Abstract
Effective collecting area represents one of principal parameters of optical systems. The common requirement is to obtain as large effective collecting area as it is possible. The paper presents an analytical method of calculating effective collecting length and its maximization for lobster eye optics. The results are applicable for a Schmidt as well as for an Angel lobster eye geometry used in an astronomical telescope where the source is at infinity such that the incoming rays are parallel. The dependence of effective collecting area vs. geometrical parameters is presented in a form of a simple compact equation. We show that the optimal ratio between mirrors depth and distance (effective angle) does not depend on other geometrical parameters and it is determined only by reflectivity function, i.e. by mirrors (or their coating) material and photon energy. The results can be also used for approximate but fast estimation of performance and for finding the initial point for consequent optimization by ray-tracing simulations.
Highlights
Lobster eye X-ray optics was proposed a long time ago in two basic concepts: Schmidt[12] and Angel[2].Schmidt lobster eye[12] can be one-dimensional or two-dimensional
The results are applicable for a Schmidt as well as for an Angel lobster eye geometry used in an astronomical telescope where the source is at infinity such that the incoming rays are parallel
We show that the optimal ratio between mirrors depth and distance does not depend on other geometrical parameters and it is determined only by reflectivity function, i.e. by mirrors material and photon energy
Summary
Lobster eye (abbreviation LE) X-ray optics was proposed a long time ago in two basic concepts: Schmidt[12] and Angel[2]. Angel lobster eye optics[2] is composed of square pores It can be viewed as a special case of the Schmidt system, where both stacks lay in the same position and they have the same radii r = r1 = r2. Some analytical equations for lobster system were presented in sources [2, 10, 12] but they do not include all parameters, e.g. zero mirror thickness is supposed. This paper follows previous work of some authors [19] in which equation for calculation of effective collecting area (length) including all geometric parameters are presented the method for taking the mirror reflectivity into account is only covered in outline. The maximum possible effective collecting area/length is found
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