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Focuses on a study which investigated the diffraction of focused truncated Gaussian beams at a circular aperture. Irradiance in planes normal to the axis; Irradiance in various planes normal to the axis; Expression for the encircled energy.

The beam quality behavior of Hermite-Gauss laser modes propagating through Gaussian apertures is analyzed.

The THz emission point on a nonlinear electro-optical crystal for generating broadband THz radiation is modeled as a radiating Gaussian aperture. With the wavelengths of the infrared pump beam being much smaller than the wavelength components of the generated THz pulse, a THz sub-wavelength radiating aperture with Gaussian profile is effectively created. This paper comprehensively investigates Gaussian apertures in focused THz radiation generation in electro-optical crystals and illustrates the breakdown of the paraxial approximation at low THz frequencies. The findings show that the shape of the radiation pattern causes a reduction in detectable THz radiation and hence contributes significantly to low signal-to-noise ratio in THz radiation generation. Whilst we have demonstrated the findings on optical rectification in this paper, the model may apply without a loss of generality to other types of apertures sources in THz radiation generation.

In his works on diffraction [Proc. R. Soc. London Ser. A204, 533 (1951)], E. Wolf introduced the Q2n function, which enters his expressions for the encircled energy. This quantity specifies the fraction of the total energy within various rings in receiving planes parallel to the geometrical focal plane. In addition to the Q2n function, another special function, called the Yn function, was used in his formulation, which had been introduced by H. H. Hopkins [Proc. Phys. Soc. London Sect. B62, 22 (1949)]. The purpose of this study is to generalize both the Q2n and Yn functions for evaluating the encircled energy in systems of focused truncated Gaussian beams by apertures of different Fresnel numbers and different levels of beam truncation. The generalized Q and Y functions are functions of more than one variable and are applicable to all nonnegative integers m; they may therefore be called the Qm and the Ym functions. Computed results are shown graphically in the form of contour lines of the encircled energy. Part II of this study [J. Opt. Soc. Am. A24, 2033 (2007)] contains an analysis of maximizing beam energy concentration on a target.

In Part I of this study [J. Opt. Soc. Am. A24, 2023 (2007)] the Q(2n) functions of E. Wolf and the Y(n) functions of H. H. Hopkins have been generalized for evaluating the fraction of the total energy in systems with focused truncated Gaussian beams by apertures of different Fresnel numbers and different ratios of aperture radius to beam radius. The generalized special functions provide a mathematical basis for a rigorous study of maximizing beam energy concentration on a target. This subject is addressed under two subtitles: (1) active focusing of a Gaussian beam onto a distant target and (2) optimizing photodetection in a focused field.

Beam quality behavior of Gaussian Schell-model beams that propagate through Gaussian apertures is analyzed.

Deviating emotion perception affects the interpretation of emotional stimuli and is linked to maladaptive emotion regulation. In adolescents with non-suicidal self-injury (NSSI), it remains unclear whether emotion regulation is altered from the earliest stage of visual emotion perception. The early visual system decomposes visual scenes into various spatial frequencies, processes these components individually, and then integrates them to form perception. Altered processing of these frequencies impacts the decoding of emotional stimuli, influencing emotion regulation from the onset of perception. This study explored emotion perception in 42 adolescent patients with NSSI and 43 healthy controls. Participants judged images of faces for emotional or neutral expressions across sessions featuring happy and sad valence. Gaussian apertures at random locations unveiled different facial areas at distinct spatial frequencies in each trial for emotion classification. Images from correct emotion classification were used to train an image classifier distinguishing emotional from neutral facial expressions in >33,000 trials per group and valence. Cross-validation demonstrated deviating performances between the NSSI and control models in classifying sad facial expressions, with the NSSI model more frequently misclassifying sad expressions as neutral. Layer-wise relevance propagation identified the underutilization of key facial features as contributors to the lower accuracy in the NSSI model. Further analyses revealed components of emotional competence as predictors of the utilization of specific facial regions for the classification of sad expressions. The disparity in identifying sad emotions suggests the utilization of different spatial frequency information as an emotion-specific avoidance strategy among adolescents with NSSI. • The emotion regulation process in adolescents with NSSI is altered from the initial perception of others' emotions. • Adolescents with NSSI misclassify sad faces by utilizing different spatial frequency information. • Key facial features were underutilized in the NSSI group, contributing to lower accuracy in emotion recognition. • Trained on 30,000+ trials, a classifier using spatial frequency achieved reliable results, closely emulating human perception. • Perceptual changes may be learned and reversible, as they rely on emotional competence. [ABSTRACT FROM AUTHOR]

Many operations of vision require image regions to be isolated and inter-related. This is challenging when they are different in detail and extent. Practical methods of Computer Vision approach this through the tools of downsampling, pyramids, cropping and patches. In this paper we develop an ideal geometric structure for this, compatible with the existing scale space model of image measurement. Its elements are apertures which view the image like fuzzy-edged portholes of frosted glass. We establish containment and cause/effect relations between apertures, and show that these link them into cross-scale atlases. Atlases formed of Gaussian apertures are shown to be a continuous version of the image pyramid used in Computer Vision, and allow various types of image description to naturally be expressed within their framework. We show that views through Gaussian apertures are approximately equivalent to the jets of derivative of Gaussian filter responses that form part of standard Scale Space theory. This supports a view of the simple cells of mammalian V1 as implementing a system of local views of the retinal image of varying extent and resolution. As a worked example we develop a keypoint descriptor scheme that outperforms previous schemes that do not make use of learning. [ABSTRACT FROM AUTHOR]

