论文标题
在奇异扰动方法中的最小镜头溶液
Minimal lensing solutions in the singular perturbative approach
论文作者
论文摘要
本文分析了在奇异扰动方法中重建晶状体电位的最小溶液的性能。这些最小的溶液对应于在扰动场的傅立叶扩展中的扩展。使用这些最小的解决方案，可以防止在田间重建中伪装物理上毫无意义的术语。实际上，扰动分析表明，源模型的少量变化将对应于磁场扩展中的高阶项。扰动分析的结果不仅对略有非圆形来源有效，而且对于更扭曲的源以订购两个。因此，最大程度地减少镜头建模中使用的术语数量至关重要。最小解决方案的另一个重要资产是，它们在源模型和镜头模型之间提供了除耦合，从而有助于打破源镜头变性问题。最小解决方案的可能缺点是低估溶液中的高阶项。但是，这种偏见具有其优点，因为使用此方法检测高阶术语将确保这些术语是真实的。考虑到大量镜头的统计分析，尤其是鉴于传入的卫星调查，这种类型的分析将特别感兴趣。
This paper analyse the properties of minimal solutions for the reconstruction of the lens potential in the singular perturbative approach. These minimal solutions corresponds to an expansion with a minimal degree in Fourier expansion of the perturbative fields. Using these minimal solutions prevent spurious physically meaningless terms in the reconstruction of the fields. In effect a perturbative analysis indicates that a small change in the source model will corresponds to the higher order terms in the expansion of the fields. The results of the perturbative analysis are valid not only for slightly non-circular sources but also for more distorted sources to order two. It is thus of crucial importance to minimize the number of terms used in the modelling of the lens. Another important asset of the minimal solutions is that they offers a de-coupling between the source and lens model and thus help to break the source lens degeneracy issue. The possible drawback of minimal solutions is to under-estimate the higher order terms in the solution. However this bias has its merit since the detection of higher order terms using this method will ensure that these terms are real. This type of analysis using minimal solutions will be of particular interest when considering the statistical analysis of a large number of lenses, especially in light of the incoming satellite surveys.
