液晶偏振测量中的一维反问题
On one dimensional inverse problems arising from polarimetric measurements of nematic liquid crystals
摘要：
我们重新审视的问题，确定介电参数的层状液晶的偏振测量最初介绍了Lionheart-Newton。经过详细的分析模型，所涉及的规模，和自然障碍的重建一个以上的介电参数，我们产生两个简单的一维逆问题，可以研究没有任何专业知识的液晶。然后，我们确认，很少可以恢复的内部配置的光滑介电参数从这些测量，并给出一个唯一性结果的两个问题之一，当未知参数满足单调性。在这种情况下，可用数据可以用拉普拉斯和汉克尔变换来表示。
英文摘要：
We revisit the problem of determining dielectric parameters in layered nematic liquid crystals from polarimetric measurements originally introduced by Lionheart & Newton. After a detailed analysis of the model, of the scales involved, and of natural obstacles to the reconstruction of more than one dielectric parameters, we produce two simple one-dimensional inverse problems which can be studied without any expertise in liquid crystals. We then confirm that very little can be recovered about the internal configuration of smooth dielectric parameters from these measurements, and give a uniqueness result for one of the two problem, when the unknown parameter satisfies a monotonicity property. In that case, the available data can be expressed in terms of Laplace and Hankel transforms.
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