientation and spatial frequency bandwidth and often bimodal orientation tuning. For comparison, we estimated SRFs for neurons in primary visual cortex (V1). Consistent with previous observations, we find that V1 neurons have narrower bandwidth than that of V4. To determine whether estimated SRFs can account for previous observations of selectivity, we used them to predict responses to Cartesian gratings, non-Cartesian gratings, natural images, and curved contours. Based on these predictions, we find that the majority of neurons in V1 are selective for Cartesian gratings, whereas the majority of V4 neurons are selective for non-Cartesian gratings or natural images. The SRF describes visual tuning properties with a second-order nonlinear model. These results support the hypothesis that a second-order model is sufficient to describe the general mechanisms mediating shape selectivity in area V4.

Estimating missing information by maximum likelihood deconvolution

The ability of iteratively constrained maximum likelihood (ML) deconvolution to reconstruct out-of-band information is discussed and exemplified by simulations. The frequency dependent relative energy regain, a novel way of quantifying the reconstruction ability, is introduced. The positivity constraint of ML deconvolution allows reconstructing information outside the spatial frequency bandwidth which is set by the optical system. This is demonstrated for noise-free and noisy data. It is also shown that this property depends on the type of object under investigation. An object is constructed where no significant out-of-band reconstruction is possible. It is concluded that in practical situations the amount of possible out-of-band reconstruction depends on the agreement between reality and the model describing “typical objects” incorporated into the algorithm by appropriate penalty functions.

Face perception: An integrative review of the role of spatial frequencies

The aim of this article is to reinterpret the results obtained from the research analyzing the role played by spatial frequencies in face perception. Two main working lines have been explored in this body of research: the critical bandwidth of spatial frequencies that allows face recognition to take place (the masking approach), and the role played by different spatial frequencies while the visual percept is being developed (the microgenetic approach). However, results obtained to date are not satisfactory in that no single explanation accounts for all the data obtained from each of the approaches. We propose that the main factor for understanding the role of spatial frequencies in face perception depends on the interaction between the demands of the task and the information in the image (the diagnostic recognition approach). Using this new framework, we review the most significant research carried out since the early 1970s to provide a reinterpretation of the data obtained.

Digital cameras: spatial image quality matters

Difficulty in understanding the relative performance and appreciating the numerous features of the ever-increasing range of digital cameras has led to the need for a simple objective test of camera quality. A method of measuring the modulation transfer function is described but, in practice, only a sector star pattern is needed to measure the spatial frequency bandwidth (SFB), which is related to resolution and the optimum print width (OPW) achievable with a particular camera, whether digital or film. The SFB of a camera divided by that of the eye in the plane of a print at arm's length and multiplied by the image format width gives the OPW. A value index (VI) is derived by dividing this number into the camera price. A pixel packing index (PPI) is the ratio of the true information content, obtained from the number of effective pixels present divided by the nominal information content, given by the stated number of pixels. It quantifies the proportion of pixels contributing to spatial image quality. Provisional results obtained using nine different cameras in the 1–4 MP range suggest that the SFB, and therefore the effective pixel size and spatial resolution, vary relatively little between cameras. A doubling of the OPW requires a fourfold increase in the number of pixels. The PPI over the full sensor area can be as little as 8%. The OPW is a useful parameter for optimising image quality settings and for comparing the quality of different cameras. The advantages are that users should be able to understand it, and it embodies both effective pixel size influencing spatial image quality and the number of pixels influencing acceptable print size. The VI, since it reflects the present highly volatile high-street prices, will only be of temporary value.

Accuracy of Subspace Mapping of Spatiotemporal Frequency Domain Visual Receptive Fields

Orientation and spatial frequency selectivities are fundamental properties of cells in the early visual cortex. Although they are customarily tested with drifting sinusoidal gratings, a recently developed subspace reverse correlation method may be a better replacement for obtaining a selectivity map in a joint orientation and spatial frequency domain at higher resolution efficiently. These two methods are examined for their accuracy and data compatibility for cells in areas 17 and 18 of anesthetized and paralyzed cats. Peaks and bandwidths of tuning curves from these two methods are highly correlated. However, spatial frequency bandwidths obtained by reverse correlation tend to be slightly narrower for the subspace reverse correlation than those from the drifting grating tests. Consistency between the two methods is improved if the entire duration of data containing signal are taken into account for the subspace reverse correlation rather than using the map only at the optimal correlation delay. Examination of convergence of the subspace mapping process shows that reliable 2-day profiles can be obtained within 5-10 min. for the majority of cells. Temporal dynamics of tuning properties are also examined more directly with the subspace mapping than with the drifting gratings. For many cells, the optimal spatial frequency shifts substantially, measured as a fraction of tuning bandwidth, over the time course of response. In comparison, the optimal orientation remains highly stable throughout the duration of response. Overall, these results suggest that the subspace reverse correlation is a better substitute for the conventional method.

