Spatial Frequency Bandwidth Research Articles

Automatic multicell identification using a compact lensless single and double random phase encoding system

We investigate the use of compact, lensless, single random phase encoding (SRPE) and double random phase encoding (DRPE) systems for automatic cell identification when multiple cells, either of the same or mixed classes, are in the field of view. A microscope glass slide containing the sample is inputted into the single or double random phase encoding system, which is then illuminated by a coherent or partially coherent light source generating a unique opto-biological signature (OBS) that is captured by an image sensor. Statistical features such as mean, standard deviation, skewness, kurtosis, entropy, and Pearson's correlation coefficient are extracted from the OBSs and used for cell identification with the random forest classifier. With the exception of the correlation coefficient, all features were extracted in both the spatial and frequency domains. Experiments are performed with single random phase encoding and double random phase encoding, and system analysis is presented to show the robustness and classification accuracy of the random phase encoding cell identification systems. The proposed systems are compact, as they are lensless and do not have spatial frequency bandwidth limitations due to the numerical aperture of a microscope objective lens. We demonstrate that cell identification is possible using both the SRPE and DRPE systems. While DRPE systems have been extensively used for image encryption, to the best of our knowledge, this is the first report on using DRPE for automated cell identification.

Numerical validation of using multisource statistically optimized near-field acoustical holography in the vicinity of a high performance military aircraft

Multisource statistically optimized nearfield acoustical holography (M-SONAH) is an advanced holography technique [Wall et al., J. Acoust. Soc. Am. 137, 963–975 (2015)] that has been used to reconstruct the acoustic field from measurements taken in the vicinity of a high-performance military aircraft [Wall et al. 139, 1938 (2016)]. The implementation of M-SONAH for tactical jet noise relies on creating an equivalent wave model using two cylindrical sources, one along the jet centerline and one below the ground as an image source, to represent the field surrounding an aircraft tethered to a reflecting ground run up pad. In this study, the spatial and frequency limitations of using the M-SONAH method to describe the field of a tethered F-35 is explored by using the same measurement geometry as at a recent test, but substituting the sound field obtained from a numerical source for the measurement data. The M-SONAH reconstructions are then compared to numerical benchmarks. A spatial region and frequency bandwidth where bias errors are low are identified and provide validation for the use of this method in tactical jet noise source and field reconstructions. [Work supported by USAFRL through ORISE and the F-35 JPO. Distribution A: Approved for public release; distribution unlimited. Cleared 07/10/2017; JSF17-714.]

Describing contrast across scales

Due to its sensitive nature against illumination and noise distributions, contrast is not widely used for image description. On the contrary, the human perception of contrast along different spatial frequency bandwidths provides a powerful discriminator function that can be modeled in a robust manner against local illumination. Based upon this observation, a dense local contrast descriptor is proposed and its potential in different applications of computer vision is discussed. Extensive experiments reveal that this simple yet effective description performs well in comparison with state of the art image descriptors. We also show the importance of this description in multiresolution pansharpening framework.

Automated measurements of human cone photoreceptor density in healthy and degenerative retina by region-based segmentation.

PurposeThe purpose of this study was to develop an algorithm based on region-based segmentation for automated calculations of human cone photoreceptor density of en face images obtained by an adaptive optics scanning laser ophthalmoscope (AOSLO).Subjects and methodsCone mosaics of 15 eyes of 15 healthy subjects were photographed by a custom-built AOSLO. The cone density was calculated at 0.5, 1.0, and 1.5 mm temporal from the fovea using a region-based segmentation method (RSM) developed in our laboratory. The cone density was also determined by a manual identification method (MIM) and a conventional spatial filtering method (SFM). The cone densities of three eyes of three patients with retinal degeneration were calculated by the three methods and compared to the results from normal eyes.ResultsThe cone densities in healthy retinas determined by the RSM at 0.5, 1.0, and 1.5 mm temporal from the fovea were 28,436, 21,233, and 13,620 cells/mm2, respectively. These densities were in good agreement with a histological study and with in vivo AOSLO studies. The cone densities determined by RSM were different from those determined by MIM with a difference of 5% in healthy eyes. In eyes with retinal degeneration, with the appropriate threshold-level settings or spatial frequency bandwidth, the cone density measured by MIM was significantly closer to that measured by RSM than by SFM.ConclusionThese results suggest that our method is more stable than conventional methods in cases of non-periodical photoreceptor structures such as the affected retinal area. Our method can be used in the longitudinal follow-up of retinal degenerative diseases and to determine the effect of therapy.

