State-of-the-art methods in high-resolution three-dimensional optical microscopy require that the focus be scanned through the entire region of interest. However, an analysis of the physics of the light-sample interaction reveals that the Fourier-space coverage is independent of depth. Here we show that, by solving the inverse scattering problem for interference microscopy, computed reconstruction yields volumes with a resolution in all planes that is equivalent to the resolution achieved only at the focal plane for conventional high-resolution microscopy. In short, the entire illuminated volume has spatially invariant resolution, thus eliminating the compromise between resolution and depth of field. We describe and demonstrate a novel computational image-formation technique called interferometric synthetic aperture microscopy (ISAM). ISAM has the potential to broadly impact real-time three-dimensional microscopy and analysis in the fields of cell and tumour biology, as well as in clinical diagnosis where imaging is preferable to biopsy.

Inverse scattering theory for optical coherence tomography (OCT) is developed. The results are used to produce algorithms to resolve three-dimensional object structure, taking into account the finite beam width, diffraction, and defocusing effects. The resolution normally achieved only in the focal plane of the OCT system is shown to be available for all illuminated depths in the object without moving the focal plane. Spatially invariant resolution is verified with numerical simulations and indicates an improvement of the high-resolution cross-sectional imaging capabilities of OCT.

The availability of a real-time non-destructive modality to interrogate the mechanical properties of viscoelastic materials would facilitate many new investigations. We introduce a new optical method for measuring elastic properties of samples which employs magnetite nanoparticles as perturbative agents. Magnetic nanoparticles distributed in silicone-based samples are displaced upon probing with a small external magnetic field gradient and depth-resolved optical coherence phase shifts allow for the tracking of scatterers in the sample with nanometer-scale sensitivity. The scatterers undergo underdamped oscillations when the magnetic field is applied step-wise, allowing for the measurement of the natural frequencies of oscillation of the samples. Validation of the measurements is accomplished using a commercial indentation apparatus to determine the elastic moduli of the samples. This real-time non-destructive technique constitutes a novel way of probing the natural frequencies of viscoelastic materials in which magnetic nanoparticles can be introduced.

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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.