Compositional prior information in computed infrared spectroscopic imaging

Multi-modal image sharpening in fourier transform infrared (FTIR) microscopy

Mid-infrared Spectroscopic Imaging (MIRSI) provides spatially-resolved molecular specificity by measuring wavelength-dependent mid-infrared absorbance. Infrared microscopes use large numerical aperture objectives to obtain high-resolution images of heterogeneous samples. However, the optical resolution is fundamentally diffraction-limited, and therefore wavelength-dependent. This significantly limits resolution in infrared microscopy, which relies on long wavelengths (2.5 μm to 12.5 μm) for molecular specificity. The resolution is particularly restrictive in biomedical and materials applications, where molecular information is encoded in the fingerprint region (6 μm to 12 μm), limiting the maximum resolving power to between 3 μm and 6 μm. We present an unsupervised curvelet-based image fusion method that overcomes limitations in spatial resolution by augmenting infrared images with label-free visible microscopy. We demonstrate the effectiveness of this approach by fusing images of breast and ovarian tumor biopsies acquired using both infrared and dark-field microscopy. The proposed fusion algorithm generates a hyperspectral dataset that has both high spatial resolution and good molecular contrast. We validate this technique using multiple standard approaches and through comparisons to super-resolved experimentally measured photothermal spectroscopic images. We also propose a novel comparison method based on tissue classification accuracy.

Investigation of the effect of super-resolution in nonlinear inverse scattering

The idea that a solution to a nonlinear inverse scattering problem (ISP) can contain information about the target on a subwavelength scale and thus allow one to achieve super-resolution (spatial resolution beyond the diffraction limit) has been around since the 1990s. However, a solid mathematical theory of super-resolution in nonlinear image reconstruction is still lacking. In this paper, we investigate the effect of super-resolution in nonlinear ISPs (both analytically and numerically) by analyzing several inverse problems in which the limit of spatial resolution can be defined precisely. The conclusions we obtain are not optimistic. Although it is possible to create examples of exactly solvable models in which account of nonlinearity in the ISP results in additional mathematically independent equations (one such example is shown herein), our results indicate that super-resolution is not achievable in any practical sense. Rather, we find that the linear subspace of possible solutions to a band-limited linearized ISP is transformed into a more general curved manifold due to the effects of nonlinearity. In the one-dimensional problem with realistic interaction that we have considered, the manifold can have a slightly smaller dimensionality that the subspace of solutions to the linearized problem but it does not contract to a point and the effect is practically insignificant.

Celebrating the new and old: editorial

New editor-in-chief P. Scott Carney makes some opening remarks and comments on special OSA Centennial activities this year at JOSA A.