Accurate and efficient velocity estimation using Transmission matrix formalism based on the domain decomposition method

Full waveform inversion (FWI) has been regarded as an effective tool to build the velocity model for the following pre-stack depth migration. Traditional inversion methods are built on Born approximation and are initial model dependent, while this problem can be avoided by introducing Transmission matrix (T-matrix), because the T-matrix includes all orders of scattering effects. The T-matrix can be estimated from the spatial aperture and frequency bandwidth limited seismic data using linear optimization methods. However the full T-matrix inversion method (FTIM) is always required in order to estimate velocity perturbations, which is very time consuming. The efficiency can be improved using the previously proposed inverse thin-slab propagator (ITSP) method, especially for large scale models. However, the ITSP method is currently designed for smooth media, therefore the estimation results are unsatisfactory when the velocity perturbation is relatively large. In this paper, we propose a domain decomposition method (DDM) to improve the efficiency of the velocity estimation for models with large perturbations, as well as guarantee the estimation accuracy. Numerical examples for smooth Gaussian ball models and a reservoir model with sharp boundaries are performed using the ITSP method, the proposed DDM and the FTIM. The estimated velocity distributions, the relative errors and the elapsed time all demonstrate the validity of the proposed DDM.

Orthogonal experiment and analysis of power spectral density on process parameters of pitch tool polishing

Mid to high spatial frequency error (MSFR and HSFR) should be strictly controlled in modern optical systems. Pitch tool polishing (PTP) is an effective ultra-smoothing surface manufacturing method to control MSFR and HSFR. But it is difficult to control because it is affected by a lot of factors. The present paper describes the pitch tool polishing study based on eighteen well-planned orthogonal experiments (OA18 matrix). Five main process factors (abrasive particle size, slurry concentration, pad rotation speed, acidity and polishing time) in pitch tool polishing process were investigated. In this study, power spectral density (PSD) based on Fourier analysis of surface topography data obtained by white light interferometer was used as the results of orthogonal experiments instead of material removal rate and surface roughness. A normalization method of PSD was proposed as the range analysis rule. Three parts of spatial frequency bandwidth were selected and discussed. Acidity is the most important factor in part 1 and slurry concentration is the most significant one in part 2; while acidity is the least influenced one in part 3. The result in each part was explained by two-step material removal mechanism. At last, suggestions in low and high spatial frequency are given for pitch tool polishing.

Retina-Inspired Filter.

This paper introduces a novel filter, which is inspired by the human retina. The human retina consists of three different layers: the Outer Plexiform Layer (OPL), the inner plexiform layer, and the ganglionic layer. Our inspiration is the linear transform which takes place in the OPL and has been mathematically described by the neuroscientific model "virtual retina." This model is the cornerstone to derive the non-separable spatio-temporal OPL retina-inspired filter, briefly renamed retina-inspired filter, studied in this paper. This filter is connected to the dynamic behavior of the retina, which enables the retina to increase the sharpness of the visual stimulus during filtering before its transmission to the brain. We establish that this retina-inspired transform forms a group of spatio-temporal Weighted Difference of Gaussian (WDoG) filters when it is applied to a still image visible for a given time. We analyze the spatial frequency bandwidth of the retina-inspired filter with respect to time. It is shown that the WDoG spectrum varies from a lowpass filter to a bandpass filter. Therefore, while time increases, the retina-inspired filter enables to extract different kinds of information from the input image. Finally, we discuss the benefits of using the retina-inspired filter in image processing applications such as edge detection and compression.

Influence of the pump wave rotation and divergence on the spatial selectivity of a four-wave radiation converter in a transparent two-component medium

The spatial selectivity of the degenerate four-wave radiation converter in a transparent two-component medium based on the electrostriction and Dufour effect has been analyzed as a function of the rotation and divergence of pump waves. Expressions connecting most efficiently the converted spatial frequency bandwidth with the rotation angle and divergence of pump waves has been obtained.

Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform.

A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances.

Iterative Fourier Transform Algorithm Based on the Segmentation of Target Image for a High-Speed Binary Spatial Light Modulator

A digital micro-mirror device (DMD) has the potential to modulate an incident wave with high speed, and the application for holographic display has been studied by many researchers. However, the quality of reconstructed image isn't good in comparison with that from a gray-scale amplitude-only hologram since it is a binary amplitude-only spatial light modulator (SLM). In this paper, we suggest a method generating a set of binary holograms to improve the quality of the reconstructed image. Here, we are concerned with the case for which the object plane is positioned at the Fourier domain of the plane of the SLM. In this case, any point in the Fourier plane is related to all points in the hologram. So there is a chance to generate a set of binary holograms illuminated by incident wave with constant optical power. Moreover, we find an interesting fact that the quality of reconstructed image is improved when the spatial frequency bandwidth of the binary hologram is limited. Therefore, we propose an iterative segmentation algorithm generating a set of binary holograms that are designed to be illuminated by the wave with constant optical power. The feasibility of our method is experimentally confirmed with a DMD.

