The spatial orientation of optical radiation sources has long been the hot topic in the aerospace and the military applications.Current researches mainly focus on the high precision orientation on the partial field of...The spatial orientation of optical radiation sources has long been the hot topic in the aerospace and the military applications.Current researches mainly focus on the high precision orientation on the partial field of view.Thus,combination of several partial fields of view is required to achieve orientation when the field of view exceeds 180°,which results in the increase of size,weight,power consumption and the cost.By defining radiation energy and direction of the optical radiation source as a vector and applying the cosine law of radiation and vector theorem,it is shown that the vector can be obtained from unit normal vectors on the three un-coplanar surfaces and from the energy projected by the optical radiation source.Based on this,an orientation method with 360° full field of view by a polyhedron is suggested,the mathematical formula for anti-multipath interference is supposed and the error upper limit is derived.The feasibility and effectiveness of this method are validated by measurements and simulation.An accuracy better than 2.866° and 0.574° is achieved when the ratio of measurement error of energy on arbitrary surface and the true value are 5% and 1%,respectively,given the matrix composed of unit normal vectors on three measurement surfaces is orthogonal.展开更多
Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned ...Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.展开更多
文摘The spatial orientation of optical radiation sources has long been the hot topic in the aerospace and the military applications.Current researches mainly focus on the high precision orientation on the partial field of view.Thus,combination of several partial fields of view is required to achieve orientation when the field of view exceeds 180°,which results in the increase of size,weight,power consumption and the cost.By defining radiation energy and direction of the optical radiation source as a vector and applying the cosine law of radiation and vector theorem,it is shown that the vector can be obtained from unit normal vectors on the three un-coplanar surfaces and from the energy projected by the optical radiation source.Based on this,an orientation method with 360° full field of view by a polyhedron is suggested,the mathematical formula for anti-multipath interference is supposed and the error upper limit is derived.The feasibility and effectiveness of this method are validated by measurements and simulation.An accuracy better than 2.866° and 0.574° is achieved when the ratio of measurement error of energy on arbitrary surface and the true value are 5% and 1%,respectively,given the matrix composed of unit normal vectors on three measurement surfaces is orthogonal.
基金supported by National Natural Science Foundation of China (Grant No.10871069)the Youth Natural Science Foundation of Shandong Province (Grant No. Q2008A08)the Youth Foundation of Qufu Normal University
文摘Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.
