Breaking Rayleigh’s "curse" and resolving infinitely small spatial separations is one motivation for developing super-resolution in imaging systems. It has been shown that an arbitrarily small distance between two incoherent point sources can be resolved through the use of a spatial mode sorter, by treating it as a parameter estimation problem. However, when extending this method to general objects with many point sources, the added complexity of multi-parameter estimation problems makes resolution of general objects quite challenging. In the first part of this thesis, we propose a new approach to deal with this problem by generalizing the Richardson-Lucy (RL) deconvolution algorithm to accept the outputs from a mode sorter. We simulate the application of this algorithm to an incoherent confocal microscope using a Zernike spatial mode sorter rather than the conventional pinhole. Our method can resolve general scenes with arbitrary geometry. For such spatially incoherent objects, we find that the resolution enhancement of the sorter-based microscopy using the generalized RL algorithm is over 30% higher than the conventional confocal approach using the standard RL algorithm. This method is quite simple and potentially can be used for various applications including fluorescence microscopy. It could also be combined with other super-resolution techniques for enhanced results. The second part of this thesis explores the potential for the Herriott cell to be used as an image-preserving delay line. In quantum imaging, entangled photons are often utilized to take advantage of their spatial and temporal correlations. One photon (“the signal”) interacts with the system to be measured and the other (“the herald”) is used to trigger the detection of the signal. However, for a typical high-sensitivity camera, there is a delay on the order of 20 ns between the trigger and the sensor becoming active allowing for the signal to be recorded. An image-preserving delay line (IPDL) serves to store a photon without distorting the spatial structure and losing the spatial and temporal correlations. It is commonly made with a series of 4f systems to repeatedly image the light field. We propose to use the Herriott cell as an image-preserving delay line. We tested 10 of the lower-order HG modes and found it was able to preserve almost all of them with high fidelities (>90%), with the only exceptions being the largest modes (HG03 and HG30) at the longest delay (7.9 m) where the fidelity was still >86%. In addition to these modes, it was also able to store general images. This application of the Herriott cell affords insights into miniaturizing IPDLs, which tend to occupy a significant amount of space. Overall, these two projects offer novel insight and application to the world of quantum imaging.