Specification of x-ray mirrors in terms of system performance: new twist to an old plot

In the early 1990s, Church and Takacs pointed out that the specification of surface figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. We demonstrate the limitations of specification, characterization, and performance evaluation based on conventional statistical approaches, including root-mean-square roughness and residual slope variation, evaluated over spatial frequency bandwidths that are system specific, and a more refined description of the surface morphology based on the power spectral density distribution. We show that these limitations are fatal, especially in the case of highly collimated coherent x-ray beams, like beams from x-ray free electron lasers (XFELs). The limitations arise due to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the problem, we treat a method, suggested by Yashchuk and Yashchuk in 2012, based on an autoregressive moving average modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example specific to the x-ray optical systems under design at the European XFEL.

Four-Wave Interaction on Resonance and Thermal Nonlinearities in a Scheme with Concurrent Pump Waves for High Conversion Coefficients

We have obtained the dependences of the conversion coefficient and the bandwidth of spatial frequencies on the intensity of pump waves for a four-wave converter of radiation for the resonance and thermal nonlinearity in a scheme with concurrent pump waves. The connection between the conversion coefficient and spatial selectivity of a four-wave radiation converter has been found.

Super-oscillation focusing lens based on continuous amplitude and binary phase modulation.

In this paper, we numerically demonstrate the advantage of utilizing continuous amplitude and phase modulation in super-oscillation focusing lens design. Numerical results show that compared with simple binary amplitude modulation, continuous amplitude and phase modulation can greatly improve the super-oscillation focusing performance by increasing the central lobe intensity and the ratio of its energy to the total energy, reducing the sidelobe intensity, and substantially extending the field of view. Our study also reveals the role of phase distribution in reducing the spatial frequency bandwidth of the super-oscillation optical field on the focal plane. Based on continuous amplitude and binary phase modulation, a lens was designed with double layer metal slit array for wavelength of 4.6 µm. COMSOL is used to carry out the 2D simulation. The lens focal length is 40.18λ and the focal spot FWHM is 0.308λ. Two largest sidelobes are located right next to the central lobe with intensity about 40% of the central lobe intensity. Except for the two sidelobes, other sidelobes have intensity less than 25% of the central lobe intensity, which leads to a clear field of view on the whole focal plane.

Evidence for adjustable bandwidth orientation channels.

The standard model of early vision claims that orientation and spatial frequency are encoded with multiple, quasi-independent channels that have fixed spatial frequency and orientation bandwidths. The standard model was developed using detection and discrimination data collected from experiments that used deterministic patterns such as Gabor patches and gratings used as stimuli. However, detection data from experiments using noise as a stimulus suggests that the visual system may use adjustable-bandwidth, rather than fixed-bandwidth, channels. In our previous work, we used classification images as a key piece of evidence against the hypothesis that pattern detection is based on the responses of channels with an adjustable spatial frequency bandwidth. Here we tested the hypothesis that channels with adjustable orientation bandwidths are used to detect two-dimensional, filtered noise targets that varied in orientation bandwidth and were presented in white noise. Consistent with our previous work that examined spatial frequency bandwidth, we found that detection thresholds were consistent with the hypothesis that observers sum information across a broad range of orientations nearly optimally: absolute efficiency for stimulus detection was 20–30% and approximately constant across a wide range of orientation bandwidths. Unlike what we found with spatial frequency bandwidth, the results of our classification image experiment were consistent with the hypothesis that the orientation bandwidth of internal filters were adjustable. Thus, for orientation summation, both detection thresholds and classification images support the adjustable channels hypothesis. Classification images also revealed hallmarks of inhibition or suppression from uninformative spatial frequencies and/or orientations. This work highlights the limitations of the standard model of summation for orientation. The standard model of orientation summation and tuning was chiefly developed with narrow-band stimuli that were not presented in noise, stimuli that are arguably less naturalistic than the variable bandwidth stimuli presented in noise used in our experiments. Finally, the disagreement between the results from our experiments on spatial frequency summation with the data presented in this paper suggests that orientation may be encoded more flexibly than spatial frequency channels.

