Approximation of Fresnel Integrals with Applications to Diffraction Problems

This article introduces two approximations that allow the evaluation of Fresnel integrals without the need for using numerical algorithms. These equations accomplish the characteristic of being continuous in the same interval as Fresnel. Both expressions have been determined applying the least squares method to suitable expressions. Accuracy of equations improves as x increases; as for small values of x, it is possible to achieve an absolute error less than 8×10-5. To probe the efficiency of the equations, two case studies are presented, both applied in the optics field. The first case is related to the semi-infinite opaque screen for Fresnel diffraction. In this case study Fresnel integrals are evaluated with the proposed equations to calculate the irradiance distribution and the Cornu spiral for diffraction computations of the Fresnel diffraction; obtained results show a good accuracy. The second case is related to the double aperture problem for Fresnel diffraction.

Diffraction Of A Plane Monochromatic Wave At The Circular Aperture And Circular Disk

In the framework of the scalar theory of diffraction of normally incident plane monochromatic wave, the intensity distribution of the diffraction field along the axis of an annular hole was found. As particular cases, the diffraction at an opaque circular disk of radius R ب λ (λ is the wavelength) and at a circular aperture in an opaque screen was considered. Accounting for the vector nature of the field of electromagnetic waves led to more correct results, including at large angles of diffraction, i.e. at sufficiently small distances from the screen (smaller and of order R), where the scalar theory, as it is known, not applicable.

Mirror Perception in Mice: Preference For and Stress Reduction by Mirrors

I measured the amount of time mice spent in a compartment with either a mirror or an opaque screen and found that mice stayed longer in the compartment with the mirror. This finding suggests that mice prefer mirrors. They also showed a preference for the mirror over unfamiliar live mice but did not show a differential preference for the mirror over a familiar live mouse (cage mate). Restraint stress caused hyperthermia (known as stress-induced hyperthermia) in the mice. When cage mates received the restraint stress together, the hyperthermia was reduced. Placement of mirrors instead of the cage mates also showed stress-reducing effects, while restraint with unfamiliar mice did not reduce the hyperthermia. These results suggest that mirrors have familiar cage mate-like social effects in mice.

Bessel Beam Diffraction by an Aperture in an Opaque Screen

The scattering of the Bessel beam by a circular aperture in an opaque screen is investigated by the geometrical theory of diffraction approach. The geometrical optics and diffracted and scattered fields are obtained. The effect of the aperture to the scattering process is analyzed. The uniform versions of field expressions are derived. The geometrical optics and diffracted and scattered fields are examined numerically.

TWO-PHOTON HIGH-DIMENSIONAL SPATIAL ENTANGLEMENT: THEORY AND EXPERIMENT

We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.

A Deep Optical Search for Substellar Candidates in the Nearby ρ Ophiuchi Star-Forming Region

We report preliminary results from a deep I-band optical search for substellar candidates in the p Oph star-forming region. The dusty molecular cloud provides an opaque screen at optical wavelengths, making the survey sensitive to faint substellar candidates near the cloud surface. Of the 89 objects detected in the oph A and oph C molecular cores, one third are substellar candidates.

Dissociation of Mechanisms Involved in Dogs’ Oriented Displacements

Factors determining spatial choice were studied in experiments conducted outdoors. Six dogs (Breton spaniel) had to choose between two paths leading to a baited feeding bowl (goal). Transparent or opaque screens were interposed between the starting-point and the goal; their arrangement was devised so as to control the length and the angular deviation or divergence of the paths. The results show that when the goal was visible (transparent screens) dogs preferred the less divergent path indicating that angular deviation was the most relevant variable. When the goal was hidden (opaque screen), they preferred the shorter path and did not take into account the angular deviation. These results suggest that two classes of mechanism underlie the selection of path in these spatial situations.