Angular aperture

About: Angular aperture is a research topic. Over the lifetime, 1771 publications have been published within this topic receiving 27257 citations.

Molecular beams and effusive flows

Abstract: Molecular flux emanating from an aperture in a beam oven and incident on a point on the beam axis is discussed. The vector flux density is characterized by its vector‐velocity (rather than speed) probability distribution. As a consequence, the integrals of the velocity components orthogonal to the beam axis yield the observed dependences of beam intensity upon aperture area and distance from the aperture. Both rectangular and circular apertures are considered. The velocity integrals for the circular aperture are exact and demonstrate how the velocity distribution of the flux density gradually changes from that of the Maxwell flux at the aperture to that of a beam flux at large distances from the aperture. (This cannot be shown with the speed distribution.) An expression then is obtained for the flux from a circular aperture incident on an off‐axis point by making use of the concept of a virtual aperture which simplifies the problem considerably. This expression then is used to calculate both the normal flux density distribution and the total flux incident on a finite plane collector. These treatments may be applied to systems with apertures and collectors of almost any shape and/or size.

Condensers for illumination systems

Abstract: A condenser lens (2) for a projection system optimizes the amount of overall brightness directed toward an aperture (3) and the uniformity of illumination at the aperture (3). The lens, when placed in the projection system, has a marginal ray which starts at the center of the light source, passes through the edge of the condenser lens, and intersects the region to be illuminated at or near its edge. The lens further has a relative zonal ray height which is selected based on the distance from the light source to the aperture. The condensing lens system is particularly useful in the construction of overhead projectors.

An imaging system in reflection mode using coherent diffraction imaging methods and using micro-pinhole and aperture system

Abstract: An apparatus and a method of imaging a reflective sample, in particular for patterned and blank DUV, EUV masks, includes making an optics system; exposing the mask to obtain an aerial image include tomographic image and developing an optical parameter of the optical system associated with the aerial image according to the micro-pinhole system using scanning coherent diffraction methods. Said apparatus comprises : a) a radiation source (10), such as an EUV source, a DUV source, a BEUV or an X-ray source, that can have a relevant low temporal or spatial coherence to emit a light beam (22); b) a first focusing element (12), such as a Fresnel plate or a toroidal mirror, in order to focus the emitted beam to the required extend; c) a mirror (16) that reflects the focused beam towards the sample (6) to be analyzed; the beam being directed at an angle of 2 to 25°, preferably at an angle of about 6°, towards the sample (6) as compared to the normal vector of the surface of the sample (6); d) a pinhole aperture plate (18) which allows with its first aperture (al) to focus and cut-off the beam diameter to the desired extent thereby forming also the beam to become more monochromatic as compared to the light beam (22) as originally emitted from the light source (10); e) a mechanism (17) to displace the sample (6) continuously or step-wise in a direction perpendicular to the normal vector of the sample surface to allow to analyze the sample (6) which reflects the light beam that has passed the first aperture (a1) of the pinhole aperture plate (18) disposed upstream of the sample (6) under the same angle of the incident light, such as 6° for example with reference to the preferred example mentioned above; f) said pinhole aperture plate (18) having a second aperture (a2) as transparent window allowing with its second aperture being disposed adjacent to the first aperture (a1) to limit the diameter of the beam reflected by the sample (6) thereby adjusting the diameter of the light beam; and g) a pixel detector (20) to analyze the reflected beam that has passed the second aperture (a2).

A note on the diffraction of a scalar wave by a small circular aperture

Abstract: The power series solution for the diffraction of a scalar plane wave incident normally on a small circular aperture in a hard screen is extended to include terms of order α12 in the aperture field,

The period of a spherical resonator with a circular aperture

Abstract: In a paper on “The Theory of the Helmholtz Resonator,” Lord Rayleigh has carried the determination of the wave-length of the fundamental aerial vibration in a spherical vessel with a small circular perforation to a second approximation, obtaining the result λ = π√(2S/ a ) . {1-9/10 a /2π c +...}, (1) where c is the radius of the sphere, a the small radius of the aperture, and S the volume of the sphere. To obtain this value he assumes a form for the normal velocity U over the aperture and adjusts it so as to lead to agreement, to a corresponding approximation, in the values of the velocity potential derived therefrom over the aperture inside and outside, so as to provide for the condition of continuity of pressure at the opening. It is the object of this note to carry the result, by a slightly different assumption for U, to a higher approximation.