# Speckle-based hyperspectral imaging combining multiple scattering and compressive sensing in nanowire mats

## TL;DR

This paper demonstrates a compact hyperspectral imaging method using speckle patterns generated by a nanowire mat, enabling wavelength multiplexing and efficient spectral retrieval with compressive sensing.

## Contribution

It introduces a novel hyperspectral imaging approach combining multiple scattering in nanowire mats with compressive sensing for improved spectral reconstruction.

## Key findings

- Achieved wavelength discrimination over a wide spectral range.
- Demonstrated effective spectral reconstruction with compressive sensing.
- Developed a micrometer-thick, highly compact spectrometer.

## Abstract

Encoding of spectral information onto monochrome imaging cameras is of interest for wavelength multiplexing and hyperspectral imaging applications. Here, the complex spatio-spectral response of a disordered material is used to demonstrate retrieval of a number of discrete wavelengths over a wide spectral range. Strong, diffuse light scattering in a semiconductor nanowire mat is used to achieve a highly compact spectrometer of micrometer thickness, transforming different wavelengths into distinct speckle patterns with nanometer sensitivity. Spatial multiplexing is achieved through the use of a microlens array, allowing simultaneous imaging of many speckles, ultimately limited by the size of the diffuse spot area. The performance of different information retrieval algorithms is compared. A compressive sensing algorithm exhibits efficient reconstruction capability in noisy environments and with only a few measurements.