Sub-Micron Spatial Resolution in Far-Field Raman Imaging Using Positivity-Constrained Super-Resolution

Abstract

Raman microscopy is a valuable tool for detecting physical and chemical properties of a sample material. When probing nanomaterials or nanocomposites the spatial resolution of Raman microscopy is not always adequate as it is limited by the optical diffraction limit. Numerical postprocessing with super-resolution algorithms provides a means to enhance resolution and can be straightforwardly applied. The aim of this work is to present interior-point least squares (IPLS) as a powerful tool for superresolution in Raman imaging through constrained optimisation. IPLS's potential for super-resolution is illustrated on numerically generated test images. Its resolving power is demonstrated on Raman spectroscopic data of a polymer nanowire sample. Comparison to AFM data of the same sample substantiates that the presented method is a promising technique for analysing nanomaterial samples.

Nanoscale Spatial Resolution in Far-Field Raman Imaging Using Hyperspectral Unmixing in Combination with Positivity Constrained Super-Resolution

“…The power of the approach and methodology were demonstrated on Raman spectroscopic data from a bundle of nanowires made of poly-(3,4 ethylenedioxythiophene) (PEDOT). 25 The HyRes methodology of this paper resulted in an order of magnitude better spatial resolution than past works on SRIR of Raman data 9–13 and a 25× enhanced spatial resolution when compared to the raw far-field data.…”

“…The sharpness of a super-resolved image is only a lower bound to, but no estimator for, the minimum resolvable distance. 12 It can become a source of high resolution when multiple super-resolved images are combined into a single high-resolution image.…”

“…Details on how to determine the detector response Htrue¯ and how to implement IPLS can be found in previous work. 12,18…”

“…18 The non-negativity constraint ensures that the resulting high-resolution concentration maps can be interpreted as physical/chemical concentrations and also allows for a solution of the ill-conditioned, and potentially ill-posed, image restoration problem without an explicit regularization term. 12…”

“…Sample preparation, acquisition of sample data and the Raman microscope's response function, and single channel super-resolution are described in detail in previous work. 12,25 The PEDOT nanowires have diameters of (100±10)nm. The Raman microscope's response function is a 2D Gaussian with full width half-maximum (FWHM) of in horizontal (FWHMx) and vertical (FWHMy) focal plane direction, respectively.…”