Exploiting disorder for snapshot spectral imaging with complex media and compressive sensing

Seeing beyond the capability of the human eye is an appealing concept, as it allows us to explore new physical phenomena. In particular, extracting wavelength information from a scene, from which we would ordinarily observe a combination of three colours, is advantageous for identifying chemical signatures of materials. Spectral imaging devices allow us to access hidden wavelength information, for example, for environmental sensing and to determine the composition of stars. It is increasingly more popular to produce compact spectral imagers that can be easily transported, however, many current approaches are limited by the dependence of device footprint on spectral resolution. In this thesis, the study of snapshot spectral imaging systems, which acquire spatial and spectral information in a single measurement, are investigated. Rather than using traditional dispersive optics, the disorder of complex media is exploited for wavelength characterisation. The first of three approaches employs a 1.7 μm multiple scattering layer of gallium phosphide nanowires in combination with a lenslet array to allow simultaneous acquisition of spatial and spectral information. A spectral resolution on order of 4 nm is achieved with a throughput of 18 %. Tikhonov regularisation (TR) and Compressive Sensing (CS), or more specifically l1-minimisation, are used to recover spectral information from 64 independent spatial positions in the image. CS is used to reduce data collection at the acquisition stage for efficient processing. Utilising a bundle of multimode fibres, a second approach is demonstrated by characterising the wavelength dependent speckle patterns produced by up to 3000 independent cores. The spectral resolution of the multicore multimode fibre is shown to be directly dependent on its length, with sub-nanometre spectral resolution achievable. Spectral information is obtained from only 16 pixels in each speckle pattern by employing CS for data acquisition below the Nyquist-Shannon limit. The angle dependence of speckle patterns is also probed to increase the aperture of the system. Finally, snapshot spectral imaging using a multiple scattering medium and a multispectral transmission matrix is presented. Using a phase retrieval technique and speckle pattern simulations, prVAMP, phase, amplitude and wavelength information are simultaneously reconstructed from one speckle pattern for up to 2 spectral components.