<p dir="ltr">Spatial heterogeneity is ubiquitous across life and the universe; the same is true for phase-separating pharmaceutical formulations, cells, and tissues. To interrogate these spatially-varying complicated samples, simple analysis techniques such as fluorescence recovery after photobleaching (FRAP) can provide information on molecular transport. Conventional FRAP approaches localize analysis to small spots, which may not be representative of trends across the full field of view.</p><p dir="ltr">Taking advantage of strategies used for structures illumination, an approach has been developed to use patterned illumination in combination with FRAP for probing large fields of view while representatively sampling. Patterned illumination is used to establish a concentration gradient across a sample by irreversibly photobleaching fluorophores, such as with the simple comb pattern photobleach presented in Chapters 1 and 4. Patterned photobleaching allows spatial Fourier-domain analysis of multiple spatial harmonics simultaneously. In the spatial FT-domain the real-space photobleach signal is integrated into puncta, greatly increasing the signal to noise ratio compared to conventional point-bleach FRAP. The order of the spatial harmonic is directly related to the length-scale of translational diffusion measured, with a series of harmonics accessing diffusion over many length scales in a single experiment. Measurements of diffusion at multiple length scales informs on the diffusion mechanism by sensitively reporting on deviations away from normal diffusion.</p><p dir="ltr">Complementing the physical hardware for inducing patterned illumination, this dissertation introduces novel algorithms for reconstructing spatially-resolved diffusion maps in heterogeneous materials by combining Fourier domain analysis with patterned photobleaching. FT-FRAP is introduced in Chapter 1 for interrogating phase-separating samples using beam-scanning instrumentation for comb-bleach illumination. This analysis allowed disentangling separate contributions to diffusion from normal bulk diffusion and an interfacial exchange mechanism only available due to multi-harmonic analysis. The introduction of a dot-array bleach pattern using widefield microscopy is presented in Chapter 2 for high-throughput detection of mobility in simple binary systems as well as for segmentation in phase-separating pharmaceutical formulations. The analysis becomes more complicated as more components are added to the system such as a surfactant. Introduced in chapter 3, FT-FRAP with dot-array photobleaching was shown to be useful for characterizing diffusion of phase-separating micro-domain smaller than a single pixel of the camera. Supported by simulations, a biexponential fitting model was developed for quantification of diffusion by multiple species simultaneously. Chapter 4 introduces imaging inside of 3D particles comprised of an active pharmaceutical ingredient (API) in microencapsulated agglomerates which exhibited strong interfacial exchange. Multi-photon excited fluorescence enabled imaging a small focal volume within the particles.</p>