三种不同结构的无透镜鬼成像实验研究

To achieve stand-off sensing applications, ghost imaging experiments with pseudothermal light were performed from transmissive to reflective cases. First, ghost images of a transmissive double-slit aperture were retrieved in a setup that both the reference beam and signal beam were collected with two different regions of a single CCD. Then a CCD and a separate bucket detector were used to record the light intensity information of the reference beam and the signal beam, respectively. By calculating the intensity correlation function of the signal beam with no spatial light distribution and the spatial dependent reference beam that does not interact with the object, ghost images of a transmissive object and a reflective object were achieved. In order to design and develop prototype systems field applicable, detailed experimental investigations were performed to compare the effect of system parameters on the quality of imaging in the transmission configuration. The results show that enough high power of light source, large sample numbers, and proper exposure time and spatial frequency bandwidth can lead to ghost image with good resolution and visibility.

Spatial and temporal characteristics of a four-wave radiation converter in a transparent medium based on electrostriction and dufour effect

Dynamics of spatial spectrum of the object wave has been analyzed for four-wave radiation converter in an optically transparent medium. It has been shown, that such four-wave radiation converter performs filtering of high spatial frequencies. Over time the spatial frequency bandwidth cut out by four-wave radiation converter decreases leaving the steady-state value.

Robust design of a silver-dielectric near-field superlens for photolithography

The transmission characteristics of silver–dielectric superlenses in photolithographic applications are studied here and are shown to introduce significant spatial frequency-specific artifacts into images of subwavelength patterns when the superlens is below a certain thickness. These artifacts have a negative impact on the fidelity of patterns produced by photoresists exposed through superlenses, which is not ideal in photolithography applications. The cause of the artifacts is identified as a mismatch between the dc transmission coefficient and the peak transmission coefficient of the superlens, which is normally placed beyond the conventional diffraction limit. We show that this mismatch can be corrected by increasing the thickness of the component layers within the superlens, with the result that the total transmission through the superlens is reduced but the range of spatial frequencies that can be transmitted without severe distortion is increased. Analyses and examples are presented for superlens designs that maximize the spatial frequency bandwidth over which good imaging can be expected; systems with a total thickness of 120–140 nm are optimal, delivering superresolution imaging over spatial frequency bandwidths of up to 6.6 μm−1.

Enhanced fractional Fourier lens with isotropic transformation media

By manipulating the principal stretches during a two-step space mapping within the framework of transforma- tion optics, the input spatial frequency bandwidth of a conven- tional Fourier lens can be extended based on an isotropic transformation material. Isotropy is important for easy fabrica- tion, low loss, and broadband application; moreover, it sug- gests a route for realizing Fourier transforms of continuous fractional order with enhanced input spatial frequency band- width. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. (DOI: 10.1117/1.OE.52.6.060501)

Inconsistent channel bandwidth estimates suggest winner-take-all nonlinearity in second-order vision

The processing of texture patterns has been characterized by a model that postulates a first-stage linear filter to highlight a component texture, a pointwise rectification stage to convert contrast for the highlighted texture into mean response strength, followed by a second-stage linear filter to detect the texture-defined pattern. We estimated the spatial-frequency bandwidth of the second-stage filter mediating orientation discrimination of orientation-modulated second-order gratings by measuring threshold elevation in the presence of filtered noise added to the modulation signal. This experiment yielded no evidence for frequency tuning. A second experiment, in which subjects had to detect similar second-order gratings while judging their modulation frequency, produced bandwidth estimates of 1–1.5 octaves, similar to estimated bandwidths of first-order channels. We propose that an additional dominant-response-selection nonlinearity can account for these apparently contradictory results.

An accurate analysis of the radiation characteristics of a plane piston transducer with phase apodization for focusing

A plane piston transducer can be focused by a continuous variation of the excitation signal phase (or time delay) over the transducer surface. Prior analyses of this scheme used the Fresnel approximation, thereby limiting the validity. Using the angular spectrum method, an accurate radiation model of such a transducer has been developed that includes amplitude and phase apodization. The derivation includes the effects of diffraction and evanescent waves without using the Fresnel approximation. Moreover, this model develops insights into radiated field characteristics, including: (a) the spatial frequency bandwidth is constant over axial depth, suggesting that spatial resolution can be improved away from the focus; (b) the phase of the angular spectrum determines the spatial resolution for a given transducer configuration—a constant phase is optimal on any observation plane; (c) focusing can significantly increase the spatial frequency bandwidth; (d) the velocity potential on a plane parallel to the transducer is the Hankel convolution of the transducer surface velocity with the Green’s function; and (e) evanescent waves decay both with increasing spatial frequency and axial depth. The analytical model and associated insights enhance understanding of the radiated field characteristics, which can be of value in the development of signal processing techniques for image enhancement.