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Chapter 21:
Total Internal Reflection Tomography for Three-Dimensional Subwavelength Imaging
Abstract
Near-field imaging has gained a great deal of exposure in recent years for its ability to resolve subwavelength structure in optically thin media. It has many variants, including total internal reflection microscopy (TIRM), photon scanning tunneling microscopy (PSTM), and near-field scanning optical microscopy (NSOM), but common to all is the use of evanescent waves for illumination and/or detection. In many instances, image interpretation is difficult, owing to the complex interaction between the incident field and the sample, as well as between the scattered field and the near-field probe. These difficulties are exacerbated when near-field techniques are applied to relatively thick samples. In addition to the problem of reconstructing a three-dimensional function of position (the dielectric susceptibility) from two-dimensional data sets (measurements of the scattered field in various planes), a thick object may exhibit strong scattering, with the consequence that the scattered field is a nonlinear function of the susceptibility. Even when the scattering is weak, the detected field may not be simply related to the subwavelength structure of the object, as it is, for example, in the case of diffraction from a 2D object. In this chapter, we will discuss a new form of near-field imaging that makes use of TIRM measurements to produce computed reconstructions of the susceptibility of the sample. This method provides tomographic views and subwavelength resolution. Since the system is free from the moving (and often ill-characterized) probe present in PSTMand NSOM, the analysis of the problem is greatly simplified. Indeed the experiment is well modeled as a half-space problem and an exact solution for the Green’s function (absent the sample) is well known. The linearized inverse scattering problem may then be solved in a computationally efficient and stable manner. In Sect. 21.2 we review the fundamentals of diffraction tomography and observe the emergence of the classical resolution limits. In Sect. 21.3 we examine the properties of near-field evanescent waves and the role they play in achieving super-resolution in a variety of near-field methods. In Sect. 21.4 we describe the basic TIRM measurement scheme and its extension to total internal reflection tomography (TIRT). In Sect. 21.5 we address the structure of the TIRT data and the development of fast, stable reconstruction algorithms, followed by numerical simulations in Sect. 21.6. Finally, in Sect. 21.7 we describe the instrument currently under construction at NASA to implement this modality.
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CHAPTER 21
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