Optical encryption and the space bandwidth product

The use of optical signal processing in the field of image encryption typically involves the use of optical transforms representing quadratic phase systems (QPS), to implement the optical Fourier transform (OFT), the optical fractional Fourier transform (OFRT), the Fresnel transform (FST) and the general linear Canonical transform (LCT). Random phase keys (RPK) or random shifting stages are applied after transformation and the process is repeated for deeper encryption. Each such stage may change the spatial extent of the complex distribution and may also change the spatial frequency bandwidth of the signal. Therefore, the space bandwidth product (SBP), which is equal to the number of discrete samples that are required to fully represent the encrypted signal (and are required to recover the original), will also change. In general the encrypted field is complex and recording must be carried out using a holographic material or using digital holographic methods. We show how the matrices associated with the effect of a LCT on the Wigner distribution function (WDF) provide us with an efficient method for finding the position, spatial extent, spatial frequency extent and SBP of the encrypted signal. Applying the technique, we review a number of methods proposed in the literature for encryption using optical systems based on the FT, FRT, FST and LCT. This technique also allows us to identify necessary parameters, i.e., we can determine the minimum size of lens apertures and the need for magnification stages at critical stages in the system.

Lateral interactions in orientation discrimination: Spatial frequency bandwidths

Lateral interactions in orientation discrimination: Spatial frequency bandwidths

Correlation of local and global orientation and spatial frequency tuning in macaque V1.

Visual cortical neurones display a variety of visual properties. Among those that emerge in the primary visual cortex V1 are sharpening of selectivity for spatial frequency and for orientation. The selectivity for these stimulus attributes can be measured around the peak of the tuning function, usually as bandwidth. Other selectivity measures take into account the response across a broader range of stimulus values. An example of such a global measure is the circular variance of orientation tuning. Here we introduce a similar measure in the spatial frequency domain that takes into account the shape of the tuning curve at frequencies lower than the peak, called the low-spatial frequency variance. Our recent studies with dynamic stimuli suggest that the selectivity for spatial frequency and orientation is strongly correlated with the degree of suppression at low spatial frequencies and off-axis orientations. Here we extend the study of the global tuning to stimulus conditions that measure the response of cells to the presentation of drifting sinusoidal grating stimuli for periods of a few seconds. We find that under such steady-state stimulus conditions there is a strong correlation between the global selectivity measures, orientation circular variance and low spatial frequency variance. Consistent with previous studies, there is a weaker correlation between the local tuning measures, orientation and spatial frequency bandwidth. These results support the idea that there are multiple factors that contribute to tuning and that suppression observed in dynamic experiments is also likely to contribute to the global selectivity for steady-state stimuli.

Parametric instabilities driven by orthogonal pump waves in birefringent fibers

The four-sideband model of parametric instabilities driven by orthogonal pump waves in birefringent fibers is developed and validated by numerical simulations. A polynomial eigenvalue equation is derived and used to determine how the spatial growth rates and frequency bandwidths of various instabilities depend on the system parameters. The maximal growth rate is associated with a group-speed matched four-sideband process (coupled modulation instability), whereas broad-bandwidth gain is associated primarily with a two-sideband process (phase conjugation). This four-sideband model facilitates the design of parametric amplifiers driven by two pump waves with different frequencies and polarizations.

Orientation discrimination in foveal and extra-foveal vision: effects of stimulus bandwidth and contrast

The parameter E 2 is used in many spatial scaling studies to characterize the rate at which stimulus size must increase with eccentricity to achieve foveal levels of performance in detection and discrimination tasks. We examined whether the E 2 for an orientation discrimination task was dependent on the spatial frequency bandwidth of the stimulus used. Two methods were employed. In Experiments 1 and 2 stimuli were presented at a fixed high level of contrast across viewing conditions. In both experiments the E 2s recovered for narrowband stimuli were larger than those recovered for broadband stimuli. In Experiment 3 we controlled for the potentially confounding effects of perceptual contrast by measuring orientation thresholds over a range of stimulus contrast levels. Only thresholds which had reached an asymptotic level, such that increases in stimulus contrast led to no further changes to thresholds, were included in the calculation of E 2. We observed that E 2s recovered in the latter condition were in the range of 1.29°–1.83° and similar for narrowband and broadband stimuli. We conclude that a failure to consider the role of perceptual contrast may result in inflated estimates of E 2.

Diffraction efficiency of a dynamic hologram in a reversible photochromic medium with allowance for diffusion of photochromic particles

Spatial resolution of a dynamic hologram in a reversible photochromic medium is analyzed, with allowance made for diffusion of photochromic particles. It is shown that the bandwidth of spatial frequencies of a thin hologram decreases over time, approaching the value determined by the diffusion coefficient and the hologram recording/erasing time. The optimum relationship between the intensity of the beam that records the volume hologram and the parameters of the photochromic particles is found for which the difference between the limiting value of the bandwidth of spatial frequencies of the volume hologram and the value of the band-width of spatial frequencies of a thin hologram located in the plane z=0 is the greatest.

Scattering coefficient reconstruction in plates using focused acoustic beams

A method has been developed and proven using highly focused acoustic beams that allows for the rapid reconstruction of scattering coefficients of a thin anisotropic plate immersed in liquid. In a single bistatic coordinate scan, nearly the entire range of wave number within the spatial and temporal frequency bandwidth of the transducer can be reconstructed. This paper also reports the development of a multiple-source complex transducer point model that includes all extrinsic factors and permits prediction of the wave number-frequency ( k– f) domain result obtained from a scan of focused transducers in a pitch-catch reflection or transmission arrangement. Extensive experiments have been performed to test the method and the model and to demonstrate transducer beam effects on the k– f domain results, leading to a very efficient method for mapping major portions of the guided wave dispersion spectrum in thin-plate media. As a demonstration of the technique, an estimate of material elastic properties in an isotropic and a transversely-isotropic plate is reported, making only minimal use of the highly redundant dispersion data. Acoustic velocities inferred from these experiments show a disparity of less than 3% from contact acoustic estimates of the same parameters in either plate.