A New Approach to Optical Microscopy of Sub-Wavelength Diffraction Structures: Shape Reconstruction from Ellipsometric Back-Focal-Plane Data

该项目的目的是利用计算机模拟来研究一种新型光学显微镜的可行性，该显微镜用于测量尺寸小于所用光的波长的三维物体的尺寸和形状。传统的光学显微镜基于对像面上光强分布的测量，不能分辨小于一个波长的空间细节。然而，所提出的光学显微镜是基于物体在物镜后焦面上散射的电场的椭偏测量。椭圆偏振测量数据允许计算光学系统的琼斯矩阵的不同分量之间的相对相位。通过求解电磁逆问题，这些位相信息被用来确定物体的形状。提出的显微镜思想应该是非常有科学意义的，因为使用从背焦平面椭偏测量获得的位相信息来重建物体形状的技术是新的。此外，该方法对样品的定位和聚焦误差不敏感，这是该方法应用于解决工业计量问题的一个重要考虑因素。建议的可行性研究将包括使用计算机模拟生成假设数据，然后用于测试各种数值算法的收敛和稳健性，以解决由假设数据重建形状的电磁逆问题。在开展可行性研究的过程中，参与的研究生将获得深入的光学成像理论知识和各种电磁数值方法的第一手经验。因此，拟议的项目对有兴趣在涉及光学和电磁学的交叉学科领域工作的研究生的教育应该有很大的价值。此外，如果可行性研究的结果看起来很有希望，未来的研究项目可能会启动，以实验测试拟议的显微镜想法。

The objective of the proposed project is to use computer simulation to study the feasibility of a new type of optical microscope for measuring the sizes and shapes of three-dimensional objects whose dimensions are smaller than the wavelength of the light employed. Conventional optical microscope based on measurement of the intensity distribution on the image plane is not capable of resolving spatial details much smaller than about one wavelength. The proposed optical microscope, however, is based on ellipsometric measurements of the electric field scattered by an object onto the back focal plane of the objective lens. The ellipsometric data allow the relative phases among different components of the Jones matrix of the optical system to be computed. This phase information is then used to determine the shape of the object by solving an electromagnetic inverse problem.The proposed microscope idea should be of great scientific interest, since the technique of using the phase information obtained from back-focal-plane ellipsometric measurements for object shape reconstruction is novel. Also, the proposed method is insensitive to positioning and focus errors of the sample, which is an important consideration if the method is to be applied to solving metrology problems in industry.The proposed feasibility study will consist of using computer simulation to generate hypothetical data, which will then he used to test the convergence and robustness of various numerical algorithms for solving the electromagnetic inverse problem of shape reconstruction from the hypothetical data. In the process of carrying out the feasibility study, the graduate student involved will gain in-depth knowledge of optical imaging theory and firsthand experience with various numerical methods of electromagnetic. As such, the proposed project should be of great value in the education of graduate students interested in working in an interdisciplinary area involving both optics and electromagnetics. Also, if the results of the feasibility study appear promising, future research projects may he initiated to test the proposed microscope idea experimentally