Fourier transform infrared (FT-IR) spectroscopic imaging combines the specificity of optical microscopy with the spectral selectivity of vibrational spectroscopy. There is increasing recognition that the recorded data may be dependent on the optical configuration and sample morphology in addition to its local material spectral response, but a quantitative framework for predicting such dependence is lacking. Here, a theory is developed to relate recorded data to the spectral and physical properties of heterogeneous samples. The modeling approach combines optical theory through rigorous coupled wave analysis with modeling of sampling geometry and sample structure. The interplay of morphology and dispersion are systematically explored using increasingly sophisticated samples to illustrate the dependence of the detected optical intensity on the spatial sample structure. Predictions of spectral distortions arising from the sample structure are quantified, and experimental validation of the developed theory is performed using a microfabricated standard from a commercial photoresist polymer. The developed framework forms a basis for understanding sample induced distortions in spectroscopic IR microscopy and imaging.

Midinfrared (IR) microspectroscopy is widely employed for spatially localized spectral analyses. A comprehensive theoretical model for the technique, however, has not been previously proposed. In this paper, rigorous theory is presented for IR absorption microspectroscopy by using Maxwell's equations to model beam propagation. Focusing effects, material dispersion, and the geometry of the sample are accounted to predict spectral response for homogeneous samples. Predictions are validated experimentally using Fourier transform IR (FT-IR) microspectroscopic examination of a photoresist. The results emphasize that meaningful interpretation of IR microspectroscopic data must involve an understanding of the coupled optical effects associated with the sample, substrate properties, and microscopy configuration. Simulations provide guidance for developing experimental methods and future instrument design by quantifying distortions in the recorded data. Distortions are especially severe for transflection mode and for samples mounted on certain substrates. Last, the model generalizes to rigorously consider the effects of focusing. While spectral analyses range from examining gross spectral features to assessing subtle features using advanced chemometrics, the limitations imposed by these effects in the data acquisition on the information available are less clear. The distorting effects are shown to be larger than noise levels seen in modern spectrometers. Hence, the model provides a framework to quantify spectral distortions that may limit the accuracy of information or present confounding effects in microspectroscopy.

A large-aperture, electromagnetic model for coherent microscopy is presented and the inverse scattering problem is solved. Approximations to the model are developed for near-focus and far-from-focus operations. These approximations result in an image-reconstruction algorithm consistent with interferometric synthetic aperture microscopy (ISAM): this validates ISAM processing of optical-coherence-tomography and optical-coherence-microscopy data in a vectorial setting. Numerical simulations confirm that diffraction-limited resolution can be achieved outside the focal plane and that depth of focus is limited only by measurement noise and/or detector dynamic range. Furthermore, the model presented is suitable for the quantitative study of polarimetric coherent microscopy systems operating within the first Born approximation.

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Infrared microspectroscopy is widely used for the chemical analysis of small samples. In particular, spectral properties of small cylindrical samples are important in forensic analysis, understanding relationships between microstructure and mechanical properties in fibers or fiber composites, and development of cosmetics and drugs for hair. The diameters of the constituent cylinders are typically of the order of the central wavelength of light used to probe the sample. Hence, structure and material spectral response are coupled and recorded spectra are usually distorted to the extent of becoming useless for molecular identification. In this paper, we apply rigorous optical theory to predict the spectral distortions observed in IR microspectroscopic data of fibers. The theory is used, first, to compute the changes that are observed for cylinders of various dimensions under different instrument configurations when compared to the bulk spectrum from the same material. We provide a method to recover intrinsic material spectral response from fibers by correcting for distortion introduced by the cylindrical structure. The theory reported here should enable the routine use of IR microspectroscopy and imaging for the molecular analysis of cylindrical domains in complex materials.

We introduce a new fluorescence microscopy technique that maps the axial position of a fluorophore with subnanometer precision. The interference of the emission of fluorophores in proximity to a reflecting surface results in fringes in the fluorescence spectrum that provide a unique signature of the axial position of the fluorophore. The nanometer sensitivity is demonstrated by measuring the height of a fluorescein monolayer covering a 12-nm step etched in silicon dioxide. In addition, the separation between fluorophores attached to the top or the bottom layer in a lipid bilayer film is determined. We further discuss extension of this microscopy technique to provide resolution of multiple layers spaced as closely as 10 nm for sparse systems.Index Terms-Fluorescence microscopy, interference, spectroscopy, ultra high-optical resolution.

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Three-dimensional image formation in microscopy is greatly enhanced by the use of computed imaging techniques. In particular, Interferometric Synthetic Aperture Microscopy (ISAM) allows the removal of out-of-focus blur in broadband, coherent microscopy. Earlier methods, such as optical coherence tomography (OCT), utilize interferometric ranging, but do not apply computed imaging methods and therefore must scan the focal depth to acquire extended volumetric images. ISAM removes the need to scan the focus by allowing volumetric image reconstruction from data collected at a single focal depth. ISAM signal processing techniques are similar to the Fourier migration methods of seismology and the Fourier reconstruction methods of Synthetic Aperture Radar (SAR). In this article ISAM is described and the close ties between ISAM and SAR are explored. ISAM and a simple strip-map SAR system are placed in a common mathematical framework and compared to OCT and radar respectively. This article is intended to serve as a review of ISAM, and will be especially useful to readers with a background in SAR.