In this paper, the use of micro lenses with non-uniform transmittance apertures as an alternative to those with uniform transmittance apertures in optical communication systems is proposed. In particular, we consider the use of micro lenses with tapered Gaussian transmittance profiles to improve the misalignment tolerance in optical interconnects. We study the effects of utilizing Gaussian transmittance profiles on the propagation of light beams and the signal to crosstalk ratio of misaligned optical systems. Moreover, we consider the use of uniform transmittance profiles in optical systems for the sake of comparison. To this end, the crosstalk optical noise is modeled at the plane of the detectors array considering the two scenarios of uniform and Gaussian apertures. This was possible after finding the optical field for both scenarios at the of the detectors array. Numerical results clearly demonstrate the significant improvement in decreasing the crosstalk and increasing the signal to crosstalk ratio in the considered optical systems upon utilizing the Gaussian profiles. [ABSTRACT FROM AUTHOR]

Variable aperture sampling reconstruction matrices have a history of being computationally intensive due to the need to compute a full matrix inverse. In the field of remote sensing, several spaceborne radiometers and scatterometers, which have irregular sampling and variable apertures, use iterative techniques to reconstruct measurements of the Earth's surface. However, many of these iterative techniques tend to over-amplify noise features outside the reconstructable bandwidth. Because the reconstruction of discrete samples is inherently bandlimited, solving a bandlimited inverse can focus on recovering signal features and prevent the over-amplification of noise outside the signal bandwidth. To approximate a bandlimited inverse, we apply bandlimited constraints to several well-known iterative reconstruction techniques: Landweber iteration, additive reconstruction technique (ART), Richardson–Lucy iteration, and conjugate gradient descent. In the context of these iterative techniques, we derive an iterative method for inverting variable aperture samples, taking advantage of the regular and irregular content of variable apertures. We find that this iterative method for variable aperture reconstruction is equivalent to solving a bandlimited conjugate gradient descent algorithm. [ABSTRACT FROM AUTHOR]

Optical approaches have made great strides towards the goal of high-speed, energy-efficient computing necessary for modern deep learning and AI applications. Read-in and read-out of data, however, limit the overall performance of existing approaches. This study introduces a multilayer optoelectronic computing framework that alternates between optical and optoelectronic layers to implement matrix-vector multiplications and rectified linear functions, respectively. Our framework is designed for real-time, parallelized operations, leveraging 2D arrays of LEDs and photodetectors connected via independent analog electronics. We experimentally demonstrate this approach using a system with a three-layer network with two hidden layers and operate it to recognize images from the MNIST database with a recognition accuracy of 92% and classify classes from a nonlinear spiral data with 86% accuracy. By implementing multiple layers of a deep neural network simultaneously, our approach significantly reduces the number of read-ins and read-outs required and paves the way for scalable optical accelerators requiring ultra low energy. Read-in and read-out of data limit the overall performance of optical computing methods. This work introduces a multilayer optoelectronic framework that alternates between optical and optoelectronic layers to implement matrix-vector multiplications and rectified linear functions experimentally [ABSTRACT FROM AUTHOR]

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In this paper, we study terahertz generation through optical rectification in reflection at normal incidence in a dielectric nonlinear crystal. We first analyze, with a nonlinear optical model, the sample parameters (thickness, absorption at both laser and terahertz wavelengths, etc.) for which a terahertz optical rectification reflection scheme is preferable to the common transmission scheme. Then, we report our experimental observations of a reflected terahertz signal generated at the surface of a ZnTe crystal. The reflected terahertz signal shares all the characteristics of a signal generated in transmission but is not limited by absorption losses in the crystal, thereby providing a broader bandwidth. At high pump laser power, the signal exhibits saturation, which is caused by the decrease of the nonlinear susceptibility due to photocarriers generated by two-photon absorption. This reflection scheme could be of great importance for terahertz microscopy of opaque materials like, e.g., humid samples or samples exhibiting strong absorption bands or to study samples for which the transmitted signal cannot be recorded. [ABSTRACT FROM AUTHOR]

In this work we theoretically introduce and experimentally examine a novel type Bessel-like beams which have an intensity distribution spherically modified by a polarization structure when compared to standard Bessel beams. Standard Bessel-Gaussian beams can be either linearly or radially and azimuthally polarized. Here, the Bessel-like beams with a Gaussian envelope, we are introducing, can have either spherically radial or meridional - azimuthal polarizations. In order to implement those beams experimentally we investigate their vector spatial spectra numerically for the case of a finite energy. A proper choice of the cone angles of individual plane wave components and sizes of Gaussian apertures, we can control experimentally intensity distribution of resulting beams. Lastly, we demonstrate that in two limiting cases we can form from our solutions either two optical needles or doughnut-like intensity patterns. [ABSTRACT FROM AUTHOR]