The approximate analytical formula for flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture was derived by the extended Huygens–Fresnel principle. Some numerical simulations are illustrated to the effects on the propagation of flattened Gaussian beams by the misaligned annular aperture. To compare the difference between annular apertured system and circular apertured system, the circular apertured system is also studied. The results show that angle misalignments and lateral displacements of aperture create asymmetrical average intensity distribution at receiving plane z = 500. The effects on intensity distribution by angle misalignments of annular aperture were small. In annular aperture case, the smooth of intensity distribution was worse with escalating obscure ratio ? in near-field; the side-lobes increased and the central lobe decreased with escalating obscure ratio ? in far-field. At receiving plane z = 500: for circular aperture, the side-lobes decreased, even to be neglected, with the increasing of truncation parameter δ; for annular aperture, the side-lobes increased with the increasing of truncation parameter δ. In addition, it is found that the aligned thin lens can fix asymmetry of intensity distribution which was caused by the misaligned annular aperture. 相似文献
In this paper, exact vibration frequencies of circular, annular and sector
membranes with a radial power law density are presented for the first time. It is
found that in general, the sequence of modes may not correspond to increasing azimuthal mode number $n$. The normalized frequency increases with the absolute
value of the power index $|ν|$. For a circular membrane, the fundamental frequency
occurs at $n = 0$ where $n$ is the number of nodal diameters. For an annular membrane, the frequency increases with respect to the inner radius $b$. When $b$ is close
to one, the width $1 − b$ is the dominant factor and the differences in frequencies are
small. For a sector membrane, $n − 1$ is the number of internal radial nodes and the
fundamental frequency occurs at $n = 1$. Increased opening angle $β$ increases the
frequency. 相似文献
Morphology of crystallized spherulites in poly(nonamethylene terephthalate) (PNT) in bulk forms, instead of thin‐film forms, was investigated using scanning electron microscopy (SEM), polarized‐optical microscopy (POM), and transmission electron microscopy (TEM). Ring textures were found to exist on the fractured surfaces or microtomed films from bulk PNT samples. By further SEM and TEM examinations, the fracture surfaces and microtomed films from the interior of the bulk display similar ring‐banded patterns as those in thin films cast on glass slides. Although the cast PNT thin films in two‐dimensional growth are known to display both Type‐1 ring bands as majority and Type‐2 ring bands as minority, this study further shows that the interior of PNT bulk exhibits mainly Type‐1 (single rings with narrower spacing than Type‐2) ring bands, and Type‐2 spherulites exist sporadically in three‐dimensional forms. From these analyses on the ring bands in the interiors of bulk‐form PNT crystallized at several specific temperatures, it can be proposed that the growth of spherulites in three dimensions is layer‐by‐layer, packing into a multi‐shells structure in three‐dimensional ring‐banded spheres.